Proceedings of the Conference on Consumption and Saving, Volumes 1 and 2 9781512818444

Table of contents :
Table of Contents
Volume I
Title
Copyright
TABLE OF CONTENTS
Introduction
Part 1 General Consumer Demand Relations
A Complete Set of Consumer Demand Relationships
The Specification of Empirical Consumption Structures
Quantity and Quality of Clothing Purchases
Comments
Rejoinder
Part 2 Durable Goods
Household Investments in Automobiles: An Intertemporal Cross-Section Analysis
Determinants of Consumer Demand for House Furnishings and Equipment
A Covariance Analysis of Locational Relationships in Furniture-Home Furnishings Expenditures
Comments
Rejoinders
Part 3 Nondurable Goods and Services
Demand Relationships for Food
Demand for Clothing
Family Housing Expenditures: Elusive Laws and Intrusive Variances
Service Expenditures at Mid-Century
Comments
Rejoinders
Volume II
Title
Copyright
TABLE OF CONTENTS
Part 4 General Saving Relations: Permanent Income and Other Theories
Consumer Expenditures and the Capital Account
The "Permanent Income" and the "Life Cycle" Hypothesis of Saving Behavior: Comparison and Tests
Windfall Income and Consumption
Comments
Rejoinder
Technical Note
Part 5 Specific Aspects of Saving Behavior
Who Saves?
Entrepreneurial Saving
The Concept of Saving
Comments
Rejoinders
Part 6 Income, Debt and Methodology
Relative Income Shares in Fact and Theory
Consumer Personal Debt: An Inter-Temporal Cross-Section Analysis
Methodology and Appraisal of Consumer Expenditure Studies
Comments
Rejoinder
General Comments

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TABLE OF CONTENTS

VOLUME I iii

Introduction . • . . . . . . Part l General Consumer Demand Relations A Complete Set of Consumer Demand Relationships Jean C rockett and Irwin Friend . • . . . . . . . . . . . . . The Specification of Empirical Consumptian Structures Andre Daniere and Elizabeth Gilboy .•.......••• Quantity and Quality of Clothing Purchases Dorothy S. Brady . . . . . . . . . . . . . . . . . . . . . • . . . Comments Margaret G. Reid . . . . . . Guy H. Orcutt . . . • . • . . . . Robert Ei sner Rejoinder Jean Crockett and Irwin Friend . . • • . . . . . . . . . . . o

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Part 2 Durable Goods Household luvestments in Automobiles: An Intertemporal Cross-Section Analysis Hendrik Houthakker and John Haldi .•••.••..• Determinants of Consumer Demand for House Furnishings and Equipment Vernon Lippitt A Covariance Analysis of Locational Relationships in Furniture-Home Furnishings Expenditures William S. Peters .• o

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Comments Ruth P. Mack James Morgan . . . . . . • . . • . . . . . . . . . . Rejoinders . . . . . . . . Vernon Lippitt . . . . . . . . . . . . . . . . . . . . . . . . . . William S. Peters . . . . . . . . • . . . . . . . • . . . . . . .

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Part 3 Nondurable Goodsand Services Demand Relationships for Food J e an C rockett . . . . . . . . . . . . . . . Demand for Clothing Morris Hamburg . . . . • . . . . . . . . Family Housing Expenditures: Elusive Laws and Intrusive Variances Sherman Maisel and Louis Winnick . . . . . . . • . . . . . Service Expenditures at Mid-Century Robert Ferber . . . . . . . . . . . . . . . . . . • . . . . • . . Comments Janet Murray and Faith Clark . . . . • . • • . • • . . . . . Jacob Mine er . . . . . . . . . . . . . . . . . . . . . . . . . . . Margaret G. Reid . . . • . . . . . . . . . . . . . . . • . • . • Rejoinders Robert Ferber . . . . . . . " . . . . . • . . . . . • . . . . . . Morris Hamburg . . . • . • . . . . • • . . . . . . . . . . . . .

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INTRODUCTION Irwin Friend

These two volumes of proceectings represent the papers, earnments and rejoinders presentedat the Conference on Consumptian andSaving onMarch 30 and 31, 1959at theWhartonSchool ofFinance and Commerce of the University of Pennsylvania, with some subsequent modifications by the contributors. They are part of the Study of Consumer Expenditures, Incomes and Savings in the United States COnducted by the Wharton school in cooperation with the Bureau of Labor Statistics under a grant from the Ford Foundation. The complete study consists of two major parts: first, 18 volumes of statistical tabulatians of expenditures and related data for 1950 and early 1951, compiled by the Bureau of Labor Statistics of the U. S. Department of Labor from field survey data covering close to 1,500 items of budget information for each of same 12,500 families and individuals in 91 representative cities; second, a series of research studies covering economic, marketing and sociological aspects of consumptian behavior, p repared by staff members of the Wharton School of the University of Pennsylvania and other academic institutions, making use of the new 1950 and 1951 data, as well as of other consumer surveys and time series materials.

The first of the se two volumes is devote d to an analysis of consumptian behavior with the primary focus of attention on the determinants of the maj or categories of consumptian rather t han on consumptian as a who le. The seeond volume is devote d mainly to an analysis of saving behavior, i.e., to the determinants of total saving or total consumption, with same attention to major categories of saving and assets, some aspects of the distribution of income and appraisal of consumer survey methodology. Because of the orientation of the Study, particular emphasis is placedon analysis of the 1950-51 B.L.S.-Wharton consumer survey data, but other survey and time series material have not been entirely neglected. Same of the papers are primarily methodological; others are substantive, offering a widevariety of interesting findings. Some are admittedly incomplete and part of larger studies to appear later in monographic form; other s are completed studies whichprobably carry the analysis of certain aspects of consumer behavior about as far as it is possible to go with presently available survey or cross-seetian data. iii

The papers, comments and rejoinders in these volumes illuminate significantly many importantareas of consumer behavior. However, they suffer from two basic deficiencies: vis., the statistical inadequacies of consumer survey data as a result of biased replies by respondents; and the conceptual inadequacies of such data in view of the need to use the m for purposes to which the y are not weil adapted-in particular, inferring inira-personal behavior over time from inter-personal camparisans at a point of time. As a result, we still do not have definitive answers to such fundamental questions as whether entrepreneurs account for the high proportion of total net saving by individuals indicated by survey data-which tagether with the known importance of corporate saving would relegate nonbusiness saving to a position of much less consequence than it currently holds in economic thought; or whether the comparatively recent "permanent income hypothesis" is a valid generalization of personal consumptian and saving behavior or simply a useful caveat that the usual marginal propensity to consume out of current income derived from single cross-seetians of households may be a significant understatement of the true propensity. Indeedone of the major contributions of thetwo volumes ofproceedings and related studies by the Studyof Consumer Expenditures, Incomes and Savings is to highlight these statistical and conceptual limitations of discrete consumer surveys (covering independent sample s of households at one or mor e periods of time) for analys is of consumptian and saving behavior over time. A number of papers indicate clearly what we can say about consumer behavior on the basis of surveydata, what we can't say, and the degree of confidence we can place in our conclusions. Admittedly, what we can't say is fullyas impressive as what we can say. However, the papers prohably go about as far as possible in the analysis of the kind of consumer surveydata currently available, and spell out the newtypes of data necessary to fill in the remairung glaring gaps in our information. The se include new institutional sources of data on savings (and consumption) and continuous household panels in lieu of independent sample s. It is encouraging to report that the exhaustive analysis of deficiencies of presently available consumer surveys in these two volumes and related studies has already had some influence in affecting relevant data collections by government and private organizations, including the decision by the u. s. Bureau of Labor statistics to experiment with continuous annual cross-section data in connectionwith the new Survey of Consumer Expenditures now under way. The Wharton School is also initiating a small-seale quarterly consumer panel in the attempt to obtain income elasticities of expenditures for major categories of consumptian which would avoid not only the usual deficiencies of cross-seetian data but also those of aggregate time-series analysis-i.e., the small number of iv

independent observations in the time-series data, the difficulty of isolating income from correlated non-income effects, of distinguishing among different typ e s of income, and of holding eonstant s tipp ly conditions, etc. The first paper in Volume I, "A Complete Set of Consumer Demand Relationships" by Jean Crockett and Irwin Friend, represents an initial and comprehensive attempt to use cross-seetian data-in this case the 1950-51 B.L.S. survey-to analyze the specific effects on all major consuroption categories of not only income but a large number of other family characteristics. By fitting multivariate regressions of the same general form to ungrouped data for all items studied, a set of mutually consistent relations adding to total consuroption is obtained. While this approach facilitates a study of the comparative effects of the same variables on the different categories of consumption, the authors note that it does not serve as a substitute for more intensive analysis of specific items of expenditure. The functional form of the general relationship used reflects elaborate pre-testing, resulting in the adoption of a linear relation between consuroption and income, a non-linear relation between consuroption and other family characteristics, with inter-action allowed for between income and certain other characteristics. The main part of the regression analysis is devoted to after-tax incomes in the $1,000-$9,999 range since such incomes are likely to be more accurately reported and to be less affected by transitory or abnormal elements than incomes at either extreme. Special emphasis is placed on isolating the effect on consuroption of asset-debt variables and income change-income expectation variables ''both be cause of the considerable discussion of their roles which has occur:t;'ed in the recent theoretical literature and because of the shortage of previous empirical information." The composite marginal propensity to consume out of incremental income in 1950 for all U. S. urban families in the $1,000$9,999 income braeket was .72 according to the Crockett-Friend analysis. This figure based on cross-seetian data is roughly consistent with the estimates of the long-run marginal propensity to consume out of personal disposable income derived from a number of per capita deflated time-series regressions relating consuroption or saving to income and liquid assets, to income, change in income and time, or to income, lagged consuroption (previous year) and various trend variables. However, as will be discussed subsequently, this figure is much lower than the long-run marginal propensity implied by the permanent income hypothesis. Marginal propensities to spend incremental income on the different categories of consuroption derived from the 1950 survey data are also presented in this paper, but in viewof the conceptuallimitations of both bodies of data only a preliminary attempt is made to integratethe se results with time-series data. In connectionwith this integration, i t is pointed v

out that contrary to the argument developed in some of the recent literature, cross-seetian income elasticities of expenditures are likely to be conceptually closer to time-series elasticities of quanUties than of expenditures. Of the family characteristics other than income, the CrockettFriend results imply that family size seeros to have the most important influence on consumption. "There is a strong positive earrelation between consuroption and size of family, when other family characteristics are held constant, due for the most part to the influence of family size on food expenditure." Age of head also has a significant influence on family consumption. "Other things being equal, the middle age groups tend to spend most on consumers' goods as a whole, the youngest families about as much, and the oldest families least. Durable goods expenditures have a strong, inverse relation to age, with the youngest age groups spending much more than other families. Food expenditures in contrast are directly related to age, but the difference between the middle and oldest age group s is rather small." Unlike earlier studies, the Crockett-Friend analysis does not find much difference in total consuroption between homeowners and renters (using the survey definitions of consuroption for these two groups) when other family characteristics are held constant, but there were sizable differences for several categories of consumption. "Thus, homeowners spent more than renters on automobiles, particularly for the upper income classes, and less on food except for low incomes." The effect of liquid assets on consumptian is in accordance with theoretical expectations only for low-income families, but the authors conclude that the effect of assets and debt generally cannot be measured adequately from the usual cross-seetian surveys. "Debt-or at least mortgage debt-had the expected type of influence, but the effect was not statistically significant." The influence of income c hanges (from the preeecting year) and income expectation (for the next year) on consuroption seeros to be erratic and at least in part not consistent with expectations. As for other family characteristics, "in the lower income brackets, nonwhite and employee families spent less on total consuroption than white or self-emplayed families. In the upper income brackets, self-emplayed families in particular had a comparatively low leve l of consumption." The authors note that in a forthcoming monograph they will be extending the analysis of the 1950-51 data to cover more detailed consuroption categories and the influence on consumptian of additional variables such as city class and education. In that monograph, the 1950-51 analysis will be supplemented by a corresponding analysis of 1956 consuroption data for some 10,000 families collected by Life Magazine. vi

The papers on "Empirical Consumptian Functions for Clothing and TV" by Andre Daniere and Elizabeth Gilboy and on "Quantity and Quality of Clothing Purchases" by Dorothy Brady are largely methodological. The former is an early progress report on an extremely ambitious multivariate analysis which attempts to explain selected expenditures in 1950with single regressions invalving some 130 parameters in the case of clothing expenditures. The Brady paper is al so a progress report on an ingenious attempt to describe as simply as possible the whole pattern of prices and quantities of clothing purchased by individuals in different income classes. The discussants of the first three papers-Guy Orcutt, Margaret Reid and Robert Eisner-raise some fundamental questions about all of the se papers but tend to concentrate on the Crockett- Friend analysis, partly be cause it is the clasest to completion with a large number of substantive results already available. Orcutt criticizes the analysis for not being multivariate enough, in view of several potentially significant variables, which had not been used in the explanation of consumptian behavior, while Re id and Eisner have the opposite complaint. The latter point out that the type of multivariate analysis carried out in the Crockett-Friend paper, which relates family consumptian to that year's income and to a number of other family characteristics, may warsen rather than improve the estimated income effect on consumptian and may give significantly biased estimates of the influence of other family characteristics as well. The theoretical basis for the Reid-Eisner position is a belief in some type of permanent income hypothesis of consumptian behavior along the Iines developed by Milton Friedman or Franco Modigliani and Richard Brumberg. In the version formulated by Milton Friedman, where current consumptian and current income are each divided into two parts-permanent and transitory, consumptian of an economic unit is a eonstant k times "permanent" or discounted, expected income; k is assumed to be independent of the leve l of permanent income but not necessarily of other family characteristics; and transitory components of consumptian and income are taken to be uneorrelate d not only with their respective permanent components but with each other so that transitory income is completely saved. Thus, if-as Reid and Eisner assume-a high proportion of family income as measured by surveys reflect transitory factors, andother explanatoryvariables (such as age, size of family, occupation, etc.) are correlated with permanent or normal income, they serve as proxy variables for it, and the coefficient of the income variable in the type of multivariate analysis carried out by Crockett and Friend is to that extent unjustifiably lowered since it is presurned to be the permanent income propensities which are relevant to the inter-temporal behavior in which we are interested. "In addition the coefficients of many of the non-income variables, vii

including some demographic variables of considerable importance to time-series analysis, will also be biased insofar as they serve as proxy variables for normal income." Mor e over, Re id and Eisner stress that the permanent income hypothesis implies that any regression of consumptian on current income derived from survey data, whether or not it is multivariate, will understate the marginal propensity to consume. One additional reason cited by Reid is that the presence of statistical error in the income variable tends to lower the regression coefficient. Eisner recommends as an alternative approach that followed by Franco Modigliani and Albert Ando in Volume II of these Proceedings to obtain the relevant permanent income propensities or elasticities. In their rejoinder Crockett and Friend point out that they are not willing to assume that, if permanent and transitory income effects are distinguished, the latter can usefully be taken as zero or for that matter the same for different items of consumption, though it is likely to be less than the permanent income effect for most consumptian items. They note that they attempted to maximize the weight of the permanent income effect in the income coefficient by eliminating the income extremes and introducingthe income-change and income-expectation variables. They argue that while this does not produce a pure permanent income effect, neither does the approach recommended by Eisner-and utilized by Modigliani and Ando-which invalves grouping families by some characteristics correlated with permanent but not with transitory income and then fitting income-expenditure regressions to the group means. The estimates of the permanent income effect obtained through the latter approach are biased if the grouping variable has any effect on consumptian in its own right, i.e., other than as a proxy variable for permanent income. Thus, if total consumptian is used as a grouping variable, the estimatedpermanent income e lasticity of total consumptian is significantly above unity. The authors conclude that perhaps the best approach utilized thus far in der iving anypermanent income elasticities from cross-seetian data is to isolate relative ly eonstant or stable income families from other families along lines followed in an earUer analysis by Irwin Friend and Irving Kravis, but that there are major difficulties in using anyof these cross-sectionestimates in time-series analysis. Crockett and Friend stress there is no plausible theoretical basis for prejudging that family characteristics other than current income are more important as proxies for permanent income than in their own right nor does the analys is the y c arr y out support such an assumption. Like the earlier Friend-Kravis analysis, they do not find the permanent income hypothesis in its usual formulatian very useful in explaining demand for particular categories of consumption. Finally, if families with relatively eonstant incomes in viii

three years (actual income in 1949 and 1950 and expected income in 1951) are assumed to be close to their permanent incomes, the Crockett-Friendanalysis arrives at the very interesting result that the regression coefficients of total consumptian on selected family characteristics are not changed significantly if "permanent" rather than current income is hel d constant. It ma y be noted here that several analyses which are more favorable to the permanent income hypothesis are presented in Volume II of the Proceectings and will be discussed later in this Introduction. One of the most interesting analyses presented at the Conference, both from the viewpoints of methodology and substantive results, is contained in the paper on "Household luvestment in Automobiles: An Intertemporal Cross-Section Analysis" by H. S. Houthakker and John Haldi. As part of the Study of Consumer Expenditures, Incomes and Savings, an effort was made to exploit the major bodies of continuous cross-section data available on consumer expenditures. These turned out to be continuous crossseetian data on food expenditures collected by the Market Research Corporation of American and corresponding data on automobiles collected by J. Walter Thompson Co. (for the Ford Corporation). Both bodies of data were made available for analysis to the Consumer Expenditures Study. The food data we re analyzed in an earlie r study by Jean Crockett ("A New Type of Estimate ofincome Elasticity of Demand for Food," Proceectings of the American Statistical Association, Business and Economics Section, 1957, pp. 119-121). The Houthakker-Haldi paper starts with the simple theory that gross investment in automobiles is in the long-run determined by the household's preferred inventory which in turn depends on income, prices and tastes. Gross investment is regarded as a "spasmodic" actjustment of actual inventories to preferred inventories. The two major features of the analysis are first the use of continuous cross-section data for the two years for whi ch such information was readily available for the same sample households, viz. 1952 and 1955; and seeond a careful valuation of the initial stock of cars for every household in each of these years and the incorporation of the influence of the stock of cars into the subsequentdemand analysis. After first deriving the customary single cross-section relations between gross expenditures on automobiles and both income and the initial stock of cars for each of 1952 and 1955, the authors make use of the continuous nature of their sample to hold eonstant specHic household or family characteristics or "tastes" which might be expected to remain invariant between the two years. The income coefficients are changed only moderate ly by holding eonstant family characteristics other than income and stock of cars, but the depressing influence of ear inventories on purchases is greatly increased. The family effects variables help to sort out families by ix

their preferred inventories; and when "tastes" are held constant, the coefficients of initial inventories are algebraically reduced. The authors note that "The substantial magnitude of the inventory coefficient implies that a year with large ear sales must normally be followed by at least one year with much smaller sales. On the other hand, the large size of the coefficient (combined with the effect of depreciation) al so implies that the aftermath of an abnormally good year does not last very long." Houthakker and Haldi explore the implications of a wide variety of relationships including those which assume that the demand relations- i. e., the income and inventory coefficients -remain the same in the two years, as well as those which allow for differences in these coefficients. They point out that some of these relationships ma y be used to test the implications of the permanent income hypothesis for explaining automobile expenditures. Their conclusion is that "At least where gross investment in autos is concerned, there is no need to distinguish permanent and transitory components of income." Two other papers dealingwith different facets of consumer expenditures on durable goods and utilizing different techniques of anal y sis we re presented by Vernon Lippitt- "Determinants of Consumer Demand for House Furnishings and Equipment," and by William Peter s- "A Covariance Analysis of Locational Relationships in Furniture-House Furnishings Expenditures." Both analyses re ly on the 1950 B. L.S.-Wharton data. The Lippitt p ap er employs analysis of variance to detect the influence of various family characteristics on the percent of family income devoted to house furnishings and equipment in 1950. Of the many family characteristics included in the analysis, age of head has one of the more consistent relationships to the share of income devoted to furnishings and equipment, with a steady inverse relationship varying from about a 50% above average share in the "under 25" age group to 50% below average for the 75 and over group. The furnishings and equipment share is, not unexpectedly, positively correlated with the relative level of housing expenditures, negatively correlated with automobile expenditures, and strongly negatively correlated with saving. Families in !arge cities tend to spend samewhat less relatively on furnishings and equipment than those in suburbs and even more so than families in small cities. The Peters paper, an interesting experiment in the use of consumer survey data for a particular type of market analysis, employs analysis of covariances to investigate locational differences in expenditures on home furnishings and furniture which are net of differences attributable to other factors that marketing men "normally take into account" in their planning. The discussants of the Houthakker-Haldi, Lippitt and Peters papers-James Morgan and Ruth Mack-comment on thewidevariety of analytical techniques and substantive findings in these three

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studies (as weil as in other papers in this Conference ). Both discussants stress the importance of changing attitudes or tastes on consumptian behavior, especially for automobiles and other durables where Morgan notes that "a small change in the average desired stock can lead to a large change in purchases, in true accelerator fashion." Mack emphasizes the need for recurrent surveys and depth studies of the genesis of buying decisions to fill in the gaps in our knowledge about consumpHon behavior. The last set of papers in Volume I of these Proceectings include "Demand Relationships for Food" by Jean Crockett, "Demand for Clothing" by Morris Hamburg, "Family Housing Expenditures: Elusive Laws and Intrusive Variances" by Sherman Maisel and Louis Winnick, and "Service Expenditures at Mid-Century" by Robert Ferber. The Crockett paper on food demand differs analytically from the Crockett-Friend paper on demand for all major categories of consumptian including food in that the former involves a meticulous examination of the form and relevant variables in a single demand relation regardless of consistency with other relations. The two major objectives of the Crockett paper are: first, to campare estimates of income elasticity of food obtained from three different types of data, viz., aggregate time series, cross-seetian analysis at a single point of time, and continuous cross-sections covering the same families at different points of time; and second, to utilize the B.L.S.-Wharton 1950 data to examine the influence on food expenditures of a number of family characteristics other than income, and to estimate the effects of distributional changes in these factors on aggregate food consumpHon over time. Although stressing the wide-range in different estimates of income elasticities of food expenditure and the still inconclusive character of her results, Crockett points out that holding eonstant many family characteristics--which not only are like ly to affect food consumptionbut are substantially correlated with income-eliminates muchof the difference between single cross-seetian and time-series elasticities, and that continuous cross-section elasticities are even closer to time-series e lasticities, since the technique of continuous cross-sections presurnably controls variation in many more variables including tastes than even a multi-variate analysis of single cross-sections. Of the family characteristics other than income, occupation of head seems to have relativelylittle influence on food expenditure, age has an inverted U-shaped effect with the middleaged spending relatively more than the younger or older groups, Negroes spend less than white families, renters more than homeowners, and families in small cities in the South significantly less than those in large cities in the North. At the methodological level, Crockett notesthat a detailedanalysis justifies the case of the functional form log F= a +b log Y+ c log n - \\'here F, Y and n

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represent food expenditures, income after taxes and size of family respectively-but not the frequently used log F /n = a + b log Y/n. In his analysis of the determinants of demand for clothing, Hamburg uses both time-series and all available large-scale budget studies, including the Life 1956 data as well as the B.L.S.-Wharton 1950 data and earUer B.L.S. surveys. He nates that both timeseries data subsequent to 1950 and the Life 1956 data point to an income-elasticity of demand for clothing of well under one, the estimate implied by earUer time-series (1929-50} and cross seetian (1935-36, 1941 and 1950} data. He is not able to isolate a plausible relative price elasticity; in the models he tests the estimated elasticities do not differ significantly from zero. Some of the more interesting effects of family characteristics on clothing expenditures include the fact that in low-income classes "blue collar" workers spend relative ly less than "w hi te collar" workers but much more in income classes over $5,000; Negro families spend more than white families at all income levels; educated families spend relatively less than other families; and families with eonstant incomes have higher clothing income elasticities than those with variable incomes. Hamburg gives as one plausible reason for the relativelyhigh expenditures on clothing by ''blue c ollar" families at upper income levels the influence of multiple-earners which was not held eonstant in his analysis. Other possible reasons that come to mind include not only the different set of consumptian values or ways of attaining social status in distinct social groups but also the effectively different set of consumptian apportunities confronting these groups. It may not be amiss to point out that this result seems to run counter to the implications of a permanent (vs. current) income type of explanation. The subtitle of the Maisel-Winnick paper, which explores the determinants of housing expenditures, is a picturesque summary of their major finding, viz., "Elusive Laws and Intrusive Variances." The y discuss carefully the reasons (including limitations of the available data) why the y and other s have not been ab le to develop a mode l which will prediet satisfactorily how much a family will spend on housing. On the other hand, they indicate that it is far simpler to prediet whether a family will buy a house, with this decision largely determined by income, age of head, and size of family. The y al so find that a significant amount of variation in the magnitude of expenditures on housing is explained by such family characteristics as race, occupation, and education, with white, white-collar and self-emplayed and better-educated families spending relatively more than the rest of the population. They do not find a permanent income hypothesis veryuseful in their attempts to explainhousing expenditures, though Margaret Reid has a quite contrary view and uses a permanent or normal income relationship to derive a higher than customary estimate of the elasticity of housing with respect to normal income. xii

Ferber finds that income, age of head and family size exert a major influence on all types of service expenditures, with other socio-economic variables appearing to be of secondary importance. Howeve r, the total amount of variation explained by multivariate analysis is rather small, and he concludes that a more satisfactory explanation will require an investigation of the substitutability between services and goods. As discussants of the last set of papers, Janet Murray and Faith Clark refer to results on variations in food expenditures from the 1935-36 Consumer Purchases Study, which generally corroborate the Crockett findings for 1950 and incidentally present same previously unpublished information, and also make same camparisans with the 1955 Survey of Farmers' Expenditures. Jacob Mincer criticizes Crockett's findings on the income elasticity of food demand and the Maisel-Winnick findings on the income elasticity of housing demand largely along the lines implicit in a permanent income explanation of consumptian behavior discussedearlier in connection with the remarks by Re id and Eisner. The first three papers in Volume II-"Consumer Expenditures and the Capital Account" by Harold Watts and James Tobin, "The 'Permanent Income' and the 'Life Cycle' Hypothesis of Saving Behavior: Comparison and Tests" by Franco Modigliani and Albert Anda, and ''Windfall Income and Consumption" by Ronald Bodkinare all cancerned in large part with tests of the permanent income and related hypotheses of consumer behavior based on the 1950 B.L.S.-Wharton data. The Modigliani-Anda and Bodkin papers consider only total saving or total consumptian but the Watts-Tobin paper al so de als with key components of durable goods expenditures and of other forms of saving. Watts and Tobin discuss and test two multivariate approachesboth stock and flow analyses-for studying the demand for durable goods and other saving items entering the capital accounts of consumers for which data were available in the 1950 survey. Perhaps the two most interesting aspects of their analysis are, first, their painstaking estimates of the stock of durables on the basis of type of good, age, and for autos price-class or quality; and, second, the novel manner in which they attempt to separate long-run from short-run income effects on the level of and change in different items in the capital account. The simple hypothesis with which Watts and Tobin start is that households endeavor to maintain a certain balance among various items in the capital account so that the change in each stock will be negatively related to the initial level of the stock itself but positively related to the initial level of other stocks. In the stock regressions, each type of capital item is related to a number of demographic, geographic, social and economic variables, with deviations in different stock regressions related to each other in separate analyses, while in the flow regressions the initial values xiii

of stocks are added to thE: other explanatory variables used in the stock regressions. To actjust for the possible deficiencies of current income as a measure of a more theoretically relevant permanent or expected income for explaining items or changes in the capita! account, the level of housing expenditures for each household is introduced into the analysis as an explanatory variable in addition to its current income. A long-run income effect is obtained by actding the current income coefficient to an adjusted housing coefficient derived by multiplying the unadjusted housing coefficient by the ratio of the mean level of housing expenditures to mean income for the middle two age classes in the sample of households analyzed. The rationale for this treatment is that the long-run actjustment of housing expenditures is one which keeps eonstant the housing expendituresincome ratio. The authors conclude that "The differences between short- and long-run coefficients for saving are definitely in the direction, if not in the amount, predicted by the permanent income hypothesis." Watts and Tobin furthe r conclude "The re is evidence that households tend to maintain so me sort of balance in their capita! accounts both between assets yielding direct services and financial assets, and between liquid assets and liabilities ... actjustments in capital account items tend to eliroinate rather than perpetuate deviations from a basic or preferred portfolio pattern." The y go on to add a qualification to their findings that frequently appears in different forms throughout the Conference, viz., "a one period cross-seetian is drastically limited in its ability to provide generalizations about the dynamics of capital account changes. . . A panel study is much better for this purpose." In camparing the Watts-Tobin findings with other results presented at the Conference, it is interesting to note that the long-run income coefficient of saving obtained by them (.23) does not seem very different from the income coefficient (.28) implied by the C rockett and Friend consumptian analys is (which does not distinguish between short-run and long-run income effects), particularly if an actjustment is made for the apparent omission of premiums on life insurance from the Watts-Tobin saving data. Bothof the se e s timates of sa ving propensities-one direct, the other indirect-do not include expenditures on durables as part of saving. The Watts-Tobin longrun income coefficients for durable goods expenditures-which differ considerably for homeowners and renters-seem definite ly lower than the Crockett-Friend coefficients; this maybe due in part to the inclusion of stocks of durables as an additional independent variable in the Watts-Tobin analysis, but one might expect this to work in the opposite direction and there is no obvious reasonfor such a difference in results. xiv

Modigliani and Ando present some new tests and comparisons confirming the conclusion of earlie r analysts that the assets-Habilities estimate of saving from consumer surveys is like ly to be better than the income-consumption estimate and stressing the basic unreliability of survey data for saving analysis. · However, the major part of their paper deals with a careful exploration of the theoretical implications of the Friedman and Modigliani-Brumberg-Ando permanent income and related life cycle theories of consumptian or saving behavior and with a number of imaginative tests of such theories. They attempt to obtain an unbiased estimate of the permanent income e lasticity of total consumptian expenditures by computing a regression of the log of mean consumptian on log of mean income over cells defined by appropriate classification criteria other than income (viz., city class, education, occupation, age and tenure). Since these regression coefficients are greater than the corresponding coefficients in the regressions of the log of mean consumptian on log of me an income for families grouped by current income level (which tends to maximize the influence of transitory income ), the authors conclude that the se findings support a permanent income hypothesis, but not in general the simplest form of this hypothesis where the permanent income elasticity of total consumptian is assumed to be unity. However, when the log of me an consumptian is related to the log of me an income for f amilies classified by the leve l of housing expenditures, which is used as the most satisfactory classification criterion for purposes of testing the permanent income hypothesis (both for families as a whole and for different groups of families), the relevant income coefficient does approach unity except for the self-emplayed and perhaps some other groups. Modigliani and Ando conclude that while the survey evidence as to the simple permanent income hypothesis-that the ratio of permanent consumptian to permanent income is a eonstant independent of the income levei-is not clear-cut, the evidence does imply "the conventional analysis explaining current consumptian in terms of current income over such a short period will significantly understate the responsiveness of consumptian to changes in available resources of a permanent nature." As Modigliani and Ando point out, their tests are not able to shed any light on the independence of transitory consumptian and transitory income, which is one of the two critical assumptions in the simple, Friedman formulatian of the permanent income hypothesis. Such tests are provided by Bodkin making use of a unique body of data from the B.L.S.-Wharton study on sizable amounts of windfall income received by individual families-the basic data consisting of the previously unanticipated National Service Life Insurance dividends paid in early 1950 to covered veterans. The reactions of the consumer units affected to these temporary changes in income discussed in Bodkin's paper are of considerable interest in XV

themselves andprovide the first direct test of the assumption in the Friedman version of the permanent income hypothesis that transitory income is entirely saved or the weaker assumption that there is a major difference in the propensity to save or consume out of ordinary and windfall income. This paper presentedat the Conference was later published in the American Economic Review, September, 1959, but is reproduced here, in view of its brevity, for convenience in following the subsequent discussion. Bodkinfinds-at least for the year and type of windfall coveredthe marginal propensityta consume or spend out of windfall income is fully as high as out of ordinary income whether expenditures on durables are or are not included in consumption. He concludes: "Hence an important theoretical result of the permanent income hypothesis appears to be contradicted by our observation of consumer behavior." The formal discussants of the Watts-Tobin, Modigliani-Anda and Bodkin papers at the Conference were Milton Friedman and James Duesenberry, but in addition a relevant note by Jean Crockett on "Biases in Estimating Income-Expenditure Regressions" is included in these Proceedings. This note, which was circulatedamong Conference participants, discusses the basic methodology used in the first two of these papers as weil as in other related papers at the Conference. Friedman, after nating the general consistene y of the ModiglianiAndo and Tobin-Watts evidence with the permanent income hypothesis, devotes most of his attention to the Bodkin paper. His initial criticism of Bodkin's findings consists of the proposition that it is implausible on any theoretical grounds that there is essentially the same marginal propensity to spend out of what is essentially wealth as out of income. However, more basically, he criticizes the interpretation of the empirical findings by stating, first, that the dividend payments understate the windfall increment to wealth since "recipients we re apparently told, or could infer, that additional annual payments would be forthcoming," and, second, that the dividend payments may be partlya proxy for permanent income. By making some as sumptians about the approximate effects of the se two factors, he feels that he is able to explain virtually all of the discrepancybetween the regression coefficient of National Service Life Insurance dividends (vs. other income) and the value predicted by the permanent income hypothesis. Bodkin in his rejoinder to Friedman replies, first, that dividend recipients we re not told about-and according to the Veterans' Administration we re given no reason to anticipate- future dividend payments; and, second, when age of household head is held constant-a variable which a priori reasoning and the Friedman discussion suggest might be the most relevant single family characteristic to catch the permanent income effect of the dividend payment-there is xvi

no noticeable change in the regression coefficients of either current income or dividends. Furthermore, he points out that even with the Friedman assumptions, if one uses the measure of consumption which is gross of expenditures on durables rather than the measure net of such expenditures, the agreement between the "adjusted" regression coefficients of dividends and other income is not nearly so close. Duesenberry remarks that the classification ofincome into permanent and transitory components seems "rather primitive" and he also questions the importance of the bias resulting from treating permanent and transitory components in the same manner. He feels, however, that this one basic strand of the permanent income hypothesis-the assumption that transitory income is saved-rests on stronge r empirical and theoretical ground than the other assumption that the ratio of consuroption to permanent income does not depend on the leve l of permanent income. Thus high permanent income families covered in two Harvard Tax Study samples had extremely high average saving ratios, and in at !east one of these samples there was a sharp rise in these ratios with rising incomes. He concludes, "It seems to me that Friedman is on strong ground when he maintains that transitory income biases our estimates of the relation between income level and the savings ratio. But he has no strong evidence that the relationbetweenpermanent income and saving is one of proportionality." Crockett discusses the assumptions and limitations in the statistical methods utilized by Watts and Tobin, Modigliani and Ando, and other authors at the Conference to measure permanent income effects. If total consuroption C is regarded as a function not only of permanent income P and transitory income T but also of another variable Z (where the latter represents some other family characteristic affecting C and in general correlated with income ), she discusses the precise relations between the regression coefficients bcz·y and bcz·P and between bcy·z and bcP·z-where Y represents current income or P + T-and the biases involved in using relations with Y as estimates of corresponding relations with P under different assumptions as to the relations of Z with P and T. She concludes with some methodological suggestions for isolating permanent income effects. The seeond set of papers in Volume II-"Who Saves ?"by Irwin Friend and Stanley Schor, "Entrepreneurial Saving" by L. :R. Klein, and "The Concept of Saving" by Irwin Friend and Robert Jones-also deal with various facets of saving behavior but are less preoccupied with the permanent income hypothesis than the immediately preeecting papers. The Friend-Schor paper, presented at the Conference and later published in the Review of Economics and Statistics, May, 1959, is reproduced here partly for convenience in following the subsequent discussion but more importantly because it gives a xvii

detailed evaluation of the saving data which serve as the basis for much of the analysis presented at the Conference-particularly for the papers in Volume II. The theme of the Friend-Schor study is perhaps best summarized by one of their concluding remarks: "In view of major deficiencies in the survey data on consumer saving, fe w definitive statements can be made about the saving behavior of different income groups in the population. This paper has attempted to evaluate the available survey data, to present and analyze new data, and finall y to actjust the se data statistically and conceptually to obtain corrected estimates of the income distribution of saving. While we feel that our estimates are about as good as it is possible to make with the data at hand and that these results constitute a definite improvement over those heretofore available, the re is no assurance that the use of mor e reliable data obtained from new sources of information might not change significantly the estimates of saving for the different income group s." The statistically adjusted B. L.S.-Wharton data imply higher saving for all income group s than the unadjusted data but also a reduction in the concentration of saving among upper income groups. However, they still point to a high degree of concentration. In 1950, the adjusted saving-income ratios ranged from a negative figure for the under $1,000 after-tax family income group to 5% for incomes between $4,000 and $5,000, and to 31% for incomes above $10,000, with the last group accounting for 4% of the population but for 58% of total saving by families. There is some reason to believe that the proportion of saving accounted for by the upper income groups has de elined seeular ly and varies inverselywith the business cycle. "In 1950, changes in cash and deposits and net business investment were the most important components of saving in the top income class, with increased equity in dwellings {before depreciation), insurance, and increased equity in other real property accounting for the rest of saving by this class. Only dwellings and insurance (including contributions to retirement funds) were important positive saving items for the middle income brackets, with increased consumer debt as a major offset. The lowest income class did not have appreciable positive net saving in any form, with major dissavingin cash and deposits and dwellings and to a lesser extent in business investment, seeurities and other real property." Several implications of these data relating to the saving behavior of important groups in the population maybe noted. Families with fluctuating incomes do not seem to show much difference from families with eonstant incomes in their sa ving (i. e., net change) in cash and deposits contrary to what might have been anticipated from theoretical conside rations. Some of the most interesting findings of earlier studies relating to the saving behavior of different groups in the population-e.g., the extremely high proportion of xviii

saving accounted for by entrepreneurs and the high saving propensities of Negroes as campared with whites-are modified by actjustment of survey data for apparent deficiencies. In addition to the statistical actjustments of the survey data on family saving, the Friend-Schor paper also makes a number of conceptual actjustments to obtain income distributions of different concepts of saving, including personal saving defined as in the national income accounts, private saving covering both personal and earparate saving, and other variants as well. These conceptual actjustments generallytend to increase the saving-income ratios, sometimes markedly, but not to change substantially the income concentration of saving. Parenthetically, an inspection of the estimates presented in this paper raises the question whether adherents of the permanent income hypothesis believe that not only the normal ratio of personal saving to income but also of the theoretically more relevant private sa ving (or forthat matter of personal saving plus c ap i tal gains or losses) is even approximately independent of the level of permanent income of the beneficial owners of such saving. The paper concludes with the caveat that a radically different type of information obtained from institutional records is needed before much reliance can be placed in any estimates of the distribution of saving among economic groups. The Klein paper on entrepreneurial saving considers not only the results of analysis of the B.L.S.-Wharton data but also other relevant data in England and in the United States. He nates that, "In the intensive investigations of personal savings by means of sample surveys in the last decade one of the most remarkable findings is the strategic importance of the role played by small businessmen, farmers and other self-emplayed persons" and discusses in great detail the "strong" evidence supporting a relatively high marginal propensity to save of the self-employed. Entrepreneurs save at a high rate because of their business saving: "They need to secure their own funds for capita! expansion because of the inaccessibility of the capita! markets to smaller firms, and because of their desire to retain full contro l of their enterprises." Klein supplements the customary derivation of income coefficients of saving for entrepreneurs and other groups through the use of two measures-food expenditures and housing expendituresas proxyvariables for permanent or long-run income. Specifically, he obtains the occupational relations between average saving and average income for families classified into groups by the size of their food and housing expenditures. He concludes that "income variability is not an overwhelming factor which explains away the occupational savings differentials." The Friend and Jones paper examines the theoretical and empirical aspects of substitutahility among different forms of saving and consumption, with particular reference to durable goods x ix

expenditures. The relationship between substitutability and stability conditions is examined, and, abstracting from a number of complications, saving plus durables (S +D) as a function of income (Y) is considered more, equally, or less stable than S as a function of Y depending on whether a- cs+ n . y) 5a- s . y which in turn depends on whether b sn. y ~ -1/2. Both cross-seetianand time-series data are used in the empirical analysis. This paper presents "fairly strong" evidence that expenditures on durables as a whole seem to be more substitutable for or competitive with saving (exclusive of durables) than with nondurables. Similarly, it is found that for most components of saving-such as cash, securities, bornes, mortgages and probably insurance-there is on the average a higher rate of substitutability between each component and the total of other saving than between that component and consumption. Howeve r, the rate of substitutability between most individual components and the total of other saving varies widely for different components and for different economic groups. The paper al so investigates the substitutability between a few selected individual items of saving (e.g., cash and securities). The authors conclude that the results support the inclusion of durables {and of other items normally included in saving) with saving rather than with consumptian in a behavioral analysis of the disposition of income into two broad categories but note a number of qualifications. The two discussants of the seeond set of papers in Volume II, Edward Denison and Arthur Okun, raise some fundamental questions though they frequently take opposite positions on the same point. Denison feels problems of reliability of the survey data developed in detail by Friend and Schor are so great as to make tenuous much of the use analysts make of the m, while according to Okun "problems of ... a c c u r a c y ... of the ... surve y data ... are probably not of primary importance." Denison questions whether expenditures on durables differ from other expenditures in their effect on saving as much as the Friend-Jones results would seem to suggest and, after raising some basic conceptual questions, notes that in a recent paper he obtained an extremely stable time-series relation between gross private saving and gross national productand that this is not improved by introducing consumer durables as an additional variable to-;ällow-~for substitutability between saving (as defined in the national accounts) and durables. Okun, on the other hand, believes that Friend and Jones have presented convincing evidence that expenditures on consumer durables compete more strongly with personal saving than with other consumption. Both discussants observe that the "personal" saving behavior of businessmen raises some question as to Klein' s ''business" saving motive as the explanation of highertotal saving by entrepreneurs. Okun, in addition, questions whether it is entirely clear that entrepreneurs are characterized by high average saving or only by high XX

marginal saving but suggests that one other possible reason for the apparently different entrepreneurial saving behavior is that "the less thrifty may tend to eschew s uch a career." The rejoinder by Friend and Jones considers the implications of several models of consumer behavior incorporating substitutability. Some additional computations are presented testing these implications for selected sample groups of families and categories of consumption; and indicating that the major competition in the consumer's budget is between D and s, to a somewhat lesser extent between N (nondurable) and S, and not between D and N, and that for the major categories of durables and nondurables tested only clothing in the nondurables group behaves like the durables in substitutability with saving. Friend and Jones stress, however, that the observed virtually complete lack of substitutability between D and N may reflect the intrinsic deficiencies of a single cross-section and that a completely satisfactory answer to this possibility will await the availability of continuous cross-section data. They question on theoretical grounds the validity of Denison's interesting time-series finding on the el o se relation between gross private saving and gross national productand point out it "seems to imply ... that as taxes go up relative to gross national product the ratio of gross saving to consuroption goes up correspondingly to maintain constancy of the saving-gross national product ratio." The last set of papers in the Conference-"Relative Income Shares in Fact and Theory" by Irving Kravis, "Methodology and Appraisal of Consumer Expenditures studies" by Helen Lamale, and "Consumer Personal Debt: An Inter-Temporal Cross-Section Analysis" by Jerry Miner-eover a wider assortment of subjects and bodies of data than those generally included in other sessions of the Conference. The Kravis paper presented here is a very brief summary of the manuscript discussed at the Conference which was subsequently published in the American Economic Review, December, 1959. This summary reproduces his major conclusions and enough of his argument so that the comments of the discussants can be followed. The empirical data he relies on are long-term time series for the most part and only to a minor extent B.L.S.-Wharton or other cross-section data. Kravis questions the rather widely accepted notion of long-run constancy in the relative share of labor in total income. He condudes that in the United States over the past half century, there has been a shift in the distribution of national income from property to labor, with the size of the shift depending on the treatment of entrepreneurial income. This shift took place prior to 1929 with comparative stability thereafter. Labor's gain since the turn of the century has been even greater in terms of personal income than in terms of national income. xxi

Lamale summarizes the highlights of her monograph on Methodology of the Survey of Consumer Expenditures in 1950 published in 1959 as part of the Study of Consumer Expenditures, Incomes and Savings and presents some additional material not available when that monograph went to press. Her work on methodology discusses the evolution of methods of collection, tabulation and analysis from earlier to later consumer surveys, makes a fairlydetailed comparison of the 1950 Surv e y of Consumer Expenditures with other surveys, and describes and evaluates the results of the 1950 Survey. On the basis of the annual Federal Reserve-Michigan Survey of Consumer Finances, Miner studies the very substanhal increase in consumer credit betweeen 1949 and 1955 in terms of changes in characteristics of consumer units using such credit during this period. Of all the variables included in the regression analysis of the amount of debt outstanding, only income appears to have a significant influence in all of the years studied. The regression residuals for the amount of debt outstanding for indebted spending units indicate that Negroes tend to have lower debt outstanding than other households, college-educated families more debt. Increasing levels of income are associated with increasing prohability of debt until quite high incomes are reached, at which point higher incomes lead to a decline in the prohability of deb t apparently as a result of substantial holdings of liquid assets. According to Miner, "Only about 25% of the increase in the proportionofspending unitsholdingpersonal debt between1949and 1955 can be attributed to c hanges in the means of the independent variables which took place during these years." The shift in eonstant termsLe., in tastes or willingness to assume debt-is advanced as the basic explanation of this increase, which took place largely between 1949 and 1953. About 25% of the difference in the mean amount of debt in 1949 and 1955 is also explained by changes in the means of the independent variables, but in this case most of the other 75% is explained by changes in the relation between debt holding and such independent variables as income change, income expectation and income rather than by changes in the eonstant terms. The discussants of these papers-George Jaszi and George Garvy-largely concentrated on the Kravis study. Jaszi raises a number of important statistical and conceptual questions relating to that study, but perhaps the basic point ·he makes is that the results Kravis obtains cannot be considered as definitive until the same methods to distinguish labor and property shares in income are applied in a great deal of industry detail. Garvy feels that it would have been more useful to confine the examination of the labor share to the "ordinary business sector" in view of the implications of the changing role of Government and raises numerous other questions relating to the utility, methodology and interpretation of the Kravis results, includingthe significance of a two-wayclassification xxii

of the national income into labor and property. The rejoinder by Kravis which attempts to answer all of these questions indicates that he has more empathy with Jaszi than with Garvy, but he does not consider that any adjustments which have been proposed (even if they we re possible to make) would be of sufficient magnitude to alter his qualitative findings on changes in relative shares over the past half century as a who le. At the end of these Proceedings there appears a "General Comment on Conference: Basic Elements of a General Model of Consumer Behavior" by Arnold Zellner who summarizes the need for and gives an outline of a general "operational" model of consumer behavior. Zellner discusses the Watts-Tobin results in the light of that mode!. To conclude, while the Conference and associated research activities have used consumer survey material to east considerable light on many significant phases of consumption and saving behavior, the results are a little discouraging in fulfilling what must be adjudged one of the most important objectives of such research-i.e., to obtain the demand parameters most relevant to the explanation and predietlon of time-seri.es behavior. The reasons for such results, particularly those involving the kinds of biases in single cross-sections which have received most attention in the recent literature, have beentouchedon earlier in this Introduction and are discussed in greater detail in the following papers. Furthe r work on this basic objective of incorporating cross-section parameters intotime-series models to correct the presentdeficiencies in such models is still under way in the Study of Consumer Expenditures, Incomes and Savings as well as elsewhere, and includes research on the use of changing regression coefficients in discrete cross-sections at different points of time to measure changing tastes, on the effect of consumption-induced income on the estimated coefficients of income-induced consumption, and on the influence on consumption of different typ e s of cyclically and non-cyclically variabletransitoryor irregular income. Substantial reservations were expressed by severalparticipants at the Conference regarding the validity of the recently popularized permanent income hypothesis in any simple and very useful form. While I share these reservations, we still do not know whether a simple variant of this hypothesis will prove a better explanation of consumption behavior than the earlier types of relationships explaining current consumption on the basis of current resources (income and assets) and either lagged income or consumption. Of course, if the empirical construct for permanent income is made sufficiently elastic-say to coincide with the best combination of the se other explanatory variables-there is no difficulty in "proving" one strand of the permanent income hypothesis, i. e., that "transitory" income is completely saved, by a simple matter of definition. The xxiii

major interest in the permanent income hypothesis then lies in the other strand which states that the eonstant term in any linear consumptian-income analysis can be assumed to be zero. I am reasonably convinced that a definitive answer to this question and to many others raised at the Conference can only be obtained through new types of information, including notably for this purpose continuous cross-section data.

xxiv

A COMPLETE SET OF CONSUMER DEMAND RELATIONSHIPS* Jean Crockett and Irwin Friend University of Pennsylvania

The 1950 BLS Survey of Consumer Expenditures collected highly detailed information on both family expenditures and family characteristics likely to affect those expenditures, for a sample of 12,500 urban families in the United States. This body of data provides a unique opportunity to examine demand relationships over the whole range of consuroption categories, to determine differences in behavior among population groups, and to assess the effects on particular consuroption items of variables not previously studied on any broad scale. This is useful not only for market analysis and a number of sociologicalpurposes but also to increase ourknowledge of the theoretical structure of consumer behavior and our ability to prediet developments in broad sectors of the economy. Two of the major aims of the present analysis are: (l) to measure income effects in such a way that they will be as free as possible from distortion by the effects of other family characteristics showing a cross-sectional earrelation with income but not necessarily correlated in the same way with income over time; (2) to determine the effects of other family characteristics so that the results of distributional changes in these variables over time may be predicted. The wealth of information available from the 19 50 BLS Sur ve y on f a mily characteristics other than income makes it possible to progress in both these directions. This analysis is to our knowledge the first attempt to study the specific effects on all major categories of consuroption (as well as on a number of

*This artide is based on research undertaken in Connection with a broad Study of Consumer Expenditures, Incomes and Savings at the Wharton School of Finance and Commerce of the University of Pennsylvania. The study is based largely on the 1950 survey of the Bureau of Labor Statistics of 12,500 families in 91 representative cities, and is being carried out in cooperation with that agency. lt is financed by a grant from The Ford Foundation. The computations in this paper were Supported by the University of PennsylvaniaComputer Center and, in part, bythe NationalScience Foundation.

l

subgroups) of all family characteristics which seem important in this connectionand for which data are available. It should be emphasized, however, that i t may never be feasible to obtain from a single cross-sectional study estimates of demand parameters which are adequate for prediction over time, either because it is not possible to measure and hold eonstant a sufficient number of correlated variables or because the parameters are themselves notstable over time. It is, for example, the conviction of the a ut hors that the effect of assets cannot be measured ad equa te ly in cross -sectional analys is uniess sa vings propensities and the purposes for which saving is undertaken can be held constant. The comparison of continuous cross seetians may be highly useful in this connection as a means of holding eonstant factors which cannot be measured and specifically allowed for in cross-sectional analys is, to the extent that these are in variant for the same families over time. Furthermore, again assuming constancy in the distribution of excluded variables, successive cross sections provide an indication of the extent to which the effects of included variables are stable over time or follow a relativelysimple time trend. A third major purpose of this paper is to provide a point of comparison with both later and earlier cross-sectional studies. An analysis of the 1956 Life study, very similar to that described here, is to be undertaken later this year. Furthermore, it is hoped that earlier studies may be rendered more comparable with the current one by actjusting them for known distributional changes in factors considered here but not at the earlier dates. While several intensive studies of particular consumptian categories are being carried out and while these should provide better insight than the present analys is inta the structure of demand for such categories, i t is the purpose of this research to investigate the effects of a large number of factors and to measure income effects net of these factors for many expenditure items covering all the major areas of consumption. This is to be done by utilizing the facilities of a high speed computer to fit regressions of the same general form to ungrouped data for all items studied. It thus becomes possible to study in a fairly detailed fashion many more items than could be handled on an indi vidualized basis, even though the form of the regression is not entirely suitable in all cases. A set of mutually consistent relationships, actding to total consumption, is obtained, and comparison of effects of particular factors on different areas of consumptian is facilitated. It is also possible and of some methodological interest to campare relationships dealing with quite different levels of aggregation within the same broad area of consumption. It is hoped that eventually the relatively "pure" income effects obtained may be usefully integrated w i t h time-series information to yield a consistent set of relationships covering the consumptian portion of a fairly detailed aggregate 2

model of income determination in the United States. Unfortunately, the results that can be reported at this time cover only a subsample of the expenditure items being studied. A word is perhaps in order as to the actvantages of using ungrouped data. One obvious advantage is that some notion may be obtained as to the relative importance of the variation still unexplained by the facto r s studied. A more important consideration from the viewpoint of the authors is that the use of ungrouped data becomes almost mandatory when a number of independent variables are included, and particularly when these variables are intercorrelated, in order to as sure sufficiently wide variance in all of them for reliable estimates of their effects. The alternative is to group simultaneausly by all the independent variables and this, if fair ly fine break.downs are used, leads to a very large number of groups indeed. For example if twenty income classes are used in conjunction with five classes for each of four other variables, the result is already 12,500 groups. Finally, we should comment on the reliability of the data being analyzed. The problem of course is not so much the sampling errors involved, since these will be providedas part of the results of our analysis, but rather the systematic biases which may enter. Generally speak.ing, there is reason to believe that the data in the 1950 BLS Survey are reasonably unbiased for income as a whole, except for the very lowest and highest income groups, and for major consumptian categories, except for alcoholic be verages and tobacco. The latter two categories of consumptian are substantially understated in the survey data, though the relevant income slopes maystill be usefuL Most of our analysis, it might be noted, will omit the extreme income groups so that this source of bias should not be too troublesome. Specification of the Model Choice of variables The 1950 BLS Survey collected information on a very large number of consumptian items. Since resources did not permit the computation of demand relationships for all these items, selection was made according to the following principles. First, it was desired to obtain relationships for a group of fair ly broad categories 1 Furthe r details are provided in Study of Consumer Expenditures, Incomes and Savings, Vol. XVIII, University of Pennsylvania, 1957 and in Methodology of the Survey of Consumer Expenditures in 1950 by Helen Lamale, University of Pennsylvania, 1959.

3

which would exhaust total consumption. In addition to demand functions for total consumptian and total durables (from which a relationship for non-durables and services may be derived by subtraction), relationships are to be estimated for the following 13 expenditure groups, adding to total consumption: food (excluding alcoholic beverages); alcoholic beverages; tobacco; housing; fuel, light, and refrigeration; household operation; housefurnishings and equipment; clothing; medical care; personal care; recreation, reading, and education; transportation; and miscellaneous expenditures.2 Secondly, demand relationships are to be obtained for a sample of more detailed items, representing various degrees of aggregation.3 Here the c hoi c e was based on a number of factors, including the homogeneity and meaningfulness of the aggregate, its importance in total consumption, the extent to which new information not available from previous studies might be obtained, general interest in the aggregate as well as the interest of particular authors associated with the Consumer Expenditures Study, and comparability with items included in the 1956 Life Survey, which are to be analyzed in a similar manner later this year. Highly detailed items as well as moderately broad aggregates were included in an attempt to test the usefulness of the model at different levels of aggregation. A sample of detailed savings items was also studied, with results which will be reported elsewhere. The explanatory variables largely exhaust the information on family characteristics collected in the 1950 survey. In the final plan they include family income after taxes, family size, age of head, race of head, occupation of head, city class, education of head, income change-income expectation pattern, tenure of dwelling unit, the two major assets items available-cash and deposits and value of owned home-mortgage debt,andnon-automotive consumer debt. 4 However, city class and education are not present in the regressions currently available. Special emphasis was put on the asset-debt variables and on the income change-income expectation 2 If certain relationships are derived by subtraction a sernewhat finer 18-group breakdown, adding to total consurnption, may be obtained. 3 These items include food eaten away from home, furniture, home freezer, mechanical dryer, men's and boys' clothing, men's and boys' footwear, women's and girls' clothing, women's and girls' fur coats,women's and girls' footwear,clothingfor children under 2 years, auto purchase, auto operation, toilet articles and prepa4rations, purchase of radio, TV etc., and paid admissions. All asset and liability items were reportedas of the beginning of the year (1950). The consumer debt item includes money owed for all major durables except automobiles. Unfortunately, the BLS questionnaire did not include data on the leve! of automobile debt.

4

variable, both because of the considerable discussion of their ro les which has occurred in recent theoretical literature and because of the shortage of previous empirical information. The debt variables appear in very abbreviated form (presence or absence of debt) because pretests indicated a disappointing lack of either consistency or a priori plausibility in the effects when different levels of debt were considered. Two reasons may be suggested for these results. It may be that the strongest effect of debt on consumptian is through the contractual requirements for repaymentand that the size of the requiredpayment is more closely related to the size of the initial debt than to the unrepaid portion, which latter was the only information available. Secondly, a high level of consumer debt is closely associated on one hand with a stage in the life cycle characterized by high consumptian and on the other hand with a highdegree ofwillingness on the part of individual families to incur debt, sothat any discouraging effects of high debt on consumptian are largely overshadowed. Information on the initial inventory of consumer durables, a third possible asset category, was not included, partly because it was not convenient to assemble but also be cause it was doubted that the broad range of items studied would be much affected, even though important effects might be expected for a few items. The family type variables was not included because it was believed that the information entailed largely overlaps that provided by the two variables, family size and age of head, and that the se two, taken in conjunction, provide more useful information than family type alone. For both food and clothing, for instance, the actual number of family members is q uite important. 6 For durables it is quite important to distinguish between a couple in their twenties and a couple in their sixties, and this the family type variable does not do. The variables relating to sex of head and length of residence in city were believed to have important effects on relatively few of the items studied. Living arrangements (based on number of meals regularly eaten at home) may have quite broad effects but the nonhousekeeping category is probably important for one-person 5 This variable distinguishes among the following family types: husband and wife families with (a) no children, (b) old e st child under 6, (c) oldest child 6-16, (d) oldest child 16-18 and (e) oldest child over 18; families with children and only one parent present; families composed entirely of adults, other than those consisting of husband and wife only; and families containing both children and adults other than parents. 6It would be usefulof course to determine how manywere children, say under 12, and how many were adolescents or adults. This type of breakdown was not readily available.

5

families only. Thus the effects attributed to one-person families should be understoact to reflect in part the relative ly high incidence of non-housekeeping living arrangements among these families. The number of earners (either full time or total) may also have quite broad effects. It was decided with same regret to omit both of the earner variables, partly because of certain peculiarities in the definition of each of them. Functional form of relationships In determining the form of the statistical relationships to be fitted, a number of questions arise. A fairly elaborate pretest, bas ed on grouped data, was undertaken to east light on the following three points, which were considered to be of primary importance: l. The nature of the income-expenditure relationships, holding eonstant a number of other family characteristics. 2. The extent to which the parameters of these relationships vary, depending on the leve l at whi ch the other characteristics are held constant. 3. The nature of the effects of family characteristics, other than income, holding income eons tant. Income was considered to be the single most important factor affecting expenditures for most consumptian items, and for this reason the first cancern was to ehoase an appropriate mathematical form for income-expenditure relationships with other variables held constant. It was recognized that same campramises might be necessary in the interests of computational feasibility and of obtaining consistency in form over the entire range of consumptian items. In many cases a different functional form than that ehosen here would be preferred for intensive study of a single consumptian category. While consideration was given to relatively complicated exponentials, including the cumulative log normal curve, the computational problems invalved appeared to be beyond the range of available resources, in view of the large number of observations, of dependent variables, and particularly of independent variables other than income that were to be incorporated. The following four models were given serious study:

= a+ b

(a)

Y

(b)

log Y

(c)

Y = a + b log X,

(d)

Y/X = a + b X,

=a

X, + b log X,

where X is family income after taxes and Y is family expenditure on a particular consumptian item. On the one hand there is same 6

reason a priori to prefer the double log form because of its somewhat greater flexibility. Howeve r, i t is hard to handle computationally for ungrouped data, where zero expenditures on same of the items studied may be expected to occur frequently. On the other hand, there is an a priori preference for the linear form because of the simplicity of aggregation both over families and over consumptian items. It will be noted that none of the above relations hips is express ed in per capita or per adult equivalent terms. Either type of adjustment, but particularly the deflation by number of adult equivalents, would have been computationally expensive; and, in addition, it was strongly felt that bothare unsatisfactory in the wideareas of consumptian where economies of scale are important, though for certain consumptian items they may be very useful. For present purposes it seemed preferable to include family size as a separate explanatory variable, in such a way as to permit i t to display nonlinear effects. A furthe r decision to re late all expenditure categories directly to income, rather than relating only total consumptian to income and individual consumptian items to total consumption, was based in part on a belief that certain types of expenditures-for example, purchase of durables, educational expenses, and abnorma! medical expenses-may be largely competitive with saving rather than with other areas of consumptian only. The danger of least squares bias may be substantially increased when total consumptian is used as an explanatory variable. None of the four models studied gives satisfactory fits over the entire income range. However, in the $1-10 thousand range, which represented 87% both of urban families and of urban consumptian in 1950, the linear form gave at least as good a fit for the major consumptian categories as either the semilog or the ratio form, in a gross test with no other variables held constant. The double log form ga ve slightly better fits in two or three cases, but the improvement did not seem sufficient to outweigh the difficulty of handling zero observations. Further investigation, limiting the variation in a number of other explanatory factors, definitely improved the linear fit in the $1-10 thousand income range. It was convenient to study in this way total consumptian and several major sub-categories, including food, clothing, housing, auto expense, auto purchase, housefurnishings and equipment, and medical care. On the hypothesis that income slopes may differ among population groups, it is to be expected that the pooling of the se groups will in itself introduce curvature-even though linearity prevails within each group-whenever the groups ha ve considerably different income distributions. In particular, the re is same reason to believe that the self employed have a relatively low marginal propensity to consume and, since their weight is much greater in the upper income 7

braekets than elsewhere, this should contribute to a flattening at the upper end of a curve based on pooled observations. Persons with high assets, even when they are not entrepreneurs, may also have a relatively low marginal propensity to consume, either because the presence of assets permits consumptian to be maintained when income drops, or because such persons are likely to be large savers by taste, or both. Asset holdings are again highly correlated with income. Negro families, which are Concentrated in the lower income brackets, mayhave an unusually high marginal propensity to consume certain items. Their assets and their access to credit are relatively low, so that they are unable to dissave substantially in the lowest income brackets, where there is strong motivation to do so in order to maintain some minimum standard of living and where white families do t end to dissave heavily. It may be, al so, that the socially accepted minima with respect to certain consumptian items are lower for Negroes than for white families. For the se reasons, consumptian of Negroes may be lower relative to white families at very low than at medium incomes. Their marginal propensity to consume will then be higher than for whit e families and the fact that the y are numerically mor e important at the lower end of the income scale will tend to steepen a curve based on pooled observations in that range. By treating separately population groups with different marginal propensities and different income distributions, underlying linearities may be revealed, if they exist. Chart l shows Engel curves for the consumptian items mentioned above, when Negroes, the self -employed, and the not gainfully employed are all eliminated, family size is restricted to two, three, or four persons, age of head is restricted to 30-59 years, and families are divided into two broad cash assets groups. Income classes 2 ($1,000-$1,999), 3 ($2,000-$2,999), 5 ($4,000-$4,999), 7 ($6,000-$7,499) and 8 ($7,500-$9,999) were studied, but major emphasis in the determination of linearity was placed on the behavior of consumptian for classes 3, 5, and 7, since class 8 is very small and class 2 is al so small when one-person families, age groups under 30, the Negroes, and the not gainfully employed are all excluded. Four points, representing classes 2, 3, 5, and 7, are shown for the low cash assets group (cash and deposits under $500). For total consumption, clothing, housing, and housefurnishings and equipment the se points follow a linear pattern very closely. The other subgroups (except medical care) are approximately linear for classes 3, 5, and 7, but show some downward concavity in the case of food and upward concavity for the au to item s when class 2 is conside red. Medical care is linear for classes 2, 3, and 5, but shows downward concavity when class 7 is added. Class 8 is not shown because of the small number of families represented (53), but generally drops below the Une indicated by the other four point s. 8

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CASI-I ASSETS ~ # 500

LINEARITY OF SELE.CTED EXPENDITUR.E- INCOME RELATIONSI-liPS FOR RESTRICTED VALUES OF OH-lER FAMILY CHARACTE.RISTICS

Four points, representing classes 3, 5, 7, and 8, are shown for the high cash assets group (cash and deposits over $500). Again the linear approximation is verygoodfor total consumptian though the class 7 average lies slightly above and the class 8 average slightly below the line determined by the larger classes 3 and 5. The class 2 consumptian average, based on 23 families and not shown, lies very much above this line, exceeding income substantially. This might be expected from the f act that families with very low income and high cash assets are likely to be below their normal income and at the same time have the ability to dissave heavily to maintain consumption. The clothing and auto purchase subgroups are approximately linear, while food tends to upward concavity and auto expense and housefurnishings and equipment to downward concavity when class 8 is considered. The last category shows some evidence of downward concavity on the basis of classes 3, 5, and 7 alone. Housing and medical care follow an S-curve. On the basis of gross tests of all 13 major consumptian categories and of the information presented in Chart l, a linear expenditure-income relationship, holding a number of other variables constant, appeared in general to provide a reasonable approximation within the $1-10 thousand income r ange, although i t was recognized that bad fits might be obtained for some of the more detailed items. As previously mentioned, this income range covered a very high proportion of urban consuroption in 1950. T here is furthermore som e evidence, based on a small sample of individual families, that heteroscedasticity is a much less serious problem here than over the entire income range, so that the weighting of observations for efficient estimation is not strongly indicated in an analysis confined to this range. A linear approximation is not acceptable, in general, beyond the $1-10 thousand range and perhaps becomes questionable near the end points of the range. To complete the income-expenditure picture, income slopes have been computed for the extremes by camparing income and consumptian averages for income class l (under $1,000) with those for class 2 and by camparing averages for class 9 (over $10,000) with class 8. While the number of families at the extremes is too small to permit all of the explanatory variables other than income to be held constant, separate slopes are obtained for white and non-white families and for several occupational groups. Family size and tenure of dwelling unit are also held eonstant in the computation and the slopes presented are averaged over these variables. A complete demand function may thus be represented by three straight lines, on e corresponding to extremely low incomes, the seeond corresponding to incomes in the $1-10 thousand range, and the third corresponding to the upper income extreme. In general, bothofthe extreme slopes are flatter than the central slope giving

lO

an S-curve effect. Only in the central portion has consideration been given to the full range of explanatoryfactors other than income. It is be lieved, partly on the basis of past empirical results, that the income slope obtained here is more meaningful than the slopes at the income extremes for casting light on the movement of aggregates over time. At the lower end assets and borrowing capacity become much more important relative to income in the determination of consumption. At the upper end many factors long discussed in the literature may contribute to the flaUening of the slope. At both extremes the slopes are much less reliable statistically than in the middle range. The incidence of large values of "transitory" income and of large observational errors is probably much higher at the extremes. The next question whi ch arises is the extent to whi ch the income slope may vary for different values of the other family characteristics. Where the effect of income (or of other important variables) is considera bly different for different population groups, it is desirable either to campute separate regressions for these groups or to introduce non-linear terms specifyingthe nature of the interaction. The seeond alternative was not attempted here since it was felt that the re was no sufficient basis, e i the r from a priori considerations or from previous empirical work, for assigning a particular mathematical form to the interactions. Tests we re carried out for the same items as shown in C hart l to determine whether income slopes were substantially affected by the following variables: occupation, race, cash and deposits, tenure of dwelling unit, value of owned home,family size, age of head, and income change-income expectation pattern. In each test, to the e:xtent feasible, the variation in other variables was restricted. The tests were based on mean income and consumptian in selected income classes for which a reasonably large sample was available. While slopes in at least one consumptian category were found to be affected by all the variables tested, it was not feasible to subdivide by all the se characteristics simultaneausly. It was felt that at least 100 observations and preferably 250 or more are required to campute a meaningful regression from data subject to such wide variance as occurs in family budget studies. In deciding which population groups should be described by separate regressions, preference was given to those groups where substantial a priori reasons existed to expect differential respanses to income (or other variables), where there was empirical evidence that the income slope for total consumptian was affected, and where two or more large subgroups appeared to be affected. It was expected that income slopes would be different for the self-emplayed than for other occupational groups, since entrepreneurs have special investment needs and apportunities which cannot always be fully satisfied by access to capita! markets and which 11

must therefore depend in part on personal saving. Earlier, more aggregative studies have indicated that, at least for total consumption, income slopes for entrepreneurs are flatter than for the rest of the population.7 It was further believed that the not gainfully employedmight show atypical income effects. This group is heterogeneous, coveringboth the retiredand the involuntarilyunemployed. It is heavily concentrated in the lowest income groups so that income slopes are hard to determine from grouped data. In the relatively fe w ca ses of moderate ly high in come, it must be presurned either that substantial income-producing assets are available or that same family member other than the head is employed. Thus the medium-income families may represent quite a different group from the preponderant low-income families, who are likely to be dependent on pensions, relief, or social insurance benefits. Negroes-because of differences in. cultural patterns, ·the unavailability of certain types of consumptian outlets, and low asset holdings and limited access to credit which restrict dissaving even at very low incomes-may be expected to respond atypically to variations in income and to other variables, such as family size, as wen. 8 Chart 2 campares income slopes for Negroes (and other nonwhite families), white self-employedand white not gainfully employed with those for white employees. In all cases family size is restricted to two, three, or four persons, age of head to 30-59 years and cash assets to lessthan $2,000. A word is perhaps in order about the choice of these restrictions, which was based on preliminary analysis of the pretest information. It will be noted later that eneperson families are samewhat atypical in consumptian behavior, in part because many of them are not housekeeping families. To a smaller degree the very large families are atypical, while the two, three, and four person families campase a relatively homogeneous group. Again with respect to age of head, the middle age groups show fair ly homogeneau s behavior, while the old and the very young are samewhat deviant. The group with cash assets less than $2,000 is far from homogeneau s bu t must be greatly reduced before homogeneity is approached. On the other hand the group with assets 7 see, for example, Irwin Friend and Irving B. Kravis, "Entrepreneurial Income, Saving and Investment," American Economic Review, June 1957, p. 278. 8studies based on data from the Survey of Consumer Finances give same evidence of interactions among the effects on consuroption of race, income, and liquid assets, but it is difficult to assess the implications of these findings for a mode! of the type considered here. See L. R. Klein and H. W. Mooney, "Negro- White Savings Differentials and the Consuroption Function Problem:• Econometrica, July 1953, p. 439.

12

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AGE. OF l-IEAD EQVATIONS ARE RE:ST~ICTED TO W~LTE E.MDLOYE.E F,t.,MILIE.S OF T'~.'O, THk'EE f)t(! FOUR PERSONS WITI-I C.ASI-I A.5::SET:S ~(_ SS T!..~ AN ~ 2000.

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; comparisons with time-series results; and use in prediction of consumptian effects of future changes in income. Only a limited amount of analysis of this type has been possible in the short span of time since we received the first UNIVAC results. Moreover, the seeond set of UNIVAC runs will permit an improved and more comprehensive analysis to be carried out. Table 3 campares the composite income slopes derived in our analysis with those implicit in simple regressions of consumptian on income for the same sample data. The income slopes for consumptian as a whole and for such major groups of expenditures as food, housing and medical care are significantly reduced by holding eonstant family characteristics intercorrelated with income, while other items of expenditures are less affected. For the first group, apparently the simple regressions impute to income effects on consumptian which to a substantial extent are really attributable to other family characteristics correlated with income. It should be noted that the simple regressions used for comparative purposes already hold eonstant race and to some extent occupation so that the differences in slope with the multiple regressions tend to be minimized. The only other reasonably comparable cross-seetian data available for comparison consist of the durable goods regressions derived from the 1949 and 1950 Survey of Consumer Finances covering a much smaller sample of both urban and rural consumer units for the years 1948 and 1949 respectively (and apparentlyusing a samewhatless inclusive definition of durables).l4 The se regressions, which related the expenditure-income ratio to a liquid 14see Lawrence R. Klein (Ed.) Contributian of Survey Methods to Economics, Columbia University Press, 1954, pp. 234ff.

37

Table 3. A Comparison of Marginal Propensities to Consume Der i ved from Multiple Regressions of Consuroption Items on Income and Other Family Characteristics with Those from Simple Regressions on Income Alone, White Employee Families with Incomes After Tax from $1,000 to $10,000, Urban, 1950 Income Slope from Multiple Regressions (See Table l)

Income Slope from Simple Regressions a

Total consuroption

.713

.797

Durable goods

.151

.158

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

.159 .045 .114 .027 .051 .138 .084

.190 .063 .119 .035 .056 .136 .084

Consuroption Items

aBased on unweighted grouped data.

Table 4. Income Elasticities of Expenditure Derived from Multiple Regressions of Consuroption Items on Income and Other Family Characteristics, White Employee Families with Incomes After Tax from $1,000 to $10,000, Urban, 1950a Income Elasticities from Multiple Regressionsa

Consuroption Items Total consuroption

• 721

Durable goods

.972

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

.544 .408 1.027 .534 .768 1.089 1.184

aFor each item of consumphon the income slope in Table l has been divided by the consumption-income ratio at the average level ofincome for all families in the 1950 B.L.S. survey.

38

assets-income ratio and age plus a eonstant term, implied a marginal propensity to spend on durables of .17 and .18 in the two years covered, somewhat higher than the .15 for 1950 in Table 3. Table 4 presents the income-elasticities of expenditures implicit in our new results for the various items of consuroption at the average level of family income. These elasticities would bear the same relationship to those derived from a simple regression of consuroption on income as the corresponding slopes in Table 3. The income-elasticities in Table 4 imply, as might be expected, that of the major categories of consuroption auto purchase is relatively most affected by changes in income, clothing and furnishings and equipment are intermediate in this respect, while food, medical care and especially housing are comparatively inelastic. While it has not yet been possible to attempt to integrate the income slopes or elasticities we have derived with time-series data, it may be of interest to compare our cross-section results with measures of "average sensitivity" of items of personal consuroption expenditures computed by the U. S. Department of Commerce from annual aggregate statistics for the period 1947-54.15 The se measures, which are the income slopes in double-log relationships of expenditures on personal disposable income, are of course conceptually different from income elasticities of demand since supply conditions, and other variables affecting consuroption and intercorrelated with inco.me, are not held eonstant sothat the earnparison le aves much to be desired. Moreover, no tests have been made of shifts in demand in the 1947-54 period, the definition of items of consuroption in the two sources are not always the same, and the aggregate statistics cover the rural as well as the urban population-in addition to the nonwhite, self-emplayed and not gainfully employed. The time-series measures of sensitivity are income elasticities of current expenditures which are equal to the income elasticities of quantities (where higher qualities are largely reflected inhigher quantities) plus the income elasticities ofprices, whereas the corresponding cross-seetian elasticities (computedfor average incomes) are likely to be closer to quantity elasticities since prices (as distinct from quality) presurnably remain fairly eonstant over the range of incomes. With these qualifications in mind, it may be noted that the cross-section elasticities (for average incomes) are lower for food, housing, medical care and auto purchase and auto expense and higher for clothing and furnishings and equipment. For two of the major categories of consumption-housing and clothing-there is no resemblance between the cross-seetian and time-series results, the former being much lower for housing and 15 survey of Current Business, September 1955, p. 29. 39

much higher for clothing. It is interesting to note, however, that the Commerce prewar (1929-40) measures of sensitivity for housing and clothing are quite close to the 1950 cross-seetian results. The high Commerce time-series measure of sensitivity for housing in the postwar years is probably du e to the transition from rent c ontroi and artificially low prices to a more normal situation over this period associated with a high positive price elasticity of expenditure on this category of consumption. The low Commerce postwar figure for clothing cannot be explained in this fashion and probably reflects a shift in the demand schedule. Al so since the demand schedule for clothing as usually measured is based on purchases instead of the more appropriate consumptian or use, it is possible that at least part of the apparent shift in demand may simply reflect the greater durability of new types of synthetic and other clothing which is not reflected in the price indices used. A preliminary attempt has been made to obtain income elasticities of demand from time-series data for clothing and housing which are not subject to as many deficiencies as the measures of sensitivity discussed above. Regressions of three general forms we re used-linear, logarithmic and logarithmic first differencesrelating real expenditure (deflated by the appropriate commodity price level) to real income (deflated by the consumer price index) and relative prices (specific commodity vs. consumer prices) for theperiod 1948-57. For clothing, the realincome elasticityderived in this manner is between . 68 and . 74 (. 68 in the log l st difference regression, .69 at average 1950 income in the linear regression and . 74 in the log regression). · The relative price elasticity is not statistically significant in at least 2 of the 3 regressions. This time-series income elasticity of clothing (roughly . 7) while much higherthan the Commerce measure of sensitivity (.2) is still considerably below the cross-sectional result (1.0) probably at least in part for the reasons discussed previously. For housing, timeseriesincome elasticities of housing similarly computed are nearly as high as the corresponding Commerce measure and much higher than the cross-seetian result. Obviously we have not been able as yet to make much progress in the integration of the new cross-sectional material with timeseries data, which partly in view of time limitations we have re garde d as largely outside the scope of the present paper. However, two points should be noted both in connection with the brief reference to time-series data which we have incorporated above and in connection with the work in this area we hope to do in the future. First, we are not necessarily assuming that single crossseetian income elasticities of expenditures however derived are theoretically equivalent to the corresponding time-series elasticities whether the latter are obtained from the usual single equation (relating real expenditure to real income and relative prices) or 40

from complete models. We simply plan to campare the two income elasticities, attempt if possible to rationalize the differences, and investigate the consequences for price elasticities of the introduction of the new cross-seetian income elasticities into the time-series equation or model. Second, abstracting from all the other difficulties of crossseetian and time-series comparison, we have referred above to our belief that cross-seetian income elasticities of expenditures are likely to be closer to time-series elasticities of quantities than of expenditures. There have been several monographs and papers in recent years which seem to have taken the quite different position that the cross-seetian income elasticities of expenditures may be regarded as the sum of an income elasticity of quality (determined by the cross-seetian price variation for the commodity in question over the income range) and an income elasticity of quantity (determined by subtraction), and that it is the last which should be campared with the time-series elasticity of quantity or the first with the time-series elasticity of expenditures. For example, Prais and Houthakkerl6 after defining the cross-seetian income elasticity of quality and quantity in the manner indicated state bu t do not develop the thesisthat in demand analysis based on time series "the income elasticities from family budgets, which are used to correct timeseries of consumptian for the effects of income variations, should be adjusted for the quality effect, since the time series are generally estimated by weighting a number of quantity series with eonstant prices." Kuh and Meyer state that, "In studies done to date, the most important [reason for divergence between cross-seetian and time series estimates of income elasticities] isthat cross-seetian elasticities almost invariably have been, because of the nature of the available data, 'outlay' instead of quantity elasticities ... Time series elasticities, on the other hand, usually are based on price corrected sales data and therefore are more akin although as we shall see, not identical to quantity elasticities." 17 The evidence which they cite in support of this position is confined to different food categories and simply shows that for the United Kingdom in 1938-39 and for Sweden in 1933, cross-seetian income elasticities of quantity, defined as the difference between elasticity of expenditures and elasticity of quality, are generally lower than the crossseetian elasticities of expenditures-which given the definition is

16s. J. Prais and H. S. Houthakker, The Analysis of Family Budgets, Cambridge University Press, 1955, pp. 112-3. 17Edwin Kuh and John R. Meyer, "How Extraneous Are Extraneous Estimates," The Review of Economics and Statistics, November 1957 ,pp. 385-9. The authors also give a number of other reasons for differences between time series andcross-seetian estimates.

41

almost an algebraic necessity-and that for Sweden the time-series income elasticities of quantity for 5 food items over the period 1921-39 are about as close to (or as far apart from) the crossseetian elasticities of quantity in 1933 as to the cross-section elasticities of expenditures. The thesis advanced by these writers and others in the recent literature that cross-section income elasticities of expenditures become more comparable with income elasticities of quantity derived from time series when they are corrected for the quality effect also computed from cross -section data seems to us either to be based on a misconception or on a body of data which is radically different from the relevant time-series data in the u. s. with which we shall be working-viz., the Commerce consumptian series and the B.L.S. price indexes. The basic problem of the treatment of quality in cross-section and time-series data arises in connection with an item of expenditure which is treated as a homogeneous and in a sense indivisible commodity in both sets of data even though the commodity may actually include several sub-categories or qualities with different prices. For example, if expenditure by a family on such an item is designated by e = pq (or price times quantity), and if there are two different qualities, then e may also be written as e 1 + e 2 = p 1q 1 + p 2q 2 • Now in cross -section data when we move from average expenditure on this commodity (e) of a fa mily in one income group to a verage expenditure (e') in a hi gher incomegroup,thene' = p'q' = ei + e;-whichisequalto p 1 qi + p 2 q~, at least theoretically, since the individual p i 's are assumed unchanged. Obviously if we now deflate e and e' by any price index with fixed quantity weights, we obtain q'/q = e'/e and the former ratio reflects increases bothin q 1 and q 2 and in the relative importance of the higher quality (say q 2 ). The difficulty which arises in practice, however, lies in the fact that we do not have the Pi 's of the different qualities in cross-section data but simply a p forthat commodity (normally representing different qualities) for each individual or income group. For example, if in moving up the income se ale, expenditure on the commodity shifts completely from the lower to higher quality, our observed data may reflect the fact that e'= p 2 q 2 whereas e= p 1 q 1 • In this situation, we may choose to regard the quantity (q') in the higher income group as p 1 q 1 (cf. with q = p 1 q 1 in the lower income group) with an associated increase in quality of p 2 /p 1 -a treatment which the recent literature seems to suggest and which may be quite useful for some purposes-or we might equallywell argue that e'/e = p 2 q 2 /p 1q 1 isthe relevantquantity comparison without any quality correction. The fact that crosssection data generally show significant income elasticities of price for the most detailed grouping of commodities (even when all other family characteristics are held .constant) ·simply indicates that the various income groups do buy different qualities of the "same" commodities. 42

The real issue confronting us, of course, is to insure comparability of treatment between the cross-seetian and time-'Series data, and for this purpose we must consider what happens in the corresponding case in time-series data where the same item is treated as one commodity even though it consists of two distinct qualities. It is our understanding that the varieties priced in timeseries price indexes in the U. s. normally remain reasonably eonstant at least over a fairly protracted period of time, i.e., that the same quality of any commodity is priced in successive time periods even if there has been an up-grading in the average quality purchased. If this is correct, we may generalize from the crossseetian case (using unprimed data to refer to a family in the lower income group in the first period,primed data to the same family in a higher income group in the seeond period) to e = pq = p 1 q 1 and e' = p'q' = p 2 (pt i /pti)q 2 where i is the varietypricedandp t jpt i represents the price movement indicated by the time series from t to t'. Then in the analysis of time-series data we may write q'/q = p 2 q 2 /p 1qb sothat if our understanding as to the nature of U. S. time-series price indexes is valid, it is incorrect to adjust the cross-seetian elasticityfor the quality factor before using it as an elasticity of quantity in conjunction with time-series data. Over long periods, some quality correction would presurnably be required but the quantitative relation between the cross-seetian and timeseries quality factor is far from clear. Without this correction, the time-series regression coefficient of quantity (or real expenditure) on realincome for eonstant relative prices is the same as the cross-seetian slope of actual expenditure on income for doublelog regressions, and the cross -section slope multiplied by a eonstant price factorl8 for linear regressions. We might note that it is extremely fortunate it is unnecessary to make a quality correction in integrating the U. s. cross-seetian and time-series data since the work invalved would be quite burdensome, particularly for the broad consumptian groups based on a large number of individual commodities which are separately priced. 1

1

Influence of other family characteristics The influence ofincome on consumption, which on the basis of pretests was assumed eonstant over the range of values of a number of family characteristics, has been found to vary more importantiy for the different groups of families in Table 2 classified by home 18

This factor is the product of the ratio of the particular commodity price in the time-series base period to the same commodity price in the cross-section base period divided by the ratio of consumer prices as a whole in the corresponding periods.

43

ownership value of home, rent paid, ana level of cash and deposit holdings. 9 The standarderrors of the income slopes are given in the appendixtables (la-19a). As might be expected, they are larger for automobile expenditures than for other consuroption items. Also, in relative terms (i.e., compared to their income slopes) the standard errors of such categories as a utomobiles, furnishings and equipment and medical care are larger than for more regularly purellased items such as food and clothing, though housing rather surprisingly is closer to the former than to the latter items in this respect. There is some indication that the standard errors of the income slopes are larger for the high asset families. The standard errors tend of course to be smaller for the larger groups of families, and the multiple earrelation coefficients for total consumption, food and c lotbing for the se group s are quite high for cross -section data (see appendix tables la - 19a). Asset variables Homeowners as a whole did not have much different income slopes from renters for total consuroption though owners of relatively expensive houses seemed to have somewhat smaller slopes than renters including high rent families. However, the re we re sizable differences in income slopes for different categories of consumption. Homeowners bad significantly smaller income slopes for food but larger slopes for housing and automobile purchases. In the case of housing this may simply reflect the fact that the groups are so ehosen as to limit variation in housing expenditures for renters (but not for homeowners) within any one group. An examination of the income-consumption relationships over the entire range of income (from Table 2) again indicates only small differences in total consuroption expenditures by homeowners and renters when other family characteristics are held constant.2 For automobile purchases, the re was a tendency for homeowners to spend more throughout the range of income, particularly for upper incomes, but this was offset by an increasingly strong tendency to spend less on food as incomes exceeded $3,500 or so. There was some tendency for renters to spend more on housing (as defined in the survey data), particularly for lower incomes, and less on clothing at lower incomes but more at higher incomes.

°

19It may be recalled that several of these groups, including the entire classification by rent paid, are consolidated in the seeond 20 set of UNIVAC runs. Many more family characteristics are, of course, held eonstant in these UNIVAC runs than in the pretests summarized in the first part of this paper.

44

Families owning houses valued at less than $10,000 at the beginning of 1950 had higher income slopes for consumptian as a whole than homeowners with houses valued at $10,000 or more, spending less at low incomes and more at high incomes. This consumptian behavior of families with low cost homes reflects a relatively high income sensitivity of most major items of expenditure. There seemed to be less difference in consumptian behavior between low and high rent f amilies than between owners of inexpensive and expensive homes. Families with large amounts of cash and deposits at the beginning of the period like families with the more expansive homes were apparently less likely to spend their incremental income on consumptian as a whole and on most major categories. The finding that the higher asset familias-as measured by value of home and cash and deposit holdings-bad lower income slopes for consumptian generally than the low asset families is consistent with the theoretical expectation that families with high assets, especially in liquid form, are less restricted in their consumptian behavior by current income. However, while consumptian of high asset families is above that of low asset families for low incomes, the reverse istrue for high incomes. This peculiar result of higher assets associated with less consumptian for the upper in come braekets is of cours e contrary to the theoretical expectation of the effect of a change in assets on consumptian for the same family. It is a result similar to that found in other cross-seetian studies of saving and presurnably reflects the fact that high asset families in a given income class are typically those with a low propensity to consume. Though it is therefore doubtful that a single cross-seetian can give any indication of the influence of a change in assets on consumption, it is still desirable to hold assets eonstant in order to isolate the income effect. Other variables It will be recalled that while income was treated as a quantitative variable, and specified types of assets as qualitative variables, other family characteristics were treated as semi-qualitative variables affecting the level but not the income slope of consumption.Zl The magnitude of these effects on the level of consumptian for specified values of the semi-qualitative variables are shown in

21 rt has already been pointed out that the seeond set of UNIVAC runs will contain two more semi-qualitative variables. In addition, it will furnish a s ornewhat more detailed age breakdown and a somewhat less detailed income change -income expectation classification.

45

Appendix Tables 1-19.22 The standard errors of these effects presentedin Appendix Tables 1a-19a are quite large. However, it may be noted that even where a semi-qualitative variable does not have a clearly significant effect on consuroption (say at the 20' leve l) for a particular group of families (classified by asset or qualitative type), the effect may be significant if the family groups are combined. Of the semi-qualitative variables, family size seeros to have the most important influence on consumption, debt status the least important. Total family consuroption goes up markedly as family size increases while other family characteristics including income remain constant. The largest increase in consumptian is associated with the change in family size from one to two persons; the further increase in consuroption associated with changes in family size from two to three persons or from three to four or more persons is samewhat smaller though still sizable. There is some indication that higher assets either in the form of cash or value of home enhance the family size effect. In other words a larger family seeros ready to increase the differential between its consumptian and that of smaller families at the same level of family-but higher per capita-income if its asset position permits (or perhaps if it is at a higher leve l of permanent income ). It is interesting though not altogether surprising that food accounts for most of the family size effect on consumption, with a strong positive earrelation between expenditure on food and family size. Most of the other size effects on specific major categories of consumptian are rather small and erratic. However, at a given level of income and other relevant variables, it appears that medical expenditures (per family) are definite ly smallest for single person families, clothing expenditures definitely highest for four or more personfamilies, housing smallest for four or more person families among renters, and furnishings and equipment generally largest for two person families among homeowners. Age {)f head also has a fairly important influence on consumptian though not so strong as size of family. 23 Other things being equal, the middle age groups {35-64) tend to spend most on

22 For this purpose, a z e ro effect on consuroption has been ar bitrarily ascribed to a particular value of each semi-qualitative variable. It ma y be noted that for convenience in exposition the se values have been changed for the seeond set of UNIVAC runs. The difference in the magnitude of the effect on consuroption for two different value s of an y semi -qualitati ve variable measure s the relationship between the indicated changes in that variable and in consumption. 23 The age breakdown used here is not so satisfactoryas that used in the forthcoming seeond set of UNIVAC runs.

46

consumers' goods as a whole, the oldest groups (65 and over) least, with the youngest families generally closer in this respect to the middle age than to the oldest families. Durable goods expenditures are strongly and inversely related to age, with the youngest age group s in particular spending much more than other families. Food expenditures in contrast are directly related to age, though the age effect is not quite so large for food as for durables and the difference between the food expenditures of the middle and oldest age group is rather small. 24 Housing is inversely related to age (except for renters with high cash assets) but the influence of age is considerably less than for durables and food. In general, the middle age groups spent most on clothing; the youngest families among the homeowners and the oldest families among the renters spent least. As might be expected, medical expenditures tended to be highest among the oldest families. The apparent influence of income change and income expectation on consuroption was erratic and not clearly in accordance with any theoretical prescription. The only reasonably consistent finding was that the eonstant income group generally spent least on total consumption, hardly an expected result. For homeowners, families with declines in income-which during the period covered consisted of temporary declines for the most part-showed some tendency to have relative ly high expenditures, presurnably attempting to maintain consumptian standards. This tendency-which is one of the few in the area ofincome c hang e and i neo me expectation that can be easily rationalized-was not very marked, however, and was even less evident for renters. Also, as might be expected, families with declining income generally had the highest medical expenditures, and renters with a temporary rise in income tended to spend less on housing than other renters. Mortgage debt for homeowners (measured as of the beginning of the year) was associated with samewhat less total consumption, particularly for homeowners with low cash assets, but the effect was not statistically significant by the usual criteria. For renters, there was no perceptible influence of consumptian debt (nonautomotive debt as of the beginning of the year) on total expenditures. Housing outlays were definitely higher for families with mortgage debt than for other homeowners but this probably simply reflects the influence of interest payments. There is some indication that families with debt (mortgages for homeowners and consumptian debt for renters) spent less on durable goods than other families.

24 With a mor e detailed a ge breakdown, tha age -group 45-64 shows the highest expenditure on food for given income and family size (see Jean Crockett, "Demand .Relationships for Food").

47

Omitted groups in the population While our detailed analysis of consuroption behavior has been confined to white, employee families with 1950 income after taxes from $1,000 to $10,000, we have also derived marginalpropensities to consume at the two extremes of the income range for white, employee families (Table 5 ); regression coefficients of consuroption on income for nonwhite, self-employed, and not gainfully employed families with income from $1,000 to $10,000 (Table 6 ); and marginal propensities at the two extremes of the income range for nonwhite, self-emplayed and not gainfully employed families (Table 7}. In all of these cases, the propensities or regression coefficients for the population group in question have been obtained by appropriately Table 5. Marginal Propensities to Consume for White Employee Families with Income After Tax Below $1,000 or Over $10,000, Urban, 1950a Income Below $1,000

Income $10,000 and Over

Total consumptian

.371

.621

Durable goods

.053

.083

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

.140 .008 .095 .002 .022 .032 .020

.115 .067 .089 .026 .054 .033 .022

Consumptian Items

aThe propensities at the two extremes of the income range are obtained by appropriately weighting the income slopes for 8 group s of families classified by home -ownership status (i. e., homeowners vs. renter s) and family-size group (l, 2, 3 and 4 or more persons). Within each of the groups of families, the income slope for each item of consumption at the lo w er end of the income r ange was der i ved by di vi ding the change in mean consumphon by the change in mean income from the under $1,000 income group to the $1,000 to $2,000 group. For families with $10,000 and over income, the income slope was obtained by dividing the change in mean consumption from the .$7,500-10,000 income to the $10,000 and over group by the corresponding change in me an in come.

48

~

co 384

-160

$ 308

.183

.187

.8HO

Nonwhite Families (a) (b)

746

167

$1771

.119

• 119

. 59G

Self-E mElo~ed (a) (b)

495

- 14

$ 63:3

• 155

. 129

. 811

Not Gainfully Employed (a) (b)

a The regression coefficients a and b in each of the three groups offamilies presented below are obtained by appropriately weighting the eonstant terms and income slopes for 8 subgroups classified by home-ownership status (i. e., homeowners and renters) and family size group (1, 2, 3, and 4 or more persons).

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

Durable goods

Total consumptian

Consumptian Items

Regression Coefficients of Items of Consumptian on Income Mter Tax for Nonwhite Families, the Self-Employed and Not Gainfully Employed Families with Income Mter Tax from $1, 000 to $10, 000, Urban, 1950a

Table 6

C11

o

b"*" indicates a small negative value.

a The se propensities are obtained in the same manner as in Table 5.

• 039

. 260 . 127 • 135 .032 . 075 . 023 . 009

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

• 026

* * . 134

*

*

*

*b

. 095 . o19 • 014

)~

. 055 .053 .075

.117

• 58

Self- Emp1o,):'ed Under $10,000 $1,000 or more

• 090

• 895

Nonwhite Families Under $1, 000

Durable goods

Total consumptian

Consumptian items

Income after tax:

• 137 • 100 . 040 • 005 • 030 • 031 .002

. 051

-50 j

Not Gainfully Emplozed Under $1, 000

Marginal Propensities to Consume for Nonwhite Families, the Self-Employed and Not Gainfully Employed Families with Income Mter Tax Below $1, 000 or over $10, 000, Urban, 1950a

Table 7

weighting the ear respanding propensities for 8 subgroups of f amilies elassified by homeownership status (homeowners vs. renters) and family-size (1, 2, 3, and 4 or more persons). Finally, the regression eoeffieients for whit e employee and other f amilies in the $1,000$10,000 ineome range, and the marginal propensities for white employee and other families at the two extremes of the ineome range, are eombined to obtain the ineome slopes (and, in the $1,000$10,000 ineome range, the eonstant terms )for the entire U. S. urban population eovered by the B.L.S. 1950 Survey (Table 8). The marginal propensities to eonsume for white, employee families are as might be expeeted samewhat less for high ineomes than for the $1,000-10,000 group but rather surprisingly are smallest for the very low ineome braekets. Automobile expense (ineluding purehase) aeeounts for most of the difference in marginal propensities between the high and intermediate income families; the food and clothing slopes are also lower for the high ineome f amilies but the housing slope is larger. For the low income brackets, the marginal propensities to eonsume are lower than for the intermediate income families in all major consumptian categories. An investigation inta this unexpected result indicates that it largely reflects family characteristics which were not held eonstant in the less detailed analysis applieable to the two extremes of the ineome distribution. Thus, over 60% of the white, ~mployee families with inGames under $1,000 were headed by persons 60 years or mor e in ag e, with 20% 70 years or mo re. Moreover, there is reason to believe that a signifieant proportion of these lowineome families had rather sizable assets. Nonwhite and not gainfully employed families in the $1,00010,000 ineome range have substantially smaller intercepts (i.e., estimated consumption for zero income) but considerably larger income slopes than white, employee families of eomparable ineome.25 In eontrast, self-emplayed families with ineomes from $1,000 to $10,000 (i.e., families with self-emplayed heads) had the largest intercepts and smallest ineome slopes of any of the groups in this income range. Nonwhite families spent less on consumptian generallythan white families for incomes up to $4,900, presurnably reflecting either lower assets or smaller normal ineome for the former group, while families headed by employed persons spent less than self-emplayed families for ineomes up to $5,500. It is

25 In connectionwith the comparative consumption behavior of non-

white and white families, it should be pointed out that low income nonwhite families probably receive unreported income in kind to a greater extent than low income white families, and also that relevant prices may be significantly different for the two groups of f amilie s.

51

~

s·

538

.154

Food excluding alcoholic beverages Housing Clothing and clothing services Medical care Furnishings and equipment Auto expense (including purchase) Auto purchase

.157

. 149

.086

• 099

.604

Income slope

a

$10, 000 or more

bThese regression coefficients were obtained by appropriately weighting those in Table l and in Table 6.

aThese income slopes (or marginal propensities to consume) were obtained by appropriately weighting those in Table 5 and in Table 7.

8

. 051

Durable goods

. 7 21

Income Mter Tax $1, 000-10,000 Constan t Incorng term b slope $1045

Income slopea

Under $1, 000

.503

Total consumptian

Consumptian items

Regression Coefficients of Items of Consumptian on Income After Tax for Average Values of Other Family Characteristics, All Sample Families Classified by Income After Tax; Urban, 1950

Table

interesting to note that for nonwhite families there was not much difference between the low and intermediate income groups in their marginal propensity to consume, while for self-emplayed families there was not much difference in this respect between the intermediate and high income groups. The composite marginal propensity to consume in 1950 for all U. S. urban families in the $1,000-10,000 income braeket was . 72 according to B. L.S. cross-seetian data analyzed in this paper (Table 8}. This figure is roughly consistent with same of the estimate s of the marginal propensity to save (out of personal disposable income) derived from per capitadeflated time-series regressions.26 Some Concluding Remarks This paper has measured the net effect of in come on consumptian indicated by cross-seetian data for 1950, holding eonstant a number of family characteristics other than income, and has also measured where possible the net effect on consumptian of each of the se other family characteristics. The rationale of holding eonstant other family characteristics in deriving from cross-seetian data the income coefficients whi ch are most like ly to be relevant to timeseries analysis of consumption-income relationships has been considered at some length, and it has been pointed out that the cross-seetian income elasticities of expenditure obtained in this paper are conceptually closer to time-series income elasticities of quantity than of expenditure. The apparent effect of income on consumptian as a whole and on several major groups of expenditure-such as food, housing and medical care-is significantly reduced by holding eonstant family characteristics intercorrelated with income, while other groupssuch as clothing, furnishings and equipment, automobile expense and automobile purehase-are affected r e l a t i v e l y less. The consumption-income relationships derived in this paper explain much more of the variation in expenditure among families in such regularly purchased categories as food and clothing than in such other s as automobilies, furnishings and equipment and medical care. There is not very mu ch difference in total consumptian between homeowners and renters when other family characteristics are held constant, but there were sizable differences for several categories of consumption. Thus, homeowners spent more than renters on automobiles, particularly for the upper income classes, and less on food except for low incomes. While our analysis has suggested that it is desirable to hold the level of cash and deposits as well as Z6rrwin Friend with the assistance of Vito Natrella, Individuals' Saving_, John Wiley & Sons, Inc., 1954, pp. 142-148.

53

other assets eonstant in is olating the income effect on consumption, it does not seem possible to measure the effect of changes in the level of such cash holdings on consuroption from the usual crossseetian data. Of the family characteristics studied other than income, family size seeros to have the most important influence on consumption. There is a strong positive earrelation between consuroption and size of family, when other fa mil y characteristics are h eld eons tant, due for the most part to the influence of family size on food expenditure. The addition of another person has a more substantial effect on consuroption for one-person than for larger families. Age of head als o has a significant eff ect on family consumption. Other things being equal, the middle age groups tend to spend most on consumers' goods as a whol e, the youngest f amilies almost as much, and the oldest f amilies the l east. Durable goods expenditures have a strong, inverse relation to age, with the youngest age groups spending much more than other families. Food expenditures in contrast are directly related to age, but the difference between the middle and oldest age groups is rather small. Of the other family characteristics, the influence of income change and income expectation on consuroption seemed to be erratic and at l east in part was not consistent with theoretical expectations. Debt-or at least mortgage debt-had the expected typeof influence, but the effect was not statistically significant. In the lower income brackets, nonwhite spent less on total consuroption than white families and employee less than self-employed families. In the upper income brackets, self-employed families in particular had a comparatively low level of consumption. We have commented in several places in this paper on the relationship of the present analysis to our future plans in the derivation of as comprehensive a set of consumer demand relations as is feasible to obtain. To summarize, we first plan to complete shortly the analysis of a seeond (and for the time being final) set of UNIVAC runs of theB.L.S.1950Surveydata relating to consuroption and its determinants. In this further analysis of the 1950 data, many more items of consuroption (36 major groups and subgroups) will be analyzed, two additional explanatory variables (education and location) will be added, and a number of changes made in the grouping of families on the basis of the results presentedin this paper. Second, we will compare these new results in som e detail with findings of other, less inclusive cross-section studies. Third, we shall carry out-hopefully by this Summer-a similar analysis of the Life 1956 Survey data on consuroption and related variables for some 10,000 families, bothurban and rural. Finally, an attempt will be madeto integratethe cross-section resultswithtime-series data and to indicate so far as possible the apparent implications of our findings for future trends in consumption. 54

01 01

5. a 5. 5 - 50.8 + 47.2 + 16. o - 83. l - 58. 7 +850. 948

+

33. o 31. 2 1.8 27. 5 + 51.3

- 26. 2 T 29.6 -371.860

b5. .... 95. 5 +174. 4 +188. 3

-117.4 - 28. 9

+602.642

eonstant term (a)

+

7.5 86. o + 39.524

+

- 69.404

+

+

6 2 6 6 l

9. 3 55. 7

lO. 33. + 3. + 9. 19. +

• 0341

... , c; hin g s and

-299. 335

-117.685 +85.829

- 84. 2 7. 2

+ 36. 3 + 70.1

+ 35.3 + 30.3

- 46.4 6. 8 +159.8 - 91. l + 30.4

...

.4 ... 18. 4 - 54. o + 26.7 6. 3

...

-i-l l

+

+

+

+221. 7 + 39.8

.1744

l. 7 + 46.1

+

+ 38. o + 93. o + 72.6

. 0651

Au to Expense

39. 6 ö4. 4 26. o

+

Equipment

F-,"~'"'

20.7 9. 9 + 24.4 - 42. o + 14. l

50. 9 - 41. 9

74. o 6 2. 4 + 17. 9

+

Care

:\teo.tca.1

~he regression for each consumptian item is of the form Y '" a+ b (income after taxes)

+ ci + di+ e i+ fi, where income is a continuous variable with the slope indicated, ci takes on the value O for 4 or more person families and the values indicated in the table for other size families, di:: O for families with age of head 55 or over, ei =O for families with income change and income expectation patterns different from those indicated, and fi = O for families not reporting debt (mortgage for homeowners, consumer debt for renters).

~

+

:;, 3 9. 8 5. o 9.8 3. 4

-:07.: +

- 20. 5 + 31.4

... 67.9 + 55. 3

-165.9 -116. 7

-155. l - 16. 4

. l 230

o

...

-253.4 - 66. 7

. 0598

- 7 3.

+

.,... 9~. 2 ·117. 6

. 1545 -100.1 -130.0 94. 2

+ + BO. 3 + 64. 6 + 55.7

. 1992

Clothing

-541. 3 -365.4 -202. 4

. 3 225

Housing

-551.5 -313. 5 -119. 2

+

Food

1.1-2.9 3. o ·3. 9 A ge of head (di) Under 35 35-54 Income ch angeincome expectation (ei) Constan t Continuous rise Continuous declin.e Temporary rise Temporary decline Debt status (f;) Has debt No debt

l. O

Income after taxes (b) Size of family (c i)

Tota~

DurJ.ble Goods Con.o...;umption Purc..:hase

Regression Relationshipsa between ltems of Consumptian and Family Characteristics, For Homeowners with Less than $lO, 000 H ornes and Less than $500 Cash, ·,vhite Employee Families with Incomes from $1,000 to $10,000, Urban 1950

Appendix Table l

. 114

23. 5. 65. 62. 53.

3 2 B 5 9

-244.947

- 55. 5 - 10.0

+ + +

+135. 2 + 7.7

+ 74.7 + 59.6 + 38. {.l

+

Au to Purchase

~

nporary decline Debt status (!j) Has debt No debt Multiple coefficient of correlation (r)

• 756

• 411

• 667

• 227

96.3 95.7

214.5 213. l

330.3 321). l

102.6 102. o

90.5 94. l 213. l 139. o 139.6

139.5 145.0 328. 2 214. 2 215. l

40.3

45. B

40.6 42. 2 95.7 62.4 62.7

48.8 43. o

102. o 89.8

157. l 138. 4

79.4 41. l 39,5

.011

Ho u sing

43.3 45. o 102. o 66.5 66.8

84.6 43.8 42. l

• 012

176. 9 91. 5 88.1

• 02ö

Food

272.4 140.9 135,7

• 040

Total Durable Goods Consumptian Purchases

• 576 .

. 357

98.4 97.8

71. il 70.6 84. 2 83.7

54.~

• 258

41. 5 43. 2 97.8 63. 8 64. l

30. o 31. l 70. 6 46, o .;s. 2 35.5 36. 9 83.7 54.6

46.8 41. 2

33. ~ 29.7

81. 2 42. o 40.4

• 011

40. o 35.3

• 010 59. 6 80.3 29. 2

.008

Clothing

Furniehin g s and Equipment

69.5 35. 9 34.6

Medical Care

Standard Errors of Regression Relationships between ltems of Consumptian and Family Characteristics., For Homeowners with Less than $10, 000 Homes and $500-$1499 Cash White Employee Families with Incomes !rom $1,000 to $10,000, Urban 1950

Appendix Table 4a

• 389

206.7 205.4

87. 3 90.7 205.4 13... o 134,6

98. 3 86. 6

170. 5 88. 2 84. 9

• 024

Au to Expense

. 243

193. 6 ~92. 3

81.7 84. 9 192. 4 125. 5 126. o

9 2. o 81. l

!59. 6 82. 6 7 9. 5

• 023

Au to Purchase

(l)

c.:l

eonstant term (a)

+2140. 256

lncomP. after taxes (b) • 5615 + Size of family (ci) -1615.1 1.0 1.1-2.9 -826.9 -580.3 3. 0-3.9 Age of head (d;) +181. 9 Under 35 + 82,5 35-54 Income changeincome expectation (ei) -285. 7 eonstant +184. 3 Continuous rise +201. 5 Continuous decline - 22.5 Temporary rise +179. 3 Temporary decline Debt status (fi) +356, 8 Has debt +358. 5 No debt

- 42. o -160. l

+352.267

+1030. 806

5. 2

+ 11.5

+ 7,3 +107. 3 +

+ + -

+323.915

68. o 30.4 82. 2 29, o 72.8

+ 53.7 + 20.0

2.1 - 36,8 + 87.7 - 39. o - 23.7

'" ('8, 8

-114. 4 +17:i. 3 - 86. 3 + 46.4 + 87.4

.0553

-102.9 - 16. 7 - 44.8

+

-119. 1 - 39.0

• 1121

+3S3. 2

+

Housing

-671.6 -404.7 -243.6

.0718

Food

-520. 4 + 46. o -124. 6

+

Total Durable Goods Consumptio n Purchase

.0986

3 l 4 l 5

+245,471

9. + 12. +200. 8, +142.

+ 38.865

6 2

o

3 l

- 19. 3 + 15. 2

+ 16.3 + 28.4

35. 4, 40. 15, 53.

• 0067

-131.9 - 98.9 - 65. 2

+

Car~

+186. 3 +131, 5

+ +

- 94,9 - 47. l

-168.8 -221. 8 - 68.7

+

Clothing

Medical

+144. 274

-194. 3 -103,4

-152, l - 36.9 - 32.8 + 74,4 - 41, 5

+246.967

+184, 4 +241. 4

- 14. 7 +2062, -168.3 -127.0 +184. 5

+251. l + 64,8

.0388

+276, 2 + 83.4

+

-440. 2 + 25.8 -181. 2

.0553

Au to ExpE'nse

- 73.3 + 76.9 + 26.2

+

Furnishings and Equipment

Regression Relationships between Items of Consumptian and Family Characteristics~ For Homeowners with $10,000 and Over Hornes and $500-$1499 Cash White Employee Families with lncomes from $1, 000 to $10, 000, Urban 1950

Appendix Table 5

-

+254. 201

+146. 9 +168. 2

+ 3. 3 +17 2. 4 - 93.6 -100, l +137,5

+137. 9 - 18. o

-396.9 19.0 -17 2. 7

. 00 l:

Au to Purchase

....

CD

Income after taxes (b) Size of family (c 1) l. O 1.1-2.9 3.0-3.9 Age of head (d;) Under 35 35-54 lncome changeincome expectation (ei) eonstant Continuous rise Continuous decline Temporary rise Temporary decline Debt status (f;) Has debt No debt Multiple coefficient of correlation (r)

. 694

• 254

.642

• 403

104. l 105.4

121. 5 123. o

261. 8 265. l

418.0 423. 2

39.3 37.4 78.5 59.5 75. 9

45. g 43.6 91.6 69.5 88.6

98.9 94.0 197.3 149.7 190.9

158.0 150. 2 315. l 239. 2 304.9

49. l 39.6

123.6 99.5

197.4 158. g

57.3 46.2

• 009 29.1 38.3 36.9

.011

Housing

34.0 44.6 43.0

.024 73.3 96.2 92.8

117. 1 153.7 148. 2

• 039

Food

• 612

93.7 94.9

35.4 33.6 70.6 53.6 68. 3

44.2 35.6

26. 2 34.4 33.2

• 008

Clothing

• 205

82.8 83.8

29.7 62.4 47.3 60.4

:n. 2

39.0 31.4

23.2 30.4 29.3

• 007

Medical Care

• 386

111.8 113. 2

42.2 40. l 84.3 63. 9 81.5

52.7 42.5

31.3 41. l 39.6

• 010

Furnishings and Equipment

Errors of RPgrPssion Relationships between Items of Consumptian and Family Characteristics. For Homeowners with $10, 000 and Over Homes and $500-$1499 Cash White Employee Families with Incomes from $1, 000 to $10, 000, Urban 1950

Total Durable Goods Consumptian Purchases

St~nd;:~rci

Appendix Table Sa

• 185

253.8 257.0

95.9 91. 2 191.3 145. 2 185.1

119.8 96.5

71.1 93.3 90.0

.023

Au to Expense

.081

228.8 231.7

86.4 82. 2 172.5 130.9 166. 9

lOB. O 87.0

64.1 84. l 81. l

• 021

Au to Purehast

C1l

C»

+147. 887

+148. 413

+253. 550

eonstant term (a)

+1260. 924

+ 81.5 - 67.5

-376.2 -402.7

- 27.9 + lO. 4

+2609. 959

-133,6 -112.4

- 18.6 -104.3 + 80.8 -142. l +137.1

- 51.1 - 13.0 +118. o + 8,0 - 51.9

-332. 5 -124. 2 -202. 7 -106. o -321. l

.1178

+ +

74.4 21.6 97.5 92.8 7. 9

+52. 9 + 49.2

- 28.2 -158. 2 - 80.3

+

+135.1 +108. 6

.0357

+266. 3 +110. 1

+

-169, o -103. 4

.1680 - 23.6 + 67.8 + 17.7

+

elothing

-730.8 -462.1 -241. 7

.1504

Housing

- 29.4 •4 + 5. l

+

Food

lncome arter taxes (b) • 6391 + Size of family (c;) 1. o -1143. l l. 1-2. 9 -705.7 3. 0-3. 9 -221.7 Age of head (d 1) Under 35 +179. l 35-54 +182. 2 !neo me changeincome expectation (e;) eonstant -598. 8 Continuous rise -306. 1 Continuous decline +269. 8 Temporary rise -211. 5 Temporary decline -117.1 Debt status (f;) Has debt -539.8 -691.0 No debt

Total Durable Goods Consumptio n Purchase .0047

41.7 12.2 81.3 65,3 69.2

+193.116

- 51.8 - 66,0

+ + + +

- 36.7 + 47.8

- 64.9 + 50,8 + 82.0

+

Medical Care

- 61. 360

+214,1 +163. 6

- 33.7 5,5 - 50.4 - 38,8 + 25.7

-

+238. 3 + 79.5

-

.0353

- 78.1 + 41.8 7,0

+

Furnishings and Equipment

Regression Relationsh!ps between Items of Consumptian and Family Characterist!cs, For Homeowners with Less than $10, 000 Homes and $1500 and Over Cash White Employee Families with lncomes from $1,000 to $10,000, Urban 1950

Appendix Table 6

.1660

.0983

+214. 808

+327. 652

-255. 6 -160. 2

-287. 3 -152. 9 -168.8 - 99,7 -337.9

-330,0 -168. 8 -215.6 - 17.2 -342.4 -212.3 +77. 7

+ 37.1 + 39.0

+ 29.6 - 47.2 4. o

+

Auto

Purehas e

+ 75.5 + 59.6

- 58.0 - 56. o + 42.8

+

Auto Expense

o:> o:>

Income after taxes (b) Size of family (q) l. O 1.1-2.9 3.0-3,g Age of head (di) Under 35 35-54 lncome changeincome expectation (e)

Multiple coefficient of earrelation (r)

No debt

Continuous rise Continuous decline Ternporary rise Temporary decline Debt status (f 1) Has debt

eonstant

Appendix Table 6a

. 684

260. 4 252.6

373. 7 362.5

554. 4 537.8 . 328

81. 9 101.0 142.8 143.5 137.3

117. 6 144.9 204.9 205.9 197. o

17 4. 5 215. l 304. l 305.5 292. 3

.742

106. 8 81. 6

153.3 117. o

227. 5 17 3. 7

• 023 187.5 g3, 4 92. 8

269. o 134.0 133. 2

• 033

Foo~

399. 2 198.8 )g7.6

. 049

Total Durable Goods Purcha.ses Consuroption

. 290

157. 3 15 2. 6

4g.s 61. o 86. 2 86.6 82. 9

64.5 49.3

113. 2 56.4 56. o

.013

Housing

. 681

115. 9 112. 4

36.4 44. g 63.5 63.8 61. l

47.5 36. 3

83.4 41. 5 41. 3

. 010

Clothing

156. 8 152. l

96. l 93. 2

• 252

4g. 3 60.8 86.0 86. 3 82. 6

30. 2 37, 3 52. 7 52. 9 50.6

• 218

64. 3 49. l

112. g 56. 2 55. 9

• 013

Furnishings and Equip1nent

39.4 30. l

!i9. 2 33.4 34. 2

• 008

Medical Care

standard Errors of Regression Relationships between Items of Consumphon and Family Ola:-acteristics, For Homeowners with Lessthan $10,000 Homes and $1500 and Over Cash White Employee Families with Incomes from $1,000 to $10,000, Urban 1950

. 290

386.8 375. 2

l 7 9 7 4

. 211

349. 9 339. 4

110, 135. 191. 19 2. 184.

143.6 109. 6

158.7 121. 2

121. 7 150.0 212. l 213. l 203.9

251. g 125.4 124. 7

. 031

Au to Purchas(

278.3 138.7 137. g

.034

Au to Expense

-.l

O)

eonstant

term (a)

Continuous dec l in e Temporary rise Temporary decline Debt status (f 1) Has debt No debt

Cont1nuous ri:o;e

Incorne after taxes (b) Stze of family (ci) !.O l. 1-2. 9 3.0-3,9 Age of head (di) lJndpr 35 35-54 lncome ch angeincome PXpectation (ei) Con s tant

+1706.097

+ 38, 565

+841, 561

+141. 767

+18 2. 7 +201. 9

+113, o + 62. 5

+ 47,3 +305. 6

+681. o +775. 2 +135, l +113, o

+ 35.9 - 39, o +212. 6 6,0 - 62.7

• 912

- 81, 2 - 24,8

+ 22,5 +54, 8 - 62,3 + 78.8 - 68, 7

+342. g

+ 19,4 - 55,8 +17 8. l +156. 9 +154, 2

-l Gl, l

-146, 5 + 66,5 -296. 7 -256, o + 97,3

+113, 6 + 42,0 - 41.5

-655. 7 -718.4 -185. l

-26 3. 8 -229. 3 75,4

• 1044

+

• 0271

+

-146, 8 - 26.3 + 7. 6 +lO!. 5 +382. o

• 1151

+187. 5 + 77. 2

+

-15 2, 7 - 15. 5

• 1676

+ 65, 2 + 88,4

+

Clothing

Housing

+136, 7 + 54,8 + 87.5

. 57 36

Food

-5 64, g -396,3 -139. o

+

Durable Goods Total Pure ha se Consumptian

+137. 119

+ 80,1 + 70.7

l, 9 30.5 - 23,1 + 33,3 +162. 5

• 1106

+236.405

+ 36. l +189.7

- 55. o + 75.9 - 72.143

- 60.0 + 40.6 -347. 2 -238. 4 +230.0

-27 4, 9 - 53. 4

+l U4, 9 + 45. 3 7. 2

+

• 090c

33, 144

+166. 5 +314. 2

- 54, 3 + 31. 2 -351. 9 -235. 3 +240,7

-294. 2 - 9 2, 8

+238.5 + 32. l - 36. 3

+

Au to PurchasE-

Au to

Expense

-104.0 + 31.4 + 17.6 - 64, 6 - 68.8

+3 39. 6 +16 2. 3

.0705

- 71. o + 31.9

+

- 47.9 + 50.2 + 18, 5

• 0097

Furnishings and Equipmcnt

-176,1 - 59, l - 10. l

+

Medical Care

Regression Relationships between Items of Consumptian and Family Characteristics, For Homeowners with $10,000-$14, 999 Homes and $1500 and Over Cash White Employee Families with Incomes from $1,000 to $10,000, Urban 1950

Appendix Table 7

00

O)

Continuous rise Continuous decline Temporary rise Temporary decline Debt status (fi) Has debt No debt Multiple .coefficient of earrelation (r)

Constan t

income expectation (e 1)

lncome after laxes (b) Size of family (c;) l. O l, 1-2. g 3.0-3.9 Age of head (di) Under 35 35-54 Income ch ange-

Appendix Table 7a

. 269

.632

162. 8 160,6

385.6 380.4

602. l 593, g

• 634

57.2 58.3 123. 7 104.0 288. l

4 l 9 3 2

. 132

165. 9 163. 6

58.2 59, 4 126. o l06,0 293. 5

7 3, 3 50, 7

7 2. o 49. 7

135. 138. 292. 246, 682,

170. 5 117. 8

266, 3 184.0

171. 4 58. g 59. o

.013

Housing

168. 2 57.8 58,0

.013

Food

211. 5 215. 7 457,4 384,6 1065,0

398. 3 136. g 137. 3

. 031

621. 9 213. g 214, 4

. 049

Durable Goods Total Consumptian Purchases

• 210

102. 6 101, 2

147. 4 145.4 . 552

36,0 36,7 77,9 65,5 181. 5

45.4 31. 3

106.0 36. 4 36.5

. 008

Medical Care

51.8 52.8 112. o 94. 2 260.9

65. 2 45. o

!52. 3 52. 3 52.5

. 012

Clothing

• 333

,133

363. o 358,0

392. o 386,7

. 130

7 8 l 184. 7 182. 2

5

127. 130. 27 5. 231. 642.

o

160. 5 110. 9

374, g 128, 9 129. 2

. 029

Au to Purehas E

137,7 140.4 297,8 250.4 693.5

17 3. 4 119, 7

404.9 139, 2 139.6

.032

Auto Expense

64.8 66, l 140.3 118. o 326. 7

81. 7 56,4

190.8 65. 6 65. 7

. 015

Furnishings and Equipment

Standard Errors of Regression Relationships between ltems of Consumptian and Family Cbaracteristics, For Homeowners wiih $10,000-$14,91111 Homes and $1500 and Over Cash White Employee Families with lncomes from $1, 000 to $10, 000, Urban 1950

O) (O

+6050. 876

+ 83.9

-1483. o -1625.0

o o

eonstant term (a)

+ 2. l +384,9 +1267.3

+196.8 +135. 7 +2447.7 +2114.1 +889. 6

-2820. -3320,

2 -105. 3

+2229. 66 3

~43.8

~02.

• 0519

+ •l +163.1

+ + 80. 4 + 64. l +402. o

. 58 31

+419. 3 -1270.4 -570. 2

+

Income after taxes (b) Size of family (ci) 1.0 1.1-2.9 3. 0-3. 9 Age of head (di) Under 35 35-54 lncome changeincome expectation (ei) Constan t Continuous rise Continuous decline Temporary rise Temporary decline Debt status (fi) Has jebt :';o debt

Total Durable Goods Consumptio n Purehas e

• 1287 • 0252

+1519.563

-456.0 -6 21. o

+317. - 82, - 66. +270. +167.

+ 47, o -110.4 +7 31. 5 +194. 7 + 49.5

+909.284

-290. o -465.0

6 6 8 6 7

+344. 6 +181. 5

+1177.0 -360,4 -219, 7

+

Housing

- 49.6 + 32.8

+ 71,5 -427. 4 -245, o

+

Food

• 0618

6 5 3 8 3

+650. 277

-132. o -216.0

-220. -220. +225. 4. + 61.

+161. 9 + 50. 4

+413,4 - 46. o -17 3. l

+

Clothing

o

+226. 882

+ 46,0 + 40.0

- 56,7 + 91. o +129. 7 +130. 3

+12~.

• 0789

+905.049

-1283,0 -1407. o

-684. o -590,0

+1449.152

~59,0

+1290. o +217. 7 +6 91. l

+ 66,7

-127.0 - 53. l

-668. l +285. 7 +334. 4

+

Au to Expense

+ 54, l -209.6 +179. 2 +913. 5 -317.9

+912, 5 7. 6

. 0311

-152. 5 - 98. 9

+

+49 2. 3 - 56.4 +171. 4

• 0237

Fur nishings and Equipment

-467. 8 -242.6 -160. o

+

Medical Care

RegreBsion Relationships behveen Items of Consumphon and Family Characteristics. For Homeowners with $15,000 and Over Hom(:'s and $1500 and Over Cash White Employee Families with Incomes from $1.000 to $10,000. Urban 1950

Appendix Table 8

• 0191

o o +1092. 766

-803, -986.

+ 9. 9 +657. 9 +1031.7 - 18. o +483. 8

-133, 2 - 55. 3

-269. l +205. o +243.3

+

Au to Purchase

o

-:J

135

2156.5 75 2. l 66~ 1 • 5

o

o

590

*Extremely large standard errors.

:;o debt J\1ultiple coefficient of earrelation (r)

Has debt

Lind('r 35 1136. 3 35-54 6 21. 4 Inconw ch angeincon:E' expectation {ei) eonstant 640. l Continuous rise 742.5 Contlnuous decline l 224. 9 Temporary rise 1493. l Ternporary declHle l 00 3. 2 Debt status (f,)

.-\ge of heacl (di)

l. O l. 1-2. 9 3. o- 3. 9

InC'mnP after te.xes (b) Size of family (c)

o29

o

* * 696

• o o

141.8 164.5 271. 4 330.9 222. 3

362. 6 420. 5 693. 9 845.8 568.3

*

251. 8 137 o 7

477 o 9 166. 6 148. 3

o

Food

643. 7 352. o

1221. 6 426. o 379. 2

.076

Total Durable Goods Consumptian Purchases

027

o

587

:~

*

130.2 151. o 249. l 303. 7 204. o

231. l 126. 4

438.7 152. g 136. l

o

Housing 035

•o

*

*

168.4 195. 4 322.4 393.0 264. o

299. l l 63. 5

567.6 197 o 9 176. 2

o

Clothing

014

• 329

*

*

70.8 82. 2 13. 5 165. 3 111. l

125. 8 68. 8

238.8 83. 2 74. l

o

Medical Care

048

o

230. 267 o 441. 538. 361.

095

*

*

7 5 4 l 5

409.5 223. 9

777. 2 271. o 241. 2

o

Furnishings and Equipment

standard Errors of Regression Relationships between Items of Consumphon and Family Characteristics. For Homeowners with $15,000 and Over Homes and $1500 and Over Cash White Employee Families with Incomes from $1,000 to $10,000. Urban 1950

Appendix Table 8a

A ut o

071

o

077

*

3 38. l 39 2. l 646. 9 788.6 529.8

600. 2 328. 2

1139 o o 397. 2 353.6

o

Expense

Au to

064

o

o

306. 9 355.9 587 o 2 715. 8 481.0

544.8 297 o 9

1033.9 360. 5 320.9

o

Pure ha se

....

-.1

eonstant term (a)

);o debt

Debt status (fi) Ha-" df•bt

Temporary rise Temporary dedine

+1317. 2 +1006. 9 -738.3G9

+419.6 +50 2. 4

-246. 5 + 94. 2 +159. l -320.3 + 22. l

-458.9 + 26. 9 +805. l +142. 3 + 58. l

• 2076

+175. l + 42. 7

+

+ 4j.G + s :1. -1

• 67 81 +213. 8 2. 4 +254. 4

+

-548.9 -783. 2 +108. 4

+2U9.213

lncome after taxes (b) Size of family (ci) 1.0 l.l-2. 9 3. o- 3. 9 Age of head (d;) Under 35 35-54 lncome change:ncorne expectation (ei) C unstant Ccntinuou~ rise Continuous declinp

Total Durable Goocis Purehas e Consumphon

• 1247

+776. 500

+3 3 2. 5 +260.8

+114. 4 22. u

+lGS.H

- 50.9 16. 9

-111.8 - 44. 2

-8 37. 2 -548. l -281. 7

+

Food

• 032':

• 0978

-130.214 289

+ ~J3.

+247. g +21.5. 7

- 53. 3 + 18.9 +170. B +109. 7 - 58. 3

- 25. 2 + 3. 6

-201. 2 -159.6 70. 3

+

Clothing

+112. l + 3 2. l

26. 6 - 41. 9 - 52. o -111.6 ~ 11. n

+ 86. o + 6. 6

+ 35. 7

+236. ~) + 8. 3

+

Houp.ing

• 0170

- 50.023

+19G.O

+215. l

- 39. 3 + 8. 6 + 8. 2 +136. 9 + 48.5

- 17. 9 - 21. 4

3. 6 - 31. l + 11.8

+

Care

Medical

.0702

-375.885

+200. 2 +163. 5

+ 93. 2 + 92.7 +189. 3 + 93.8 +120. 4

+12··. 6 + 52. 5

+ 72. 2 +123. 6 + 49.8

+

Furnishings and Equipment

Regression Relationships between Iterns of Consumptian and Family Characteristics. For Homeowners with Less than $10 .. 000 Homes and Cash Not Reported White Employee Famille s with !neo mes from $1.000 to $10, 000, Urban 1950

Appendix Table 9

• 19 26

Au to

• 1306

-605. 844

~635.

730

+500.8 +605. 2

- 38~. l •6 + 12. 3 -414.9 - 77. 5

-4 34. o - 57. 4 + 15.7 -499. 3 - 87.0 +370. 8 +510. 7

+ 26.6 58.3

+166. 2 -l H. 7 +204. 9

+

Purchase

+ 84. 2 + s. l

+218. 5 - 89.0 +286. 7

+

Au to Expense

-t N

Continuous r is e Continuous decline Temporary rise Te mporary decline Debt status (f;) Has debt No debt Multiple coefficient of earrelation (r)

eonstant

lncome after taxes (b) Size of family (ci) 1.0 1.1-2. 9 3.0-3,9 Age of head (di) Under 35 35-54 Income changein come expe ctation (e i) 131. 5 142.4 287 .l 203. l 19B. 9 731. 8 736. o

209.5 226.7 457. 3 323.6 316.8

1165,4 117 2. 1 • 417

163. 3 119. 2

260. 1 1B9. 9

• 765

355. l 142.4 134. 3

.033

565,5 226, B 213.9

.054

Durable Goods Total Purchases Consuroption

36.4 39,4 79.5 56.3 55. l 202.7 203.9

67, 2 72.7 146.7 103, B 101. 6 374. o 376, 2 . 329

45, 2 33.0

83,5 60,9

,722

98.3 39.4 37,2

• 009

Housing

l Bl. 5 72. B 6B. 6

• 017

Food

• 636

26 2. 2 263. 7

47,1 51. o 102. 9 72. B 71. 2

5B.5 42.7

127, 2 51,0 48. 1

. 012

Clothing

• 230

173.8 174.8

48,2 47, 2

33. B 6B, l

31. 2

38.B 2B. 3

84,3 33,8 31. B

.008

Medical Care

46. 2

• 409

257. l 25B. 6

100.9 71. 4 69.9

so. o

57.4 41.9

124,7 50.0 47. 2

• 011

Furnishings and Equipment

standard Errors of Regression Relationships between ltems of Consumptian and Family Characteristics. For Homeowners with Lessthan $10, 000 Homes and Cash Not Reported White Employee Families with lncomes from $1,000 to $10, 000, Urban 1950

Ap;:>endix Table 9a

,o

B63, 7 86B, 7

155, 2 168,0 338,9 239, B 234, B

192. B 140,7

419. l 168, 1 15B.5

• 040

Au to Expense

• 329

693, o 697. o

124.6 134, B 271. 9 192.4 !B8.4

154,7 112.9

336, 3 134.9 127.2

.032

Au to Purehas e

(,\)

-:J

Conötant term (a)

No debt

Continuous rise Continuous decline Temporary rise Temporary decline Debt status (fi) Has debt

eonstant

Income after taxes (b) Size of family (c 1) l. o l. 1-2. 9 3. 0-3. 9 Age of head (d;) Under 35 35-54 Income ch angeincorne expectation (1.'\)

+ 53.5 +212. 5

+150. l +195,4 +1%. 477

-182. 3 - 38. 8 -318, 7 + 23.9 -290.5

-155.0 - 49. o -341. 3 +304. o +250. l

+1704. 990

+354, l + 36,6

.1138

+219. o + 51,5

+ - 30,4 -146. 4 + 5. o

• 6433

-78:1.5 -691.7 + 29.0

+

Total Durable Goods Consumphon Purchase

• 1625

+950. 089

-227. 5 -211.4

- 37.6 + 60.5 4. 6 -131. 7 + 46.5

- 75.6 - 29.6

-544. 6 -301,5 -165.6

+

Food

.0588

+102. 368

+ 88.9 33,8

+ 51. o - 17. o -149. 8 +139. 6 + 78. l

+ 21.2 + 75.7

+ 70,4 + 75.3 + 33.0

+

Housing

• 1037

4. 5

- 75. 169

+ 67. 8 + 88. 3

+129, 5 - 34.4 +141. 6

+ 27. 7

+

+ 66.3

+ 25.2

- 79, l -113. 9 + 6. 8

+

Clothing

• 0105

+223,534

+ 12.6 + 27,2

+ 89. l + 11.5 +111,2 +58, 7 3. 7

- 58,2 - 71, o

-183. 2 - 89.2 + 26,5

+

Medical Care

. 0312

• 1333

+ 92, 255

+130. 3 +251,9

- 53, o - 15.8 + 42.858

-290, 8 - 39,4 -418.3 - 10. l -212. 5

+111. 3 -121. 3

+ 98, l -l 7 3. 7 - 57. 9

+

Au to Expense

+ 64,1 6, 7 - 11. l + 17. l - 33. 4

+197. 6 +128. 3

33.9 + 36.9 +54. 7

+

and Equipment

Furnishings

Regression Relationships between Items of Consumptian and Family Characteristics, For Homeowners with $10~ 000-$14,999 Homes and Cash Not Reported White Employee Families with lncomes from $1, 000 to $10,000, Urban 1950

Appendix Table 10

. 0855

+ 36.394

+113.1 +233. 8

-255. l - 36. 4 -304.9 - 68, 9 -217.5

+ 88.7 - 94.6

+ 62.4 -139.3 - 50,6

+

Au to Purehas e

""'

-3

Temporary decline Debt status (f;) Has debt No debt Multiple coefficient of earrelation (r)

Temporary rise

lncome after taxes (b) S1ze of family (c;) l. O 1.1-2.9 3.0-3.9 Age of head (d;) Under 35 35-54 In come ch angeincome expectation (ei) Constan t Continuous rise Continuous decline 130. 138. 28 2. 2Ul, !90.

220. 235. 478. 371. 3 21.

. 696

454.7 461. 4 . 294

268. 5 27 2. 5

2 8 5 5 l

18 2. 2 128. 8

308. 5 218. 2

5 l 3 6 9

269. o 140. 8 136. 3

. 031

455.6 238. 4 230. 8

. 053

.684

!33. 9 135. 9

64.. 9 59. 2 140.8 lOB. 4 94.8

90. 8 2

~4.

134. l 70. 2 67. 9

. 015

Food

. 305

l 21. 3 123. l

58.8 6 2. 7 127. 6 99, 2 85.9

82. 3 58. 2

121. 6 63.6 61. 6

.014

Housing

. 638

85. 3 86.6

•o

116. 5 118. 2

• 231

•o

• 215

246. 3 249. 9

292. o 296.3 102. 3 103. 8

167. l 118. l

246. 7 129. l 125. o

• 028

119. 4 127. 3 259.1 201. 3 17 4. 4

56. 5 60. 2 122.6 95. 2 82.5

41. 3 44. l 89. 7 69. 7 60.4

198. 2 140. l

292.6 153. l 148. 2

.034

Auto Purchas,

141. 6 151. o 307.2 238.7 206.8

69. 4 49. l

79. o 55. 9

57. 9 40. 9

Au to

E:xpense

49.6 52. 9 107. 6 8 3. 6 7 2. 4

lO 2. 5 53.6 51.9

• 011

Furnishings and Equipment

116. 7 61. l 59. l

• 013

Medical Care

85.5 44. 7 43. 3

• 009

Clothing

F.rrors of Regression Relatior:.ships bet'wVeen Iten1s of Consuntption and Family Characterisiics, For Homeowners with $10,000-$14~ 999 Homes and Cash Not Reported White Employee Families with !neo mes from $1, 000 to $10, 000, Urban 1950

Total Durable Goods Consu mption Purchases

Stand::~rrl

Appendix Table l Oa

-J CJ1

+3301. 046

+27 3. 7 +198. 8 +378. 644

+392. 5 +354,5 + 39, 258

+2557. 444

- 98. 9 -319,6 -199. 7 +298. 4 +116. g

-1733.7 -1413. o

3 l 9 8

- 68. 4 + 58,4 +236. 3 -146, 7 +445. 8

+315. -30 3. +38 2. -447. + 84.

o

• 0617

-151. 8 -100,5

+

- 914. +169. 2

• 1916

-967.4 -156.0

+

Housing

-6 29. 5 -216, 7 -200,5

. 0169

Income after taxes (b) + . 7168 Su;e of family (el) 1.0 -3909.9 1.1-2. 9 -1339.1 3.0-3.9 - 47b. l Age of head (di) Under 35 -1617.7 35-5 4 +313, 9 In come changPincome expectation (ei) Cont:;tant +443,8 Continuous risc ·698, 2 Continuous decline +369. l Temporar:y rise -841. 8 Tempe>rary decline +1327.3 Debt status (fi) -1010,8 Ilas debt :'\o deht -1275,8

Food

-775.5 -395. 2 -127. 3

Purehas e

-156. 3 -161. 8 +184, 7

Durable 'Guods

Total

Consumphon

Cnnstant tprm (a)

Ap p e n d ix Table Il

• 0105

• 1117

-322.026

+ G6. 2 - 33, 7

+258. l +173. l +231. 594

- 19. 2 -153.2 - 71.4 -265, 9 +347. 6

33,6 + 64, 3

- 41. 5 - 84.3 + 22.2

+

Medical Care

+181.0 +239. 6 + 43.9 + 9, 7 - 29, 8

8, 4 +116. 2

-313,6 - 56. 9 - 24.6

+

Clothing

Au to

+1957.959

-1785.3 -1647. 4

+ 15.5 -230. 2 +758. 4 -171.9 -406, l

+217. 211

83. 4 + 52. 7

+416. 5 + 49. 4 -218.3 -263,8 +460, 5

-6 22, l -121, 2

-476. o + 80,4

• OG Il -704,4 +124. 9 +262, 7

+

Expense

-5 26. 8 - 38. 8 +226. l

.0322

Furnishings and Equipment

Regression Relationships between Items of Consumptian and Family Characteristics. For Homeowners with $15.000 and Over Homes and Cash Not Reported White Employee Families with lncomes from $1,000 to $10,000, Urban 1950

Au to

. 0430

- 70,389

+160. 7 +278. 2

+353. 5 - 14, 9 -249.7 -283. 6 +456, o

-494. 2 -2 21. o

-764. 0 + 76, 8 + 90.6

+

Purchase

O)

-::J

• 0178 • 0992

+424. 189

+270. 436

- 42. l - 75. 2

+ 88.5 +142. 9

81. o 78.7

-104. 243

+ 33.4 + 26.4 - 32. l 9. 8 +343. 2

- 10. 4 + 15. o 8o.8 6.3 - 63. 8

.4

29. 6 1.6 + 32. o - 37. o

+

.0427

• 0668

-1476.8 -1610.2 +1361. 803

-19.143

+142. 9 +181.7 +338. 5 +130. 5 +127. 3

+40 2. l +283.8

+164. l +357. 2 +595. l

+

Au to Expense

+ 26.0 + 78. o

- 53. 9 +132. 2 +148. 4 - 70.4 - 35.6

+17 3. 2 + 58.3

+

- 81. l - 43. o

• 0139

-182. 5 54.4 - 46.4

+

Furnishings and Equipment

-138. o - 15. 6 + 29.6

+ 73. 3 + 85. 2

- 47. o - 81. 9 + 31.4

+

Clothing

70.4 - 32. 2

+ 24.8 + 75. 2 + 38.4

+

Housing

Medical Care

Regression Relationships between Items of Consumptian and Family Characteristics, For Renters with Lessthan $750 Rent and $1500 and Over Cash White Employee Families with !ncomes from $1,000 to $10,000, Urban 1950

Appendix Table 16

• 0356

+lO 11. 942

-1101. o -1224.4

+ 93. 3 +17 4. 8 +324. l + 84.3 +130. 8

+322. 6 +214. 4

+164. 2 +250.7 +486. 4

+

A ut:) Purchase

C»

00

*Extremely l arge

• 049

.036

138.7 129. 4

138. 6 135, 7 305.4 202.9 208. 9

* * . 359

191. 9 187. 9 422.9 281. o 289.3

*

*

. 665

206.9 181. 3 200.4

192. l 17 9. 2

286. 5 251. l 277.5

standard errors.

Continuous rise Continuous decline Temporary rise Temporary decline Debt status (f;) Has debt No debt Multiple coefficient of conelation (r)

eonstant

lncome after taxes (b) Size of family (ci) 1.0 1.1-2.9 3.0-3.9 Age of head (di) Under 35 35-54 lncorne changeincome expectation (ei)

Total Durable Goods Purchases Consumptian ,019

• 202

.o

.533

*

*

*

*

*

*

40.9 40.0 90. l 59. 8 61. 6

40.9 38. l

61. o 53.5 59.1

• 010

Clothing

26.5 26.0 58.5 ;·.a. 9 40.0

26.6 24.8

39,6 34.7 38.4

.006

Housing

73. 9 72.4 16 2. 9 108. 2 111. 4

74.0 69.0

110.3 96.7 106.9

Food

• 369

.393

. 267

* *

.

*.

*

136.7 133. 8 301. l 200. l 206. o

51. l 50.1 112.7 74. 9 77. l 40.5 39.6 89.3 59.3 61.0

204. o 111. 8 197.6

• 035

Au to Expense

136.8 127.6

76.4 66.9 74.0

• 013

Furnishings and Equipment

51.2 47,7

40.5 37.8

60.5 53. o 58.6

. 010

Medical Care

Standard Errors of Regression Relationships between Items of Consumptian and Family Characteristics, For Renters with Less than $750 Rent and $1500 and Over Cash White Employee Families with lncomes from $1,000 to $10,000, Urban 1950

Appendix Table 16a

Au to

• 197

* *

124.4 121. 8 274.1 182. l 187. 5

124.5 116. l

185. 7 162. 7 179.8

.032

Purehas e

..;J

CXl

lncome after taxes (b) • 1619

• 0730

+487. 582

+499, 539

-263.830

eonstant term (a)

+1254. 953

+ 30.3 + 99.8

+344. 2 +452. 7

l

o

6 4 5

+288. 3 +337. 7

-145. -132. -183, -154. + 76.

97. 8 - 96.5

+117. 6 + 40.7 +150. 5

+

+ 21. 7 - 92,4 -352, 3 -485. 9 +214. 5

-110, l - 14. l

-844. l -381. 9 - 49. l

+

H ou sing

-214.8 -247.8 -758. 4 -903. o -349. o

+616. l + 49. 9

• 1114

+ 31. o -188.0

+ - 49. 3 +134. o +376. 7

• 7325

-1479.1 -502.8 +577. o

+

Food

In come changeincome expectation (ei) -327.8 Constan t -664. o Continuous rise -254. l Continuous decline Temporary rise -2472.8 + 82, 9 Temporary decline Deb\ status (fi) +610. 9 Has debt +1128.7 No debt

l. O 1.1-2.9 3. 0-3. 9 Age of head (di) Under 35 35-54

Size of family (ci)

Total Dur..1ble Goods Purchase Consumphon

. 1286

,0184

- 66.6 -136. 6 +308, 830

: 92,654

+143. 2 + 40.7 +135. 9 -170.6 +l 06. 7

-132. 8 - 54. 2

-204,6 + 37.8 + 81, 2

+

+124.8 +162. 4

- 55. 2 - 89. 6 + 30.3 -141. 5 - 46.2

+ 31.7 + 22.3

-188. 2 -100,5 + 7.6

+

Clothing

Medical Care

Au to

• 0447

-124.881

-291.433

+332. 9 +458. o

+469,9 +498. 3 + 76.6 - 80.9 + 59,494

- 65.5 -101. 2 -339.0 -478. 2 -245.8

- 86.7 - 89.4 -443,5 -432. 5 -228.7

+294.8 - 95. 7

+ 91.4 - 10,3 +122. 3

+

Purehas e

-130, 5 - 68. 2 -28 2. 6 -338. 5 - 46, 2

+248. 2 - 83, o

• 0625

+279. o + 70. l

+

27.9 - 52,9 + 15.5

• 0437

Au to Expense

- 79. l +131. 3 + 36. l

+

Furnishings and Equipment

Regression Relationships between Items of Consumptian and Family Characteristics. For Renters with $750-$1249 Rent and $1500 and Over Cash White Employee Families with lncomes from $1,000 to $10, 000, Urban 1950

Appendix Table 17

00 00

* Extremely

• 025

• 013

• • 453

• 64g

. 40 l

. 612

*

•

•

•*

,,

60. 5 56. o 144, 5 145.1 94.8

110.6 102. 5 264.3 265. 4 17 3. 4

192. g 178. 7 460. 9 46 2. 9 302,4

433.3 40 l. 5 1035.4 1039.9 679,3

*

. 438

*

•

101,9 g4,4 243.6 244.6 159. 8

116. 9 107.3

6g,3 63. 6

126, 8 116, 4

64.6 68,4

.023

Clothing

156. 4 108,9 115. 3

221. l 203. o

n.8

496.8 456. l

169, 7 118. 2 125.7

Ho u sing

296, o 206, l 218. 2

.044

Food

665,0 463, o 490. l

,ogg

la r ge standard errors.

No debt Multiple coefficient of earrelation (r)

Has debt

Continuous rise Continuous decline Temp:>rary rise Ternporary decline Dcbt status (f;)

Co~stant

Size of family (ci) l. O l. l- 2. 9 3. 0-3. g Age of head (d;) Under 3535-54 Income changeincome expectation (ei)

!neo me after tax e s (b)

Total Durable Goods Consumptian Purchases

,182

•*

• 278

•*

106.4 98.6 254, 2 255,3 166, 8

122. o 112. o

85. o 78.0

74. l 68,7 1·77. 2 178. o 116.3

163, 3 113. 7 120. 3

• 024

Furnishings and Equipment

113.8 7g, 2 83, g

.016

Medical Care

Standard Errors of Regression Relationships between Item s of Consumphon and Family Characteristics. For Renters with $750-$124g Rent and $1500 and Over Cash White Ernployee Fami!ies with Incomes from $1,000 to $10,000, Urban 1g50

Appendix Table 17a

Au to

•o

*

195. l 180.8 466, 2 468. 2 305.8

223.7 205,3

299,4 208.4 220.6

.044

Expense

.o

*

170.9 158.4 408.4 41 o. 2 267. 9

195. 9 179. 9

262. 3 182.6 lg3, 3

. 039

Au to Purchase

co

00

Income arter taxes (b)

o

eonstant term (a)

No debt

Has debt

Temporary decline Debt status (fi)

Continuous rise Continuous decline Temporary rise

eonstant

1.1-2.9 3.0-3.9 Age of head (d;) Under 35 35-54 In come changeincome expectation (ei)

l.

Size of family (c;)

. 1280

-144.813

+1078. 875

+272. 080

- 28,8 - 38,7

- 93,9 - 87 o o

- 19. 5 + 92.1

-490.6 -361,0

+2006,896

+ 26.3 + 51.6 + 63,7 +50, 7

+480. 215

-309.7 -374.3

25.3 55.2 60. 2 76.9 58. B

+ -

+ 51.6

26,7 - 43.7 +106, l - 95, l + 25,0

-179.1 -115. 4 -265. B +159. 9 -348,9

-199. 2 -109,7 - 37. o 45. l -342. 4

-155. 2 -126,4 - 44.8

+102. 067

- 74.8 - 33.3

+ 5. l

- 52.1

+ 25.4 8, 9

+ 25.4

- 17 o 2

+ 9, 7

- 61. 7 + 20,2 + 24.8

• 0282

+

• 0894

+

+ 81.9 +152. 6

. 0352

5, 2 + 23.3

+

- 48, 7 + 21. o

1319

Clothing

+321. 6 +248. o

o

Housing

4. 9 + 47. l + 6, o

+

Food

Medical Care

-637 o 3 -427 o 7 -261. l

+369, 7 +558,8

+ -189,8 - 69,7 + 87 o 5

58 37

-1284,4 -581,3 -135. 3

o

Durable Goods Total Consumptian Purchase

+

Appendix Table 18

,0263

. 1528

-205,012

-118. 9 - 23, l

+ 76. o +53. 2 + 30.132

-214.4 -132, 2 -245,6 + 28. l -194. 7

+231. 6 +166, 2

- 14, o + 29.4 +167 o 2

+

Au to ExpE'nse

+ 8.4 + lO. 2 - 49.8 +129. 4 - 57.5

+ 72,7 + 62.6

-116.0 - 34. 3 19.4

+

Furnishings and Equipment

Regression Relationships between Items of Consumptian and Family Characteristics, For Renters with Less !han $750 Rent and Cash Not Reported White Employee Families with lncomes from $1,000 to $10,000, Urban 1950

o

1015

-174,868

-133,5 - 34, l

-175.3 -113. 5 -209. 4 + 2. 7 -241. l

+186, 6 +154. 7

+ 29.6 + 7. 9 +125. 4

+

Au to Purehas e

co o

rise decline rise decline

Debt status (f;) Has debt No debt Multiple coefficient of earrelation (r)

Continuous Contir1uous Temporary Temp:Jrary

eonstant

Size of family (ci) 1.0 l. l- 2. 9 3. 0-3.9 Age of head (di) Under 35 35-54 lncome changeincome expectation (ei)

Income after taxes (b)

. 798

955.8 940. l • 454

623. o 612. 8

88.4 91.4 237. 7 172.3 129. 7

135. 6 140. 2 364.6 264. 3 lgg_o

• 757

304. l 2g9. l

43. l 44.6 116. o 84. l 63. 3

50.5 45. l

103. 6 92.5

158. 9 141. 9

.012 59.4 47.8 49.8

Food

121. 7 g7. g 102. o

• 025

Durable Goods Purchases

186. 8 150.3 156. 6

• 038

Consumptio n

Total

. 261

200. o 196. 8

28.4 29.3 76.3 55. 3 41. 6

33. 2 29.7

39. l 31.4 32.7

• 008

Housing

. 623

253. 7 249.6

36. o 37. 2 96.8 70. 2 52. 8

42. 2 37.6

49.6 39.9 41.5

. 010

Clothing

• 276

185. l 182. o

26. 2 27. l 70.6 51. 2 38.5

30.7 27.4

36. l 29. l 30.3

• 007

Medical Care

. 313

240.9 236. 9

34. 2 35. 3 91. 9 66.6 50. l

40.0 35.7

47.0 37.8 3g.4

. 009

Furnishings and Equipment

Standard Errors of Regression Relationships between ltems of Consumptian and Family Characteristics .. For Renters with Less than $750 Rent and Cash Not Reported White Employee Families with lncomes from $1,000 to $10,000, Urban 1950

Appendix Table 18a

. 40 l

656.6 645.8

93. 2 g6. 3 250.4 181. 6 136. 7

log. 2 g7.5

128. 3 103. 2 107.5

. 026

Au to Expense

Au to

. 297

603. 6 59 3. 7

85. 7 88.5 230.3 166. g 125.7

100. 4 89.6

117. g g4. g 98. g

• 024

Purchase

......

co

eonstant term (a)

+1135. 753

Income arter taxes (b) . 7610 + Size of family (c 1) -10B9. 3 1.0 1.1-2. 9 -671,6 3.0-3.9 -286.1 Age of head (di) Under 35 - 1B.1 35-54 +397. 7 Income changeincome expectation (ei) eonstant 4. 8 +57. 8 Continuous rise +417. 3 Continuous decline +559. 7 Temporary rise Temporary decline +1002, 6 Debt status (fi) Has debt +5 23. 4 +224,8 No debt - 25. 2 - 73.4 + 34,7 - 19.0 +103, 5 -174.8 - 10. 9 +52B. 679

+ 2. 4 - 12. 9 +133, B +113. B + 42.5 +726. 7 +761. 7 +104. B7 2

+266. g +150. 8 + 75, 6 +1004, 9 +554. 6

-931. o -907.5

+63B. B36

- 1B.5 - 62.5

• 0647

+149. o + 49.4 + 97. B

+

-24B. B - 35. B

.1590

+500. o +491, 7

+

Housing

-566. o -409.B -.231. 3

• 1007

Food

-454. 2 - 64.6 - 18. 9

+

Durable Goods Total Purchase Consumptian .1489

,0549

-123. 7 - 23.5 + 46.056

+154. 092

+ 4. 8 + 74,B +149. 4 - 56,2 - 22. l

+ 18.8 +124. 5 +204. 4 +359. 6 +393. 6 -297. 7 -380.6

- 94,0 -125. l

+ 43.5 + 39,6 + 92.7

+

+ 41.7 +173. 6

- 44.8 -159.3 -100.4

+

Clothing

Medical Care

.0548

+2B7. 237

-523. 6 -419,5

+156.9 +131. o +224. 9 +561. 9 +415, 7

+23B.6

+214, 1

-140.9

- B9.6

-259. 9

+

Furnishings and Equipment

Regression Relationships between ltems of Consumptian and Family Characteristics, For Renters with $750-$1250 Rent and Cash Not Reported White Employee Families with Incomes from $1,000 to $10,000, Urban 1950

Appendix Table 19

.0904

• 0390

+258. 384

+217. 040

-269. 5 -423. 9

+ 49.0 - 86. 9 -206. l +305. 3 + 67.3

+17B. o - 45.5 -22B. 9 +294. B +252. l -462, 9 -6 23. 7

+235. l +233. 5

-129.5 + 51. 6 + 99. l

+

Au to Purehas e

+290. 4 +350. l

-158.1 + 61.5 +185.4

+

Au to Expense

t-:l

cc

176.2 1g2. o 346.6 451. 7 242.0

• • . 327

299. l 325.8 588.0 766. 3 310. 6

•

.747

*

214.9 188.4

2g6. g 190.5 198.2

.041

Purchases

Durable Goods

364.6 319. 7

503. 7 323.3 336.4

. 070

*Extremely large standard errors.

Continuous rise Continuous decline Temporary rise Temporary decline Debt status (fi) Has debt No debt Multiple coefficient of correlation (r)

eonstant

3. 0-3. g Age of head (di) Under 35 35-54 In come changeincome expectation (ei)

l. O l. 1-2. g

lncome after taxes (b) Size of family (ci)

Total Consumptian

.626

*

*

96.2 104.8 189. 2 246.6 132. l

117. 3 102.9

162. l 104.0 108.2

. 022

Food

*

• . 584

.423

88. l 96.0 173.3 225.8 120.9

107.4 94.2

148. 4 95.2 gg_ l

. 026

Clothing

•*

59. 7 65.8 117. 3 153.0 81. 9

72. 7 6:L 8

100.5 64.5 67. l

. 014

H ou sing

. 366

*

*

56.6 61. 7 111. 4 145. l 77.8

69.0 60.5

g5.4 61. 2 63.7

.013

Medical Care

Au to

* . 277

* . 237

*

154,4 168.3 303.7 395.8 212. l

113. o 123. 2 222.3 28g.7 155.2

*

188.3 165. l

260.2 167.0 173. 7

. 036

Expense

137.8 120.8

190.4 122. 2 127.2

. 026

Furni.shings and Equipment

Standard Errors of Regression Relationships between Items of Consumptian and Family Characteristics, For Renters with $750-$1250 Rent and Cash Not Reported White Employee Families with Incomes from $1,000 to $10.000, Urban 1950

Appendix Table 19a

Au to

.o

*

125.8 l:J7.1 247.5 322.6 172.8

153.4 134.5

212. o 136.0 141. 5

.02g

Purchase

THE SPECIFICA TION OF EMPIRICAL CONSUMPTION STRUCTURES* Andre L. Daniere and Elizabeth W. Gilboy Harvard University

I.

Cross Section Data and Consumptian Functions in Input-Output Analysis

A.

Background

A number of experiments have been undertaken at the Harvard Economic Research Project in connection with closing the inputoutput system for households. They have been cancerned so far with the static input-output model, although the eventual aim of our consumptian research is a dynamic system integrated with other dynamic elements in the economy, such as technological c hang e, within the input-output framework. Simple, homogeneous consumptian (or household) coefficients, directly comparable to the technical coefficients for the industrial sectors, were derived and used in early applications of interregional input-output models. 1 Coefficients based on linear (but not *The mode! and preliminary empirical results presented in this paper form part of the continuing research on the household sector of the United States economy conducted by the Harvard Economic Research Project. The authors wish to acknowledge the assistance of Mrs. Marjory Richardson and Mrs. Virginia Nail in the preliminary statistical work. Thanks are also due to the Littauer Statistical Laboratory for the use of its computational facilities. Our special thanks go to Mrs. Patricia Anderson for her care and diligence in the process of sorting and tabulating the data, an essenhal preliminary to the specification of the regression structure. Professor Kurabayashi of Hitotsubashi University has also contributed to the development of intended tests of our crossseetian regressions. This paper owes much to many informal discussions with Professor Guy Orcutt over the past two years--afact which in no way engages the latter's responsibility for malformations discovered in our product. 1 Moses, L. N., "The Stability of Interregional Trading Patterns and Input-Output Analysis," American Economic Review, December, 1955. (For example.)

93

homogeneous) functions of expenditure and income, were computed from time series for a 20-industry input-output matrix for initial experiments with the Leontief dynamic model. 2 Similar coefficients were derived from cross-seetian data (the 1935-36 Consumer Purchases' Study) for some 50 seetars of the 1947 BLS 192-industry classification system. In this case, non-linearity was handled by dividing the income distribution of households into two income ranges, below and above $4,000, and computing coefficients for each income range. 3 The first two set s of coefficients we re admittedly stop-gap approximations; from the third set, based on the 1935-36 data, something better was expected. Howeve r, the inadequacy of the results was such, even in very short-range predietians of individual and aggregate consumptian expenditures, that an entirely new approach was instituted. B.

The current approach

This approach invalves the initial use of all obtainable information on variables affecting household behavior, whether these variables are endogenous or exogenous to the input-output system. 4 Consumptian functions for individual items are to be built in two steps. The first invol ves derivation of cross sectional functions in the two major post war survey years, 1950 (BLS survey) and 1956 ("Life" survey). The seeond will consist of attempts at relating time shifts in cross seetian coefficients to time itself, to the market history of individual itemsand to changes in relative socio-economic position of families identified by absolute magnitudes of included characteristics. Alternative measures of aggregate consumptian (NID series) and other survey material (Michigan Survey Research Center) will be adduced at this stage to correct estimates and extend the time series coverage with respect to purchases of durables and other net asset changes. The authors hold to the belief that the dichotomy between "cross-seetian" and "time series" coefficients has been exaggerated as a result of careless t reatment of either set of data. They expect that fair predietians can be achieved without recourse to the "seeond step" outlined above, even though substantial improvement should result, particularly in long-runprojections, from a time comparison of cross-seetian structures. In short, they find that a)purchases of 2 see Gilboy, E. W., "Elasticity, Consumption, and Eecnornie Growth," American Eecnornie Review, May, 1956. 3 see Berman, B., Report on Research for 1955, Harvard Economic Research Project, (Hectographed), pp. 59-93. 4 classification of consumer expenditures inta input-output categories is disregarded at the outset andwillnot be attempted until the final stages of the procedure.

94

specHic item s are significantly influenced by som e twenty variables available in the 1950 BLS survey, and b) the effects are generally non-linear and subject to strong and widespread interactions. Because of (a), it is cleart that a time series regression on income alone will ab sorb the effect of changes in the distribution of f amilies along other variables to the extent that such c hanges are correlated with income. 5 Because of (b}, it is also clear that the coefficients of a wrongly specified cross-seetian regression (i.e., one additive and linear over the full range of all variables) will be of little meaning. Computing such a regression on some or all available variables and applying the resulting coefficients to the relevant means in the year of prediehon is bound to generate poor resultsand, if the prediction is repeated over a period of years, to overemphasize the "difference" in income elasticities. Our first goal is, therefore, to obtain a satisfactory specification of the structure of consumptian functions in a cross seetian of U. S. families and to estimate their parameters. The structure incorporates a large number of variables (including stocks and changes in income from the previous year) and displays only partial linearity and additivity in a form which the remainder of the paper will describe more fully. Application of the resulting coefficients to U. S. family distributions in successive years will show to what extent the low predictive performance of cross-seetian regressions in past experiments has been due to inappropriate specification of the st rueture s. Our final tabulatian of the consumptian function for any individual item will involve the division of households inta a number of sub-seetars identified by vectors of contiguous values of a few family characteristics (including income) and ehosen in such away as to eliminate significant interactions of explanatory variables within sub-sectors. In each cell, consumptian of the item is expressedas a linear function of "dummy" variables, each of which takes one or more specified values for families whose characteristics fall in a specified range, and value zero otherwise. Ignoring at this stage dynamic changes in the matrix of coefficients, predietian of total household consumptian will then require generation of the following information: a) joint distribution of households over sub-sectors; b) within each sector, marginal distribution of households over each characteristic, in the form of a mean value of the characteristic and a total of included households for each specified range. 5see also Jean Crockett, "Population Change and the Demand for Food, 11 preliminary paper de livered at the National Bureau of Economic Research Conference on the Interrelations of Demographic and Economic Change, Princeton, New Jersey, December 5-7, 1958.

95

The input-output system, however, can, in its present form, generate only a distribution of income earners by income level and occupation {by industry), with multiple counting for wage earners engaged in several occupations. Exogenous information on the distribution of households over other relevant characteristics will, therefore, need to be introduced or, alternatively, the model will have to be expanded so as to generate this information. Early applications of the proeecture will necessitate an exogenous determination of the distribution of families over characteristics other than income and occupation, with an integration of this information with t hat on the in come -occupation distribution generated by the system. II.

Alternative Linear Regression Structures

In selecting a multivariate model whose parameters are to be estimated from a particular sample, the tendency has been until recently to limit one's choice to regressions additive and linear over the full range of available variables. More precisely, usual structures assume that a) the effect of each explanatory variable is margirrally additive to that of all others and b) the additive effect is linearly related to the magnitude of the variable. The superiority of this model in terms of saving of degrees of freedom andease of aggregation is well realized. In addition, its formal properties have been developed in such detail that, unless an alternative obviously suggests itself, it is employed almost as a matter of cour se. Mu ch of what this paper has to say deal s with methods of specifying alternative structures which, on some generally accepted-hut often implicit-criteria, are deemed to be preferable. In order to take the maximum advantage of e stablished formal analys is and methodology, ou r choice is limit ed to structures which retain the formal properties of additivity-linearity in the variables the y include; the latter, how ev er, may be "dum mi e s" which are non-zero for specified combinations of values of the original variables and take value zero otherwise. As this proeecture is not familiar to all prospective readers, it was considered advisable, before discussing the problem of choice between models, to describe and evaluate the type of regression structures we are cancerned with.

A.

Special Notation

The following notation has been adopted after much consideration. Even though the reader may judge it unnecessarily involved for a gen':!ral discussion of additivity and linearity, it will be found

96

indispensable for the specification of the type of structure we finall y offer. 6 Given n family characteristics i =l, 2, ... , n described by n variables x 1 , x 2 , ••• , xn, wedefine twoadditional setsof variables: l) The variable x r 1 s h r 2 s 2. • • • • r n Sn measured for any family' takes value l if, for that family

where r i and s i are coded values of characteristic i; takes value O otherwise. 2) The variable xrt st, r2S2 • . . . • rk Sk •.••• r n Sn has the same definition as above, except that it takes the value xk of charaderistic k, rather than l, when the n characteristics fall within the specified intervals. 7 In addition, a) if, for any characteristic i, the interval reduces to one value u i• that value is inserted in i th position in place of r i s i. b) if, for any characteristic i, the interval covers the whole range of the characteristic, the symbol * is inserted in ith position in place of r i si. B.

Maximum stratification

Under ideal conditions-an opportunity to draw large size samples in as many cells as we see fit to create-estimation problems would l ar gel y disappear. With no cancern for degrees of freedom, and assuming that we have information on the values x v x 2 , ••• , x n taken by characteristic l, 2, ... , n of sampied f amilies, we would divide the population into as many cells as can be identified by different vectors of values of the n characteristics and estimate the family expenditure (our dependent variable y) 6 An alternative to the notation adopted in this paper can be found in the use of multiplicative dummy variables. Although this would avoid the use of uniamiliar symbols, the alternative was discarded as too cumbersome. 7we eventually introduce a third variable:

x rlsl,

r2s2, .. ,_, (rksk),

•.• , rnsn

which is a specified linear function of xk when the characteristics fall within the specified intervals.

97

within each cell. If m h m 2 , ••• , mn are the numbers of possible values (or arbitrarily ehosen small intervals) of characteristics l, 2, ... , n, the number of cells would come to n

N

=l\ i = l

mi

Note that the expenditure of a family can still be expressed in additive-linear regression form through use of the first set of variables defined above. The means of the N cells formed by all earobinations of values of the n characteristics are then estimated as coefficients of the following regression: (l)

y =

b u1,

u 2 , ••• , u n

X u1 ,

u2 ,

••• ,

Un

'

(i = l, ... , n)

where a) each characteristic has been coded from O to m i - l and b) each Xu 1 , u2 ••••• un is associated with a multiplicative coefficient bu 1 , u 2 , •.• , un identified by the same subscript. Even if sampling conditions we re such that we could obtain fair estimates in this fashion, the set of b coefficients would, however, remain of limited usefulness. More often than not-and this is the casewithin our input-output structure-we are interestedin predieting aggregate expenditures of families rather than the expenditure of one particular household or of a group with well-known characteristics. A computation of aggregate expenditure on the basis of this model requires a knowledge of the joint distribution of families over all val u e s of every characteristic. For a set of characteristics such as that contained in the 1950 BLS survey, this information is not made available on a yearly basis and the projection of family distribution over thousands of cells is both an awkward and a doubtful proposition. C.

Overall additivity

If on the other hand, the effect of a characteristic i = k is additive over the whole space, i.e., if for any two values u~ and u~' of characteristic k

bu1,

l

••• , u k , ••• , Un

where b k< u'k u~) is a eonstant independent of the vector of remaining characteristics (u 11 . . . , uk_ 1 , uk+l• ... , un), the regression can be significantly simplified.

98

Relating all uk's to the O code of variable k, we have:

Substituting in (l) and factoring out, we get: y=

L

u=O, ... ,mi-1

hut, ... , uk-1'

(2}

ffik-l +

L

bk('JP)

Uk=l

O,

. . . , un

x .. •... '

uk' • • •'

xu l,

. . . , uk- 1 ,

*, uk + l, ... , u 0

*

(i = l, ... , k-1, k+l, ... , n)

The number of parameters has now been reduced from n

N

=TI i=l

m

to N/~, plusanindependentdivision into mk-1 groups. Foraggregationpurposes, it is enough to have the joint distribution of families over all values of non-k characteristics and the marginal distribution of families over values of the k characteristic. Were the effect of all characteristics completely additive, the regression would reduce to (3} y=b

0,0, ...

'o

The division is now into n

L

i= l

m

- (m-1}

independent groups. Aggregation requires only a knowledge of the marginal distribution offamilies over values of each characteristic; i. e., if a .. describes the number offamilies with value U i of characteristfc the aggregate expenditure is given by

l

99

n

E=

L i=1 n

mi bo, o, .... o

mi -1

+L L i=1 u. =1

n.l u i

bi(u.o) 1

x.* '

' • • ·- '

u. l

' ••• '

*

1

D.

Partial additivity

Regressions (1) and (3) represent extreme situations with respect toadditivity. The additivityassumption will not, in general, be valid over the whole space of family characteristics. However, given any vector of values of any characteristic, additivity may hold forthat vector in association with specific sets of n-1 vectors selected from the remaining characteristics. Thus, even though we cannot expect to realize all the gains in estimatlon and aggregation that would result from perfeet additivity, much can be done to reduce the number of variables and to "marginalize" the necessary knowledge of family distribution. As an example, consicter a variable E (expenditure of family) and three explanatory variables x 1 , x 2 , x 3 desertbing family characteristics 1, 2, and 3: x 1 takes four values, coded O, 1, 2, 3 x 2 takes five values, coded O, 1, 2, 3, 4 x 3 takes three values, coded O, 1, 2. A regression of type (1) would contain 4 x 5 x 3 = 60 terms, and no purpose would be served by writing it in full. Suppose, however, that we have the following information: a) the effects of x 2 and x3 are additive to one another within each of the following two regions of the ~ x 3 subspace:

[x3 = O, 1, 2

x 2 = O, 1, 2)

= Region I

[x3 = O, 1, 2

x 2 = 3, 4

= Region II

b) the effect of x 1 is additive to that of all ~x 3 combinations over its whole range. The regression would then reduce to the following expresston which involves only 12 parameters. In order to alleviate the notattonal bur den, the b coefficients are simply numbered in their order of appearance. 100

(4)

E=~

xl, *. *

+~

+ b4 x. ,02,* + bs

x2, *, * + b3

x3, *. *

x

x

*. 02. l

x.

+~

l'*

f

+b

6

+ b8

+bgX•,34,* + blO x • . 34. l +bll + bl2 x.

f

*, 02. 2

x. 2 *

x.. 34. 2

4 J*

Nate that (4) represents a definite saving over what would obtain by simply dividing the space of n variables into subspaces within which overall additivity holds for all variables, and writing separate regressions of type (3) in each subspace. In the present example, a division of the total space inta a minimum of two blocks, as shown in the diagram below, is necessary to obtain subspaces having the property of overall additivity of each effect. They are: DIAGRAM l

x 1 =O, l, 2, 3

x 1 =O, l, 2, 3

II x 2 = 3, 4

I x 2 =O, l, 2

x 3 = O, l, 2

x 3 =O, l, 2

2

o

o

l.

'!o

101

4

Writing a regression in each block, the one in block I would include lines l, 2 and 3 of (4)8 and the one in block II, lines l, 4 and 5 of (4),8 with the result that three more parameters would have to be estimated than in (4) itself. The latter takes advantage of the additivity of the effect of characteristic 3 over all combinations of x 1 and x 2 , whether these belong to one or the other subspace. Note finally that if the effect of all three characteristics had been additive without restrictions, the regression would have taken form (3), which in the new b notation reads:

+ bg X.,* • l + bl O X* • * • 2

,

This, with 10 parameters, represents a saving of only two parameters over structure (4). E.

Overalllinearity of effect

A further gain can be aehieved under conditions of linearity of the additive effect of a variable. Note first that the seeond sum in regression (2) can be expressed in terms of variables belonging to the seeond of the two sets defined earlier. We then have: y

(2')

==

bu l,

L

u 1=0, ... , m 1 -1 ... ,

mk-1 +

'\'

~

uk- 1 ,

O, uk + 1 , ••• ,

bku k X* , * , •••

,

-uk•

un

.•• ,

x u 1 , ••• ,

uk _ 1 ,

*,

uk

+ 1 , ••• , u 0

*

~=l

(i

==

l, ... , k-1, k+1, ... , n)

Where bkuls = bk(ukO)/u~ · If in ~2') all bku s (~ = l to mk - l) are equal and we eall their unique value bk ~ we have Ssubstituting the relevant interval of variable 2 in the subscripta of line l.

102

-uk,

~-l

..• ,

* = bk L'\' uk

=l

x. , * , ... , -uk, •.. , * *.

(Note that

x.,*,

*

takes the value of characteristic k whatever the associated values of other characteristics and is thus the equivalent of the original variable xk.) Regression (2') then reduces to y=

(5)

L

ui=O, .•• ,mi-1 b

u 1 ' • • • 'u k- l' O' u k+ P

+ bk

*· ....

x ........ k

th

xu 1 , .•• , u k -1 ' * , uk + 1 , ••• , u n

un

*

(i = 1, ... , k-1, k+l, ... , n) If all effects are additive and linear overall, regression (3) reduces to:

(6)

n y=b o, o, .... o + b. i=l 1

L

x. •

' , .••

•

,th""''

•

This, in rather awkward fashion, represents the familiar regression form. We now have only n variables and n+ l parameters to estimate, and aggregation requires no more than a knowledge of the mean value of each characteristic over the whole population.

103

F.

Partial linearity

Again, and in spi te of the operational attractiveness of form (6), we cannot expect the linearity assumption to be valid beyond certain additive variables, or, even more likely, vectors of the se variables in association with specific vectors of other variables. l. Linearity over the full range of additive variable.

Going back to the previous example, assume that we have linearity of the effect of x 1 from codes O to 3 and linearity of the effect of x3 from codes O to 2 within each of the two x 2 ranges (x 2 =O, l, 2 and x 2 = 3, 4), where this effect is Separately additive. The regression will then reduce to eight parameters: (7)

E=

+b4x*.l,*

in which the b coefficients are again numbered in their order of appearance. 2. Linearity over successive intervals of additive variable. This, however, invalves linearity over the full range of e i the r x 1 or x 3 • A more usual (and less attractive) situation is one of linearity over successive segments of a variable. Diagram 2 below depicts the effect (~e) of such a variable x within a region in which i t is additive: DIAGRAM 2

104

a)

Callr, s, t, v, the values of x correspondingto thefour extremities of our linear segments.

b)

Call X (r"v) a variable taking value (x-r) for families with rsx:::: s, value (s- r) for families with s< xsv, value z e ro otherwise. X< sv) a variable taking value (x-s) for families with s::::x::::r, value (t-s) for families with t)

1941

---

50

Dodge

50

DeSoto

so

Chevrolet

Chrysler

--

50

Cros1ey

50

Buick

1940

CadilJac

-------

Make

------

-;ode1 y;:r

TABLE Ul. ""

the (freehand) regression line was considerable. The decimal in the percentages in Table I is not statistically significant. The estimates for 1952 were based on the model years 1940-1942 and 1946-1952; those for 1955 on the years 1946-1955. Table I shows a marked rise in the depreciation rate between the two years of observation, but the ranking of the various makes did not change substantially. In both years the more expensive and the less popular makes tended to have the higher depreciation rates, Cadillac being the well-known exception. This implies (with the same exception) that all ear s aged 8 or 10 years are worth much the same irrespective of make. Mter that age the originally more expensive cars may be worth less, mainly because replacement parts cost mor e and gasoline consumptian is higher. 1t will be noted that Table n contains some values for 1953 models, and Table m for 1956 models, although these were not yet on sale on July l. They were included because some households bought new ear s late in the survey years, after the new models came out. The values given are based on new-ear prices (less discounts, if any) with an appropriate adjustment.

In order to isolate the influence of price changes some calculations were also made in which quantity data on investment and inventories in 1955 were evaluated according to the price patterns prevailing in 1952. Thus a four-year old Chevrolet (model year 1951) bought in 1955 was assigned the same moneyvalue as a fouryear old Chevrolet (model year 1948) bought in 1952. Since the rnadel years 1942 through 1945 were missing in Table II it was necessary to interpolate in that table, for which purpose the observed semi-logarithmic relation between age and price was u sed.

3.

Tabulatians of the Survey Data

The Tabulatians in Tables IV, V, Va and Vb are based on all families represented in 1952 or 1955 (or both) who owned a ear at any time during either of those years, and for whom adequate data were available. The proportion of sample households who did not own a ear was very small and certainly much smaller than in the population as a whole. This was eaused partly by biases in the selection of sample members, and partly by censoringthe sample after it had been taken. It did not seem advisable to attempt dubious actjustments to allow for the underrepresentation of no-ear families, and those that were in the sample were left 180

out. 3 The term "all households" used in the remainder of this paper should be interpreted with the above restrictions in mind. Tables IV and V summarize the principal characteristics of the households in the form of cross-classifications by income and initial inventory. They refer to six income groups, for each of which four levels of initial inventory were distinguished; in addition, data are given for certain aggregates (labelled "all"). Mean incomes are given in column 6 for each subgroup and aggregate, except where incomes over $7500 were involved; as noted earlier, the latter incomes were not specified. Column 7 gives the mean initial inventory obtained by pricing cars held at the beginning of the years by the values given in Tables II and III. From the Iines marked "all" it will be seen that the initial stocks were closely related to income (at least for groups of households-for individual households there is very considerable scatter). A comparison of TablesIV and V reveals an increase in the proportion of households in the high in come b rackets, in accordance with the national trend of personal incomes. It also shows a marked fall in initial inventories from 1952 and 1955 at all levels of income, which should no doubt be attributed to the decline in ear values (particularly for used cars) apparent in Tables I, II, and III. Another diffetence between the two years is the distribution of households by initial inventory. Since initial in ventories we re higher in 1952, there were, of course, relatively more families in the higher stock groups, but apart from this factor there is a distinct lack of familieswith initial inventoriesbetween$400 and $800. This may be explained by the suspension of ear productian during the war years and the small output just after the war. Table II shows that, at the price pattern prevailing in 1952, cars produced in those years would mostly have been in the $400-$800 range. The most interestingfigures in TablesiV and V are those given in columns 8 and 9, which have also been charted in Figs. l through 4. 4 3A mueh larger number of families had to be left out beeause the information on their ineome or on the ear they owned was ineomplete or patently erroneous; this includes all families who at any time owned a foreign ear. Of the 4549 households on whom some data were originally available for 1952, 497 were omitted beeause their ineome was not given, 67 because they did not own a ear, and 683 because of incomplete or defective information on ears owned. Of the 4393 households in the 1955 sample, 103 did not owna ear, and 719 were omitted beeause of imperfect data. 4In the first two diagrams the mean income of the top income group wasputat $11,000, a crude estimate obtained byassuming that ineomes of $6,000 and over follow a Pareto distribution. Since there is only general evidence for this assumption, the estimate was used merelyfor the purpose of drawing Figs. l and 2; it has not been used for any of the ealeulations. Nate also that Figs. 2 and 4 are based on Table V and therefore express values in 1955 prices.

181

00 N

1-0

l

l

l

76-over

all

l

60-75

50-59

l

40-49

0-390 400-790

all

!4oO-over

0-390 400-790 Bo0-1390

all

1400-over

0-390 400-790 Bo0-1390

all

1400-over

0-390 400-790 800-1390

l4oO-over all

0-390 400-790 Boo-1390

all

1400-over

0-390 400-790 800-1390

all

800-1390 1400-over

0-390 400-790

800-1390 ll4oO-over all

l

30-39

0-29 l

676 338 1215 1073 3302

381

230

16 13 122

39 28 166

577

210

208 91 234 214 747

105

5 7 33 6o

ll2

~~9

16 9 38

25 14

67 53

2lj.7

2?

120

)130

47

32 19

l{/)

252

98 65

156

]l

17~

722

59 28 38

9

ll7

71 14 23

202

2)4 Bo 182 94 610 3

l

l

2 13 55 80

lO

E l2

o

o

2 6 y

o

12 13

o

l

o

14

4

o

l

20

6 :l

o

12

6

l

4

(8)

(9)

-

299 220 153

951 196 614

4346 4]82

---------

-----

64o8 6457 6493 669l 6;75

5272

67

434 317 220

98

ll29

16 - 181 2

-

+ 134

+ 237

290 186 638 1092 1919

257 172 137 194

o

- 119

+ 386 + ')26 + 115

- 124 4

2

+ !+61 + 196

450 682 324 254 299

539 ]26 190 200 235

209

-202 2

+ 369 + 191 + 26

8o

9?0

957 909 889

948

1202

1176

1108

1440 1270

95)

910

1324 1013 839

1170

1199 989 641 034

8]8

919 752

+ 104

856

'(06

974 869 787

617 766

710

$ 742 97'o

+ 244

- 34 -211 - 22

164

(lO)

Gross invcstment per housr:hold vith positive gross inv.

5

+

- 220

-

+ 123

178 637 1145 2207 1721

1926 1374

llo8

215 648

1217

191 628 1104 1827

5249 5262 )278 3?.75

1780 1083

4370 4)76 4369

1092

1831

3401

_::,417

3l.-OO

3>!1

3394

+ 230

284 246 113 79 171

7

193 (46 1070

80 - 280

+ 162 + 52

~

Net investmcnt per household

+

lO

170 97

206

$

Gross investment per household

138

1952

1945

$

(7) Ini tia! inventory per household

(2)

Ba.sic data for sa'T!p:e househo:._ds present in 1952, with V3.lues at 1952 prices

Initial inventory

TABLE IV.

(ll)

31 27 19 20 22,6

31 54 27 26 28

41 32 23 25 26

37 26 22 20 24

33 ?9 19 13 21

29 28 15 18 22

1.9

lO

28 18 13

householdo: with positive gross investment

% of

(,)

..... 00

l

fl.

l

~

76-ovf'r

6o-75

l

0-390 47,200

2,1117,6!!0

15,834.~0

.

-.195 (.017)

.

.073

(.007)

GSci

2950

(le)

All F amilies

Al, Bl, Cl {ltJSS)

-------

2921

-- ---

Non-zeto Gross lovestment

A~- (1952-)

All Groups With !ncome LessThan $7600

TSS Adjusted

\le an

SS Error

2 R

lnventory, S0 j

i. •rransitory~ Jnventory, sij- SOJ

h.

g 1955 Stock in 19S2 P"ces, S5.,

f. 1955 stock, 55

e_ 1952 Stocil, S2

i'SS

2 R

Income, Yoj

d. "Trans1torv• lncome, Y, 1 - Y01

c.

195.S lncome, Y5

a_ 1952 Inrome, Y2

~-

-\_1, A2,

All Fam1:n•s

~-

TABLE VID

~051

.604

.034

.lSr'i

. .

.[191

.211

384,240

8,869,808

1,8"-2,734

10,752,542

.

. .

-.144 (_029)

(.011)

.

.095

.545

2-'i5,42l

2,1fi8,R55

2,011,049

4,1i9,904

.

-.203 (.QQS) -.157 (.110)

(.03/i)

.l5h

(.1)111

·~$1 ·~'" _L_.~l22

121,9Cl2

3,539,112

508,234

4,047,346

.

.

-.117 (.017)

.

.034

(,OOf,)

'"'"'l ""'"

424,430

8,252, 705

11,508,387

19,761,092

.

UR (.019)

Gs;

973

(22b)

SUMMARY OF STATISTICAL 1,100ELS USED TO EXPLAIN GROSS

-

.021

.053

.632

.065

·'"

122,369

102,179 4,578,820

217,288 5,452,370

.067

.821

750,108

1,151,134

5.3113,994 '

145,244 11,299,995

l

2,16~.!!55

2,011,049

4,179,904

.

.

-.6R1 (.156) -.f\95 (.178)

(J)(-4)

.094

-.024 (.072)

l

.Mil

-.075 (.084) -.697 (.150)

.163 (.040) .050 (.0;9)

()19

.621!

.065

.628

.Ofil

.622

.059

.816

122,369 767,463

217,288

1,151,134]

127,889

2,168,855

12,011,049

l 4,179,904

l

l

l

G2j, GSj

135

(25)

Non-zero Gross lovestment

5,500,989

4,730,992

5,363,994 2

6,299,995 1 6,299,995 1

5,507,070

650,451

10,745,437

1,763,201

12,508,1138

-.370

-.050 (.01!11

826,~1

12,634,056

2,011,049

14,799,8&8

.

-.027 (.021) -.394 (.027)

l

(.013)

.087

.051 (.007)

G2J' GS~i

1678

(20)

615,784

12,634,056

2,011,049

14,7'l9,888

-.027 (.021) •. 381 (.028)

(.013)

.057 (.008)

(.014)

.061

GWGSj

lfi711

1!7)

.057 (.008)

l

l

All F amilies

•withinlBetween" Covariance Analysis

G2i' G~;

lf\78

135 G2j' GSj

(16)

1241

lovestment

700.444

10,745,437

1,7fi3,201

12,SOR,I13R

021 (.016)

G2, GSc

1678

(19)

Variable Gross

N011-zero

"Taste~

f-64,403

12,1i34,05fi

2,165,832

14,799,81\R

.

(.033) -.393 1.03t')

-.363

.07R (.015)

(.018)

Gli' Gs,

167R

(lO)

F amilies

·\11

------

CovarianceModelsW,th

Gfoup Al Only (1952 and 1955 lncome LessThan $7600)

INVEST~ENT

In the statistical models reviewed here, however, none of this last set of factors is explieitly ineluded. 30 (2) Type of Data. Four of the six studies seleeted for review use time series exclusively; of the remaining two, one (Bandeen) uses cross-section data grouped by states and the other (Farrell) employs grouped data from the 1941 B.L.S. household survey (Farren also uses time series data). Our study appears to be the.tirst to analyze individual household data for more than one year. Other information pertaining to the data employed can be found in Table IX, Column two. (3) Purpose. Some authors-notably Roos-von Szeliski and Chow-have attempted rather complete explanations of the demand for the total stock of automobiles and the sales or purehases of new ears. Bandeen, on the other hand, limits himself to investigating the effeet of ineome and population density on new ear sales, and B rems has an even simple r stock growth mode l the so le purpose of which is to guide investment decisions by predieting long-run equilibrium demand. Farrell's model appears designed to study both the interrelationships between the new and used ear markets and the demand for new cars. (4) Statistieal Implementation of the Mode l. The statistical estimation of parameters and the testing of hypotheses require operational definitions of the variables employed in the model, and the investigations reviewed here refleet considerable variation in this respect. In order to facilitate comparison the various definitions that have been employed are summarized in Table IX, along with the income and price elasticity (when given). Disposable personalincome (D.P.I.), deflated, is recognized as a better explanatory variable than either national income or GNP. Howeve r, the definition of disposable in come ( column three of Table IX) has been further defined by Roos and von Szeliski as "supernumerary income"31 and Chow, in one of his equations, has used Milton Friedman's coneept of "permanent" or "expected" ineome. 32 To complicate comparison even more, income is used by some authors on a per capita basis and by others on an aggregate basis. The price of automobiles has entered the various models in the following ways (column four of Table IX): as a price index for all new cars (e.g., the BLS index), as a price index for low-priced 30some of them are considered in the extensive stud y by Wallander [ 17], which reached us too late for analysis in this survey of other work. 3loefined as personal disposableincomeminus an arbitraryamount for "necessitous living expenses" ($200 per person in 1923). 32"Expected" income for a given year is, according to Chow, a weighted average of measured income for each of the last eight years. 214

1:\:1

.... c.TI

Before 1926:

Value of cars bought less value of

Canpiled from newspaper ads and N.A.D.A. trade handbooks

l

1955

Refers to gross investment in new and/or used cars by survey households during s. yes.r; i.e., short-run elasticity. Preferred Inventory, derived frcm equation (18) above. Der i ved indirectly,

]}

f2/

Refers to the cons=ption of autcmobile services, which is the est:Lmated deprecia· t1on of •otal stock. ·

~/

(Around -1.0)§/

Refers to demand for the total stock of autcmobiles.

.~

1.020'

1t

.e/d

~

not given

cred!to~::sy

Reflecting c re di t tenns: -0.55 to -0•59 not reflecttng

not given

A "dynamic" concept of elasticity, referring to the annual change in new ear sales and the annual change in inc=e.

models incorporating a "fWilily effect"

not given

21

~

not given

-0.?4 to -l.56l;

~

l

Also uses concept of "equilibriUI!I" or average ra te of growth

).8o

lt.oo

0.9

given

l/

'·'

-0.29 to ·3-59-

Selected years:

2J

Estimated for eacb make of ear but not directly used in mode l

Scme models a variable Which reflects

?_/

lilasticity (lO) All years: 2/ -0.65 to -2.5-

Estimates of'

Ll4 to 2.03

2t.o5

L5

ID.cane Blast! city (9)

Reports, National Used Car Market Reports, lnc.

Est. $ value of cars held at beginning of the year

Average age of cars scrapped

Appears impl ici tly hecause model uses first differences (i.e., change in total stock}

Estimated loss (in dollars) of keeping a ear an additionaLEar

substitute the stock of money for inccme

(8)

Other

Refers to the demand for new cars, or gross investment (i.e., sales or purchases of ne·~ cars used in the regression equation).

~ ~ ~ ~ ~ ~

Household inccme after tax, as reported

Individusl households, 19)2 and 1955

Total cars in opera-

sold

U=

in operat i on

Brok e by states and by age

Annual depreciation~ difference in price between iyear old model and (i + 1}-year old model

Number of cars in operation, broken down by age groups

T

l

eonstant percentt.ge depreciation rate

Theoretical scrapping (in physical units) predieled by applying shirting mortality table to age distribution of existing stocks

(7)

Depreciation or Scrapping Rate

Estimate value of total stock (each age group times appropriate price)

Number ol cars in operatian

(G)

N\Jillter of

new cars sold

sold, per capita

Number of

sold, monthly and annual

c of

(51

not used in

Based chiefly on B.L.S. wholesale autcmob1le price index

~Books Y

Ccmp1ltC'd frcm

::::1/n ~

Arithmetic mean of Chevrolet, Ford, and Plymouth prices as

Arithmetic mean of prices advertised in Chicago, Washington, Salt IB.ke, and Los Angeles newapapers

Arter 1926: ar i thmetic mean of Chevrolet, Ford, and Plymouth pri:x~e- :>:x~ Re) A

(Re)A is the pooled regression:

('LxRe

YRe

+ L'X (Re)A y (Re)A ) ~· 253

( Lx 2

Re

+

L

2 ) x(Re)A

for part of the variation in expenditures which the analysis of covariance attributes to variation among cities. In a sense, the standard analysis of covariance allows the specific f actors or "treatments" a priority in accounting for over-all variability among the observations. Employment of the residua! regression allows the regression variable to account for variation only after the effects of the classification variables on both the dependent and the regression variable have been removed. Use of the inter-city incomeexpenditure regression reverses this priority and is justified by what we assume to be typical practice in market forecasting. That is that the market forecaster would consider income as the prior independent variable, and would add other variables if they promised to materially improve forecasts made employing income alone. Analysis of the gross income-expenditure variation by cities will indicate how much of the inter-city variation in expenditures can be explained by income as a predieter. The higher the proportion of inter-city variation so explained, the less is the need for ad hoc recognition of city by city differences in expenditure levels. I.

Can a single inter-city income-expenditure regression be employed without regard to region? The inter-city regression coefficient, bRe= ~xRcYRc + ~x~c), makes no allowance for region. Individual inter-city regression coefficients for each region can al so be determined. be be

l

2

=~XC

l

=~XC

yC l

2

+~XC

y C + ~XC 2 2 2

be = ~xc y c + ~x~ 3

l

2

3

3

3

If region has no effect upon the applicability of the overall regression represented by bRe, we should expect expendi ture estimates employing bRe over all regions to be as effective as regional estimates employing bc 1 , bc 2 , and bc3 • An "F" test for the additional explanatory power of the regional regressions tagether with the differing regional means is employed.

J.

If a single inter-city income regression is not applicable over

all regions, is the failure due to varying inter-city regressions within the several regions? This question calls for a test of the difference in error variance employing a "pooled" intra-regional regression coefficient

b_= (~xc Yc + ~xc Yc + ~xc Yc ) + (~xc2 + ~x2 + ~x2 ) 1 1 2 2 3 3 1 c2 c3 c 254

K.

and the sum of error variances resulting from employment of the individual regional regressions. If a single inter-city regression cannot be employed over all regions and the several intra-regional regressions are accepted as equal, does the failure arise from a non-linear regression among regional income and expenditure means? If not, does failure arise from a difference between a linear regression among regional income-expendi_ture me ans and the pooled linear regression among cities within regions? These questions i n v o l v e the inter-regional incomeexpenditure relationship which, if linear, can be expressed by: bR :::

L.

2

~~YR + ~XR

If either question must be answered negatively, evidence is strong that the income-expenditure relationship among regions differs from the corresponding relationship among cities within regions. A negative conclusion to question J im pliesthat the re is no single income-expenditure relationship among cities within regions. In this event, question K would not be asked, and the individual inter-city regressions for the several regions would be examine d mo re closely. Is the re a significant variation in expenditure levels among the several classes of the non-locational factor, and does this pattern of variation differ among regions? Here we return to the conventional analysis of variance test for "treatment" means, but since the same levels of the non-locational factor are repeated regionally, we test also for the interaction of region with the non-locational factor.

Application of Analysis to Furniture-Home Furnishings Expenditures The framework of analysis just outlined has been applied in studying locational variation in expenditure levels for four commodity classes as well as total expenditures in the furniture-home furnishings group. The study to be examined here employs mean family expenditures by size of family in twenty larger cities in the north, fourteen in the south, and fifteen in the west. The series of significance tests are summarized in Table 1. Locational variation in original expenditure levels is present in total expenditures as well as in all expenditure classes. Both regions and cities within regions contribute significantly to this variation in total expenditures and in equipment. The regional factor is lacking in household textiles and furniture, but apparently represents the primary source of locational variation in floar

255

TABLE l Locational Variation in Expenditure Characteristics for Furniture-Home Furnishings - Analysis Employing Size of Family ------

Significance Test A. Locational variation in expenditures B. l. Locational variation arising from regwns 2. Locational variation arising from cities within regions c. Residual income-expenditure regression D. Locational variation in expenditures actjusled for residua! incomeexpenditure regression E. l. Locational variation in D. arising from regions 2. Locational variation in D. arising from cities within regions F. Income-expenditure regression among cities G. Locational variation in expenditure actjusled for inter-city incomeexpenditure regression H. Locational component in inter-city income-expenditure regression I. Difference belween inter-city in come -expenditure regression and inter-regional or intra-regional regressions J. Variation in I. arising from varying intra-regional regressions K. Variation in I. arising from variation between inira-regional and inter-regional income-expenditure relationships L. Variation in expenditure - size of family relationship by regions

Total

s

Equipment

s

s s

s

s

s s "'"*

s

s

s s

s

s

s

s

s

s

s

s

s

s

s

s

s

s s

s s

s

s

s

s s

s

s

s

s

--~'·----

coverings expenditures. Table 2 summarizes more particular data concerning these gross locational differences. Where region contributes significantly, expenditure levels of western cities are high. Expenditure levels of southern cities are notably low in floar coverings; their higher than average level of equipment expenditures will receive more comment later. As anticipated, income is found to exert a significant effect on all classes of expenditures after the influences of location and of family size have been removed from both variables. This incomeexpenditure relationship is sufficient to account for the significance of locational variation in household textiles, floar coverings, and furniture expenditures. In these classes, differing locations are not a significant source of expenditure variation apart from differences which could be explained by differing income levels in the absence of any locational factor. In total and in equipment expenditures, however, net locational variation remains, and both regions and cities within regions contribute significantly to it. Som e details concerning this situation can be extracted from Table 3. 256

TABLE 2 Average City Expenditure Levels by Regions and Variability in Expenditure Levels Among Cities

~rmtu.re-Hom~A-;e_rage Furmshmgs Expenditures

All

Cit; Expenditure Levels

---r;_;

North

l

l $268.471260.00

Total Household Textiles Floor Coverings Furniture

Equip~~n_t_ lncome ($ hundreds)

33.60

l l

25.24 63.18

26.43 61.48

West

246.05

300.68 1 31.07' 33.37

35.55

• :

South

l

l ·

l 18.20 .

1

57.17

~

E~ed ~ D--;v~

. All Withm Among Residua! Cities Region l Regions $41.7 5.7

61.81S7.6 7.7

l

1M.S

7.5 l

(9.2)

30.21

9.4

11.7

(10.6)

23.4

l 71.04

16.3

20.2

19.4

(27.3)

94 •. 16

1

4_lJ.48

l ~ 36.8~

96.8..2.1106.32 t---1_2._4--J-20_._5-+--1_7_.9--t- 48.6 41.30

i

2.3

5.2

4.5

11.8

) Source of variation not found significant at 5% leve!.

TABLE 3 Characteristics of A verage Expenditure Levels Adjusted for Residua! Income- Expenditure Regression Adjusted Expenditures

Estimated standard Deviation in Adjusted Expenditures

North

IntraRegional

Inte rRegional

Total FurnitureHome Furnishi ngs $244.43 275.24 294.18

36.6

68.2

Equipment

18.2

56.7

south

West

79.85 103.11 104.92

Here we find that removal of the residua! income effect from regional expenditure levels in total furnishings group expenditures leaves the westhigh and reverses the standing of northern versus southern cities. Expenditure levels in the north are considerably below what would be expected on the basis of a non-locational income- expenditure relationship, and southern expenditure levels are similarly high. This same tendency prevails in equipment. In both instances, the covariance between adjusted regional expenditures and income would be, on balance, negative. That is, incremental expenditures accompanying a given change in income leve! among regions are less than the corresponding increment existing apart from locational variation. An otherwise expected 257

TABLE 4 Income-Expenditure Regressions for Forty-Nine Cities and Standard Deviations in Expenditure Levels Actjusted for Regressions Furniture- Ho me Furnishings Expenditures Total

,----r

Estimated a Expenditures

Regression Coefficients 1 Est. a Original f-------Expenditures i Inter-City Residua! Actjusted (l) (2) i Inter-City : '

Actjusted by (1)2

Actjusted by (2)

8.46

7.93

(.48)

$45.3

44.8

7.7

1.24

.74

.50

4.6

4.9

Floor Coverings

11.7

1.45

1.13

(.32)

9.2

9.1

Furniture

20.2

2.12

1.67

(.45)

17.3

17.2

Equipment

20.5

(.31)

1.7~-

20.7

21.0

Household Textiles

$61.8

l l

-1.40

l

l Dollars of expenditures per $100 in come inc rement. ( ) indicates regression coefficient differing insignificantly from zero, ernploying 5o/o signifiicance level. 2The sums of squared deviations about the inter-city regression cannot exceed those for city means about the residua! regression. However, the inter-city regression results in the loss of an additional degree of freedom from the adjusted city expenditure levels.

income- expenditure relationship appears to be dampened when the regional factor is interposed. Table 4 shows this same phenomena appearing among cities within regions in equipment expenditures. Adjustment of city expenditure levels for the non-locational incomeexpenditure regression leaves expenditures among cities inversely associated with city income. Differing income levels among locations generally, the n, seem to produce markedly less effect on equipment expenditures than do corresponding income differences in the absence of the location factor. Gross income-expenditure variation among cities is significant in total furnishings group expenditures and in all commodity classes except equipment. Expenditure differences adjusted for this regression follow the pattern observed in connection with the residua! regression, with net locational variations persisting only in total and in equipment expenditures. Table 4 reveals thatadjustment for inter-city income-expenditure variation as campared with regression net of the locational factor matters little in total, floar coverings, or furniture expenditures. In household textiles, however, estimates are materially improved by using the gross inter-city regression. This is occasioned by a distinct locational component in the gross regression. A greater regression coefficient exists among locations than in their absence. Locational differences thus enhancethe effect ofincome onhousehold textile expenditures. The influence of location in dampening the income effect in equipment expenditures has already been mentioned. The result is, in fact, to completely offset the otherwise prevailing positive relationship, 258

leaving an insignificant gross inter-city regression coefficient. These modifyinginfluences of location are measured bythe significant adjusted inter-city regression coefficients in the household textiles and equipment classes. Table 5 presents further information relating to the gross intercityincome-expenditure regressions. In all cases ofsignificantregression, the income-expenditure relationship is relatively elastic. Elasticity is highest for floor coverings and relativelymoderate for furniture and total furnishings group expenditures. The success of employing differences in income level to "explain" varying expenditure levels of cities is greatest in household textiles. TABLE 5 Characteristics of Inter-City Income Expenditure Regressions Among Forty-Nine Cities Regression Coefficient ($per $100. income change)

Elasticity at Mean1

Sample Coefficient of Determination

$8.41

1.27

.474

Household Textiles

1.24

1.49

.656

Floar C overings

1.45

2.33

.398

Furniture

2.12

1.36

.281

Equipment

(.31)

.13

.006

Furniture- Ho me Furnishings Expenditures Total

l

. (bRcX) Y 2( ) differs insignificantly from zero employing 5% significance leve l. 7

The applicability of these regression coefficients within all regions and inter-regionally is accepted in household textiles, floar coverings, and furniture. In total furnishings group and in equipment expenditures the overall inter-city regression is not found universally applicable. Results pertinent to these locational differences are found in the following table. In all instances we have to regard the separate intra-regional coefficients as estimates of the same (pooled) intra-regional coefficient (see Table l). In both instances of failure of applicability of 259

TABLE 6 Characteristics of Individual and Pooled Regional Inter-City and Inter-Regional Income-Expenditure Regression Coefficients l Furniture-Home Furnishings Expenditures

Inte rRegional North south West Pooled Coefficient Regional Coefficients

$7.46

13.82

7.99

9.57

4.42 3

1.12

1.47

1.75

1.38

.73

.97

1.62

1.84

1.38

l. 70

Furniture 2

2.33

2.95

1.72

2.38

1.24

Equipment

-.73

2.28

1.83

.83

-1.50 3

Total Household TextilesZ Floor Coverings 2

1$ per $100 income change. 2Regional and inter-regional coefficients not judged significantly 3 different from inter-city coefficient. Inter-regional regression notacceptedas linear.

the inter-city regressions, the testprocedures single out non-linear inter-regional regression as the cause. Study of the average city expenditure and income levels by region (Table 2) will reveal that western cities, with an average income leve! just moderately above that for all cities, have average total and equipment expenditures markedly exceeding northern cities with higher income levels. The income-expenditure relationship described by the three pairs of regional averages is in both instances an inverted "V," with the west at the apex. The inverted "V's" are tilted, sothat if one were to compute a linear regression coefficient, it would be positive for total furnishings group expenditures and negative for equipment. This tendency for expenditure levels in the west to be high and in the north low in relation to income levels is present to a lesser extent in furniture and floar coverings. Manifestly the tendency is not marked enough to affect the significance tests employed. The pursual of locational differences in expenditures and income-expenditure relationships has led to intra-regional and inter-regional expenditure d i f f e r e n c e s, individual incomeexpenditure regressions among cities within regions, a pooled intra-regional regression, and an overall income-expenditure regression among cities without regard to region. While the se have 260

all been considered in terms. of significance tests, it seeros worth while now to summarize some implications in purely descriptive terms. In Table 7 are the results of alternative ways of attempting to account for the sums of squared deviations of city expenditure levels from the grand mean level. As the most effective means we can employ specific regional differentials earobined with individual regressions within the regions. Alternatively, we might employ the same regional differentials and a single (pooled) intra-regional regression, or disregard specific regional differentials and employ only an overall inter-city income-expenditure regression. In the first alternative estimating effectiveness will be sacrificed intraregionally, and in the seeond losses are possible both intra and inter-regionally. TABLE 7 Summary of Alternative Means of Accounting for Inter-City Variation in Expenditures Furniture- Ho me

Furnishings Expenditures Total

Proportion of Inter-City Sum of Squares Intra-Regional Inter-Regional .116

.884

Proportion of Inter-City Sum of Squares Explained by (l)

(2)

(3)

.650

.607

.474 .650

Household Textiles

.940

.060

.717

.694

Floor Coverings

.833

.167

.467

.446

.398

Furnit ur e

.924

.076

1.360

.350

.281

Equipment

.766

_-2~J.361

.268

.006

(l) Regional Regressions plus Regional Means

(2) Pooled Regional Regression plus Regional MeCinS (3) Inter-City Regression

Estimating efficiency holds up well for the pooled regional regressions in most instances. This is not surprising in view of the prior acceptance of equality of intra-regional coefficients. In equipment, where the pooled regression does not stand up descriptively, the test of equality of regional coefficients produceda value of "F" with a prohability only slightly above .05. The regression coefficients among the "sample" cities are higher in the south than in the we st, and negative in the north. Disregarding region in favor of an overall inter-city regression is disastrous in equipment expenditures. Here more than in any other expenditure class, a substantial portion of the sums of squares are produced inter-regionally and, as we have found, not adaptable to a linear regression. Within regions, the income-expenditure relationships for the sample cities

261

vary considerably from the best fitting intra-regional regression, l et alone from a regression whi ch has a heterogeneous inter-regional component mixed in. The single inter-city regression was also rejected in total expenditures, but it can be used for the sample cities with fair results. In household textiles the overall city regression is very nearly as effective as the first two methods. Interest has been center ed thus far on locational differences to the exclusion of the secondary classification variable, size of family. standard tests show the overall effect of size of family to be significant in all expenditure classes. Of cancern as a facet of locational variation is whether the pattern of expenditure variation with family size differs among regions. Except in household textiles this is found to be so. To point up these varying patterns, regional expenditure levels by size of family are presented in Table 8 adjusted, however, for gross regional differentials. No clear pattern summarizing the different size of family relationships by region applies over the several commodity classes. A tendency for total TABLE 8 Furniture and Homc Furnishings Expenditure Levels by Size of Family and Region Actjusted for Overall Regional Differences -----··--

-~-

--------

---

-----

. H , Size of Family (Persons) Furmture- ome i--~~__ ---,------,-------Furnislungs Expend1tures l One l T\\ o Three l Four l Fl v~ S_I_x__{)l'_More l Al~ 1

Total

304.11331.9~333.51

i 73.11252.2

North south West

68.2 250.7 305.0 306.1!315.9 99.5 261.0 300.8 337.3 347.5 53.9 246.1 305.9 361.2 1 343.9

Household Textiles

13.1

Floor Coverings

29.0

35.5

l

316.1

[268.5

365.2 264.6 298.7

1268.5 . 268.5 i 268.5

40.7

43.3

40.1

33.6

27.7

32.5

27.9

25.2

6.3

24.7

32.3

3.0 13.6 3.9

24.6 20.2 29.1

l 32.4 26.6 37.4

26.1 32.0 25.8

29.7 35.5 33.4

35.6 23.2 21.7

25.2 25.2 25.2

15.7

68.0

77.8

87.0

72.4

58.2

63.2

North south West

! 16.0

71.1 69.4 62.6

77.7 81.4 75.2

71.1 78.7 114.4

73.8 76.1 67.2

69.1 48.7 62.6

63.2 63.2 63.2

Equipment

23.4

106.7.113.7 121.0

113.6

94.2

115.1 125.81 88.5 108.11114.6 113.01 101.4 31.41 85.9 103.9 117.4 124.71 84.61107.3!108.8l128.3l___ 122.8 l 12.B

94.2 94.2 94.2

North south West Furniture

North south West

l

24.7 6.91

86.6

l

------~- _____l_

262

expenditures to "peak" at four or five person families in the south and we st is absent among northern cities. This intermediate "peaking" is repeated in equipment expenditures in southern cities. In furniture expenditures an extremely low level for "six or more" person families in the south and the unusually high level for four person families in the west probably contribute substantially to the regional discrepancy. Additional Findings and Comments The same set of tests were also applied to data for the fortynine cities with age of head of household as the secondary classification variable. The results achieved in this analysis, which obtains locational differences by averaging over a different non-locational factor, are of so me interest. Differences in the results of the series of tests as between two such analyses can arise from the interaction of the omitted secondary factor with the locational factor. Some differences will arise from different levels of residua! variances against which the locational differences are tested. The residua! variances ma y be fair ly !arge if so me of the "cell" me ans represent very small numbers of families. The result may be insignificant locational differences where use of another secondary factor produced significant differences. This occurs in fact in total furnishings group expenditures employing age of head, where a very few "extreme" values account for large residua! error terms. The expenditures involved, however, were of a miscellaneous sort not included in the specific commodity classes. In the several commodity classes the analysis employing age of head agreed with the "size of family" analysis in several key respects. These were significant gross locational variation in all commodity classes, significant inter-city incomeexpenditure regression in all classes except equipment, insignificant inter-city expenditure variation net of this regression in all classes except equipment, and acceptance of a single. inter-city income-expenditure regression both intra and inter-regionally in all classes except equipment. Some added force is thus given to these specific findings. The "age" analysis finds both region and intra-regional city variation contributing significantly to gross locational variation in all commodity classes, and this is in "agreement" with the "size" analysis only in equipment expenditures. Conclusions depending on the differences between the inter-city and residua! income regressions vary in the two studies. This is reflected in the finding of significant locational components in the inter-city regressions in the "age" analys is in floor coverings and fur ni ture as weil as household textiles, hut not in equipment. Significant adjusted inter-city

263

regressions_ were found only in the latter two groups in the "size" analysis. A comparison of the several regressions in the two studies in household textiles, where the tests lead to the same findings, is given below. Regression Coefficients ($ per $100 income)

"Size" Analysis "Age" Analys is

Inter-City Regression

Actjusted Sample CoefInte r- E lasticity ficient of City Determination

Inte rCity

Residua!

1.237

.742

.495

1.49

.656

1.184

.393

.791

1.44

.554

Here, as we ought to expect, the inter-city regressions are similar. But the residua! regressions, in volving the removal of the effects of different factors in addition to city, are different and le ad to different adjusted inter-city regressions. Thus the rueaning of a "locational component" in the inter-city regression varies between two such studies, and we should not expect necessarily parallel results for tests depending on these differences between the intercity and residua! regression coefficients. An attempt was made to see if size of city, measured by the logarithm of population, was related to the original expenditure levels of the forty-nine cities and to the expenditure levels adjusted for the inter-city income-expenditure regression. Interest centers particularly on the latter in that a substantial relationship there would permit estimates of city expenditure levels to be further improved by invoking the city si z e facto r. To the extent that population is related to income among cities, it will be related to the expenditure variance explained by the income variable. In fact, the regression coefficient of original expenditures on population will be the sum of the regression coefficients for the vari an c e explained by income on population and the variance unexplained by income on population. Results in these terms along with the corresponding coefficients of determination for the sample cities are indicated in Table 9. The results are "unimpressive" except for equipment expenditures. In household textiles there appears a moderate positive relationship between original expenditures and city size. This is, however, subsurned in the income-expenditure relationship, so that population is of no avail as an incremental explanatory variable. In equipment, city expenditure levels adjusted for income levels can with some benefit be further adjusted by city size. Smaller cities 264

TABLE 9 Regression Coefficients and Sample Coefficients of Determination for Population-Expenditure Relationships Among All Forty-Nine Cities 1 Regression Coefficients . Sample Coefficients of per log Population . Determination C a t egory o f E xpen ct·1C a t egory o f tures Expenditures .

1

Furniture-Home Furnishings Expenditure

1

Total

(l)

(2)

(l)

(2)

i $25.841 $43.47 $-17.63 .05

.27

'

Household Textiles l 6.31 • 6. 38 7.52 Floar Coverings 3.72 l l Furniture 4.10 10.94 Equipment i -16 26 1.601

(3)

- .07 l .18 - 3.80 .03 - 6.84 .01 -17.86 .17

.27 27 .27 .27

(3) l.o4

l

l .00 .05 .04 .21

(l) Original (2) Explained by lncome (3) Unexplained by II1Come

are associated with higher income-adjusted expenditure levels. The cities invalved cover a range of approximatelytwologarithms. The resulting adjustment difference of $35 from smallest to largest cities appears substantial in relation to the mean city equipment expenditure leve! of approximately $94. Income level and .size of city represent two different kinds of variables which one may use in an attempt to explain locational variation. Income is a characteristic of individual families at a given location as weil as of the population collectively. Size of city is, of course, a characteristic only of the population aggregate. Any relation of expenditures to a variable of the latter sort is inherently a locational relationship, though it may or may not differ regionally. Relationships of expenditures to variables of the first kind may have different characteristics among individuals from those prevailing among groups at different locations. This differentiation is suggested by the locational components in the incomeexpenditure regressions found in household textiles and equipment, although we do not find this by comparison with an inter-family regression. Consideration of how such a difference could arise might be fruitful, however, in suggesting hypotheses concerning the two locational components we have found. One possibility is differing distributions of income among families at different locations. These would notaffect inter-family relationships but could, in earnbination with the inter-family income-expenditure relationship, 265

influence the aggregate regression. The lack of an appreciable gross income-equipment expenditure relationship among cities could arise from a less varied income distribution among families in cities with lower average income levels. If these are also the smaller cities, an inverse relationship between population size and both income-adjusted and original expenditure levels could result. In a like manner, the relationship among average income levels of groups, the income distributions within the groups, and the interfamily income-expenditure relationship could be such that the income-expenditure relationship among groups, whether they differ locationally or not, would contain an increment in excess of that found among individual families.3 Thus it is possible for the locational component in the inter-city regressions to reflect differences not inherently locational, that is differences that can be explained by differing characteristics of families variously located rather than by postulating the acceptance of different patterns of living by similar f amilies differing only locationally. Perhaps a most crucial variable omitted from the study here is home ownership. In some related studies employing the hinefold region and city type breakdown in combination with various pairs of factors selected from among family size, family type, occupation, education, and age of head, we plan to introduce this variable. Income will be averaged out and proportion of homes owned introduced as the regression variable in covariance analyses of expenditure levels among population subgroups formed by the two classification variables in combination with the city class facto r.

3In both this and the preceding situation a non-linear incomeexpenditure relationship amongfamilies would seem to be required. The locational component in the inte r- city regression could then be said to arise from failure to use the proper form of inter-family regression. The major point here is to suggest that demographic factors interacting with the locational factor may yet be the "unknown cause" of the locational regression component.

266

COMMENTS by Ruth P. Mack National Bureau of Economic Research

H. S. Houthakker and John Haldi analyse information on auto buying obtained by J. Walter Thompson Company from about 3500 families in both 1952 and 1955. About a half of the families were in the panel both years. Information was obtained on family income up to $7500, on the sorts and ages of cars owned and purchased, and on a few other matters such as family type and location. The information about auto s owned and purchased was converted to dollar values by means of prices of many makes of used cars of each age. These price tabulatians for 1955 and 1952 are very interesting in themselves. Prices of new c ars we re about 100 dollars higher for the popular price cars in 1955 than in 1952. But the prices of used cars were several hundred dollars lower. The difference increased with age; a rough weighted average of annual depreciation was about 25 percent in 1955 and 16 percent in 1952. Obviously, the conversion to value terms on the basis of such different values in 1952 and 1955 raises all sorts of questions of a practical and, particular ly, theoretical sort. But a table, (5b), found well along in the monograph, is reassuring: the major results are not changed by re-evaluating 1955 purchases, ownership, and depreciation at 1952 prices. The authors examine how, in 1952 and in 1955, gross and net investment in automobiles are associated with inventories at the beginning of the y ear and family in come du ring the year. The y u se regression analysis in whi ch each family unit is a datum. They use class summaries for 7 income and 4 inventory groups. These are straightforward and illuminating methods. However, as always in cross seetian studies, the great majority of the family differences on auto expenditure remain unexplained. Preliminary tests indicate that allowing for location, family size, and age of respondent would not help so the authors make a bold move. They use covariance analysis to isolate "all factors which are presurned to be approximately eonstant between 1952 and 1955." These factors are visualized as tastes and other characteristics of the family. The idea is immediately appealing as a rough and ready way of latching hold of many things that ought to be "held constant" in 267

evaluating the strength of specified influences on patterns of family expenditures. B ut I findit very difficult to stipulate the exact me aning of the new parameters-those devoid of "family effects." The variables have some resemblance to change for each family over the period, and this worries me since the y do not seem to be always read with this characteristic in mind. The re may be mo re impounded in "family effects" than is desired. Nevertheless, it seems clear that the calculations are meaningful and informative. What are the lessons they teach? One major finding is that gross investment in autos (defined as the market price of the ear or cars bought minus the market price of the ear or cars sold) is highly sensitive to the number and age of the cars that people own. The influence of consumers' automobile inventories on new buying seems about on a par with that of family income. This is an interfamily principle and mayor maynot apply intertemporally. Analytically, total influence of stock on buying is the net impact of three sorts of influences. l. Transportatian service now owned. This dominant influence of stock, which is evident in the negative sign of the stock coefficient, reflects the fact that ear s are bought at l east in part for the transportaHon service the y supply. The more such service is available in one's present stock of autos the less, other things the same, one needs to acquire. 2. Others' stock. A seeond influence of stock carries a positive sign. It is the influence on buying of the stock of others. A new two-color auto in the neighbor's yard in 1955 probably eaused neighborhood buying to rise rather than fall. 3. Replacement pressure for desired stock. If people have attained som e leve l of stock to whi ch they feel accustomed, they have a desire to maintain stock at that level. To do so, the ravages of time and use must be replaced. The larger is desired stock, the greater the annual detericration which there is a tendency to replace by current buying. This provides a link whi ch carries a positive sign between long-term levels of stock and the buying of new autos. Houthakker and Haldi locate a leve l of "preferred stock" which at times is discussed as if it was meant to have the long run implications of the replacement-pressure leve l. Statistically, the authors locate it at the point where, for each income group, the regression of net investment on initial inventory erosses the zero line. So defined, preferred stock shifts upward with family income, and this is consistent with the notion of a replacement-pressure level operating in the long-run. What is not consistent is that the income sensitivity of the preferred level increases very substantially in 1955 relative to 1952. Clearly, changes of a short-run nature are

268

attaching themselves to the measure and thereby changing its meaning. I cannot, therefore, agree with some of the authors' interpretations of "preferred stocks." Actually, I suppose the influence of other s' stock and the replacement-pressure level appear in the eonstant in the equations and, perhaps, in the fact that the gross coefficient of inventories was a smaller negative number (since these stock influences carry a positive sign) than the coefficient net of family effects. The chief stock influence which is isolated and measured is that of one's own stock-transpartatian service owned-on buying. The author's ''best estimate" isthat gross investment is reduced by 35 or 40 cents for every dollar's worth of auto stock held at the beginning of the year. This estimate abstracts from familyeffects; without doing so, the figure would be 13 or 16 cents. Perhaps a combination of the two would be a better figure, but in any case the influence is substantial. This has an interesting consequence. A year of very high sales must be followed by a year or so with lower sales. However, if the depreciation implicit in the stock calculation is actually the depreciation to which people are sensitive (depreciation implicit in used ear prices was 26 percent per year in 1955), the aftermath of excessive buying cannot last very lang. This is a straight acceleration mode l in which a short life span seems to imply damped fluctuations of a few years' duration once a disturbance occurs. It would be useful to try to sharpen the time interval that the findings suggest under the assumption of a eonstant ownership objective. But the real innovation in the Houthakker-Haldi analysis is the demonstration that the ownership objective is anythingbut constant. On this all sorts of evidence is presented: l. When 1955 is campared with 1952 and income and beginning year inventories are held constant, gross investment is found to be larger, more sensitive to the level of income, and more sensitive (inversely) to the leve l of inventories. This is true when inventories and purchases are valued at current new-and-used-ear prices, or when they are valued at 1952 prices in both years. 2. In spite of the fact that depreciation was as surned to be substantially higher in 1955, net investment (gross investment less depreciation) was higher (income and inventories held constant) in 1955 than in 1952. Likewise, it had a higher income elasticity and a higher (negative) beginning-inventory elasticity in the laterthan earlier year. The assumption of linearity for the income influence seemed less justified in the later year. Conversion to eonstant prices did not change these findings; indeed it accentuated the greater negative inventory elasticity. 269

3. The level of "preferred stocks" was materially higher in 1955 than in 1952 at all but the two lowest income levels. The difference was greater the higher the income. 4. Used ear prices were lower in 1955 than in 1952. By demonstrating the presence of these shifts in consumer schedules this investigation has, I think, made an important contribution to the study of consumer buying. It is essential to pursue these insights by checking the empirical findings and explaining t hem. Let me imitate the Houthakker-Haldi boldness, without imitating their good judgment, by speculating about possible explanation of the phenomena they reveal. First, do the phenomena represent primarily a shift in supply rather than in demand schedules? There was a steel strike in 1952, and productian bad been under some restriction in 1951 and 1952. But there are several reasons why information in the survey and elsewhere do not see m to sit well with the notion that the differences between 1955 and 1952 were primarily eaused by short supply in 1952: lower income sensitivity of gross investment and preferred investment, in contrast to simply lower buying all around, does not seem to reflect restricted supply in 1952, nor does the fact that Regulation W was removed early in the year and buying started to pick up in the first quarter. If new ear buying is charted against consumer income, such buying, except in the third quarter of 1952, is only very slightly below its trend line-far less below the line in 1952 than it is above it in 1950 and 1955. The behavior of prices also seems inconsistent. True, used ear prices rose markedly in 1952 but they remained high in much of 1952, though supply bad been unrestricted atleast since mid-1952. In 1955 it was used ear, not new ear, prices which were relatively low. Also the prices of old new ear s we re low relative to the price of newer used cars. The Federal Reserve Board survey of installment buying in 1954 and 1955 showed that there was a marked shift in 1955, both toward the buying of new cars rather than used cars, and in the buying of the better new cars relative to the older ones. 1 Obviously, these shifts in relative prices reflect shifts in consumer choices. If price change had been primarily the result of supply conditions, it would have stimulated shifts in demand of the opposite sort than those observed. If we grant that strong changes indemand schedules must have occurred, i t is possible that the y we re eaused by the impact of som e particular influence. The foremost candidate is change in the terms

1 Consumer Installment Credit, Part IV, Financing New Car Purchases, A National Survey for 1954-55, Board of Governors, Federal Reserve System.

270

ofinstallment credit. Down payments were decreased and rnaturities lengthened after the middle of 1954 sothat the monthlypayments on installment contracts were, the Federal Reserve Board study found, about the same in 1955 as in 1954, in spite of the higher consumer incomes and more expensive cars that were bought. Credit sales as a percent of total new ear sales were higher in 1955 than in 1954 and still higher in 1956. Total expenditures (accruals) on autos ran way ahead of cash outlays in 1956. It is likely that at least part of the shift between 1952 and 1955 may have resulted implicitly from these more favorable credit terms in 1955. Here again, proof is difficult. My own guess is that though it certainly contributed it could hardly be a major explanation. For one thing favorable terms continued in 1956, yet the bulge in buying did not. Moreover, changes in installment terms and their utilization we re a very favorable influence in 1952, too. Again the higher income and inventory elasticities (rather than simply higher levels of buying) seemat odds with the importance of credit as a main explanation. Increased use of credit in 1955 was more notable for upper than for lower income families. A final explanation of the Houthakker-Haldi findings is simply that the desire to own a new ear took a jump. Perhaps it was the farnous sweep-around windshield and two-tone paint. The wish to display the "new look" may have been strong for the most staid, but the Federal Reserve Board Survey showsthat children particularly put their shoulder to the new wheel. OWnership of new cars was relatively higher in families with children under 18 than without them. All this makes sense of a sort. If an intensified de sir e to own a new ear was an essential characteristic of 1955 auto buying, a sufficient phenomenon is simply a shift in the time when a purchase is made. The total number of new cars purchased over the decade need not be affected. If so, the bulge has as a necessary counterpart a corresponding reduction in purchases in 1956 and 1957. There really seems nothing extraordinary about a bulge of this sort for a commodity which supplies primarily a replacement need. There were probably about 42 million car-owning households in the beginning of 1955. The fact that 7.2 million cars were bought rather than perhaps a short 6 million, the large majority for replacement, does not represent a heavy distortion of replacement demand. The distortion lies in its fortunate impact on Detroit. What then are the patterns of change over time that this 2-year interfamily study has revealed? The changes are partly indicated by different schedules in the two years and partly by what interfamily differences each year imply about h:itertemporal differences. l) There is a suggestion of trend change associated with trends in income or trends in preferred inventories, income the same.

271

2) The income link would also be responsible for paraHel short-term movements of auto buying and income. Perhaps the interfamily coefficient understates its magnitude. 3) Eccentric changes in buying may be set off by alteration in the wish to buy a new ear in combination with other favorable factors. A spurt of this sort would necessarily be followed by a earrespanding decline, other things the same. Turn now to Vernon Lippett's study. Again I want to concentrate on change. Lippett analyzed family purchases of a different sort of durable goods, household furnishings and equipment. By means of variance analysis he studied the impact on buying of five selected variables. The analysis is flexible in that it does not impose a functional form on the data and yet permits the estimation of each parameter, the other four held constant. Mter taking each of the five variables into account, the unexplained residua! is correlated with a number of other variables. These secondary and incomplete earrelations suggest further work that might prove useful. Most of the variables that Lippett analyzes are not given to rapid change from year to year. Exaroples are: age of the head of the family, the family type, family size, and (analyzed only secondarily) education of the head of the family, number of earners, type of city, occupation of the head of the family. Howeve r, certain of the variables w hi ch we re found to have significant influence on buying are subject to substantial change as time moves on. Family income proved to be important in that the percentage of income spent on furnishings remained approximately eonstant through most of the income range. Whether this income elasticity of about one would apply over time, we do not, of course, know. The percent of income spent was high for the lowest incomes and samewhat low for families with income over $7500. This divergent behavior for the very low and very high income groups raises the suspicion of the influence of income change. The open -end low in come group is like ly to be populated by a l arge number of families whose income has recently fallen. Conversely, the upper income groups often have alargerthan average proportion of families whose income has recently risen. However, actual and expected change in income are items submitted to secondary analysis: expenditure appeared to be samewhat higherfor either rising or falling incomes than it was for stable ones. It is hard to say on the basis of this evidence whether we would expect furniture buying to respond to the first difference in income as weil as to the level of income. The study certainly points to a question requiring more investigation. The most dramatic variable was home tenure. Families that had bougl;lt a house in 1950 or in 1951 had a furnishing-income ratio that was two or two and ahalf times as high as other families. And 272

those who owned at the end of the year and had rented earlier likewise had an extremely high ratio. It would be useful also to know the influence of a move, whether or not tenure was affected. Clearly expenditures on house furnishings willspurt when home building spurts. Here then we also have some suggestion of potentially lumped buying, though certainly of a very different kind from the one featured by the Houthakker-Haldi material. William Peters used covariance analysis to study differences in spending among regions and among cities within regions. He observed differences in total expenditure on home furnishings and on four subdivision of the total. Significant differences were found to exist. But the results are difficult to digest. Particularly, there is little to be culled from them about change. We want to know whether the intercity differences are due to intercity differences in home ownership, family size, and the like, or to the size of the city, the differential autocracy of the Mrs. Jones'es, or whatever. Part of the difficulty in the study may be one of exposition; it is hard to tell what factors are being held constant. But in part, the difficulty lies in the fact that enough variables, or perhaps the mo re important variables, are not controlled. Peters mentians that he plans to u se home ownership as an additional variable, and certainly Lippett's study suggests that new home ownership, and perhaps a recent move, elements in which cities could differ markedly, should also be isolate d. In short, the ingenious tool that Peters has devised still has work to do, a fact that no one knows better, and I trust enjoys more, than he does. I am slighting the study because it has little obvious hearing on change over time, the issue on which I have tried to concentrate. These studies, then, support much that has been known before; they amplify and refine this knowledge. They also highlight a question which, though certainly not new, has not to my knowledge been thus effectively spelled out. The Houthakker-Haldi study, particularly, encounters head on the question of whether interfamily differences in spending apply intertemporally. Bu t instead of answering it, it raises a new complication. It shows that interfamily patterus are themselves subject to change from one year to the next. At least in connection with the automobile buying spree of 1955, the demand schedules of many people seemed to have undergene a change. If this kind of thing occurs often, it is important to know that it does, to know how large the effect can be, and how long it takes for the movement to rise and to recede. In the case of a commodity selling in vast volume, such as autos, these questions have important hearing on the health of the economy as a whole. In any case, they have important hearing on the health of the industry immediately concerned. But there is perhaps, a more important question at issue than the understanding of what may be simply an occasional buying spree 273

in a particular commodity. Our extensive empirical study of consumption has really failed to provide ways to determine whether consumers' demand schedules change in connection with cyclical fluctuation. This is why, though we give lip service to the increasingly important part that consumers play in business fluctuation, we are really at a loss to say much about it. I think the papers this afternoon point to a way to learn what we need to know. I shall summarize the lesson by focusing it on the problem of understanding the buying spree, but what is said applies to the understanding of any aspect of change in consumer buying. Time series can, of course, say quite a bit about whether buying of particular commodities is subject to spurts. In the case of · automobiles, these spurts seem to be evident simply in the relationship of auto buying to income. The regression of quarterly purehas i ng on income has in the post-war period a wave-like motion, which has poor conformity to business cycles. This is in marked contrast to purchases of other durable goods which seem to follow consumer income far more docilely. Houthakker and Haldi have pointed to a seeond and prime technique for studying not only change in buying over time but also the structure of change-recurrent surveys. But surveys for large sample s are exceedingly expensive and therefore perhaps impractical. Here Lippitt's study, and others like it, carries a clue to how costs could be brought down to manageable proportions. It is clear that family size andother attributesplay an importantpart in eausing different families to spend different amounts on a selected group of commodities. Have we not now arrived at a stage of knowledge when it would be valuable to specialize our questions? Certainly it is important to learn more about the purchases of families of different sorts. But if we are interestedin change over time, why not minimize variance in the sample (and consequently the necessary size of the sample) by sampling only one familytype and making repetitive surveys of this limited group. There is every reason to believe that appropriate selection of the type would yield conclusions that would be applicable to patterns of change for the buying of other types. The recurrent survey is a missing link in understanding the history of consumer buying. But we aim to go further than the study of history or even the forecasting of history. We are interested in the practice of medicine in the stud y of consumer economics. For this purpose we need to go behindaggregates, expressedas sums, means, or parameters, and learn about how buying decisions develop for the individual and how they propagate among individuals. This is especially important ip. connection with episodes of the sort that Houthakker and Haldi encountered in the buying of automobiles-episodes that involve, in so me sense, overbuying with c o n s e q u e n t later underbuying. 274

Knowledge of how these episodes develop is necessary to the practice of medicine in consumer economics in the sense not only of effectuating policy but of defining it. I think it is possible, for example, that industry itself may sameday wish to avoid, rather than to encourage, buying sprees. I do not see how we can make much headway in understanding, forecasting, and evaluating these episodes until we know, first, how a decision to buy typically matures. At least in the lower and middle income ranges the purchase of an auto is not "impulse buying." (How could it be, when monthly installment payments in 1955 averaged 15 percent of disposable income ?) How doE-_ a decision to buy a ear generate ? What are typical profiles of these individual decisions? Immediately after a ear had been purchased the leve l of interest in another acquisition would presurnably be zero for a while. But does it then swell slowly towardan asymptote-the level at whichpurchase occurs? If so, as interest consolidates and starts the gradual part of its approach to the decision level, some outside influence could easily boost interest to the purchase point. The shape of the decision curve tells over what period of time a boost would be likely to succeed in shifting the decision ahead. If on the other hand a purchase decision were abrupt-interest rising swiftly to the purchase point when once the period of immunity had lapsedbuying would be more independent of small influences that might shift the date of the purchase, unless, indeed, it were these small influences that themselves typically accounted for the whole purchase decision. Next, how does the individual decision spread? Perhaps a critical question here is the extent to which the product is advertised by the company rather than by "the man who owns one." I have touched on this point before in connection with the positive influence of other s' stocks on buying. If automobile purchasing responds primarily to commercial advertising and display, a spurt in buying might be effected with great speed. Indeed, it could be virtually instantaneous throughout the area covered by the publicity campaign. Of course, it would not be instantaneous, because some people convince harder than others, and the frequency distribution of convinceability would space-out buying in a corresponding way. If, on the other hand, advertising by consumers were important-if the new ear in the neighbor's garage were strong argument for a new ear in mine-then the spurt in buying for the economy as a whole would build up cumulatively over a period of time. A geometry would have been added. I have suggested that we need to open up our studies of consumer behavior to the possibility of learning that buying and saving changes in response to factors that are not easily incorporated in multivariate analysis of time series. A triple attack is indicated. In addition to the study of time series, I suggest the selective sample 275

recurrent survey, and the depth studyof the genesis of buying decisions. What use are elaborate techniquesfor randomizing a sample at a given time when there is reason to believe that it will not be a random drawing over the period to which it is, in effect, applied? Since, at best, recurrent surveys must be spaced a year or more apart, depth knowledge of how decisions formulate and spread is necessary to interpolate behavior over the missing quarters or years.

COMMENTS by James Morgan University of Michigan

I find all the papers at this conference fascinating both for the variety of methodological problems, solved and unsolved, and for the substantive results. There are many possible research strategies in the analysis of cross seetian data, and I want to spend some of my time discussing these, but first let me discharge my obligation by some specific comments on the three papers. Hendrik Houthakker and John Haldi have thrown new light on the importance of initial stocks of a durable (ear) in influencing subsequent purchases. They did this by using first differences to eliminate what one might call a "positive personal idiosyncrasy correlation," between stocks and purchases. Some people like cars, like to buy them new and frequently. Others don't. If one had enough variables measured relating to individuals, these differences might be accounted for, but it isn't likely in most surveys. Fred May in a dissertation at Michigan using Survey of Consumer Finances data took account of this by using as a dummy variable in a regression "whether the present ear was bought new or u sed." At any rate, using each of their two years, 1952 and 1955, separately, Houthakker and Haldi found coefficients for initial stock (a value measure) of -.127 and -.160, in explaining "gross investment in cars" during the year. When however, they took the difference between 1955 and 1952 investment as the dependent variable, eliminating any unchanged individual differences, since these were the same individuals, the coefficients for initial stock (kept separate) jumped to -.363 and -.393, nearly three times as great. This indicates how much the depressing influence of stocks on purchases had been hidden by the spurious earrelation (positive) of both stocks and purchases with situational and idiosyncratic variables. Any model makes assumptions. The authors have assumed that the effects of income on investment in cars is the same for all individuals in one year (and linear), bu t at least potentially different 276

between years. They also assume that individual differences affect the leve! of expenditures (not the income regression coefficient), and in the same way e very year. The income coefficient was h,_gher for 1955 than for 1952 whether the years were taken separately, or combined using the change in investment as dependent variable. One could try other models and other assumptions, but the main result is a neat contribution and deserves applause. I should like to see the same analysis tried with one of the reinterview sets of the Survey of Consumer Finances, where the expenditure data would be for adjoining years rather than several years apart, and free from the unusual aspects of 1955, or in our Ford panel with five interviews over three years. It might also be worth considering whether people think of stocks in terms of value or age of the ear. The latter could be triedas a substitute variable. The findingthat the differences between 1952 and 1955 could not have resulted simply from "redistribution" but must have involved also some real changes in individual attitudes, preferences and behavior is similar to a finding by Jerry Miner in another paper to be given at this conference, with respect to the use of consumer credit. It also agrees with many other findings from Survey Research Center data. A warning is in order. Professor Houthakker and Haldi 's paper might appear to have provideda mechanism for eliminating noneconomic variables by assuming them stable over time. We must distinguish in our theories stable differences between people in their habits and ways of doing things, on the one hand, and changing differences in the attitudes and predispositions which result from changing interactions between the individual and his environment. The authors have shown that the effects of changes in initial stock are underestimated in a single cross-seetian study by earrelations between both stock and purchases and people's ear buying habits. Changing attitudes, however, can easily change the effects of income or of initial stock on purchases (or simply change purchases). The income effects in Houthakker and Haldi 's data change dramatically between 1952 and 1955, more than can be explained probably by the steel strike in 1952 or the changing credit availability in 1955. It is one thing to show that for individuals, changes in initial stocks result in changes in subsequent purchases, and another to argue that the re is a stab le stock effect over time, i. e., that one can prediet ear sales using only variables like income and initial stock. A small change in the average de si red stock can le ad to a !arge change in purchases, in true accelerator fashion. Next in ascending order of statistical camplexity is Vernon Lippitt's paper. He has a different problem, uses a different but still probably appropriate model: ~ = K + a. + !3; + Y; . • . . +u. I

i

1

1

277

where E is expenditure on household furnishings and equipment, I is income, K is a constant, and the a i, {3 i, yi etc. are tables of the additive effects of belongingto aparticular income, home ownership, age, family type or family size class. U is the unexplained component. By "tables" we meanthat each class of a characteristic, e.g., age, has a plus or minus number attached, indicating that one would expect the proportion of income spent on household furnishings to be that much greater or smaller than average because the family head is in that age class. The rnadel assumes that expenditures form rays through the origin of an E-I grid with slopes affected by the other characteristics of the family, i.e., that everytbing including income interacts with income in its effect on dollar expenditures, or put another way that things influence not dollar expenditures but the proportion of income spent. I think this is a good assumption for durables, and also used it after much exploration in my article in the American Economic Review (December, 1958). The rnadel also assumes that the effects of the various factors are additive, but makes no assumption about the scaling of the subclasses of each characteristic, e.g., about the coefficient for each age group. The method is very flexible in this way, using the data themselves to determine these coefficients so as to minimize the error in predieting anindividual's behavior. It is almostequivalent to assigning a dummy variable to all but one class of each of the factors, and inverting the matrix as in any regression problem. The results are slightly different, and easier to read, because K is the overall mean, and one has an expected deviation from the mean for each class of each factor, whereas the dummy variable regression approach lumps the effect of one class of each factor in with the eonstant term and expresses the effects of the other classes as deviations from the zero one. The regression approach uses more rnachine capacity but produces standard errors for the dummy variable coefficients (though there are problems with the meaning of such standard errors anyway). The Lippitt program can handie a large number of factors (10) and classes of each factor (10), and gets the results by an iterative process. One could not, with this much detail and this many factors, allow for non-linearity in the factors too (interactions), for this would involve using the detailed subgroups. For example, 7 age, times 8 family type, times 9 income, times 5 family size, times 5 ownership groups would make 12,600 subcells! One must cut this down either by assuming away interactions, or by using fewer classifications as I did, and as Robert Ferber in a paper at this Conference did. It should be noted that Ferber and I both found significant interadion effects. On the other hand, if one can get along without interactions, it is easier to use the results to make extrapolations on the basis of expected demographic changes in the population.

278

Having found the effects of the five factors he started with, Lippitt examines the residuals, with the warning that in so far as other factors are correlated with those he has already used, their effects will already have been removed from sight. The finding that those with stable incomes spent less than those whose income rose or fell after taking account of other factors, coincides with findings of several other investigators. The additivity assumption could be tested. It should be added that still another approach to the scaling of the factors was used by' Jerry Miner who used one body of data to build scales for each factor, then used the se scales as variables in a multiple regression. The data can then only shift the whole level up or down, or rotate the scale by providing it with a regression coefficient different from unity. As to Dr. Lippitt's "hopes" all we know about weighting from index number theory indicates that it would take dramatic shifts in population characteristics to change the final result appreciably. Worse still, we can expect more young married people and more old people, and the effects both on expenditures on durables and on the distribution of income, tend to go in opposite directions. The need for repeated surveys is of cour se obvious and we are currently seeking ways of continuing the Survey of Consumer Finances. As to Dr. Lippitt's "doubts," I agree, as I do with his needed improvements, though I might add that his needs l, 2, 3 for cars, and 5 are already met in the Survey of Consumer Finances. In summary, Dr. Lippitt's results are interesting, and I think his technique a very useful one that should be more widely used. Coming now to Professor William Peters' still mor e camplex analysis, we find it necessary to try to explain simply what he has done. Perhaps this will at least make it clear to me! Instead of as surning that expenditures, or change in expenditures or the expenditure-income ratio behave additively with respect to explanatory factors, Peters assumes only that E = a +bi and that either a or b or both can vary from subgroup to subgroup. He is specifically cancerned both with the measure of the differences, with the explanatory power involved, and with the statistical significance of the differences (in a's or b's). Then to make matters still more complex, he is using what is frequently called a "nested design," cities within regions, and education (or family size or home tenure) within cities. The n to answer the question whether cities or regions really differ apart from the effects of different average income levels, he reverses the rnadel and asks whether cities account for any of the residua! variance from inter-city regressions. A final camplexity arises from the fact that the analysis is based on subgroup means as the basic data.

279

The results are complex, too, of course, but it is interesting that for some components of expenditure, income is sufficient, and location (region-city) add nothing, whereas for others location does contribute to the explanation. Of course, it is still difficult to say whether the differences result from differences in tastes or in costs of living (prices of these and other items). To understand simply what added explanatory power means, conside r fitting a single regression E = a +b I to the subcell means, then fitting separate regressions for some population subgroups characterized by region, city, age. The total pooled unexplained variance will be smaller in the seeond case, and if it is sufficiently smaller to make the loss in degrees of freedom worthwhile, then the detail adds explanatory power. T here is a price for letting the data tell one so much, of course-the meaning of tests of significance becomes more doubtful. There is an even more serious problem relating to the nature of the basic data. That has to do with the nature of multi-stage stratified samples, and the interpretation of random sample statistics when applied to such samples. None of the papers at this Conference deal explicitly with this problem, and I only raise it here because the technique and variables u sed by Mr. Peters may make it a more important problem than usual. (See Leslie Kish, "Conference In tervals for Clustered Sample s," American Sociologi c al Review, 22, April, 1957, 154-165.} I am not referring to the use of group means as basic data-this raises problems of its own which I have discussed elsewhere, (American Economic Review, Dec. 1958, p. 600), but the effects of clustering and stratification. When one di vides such a sample on criteria that cut across the dimensions of stratification in the sample, the clustering may still make things look more significant than they are. One can think of this crudely as the sample having fewer independent observations (and the tests fewer degrees of freedom) than in a randoro sample. The more the clusters-counties, cities or areas, blocks-tend to have greater homogeneity within than between, the less real information. For instance, if one clusters two interviews to a city block, and wants to estimate the proportion who are non-white, the seeond interview in each block gives very little additional information-H could be predicted from the results of the first in this case. When one divides the sample on the same criteria as used in stratifying it originally, things are even worse. Within any one regionthere may be only 15-20 primary sampling points as against 66 for the country as a whole (using Survey of Consumer Finances as an example). Hence the sampling errors of measures within region are much larger relatively to the number of interviews. I do not profess to be able to solve these statistical problems, but I submit they are probably serious for region and city within region breakdowns. 280

Also, when one is using area breakdowns, why not actually measure local factors and use them as variables? One of the actvantages of area prohability samples, not sufficiently used by any of us, is that we know a great deal about the place where each respondent lives. We can pool locations, but use these facts as explanatory variableso For instance, in a political study at the Survey Research Center, it was found that the percent unemployed in the county in 1949 (from Census data) was related to attitudes toward government employment guarantees in a survey Conducted in 1954, particularly for white collar workers-the blue collar being mostly in favor anyway, and the professionals mostly against. Mr Peters did try city size, but one might try also an index of housing costs (the on e component of lo c al c ost of living indexes which re ally varies a lot), or percent employed in agriculture, or median income level (in 1949). Finall y, as to "proportions of variance explained," clearer distinctions need to be made by all of us between explaining the sample data and explaining the population. Take a simple example: o

Sum of Squares Total sum of s quares

2

~~yi

-

Between

~ (:;)

Within

~

Where the model is:

(~~Y) 2

ay 2

Mean square is an estimate of:

N-I

N 2

(~~y.) 1

N

- T i) 2 (y i ni

Y;

d/f

(~~Y;)

-

K-I

a/

N-K

a c2

+

2

ni an

2

N

y+Cl'i+Ui

a I32 + a E2

The variance is camposed of that attributable to differences between groups, and that remaining unexplained as (pool ed) variance within groups. The partitioning of the sum of squares in a sample, however, provides estimates given in the last column, where the iii is a camplex average number of cases per cell for which Ganguli has provided the following for mula in the c ase of unequal cell sizes: ni =_l_ [N _..!_ K-1

~ n

N ;=1

231

2]

1

Hence, using the proportion of the sum of squares called "between" as an estimate of the proportion of the population variance explained is always an overestimate. Robert Ferber in his paper for this Conference makes this distinction correctly, but the casual reader might easily overlook it. The reason why the above is true is that one is estimating the effects of some factor or explanatory variable from a sample. In going back to a population, the estimates of the parameters of the relationship may turn out to be wrong, explaining less of the population than they did of the sample. One could, of course, explain the data in a sample of 100 perfectly with 99 dummy variables, but this tells you little about how well these 99 dummy variables would prediet the rest of the population. This leads me to my remarks about strategy in the analysis of data. We have choices of two main types in analyzing cross-section data (or any data). One typ e of choice is the choice as to the amount of theory and of restrictive assumption which we impose. The other choice is to the relative emphasis on: significance tests measurement and estimation of parameters and relationships selection between alternative hypotheses in terms of their power in explaining the sample or predieting the population. These choices are not independent, of course. The more theoretical restrictions one imposes, the more he focuses attention on testing and measurement in a restricted sense, and the less he is able to be sure that there is not some alternative model which would explain reality as well or better. The more one goes to the other extreme to let the data speak for themselves-determining scales, and which variables and which interactions are to be retained by what the data show-the less meaningful tests of significance become. How many degrees of freedom are lost when one keeps looking at the data, trying things, building scales for non-measured variables out of the data? I don't mean to decry this seeond approach. Indeed, at the present state of our knowledge, our main problem is probably exactly this-seleeting among alternative hypotheses, and finding measurable variables that seem to be working in explaining behavior. We might think in terms of the following diagram:

282

Method

Principal Purposes

No Restrictive Assumptions or Theory (Many Hypotheses)

Assume Additive. Effects

Assume Linear or "Linear-inLogs• Relations

Assume scales

High! y Special Theory and Restrictive Assumptions

Test Theory Breaks Down

Significance Tests

Measurement: Estimation of Parameters

Selecting Am on g Variables and Theoretical Models (According to Their Predielive Power)

Cannot Tell About Alternatives, Not Iovestigated

The oval represents the feasible approaches, and research strategy consists of deciding on the lower left exploratory, item-selection, prediction-development strategy versus the upper-right testing of the implication of a highly specified theory plus some statistical assumptions. The papers of Daniere and Friend-Crockett are examples of "lower-left," that of Modigliani and previous work of Friedman of "upper-right" strategy. Lippitt makes more assumptions (about the absence of interactions) than Ferber, and Miner more (about scales) than Lippitt. There is of course always more chance of making one type of statistical error than the other. Since our measures are subject to errors, and our variables may not even be goodestimators of the theoretical constructs we want the m to represent, we are very like ly to find no relationship in the data when a real relationship exists.

283

It is for this reason that the "lower-left" strategy appeals to many of us. Sametimes, of cour se, we gradually im pose o ur restrictions with a certain low cunning after having laoked at some data. Jerry Miner had to use data to build the scales he u sed in his regressions, while Vernon Lippitt let the data build their own after assuming additivity. Robert Ferber didn't want to assume additivity so was forced to use fewer factors and fewer levels of each. Finally, there is a remaining problem that sometimes we do not, when we set up our investigative models, relate them clearly to a theory of behavior. We are using proxy variables for the most part. Milton Friedman has argued that income during the past year is not a good proxy variable for ability to spend, but is biased in particular and disturbing ways. He suggests "permanent income" as an instrumental variable. I submitthat this is only one example and per ha ps not the most important on e, of problems of proxy variables, and the i r relation to theoretical constructs. Take family size, for instance. This clearly affects the meaning of a given dollar income (however permanent) in terms of the marginal utility of money. It also makes a difference in the pre s sures to spend for the particular item under investigation. If one puts income and family size inta a regression as t wo variables, the positive effects of the latter on the need for, sa y, a larger ho me, and the negative effects onability to pay for it, may leave family size looking ineffective as a variable. If we want to know the effects of "real income" or of "family size," we ha ve no choice other than to impose so me sort of theoretical assumptions. (For a case with food, see S. J. Prais, "The Estimatian of Equivalent Scales from Family Budgets" Economic Journal LXIII, December, 1953, 791-810.) --

And not only do past and expected variations in income affect its meaning, b ut als o, probably, who earns it, and whether i t is property or wage income. A great deal of the difference between incomes of families in this country arises because of differences in the number of earners. Expectations about the permanence of the wife 's e m playment, allocation of her earnings to special purposes, and even the unwillingness of FHA and other lenders to consicter her income in granting loans, all affect consumer behavior. Implicitlybehind our simple "proxy variables in sheep's clothing" is a eausal theory that says that a consumer decision depends onsituational factors making the particularobject important,ability to spend the money in view of .competing needs, and attitudes and standards of living. Until we figure out how to relate the measured variables to the theoretical ones, the problem of "identification" re mains serious. We cannot always eliminate attitudes, standards, and "personality facto r s" by Houthakker and Haldi 's ni c e scheme, and may have to measure them directly, or figure out proxies for 284

them too, e.g., whether the people grew up in the rural south, or their verbal attitudes toward installment credit. To be even more specific, we can regard the individual as having certain fitable personality patterns, on which impinge changing externa! situations, producing both attitude change and changes in behavior. The Houthakker-Haldi technique can eliroinate the effects of interpersonal differences that don't change over time, but cannot deal with attitude change, learning, etc. (See Katona, George, "Attitude Change, Instability of Response and Acquisition of Experience," Psychological Monographs, 72, 1958.} So we need more explicit formulatian of a dynamic theory of consumer behavior that can deal with changing attitudes, and resulting changes in the way in which externa! situations affect behavior. Finally, we need mor e explicit recognition of the decisionmaking process as a group process in the family or spending unit. A. G. Hart has called the theory of consumptian a bachelor theory, and remarked that if one inserted "family" in place of "consumer" in much theoretical writing, it becomes gibberish. If decisionmaking roles are socially ordained, and decisions each delegated, then we can solve this problem simply. I suspect that it won't be that easy. (See my "Household Decision Making," in Consumer Behavior, Vol. IV, Nelson Foote, ed., forthcoming.) Economists are on the frontiers of new research possibilities, and we should take full advantage of them. Existing survey data vastly expand the possibilities which were once limited to financial record data collected for other purposes. The possibilities for including in future surv e y s variables whi ch are at l east proxy measures for theoretical factors never before testable makes them an extreme ly powerful tool for the development of economic knowledge.

REJOINDER AND SUPPLEMENTARY REMARKS by Vernon Lippett

Analysis of Family Expeditures Within Income Classes After the preceding paper was completed, a check was made on the variability of expenditures among families at different income levels and also on the accuracy of prediction of dollar expenditures for individual families. The variability of family expenditures is very great. There were families who spent nothing for house furnishings and equipment during the survey year in all but the top income class, and in most classes there were one or two families who spent more than ten times the average for the income class. As shown in the following table, the standard deviation for dollar 285

~

O)

(X)

L-------

390 222 155

1415 1022 549

$3000- 3999 $4000 - 4999 $5000 - 5999

$6000- 7499 $7500- 9999 $10,000 & over

279 613 1035

< $1000 $1000- 1999 $2000- 2999

Income Class

_c_

No. of Families

418.87 447.21 830.70

220.02 329.57 382.36

$ 44.80 75.69 159.32

Average Expenditure

467.1 438.2 1,737.7

250.0 382.5 426.4

121.5 207.0

$ 216.3

standard Deviation

1.12 0.98 2.09

1.14 1.16 1.12

4.83 1.61 1.30

Coefficient of Variation

431.9 438.2 1,507. 7

246.8 365.2 410.9

117.0 195.7

$ 215.5

standard Error of Estimate

Analysis by Income Classes of Variability of Dollar Expenditures for House Furnishings and Equipment, City Families in the North, 1950

15.4% 1.8% 26.7%

2.8% 9.2% 7.8%

2.2% 7.9% 11.0%

Explained as to Total Sum of Squares With in Clas s

expenditures varied greatlybetween income classes. The coefficient of variation exceeded l. O in all but one income class and reached values of 2.1 and 4.8 in the top and bottom income classes respectively. How well di d the results of the analys is of variance calculations prediet the expenditure of individual families? To answer this question dollar expenditures were calculated for each family from knowledge of the five main family characteristics. (The expenditure percentage computed from the effects of the five characteristics was multiplied by the income of each family to yield predicted dollar expenditures.) The difference between the calculated and actual dollar expenditures constituted an error of estimate who se variance was compared with the total variance of dollar expenditures for individual families. Such comparisons were made within the nine income classes, and the results are shown in the accompanying table. The percentage of the variance within each income class which was explained by the five main family characteristics ranged from 1.8 percent up to 26.7 percent in various income classes. Overall 26.3 percent of the sum of squares for individual family expenditures about the grand mean was explained by the five main family characteristics. This is a good result for such cross-section data, corresponding to a earrelation coefficient of over 0.5. This applies, of course, to the 5680 families in the sample which were used for determining the 34 eonstants representing the effects of the five family characteristics on the expenditure percentage. Comments on Remarks of Discussants With regard to the points raised by the discussants of my p ap er, there are only a few points which might well be clarified. Morgan comments at one point in his discussion that: "The model assumes that expenditure.s form rays through the origin of an E-I grid with slopes affected by the other characteristics of the family, i. e., that everytbing including income interacts with income in its effect on dollar expenditures, or put another way, that things influence not dollar expenditures but the proportion of income spent." Since income is one of the family characteristics which interacts with income, the predicted points for dollar expenditures versus income for families similar in all characteristics except income could well lie along a curve in the E-I grid, and need not form rays through the origin. I feel that this added flexibility of the model used here is a definite improvement over the model used by Morgan in his article in the AMERICAN ECONOMIC REVIEW, December 1958. At another point Morgan comments that: "One could not, with this much detail and this many factors, allow for non-linearity in 287

the factors too (interactions), for this would involve using the detailed subgroup s." The effects of various family characteristics maybe non-linear in the sense that the net effects plotted in Charts 1-5 do not yield straight lines. However, it is true that the predietar equation usedneglects interactions other than with income, i.e., it assumes that the effects of other family characteristics on the expenditure percentage are additive. If significance tests or exaroination of tabulateddata suggest that additional interadions are important, it would be well to determine their nature and to modify the model as necessary to account for them. One good way of exploring interactions is to campute the expenditure percentage or the dollar expenditure for each family from the initial predietar equation and the n to campute the error of prediction for each family. Finallythe errors of prediction maybe averaged for families classified in various two-way table s, in order to determine the patterns of interaction between various pairs of family characteristics. An example of such an exploration is contained in my book on "Determinants of Consumer Demand for House Furnishings and Equipment," pages 54-56. Morgan's point is well taken that the analysis of variance used in my research is equivalent to a multiple regression rnadel in which a dummy variable is assigned to all but one of the classes of each of the family characteristics. One solution can readily be converted into the other. The form with the eonstant term equal to R does seem easier to grasp and explain to other s. However, for purposes of camparing results of surveys taken at different times, with different values of R, it is sometimes desirable to define a "standard family" by specifying into whi ch c lass of each of the main characteristics that family falls. Then the convenient form of the predie to r equation has the expenditure percentage for the "standard family" as the constant, and the "net effect" is zero for the class of each characteristic which contains the standard family. Morgan questions whether normal shifts in distribution of families by a few main characteristics would appreciably affect aggregate spending. If one assumes the effects of the various family characteristics to be stable over time, the historical changes in the distributions of families by four main characteristics between 193536 and 1950 would have had an appreciable effect on the aggregate percentage of disposable income spent for house furnishings and equipment. (Calculations to this point are presented in pages 99101 of the book cited above, using net effects calculated from data in the 1935-36 BLS Study of Consumer Purchases.) I have reservations regarding Mrs. Mack's suggestion that the high expenditure percentage at low incomes and the low expenditure percentage at high incomes may be explained as an effect of recent income change for families in those i neo me brackets. Some surveys do not show this rise in the expenditure percentage at low incomes.

288

Also the averaging of residuals reported in this study suggests that the effect of income change is small and that it is upward both for rises and declines in income. Mrs. Mack, in particular, emphasizes the need to develop a dynami c the or y of consumer behavior. Be i ng interested primarily in forecasting consumer expenditures, I agree wholeheartedly with this emphasis. Her suggestion for conducting repeated surveys restricted to homogeneous groups of families may well be useful in this regard. I suspect that it would be desirable, however, to use several groups of families from different income levels and from different stages of the family life cycle. At least there is some suggestion that families at different income levels responded different! y to the changing market conditions between the consumer surveys conducted by the U. S. Government in 1935-36, 1941, 1950, and by Life Magazine in 1956 and the postwar Survey Research Center "Surveys of Consumer Finances" analyzed by Morgan in his article in the AMERICAN ECONOMIC REVIEW.

REJOINDER by William S. Peters

In general I have found the discussants' comments at this conference extremely interesting and penetrating, of equal value with the many stimulating papers. I have very little argument with James Morgan's and Ruth Mack's comments on my paper specifically. Professor Morgan points out that I have attempted to test differences among levels and among regression coefficients at the same time, as well as, in certain instances, to measure the explanatory power of the variables invoked. His comments on the problem of measuring the true sampling errors when examining differences that either run parallel to or cut across the stratification factors in a cluster sample are pertinent indeed. Surely when this is compounded with the use of group means, the real prohability levels to be attached to various significance ratios are samewhat in doubt. Still, as I have emphasized, the employment of a series of such tests appears to be the most practical means for filtering out, from the mass of data in the expenditure studies, the effective factors from among a camplex of influences which are of cancern to the investigator. As long as one specifies his series of questions in advance, is it re all y wrong to ask many questions of the data? The usual ans wer is that if we ask many questions, we are bound to find something statistically significant to talk about even where no differences in 289

the parameters exist. This is certainly true, but it is no worse than the chance of error we run in asking the same question of different sets of data, or different single questions of different sets of data. In any situation, we have to abide this chance of error to engage in any statistical inference whatever. I like Morgan's general observations on research strategy, and temperamentally prefer, as he does, a little more emphasis on theory-testing as opposed to casting about with the statistical fish-netto see what we can catch. However, I wonder if the economic geographers, de magrapher s, and other s interested in locational differentiation have given us theories in a form susceptible to empirical testing. Ruth Mack's primary interest, judging from her comments, is in change over time. More specifically, she points out how critical is the need to go be hind the aggregates which time series data represent, and seek an understanding of the casual factors in the myriad of buying decisions making for aggregate change. At the very least she wants some light shed on the process of consumer decisionmaking. I fully agree, and would suggest that spatial differences are an aggregate very much analogous to time changes. That is, we can ascribe a residua!, or otherwise unexplained variance component in an analysis to space or region much as we can to time, without having any nation of what specific factors are really responsible. Time and space, in this sense, are proxy variables for a host of more specific variables that we have failed to include. Now if the manner of interaction of these excluded variables does not change materially, the proxy variable ma y be an acceptable one for predictive or forecasting purposes. But this is just a hope, and in any event we will not learn anything from this kind of a predictive mechanism that will enable us to design better estimating tools for the future. We will not find what the really critical factors are by treating them in this aggregate proxy fashion. This is what my interest has really been in adapting variance and covariance methodology to the study of locational variation. By way of illustration, le t me summarize so me substantiv e findings from my p ap er, and some directions I think this kind of analysis suggests for those interested in tracing the process whereby individual differences are translated into aggregate locational differences. In the example employed, 49 cities in three regions and size of familyare the "treatments," and average income leve l of population subgroup s formed by the se facto r s is the regression variable. Four sub-classes as well as total furniture-home furnishings expenditures are treated individually. The following are the principal finding s: l. Gross locational variation in all expenditure sub-classes, in some cases significant both regionally and within regions, in other s only one of these aspects is significant. 290

2. Locational variation net of income only in equipment and in total furniture-home furnishings group expenditures. 3. A significant locational element in the inter-city income expenditure relationship in household textiles and in equipment expenditures, a reinforcing factor in the first instance and a dampening factor in the second. 4. One inter-city income expenditure regression without regard to region is satisfactory except in equipment and in total furniturehome furnishings expenditures. In these two cases, inter rather than intra-regional conditions are held responsible. It would be interesting to examine the extent to which the high expenditures in the west and low expenditures in the north in relation to income reflect price differences, quantity differences, or both. While we did not find significant regional differences in the various intra-regional income-expenditure regressions in the analysis described in the paper, I would suggest that the following differences observed fairly persistently in the several expenditure sub-classes both in this and two related analysis warrant same attention: l. Inter-city income expenditure regressions are frequently quite moderate in the north and fairly high in the west. 2. Despite the high inter-city regression coefficients in the west, we have found no instance in which this regression is significantly different from the residual regression. That is, no instance in the west has produced a significant locational regression component. 3. In the north, about one-half of the inter-city incomeexpenditure regression coefficient in household textiles is a purely locational phenomenon. These and other tendencies suggest an interesting kind of hypothesis. Do we have certain regions in which, despite greater variability in expenditure behavior among individuals and among non-locationally defined sub-groups, the way in which these individuals or groups combine locationally leads to less variability among groups at different locations? Do we have, for instance, individual conformity but aggregate differentiation locationally in the north, but individual disparity and aggregate sameness in the west? What would be reflected here are two sets of force s acting upon consumptian activities. First we have the economic and familyfactors conditioning individual consurning units ... income, size and type of family, etc. combined with social and family pressures to maitft:ain same normal or acceptable leve! of living. Second, we have a set of forces of a more aggregate sort tending to foster locational specialization for the carrying out of different kinds or levels of consumptian patterns. The latter are analogous to the patterns of occurrence of natural resources which dictate locational

291

specialization in productian activities. Along with the size and productive diversification of the metropolitan economy, do we have a process of consumer location which is consumptian oriented? Are areas be coming specialized to facilitate the pursuit of particular patterns of living and consurning? This very specialization acts as a deterrent to intra-area variability in spending behavior at the same time that it produces inter-area differences. An economy less highly specialized for consumptian will exhibit a diversity of expenditure patterns within areas. When consumers' decisions as to location are not made with a view to consuroption anticipations, net locational differences in expenditure patterns are reduced. As the growth and influence of regional metropolHan economies increases, we could well see at the same time a dimunition of any remaining regional differences and an increase in locational variation in expenditure patterns within regions. Thus we see an interaction between the conditioning effect of location and the process of consumer choice. To the extent that families select locations with a view to consuroption anticipations, examination of locational variation in expenditure patterns will reveal a result of the process of consumer decisions about consumptian rather than a series of limitations on consumer choice imposed by facto r s such as elimate, topography, custom, and culture. Perhaps we need to devote attention not only to how the consumer chooses at a given time among rather narrow consumptian alternatives, but how his consumptian preferences, in very broad terms, may become a factor that determines or conditions a number of other important decisions in the life eye le of the individual or family.

292

DEMAND RELA TIONSHIPS FOR FOOD* J e an Crockett University of Pennsylvania

One of the major purposes of this study is to campare and reconcile, insofar as possible, estimates of the income elasticity for food obtained from three types of data: time series of aggregates, cross-sectional analysis at a single point of time, and continuous cross seetians covering the same families at different points of time. A seeond major purpose is to utilize the B. L.S. 1950 data to examine the influence on food expenditures of a number of family characteristics other than income and to estimate the effects of distributional changes in these factors on aggregate food consuroption over time. A third aim is to combine the findings of the first two parts in developing a demand function for food in terms of real income, relative prices, distribution of relevant family characteristics such as age, race, and location, income change and perhaps other variables. A final aim is to examine, again using the B.L.S. 1950-51 data,l the effects of income and other family characteristics on expenditures for certain food subgroups. These four projects are only partially completed at the present time. Little work has been done on the last two and they will not be discussed here. Estimates of the Income Elasticity In general, time series relationships, when variables are deflated for price movements, give substantially lower values for the income elasticity than cross-sectional analyses for a single point of time. For example, using time series, Tobin gets a value of .27 for the United States;Z Wold and Jureen, values of .23 and .28

*This paper is based on research undertaken in connection with the Wharton School Study of Consumer Expenditures, lncomes and Savings. l Detailed items of food expenditure are avai1able only for a 7 -day period in the Spring of 1951. All other data are for the entire year 1950. ZJames To bin, "A Statistica1 Demand Function for Food in the U.S.A.," Journal of the Royal Statistica1 Society, Part Il, 1950, p. 134.

293

(depending on the period covered) for Sweden; 3 and Marguerite Burk .21 and .234 (depending on the period covered) for the United States. However, Girshick and Haavelmo, using a complete system of equations, get a marginal propensity to consume of .25 (plus a further effect for lagged income), which implies a very high income elasticity. 5 The author has obtained values in the neighborhood of .35 - .40, using regressions linear in the logarithms, and much higher values, using regressions based on changes in the logarithms. A longer time period is covered than in the studies cited above and price is treated as the dependent variable. Cross-sectional estimates of the income elasticity for food fall for the most part in the neighborhood of .50. Tobin obtains .56 for the United States in 1941; 6 Stone estimates .53 for the United Kingdom in 1938;7 Wold and Jureen obtain .51- .53 for Sweden in 1933;8 Faith Clark, et al. estimate .40 for the United States in 1948;9 Marguerite Burk obtains values ranging from .31 to .58 for the United states from several cross-sectional studies of which the earliest refers to 1935-36 and the latest to 1950.10 Differences among these cross-sectional estimates may be accounted for in part by differences in the definition of the variables, in the population groups covered, in the number of variables other than income which are considered and in the mathematical form of the regression. In part they may reflect behavioral shifts over time. The time series estimates are, of course, subject to criticism on the grounds of the small number of degrees of freedom available, the substantial correlation existing between real income and the relative price of food, the shifts over time in many factors not included in the regression (e.g., introduction of new products), and the possibility of least squares bias in estimates based on a single equation. The last objection does not appear to be serious, if relative price rather than quantity consurned is treated as the 3Herman Wo1d in association with Lars Jureen, Demand Ana1ysis, John Wiley and Sons, Inc., New York, 1953, p. 303. 4Marguerite C. Burk, "!neo me -Food Re1ationships from Time Series and C ros s -Section Surveys ," Proceedings of the American Statistica1 Association, Business and Eecnornie Statistics Section, 1957, p. 103. 5M. A. Girshick and Trygve Haave1mo, "Statistica1 Ana1ysis of the Demand for Food," Econometrica, 1947, p. 109. 6Tobin, op. cit., p. 119. 7Richard Stone, The Measurement of Consumer Expenditure and Behavior in the United Kingdom, 1920-38, Cambridge University Press, 1954, p. 327. 8Wo1d and Jureen, op. cit., p. 260. 9Faith Clark, et al., Food Consuroption of Urban Families in the United States, Agricultural Information Bulletin No. 132, USDA, 1954, p. 39. lOMarguerite Burk, op. cit., p. 104. 294

dependent variable and if it can be argued, as for example Fox has done, l l that quantity consurned depends largely on productian and this in turn depends for the most part on exogenous variables such as weather and on decisions taken in the previous year rather than current y ear incomes or prices. The n the two "independent" variables, quantity consurned and real income, may be said to affect the "dependent" variable, relative price, without being substantially affected by it. The ordinary cross-sectional estimates based on a single time point are subject to the criticism that many family characteristics which not only are likely to affect food consuroption but also are substantially correlated with income have not been held constant.l2 There is evidence that large families, white families, families living in !arge cities or suburbs in the North, and families with middle-aged heads, alltend to spend more on food than other farnilies at the same income level. Since these families are relatively more frequent at high than at low incomes, the failure to hold these factors eonstant may be expected to lead to unduly high estimates of the income elasticity. Two pieces of evidence may be offered in support of this contention. First, an analysis of income and consuroption for the same cross section of families at two different time points has been carried out as part of this study.l3 The results, which were reported at the September 1957 meetings of the American Statistical Association, lead to an income elasticity estimate of .23, quite in line with a number of the time series estimates but considerably lower than those obtained from cross seetians at a single point of time. This istrue not only in comparison with the cross-sectional studies by other authors mentioned above but also in comparison with single time point estimates from precisely the same body of data. 14 The sample used consisted of about 1,000 families from the consumer panel of the Market Research Corporation of America, which reported average weekly food expenditures as well as income and other family characteristics for the two years 1951 and 1953. The regression used related changes in the logarithms of 11 Karl Fox, The Analysis of Demand for Farm Products, USDA, Technical Bulletin 1081, 1953. 12 Another possib1e criticism is that 1east squares bias may be present in this case a1so, to the extent that some part of income, particu1ar1y that resulting from additiona1 workers, may be the result of high consumptian desires. 13Jean Crockett, "A New Type of Estimate of the lncome Elasticity of the Demand for Food," Proceedings of the American Statistical Association, Business and Eecnornie Statistics Section, 1957, pp. 117-122. 14For 1953, using a regression of comparable form, an income elasticity of .36 was obtained.

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food expenditureto changes in thelogarithms ofincomeand of farnHy size. It was shown that such a regression prevents distortion of the income elasticity estimate from the effects of family characteristics not included in the regression insofar as these remain eonstant between the two cross sections. However, the estimate obtained is subject to the shortcoming that changes in food e:xpenditure may lag behind changes in income so that the full effect of the observed income changes may not have been reflected in the observed e:xpenditure changes. 15 To minimize this difficulty, the income figures used were three-year averages rather than single y ear incomes, and cases of extremely !arge income change wer e omitted. A seeond piece of evidence as to the effect of omitted variables in distorting income effects is obtained by camparing the income slope obtained by Crockett and Friend, 1 6 in a linear mode! which takes account of a !arge number of variables other than income, with a gross estimate of the income slope holding fewer variables constant. Forwhite employee families in the income range $1 - 10 thousand the inclusion of family characteristics other than income lowers the income slope by about .03, implying a lowering of the income elasticity by about .10 at the income mean. This is a smaller decline than that implied by the MRCA data, but it is in the expected direction, and the point should be kept in mind that the technique of continuous cross seetians presurnably controls variation in many more variables (including tastes) than does the UNIVAC study. Still further evidence as to the distortion of income effects may be obtained from an intensive analysis of the relationship of food expenditure to income and other family characteristics from the B.L.S. 1950 data, using a model more closely tailored to the specific behavior of food expenditures than the Crockett-Friend mode!. Such intensive analysis is the seeond of the major goals of this study, and progress along these Iines will be reported below. Using grouped data, regressions were fitted of the form log F = a + b log Y + c log n, where F is family food expenditure (excluding alcoholic beverages), Y is family income after taxes and n is family size, for four subgroups within which the effects of race, city class, cash and 15 Results reported elsewhere in this volume indieate that in general families with a eontinuing rise in ineome spend less on food than eonstant ineome families. At low ineome, families with temporary ris e s in ineome spend less and those with temporary deelines spend more than eonstant ineome families. See lrwin Friend and Jean Croekett, "A Complete Set of Consumer Demand Relationships." 16op. cit.

296

deposits, age of head and tenure of dwelling unit were held relatively constant. For families with low cash assets (less than $500), estimates of the i neo me elasticity ranged from .51 to .53 for renters and from .43 to .46 for homeowners, averaging .48 overall. Results from the Crockett-Friend study imply that income elasticities for families with cash assets exceeding $500 (about one-third of the sample) are lower by about .lO at the income mean than for families with smaller cash assets. Thus a rough estimate of the average elasticity over all cash assets groups would be .45. This may be campared with the average value of .52 obtained when only age and family size are held constant. (See below.) On the basis of the available evidence it does not seem Iikely that the cross-sectional income elasticity can be lowered by much more than .l by holding eonstant other relevant family characteristics. In this case a substantial gap still remains between time series and most cross-sectional estimates. In part this gap may reflect differences in concept. The crosssectional expenditure elasticity incorporates quality shifts. If the Department of Agriculture index of food consumptian is used for time series analysis, some types of quality shifts (i.e., from cereals to meat) will be incorporated, while others (i.e., in the proportion of food eaten away from home or in same cases in the proportion eaten in highly processed form) are not incorporated. It may be that cross-sectional elasticities for food eaten at home would be mor e directly comparable than those for total food with the U.S.D.A. series. On the other hand, if deflated food expenditures (Department of Commerce series) are used, most quality shifts should be reflected. This series, however, covers a relativelyshort period and is subject to certain statistical difficulties not encountered with the U.S.D.A. series. It may be also that habit persistence affects time series estimates more strongly than cross-sectional estimates, both in the sensethat complete actjustment to a new level of income (even if it is expected to be permanent} requires same time and in the sense that little or no actjustment may be attempted to a leve l ofincome considered to be either abnormally high or abnormally low. In time series it is of course true that large differences in income are necessarily associated with !arge income change, while this is true in much smaller degree of cross-sectional observations. It is also conceivable that the proportion of times series variance in income attributed to changes in "permanent" income may be smaller than the proportion of cross-sectional income variance so attributed. If so and if food consumptian responds more strongly to income variation which is expected to be permanent than to that which is

297

not,l 7 then this consideration helps to explain the gap between the time series and cross-sectional estimates of the income elasticity for food. However, for certain other consumptian subgroups analogous assumptions would have the reverse effect of making reconciliation even more difficult. Effects of Family Characteristics Other than Income The seeond part of this study is cancerned with examirung, from the B.L.S.1950 data, the effects on food expenditures of family characteristics other than income. It should be emphasized that the same dangers are invalved in using a single cross seetian for this purpose as for the estimation of income effects-that distortion may arise from earrelation of the variables studied with others not included in the analysis. However, this problem is minimized in the 1950 data because information is available on a very large number of relevant family characteristics. Only in the case of cash assets isthere reason to believe that cross-sectional estimates of the effects are highly unreliable. Here it is not possible to contro! for the earrelation which presurnably exists between ramilies with high cash assets and those with high saving propensities. A number of advance indications of the effects to be investigated may be obtained from the pretest for the UNIVAC program described in the Crockett- Friend paper, 18 as well as from ~ priori considerations and earlier studies. The pretest indicates that family size strongly affects the level of food expenditure and may also affect the income slope. Age of head appears to affect level, with the middle-aged ramilies consistently spending more for food than either the younger or the older group, but does not affect the income slope. Occupation appears to affect neither level nor slope, while Negroes spend less but show about the same income slope as white families. Renters not only spend more on food than homeowners but show a steeper income slope than owners of relatively inexpensive houses. Families with high cash assets show a flatter income slope than those with low cash assets and actually appear to spend less than the low cash group at upper 17 Under the hypothesis that certain portions ofincome (say P) have different effects on consumphon than other portions (say T), it is clear that both cross- sectional and time series analyses will yield some kind of weighted average of the two effects. In this case it becomes desirable to estimate each effect separately. Uniess the T-effect is assumed to be zero, this is an exceedingly difficult proposition and one which would seem to require data of the continuous cross-section type with special emphasis on the changes in, and attitudes toward, particular components of family income. Isop. cit.

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income levels. While the first result may be credited, it seems probable that the seeond result reflects not a tendency on the part of high assets to discourage food expenditures at high incomes, other things being equal, but rather the heavyweight of high savers among high cash holders at all incomes-a factor which is overbalanced at low but not at high incomes by the stimulating influence of high assets on consumption. Income change-income expectation pattern seems to have little effect on either level or slope, except that the rather small "temporary increase" group shows a somewhat steeper slope than the others, perhaps because such an increase in income is more Iikely to go into durables (and so less Iikely to affect food) at low than at high incomes. The "continuing rise" group has a lower level of expenditure than the "constant income" group throughout. The effects of family size, race, city class, age of head and occupation have all been examined by computing separate regressions from frequency weighted grouped data, largely obtained from the published tables,l9 for different classes or subdivisions of these variables. The regressions used were linear in the logarithms, since on a gross basis this type of relationship provides good fits over income classes 2 - 9. Income class l was excluded for white families but not for Negroes. For the former, but not the latter, the class l points lie consistently and substantially above the Iine determined by the other income classes. The problems arising from the use of arithmetic means of grouped data in a logarithmic regression are recognized, bu t i t is believed that arithmetic means are approximately equal to the more appropriate geometric means in all but the highest income group. Family Size Logarithmic regressions of fa mily food expenditures on family income after taxes were computed for white families in each of three city classes-large cities in the North, large cities in the South, and large cities in the West-for each of six family size groups-one person, two person, three person, four person, five person, and six or mor e person families. Other city classes yielded samples too small for meaningful results. The income elasticities obtained for different family sizes were then compared. For family sizes 2 - 5, values were obtained ranging from .44 to .51 for !arge cities in the North, from .43 to . 55 for large cities in the South and from .46 to .53 for large cities in the West. Variation within this rang e show ed no consistent pattern, except that four person families showed the lowest elasticity in all three city classes, while three 1 9study of Consumer Expenditures, Incomes and Savings, Vol. III and Vol. XVIII, 1956 and 1957.

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or five person families showed the highest. The elasticities for one person families fell above the 2 - 5 person range for large cities in the North (.57) and in the West (.59), but not in the South (.46). The elasticities for six or more person families fell above the 2 5 person range for large cities in the West (.58) and in the South (. 70), but in the latter case the sample was so small (55 families) as to be highly unreliable. Since standard errors ran in the neighborhood of .03 - .07, it is clear that there is no conclusive evidence of differences in elasticity among the family size groups, though there is some slight indication that the elasticity may be a little higher for one person and for six or more person families than for the intermediate family sizes. 20 The hypothesis is then entirely tenable that the elasticities obtained for the various family size groups within each city class are independent estimates of a single elasticity appropriate to all family size groups. An im proved estimate of this elasticity may then be obtained from a weighted average of the estimates for individual family sizes. If the further assumption is made that the residua! variance about the population regression is the same for each family size, then the appropriate weight for each estimate is the sample size times the variance of the independent variable in the corresponding regression.2 1 Using such weights, the following elasticities were obtained for the three city classes: !arge cities in the North, .487; !arge cities in the South, .500; !arge cities in the West, . 504. Again it seems reasonable to assume that these are independent estimates of a single elasticity which is eonstant over the city classes considered, and an over-all weighted average of .495 was obtained. (For 2 - 5 person families only this average is .483.) Using the over-all elasticity estimate, eonstant terms were computed for each family size in each of the three city classes, in order to observe how the leve l of food expenditures varies with family size under the assumption that the elasticity is independent of family size. The variation of leve! with family size was quite similar for the three city classes; and, averaging over city classes, the shifts in leve! of the logarithm of food expenditure from family size l to each of the other family sizes were found to be approximately proportional to the logarithm of family size, the factor of proportionality be i ng about . 32. This implies that the family size effect on food expenditure is in fact linear in the logarithms and, taken in conjunction with the finding that elasticity differences are 20 Tobin's chart (James Tobin, op. cit., p. 118) strongly indicates a higher elasticity for his largest (open ended) family size group than for other family sizes. However, Faith Clark et al. (op. cit., p. 39), utilizing 1948 USDA data, do not obtain higher elasticities for the largest family size group. Zlsee Wold and Jureen, op. cit., pp. 225-6.

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not significant for different family sizes, justifies the use of the mode l (l)

log F = a + b log Y + c log n

It does not justify the use of the model

F y log - = a + b log n

n

since this implies a factor of proportionality equal to 1-b, or around .5. Race and City Class Regressions of the form (l) were then computed for white farnilies and for Negroes in large cities in the North and in all three city classes in the South. As indicated above, income class l was included in computing the relationships for Negroes but not for white families. Regressions were computed without a racial break for the remaining city classes. In this way a test was made both for the effects of race and for possible differences in behavior between families living in large cities and those living in suburbs or small cities. The following regressions were obtained (standard errors indicated in parentheses): Large cities in the North, white (2)

log F = 1.210 + .480 log Y+ .345 log n (.016) (.016) Suburbs in the North, all races

(3)

log F

= 1.084 + .508 log Y+ .369 log n (.020)

(.022)

Small cities in the North, all races (4)

log F

= 1.076 +

.497 log Y + .402 log n (.026) (.026)

Large cities in the South, White (5)

log F = 1.125 + .497 log Y+ .329 log n (.017) (.018) 301

Suburbs in the South, white {6)

log F = 1.353 + .440 log Y + .273 log n (.040) (.039) Small cities in the South, White

(7)

log F = 1.006 + .523 log Y + .326 log n (.029) (.029) Large cities in the West, all races

(8}

log F

= 1.132 +

.497 log Y+ .297 log n (.020) (.018)

Suburbs in the West, all races {9)

log F

= 1.096 +

.509 log Y+ .285 log n (.023) (.024)

Small cities in the West, all races (10)

log F

= 1.234 + .456 log Y+ .382 log n (.027)

(.029)

Large cities in the North, Negroes (11)

log F

= .964 + .549 log Y+ .246 log n (.034)

(.031)

Large cities in the South, Negroes (12)

log F = . 746 + .605 log Y+ .226 log n (.033) (.032) Suburbs in the South, Negroes

(13)

log F

= .497 + . 702 log Y+ .102 log n (.065}

(.062)

Small cities in the South, Negroes (14)

log F

= .737 + .625

(.078)

log Y+ .112 log n (.071)

The estimates ofincome elasticity range from .440 to .523 for the first nine regressions, bas ed either on whit e families or on all 302

races combined. In view of the standard errors involved, the differences are not significant even between the two extreme groups. The estimates of the family size elasticity range from .273 to .402, and in this case the difference between the extreme groups is clearly significant. The northern city classes show similar family size effects, which are in all cases larger than for the corresponding southern and western classes. In all cases the small cities show larger family size effects than the suburbs in the same region, and in two cases out of three larger effects than for large cities in the same region. Large cities and suburbs in the south and West appear to form a homogeneous group, showing very similar family size effects (.273 - .329), which are low relative to the other city classes. It will be observed that this group of city classes is characterized by relatively rapid growth in the preceding decade and relatively high pressure on housing facilities. A possible hypothesis is that the rise in housing costs associated with the addition of another family member (holding income constant) is high in such areas and that the increase in expenditure on food is correspondingly curtailed. On the other hand, in less rapidly growing areas, where housing is less tight, families may feel freer to expand food expenditures with an increase in family size. If it is assumed that the family size elasticity and the residua! variance from the regression (l) are in fact the same within the rapidly growing group of cities classes, a weighted average elasticity for this group is found to be .302, while on similar assumptions a weighted average for the slowly growing group is found to be .359. The difference is highly significant. On the other hand, uniess the city classes are grouped in this particular way there is no compelling reason to discredit the hypothesis that the family size elasticity is invariant over city classes. A weighted average of the family size elasticities over all nine city classes is found to be .335 and only one out of nine, small cities in the North, is significantly different from this at the 5%, though not at the l%, leve!. The difference between the northern city classes as a group and the southern and western group is significant at the 5% but not the l% level. The same finding applies to the difference between small cities and metropolHan areas. In order to compare levels of food expenditure for the nine city classes, it is convenient to retain the hypothesis that family size elasticities as weil as income elasticities are invariant. A weighted average over all nine city classes may then be computed for each type of elasticity, using weights which are proportional to the sampling variances of the estimates on the assumption that the residua! variance from the universe regression (l) is in fact the same for each city class. eonstant terms may then be computed for each city class, using the average income and family size elasticities. The following regressions are obtained: 303

Large cities in the North, white (15)

F== 1 5 .3 y.4885 n.3346

Suburbs in the North, total (16)

F == 14.8 y.4885 n.3346

Small cities in the North, total (17)

F == 13.7 y.4885 n.3346

Large cities in the south, white (18)

F = 14.2 y.4885 n.3346

Suburbs in the south, white (19)

F = 14.1 y.4885 n-3346

Small cities in the south, White (20)

F== 13.3 y.4885 n.3346

Large cities in the West, total {21)

F

= 14.0 y.4885 n·3346

Suburbs in the West, total (22)

F == 14.0 y.4885 n.3346

Small cities in the West, total (23)

F = 13.8 y.4885 n.3346

It will be observed that levels are almost the same for six of the city classes: small cities in the North, large cities and suburbs in the South, and all three Western classes. Levels are samewhat higher for large cities and suburbs in the North and a little lower for small cities in the south, per ha ps the only class where the home garden is still of some importance as a source of food. The latter group spends about 13% less, for the same income and family size, than the highest group, !arge cities in the North.

Turning now to the four city classes for Negroes, we find that none shows an income elasticity significantly different from the 304

weighted average (.591). The figurefor Negroes in !arge cities in the North (.549) is intermediate between the average for Negroes in the three Southern classes (.615) and the average forwhite families or all races combined in the nine city classes (.488), and is not significantly different from either. The average for Negroes over four city classes is quite significantly higher than the average for white families or all races over nine city classes. None of the family size elasticities for Negroes is significantly different from theweighted average over the four city classes (.219). There is same suggestion that the elasticities are lower in small cities and suburbs in the South than in !arge cities in the North or South, the difference being significant at the 5% level, but not at the l% leve!. The average elasticity for Negroes over the four city classes is quite significantly lower than the average for white farnilies or all races over the nine city classes (.335). Levels of food expenditures for Negroes in various city classes may be campared on the assumption that income and family size elasticities are in all cases equal to the weighted average over the four city classes. The following regressions are then obtained: Large cities in the North, Negroes (24)

F

= 6. 78 y.591 n.219

Large cities in the South, Negroes (25)

F= 6 . 24 y.591 n.219

Suburbs in the South, Negroes (26)

F= 6 . 40 y.591 n.219

Small cities in the South, Negroes (27)

F

= 6.23 y.591 n.219

Clearly there are no differences in level among the three southern city classes, and the southern level is only about 8% below that for Negroes in large cities in the North. In general, the levels for Negroes arewell below those forwhite families, the differences in !arge cities in either the North or South ranging from about 20%

305

for a five person family with an income of $2,000 to about 5% for a two personfamilywith an income of $4,000.22 A word is in order as to possible reasons why significant differences between races in income slope di d not appear in the UNIVAC pretest. There is first the purely technical point that the finding that Negroes have the same marginal propensity but substantially lower expenditure levels than white families implies a samewhat higher elasticity for Negroes at any given income. In addition the inclusion in the present analysis of the lowest income group among Negroes tends to raise the income slope, while the inclusion of the highest income group tends to lower the income slope for white families. In both cases a fair degree of curvilinearity is thus introduced inta the expenditure-income relationship between the natural (though not the logarithmic) variables. Finally the lower family size elasticity for Negroes tends to offset the higher income elasticity in the pretest situation where considerable variation in family size is still permitted. Age of Head The effects of age and occupation have also been studied by fitting regressions of the form (l) for various age and occupational groups. For age groups the following regressions were obtained (standard errors in parentheses): Age of head under 25 (28)

log F A ge of

(29)

he~d

= .969 + .543

(.033)

log Y+ .229 log n (.028)

2 5-34

log F = 1.084 + .510 log Y+ .289 log n (.017) (.015)

22some part of the difference in income elasticities between white and Negro families may arise from the fact that low income Negroes probably depend on food received without money expenditure (either as payment in kind for services or from home gardens) to a larger extent than do lo w in come w hi te f amilie s, w hi le s u ch food is likely to be unimportant for middle income families of either race. lt is also possible that dependence on food received in kind is greater for large Negro families than for small, and if so, this would contribute to the very small family size elasticity observed for Negroes, particularly in the South.

306

Age of head 35-44 (30)

log F= .904 + .562 log Y+ .316 log n (.025) ( .026) Age of head 45-54

{31)

log F = 1.099 + .510 log Y + .329 log n (.013) (.013) Age of head 55-64

(32)

log F = 1.092 + .512 log Y + .345 log n (.017) (.019) Age of head 65-74

(33)

log F = 1.210 + .472 log Y + .326 log n (.022) (.029) Age of head 75 and over

(34)

log F = 1.010 + .514 log Y+ .426 log n (.034) (.045) While the re is som e variation in the income elasticity e s timates,

it does not seem to follow any meaningful pattern. For four of the

age groups estimates of .51 are obtained, with samewhat higher values for the under 25 and the 35-44 group and a samewhat lower value for the 65-74 group. The weighted average (again using weights which are proportional to sampling variances under the assumption that residua! variance from the universe regression is the same for all age groups) is found to be .522; and only one group out of seven, the 65-74 group, is significantly different from this at the 5% level. The family size elasticity rises steadily with age, probably reflecting the lower incidence of small children in the larger farnilies as ag e of head rises. However, within the ag e rang e 2 5-7 4 the differences are quite small, with only the two extreme groups showing large deviations. A weighted average of .317 is obtained. Both extreme groups are significantly different from this average at the 5% level, and for the youngest group the difference is significant at the l% level. Since the two extreme groups are small and since it is believed that the differences in elasticity are due not to age effect per se but to failure to distinguish between small children and adolescentsor adults in the family size variable, the hypothesis has been retained that bothincome and family size elasticities are invariant with age; and levels for each age group have been computed using the average elasticities obtained. This proeecture gives rise to the following regressions. 30'1

Age of head under 25 F = 10.2 y.522 n.317

{35) Age of head 25-34

F = 10.6 y.522 n·317

(36) Age of head 35-44

F = 11.2 y.522 n·317

(37) Age of head 45-54

F= 11.6 y.522 n.317

{38) Age of head 55-64

F= 11.6 y.522 n·317

{39) Age of head 65-74 (40)

F = 11.1 y.522 n.317 Age of head 75 and over

(41)

F = 10.4 y.522 n·317

It appears that the effect of age on levels of food expenditure is parabolic. Expenditures for given income and family size are highest in the age range 45-64 and are 10% or more lower for very young or very old families. The above regressions make no attempt to control for the effects of race or city class. This may distort age effects to the extent that age is correlated with either of these variables. It will be observed that income elasticities run samewhat higher than in the race-area regressions, suggesting that the failure to control these variables leads to greater distortion of the income effect than the failure to control for age in the race-area regressions. In an attempt to control simultaneausly both age and city class (though not race), regressions by age were computed for large cities in the North only. Income elasticities ranged from .44 to . 51 and family size elasticities from .31 to .36 for families with age of head between 25 and 74. For the youngest families the income elasticity was substantially higher and the family size elasticity substantially lower than these ranges, while for the oldest families the income elasticity was slightly higher and the family size

308

elasticity strikingly high er. Both of the extreme groups invalved such small numbers as to be statistically unreliable, however. The average income elasticity over all seven age groups was .49 and this may be campared with values of .480 for white families and . 549 for Negroes obtained without regard to age. Occupation Regressions of the form (l) were computed for seven occupational groups for large cities in the North only. Income elasticities ranged from .48 to . 58 for six of the groups, but w er e much lower, .40, for the self-employed. Family size elasticities ranged from .29 to .32 for five of the groups but were samewhat higher (.35) for the self-emplayed and much higher (.44) for the not gainfully employed. To a large extent the not gainfully employed group overlaps the oldest age group, which was also characterized by a high family size elasticity. It is not clear whether this result is du e to the occupational or the age effect. If levels are computed for each occupational group using average values for the two elasticities-a questionable procedure since neither the self-emplayed nor the not gainfully employed group may reasonably be considered as homogeneous with the employee group-no substantial differences in level are found. Expenditures are highest for the self- employed and the clerical groupsand lowest for the not gainfully employed and the s killed workers, bu t in no case do the differences exceed 5%. Summary The findings as to the effects on food expenditure of family size, race, city size, age and occupation may be summarized as follows. Family size does not appear to affect the income elasticity at l east in the 2-5 person rang e. The re is som e suggestion that both one person families and very large families may show samewhat higher elasticities. The effect of family size on (the logarithm of) food expenditure is proportional to the logarithm of family size. These two findings suggest the use of regressions of the form (l) in studying food expenditure. City class does not affect the income elasticity significantly, bu t may affect the family size elasticity. For white families or all races combined, the latter appears to be substantially higher in slowly growing than in rapidly growing areas. There is same indication that it is higher in the North than in the South and West and higher in small cities than in metropolHan areas. Levels of food expenditure are found to be relatively high for metropolHan areas in the North and relatively low for small cities in the South. 309

Race appears to affect not only expenditure levels, but income and family size elasticities as well. The income elasticity is higher for Negro families than for white, while the family size elasticity and the level for given income and family size are both lower throughout the relevant portion of the income distribution. Age of head does not affect the income elasticity but the family size elasticity appears to be relatively low for the youngest and high for the oldest families. The effect of age on expenditure levels is parabclic with the age group 45-64 showing the highest expenditure for given income and family size. The self-employed show a clearly lower income elasticity and a somewhat higher family size elasticity than other occupational groups. The not gainfully employed, like the oldest age group, show a very high family size elasticity. Over-all differences in level are small among the occupational groups. Regressions confined to families with cash and deposits less than $500 and holding eonstant a number of other family variables show income elasticities for food in the range .51 - .53 for renters and in the range .43 - .46 for homeowners, suggesting a difference of about .08, depending on tenure. Family size elasticities ranged from .27 - .37 for renters (depending on city class) and from .40 .43 for homeowners. A paper presented at the National Bureau Conference on Demographic and Economic Change (Princeton, December 1958) ind.icates how the above information on ag e and race-area effects can be used, under theassumption that these effects remain invariant over time, to estimate the impact on aggregate food expenditure of expected shifts in the age and geographical distribution of the population. 23

23 Jean Crockett, "Population Change and the Demand for Food."

310

DEMAND FOR CLOTHING* Morris Hamburg University of Pennsylvania

The purposes of this paper are (l) to study movements in the income sensitivity of clothing expenditures in Urban U. S. du ring approximately the past 25 years and (2) to examine the influence of various family characteristics on this income sensitivity. Data from four different U. S. budget studies are primarily utilized in connection with the first purpose although same time series evidence is also presented, while information from the two most recent large scale budget studies are used for the second. Income Sensitivity of Clothing Expenditures Over the Past Quarter Century In an earlier paper, 1 it was indicated that one of the most striking aspects of consumer expenditure patterns in the post World War II period has been the persistent decline in the proportion of consumer disposable income which has been spent on clothing. Recently revised Department of Commerce data on clothing expenditures (including footwear, accessories, cleaning, repair and maintenance) as a percentage of disposable personal income show a decUne from 12.9 percent in 1948 to 9.8 percent in 1957. At no time during this period did the percentage in any year exceed that of the preeecting year. When expressed in terms of 1947-1949 eonstant dollars, the decline was not as sharp, dropping from 12.8

*This paper is based on research undertaken in connection with the Wharton School Study of Consumer Expenditures, Incomes and Savings. The author is indebted to Professor Irwin Friend for extremely helpful comments and advice. l Hamburg, M., 11 Some Experiments with Demand Relationships for Clothing," Proceedings of the Business and Economic Statistics Section Meetings (1957), American Statistical Association, Washington, D. C., 1958.

311

percent to 11.0 percent from 1948 to 1957 .z Actually, this downward movement is not merely a post World War II phenomenon because the corresponding percentages for the period 1929 through 1941 indicate a rather steady decline from 13.5 percent to 11.3 percent in current dollars and from 16.4 percent to 12.8 percent in 1947-1949 eonstant dollars. Time series multiple regressions 3 for the period 1929-1955 as compared to those for the period 19291950 indicated generally samewhat lower marginal propensities and income elasticities for clothing for the longer period reflecting the failure of real per capita clothing expenditures to keep pace with rising real incomes in the post-war years. The author concluded the earlier paper conjecturing that the shift in the income sensitivity of clothing expenditures suggested by time series data might be revealed by cross section studies subsequent to the 1950 BLS - Wharton Study as well. Since the 1956 LIFE Magazine Study of Consumer Expenditures is now available, comparisons of these data and the earlier cross section studies may be made as well as comparisons with time series results. At least with respect to income elasticities and marginal propensities to spend on clothing, the imprudent speculation concerning data not yet examined seems to have been verified. Frequency weighted logarithmic linear regressions derived from grouped data indicate a drop in the before tax income elasticity of urban family clothing expenditures from about 1.0 in 1950 to about 0.6 in 1956 (Table 1). The same figures were obtained (to one decimal place)for urban women's and girls' clothing expenditures (Table 2). This decline may be contrasted with the earlier constancy of the income elasticity of clothing expenditures as determined at the points in time between 1935-36 and 1950 when large scale budget studies were conducted. The after tax income elasticity for urban family clothingwas eonstant at 1.1 for 1935-36, 1941 and 1950while 2Subsequent Department of Commerce rev1s1ons raise the 1957 figures to 10.1 percent in current dollars and 11.3 percent in 1947-1949 eonstant dollars. However,the generalization concerning the post war decline through 1957 remains unchanged. The corresponding percentages for 1958 show an increase over 1957, with a figure of 10.3 percent in current dollars and 11.9 percent in eonstant 1947-1949 dollars. 3 The data used were annual observations of the following variables for both periods excluding the years 1942 through 1946: Per capita deflated clothing expenditures ( 1950 eonstant dollars; the clothing component of the BLS consumer price index was used as a deflator) Per capita deflated disposable income ( 1950 eonstant dollars; the consumer price index used as a deflator) Relative price of clothing (clothing component of the consumer price index divided by the consumer price index)

312

the corresponding figures for urban woments and gir1st clothing were 1.1 in 1935-36 and 1.0 in 1950. The before tax margi~ propensity of urban families to spend on clothing declined from 11 percent to 7 percent from 1950 to 1956 (Table 3). The corresponding figures for urban women ts and gir l s t clothing expenditures we re 5 percent and 4 percent (Table 4). In both cases cited, after tax marginal propensities increased somewhat or remained stable from 1935-36 to 1950 according to budget study data. Before turning to a study of variations in income elasticity by family characteristics, it seems appropriate to indicate briefly the nature of the computations and the samples used in the different surv e y s. The cross sectional marginal propensities and income elasticities discussed throughout this paper, except where specifically indicated to be otherwise, are population weighted regression coefficients computed from data grouped by income classes. For all but the 1956 LIFE Study, the original data were given by annual money income after tax classes. The LIFE data were classified by before tax income classes. A further complication is that the respondents in the LIFE Study we re not required to state total money incoine in dollar terms, bu t rather in el ass intervals. Average befor e taxineomes were notavailable, therefore, and had to be estimated.4 Since no data were collected in the LIFE Study on after tax incomes, comparisons between 1950 and 1956 findings have been based on coefficients u sing before taxincome or total consumptian expenditures as the independent variable. It was possible to compute s uch coefficients because in both the Wharton - BLS and Life studies, total consumptian expenditures were given by income classes and before tax incomes were given in 1950 and were estimated in 1956 by income classes. Regression coefficients computed from cross seetian data are summaries of microeconomic behavior. It would, of course, be desirable for the micro-unit to remain eonstant among budget studies. This is an ideal, however, and the inevitable differences are present in the four studies considered here. The budget study data reported on in this paper pertain only to U. s. urban families because these were the only data available for 1950 and similar figures were obtainable for the other periods. The definition of 4 Arithmetic mean before tax incomes were estimated by methods given in Leibenberg, M. and Kaitz, H., "An Income Size Distribution from Income Tax and Survey Data, 1944," Studies in Income and Wealth, Volume 13, National Bureau of Economic Research, N. Y., 1951, pp. 442-445. Briefly, the estimate for the under $2000 income class wasbased on alagnormal curve;the estimates for $2000 to $5000 classes were based on a straight line density function and those for income groups of $5000 and over upon a Pareto curve.

313

Table l. Results of Logarithmic Linear Regressions of Urban Family Clothing Expenditures on Urban Family Income for Four U. S. Budget studies a

1935-36

1941

1950

1956

a

-2.44

-2.36

1.17 -1.04b

0.52b

b

1.09

1.09

1.06 1.02b

0.61 b

G

0.19

0.00

0.11 o.oob

0.63b

(J b

0.04

0.00

0.01 o.oob

0.17b

r

0.99+

0.99+

0.99+ 0.99+b

0.90b

a

a All coefficients we re derived from frequency weighted regressions of grouped data. The extreme income groups were omitted in each period; i.e., in 1935-36 and 1941, families with after tax incomes of $500 and under and. $10,000 or over;.in 1950 families with after tax incomes of $1,000 and under the $10,000 and over; in 1956 families with before tax incomes of $2,000 and under and $1 O,000 or over. The se c hoi c e s we re dictated by the data available. bBefore tax income was used in calculating these figures. ln all other cases, income is after tax.

Sources: The data for Table s 1 through 4 we re obtained from the following sources:

1935-36

Family Expenditures in the United States, National Resources Planning Board, U. S. Government Printing Office, Wash., D. C., 1941.

1941

"Income and Spending and Savingof City Farnilies in Wartime," Bulletin No. 724 of the U. S. Bureau of Labor Statistics, U. S. Government Printing Office, Wash., D. C. 1942. Study of Consumer Expenditures, Incomes and Savings, Statistical Tables, Urban U. s., 19501951, Volume 18, University of Pennsylvania, 1957 . . Life Study of Consumer Expenditures, N. Y., 1957.

1950

1956

314

Table 2. Results of Logarithmic Linear Regressions of Urban Women's and Girls' Clothing Expenditures on Urban Family Income for Three U. S. Budget Studiesa 1935-36

1950

1956

a

-2.76

-1.30 -1.18b

0.34b

b

1.11

1.01b 0.97

0.61b

a

0.19

0.45 o.oob

0.75b

(J b

0.04

0.00

0.21b

r

0.99

0.99b 0.99

0.86b

(J

0.0~

aAll coefficients were derived from frequency weighted regressions of grouped data. The extreme income groups were omitted in each period; i.e., in 1935-36, families with after tax incomes of $500 and under and $10,000 or over; in 1950 families with after tax incomes of $1,000 and under and $10,000 and over; in 1956 families with before tax incomes of $2,000 and under and $10,000 or over. These choices were dictated by the data availab1e. bBefore tax income was used in ca1culating these figures. In all other cases, income is after tax.

"families" and "urban" differs from study to study somewhat as follows. In 1935-36 the family consisted of two or more persons living together as one economic unit having a common or pooled income and living under a common roof. Families receiving relief at any time during the schedule year were excluded. The urban sample included cities in all size classes and was supposed to represent all families living in cities with populations of 2500 or mo re. It covered geographic regions which included most of the U. S. Suburban families we re virtually unrepresented in the sample. The 1941 study oflncome, Spending and Saving of City Families in Wartime also included cities in all size classes above 2500 in population. Single consumers, however, were represented as well as families of two or more persons. This was true in the two subsequent budget studies as well. The 1941 study covered communities "so selected as to give proper representation to each (l) city-size group, (2) proximity to a metropolis (for cities under 50,000), (3) each region and state, (4) low, medium and high-rent cities, (5) cities of differing racial composition." The 1950 Study of Consumer Expenditures sample represented "all urbanized areas, c i ties 315

Table 3. Results of Arithmetic Linear Regressions of Urban Family Clothing Expenditures on Urban Family Income for Four U. S. Budget Studiesa 1935-36

1941

1950

1956

a

-2.37

-12,59

-25.92 -2.74b

25.71b

b

0.08

0.11

0.12 0.11 b

0.07b

(]a

9.21

4.96

35.3\ 10.14

9.84b

(]b

0.00

0.00

0.01 o.oob

o.o2b

r

0.99+

0.99+

0.99+ 0.99+b

0.90b

aAll coefficients were derived from frequency weighted regressions of grouped data. The extreme income groups were omitted in each period; i.e., in 1935-36 and 1941, families with after tax incomes of $500 and under and $10,000 or over; in 1950 families with incomes of $1,000 and under and $10,000 and over; in 1956 families with before tax incomes of $2,000 and under and $10,000 or over. These choices were dictated by the data available. bBefore tax income was used in calculating these figures. In all other cases, income is after tax.

and incorporated place s of 2500 or mor e inhabitants." The cities were stratified by various area characteristics correlated with consumer expenditure patterns. The family definition was quite close to that in 1941 including single persons as well as families of two or more persons. In 1956, the LIFE Study of Consumer E:xpenditures dealt with a sample of households in the U. S., both rural and urban. The data in this study, however, were not separated into rural and urban classifications. To obtain urban U. S. estimates for purposes of this paper, LIFE data for central cities and rest of metropolHan area for metropolHan markets with population of 500,000 or more, for the central cities of metropolHan markets under 500,000 and communities of 2500 or more were combined. Household rather than family e:xpenditures data were tabulated in this study. There was no test of pooling of income or e:xpenditures. The household is, therefore, much more inclusive than the family covering such non-related individuals as boarders, servants, friends, etc. The four budget studies also differed, of course, with respect to cyclical levels, relative price structure, product availability for 316

Table 4. Results of Arithmetic Linear Regressions of Urban Women 's and Girl s' Clothing Expenditures on Urban Family Income for Three U. S. Budget Studiesa 1935-36

1950

1956

a

-.22

-13.00 -2.85b

15.9Gb

b

0.05

0.06 o.o5b

o.o4b

(J

7.28

8.90 7.97b

7.44b

(]b

0.00

0,00 o.oob

o.olb

r

0.99

0.99+ 0.99+b

0.87b

a

a All coefficients we re derived from frequency weighted regressions of grouped data. The extreme income groups were omitted in each period; i.e., in 1935-36, families with after tax incomes of $500 and under and $10,000 or over; in 1950 families with after tax incomes of $1,000 and under and $10,000 and over; in 1956 families with before tax incomes of $2,000 and under and $10,000 or over. These choices were dictated by the data available. bBefore tax income was used in ca1cu1ating these figures. In all other c as e s, income is after tax. clothing and other goods and services, population distributional characteristics and other factors influencing the demand for clothing. It should be noted at this point that while this paper concentrates rather heavilyupon cross section information, several mathematical functions which integrated both time series and cross seetian data we re presented in the author's earlie r study of clothing expenditures. Perhaps it would be useful to indicate briefly the nature of some of the earlier exploratory work. Clothing expenditures as a whole (or women's and girls' clothing) were used rather than individual commodities, and e:x:periments were made with the derivation of various types of demand relationships. Single equation clothing demand functions using time series data for the periods 1929-55 and 1929-50 excluding the war years have already been referred to. Deflated clothing and income data we re u sed as well 317

as a relative price of clothing variable. Generally, the results indicated an income elasticity of about 1.00 and a marginal propensity of about 12% for the period 1929 through 1950 with a considerable drop if later post war years were added. The relative price elasticity of clothing did not differ significantly from zero. A simple complete structural system including a supply as well as demand function was al so derived. The system represented an integration of cross seetian and time series data. Basically time series data were used but a net marginal propensity to consume clothing as determined from the 1950 Wharton-BLS budget study was insertedfor one of the coefficients. Another experiment invalved an application to clothing expenditures of a method first used by Marschak for pooling time series and budget data. In general, all of the functions fitted through 1950 gave poor fits when extrapolated beyond that year because of the failure of real per capita clothing expenditures to keep pace with rising real incomes in the post war years. Relative price elasticities were generally unstable bu t did not usually differ significantly from z e ro. Income Elasticity Variation by Family Characteristics, 1950 Income elasticities for total family clothing and women's and girl s' clothing expenditures will now be considered by various family characteristics for 1950. Women's and girls' rather than men's and boys' clothing expenditures were studied because it was felt that the former were probably more sensitive to changes in status. The Wharton-BLS Study for 1950 included alarger number of classificatory variables than any previous consumer expenditures survey. The results given in this particular seetian indicate the effect on income elasticity of these variables considered one at a time. Such an analysis represents, of course, only a rueasurement of the gross effects of these variables. Thus far, however, very little is known even about these gross effects. Attempts to allow for the presence of other variables are made in subsequent analyses in this paper with particular reference to 1950 and 1956 data. In the tabulatians given in the preeecting seetian very high earrelation coefficients we re obtained for the various relationships studied. This result is, of course, not very surprising for grouped data. Both the highest and lowest income classes were excluded in those calculations. For all other calculations given in this paper, unless specifically indicated, only the lowest income class was dropped. In general, double logarithmic linear regression lines provided excellent fits for clothing expenditures and income data, when only this lowest class was excluded. The bottom income class

318

contained many families headed by retired or unemployed individuals and the proportion of income spent for clothing by families in that el ass was substantially high er than for other families. Income elasticities for the LIFE data are not shown here because of the necessity to estimate average income for every cell in the cross tabulations. It is felt that the required income estimates would be extremely tenuous. Elasticities for both 1950 and 1956 classified by v~rious social, economic and demographic variables are given at a later point, however, using total consuroption as a proxy variable for income. The cross sectional elasticities given in this section used as basic data averages of annual net money income and clothing expenditures by annual net money income classes for U. S. Urban families, deleting those with incomes of less than $1000. The effect of family size on these elasticities is exaroined first. Family size The changes observed in the income sensitivity of total family clothing expenditures and women's and girls' clothing expenditures were quite similar as family size increased. For both of these clothing expenditure classifications, income elasticity was lowest for single consumers, increased considerably for two person families, dropped off somewhat for three, four and five person families and was highest for the largest families with six or more persons. It is perhaps surprising that the elasticities are so low for single consumers. For women's and girls' clothing, however, there is a statistkal quirk that makes the figures not very meaningful. The basic clothing expenditures data for each income class are total expenditures for women's and girls' clothing divided by total number of single consumers, both male and female. Since the percentage of males tends to increase as the income scale is ascended, the averages for women's and girls' clothing expenditures are Table 5. Income Elasticity Coefficients for Clothing Expenditures by Family Size Classes, U. S. Urban Families, 1950 Family Size

Total Family Clothing Expenditures

Women's and Girl s' Clothing Expenditures

Single consumer Two persons Three persons Four persons Five persons Six or more persons

0.61 1.01 0.89 0.91 0.88 1.05

0.53 1.02 0.95 0.98 0.95 1.15

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deceptively low in the middle and higher income classes. Thus, the income elasticity coefficient tends to be very low. Although this statistical peculiarity does not apply for total family clothing expenditures, its income elasticity coefficient is also very low for single consumers. This suggests that clothing is not very high on the scale of priorities for single consumers as income is increased. It does not come as a surprise that the income elasticity for total familyand women's and girls' clothing expenditures for two person families is higher than for three, four or five person consumer units. The two person families are mostly married couples without children, while the three, four and five person families are mostly married couples with one, two, and three children. These two person consumer units increased their clothing expenditures by about the same percentage as income increased, moving from lower to higher income units. The families with one, two and three children did not place the same importance on clothing expenditures. Elasticity coefficients less than unity were observed for these familias for both clothing categories studied. The use of "hand-me-downs," particularly for the families with two and three children, would tend toward lower elasticities as campared with childless couples. The quite elastic clothing expenditures of the largest families perhaps reflect the idea that there is a practical limit to the number of times "hand-me-downs" can be utilized. A number of these larger familias contain adults in addition to the head of the family and his wife. Among these families, the ones with the higher incomes often attain these higher incomes through the earnings of the other adults. These adults, particularly if they are late teenagers or in their early twenties, might be expected to be relatively high spenders on clothing. Age of family head For both total family clothing and women's and girls' clothing, the income elasticity of expenditures increased in general as the age of family head increased (Table 6). Using the terms inelastic and elastic to denote income elasticity coefficients less than and gr e ater than unity, both categories of clothing expenditures we re inelastic for families whose heads were less than 45 years of age, about at unit elasticity for families whose heads were 45 to 55, and elastic for familieswhose heads were olderthan 55. The extremes were quite marked. The income sensitivityof total family expenditures for clothing is about two time s as high for the oldest families as campared to the youngest; for women's and girls' clothing, it is almost three time s as high. It may be noted that the very low slope coefficients for the youngest age group (under 25) and for single consumers (Table 5), no doubt, particularly reflect the intaraction of age and family size effects. The pattern observed probably 320

Table 6. Income Elasticity Coefficients for Clothing Expenditures by Age of Family Head Classes, U. S. Urban Families, 1950 Age of Family He ad

Total Family Clothing Expenditures

Women's and Girls' Clothing Expenditures

Under 25 25-35 35-45 45-55 55-65 65-75 75 and over

0.69 0.87 0.87 1.02 1.09 1.09 1.33

0.50 0.86 0.83 0.99 1.06 1.16 1.41

reflects the fact that the younger families at the earlier stages of the life cycle are most actively invalved in the acquisition of homes and associated consumer durables and therefore place a relatively low priority on clothing purchases as income rises. Also, the purchase of luxury type clothing whose income elasticity is high is quite limited in this younger group. On the other hand, in the older families especially where homes, furnishings and other durables are frequently wholly paid for and where children have married and have left the home, increased spending on clothing takes place as income increases. It might be noted that if the families with incomes of under $1000 had been included, the elasticities for the oldest families would have been much less elastic. The figures for the under 25, 65 to 75 and 75 and over age groups have the lowest reliability because of the small numbers of consumer units in high income classes. Occupation of family head Both total family clothing expenditures and s pending on w omen' s and girls' clothing were income inelastic for white collar worker families and income elastic for non-white collar worker families (Table 7). The lowest elasticities were observed for families of clerical workers while the highest elasticity recorded was for spending on women's and girls' clothing by families of skilled craftsmen. The lower elasticities of the "white collar" families reflect high levels of clothing spending at low incomes and relatively small increases in this spending as the income scale is ascended. The percentages spent on clothing by clerical and sales workers in the $1000-$2000, and $2000-$3000 net income classes (15.0 percent and 12.8 percent) we re higherthan for any other occupational group 321

Table 7. Income E lasticity Coefficients for Clothing Expenditures by Occupation of Family Head Classes, U. S. Urban Families, 1950 Occupation of Family Heada

Total Family j Women's and Clothing Girls' Clothing Expenditures Expenditures

Self -employed Salaried professionals, etc. Clerical and sales workers Skilled wage earners Semi-skilled wage earners Unskilled wage earners

0.89 0.93 0.89 1.11 1.01 1.13

0.95 0.90 0.70 1.26 0.99 1.12

aData for the "not gainfully employed" category are not shown because of the small number of observations in middle and upper income classes.

at the same income levels. The corresponding figures for low income "salaried professionals, etc." were al so high (13.3 percent and 11.5 percent). This would seem to indicate a relatively high minimum amount of necessary spending on clothing for "white collar" workers. On the other hand, clothing spending of "blue collar" workers was relatively low at low income levels, e.g., 10.6 percent and 10.9 percent for unskilled wage earner families with $1000-$2000, and $2000-$3000 net income, but was much higher than that of "white collar" workers at higher income levels, starting at about $5000. On the average, there were more earners in the se high income "blue collar" families than in high income ''white collar" families. In other words, many of the former families obtained their incomes by having more than one member at work. It is probable that the additional clothing spending required because of this multiple earner situation accounts to a large extent for the high levels of clothing expenditures by high income "blue collar" families.

The sensitivity of clothing expenditures to income changes is not so different between white and Negro families as one might perhaps have supposed (Table 8). The income elasticity coefficients are about the same for total family clothing expenditures, while the coefficient for white families was about 17 percent higher than for Negroes in purchases of women 's and girl s' clothing. However, for every income class included in the regression, the percentage of income spent on both total family clothing and w omen 's 322

and girls' clothing was higher for Negro than for white families. For white families with the highest incomes ($10,000 and over), both categories of clothing spending dropped off to lower percentages of income than for any other income class. Fornegro farnilies with the highest incomes these percentages were still very high, running seeond only to those of the families with $7500 to $10,000 net income. It appears, therefore, that Negro families at all levels of income studied spent more on clothing than did white families. Table 8. Income Elasticity Coefficients for Clothing Expenditures by Race Classes, U. S. Urban Families, 1950 Race

Total Family Clothing Expenditures

Women's and Girls' Clothing Expenditures

White Neg ro

1.05 1.04

1.02 0.87

Home tenure Among home-owners, the income elasticity of clothing expenditures was lowest for families which had purchased a home during the year of the study (Table 9). Elasticities were highest for farnilies which had bought their homes prior to 1946 and intermediate for families which had bought homes from 1946-1949. This was Table 9. In come E lasticity Coefficients for Clothing Expenditures by Home Tenure Classes, 1950 Family Home Tenure Status

Total Family Clothing Expenditures

Women's and Girl s' Clothing Expenditures

0.80 0.88 1.01 1.08 0.92

0.75 0.84 1.04 1.09 0.92

Owner at end of rear; renter earlier Bought home in 19502 Bought home from 1946-1949 Bought home before 1946 Renter at end of year

1 This class pertains to farnilies which were horne owners at the end of 1950, bu t we re renters earlie r in that y ear. 2 This class pertains to farnilies which bought hornes in 1950 and were also horne owners earlier in that year.

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t rue for both total family and wo men' s and girl s' clothing expenditures. These findings are consistent with the nation that the most recent home purehasers are more actively invalved in the purchase of consumer durables and homefurnishings than are home owners of longer standing. Therefore, the more recent home buyers, passing from families of low income to those at the upper end of the income scale, are less apt to exhibit differences in clothing spending which are proportionate to income differences than are ho me owners of longer tenure. All persons passess stocks of clothing items. Upon purchase of a home, however, many families must acquire for the first time various durables and homefurnishing item s that have come to be look ed upon almost as necessities. Since theselatter items generally take precedence, the purchase of clothing by new home buyers is perhaps basically of a replacement nature. There would then be a tendency for relativelylittle variation along the income scale in such purchases. At least, it seeros reasonable that there would be less variation than for families which had acquired stocks of the aforementioned durables and housefurnishings. In come elasticities of clothing spending for renters we re higher than for the most recent home owners, but were lower than for other home owners. When average propensities to spend on clothing were considered, however, renters we re the highest spenders on total family clothing and we re tied with ho me owners of longest tenur e for highestspending on women's and girls' clothing. Among home owners, the pattern for these average propensities was the same as for income elasticities with the figures increasing as length of home tenure increased. Education It might perhaps be expected that the income elasticity of clothing expenditures would decrease as we pass from groups of farnilies headed by individuals with relatively little education to farnilies in which the head has a greater amount of educational training. That is, it can be argued that infamilies where the head has only a grammar school education, higher income does not tend to be reflected in expenditures on the home and its furnishings, on education, travel and similar item s to the extent that is true for families headed by individuals with more education. Therefore, the former type of family with high incom~ tends to maintain about the same or even a slightly higher percentage of income spent on clothing than the analogous lower income family. Income el as ticity coefficients for 1950 did show this decUne up through the level of college graduates (Table 10}. For families where the head has some postgraduate college education, however, the elasticities for both

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clothing classifications rose above those of all but the under 8 years of education group. Average propensities to spend on both categories of clothing, however, generally vari ed inversely with amount of education, with the lowest percentagas appearing in the "over 16 years" class. As a generalization, therefore, these data suggested that the precedence attached to clothing spending tended to decline as education increased. Table 10. Income Elasticity Coefficients for ClothingExpenditures by Education of Family Head Classes, U. S. Urban Families, 1950 Education of Family Head

Total Family Clothing · Expenditures

Women's and Girl s' Clothing Expenditures

Under 8 years 9 through 12 years 13 through 16 years Over 16 years

1.09 0.99 0.87 1.00

1.12 0.90 0.84 1.04

Level of mortgage debt When classified by level of mortgage debt outstanding, urban home owner families revealed relatively small differences in income sensitivity of clothing expenditures (Table 11). The debt groupinga were different levels of first mortgage debt outstanding as of January l, 1950. For all debt classes but one, the income elasticity coefficients ranged only from 1.02 to 1.15. No particular importance is attached to the exception, the $1000-$2000 mortgage debt class, where the coefficient was 1.4. There was a slight suggestion of a decline in the coefficients beyond the $1000-$2000 class. The general effect of debt on consumer behavior is, of cour se, by no me ans el ear. Perhaps the above findings, how ev er, are in one particular a bit contrary to a priori expectations. Farnilies with less than $1000 of mortgage debt were older, on the average, than other families and had often reduced their debt over a longperiod of years. Considering the families with debt of $1000 or more, perhaps we would have expected income elasticities to have increased as we ascended the debt scale rather than the suggestion of a declin e. As we move to high er debt classes, the burden of debt and the consequent contractual repayment requirements would seem to weigh increasingly heavily upon the lower income classes. If clothing were one of the expenditures groups which suffered because of this pressure, the regression lines would be depressed increasingly at the lower income end of the scale, making 325

for increasing elasticity coefficients as debt increased rather than the observed suggestion of a decline. Table 11. Income Elasticity of Clothing Expenditures by Beginning of Year Level of Mortgage Debt Classes, U. S. Urban Home Owner Families, 1950 Level of Mortgage Debt

Total Family C1othinga

Non e $1-$1000 $1000-$2000 $2000-$3000 $3000-$5000 $5000-$7500 $7500-$10,000 $10,000 and over

1.05 1.13 1.39 1.15 1.09 1.09 1.11 1.02

aBecause of technical problems in obtaining women's and girls' clothing spending data by the classifications shown in Tables 1114, only income e1asticities for total family clothing are shown.

Percentages of income spent on clothing were virtually eonstant among debt classes with the entire range of variation running only from 10.6 to 11.3 percent. In summary, therefore, the tentative conclusion would seem to be that mortgage debt had relatively little gross effect on income elasticities for clothing spending. Income change The effect of past income change on consumptian has beenfrequently discussed in economic literature. The usual reasoning is that because of a stickiness of consumptian habits, there is a lag in actjusting consumptian to new levels of income. Therefore, farnilies experiencing declines in income t end, according to this reasoning, to have high consumption-income ratios and families with increases in income tend to have low ratios. There are no definitive conclusions on this point with regard to average elasticities and very little work has been done on the differences in income elasticity of spending of these groups. Much has been written recently which takes the point of view that whether the income change is regarded as "transitory" or "permanent" is the basic determinant 326

in the family's consumptian behavior. In Table 14, families have been combined into classes which permit an examination of the effects of income changes of differing degrees of permanency on clothing spending. Here, however, we are simply cancerned with the differences in income elasticity of clothing spending by income change groups. Families in the Wharton - BLS survey were asked whether their incomes in 1950 were higher than, lower than, or the same as in 1950. Disregarding the "didn't know" class, the farnilies which experienced an increase in income had the lowest clothing income elasticity coefficient (Table 12). The nattening of the regression line for this group implies that among families experiencing increases in income, the spending on clothing of the high income families was a samewhat lower percentage of income than that of families with lower incomes. The clothing elasticities for families whose incomes remained the same and for those whose incomes declined were about the same, at a level about ten percent higherthan for the families which had experienced increases. Table 12. Income Elasticity Coefficients for Total Family Clothing Expenditures by Income Change Classes, U. S. Urban Families, 1950 Income Change Classes (1949 to 1950)

Total Family Clothing

Income increased Income about the same Income decreased Didn't know

0.95 1.06 1.05 0.92

Income expectations Turning now to expectations with regard to income, we find families in the Wharton - BLS survey classified as to whether they expected a decrease, an increase, no change in income from 1950 to 1951, or didn't know. The received theory on the spending propensities of such groups is that families with anticipations of income increase will have greater tendencies toward current spending than those expecting declines in income or than those with very uncertain expectations. Insofar as clothing expenditures are concerned, the group with the highest income sensitivity was the one that expected income to remain about the same (Table 13). This group 's e lasticity coefficient was about 10 percent higher than that of f amilies expecting an increase or who we re uncertain about the i r expected incomes. The group which expected income declines had an even slightly lower coefficient than the latter two groups of families. 327

Table 13. Income Elasticity Coefficients for Total Family Clothing Expenditures by Income Expectation Classes, U. s. Urban Families, 1950 Income Expectation Classes (1950 to 1951)

Total Family Clothing

Income expected to decrease Income expected to be about the same Income expected to increase Didn't know

0.94 1.07 0.98 0.98

The caveat must again be made that generalizations from such gross associations must be approached with caution. Upon closer examination, it appears that the proportions of families with expectations of eonstant incomes is highest in the income groups below $2000. There are a large number of retired individuals and pensioners in these classes. Although the bottom income class (under $1000} has been dropped in all of these calculations, the lower clothing spending of the older group tends to depress the regression line at the lower end of the income scale. This factor alone could explain a substanhal part of the difference in the observed coefficients. Constancy of income The two foregoing breakdowns of families by income change and income expectation were combined to yield a single classification according to permanency of income over a three year period 1949-1951. For example, families whose incomes in 1950 were reportedas the same as in 1949 and whose expected incomes in 1951 were the same as in 1950 were classified as eonstant income consumer units. The definitions of the other groups are indicated in Table 14. Families with eonstant incomes over the three y ear period had the highest income elasticity of clothing s pending (1.09). Consumer units which had experienced permanent declines in income had by far the lowest coefficient for all groups considered (0.77). An interesting pattern of expenditures emerged depending upon whether families anticipated their changes in income to persist. For example, families which experienced a temporary decline in income (decline from 1949 to 1950, anticipated increase from 1950 to 1951) had the seeond highest elasticity (1.04) of the groups considered, substantially high er than for the permanent decline el ass. This implies that in the middle and upper income classes if the decline in income was viewed as temporary, s pending on clothing continued at average levels about as high as for lower income families. On 328

Table 14. Income Elasticity eoefficients for Total Family elothing Expenditures by eombined Past Income ehange and Income Expectation elasses, U. S. Urban Families, 1950 eonstancy of lncomea

Total Family elothing

Temporary increase Permanent increase eonstant eonstant with anticipations of change Permanent decrease Temporary decrease

0.91 0.96 1.09 0.98 0.77 1.04

aFamilies were classified as follows by their income change from 1949 to 1950 and the i r statements ofincome expectation for 1951: Temporary increase - Income in 1950 higherthan in 1949; income in 1951 expected to be lower than 1950 or didn't know. Permanent increase- Income in 1950 higher than in 1949; income in 1951 expected to be higherthan or the same as income in 1950. Constant- lncome in 1950 the same as in 1949;income in 1951 expected to be the s am e as in 19 50. Constant with anticipations of change - Income in 1950 the same as in 1949; income in 1951 expected to be higher than or lower than in 1950 or didn't know. Permanent decrease - Income in 1950 1ower than in 1949; income in 1951 expected to be 1ower than or the same as in 1950. Temporary decrease- Income in 1950 lower than in 1949; income in 1951 expected to be higher than in 1950 or didn't know. These clas sifications follow those used by Katona and Klein in Katona, G., "Effect of Income Changes on the Rate of Saving," Review of Economics and Statistics, Vol. 31, May, 1949, pp. 95103 and Klein, L. R., Estimating Patterns of Savings Behavior from Sample Survey Data, Cowles Commission Papers, New Series, No. 55, pp. 443-445.

the other hand, if the decline in income was viewed as being more permanent, spending on clothing by the high income receivers was cut back quite sharply. This suggests the interesting notion that the middle and upper income classes when faced with rather permanent advers e movements in their incomes viewed clothing spending as an expendable item in their fight to maintain standards of living. If the decline was viewed as merely "transitory," however, spending on clothing continued unabated. 329

On the other hand, the differences in the income sensitivity of clothing spending between families which experienced temporary or permanent increases in income we re not nearly so marked. The elasticity of clothing spending for both groups of consumer units was samewhat below unity. Again, the point made above about the values of middle and upper income families during periods of income change seemed to be operative. Since the families with temporary increases in income had a slightly lower coefficient than did families with permanent increases, it would appear that the higher income families who anticipated declines in income cut back on clothing spending. 1950-1956 Camparisans

The purpose of the ensuing seetian is to draw some camparisons between demand relationships for clothing in 1950 and 1956. All of the demand functions presented thus far have used some form of income as the independent variable. In this section, elasticity coefficients are based upon total consumptian expenditures rather than income. It was felt that this choice of independent variable was necessary in order to make meaningful comparisons between the 1950 and 1956 data. The difficulty of estimating average income for all income classes within each family characteristic for 1956 has been referred to previously. The argument for the use of total consumptian expenditures as the correct regresser for elasticity and propensity coefficients may, of course, also be made on theoretical grounds. It has been maintained that the income accruing to a family or household in a particular year is not a very appropriate index of the family's level of living nor is it as good a determinant of the distribution of family expenditures among commodities as total consumptian expenditures.5 Another point of view isthat permanent income status for a group of families may be more properly measured by total consumptian expenditures than by an income variable. As a matter of fact, Friedman, when dealing with grouped data, would by explicit choice calculate propensities and income elasticities for commodities from averages of total expenditures and average expenditures on the commodities by "measured income" classes. b The averages are viewed as estimates of the mean permanent components of the consumptian of the commodity and of total consumption. For 5 see e.g., Prais, S. J. andHouthakker, H. S., The Analysis of Family 6 Budgets, Cambridge University Press, 1955, pp. 80-81. Friedman, M., A Theory of the Consumptian Function, Princeton University Press, Princeton, 1957; pp. 207-208.

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convenience of reference, such elasticity coefficients are referred to in this paper as "expenditures elasticities." Some comments have already been made on the difficulties of obtaining comparability between estimates made from the 1950 and 1956 data. Additional difficulties arise in comparing expenditures elasticities or percentages of total expenditures allocated to clothing. The definitions of clothing expenditures appear to be very similar in the two studies but the definitions of total expenditures are not entirely parallel. "All goods and services" expenditures in the 1956 LIFE Study differ from the comparable 1950 Wharton BLS data on "expenditures for current consumption" by the exclusion of spending on education and travel accommodations and the inclusion of home improvements and mortgage repayments. The percentages of total expenditures going to clothing appear to be uniformly too high in the LIFE data, probably because total expenditures are too low. An indication of this is given by earnparisons with Department of Commerce aggregates. After a rough actjustment for the more important conceptual d1fferences, blown up LIFE figures for average expenditures on all included goods and services account for about 86 percent of Department of Commerce personal consuroption expenditures. 7 The Wharton - BLS 1950 Study shows adjusted estimates for survey urban expenditures for current consuroption excluding housing to be 98.6 percent of the corresponding national accounts figure.s Another indication, perhaps, is given by a comparison of survey percentages of clothing to total expenditures with the analogous Commerce figures. The LIFE figure of 12.0 percent contrasts with the Commerce number of 11.0 percent. 9 The LIFE percentage for Urban U. S. alone is even higher - 12.7 percent. On the other hand, a similar camparison of the 1950 Wharton - BLS (Urban) and Commerce figures gives 11.5 percent and 12.2 percent, respectively. It seeros li.kely that comparisons of average propensities between two budget studies would not be as reliable generally as comparisons of income el asticities or marginal propensities. The LIFE income distribution has the deficiency to which almost all consumer surveys are subject of including too few families 7Mortgage payments and borne improvements must be added to the Department of Commerce figures while imputed rents on owneroccupied dwellings, imputed expenditures on the services of finandal intermediaries, education, trave l accommodations, and consumption expenditures on nonprofit institutions must be subtracted. Sstudy of Consumer Expenditures, Incomes and Savings, Statistical Tables, Urban U. S., 1950-1951, Volume 18, University of Pennsylvania, 1957, pp. xxxviii and xxxix. 9The Department of Commerce figure is clothing, accessories and jewelry as a percent of personal consumption expenditures.

331

in high income groups. A comparison was made, therefore, of the expenditures elasticities, marginal and average propensities obtained for total household clothing expenditures when each of three other income distributions were assumed for 1955)0 That is, the proportions of families or households falling in the different income classes we re u sed as weights in the calculation of the e lasticities and propensities. Income distributions of the Federal Reserve - University of Michigan Survey of Consumer Finances, U. S. Bureau of Census Population Reports and the Department of Commerce National Income Unit were used for this purpose. In all cases, total expenditures was the independent variable. The results are given in Table 15. The differences in the coefficients obtained using the four weighting schemes were rather small with the exception perhaps of the difference arising from the rather low expenditure elasticity when Department of Commerce weights were used. The differences between the lowest and highest coefficients were 3 percent for the marginal propensities, less than one percent for the average propensities and about 8-1/2 percent for the expenditure elasticities. The LIFE expenditure elasticity (1.143)was approximately 8 percent higher than the figure using Commerce weights (1.057). The Commerce income distribution is perhaps the most accurate because of its actjustment of survey data on the basis of income tax and other externa! information. It is not possible to generalize about the effect of these income distribution differences on the coefficients computed for subclassifications of the LIFE sample. The above camparisans sugges t, however, that the set of weights used is not particularly important for marginal and average propensities and that elasticities calculated from the LIFE data using LIFE frequencies as weights are samewhat on the high side. Actually, of course, for some classifications of the LIFE data, the only weights available we re the LIFE frequencies. In all of the comparisons which follow, LIFE frequencies have been used as weights for coefficients computed from the 1956 LIFE expenditures data. Life cycle effects Much attention has been devoted recently in sociologkal work to the influence of the stage of a family in its life cycle upon various types of behavior patterns. Very little analytical work, however, has been done on life cycle effects on the consuroption of 10 The LIFE tabulatians provide 1956 expenditures data by 1955 income classes. Therefore, the before tax income distributions for 1955 were used in this comparison.

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Table 15. Expenditures Elasticities, Marginal and Average Propensities to Consume Clothing, Using the Frequencies of Four Different Income Distributions as Weights, U. s., 1956 Source of Income Distribution

Marginal Propensity

Average Propensity

Expenditure Elasticity

Life S.C.F. Census Commerce

.133 .136 .134 .137

.119 .120 .120 .120

1.143 1.147 1.131 1.057

Notes: l. For discussion of definitions of income units, see Census reference cited for row 3 of Wharton school Study of Consumer Expenditures, Incomes and Savings, Vol. 18, p. xxxiv. 2. The marginal propensities and expenditures elasticities were calculated from frequency weighted arithmetic straight line and double logarithmic regressions, respectively. In all cases, total expenditures was the independent variable. The average propensities are the ratios of clothing to total expenditures for all households combined. Sources: Row l. Distribution of "households." Alfred Politz Research, Inc. Characteristics of U. S. Dollar Markets, Conducted for Life, July, 1957. Row 2. Distribution of "families" (including singleperson units), Federal Reserve Bulletin, August, 1957, p. 892. Row 3. Distribution of "families and unrelated individuals." Consumer Income, Current Population Reports, Series P-60, No. 24, April, 1957. Row 4. Distribution of "families and unattached individuals." Survey of Current Business, J une, 1956, p. 10. different types of commodities. Attempts to measure life cycle position have centered on the age of the household head, family size and mor e generally on the combination of family size and ages and number of children. In the LIFE Study, each household was placed into a life cycle class, following the method developed by 333

the Survey Research Center of the University of Michigan. These classes start with no children homes, where the head of the household was under the age of 40, married or unmarried. They proceed through the young married couple period, where the head of the household was under 40, with at least one child under the age of 10. The third stage are households with children between the ages of 10 and 19 only. The fourth and fifth stages, respectively, were married heads 40 years or over, with no children under 20 living in the household; and single heads, 40 years or over with no children under 20 living in the household. The Wharton - BLS Study contained a classification of consumer units by family type which permits some reasonably close comparisons with the aforementioned life cycle data. These family type classes were husband and wife only; husband and wife with oldest children running from under 6 to 18 or over; one parent families with oldest child under 18; other adults only (18 or over), no children of any age; and all others. To round out the discussion in this seetian of life cycle effects on clothing expenditures, the separate effects of family size and age of head of household are also considered. A couple of parenthetical remarks are pertinent at this point. Major emphasis in the camparisans which follow is upon the persistence or lack of persistence of the various family characteristic effects on clothing expenditures. It is felt that relatively little can be said about differences in levels of expenditures elasticity coefficients or percentages of total spending going to clothing at the two points in time, 1950 and 1956, when one considers the large elements of non-comparability in the two bodies of data, a problem which becomes particularly troublesame in sub-group comparisons. However, where it appeared feasible, limited camparisans were made, usually of elasticity coefficients, since the levels of average propensities are so much more affected by the differences in definition of total expenditures referred to earlier. Another point concerning the expenditures elasticity coefficients is that they are consistently larger than the income elasticity coefficients given earlie r. This is because of the relationship that an elasticity of clothing expenditures with respect to total consuroption is equal to the elasticity of clothing expenditures with respect to income divided by the elasticity of total consuroption with respect to income. The last narned elasticity is virtually always less than one, which yields the result given above. Perhaps the most striking feature of the life cycle pattern of clothing spending is the sharp decline in expenditure elasticities over the first three stages (Table 16). This expenditure elasticity for total household clothing expenditures in 1956 dropped from 1.39 for the young single individuals and young married couples with no children to 1.16 for households with children under 10 years to 0.88 334

t1l

(.:l (.:l

1.37

1.00

No children under 20, married head 40 or older

No children under 20, single head 40 or older

---·-·--·-

0.88

0.96

1.38

1.07

1.31

1.16

Children under 10

Children 10-19 only

1.49

Women's and girls' clothing . expenditures

1.39

Total household clothing expenditures

No children, single or married head under 40

Life cycle class

Elasticity coefficients

13.0

11.4

13.4

11.5

12.4

Household clothing as a percent of total household expenditures

9.4

7.6

8.7

6.5

8.0

Women's and girls' clothing as a percent of total household expenditures

Table 16. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Life Cycle Classes, 1956

for households with children from 10 to 19 years. The corresponding figures forwomen's and girls' clothing expenditures were 1.49, 1.31 and 1.07. The elasticities ro se markedly in the next stage of the life cycle, i.e., households with married heads, 40 years or over in age with no children under 20 and declirred sharply in the final stage, i.e., households with single heads, 40 years or over in age with no children under 20. The results observed for the "family type" classifications in the Wharton - BLS Study were quite similar to this life cycle pattern. Consideringfamilies where both parents were present, chiidless couples had high expenditures elasticities (1.38) relative to those of families with children under 18 years of age. Elasticities for families with oldest children under 6, 6 to 15 and 16 to 17 were 1.09, 1.11 and 1.13, respectively. Families where the oldest child was 18 years or over had the highest elasticity of all family types studied (1.43). As in the LIFE data, there was a sharp drop in this elasticity for consumer units where only one parent or only "other adults" were present. Thinking of these expenditures elasticities as an expression of priorities in the spending behavior of American families, it would seem that clothing spending increases quite rapidly as income increases for the young adult and young married couple without children. As children come along, the pressure of other expenses is felt, and clothing spending does not go up with income quite as rapidly as before. A further decline in the expenditures elasticity of clothing spending takes place as the children move into their teens. Once the children reach about 18 years of age and remain in the household group but get jobs and begin to earn their own livelihoods, family spending on clothing moves up very rapidly as income and total spending rise. Moving into the last family cycle stage, where only one of the parents is still living, this elasticity of clothing spending drops down substantially. It is not surprising that the households with teen age children, which had the lowest elasticity of clothing expenditures, had the highest average propensity to spend on clothing. In statistical terms, one might perhaps expect a rather high inverse earrelation between the "a" and "b" values in logarithmic linear regression equations. That is, a low value for the slope of the line would tend to be associated with a high intercept value and similarly a high percentage of total spending going to clothing. One might argue that, forthese households, the minimum required level of spending on clothing is quite substantial and that even though the increase is relatively small as one aseenda the income scale, the average remains quite high. The same phenomenon of low elasticity and high average propensity was characteristic of the families headed by a single parent (usually a widow) with no small children. The average propensity 336

for spending on women 's clothing was particularly high. Perhaps the explanation here runs along the following lines. Very frequently, in homes with one surviving parent, the house is fully or almost fully paid off and the major replacements of housefurnishings and equipment have already been made. Spending in categories like recreation and trave l tends similarly to be low. Income and total expenditures are at quite depressed levels. Therefore, the spending that does take place in the "necessity" items of clothing tends to represent higher fractions of total expenditures than in earlier family cycle stages. To comment on the pattern in just one other family cycle phase, the opposite situation on high elasticity and low average propensity was observed for the households with married heads, 40 years of age and older with no small children. It is interesting that, since this older group of f amilies is usually thought of as constituting the bulk of the replacement market for housefurnishings and equipment, its average propensity to spend on clothing was quite low. Turning now to the effect of age of the headof family or household on clothing spending, again certain consistencies appear in both the 1950 and 1956 data but there is far from perfeet agreement (Tables 17 and 18). The pattern for average propensities in both years ran as follows. There was a drop from the youngest families (head under 25 - Wharton - BLS data; under 30 - LIFE) to the next age class (25 to 35 - Wharton - BLS; 30 to 39 - LIFE); a rise to a maximum for families headed by middle age persons and a declin e for the oldest families. The peak for both set s of data appeared in the middle age years when teen-age children are most probably present (45 to 55 years - Wharton - BLS and 40 to 49 LIFE) whi ch is in accord with the l if e cycle findings. The LIFE data suggest that the c rest of spending on women 's and girls' clothing occurs somewhat later (50-64) than for clothing spending generally. This does not show up in the 1950 figures. Furthermore, the LIFE data do not indicate as sharp a dropoff after the peak is reached as is suggested by the Wharton - BLS Study. The elasticity patterus by age are not consistent between the two sets of data. The 1950 data present a picture of increasing elasticities across the entire age range whereas the 1956 pattern is quite similar to the one given above for the average propensities. It would be extremely difficult to unravel the eauses of these differences, and no attempt is made here to do so. Since there are so many other factors operating to determine these patterns, perhaps the most fruitful point of view is to defer any conclusions on age effects until their joint effects with other variables are examined. Another important variable in determining life cycle patterns is the size of family. The effect of family size on income elasticity of clothing spending was noted earlier (Table 5) when net annual 337

"'"'OJ 1.08 1.09 1.29 1.36 1.43

25-35

35-45

45-55

55-65

65-75 --··--

0.65

Total family clothing

Under 25

Age of family head (in years)

L_

-------

1.52

1.32

1.25

1.02

1.06

0.65

Women's and girls' clothing

Elasticity coefficients

4.7

5.8 10.9 8.8

6.3

6.0 12.3

12.3

5.0

5.4

11.7 11.2

Women's and girls' clothing as a percent of total expenditures

Family clothing as a percent of total expenditures

Table 17. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Age of Family Head Clas ses, U. S. Urban Families, 1950

(,.) (,.)

co

6.2 7.9 8.5

10.7 13.3 12.7 11.9

1.15 1.35 1.13 1.14

1.02

1.20

1.08

1.00

30-39

40-49

50-64

65 and over

8.3

6.7

11.1

1.40

1.07

Women's and girls' clothing as a percent of total household expenditures

Under 30

Household clothing as a percent of total household expenditures

Women's and girl s' clothing expenditures

Elasticity coefficients

Total household clothing expenditures

Age of head (in years)

Table 18. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Age of Head, U. S. Households, 1956

money income in 1950 was used as the independent variable. The expenditure elasticities for 1950 revealed about the same pattern (Table 19). No family size data for 1956 were available from materials used at the time this paper was written. Perhaps one point is worthy of mention in passing. The highest income and expenditures elasticities were observed for two person families in both family clothing and women's and girls' clothing. It was indicated earlier that the expenditures elasticities in the first family cycle stage, single or married head under 40 with no children, were highest over the life cycle. Since the elasticities for single consumers were very low, according to the 1950 data, it would appear that the elasticities for this first life cycle stage would be even higher if young single consumer units were deleted. The average propensities show a steady increase with size of family for two or more person families with those for single consumers samewhat in excess of those for two person families. It, therefore, seeros that even though clothing spending may not rank high on the list of priorities for families with children as income (total spending) increases, the percentage of income (total spending) going to clothing steadily increases with increasing family size. Education of family head The overall tendency for families where the head had at least completed grammar school was for increasing expenditures elasticities as years of education increased (Tables 20 and 21). However in 1950, families headed by individuals with 8 years of education or less had the highest elasticities and in 1956 households where the head had not completed grade school had the lowest elasticities. As indicated ear lie r, the income elasticities of clothing spending in 1950 exhibited declines with increasing education except for families headed by people with more than four years of college education (Table 10). This difference in results between the two types of elasticities may be explained by the higher savings to income ratios of the upper income groups. Both surveys suggested that average propensities were highest for families headed by persons with at least a high school education. Since education and income are highly correlated, this again reflects higher savings ratios of the higher income groups. Occupation of family head Although the occupational classifications used by Wharton BLS and LIFE studies we re not the same, 11 some tentative 11 The Wharton - BLS classification was based on the Bureau of the

Census

Occupational

Classification

340

System,

except that (Continued)

(,.:>

~

""' 1.36 1.21 1.25 1.11 1.24

Three persons

Four persons

Five persons

Six or more persons

1.16

Total family clothing

Two persons

Single consumer

Family Size

1.36

1.19

1.30

1.25

1.37

0.61

Women's and girls' clothing

Elasticity coefficients

14.1

12.8

12.3

11.3

10.1

10.3

Family clothing as a percent of total expenditures

6.9

6.2

5.9

5.5

5.1

5.6

Women 's and girls' clothing as a percent of total expenditures

Table 19. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Family Size Classes, U. S. Urban Families, 1950

t'-'

"'"

w

1.09

1.17 1.22 1.25

9 - 12

13 - 16

Over 16

1.27

1.19

1.38

Women's and girls' clothing

1.37

Total family clothing

Elasticity coefficients

8 years and under

Education of family head (years completed)

5.6 5.6 6.0 5.8

11.4 11.9 11.9

Women's and girls' clothing as a percent of total expenditures

11.2

Family clothing as a percent of total expenditures

Table 20. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Education of Family Head C lasse s, U. S. Urban Families, 1950

.!>-

t.)

t.)

-

--

8.7 ··--·

13.2

1.37

1.28

Same college or beyond

----··

7.9

12.4

1.25

1.25

Finished high school

----·

6.6 10.2

0.89

1.01

Same high school

-

6.4

10.8

0.94

0.86

Finished grade school

-- ---·

7.0 11.6

0.71

Women's and girls' clothing expenditures

Women's and girls' clothing as a percent of total household expenditures

0.73

Total household clothing expenditures

Household clothing as a percent of total household expenditures

Did not finish grade school

Education

Elasticity coefficients

Table 21. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Education Classes, U. S. Households, 1956

generalizations appear possible. In both studies, the highest average propensities to consume clothing were observed for the clerical and sales workers (Tables 22 and 23). Requirements of good grooming earobined with the relatively low levels of total spending for the bulk of families in this classification would appear to be reasonable explanations of this observation. Expenditure elasticities for clerical and sales workers were quite low, however, with the exception of the women's and girls' clothing figure for 1956. In the Wharton - BLS Study, clerical and sales workers' elasticities were lower and in both studies average propensities were higher than for all other occupation of head groups. This tends to confirm the suggestion given earlier that the "white collar" employee while faced with a relatively high level of minimum expenditure on clothing because of his "life style" does not have clothing high on his scale of priorities, and tends not to increase spending on clothing as income goes up as rapidly as do other group s. The highest expenditures elasticity for household clothing spending in 1956 was in the professional and semi-professional group. There was no comparable classification in the 1950 study where the self-emplayed professionals were grouped with other self-emplayed persons including businessmen and artisans. This self-emplayed class had very high elasticities (1.36 for total family clothing and 1.44 for women's and girls' clothing) seeond only to those of skilled wage earners. Elasticities for salaried professionals, officials, etc. were quite low, 1.16 and 1.12. This would seem to suggest therefore, that the quite high coefficients obtained in the LIFE data for the "professional, semi-professional" group were primarily attributable to the self-emplayed individuals such as medical doctors, lawyers, etc. One other persistency in the two bodies of data was the very low average propensity to consume clothing by the skilled wage earner group designated as "craftsman, foreman" in the LIFE Study. In both studies for family or household and women's and girls' clothing, average propensity coefficients for the skilled groups were lower than for all other occupation groups. Expenditures elasticities of skilled workers, how ev er, appear to have dropped rather sharply from 1950 to 1956. The pattern that emerges for skilled workers, therefore, is one of consistently low levels of clothing spending with a decline in the expenditures elasticity of this spending. (Continued) self-ernplayed persons, including businessrnen, professionals and artisans, were separated from salaried managers, officials and professional workers. The LIFE classification was made in accordance with the Department of Cornrnerce "Alphabetical Index of Occupations and Industries."

344

01

(.:> ~

1.43 1.16 1.20

Skilled wage earners

Semi-skilled wage earners

Unskilled wage earners ---

1.07

Clerical and sales workers

-~

1.16

1.36

Total family clothing

Salaried professionals, etc.

Self employed

Occupation of family head

5.4 5.7

11.2 11.4 11.5

1.63 1.14 1.19

6.2

12.2

0.84

5.2

5.9

6.1

12.0 11.9

Women's and girls' clothing as a percent of total expenditures

Family clothing as a percent of total expenditures

1.12

1.44

Women's and girls' clothing

Elasticity coefficients

Table 22. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Occupation of Family Read Classes, U. S. Urban Families, 1950

CT.>

""'

c,.,

1.28 0.57

Operative, nonfarm

Service worker ----

1.19

Craftsman, foreman

---------

1.05

Clerical, sales

---

1.06

1.37

--

Total household clothing expenditures

Proprietor, manager, official

Professional, semiprofessional

Occupation of head

0.73

1.41

1.07

1.19

1.16

1.35

Women's and girls' clothing expenditures

Elasticity coefficients

13.3

11.8

10.6

13.4

11.9

13.2

Household clothing as a percent of total household expenditures

-

8.7

6.6

6.5

9.6

7.8

7.7

Women's and girls' clothing as a percent of total household expenditures

Table 23. Expenditures Elasticities for Clothing Expenditures and Percent of Clothing to Total Expenditures by Occupation of Head Classes, U. s. Households, 1956

Expenditures elasticities for service workers 12 we re particularly low in 1956 although the percentages of household clothing and women's and girls' clothing tototal expenditures for this group were seeond only to those of clerical and sales workers. It is certainly not possible from the data examined thus far to draw very rueaningful conclusions concerning changes in expenditures elasticities or average propensities for homogeneous subgroups from 1950 to 1956. Consumer units headed by older individuals, by individuals with little education and by skilled wage earner s and households with teenage children seem to be the major groups which experienced declines in expenditures elasticities for clothing. Levels of average propensity coefficients seem not to be comparable in the two periods, but it appears that average propensities to spend on clothing were highest for consumer units with teenage children, large size families, families with middle aged parents (about 40 to 55 years), units headed by individuals with at least some college education and families of clerical and sales workers. They were lowest for families headed by young people, small families, units headed by individuals who had not finished high school and families of skilled wag e earner s. Multivariate Analysis The foregoing analysis was restricted to the study of the association of elasticity and average propensity coefficients with various socio-economic variables, considered one at a time. The limitations of such a technique because of the l arge number of other determining variables, possible interactions, etc. are well known. Insofar as published tabulations are concerned, however, the above analysis required tabulations of clothing expenditures crossclassified by two "determining" variables, income and one other facto r. WhEm expenditures data are cross tabulated by mo re than two variables, even in the largest budget studies, many of the cells become extremely thin. For this reason, the Wharton - BLS published tabulations were not carried beyond cross-classification by three variables. At the time this paper was written, only two-way cross-classifications were available from the LIFE data. Of course, one method of grappling with the methodological problem under discussion, if one has access to the cards representing individual f amilies, is to attempt a full blown multivariate analys is. On e 12 LIFE's definition for this group is, "Service workers are in occupations demanding little special skills and include private household workers as well." Unskilled workers and laberers we re classified as "operatives." Semi-skilled workers we re als o included in this latter category.

347.

multiple regression rnadel estimated from individual family cards for 1950 is discussed later, as well as some preliminary resulls from a multivariate analysis run on Univac. In the following few paragraphs how ev er, we cancern oursel ves with expenditures e lasticities, cross-classified by two variables, computed from the Wharton - BLS published tabulatians for Urban U. S. in 1950. That is, this brief analysis utilizes the published three-way crossclassifications to get at the joint effect of two variables on the expenditures elasticities of clothing spending. The effects of family size and age of family head, occupation and age of family head, and race and family size are considered in the order given. Family size and age of head It was noted earlier that expenditures elasticities for clothing increased with age of family head and no steady increasing or decreasing pattern emerged by si z e of family. Upon crossclassification by family size and age of head, it becomes clear that this tendency of increasing expenditures elasticity with age does not begin for families with children until there are two children present (Table 24). Only the data for three, four and five person families, age classes 25 through 65 years were here considered. These classes for family size and age were used in the following two cross-classification analyses as well. The data became too thin in other groups to survive three-way cross-classification. In three person families, elasticities declined throughout the age classes considered; in four person families, beyond the youngest families headed by individuals from 25 to 35 years, they increased; and there was a tendency to increase with age in the five person families. The tendency toward higher elasticities for the older families in the four and five person households probably reflects a point made previously, namely, the presence of late teenagers and children in their early twenties. The higher income families often have children in the labor force, and these individuals tend to be high spenders on clothing. It appears that in the smaller families, i.e., three persons, as age increases the precedence of clothing spending, as expressed in expenditures elasticities, declines.

Now, examining the effect of increasing family size, with age held constant, only one reasonably clear tendency is revealed. That is, the elasticity coefficients increase with increasing family size for the older families. Since the presence of income earning young adults is more probable in these older families as family size increases, this would seem to lend support to the previously expressed nation of the effect of these individuals on clothing spending patterns. 348

Table 24. Expenditure Elasticity Coefficients for Clothing Expenditures by Family Size and Age of Family Head Clas ses, U. S. Urban Families, 1950 Family size and age of head

Total family clothing

Women's and girls' clothing

Three persons 25-35 35-45 45-55 55-65

1.28 1.15 1.14 1.07

1.32 1.18 1.11 1.04

Four persons 25-35 35-45 45-55 55-65

1.27 1.08 1.15 1.13

1.51 1.07 1.16 1.20

1.08 1.09 1.20

1.11 1.11 1.40

Five persons 25-35 35-45 45-55 55-65

*

*

>'fUnreliable results were obtained for this classification because of the unusually high level of clothing spending of a small number of sample families in the $6000-$7500 income class.

Occupation and age of head When account is taken of the occupation of the head of the family, the previously observed tendency for expenditures e lasticity coefficients to increase with age of head becomes somewhat modified. Except for the unskilled wage earner group, insofar as spending on clothing for the entire family is concerned, the peak in expenditures elasticities seemed to come in the period when the head of the familywas about 45 to 55 years of age (Table 25). In spending for women's and girls' clothing, the highest elasticities occurred either in the 45 to 55 age group or 55 to 65. Two interesting exceptions were the self-employed and salaried professionals, etc. group s which had very high elasticities in the youngest åge group, 25 to 35. This was not attributable to the high spending on women's clothing in the upper income groups, but rather to the very depressed spending in the lowest income classes. No doubt 349

Table 25. Expenditure Elasticity Coefficients for Clothing Expenditures by Occupation and Age of Family Head Classes, U. S. Urban Families, 1950 Total family clothing

Women's and girls' clothing

Self -employed 25-35 35-45 45-55 55-65

1.38 1.20 1.44 1.18

1.71 1.31 1.48 1.47

Salaried professionals, etc. 25-35 35-45 45-55 55-65

1.05 1.08 1.18 1.14

1.26 0.95 1.07 0.94

Clerical and sales 25-35 35-45 45-55 55-65

1.04 1.05 1.23 1.08

0.74 0.76 1.04 0.90

Skilled wage earner 25-35 35-45 45-55 55-65

1.29 1.27 1.92 1.70

1.63 1.41 1.48 1.89

Semi-skilled wage earner 25-35 35-45 45-55 55-65

1.05 1.01 1.39 1.31

1.20 1.01 1.34 1.15

Unskilled wage earner 25-35 35-45 45-55 55-65

1.08 0.96 1.30 1.35

1.10 0.82 1.32 1.35

Occupation and age of family head

350

this reflects the fact that in the early years of marriage in these lower income families the wife willingly foregoes spending on clothing. Also, to a certain extent, these data may reflect the later average age of marriage of the professional men. The highest elasticities observed we re for total family clothingskilled wage earners, age of head 45 to 55 and for women's and girls' clothing-skilled wage earners, age of head 55 to 65. Frequently, in these families, the wife is a supplementary income earner, especially when the children are grown. It appears that spending on clothing, particularly wo men 's apparel is quite high in such households. This very often simply is a reflection of the increased clothing requirements of the woman who works as campared to her counterpart in the horn e. Race and family size It was previously noted that the difference in income elasticity of clothing spendingwas quite small between white and Negro families. The expenditures elasticities forthese two groups of families show some marked differences by family size classes (Table 26). ForNegro families, expenditure elasticities declined with increasing family si z e for both total family and wo men' s and girl s' clothing spending. For whites, there was an increase from three to four person families, then a decline. The coefficients for families of five persons were particularly low for the Negro families. One may hypothesize that the hand-me-down system is mo re intensively practiced amongthe non-white than white families and that inNegro families with more than one child, clothing spending has a low order of priority as income increases. In particular, the elasticities

Table 26. Expenditure Elasticity Coefficients for Clothing Expenditures by Race and Family Size Classes, U. S. Urban Families, 1950 Race and family size

Total family clothing

Women's and girls' clothing

White families 3 persons 4 persons 5 persons

1.18 1.29 1.23

1.28 1.41 1.34

Negro families 3 persons 4 persons 5 persons

1.25 1.03 0.70

1.23 1.06 0.74

351

for women's and girls' clothing were substantially lower forNegro than white families in the 4 and 5 person consumer units. Multiple Regression Equation The income sensitivity of clothing expenditures has been studied in this paper by various classifications of other variables, but now we turn to a method which allows more explicitly for the simultaneous effects of these other factors, namely, multiple regression analysis. The choice of the independent variables to include with income in the regression equation is in most part a subjective one, turning very largely on the point of what questions are being asked of the data. Because of the interest in life cycle effects on clothing spending, family size and age of head of household were selected as additional regressors. A four variable least squares regression was therefore carried out, using the 1950 Wharton - BLS data, with total family clothing expenditures as the dependent variable and family net annual money income, family size and age of head as the independent variables. Before giving the specific formulatian of the mathematical model and the results of the analysis, it is perhaps appropriate to mention a methodological point. As Wold points out, the two main purposes of regression analysis are the estimation or prediction of one variable, given one or more other variables and the derivation of casual explanations of one variable as a function of one or more variables.l3 In the case of demand analysis, where single equation demand functions are emplOjed, we specify one variable as being dependent on the other s . 1 Sometimes the nature and direction of dependence is not a simple matter. If total consumptian and income are the dependent and independent variables, respectively, in a two variable single equation demand function and the problem is not simply one of prediction or estimation, it is not at all clear that for some families the implied direction of causatian is correct. That is, not infrequently, the family determines the standard of living and way of life that it shall have and then attempts to obtain the income to maintain that standard. Sametimes this, for example, means that there must be more than one income earner in the family. In the case of clothing, however, which represents a relatively small percentage of total spending, it seems reasonable to t reat clothing expenditures as the dependent variable, arguing that for most families the level of such spending actjusts 13Wold, H. and Jure en, L., Demand Analysis, John Wiley &: Sons, Inc., New York, 1953, page 30. 14 Wold, H., op. cit. pp. 32-33. Wold refers to this as "unilateral eausal dependence."

352

itself primarily to income and secondarily to other variables. Furthermore, for variables other than income, such as family size and age of head, it would not appear to make much sense to argue in favor of the reverse direction of causality. Parenthetically, the problem posed here has been present throughout the analysis, of course, but it becomes more apparent upon consideration of an explicit multiple variable mathematical formulatian of a demand relationship. Turning now to the mode! itself, if a simple !east squares linear equation were employed it is clear from the data that efficient estimates would not be obtained. As might be expected, heteroschedas ticity is present with the variance of clothing expenditures increasing with income. The effect of this lack of constancy in dispersion is reduced considerably by a logarithmic transformation on both clothing expenditures and family income. For purposes of simplicity of computation and as a first approximation to their effects, size of family and age of head were handled linearly in natural numbers. The specific form of the function employed, therefore, was: log where C X1 X2 X3 u

c =a + bl

log

xl

+ b2

x 2 + b3 x3 + u

= total family clothing expenditures (in tens of dollars} = family net annual money income (in hundred of dollars)

= average number of persons in the family during theyear

= age

of the head of the family

= assumed to be a random residua! reflecting the effect

of omitted variables A further advantage of the logarithmic transformation used above, if interest is centered on the effect of income on clothing spending, is that the income elasticity of such spending is given directly by the coefficient b 1 • Consumer units with incomes of less than $1000 were not included in the analysis. The remaining 10,534 families were grouped by income, family size and age of head classes to simplify the problem of running the regression.l5 The results of a frequency 15 seventy-two groups were estab1ished by the cross-classification into the following 8 income, 3 fami1y size and 3 age of head classes: Income: $1000-1999; 2.000-2.999; 3000-3999; 4000-4999; 50005999; 6000-7499; 7500-9999; 10,000 and over. Family Size: 1-2..9; 3-4.9; 5 and over. Age of Head: Under 39; 40-59; 60 and over. For a discussion of the loss in efficiency in the use of this proeecture see Prais, S. and Houthakker, H., The Ana1ysis of Family Budgets, Cambridge University Press, London, 1955, page 59.

353

weighted regression applied to the grouped means is given below. The estimated standard error of each coefficient and the gross multiple coefficient of determination are also shown. Log

c=

0.1929 + 0.9154 log X 1 + .0318 X 2 (.0311)

(.0049)

-

0.0026 X 3 {.0005)

R" 2 = 0.9452

All of the regression coefficients differ significantly from zero and appear to be reasonable according to previously computed coefficients and knowledge of the effects of the factors involved. The partial income elasticity of 0.92 after netting out the effect of family size and age is only slightly lower than the gross 0.94 figur e cited earlier in this paper, when these other variables were not taken into account. The latter figure rose above unit elasticity (1.06) when both the lowest and highest income classes were excluded. Thefamily size effect was positive and the age effect negative which incidentally agrees fairly well with the observation of the gross effects of these variables on family clothing expenditures. The a verage dollar expenditure on clothing increased steadily from $186 for single consumers to $704 for six or more person families. The negative effect of age of family head on clothing spending is apt to be a misleading idea if not properly interpreted. Actually, average expenditures on clothing increased to a peak at 45 to 55 years, then declined more sharply than they rose. Even when families in the same income and family size classes are considered, this effect does not entirely disappear. There is reason to believe, therefore, that the linearity assumption for age is an oversimplification and that perhaps a parabalic form should be experimented with in future work. UNIVAC Multivariate Analysis The foregoing analysis attempted to allow explicitly for the . simultaneous effects of several variables upon clothing expenditures, but there were a large number of other variables whose effects were left uncontrolled. The usual dilemma presents itself. If a very simple model is used with say one explanatory variable, resultant analyses may be faulty because of the failure to take account of other effects. On the other hand, as the camplexity of the model is increased, the number of observations at different levels of the variables decreases. It was seen, for example, that even. with the approximately 12,500 observations in a three-way classification in the Wharton - BLS Survey, there were a large number 354

of cells with less than five observations. In fact, there were quite a few cells with no observations at all. Although other purposes are served as well, an attempt to resolve this dilemma is being made in a multivariate analysis of the Wharton- BLS data on a UNIVAC computer. Sincethe methodology of this analysis is spelled out in detail in a paper given by Jean Crockett and Irwin Friend 1 6 at this conference, only the briefest sketch of it will be given here. Nearly all of the family characteristics available from the 1950 survey were utilized in the analysis. In an effort to increase the basic homogeneity of the group studie d, the families of Negroes, the self-employed and the not gainfully employed were excluded. Regressions of the form y

=a

+

16

i~l

bixi were fitted to the remain-

ing individual familydata where the y' s represent items of expenditures and the x's refer to net annual money income, family size, age of head, income change-income expectation pattern and presence of debt. Income (x 1) was in dollars but for allother variables, x 2 through x 16 took on only the values of O or l depending upon the classification of the family by the above mentioned characteristics. 17 Separate regressions were computed for families grouped by value of home or amount of annual rent paid and level of cash assets. 18 In summary, therefore, the UNIVAC runs provided marginal propensities for groups of families classified by two economic status variables holding eonstant the effect of several other demographic and economic factors. Average propensities were obtained by dividing average expenditures by average income. Income elasticities were estimated by dividing marginal propensities by average propensities. Average propensities and income elasticities for

16 see Crockett, J. and Friend, I., "A Complete Set of Demand Relationships." 17 The classifications used in this ana1ysis were: family size (x 2 - x 5 ); l, 2, 3, 4 or more age (x 6 - x 8 ); less than 35, 35-54, 55 or more income change income expectation pattern (x 9 - x 14 ); eonstant 3 year income, continuous decline in income, temporary rise in income, temporary fall in income, all others presence of debt (x 15 - x 16 ); home owners with and without mortgage debt and renters with and without inatallment debt. Education and city class are to be included in later analyses. 18value of home is the estimated market value of an owned home at time of interview. Level of cash assets refers to the amount of cash in banks, savings and loan shares, credit union shares, postal savings, and cash on hand on January l, 1950.

355

total family clothing were computed as indicated above and are given in Table 27. For homeowner families, the average propensity to spend on clothing increased with level of cash assets held. This was true for each value of home class considered. Amounts of asset holdings, of cour se, affect expenditures in many different ways and to a large extent are themselves the reflection of past spending behavior. Furthermore, cash holdings maygenerally represent only a small part of total assets, but are undoubtedly an important component insofar as spending patterns are concerned. The results given above suggest the operation of the "enabling effect" of cash holdings on clothing spending of homeowners. That is, cash holdings act in a permissive way and allow for spending potentials in excess of current income. Income elasticities, on the other hand, were highest for the homeowners with lowest cash assets. Interestingly enough, families with both lowest cash assets and lowest valued homes had the highest elasticity observed, while families with both the highest cash assets and highest valued homes had the lowest elasticity. The marginal propensity to spend on clothing of this latter group with high assets was extremely low (0.62) running about 40percent to 50percent below that for other groups of homeowners. This would appear to suggest a substantiation for clothing expenditures of the nation that the income sensitivity of spending by consumers with large assets tends to be low. Renters in the same cash asset classes as homeowners had uniformly higher average propensities to spend on clothing. One might have perhaps predicted this result a priori because of the expected greater spending on the part of homeowners for consumer durables to equip the home, with clothing being a likely candirlate for expendability. As was true for homeowners, these average propensities tended to increase with increasing cash assets, although the relationship was not so consistent. There also was a tendency for income elasticities to decline with increasing cash assets. The above quite abbreviated summary of findings is meant to serve merely as an illustration of the nature of some preliminary results of an analysis which attempts to deal with the problem of obtaining measures of income sensitivity of expenditures while accounting for the effects of many of the other variables that are relevant. No attempt is made here to describe the detailed effects of variables suchas family size andage within the subgroups of farnilies given above. When the UNIVAC runs are available for individual commodity expenditures as well as for rather global subgroups such as total family clothing, penetrating new insights inta consumer expenditures behavior should become possible. 356

27. Income Elasticity and Average Propensity Coefficients for Clothing Expenditures for U. Families Classified by Home Tenure Status, Value of Home or Annual Rent Paid and Beginning of Cash Assets, 1950 Value of Home Homeowners with cash assets of: Less than $500 $500-$15000 $1500 and over Not reported

Less than $10,000

$10,000-$15,000

Over $15,000

Average Propensity

Income E lasticity

Average Propensity

In come Elasticity

Average Propensity

.104 .105 .107 .101

1.19 1.03 1.10 0.97

.105 .109a .115 .108

1.06 0.91a 0.91 0.96

.102

Elasticity

.119 .105

Amount of Annual Rentb Renters with cash assets of: Less than $500 $500-$1500 $1500 and over Not reported

Less than $750

$750-$1250

Average Propensity

Income E lasticity

.113 .120 .110 .117

1.04 0.90 0.90 0.76 ----·

·-

Average Propensity .115 .119 .126 .129 -------··

In come E lasticity 1.25 1.07 1.02 1.16

---·

· · · - ~----------

aThese figures are for the $10,000-$15,000 and over $15,000 va1ue of home classes combined. bNo figures are shown for the over $1250 rent class because of the paucity of observations.

Further Work This interim report on the demand for clothing suggests a number of areas where further study is required. More intensive work must be done on an integration of cross sectional and time series data particular ly taking inta account changes in diatributianal factors. More experimentation is needed with simultaneous equation systems which include supply as well as demand equations. A better treatment than was feasible in this paper is needed on the problem of the joint effects of social, economic and demographic factors ontheincome sensitivity of clothing spending. Also, analysis is needed on the individual items of clothing. The UNIVAC runs earlier referred to will be of considerable assistance on the latter two problems. Finally, it is hoped that future work will east more light on the reasons for the downward shift in clothing's share of the consumer dollar and in the income elasticity of such spending and maypermit a separation of shifts in tastes from other factors.

358

FAMILY HOUSING EXPENDITURES: ELUSIVE LAWS AND INTRUSIVE VARIANCES* by Sherman J. Maisel University of California and Louis Winnick New York City Planning Commission

Some Tentative Conclusions Our probe into the housing data of the Study of Consumer Expenditures yields one main conclusion: housing expenditures of American families are far too diverse to be explained by simple principles. Much of this di versity is real, i. e., inherent in consumer behavior. Choice of housing (which necessarily means choice of community and neighborhood) is a response to an extremely complex set of economic, social, and psychological impulses. However, much of the variation whi ch has been uneovered can also be attributed to the unsuitability of cross-sectional budget data for the derivation of "laws" of housing demand. Adjustments in housing arrangements to changes in individual circumstances are notoriously tardy and discontinuous. Budget data for housing therefore represent an amalgam of current attributes (age, occupation, income, etc.) with a variety of housing decisions made in the past, or which may, in varying degrees, anticipate the future. Further, a large-scale survey of consumer expenditures must, as a practical matter, employ definitions and classifications which facilitate reporting and tabulation. However reasonable the adopted rules, they will not be equally useful to all investigators. In particular, the failure (a) to maintain a dislinetlon between mortgaged and nonmortgaged homeowners, and (b) to report the contractual mortgage repayments of indebted owners, gives rise to *This article is based on research undertaken with aid from the Real Estate Research Program, Bureau of Business and Economic Research, University of California, Berkeley. We wish to acknowledge the aid of Parker Fowler, Jr. in programmingfor the electric computer the original data from the Wharton-B. L.S. Study of Consumer Expenditures. We also appreciate his aid and that of Alan Davis and Jeanne Weil in the statistical computations.

359

large if artificial differences. These affect not only the analysis of the housing sector bu t of other consumptian relationships as well. It is not that no connections can be traced between reported housing expenditures and socio- economic variables. Indeed, many distinct patterns in housing expenditures and choice of tenure emerge and are described in our paper. Bu t when an attempt is made to measure the strength of these relationships, they are found to be feeble. They show up most clearly in group a verages and tend to become progressively weaker when the data are disaggregated. In the ungrouped data (individual families) none of the independent variables tested accounts for more than a small proportion of total variance. The main positive result of our negative findings is to point up the need for improvements in methodology. It is doubtful that reliable housing demand relationships will ever be formed until cross-sectional data are supplemented by longitudinal and attitudinal studies and until a more clear-cut definition of housing consumptian is established. I. Problems in Measuring Consumers' Housing Behavior It would be fair to say that recent discussions of demand relationships formed from cross-seetian data have centered on the choice and quality of independent variables. How valid a measure is current money income? How can life cycle be best introduced inta regression equations? Should household inventories or liquid assets be included in the right-hand terms? Such questions are as pertinent for housing as for food or automobiles. But in the case of housing, more so than with other consumer goods or services, derived demand relationships are also seriously affected by the definition of the dependent variable and the manner in which the relevant data are reported and tabulated. What constitutes the appropriate measure of housing consumptian whose level and variations we are interested in explaining? Should we cancern ourselves with the capita! values of occupied dwelling units, or with current consumptian flows? With economic measures of consumptian or with cash expenditures? With outlays for reproducible shelter or for shelter and environment? With "pure" shelter or shelter plus various complementary goods and services? Such questions arise because of the many different interests in housing. Same are cancerned with housing demand analys is primarily as a tool for f arecasting residential construction or mortgage financing requirements. Others are cancerned with housing as an index of welfare or standards of living. The attention of still others is fixed on housing's role in the allocation of family budgets among competing markets.

360

Our studywas primarily directed toward measuring consumer's housing behavior in relation to general demand theory. We were interested in knowing what sacrifices of economic goods or resources a family is willing to make in order to meet its housing requirements. Because of the many unique economic and institutional factors associated with housing, it is difficult to determine which measurement of costs or expenditures comes clasest to the concept of economic sacrifice. It also is hard to decide when a given outlay represents a sacrifice made for housing rather than for the satisfaction of other wants. Housing is trad ed in bothan asset market and a service market so that housing consumptian may be measured either through capita! stock and its changes or through current flows. Since housing is fixed in location, consumers buy, not merely a quantum of housing, but also a package of environmental and governmental services which often have little to do with shelter as such. Because of the extreme durability of housing and the large proportion of homes financed by debt, very sizable differences arise between the economic value of current housing services consurned and the amount of current cash outlays. Finally, legal arrangements and personal preferences permit widevariations in the amount and type of complementary goods and services included in housing payments. Ideally, one could explore demand relationships for each alternative definition of housing consumption, campare results, and retain that relationship which offers the best explanation and has the greatest predictive value. In practice, however, available data restrict the choice of the dependent variable. Worse yet, available data, including the Study of Consumer Expenditures, do not provide consistent measures of housing consumptian among indi vidual consumers or groups of consumers. Inconsistencies in definition and classification, examples of which are summarized below, increase the dispersion of the dependent variable. Such "contributed" dispersion is added to the dispersion indigenous to consumer behavior and weakens the explanatory power of independent variables. stock versus flow As already noted, housing demand relationships can be obtained either from asset values of occupied dwelling units or by measuring current housing consumptian as approximated, say, by rent or rental value. The derived results would presurnably be similar but not identical. Similarity would be insured by the fact that the ca pi tal value of a dwelling unit is related to its current rent or rental value. Dis simHarities would be eaused by the fact that rent or rental value does not form a eonstant ratio to capita! value because of variations in (l) investment risks, resulting in differences in required yields which must be recovered from rent, and (2) real estate taxes and property maintenance.

361

Whether capita! or rental values would give the best results is not now known. By either approach one important gain could be achieved-the combination of owner and renter families into the same demand equation. Separate analyses of each tenure group, now virtually unavoidable, may result in a misstatement of the true impact of important independent variables. For example, higher income is accompanied by higher homeownership rates. On the average, owners occupy larger and better dwellings than renters since, apparently, the change in tenure is associated with a desire to consume mor e housing. Consequently, an increase in income whi ch brought a renter into homeownership would ordinarity be accompanied by a larger increment in consumptian than if the family were merely to move upward in the rental housing scale. The assetapproachhas never, to our knowledge, beenattempted in budget studies. While values of owner-occupied homes are frequently collected in surveys, no similar data have ever been presented for renter-occupied units. 1 Since the Study of Consumer Expenditures (referred to hereafter as SC E) was primarily cancerned with consumptian flows rather than with consumer assets, there was little reason to report data on house values. True, market values of owner-occupied housing were collected, but mainly for the purpose of measuring changes in net worth. The val u e data appear in none of the published volumes and we re punched on the card s obtained by us only in stratified groups of" levels of housing," not readily useful for regression analysis or for camparisans with rental housing. Tenure and Mortgage Payments Neither, unfortunately, did the SCE obtain consistent data on current housing consumption. The SCE set out not to measure consumptian as such, but consumptian expenditures. While for renters cash outlays and current housing consumptian are closely related (subj ect to the qualifications listed below), the same is not at all true for owners. 1 0n the grounds that (a) the values of rental real estate are determined in what are essentially investor rather than consumer markets and (b) it is difficult to allocate the total value of a multi-family property (the only values which can be observed) among individual dwelling units. The 1950 Census of Housing (Vol. IV, Residential Financing) reported d a t a on values of mortgaged rental property. These data, however, are rendered almost useless for consumer studies not only by the omission of unmortgaged rental housing (almost half of the total) but also by separation from the regular Censuses which contain the needed tabulatians of household characteristics.

362

An owner' s economic sacrifice for housing is measured partly by the amount of cash he pays for such items as taxes, inte{est, and insurance. Even mor e important, however, are likely to be opportunity costs or those which require imputations such as interest on the equity and depreciation or appreciation in the capita! value of the house. Two owner families with identical homes will report entirely different cash expenditures depending on the amount of mortgage indebtedness and contractual mortgage terms.Z It is known that the incidence of mortgage debt varies widely with such characteristics as occupation, location, income and especially age of head, (Table 1). In most income classes, for example, only one-third of owner families with a head 55 or moreyears old reported mortgage debt campared to mor e than 80 percent of heads under 35. This means that, when measured by current outlays, the actual housing consumptian of the elderly tends to be understated relative to the young. As seen in Table 2, the existence of a mortgage debt makes for considerable disparities in reported housing expenditures but not necessarily in housing consumption. Because of the size of these differences, we were led to subdivide homeowners inta mortgaged and nonmortgaged groups, thereby foregoing any prospect of deriving a single demand relationship for all households combined. The failure to report the full economic costs of consumptian does not necessarily impair the usefulness of the data. For many kinds of inquiries, housing analysts would prefer to deal with the monthly or annual burden of cash outlays rather than with the economic concept of rental value. The cash concept often comes closer to the consumer's way of looking at housing. But SCE data fall short of a full cash budget since mortgage amortization, i.e., the portion of contradual debt service which goes toward the reduction of mortgage debt, is treated as a change in net worth rather than as an item of current housing expenditure. This fault cannot be corrected since the amount of mortgage repayment entered into the net worth account includes not only contradual amortization, but also voluntary prepayment (such as takes place when a house 2A preferred datum would have been the rental value of owned ho me s. This would me a sure the consumptian of housing service s as the rental income foregone by an owner who chooses to occupy a dwellingunit ratherthan selling thehousing services toa renter. Whether rental value is a fullyvalid measure of current housing consumptian gives rise to questions which need not be discussed here. Residential appraisers are quite firm in their dietum that occupancy has greater utility for an owner than for a renter. As a result a renter-occupied house would be valued at a lower figure than the same house with an owner occupant.

363

O)

C.:l

.,..

51

65

Skilled, semi-skilled, unskilled wage earners am not gainfully emp1oyec1,

5::/

72

30 40 100

41 43

Clerical and sales workers.

45

28

36 37

Lf8 43 100

2S

39 38

18

33

36

42

52

15

1S

32 34

16 35

17

29

39

32

37

27

79

53

63

6LJ

68

69

Unss der 3 5- or 3S 55 ;,lo re

~-~Head

40

36 100

54:

50

lf8

30

61

67

49

38

44

52

43

31

36

51

'p_/

42

35

37

39

63

35

32

34

35

53

Self-employed, sa1ariec1 professiona1s, officia1s, etc.

--------

37

46

30

so 27

36

51

51

46

61

6 or Mor e Persons

Fami~l'-~~---

13 l 2 3-S Years Years or 9-12 or Per Per- PerLess ~~_E.r s _ Mor e a/__Jd_iJ.._.§E.!)_._.E2.Il.IL_sons 8

Educa_tion_ _ Occupation ___

!_l

59

46

41

$7' 500-$10, 000

40

37

41

$6,000-$7,500

51

33

$5,000-$6,000

29

37

$Lf, 000-$5,000

48 40

40

41

$3,000-$4,000

61

Small Cities All Regions

35

52

52

Nor t h

and Suburbs, south and Hest

$2,000-$3,000

Income

Subur b s,

Cities and

Location Citie_s____

Percent of Owners without Mortgages by Income and Other Selected Characteristics

Table l

c.n

0:.

~

$388 444 515 559 594 675

$528 580 656 716 822 879

$520 590 650 709 826 921

$456 547 657 732 810 947

Owners

$491 583 671 742 869 941

Renters

All Urban Families

aBased on subset of approximately 8, 000 families as explained in Appendix B.

Source: Study of Consumer Expenditures.

$ 2' 000-$ 3' 000 $3,000-$ 4,000 $4,000-$ 5,000 $5,000-$ 6,000 $6,000-$ 7,500 $7,500-$10,000

Income Class

Selected Urban Familiesa Owners Without With Mortgages Mortgages Renters

Average Housing Expenditure by Tenure and Presence of Mortgage Debt

Table 2

is sold). The omission of contractual repayment eauses an understatement in the cash housing expenditures of mortgaged owners (estimated to be for most mortgaged owners between $100 and $300 a y ear). This means again that, as far as the reported data are concerned, the differences in housing costs between renting and owning as seen from the point of view of consumers become badly blurred. 3 It also means that simple two-way tenure groupings, i.e., owners and renters, the usual way of classifying tenure in consumptian studies, may result in serious biases. Owner expenditures represent mergers of two totally dissimilar groups, with mortgaged owners spending samewhat more on housing than equivalent-income renters and nonmortgaged owners spending less. The combined average expenditures of all owners depends on the relative proportions of the two groups in any major cell. Since (as Table l shows)these proportions vary greatly with other variables, observed differences frequently make little sense. For example, reported housing expenditures will be shown as differing by five percent for education groups and by over 15 percent among lifecycle groups. It is probable that actual housing consumptian levels would diverge by much smaller amounts while cash outlays would differ by much larger sums. The Problem of Complementarity A series of questions also arises in any effort to distinguish housing expenditures as such from expenditures on items which are complementary to the dwelling unit but which can be, and often are, purchased inseparate markets. First, since currenthousingprovides services only at fixed locations, housing expenditures must include a payment for what might be called "environmental factors." The consumer buys not only a given amount of housing, but a site as weil, obtaining thereby varying mixes of access, convenience, municipal services and job opportunities. Differences in housing expenditures due to variations in site values and local taxes are, to an important extent, disguised expenditures for other goods and services. Thus, a family which pays $100 a month for an apartment in the city' s core rather than 3we should also like to add our warning that the distortions which arise because of failure to take account of the sizable differences in cash expenditures (or of econornic costs and benefits) of rnortgaged and nonrnortgaged owners affect not only analyses of the housing sector but those for total consurnption as well. Variations between identical consumers which can arnount to hundreds of dollars are too large to be ignored, especially since the errors are not randorn.

366

$60 in an outlying ring may actually be saving most or all of the difference in transpartatian costs. Similarly, the real estate tax bill for municipal services contains payments for items which might be reported in accounts other than housing. One family may e le et a community with high taxes because its school curriculum is enriched with music and dancing lessons. Another family mayehoase a low tax community because its children go to private or parochial schoolsand take their music and dancing lessons elsewhere. The seeond family would be reported as having lower housing costs and higher education costs. Likewise, lower taxes may mean higher expenditures for insurance, garbage collection, or medical services. The housing accounts in the SCE are also debited for a Iong bu t variable list of goods and services whi ch are required for the effective utilization of living space. These items run the gamut of consumer durables, household operation, recreation, and transpartatian (employing the nomenciature of the SCE). According to long tradition, such utilities as cooking and heating fuels, electric power and water are generally regarded as part of housing expenditures. The re is less agreement, how e ve r, with respect to the c ost of kitchen and laundry equipment (washer, driers, stoves, refrigerators, etc.), furniture, garage space, cleaning materials, etc. Why, for example, should the outlay for a kitchen stove be included under ea_uipment and cooking gas under housing? Is the cost of electricity for radio and television a housing or a recreation expenditure? Questions such as these relate to a larger problem-whether consumptian expenditures are best grouped bypurpose or by object of expenditure, or, better y et, whether expenditures should be Iisted according to the goals the family is trying to achieve or by the means employed to achieve them. In other words, should family accounts, like fiscal accounts, be analyzed as a program budget or aline budget? Under a familyprogram budget the goal of "nourishment" would include not only expenditures for food and beverages, but also for kitchen equipment, dining furniture, cooking fuels, pots, pans, dishes, and vitamins now Iisted under a variety of other headings. A program classification would probably yield better insights inta consumer behavior and motivation; "object" classifications are most suited to the analysis of markets as seen from the producer's viewpoint. To be sure, were consumptian data subdividedas finelyas we would like, the investigator could regroup all accounts by whatever principles of classification best served his hypotheses. Arguments over systems of classification can easily become tedious. Logically flawless classifications are rare. Most people would be willing to accept a considerable degree of arbitrariness provided the groupings meet the test of interna! consistency. That is, after a decision that utilities belong to housing and kitchen 367

equipment does not, each family' s accounts would be east in the same way to avoid duplication and incomparability. But SCE data do not entirely meet this test. Thus the rent paid by a family is Iisted under housing regardless of the items included in the legal contract. While a flat charge for gas and electricity is frequently included in the rent bill, the majority of renters and virtually all owners pay for the m separate ly. Likewise, most apartment dwellers do not pay separately for heating, while the opposite is true for renters and owners of single-family ho mes. In our statistical analyses, we have reduced to some extent errors arising from this source by actding to housing costs all reported outlays for fuel, light, and refrigeration. 4 We have, however, been unable to correct for inconsistencies in other types of housing-related expenditures. For example, in those cases where furniture has been included in rent, housing is being charged for an item Iisted elsewhere for most families. Similarly, where a landlord supplied stove and refrigerator to his tenant, the annual charge appears under rent; if a tenant purchases his own, the full cost appears under equipment. 5 Two final notes: First, the data on rents collected in 1950 are affected by rent controls which then covered perhaps a majority of urban renter units. Average expenditures on rent are therefore lower than would have been the case in a free market, but we have no sure way of knowing what distortians occur in elasticity coefficients and other parameters. The interaction among housing submarkets is so great that had a free market prevailed the rents on many units would have been reduced as the rent on most increased. Second, we have been unable to deal with the physical characteristics of housing since such data were deliberately excluded from the SCE. Just what consumers got for their housing dollar in 1950, or how expenditures break down by quantity and quality of housing, cannot be related to budget data although a limitedamount of information is cited from the 1950 Census of Housing. 4The dispersion around regression lines fitted to housing plus utiiities was substantially less than for housing alone. 5The landlord supplying furniture or kitchen equipment is presumed to raise rent by anamount equal to the depreciation and maintenance costs of the durable plus a return on his investment. In New York City, the Rent Control Commission allows about $3.00 a month, or $36 a year, for a stove or refrigerator. Charges for furniture are more variable but may run to 30 percent or more of contract rent.

368

II. Methodology Our study of housing demand relationships attempts to test empirically same aspects of the conventional theory of consumer behavior, i.e., that a consumptian unit's expenditures on housing can be explained by its income, size, location, and the status of the unit's head as reflected by age, education, and occupation. The test hypothesis was that the foregoing attribute should result in statistically significant differences in expenditures among families classified inta separate subgroups based on each attribute. When such apparent influences were found, an effort was made to measure the degree of relationship. We startedwith an analysis of average housing expenditures of selected groups of urban consumers as published in the one- and two-way tables of the Study of Consumer Expenditures. The published data are useful in providing initial clues both as to the nature of intergroup differences and of such parameters as marginal propensities and income elasticities. At the same time, average expenditures as reported in simple tabulatians are quite deficient as indicators of behavior because they cover up large and often overwhelming amounts of dispersion. The problems which result from the compression of dispersion in the published data will be discussed later. But, to give an example, in calculating the regression of mean housing expenditures on mean income, income alone appears to account for 95 percent or more of the differences in expenditures. Very little is left to be explained by other family characteristics. Similarly, when an analysis of variance is performed to determine the significance of differences between average expenditures in two-way classifications, the income effect again predominates; differences derived from other methods of classification turn out to be borderline. 6 The Problem of Interaction But much more important is the interaction which exists between classifying variables. Simple one-way or two-way classifications draw in a host of other variables which have a bearing on the results. It goes without saying that apparent differences or 6The process of grouping so reduces our knowledge of the form and amount of variance that no clearly positive or negative answers result from the tests. Grouping also gives rise to the problem of an unequa l numbe r of o b s e rvations in e a ch of the groups. In s u ch cases the use of either weighted or unweighted means is likely to give samewhat erroneous answers. Cf. W. G. Cochran and G. M. Cox, Experimental Designs, 2nd Edition, Wiley and Sons, In c., New York, 1957), Chapter 14.

369

simHarities in spending between large groups of the population may simply reflect the intrusion of varying proportions of other family characteristics. 7 The problems of interaction can be met either by multipleregression using numerous variables or by fitting individual equations to finely subdivided groups. The derivation of unambiguous multiple and partial regression coefficients requires independent variables which are either quantitative in their original form or which can be transformed into meaningful scales. Most of the variables which are worth testing, i.e., occupation, location, race, tenure, type of family, fail to meet these criteria. Though transformation to some type of logical scale was considered, we could devise none which we did not feel to be arbitrary. One could never be sure to what extent the results would be influenced by the adopted scaling. Other variables such as age of head, family size, and education, while expressed numerically, do not readily lend themselves to linear equations. The re is no regularity of progression of expenditures among the classes. For these reasons, we decided to concentrate our analyses on a large number of family groups subdivided by multiple characteristics. The Analysis of Covariance In every case, the analysis of the two-way published classifications was supplemented by an analysis of covariance in which we tested the effects of other variables on the residuals from expenditure-income regressions. Individual family reports were divided into subgroups based on either two or three variables of classification. Within each of these subgroups, the regression of housing expenditures on income was formed and residuals estimated. (The methods and tests used in the analysis of covariance were standard and are described in Appendix A.) In effect, the hypothesis tes te d was that the u se of a particular variable of classification would either reveal differences among the subgroups in income elasticities or in adjusted mean expenditures. 7 Even at best, relationships derived from grouped data enable us to say something only about the group rather than the individual family. This has im portant practical significance since government housing programs seem to ignore the wide variation around group averages. For example., government policy-makers frequently assume a unique relations hi p between housing expenditures and income. Strong efforts are then made to bring housing prices and monthly payments into line with some predetermined "normal" ability-to-pay for each income class. Conversely, mortgage credit is often denied those willing to accept "abnormally" heavy housing burdens.

370

It would have been desirable to have added fourth, fifth, or sixth variables of classification simultaneausly in order to reduce still furthe r the possibility of interaction. But this was not feasible because of the limited number of cases available. The addition of even a fourth variable resulted in a large number of small or empty cells. Instead, we combined or reclassified the data in whatever way seemed desirable for testing individual variables. For the analysis of covariance, only families in the $2,000 to $10,000 income braekets were included. We also excluded certain groups offamilies with atypical housing arrangements, e.g., farnilies with heads over 65, nonwhites, rent-free, non-housekeeping, and families who shifted tenure during the year. Reported housingincome relationships of such families, who are distributed unevenly among the main subgroups, are quite unusual and capable of biasing the results. The number and characteristics of the excluded groups are described in Appendix B.

III. The Relationship of Housing Expenditures to Income The influence of income (without differentiating between permanent and transitory components) appears pervasive. Whatever the principle of classification, housing expenditures are seen to rise with income but at a lesser rate. As is clear from Table 3, and also from the tables in the Appendixes, average housing expenditures, including utilities and negligible amounts spent for vacation housing, show a clear tendency to increase for Successively higher (measured) income groups. Thus, families with measured income of less than $1,000 before taxes reported $335 annual housing expenditures, families with $4,000 to $5,000, $662, and families with more than $10,000, $1,474. In proportion to measured income, housing expenditures decline from 53 percent for the lowest income group to 7. 7 percent for the highest (Table 3). For all families combined, the housing share was 14.1 percent before income taxes, 15.2 percent of income after taxes, and 15.7 percent of total current consumptian expenditures. The extreme negative slope of the average propensity curve is sharply reduced by omitting families with low and high incomes, i.e., under $2,000 and over $10,000, and still further reduced when housing shares are related to consumptian rather than to income. In fact, for families with income of more than $5,000, housing as a share of total consumptian tends to be fairly constant, ranging between 13 and 14 percent. The inclusion of other variables of classification does not alter the over-all form of the relationship. Average expenditures 371

w

1:\:)

-:J

Source:

$

$

596

335 384 479 566 662 733 829 944 1,454

Average Housing Expenditures

14. I%

53. 3% 24.4 18.0 15. 3 13.8 12. 4 11. 4 10. l 7.7

Study of Consumer Expenditures, Vol. XVIII. expenditures for fuel, light and refrigeration. come data are money income after taxes.

All Families

Under $ l, 000 $ l, 000-$ 2, 000 $ 2, 000-$ 3, 000 $ 3, 000-$ 4, 000 $ 4, 000-$ 5, 000 $ 5, 000-$ 6,000 $ 6,000-$ 7,500 $ 7, 500-$10,000 $10, 000 or More

In come Clas s

15.7%

26.2% 21. 7 17.6 15.9 14. 9 13.9 13. 7 13.3 13. 5

Housing expenditures include In subsequent tables all in-

15. 2%

54.6% 25. l 18.9 16. 2 14.8 13.5 12. 5 11. 2 9. l

Housing ExpEnditures as a Percent of Income Income Total ConsumpBefor e After Taxes Taxes tio n

Average Housing Expenditures as a Percent of Current Income and Consumptian Expenditures, U. S. Urban Families, 1950

Table 3

vary withinparticular groups but the values cluster about the averages found for all families.8 Mean expenditures in relation to mean income give indications of a clear relationship, whose form and magnitude can be examined mor e closely in simple regressions. Linear regressions were calculated of the form: Y= a+ bX and (log Y) = a + b (log X) where Y was housing expenditures including utilities and X was income after taxes. In an attempt to improve the fit of the regressions we also testedthe forms of: y X= a+ bX and

Y= a+ b(log X). However, neither of the latter gave an improved fit over the loglog equation which became our main tool for the analys is of covariance. Before fitting regressions, the published data were combined into larger groups, no more than three for each variable. By merging comparable subgroups, not only are the data easier to follow bu t more observations are available for testing relationships in later stages of analysis. As noted before, families with less than $2,000 and more than $10,000 income were omitted since examination showed that the fit of regression Iines to the extremes of the income classes was quite poor. The list of regression coefficients presented in Table 4 indicates, with one exception, that both the marginal propensities and income elasticities for housing expenditures of different groups of families are quite similar. Regressions fitted to me an income and housing expenditures of six income classes indicate a marginal propensity of .075 for all families, with a range for the 17 groups tested of between .068 and .093. The log-log regressions yield an elasticity coefficient of .605 for all families and a range of .490 to . 721. The coefficients of determination (r 2 ) for all group s were, as might be expected, quite high for both the linear and log-log relations, with the latter form of equation offering, on the whole, the superior fit. 8 The significance of differences in average expenditures as tested by an analysis of variance is discussed in the next section.

373

.,..

(o) -;J

.776 .886 .932 .798 .956 .733 .156 .653 .726

Education 8 years school or less 9-12 years school 13 years school or more

Family Size 2 persons 3-5 persons 6 or more persons

Age of Head Under 35 35 to 55

1.076 . 981

. 532 .795

Occupation Self-employed, salaried professionals, officials, etc. Clerical and sales workers Wage earners and not gainfully employed

Renters

~r s

Tenure

.591 .574

.512 . 572 .721

.518 .519 .560

.550

.490 .508

.624 . 557

.989 .995

.967 .982 .990

.966 .987 .984

.950

.957 .940

.989 .980

Log-log Relations 2 a b r

266.06 279.28

299.17 290.01 193.19

280.64 311.38 336.30

255.51

399.42 322.83

$254.65 285.32

.083 .084

.080 .081 .093

.068 .078 .078

.077

.073 .079

.086 .085

Linear Relations a b

Marginal Propensities and Income Elasticities of Selected Groups of Housing Consumers, 1950

Table 4

.943 .987

.989 .989 .955

.949 .943 .983

.958

.899 .950

.962 .990

r

(}l

-;J

CA)

Source:

.438 .605

.565 .614

.742 .562

1.206 . 591

.551

.821

.497

.994

.%3 .938

1.000 .995

.984

1.000

Study of Consumer Expenditures, Vol. XVIII.

Total all families 9 income classes 6 income classes

Location Large cities and suburbs North Large cities and suburbs south and West Small cities, all regions

Age of Read 55 or more

r2

Relations b

a

Lo~-lo~

Table 4 (continued)

318.40 283.00

271.08 255.47

296.29

325.90

a

.065 .07 5

.079 .083

.083

.069

b

Linear Relations

.972 .990

.978 .959

.966

.970

r2

When regressions were fitted to smaller subgroups, the range of marginal propensities and elasticities of demand widened. However, the slopes of individual regression lines derived from subgrcups did not differ significantly from the weighted average slope obtained from the major group. On the other hand, the average slope for the subset of families used in the analysis of covariance differs decidedly from that for all families as reported in Utle published volumes. For income classes between $2,000 and $10,000 the comparative regressions are: Y;::; $283 + .975X (full sample) Y= $350 + .060X (adjusted sample) log Y;::; .592 + .605 log X (full sample) log Y= 1.120 + .430 log X (adjusted sample) The cause of these differences is clear. The full sample includes many groups with either zero or extremely low expenditures (rent-free, nonhousekeeping, etc.). This leads to a relatively low height at the point of origin and a more pronounced slope. We feel, however, that this high er slope can mislead the analys t. Am ong the atypical families included in the full sample are many who cannot increase their expenditures with income in the form assumed by the theory of consumer demand. For this reason, the smaller coefficients found for the subset of families appear to be a better estimate of the underlying elasticities. This important qualification aside, the coefficients of regression show no surprising results. The demand elasticities are in the range reported by other studies. There are no pronounced differences in reactions to increases in incomes among various subgroups. Variations in the income elasticities and marginal propensities of most subgroups appear to be almost random around the over-all averages.

IV. The Significance of Other Variables of Classification As noted, our proeecture was first to examine the general twoway classifications as derived from the published data in the Study of Consumer Expenditures. This was followed by the preparation of additional three- and four-way classification tables from the individual cards. The campilatians from the published data are included in the body of the report while the additional classifications are shown in Appendixes C and D. In all cases income forms 376

one of the independent variables. Tenure (renters, mortgaged owners, and nonmortgaged owners) has been kept separate in all three- and four-way groupings. Other variables examirred include race, family size, education, location, and age of head, taken singly or in combinations. Location The largest average expenditures for housing ($717) were made by consumers in Northern suburbs and the smallest ($456) by the residents of small Southern cities. Geographical differences, though greatly narrowed, persist within income groups (Table 5) owing partly to regional differences in climate, type of structure and price levels. Thus, for families with $3,000 to $4,000 income, housing expenditures ranged from $471 in Western suburbs to $600 in the small cities and suburbs in the North. In the three- and four-way tables of Appendixes C and D some location groups are combined and the effect of tenure and education variables held constant. Differentials by location contirrue to be statistically significant, especially the higher level of expenditures in Northern large cities and suburbs (including the North Central cities), compared to the remainder of the country. However, the expenditures of renter families, particularly above the $3,000 income level, fail to reflect this locational difference. Perhaps rent controls were more widespread and effective in the Northern areas at the time of the survey. It is also possible that in large Northern cities, where there are more highly organized rental markets and a wider choice of units, renters were better able to fulfill their needs at a lower cost.

Another geographical finding worth citing is that, according to SCE data, suburban families in 1950were not notably "homogenized" with respect to age or income. The exodus of chiid-rearing farnilies to the suburbs had apparently not yet resulted in the high degree of uniformity in social and economic characteristics reported in new subdivisions such as Levittown and Park Forest. In the North and West, for example, average age of family heads was identical in suburbs and large cities, and the difference in proportions of heads aged 35-44 was negligible. There were, moreover, similar distributions of income. Large cities did contain somewhat higher proportions of low-income families and lower proportions of high-income families, but in the middle-income range ($3,000 to $6,000), the proportion of all families in large Northern cities (52 percent) was only slightly less than in the outlying suburbs (55.6 percent). Continued migration since 1950 has probably accentuated city and suburban differences but the middle-class is even now far

377

~

-:J 00

747 841

733

806

946

$5,000-$ 6,000

$6, 000-$ 7, 500

$7, 500-$10,000

$

900

794

688

662

568

476 $

1,035

933

823

789

813 941

602

560

687

599

507

518 $

Suburbs south

North

Source: Study of Consumer Expenditures, Vol. IV.

869

628

553

435

680

$

$4,000-$ 5, 000

506

570

$

Large Cities south West North

$3,000-$4,000

$2,000-$ 3, 000

In come Clas s

$

1,005

663

683

579

471

475

West

$

917

950

l, 005

843

707

753

538

369

620

$

$

827

7 28

696

619

536

430

Small Cities south West

700

600

511

North

Average Housing Expenditures by Income and Location, U. S. Urban Families, 1950

Table 5

from extinct in the core of the metropolis. 9 The statement that the central city is becoming a place only for the rich and the poor (a statement whi ch can be found as far back as the 1870's) requires the utmost qualification. Often overlaoked is the fact that a high proportion of city dwellers without children and child- rearing f amilies in minority groups fall into the middle-income group. Exodus to the suburbs has doubtless been far more selective with respect to family type than with respect to age or income. Family Size As family size increases, the housing decisions of consumers are placed in conflict. More living space is needed at the same time as urgent needs are imposed on the budgets for food and clothing.1 O And, other things equal, !arge r dwelling units cost more money. The evidence indicates that the !arge family attempts to meet its need for larger dwelling units and more of every other necessity simultaneously. According to Census data, average size of dwelling unit-measured by number of rooms-increased with each increase in family (household) size. Thus, in 1950, five-person households occupied an average of 5.40 rooms campared to 4.39 rooms for two-person households. At the same time, SCE data show that, withingiven income groups below the $5,000 level, very large families tended to spend less on housing than did two-person households. Obviously more space for less money implies same sacrifice in housing standards. Census data indicate that in 1950 large households occupied relativelyhigh proportions of dilapidated housing. Large households also accounted for the bulk of overcrowding, i.e., dwelling unit size does not increase as fast as household size, resulting in a more intensive utilization of space. 9 At the start of 1957, the Census' s 1956 National Housing Inventory showed that 52.5 percent of the households who reported income in central cities were within the braekets of $3,000 to $7,000. In the remainder of the Standard Metropolitan Areas 53.8 percent we re in the se braekets. lOrn fact, except perhaps for refrigerators and some types of furniture, few consumer durables bear such a close size relationship to the number of people for whose use they are intended. The re is a much wider r ange, as well as a mor e continuous distribution, in the sizes of dwelling units offered on the market than in the sizes of automobiles (measured in terms of seating capacity), washers, driers, vacuum cleaners and so forth. There is a greater likelihoad that two-person and five-person households will bu y the same si z e ear than the y will buy or rent the same size dwelling unit.

379

o

(X)

(,.)

$406 520 608 733

$464 579 647 679

565 656

858 913

854 955

732 839 965

686 763 794

668 719 840 977

613 778 618 790

$4,000-$ 5,000

$5,000-$ 6,000

$6,000-$ 7,500

$7,500-$10,000

Source: Study of Consumer Expenditures, Vol. XVIII.

911

578

569

$459

518

$493

6 or mor e

5

Nu m ber of Persons 4 3

$3,000-$ 4,000

2

$508

l

$2,000-$ 3,000 $426

Income Clas s

Average Housing Expenditures by Income and Family Size, U, S. Urban Families, 1950

Table 6

Age of Head Tabulatians by age of head show that housing expenditures, like total consumption, follow the cross-seetian life cycle of rising and declining income. The housing life cycle, however, has smaller amplitude. For all income classes combined, expenditures for housing averaged $469 for heads under 25, were at a peak of $654 for heads aged 35 to 44 (the age interval in which both family size and total consumptian expenditures were at a maximum) and declined to $472 for heads 75 and over. Omitting the youngest and oldest age groups within a given income class, the range in housing expenditures among age classes from 25 to 64 averaged only about $24 a year or less than $2 a month, much narrower, relatively and absolutely, than the range among these classes in income and total consumption. In relation to measured income and consumption, the cash housing expenditures of the elderly (65 or more) were quite high. Although age-expenditure data shown here are strongly affected by the interaction of other variables, housing expenditures over the family life-cycle tend to be much "stickier" and affected by more discontinuous changes than is the case for many other forms of consumption. This is because of the greater costs and frietians of actjusting housing arrangements to changing family circumstances. In the later stages of the life cycle, for example, shrinking family size results in almost automatic reductions in food and clothing expenditures and usually in reduced purchases of durables, but much less often in contractions of housing consumption. Neighborhood attachments, the desire for extra space for family visits, the relatively low cash cost of maintaining a house with little or no mortgage debt, and the difficulty of finding inexpensive rental units all make for maintenance of the status quo. When atypical consumer groups are omitted and the remaining families are analyzed by a four-way classification of income, tenure, age, and family size, many of the apparent differences narrow or disappear. A major share of the variations between age and size groups as reported in the published data appear to reflect the high preponderance of nonrent or nonmortgage paying consumer units am ong both the very young and aged and in single- consumer households. Race Negro families spent less on housing in 1950 than white farnilies of the same size and with the same measured in come (Table 8 ). The differences we re most evident among lower income groups and in the South campared to the North. Lower spending on housing on the part of Negroes was accompanied by high savings and, in

381

~

w ()O

674 l, 115

$6, 000-$ 7, 500

$7, 500-$10, 000

$

863

814

738

662

559

472

25-35

$

l, Oll

863

745

657

584

488

35-45

Source: Study of Consumer Expenditures, Vol. XVIII.

708

$5,000-$ 6, 000

526

432

578

$

Under 25

$4, 000-$ 5, 000

$3, 000-$ 4, 000

$2, 000-$ 3, 000

In come Clas s

$

950

844

722

682

559

487

45-55

Age of Head

-

$

878

760

719

663

566

486

55-65

$

Average Housing Expenditures by Income and Age of Head, U. S. Urban Families, 1950

Table 7

858

883

733

668

568

476

65-75

$

l, 900

774

755

623

612

490

75 or mor e

CA)

C-' 00

333 297

443

400

3 persons

4 persons

$425 387 392

$520 510 476

$2,000-3,000 White N e gro

568

578

$574

530

577

$512

$3,000-4,000 White Negro

Income

Source: Study of Consumer Expenditures, Vol. XVIII.

$324

$414

$1,000-2,000 N e gro White

2 persons

Family Size

661

685

$666

564

686

$737

$4,000-5,000 White N e gro

Average Housing Expenditures by Income, Family Size and Race, U, S. Urban Families, 1950

Table 8

relation to total consumption, !arger outlays for food and especially clothing. Among families with $4,000 or more income, racial differences in spending were not consistently in the same direction. Housing expenditures of Negroes are, of course, so affected by racial discrimination as to make it difficult to interpret the data. (For this reason we have excluded Negro families from the main body of our analysis.) Do Negroes have poor quality housing-as shown in Census data-because they C11oose to s p end less or do they spend less because only inferior housing is available? Probably both factors play a part. Other studies reveal that Negroes have a preference for existing over new housing even when the latter can be obtained at moderate prices. There is also a tendency even among middle-class Negroes to reduce family housing space by sharing with lodgers. At the same time, some of the effects of racial discrimination are disciased in Census tabulatians which show that Negroes live in housing of inferior quality even when paying the same rent or price as whites. Occupation and Education Judging solely from simple group averages, white collar workers and the self- employed within the me asur ed in come classes of $2,000 to $10,000 tended to spend more on housing than bluecollar workers. For example, in the $3,000 to $4,000 income group, salaried professionals spent $658 and the self-employed, $619, campared to $552 for skilled workers, $514 for the semi-skilled, and $525 for the unskilled (Table 9 ). Housing expenditures for those not gainfully employed also tended to be quite high. This last group, how e ve r, is comprised mainly of the retired whos e current housing expenditures are determined largely by housing decisions made at earUer stages in the Iife cycle. Tabulatians by education yield a pattern consistent with that for occupation. In givenincome classes, housing expenditures were higher for family heads with the most schooling. In the $3,000$4,000 income group, heads with 13 to 16 years of school spent $627 on housing campared to $576 for those with 9 to 12 years and $521 for those with schooling of 8 years or less (Table 10). When the effects of education and occupation are tested by the analysis of covariance, significant differences are found. For example, in the analysis of education (income, tenure, and location constant), variances significant at the .01 leve! are found inseven of nine cases. The remaining two are subgroups of owners without mortgages whose residua! variance is extremely high, but even so they nearly meet the .01 test. The test of occupation with tenure and family size eonstant again shows significant divergencies. When education and occupation are separated from each other however, the result is extremely interesting (Table D-7). A clear 384

c.n

o:>

w

943

916 l, 032

781

959

$6,000-$7,500

$7,500-$10,000

Source:

875

795

745

Study of Consumer Expenditures, Vol. XVIII.

805

663

$5,000-$ 6,000

589

814

786

696

627

55 2

474

$

531

$

787

658

510

728

$

$4, 000-$ 5, 000

538

619

$

SelfEmployed

Occu.eations Skilled W a ge Earner s

Clerical and Sales Workers

$3,000-$ 4,000

$2,000-$ 3,000

In come Clas s

Salaried Professionals

$

784

737

674

600

514

453

SemiSkilled

Average Housing Expenditures by Income and Occupation, U. S. Urban Families, 1950

Table 9

$

612

775

607

612

525

430

Unskilled

$

l, 165

808

781

678

616

494

Not Gainfully Employed

O)

CXl

c,.)

631 698 860

$5,000-$ 6, 000

$6,000-$ 7, 500

$7,500-$10,000

$

888

877

745

659

576

513

9-12

$

963

897

824

7 26

627

499

13-16

Years of School

Source: Study of Consumer Expenditures, Vol. XVIII.

625

521

$4,000-$ 5, 000

$3, 000-$ 4, 000

439

$2,000-$ 3, 000 $

8 and Under

In come Clas s

$

l, 366

934

819

759

707

650

16 or Mor e

Average Housing Expenditures by Income and Education, U, S, Urban Families, 1950

Table lO

$

l, 051

904

823

731

635

516

13 or Mo re

example of intercorrelated variables is demonstrated. The apparent influences of education and occupation, each of which have been cited as major forces in other studies, turn out not to be independent or additive. More education and a higher job status both lead to samewhat higher housing expenditures. When either education or occupation is considered with the other variable constant, their apparent influence is considerably reduced. What this indicates is a joint status as might appear on a more complete sociological scale. Higher status can be reached either through education or occupation. Howeve r, if a family attains higher status through occupation, differing educational levels will have but slight influence on its expenditures. Similarly, the more highly educated groups show housing tendencies which are independent of their reported occupations. These data may furnish a further interesting sociological lead. Since occupation and education are measured with income held constant, they point to status effects which are independent of current income. Howeve r, the divergencies eaused by these status variables, though statistically significant, are relatively small in comparison to the effects of family income. Tenure Despite the widespread existence of rent contro l in urban areas in 1950, annual housing expenditures for renters, as reported in the SCE, tended to exceed those for owners. At $2,000-$3,000 the comparable figures were $491 and $456; at $4,000-$5,000, $671 and $657; at $6,000-$7,000, $869 and $810 (Table 2). As noted earlier, much more crucial are the differences between mortgaged and other owners. Even omitting contractual repayment of mortgage debt, encumbered owners had cash outlays at least 25 percent higher than unencumbered owners in the same income class. The differences in payments by tenure were highly significant in all cases. Were a rough allowance made for annual contractual debt repayment, housing expenditures for mortgaged owners would be measurably higher than for renters of the same income, a fact more in accord both with common observation and with Census distributions of dwelling unit rents and values by income. As we noted, this disparity in reported housing consumptian of homeowners, which stems from the definitions employed in the SCE, greatlyweakens the interpretative value of both the published tabulatians and the results of our regression analyses. V. The Variability of Housing Expenditures A source of eonstant perplexity throughout our analysis was the relative ly small share of total variation in housing expenditures 387

that could be explained by seemingly important economic and social variables. While, as the preeecting seetian makes clear, housing expenditures reflect the play of a number of independent variables, the degree of each relationship appears to be weak. This is true despite the exclusion from the sample of groups which would have added greatly to total variance. Income, the most significant factor, accounts on the average for only 10 percent of the total variance in housing expenditures. Tenure, the next most important variable, accounts for about 6.6 percent of the residua! variation. The influence of other variables is even smaller. Education (including its intereorrelation with occupation) explains 3.5 percent, location 2.0 percent, while other variables have even lesser explanatory roles. Holding four variables eonstant simultaneausly in an analysis of variance enables us to explain 23 percent of the initial variance around the me an of the logs of expenditures. Two reasons can be advanced for these rather disappointing findings. One is the tremendous magnification in variance when original observations are substituted for the grouped data most commonly used in previous explorations. The seeond invalves a lang overdue recognition of an innately wide range in the housing arrangements of seemingly identical types of families. Grouped Versus Nongrouped Data Most familybudget demand analys is in the pas t has been bas ed on an analysis of average expenditures within income classes. In many cases, no other approach was possible because only averages were available. Use of group averages also saves a great deal of time and expense. This is true even where there is access to modern high-speed computers. Grouped data, when weighted by the number of observations in each group, gives an unbiased estimate of the regression coefficient. At the same time, because grouping sharply reduces the number of degrees of freedom, tests of significance become somewhat less powerful. In other words, while a regression coefficient derived from grouped data is a satisfactory estimate of the coefficient which would be obtained from ungrouped data, a larger standard error will result because of the decrease in the degrees of freedom. 11 On the other hand, the earrelation coefficient obtained from grouped observations is not a satisfactory estimat e o f the 11 The va rian c e f o r the re g re s s i on coefficients depends upon the square roat of N and the confidence limits are also wider for small sample s. Thus the width is directly related to the number of degrees of freedom in the respective samples. The effects of these differences are shown in the final tables of Appendix D.

388

earrelation coefficient obtainable from individual observations. A earrelation coefficient based on groups offers a measure of the proportion of changes in average expenditures related to changes in average income. Even high earrelation coefficients can tell us little about the response of individuals to changes in incomes.lZ Most of the original variance is lost in the process of grouping and cannot be recovered. These facts are evident in Table 11. Here we campare the regressions and earrelation coefficients obtained in one of our three-way classifications using individual and grouped data. The regression coefficients are quite similar, i.e., the variations appear to be random. The r 2 ' s, on the other hand, appear to have but little or no relationship. Those for the grouped data average .876, while those for the individual observations average only .110. Clearly, there is a startUng increase in the explanatory power of income change when applied to groups rather than to individual families. Of course, a much wider possibility exists for sampling variations among the coefficients for the grouped data in contrast to those for the individual observations. Thus the 95 percent fiducial limits for the average r of the grouped data are r = .515 and r = .993; for the individual observations they are r = .328 and r = .336.

Possible Reasons for the High Residuals What implications arise from the primarily negative results of our statistical tests? That is, why should the influence of seemingly important variables proveto be so weak? One possibility, of course, is that our methods have been too crude and that more significant results might have been obtained by better and more camplex statistical techniques. This we doubt. As a check on our results, we subdivided large groups into the most homogeneous subgroups consistent with sufficient observations for statistical reliability. We utilized cells classified by all selected variables simultaneausly. Thus we had cells in whi ch all f amilies we re white, mortgaged owners, with heads from 35-55, wage earners, having between 9 and 12 years of education, with families of 3, 4, or 5 persons, located in large northern cities and suburbs. Moreover these groups had already been adjusted for rent-free families, and those who changed tenure, making each cell the equivalent of at least an eight-way tabulation. lZFor a more c0mplete exposition see S. J. Prais and H. S. Houthakker, The Analysis of Family Budgets, (Cambridge, Eng., University Press, 1955) pp. 5.9-63.

389

1:..:1

co o l, 055 816 334

l, 760 1,010 5 26

Renters Large northern cities and suburbs Large western cities and suburbs Small cities

697 497 320

Number of Observations

Owners with mortgages Large northern cities and suburbs Large western cities and suburbs Small cities

Owners without mortgages Large northern cities and suburbs Large western cities and suburbs Small cities

Subgroups

o

o

495 481 723

393 0538 473

o

o

o

o

477 402 . 508 o

843 660 . 800

907 850 . 771

o

926 . 902 0867

o

o

o

o

Grou,eed Data r2 b

Comparison ofIncome Elasticity Coefficients from Grouped and Ungrouped Data

Table 11

487 379 . 476

47 2 471 .612

o

383 . 50 3 . 520

o

o

o

o

111 052 . 083

113 098 . 127

0108 0130 . 146

o

o

o

o

In di vi dual Data r2 b

Analysis of the relationship between changes in expenditures and income in these homogeneous groups produced little improvement over the findings previously cited. The residual variance of expenditures on housing was still enormous. Less than 14 percent of the total variance was accounted for by income. The income elasticities were of the same magnitude as those obtained from individual observations in the larger and more heterogeneous group s. Some reasons for the failure to find higher earrelations have been developed earlier. lt is quite possible that better explanations of differences in housing consumptian would have been obtained if the reported expenditures came closer to either the cash flow or economic concept of consumptian and if all housing payments were tabulated in accordance with a more clearly defined package of services. Another possible explanation is the unsuitability of a single year as a basic accounting period for housing. Maintenance and repair costs may vary wide ly from year to year. As a result som e f amilies will ha ve significantly mor e expenditures of this typ e in one year than will other s. This is probably one of the reasons why the variance among families in houses without mortgages averages near ly 50 percent mor e than for owners with mortgages. One type of payment- mortgage interest is absent from the reports of nonmortgaged owners with the result that irregular expenditures on repairs and maintenance, even if of the same average amount for all owners, will cause greater relative variance in the nonmortgaged group. The sharp difference in expenditure variances, with ratios of 1.0 for renters, 1.3 for owners with mortgages, and 2.0 for owners without mortgages, indicates a still more basic reason for weak correlations. The housing expenditures will notadjust to changes in income (or other characteristics) as rapidlyas will other types of expenditures. There are significant loyalties to one' s ho me, neighborhood, schools, etc., which are not lightly broken. Such frictions, added to the heavy costs of transferring properties, cause decide d discontinuities in any family' s housing demand curve. The average family makes only a few moves over its Iife cycle. During the period between moves many changes will happen. Income and occupation may alter. The head will age. Family size will fluctuate. Even if these shiits were to cause movements in the family' s utility function, actjustments to the new situation would occur only at relatively Iong intervals. The !arge variances, therefore, may simply reflect the fact that a family has changed its characteristics since the time when it last made a basic housing decision. This would account for the rising variances as we move through tenure groups. The group which adjusted its housing arrangements most recently (i.e., 391

renters) has the least variance and the group with the longest occupancy (unmortgaged owners) has the most.l3 While all of the foregoing are logical reasons why housing expenditures are so diverse, they maynot be the best explanation. It might be equally correct to assume that, be cause of the wide choice of housing available to the average family, tastes can be expressed in a tremendous variety of ways. As a result any family's utility function mayhave only a slight relationship to economic variables. They may depend far more on family history, on the characteristics of the local market, on psychological makeup, and a host of other elusive factors. VI. The Permanent lncome Hypothesis It is clear that the results of the previous seetian are related to much of the discussion which has arisen with respect to the permanent income hypothesis. 14 We have argued that, faulty data aside, the !arge variance implicit in housing expenditure-income relationships results partly from actjustment lags and partly from the wide range in individual preferences. But it is also possible that empirical demand elasticities are affected by the use of data which refer to a single year in a market where longer planning periods are common. According to the permanent income hypothesis the relevant measures of income and consumptian should span longer periods of time. Suitable actjustments in empirical data will result in more accurate estimates of theoretical constants. The hypothesis requires the assumption of a zero earrelation between transitory and permanent components of income and consumption. "The assumption that the third correlation-between the transitory components of income and consumptian-is zero is a much stronger assumption. It is primarily this assumption that introduces important substantive content into the hypothesis and makes it susceptible of contradiction by a wide range of ph enamena capable of being observed. " 15 13This suggests that better relationships might be derived by concentrating on recent hornebuyers. Two difficulties, however, with such an approach are (a) recent hornebuyers constitute so small a porportion of effective housing demand that the results cannot have widespread application, and (b) the credit rules of rnortgage lenders "artificially" restrict the variance which would be found in a perfeet capital rnarket. 14cf. Milton Friedman, A Theory of the Consuroption Function, (Princeton University Press, Princeton, 1957) Chs. 2 and 3. 15 Ibid p. 27.

392

In the housing market, at least, this zero earrelation appears improbable. Lags in the actjustment of either current or planned expenditures to changes even in permanent income are quite likely to be long. Indeed, actjustments may not be made at au.16 If failures to actjust are considered as transitory negative deviations from the permanent consumptian level, it is probable that in any given time period there will be a decided negative earrelation between transitory expenditures and permanent income. In effect, our previous discussion stated that, at least for housing and related expenditures, there are valid reasons for expecting average expenditures at any time not to actjust to changes in permanent income. Not transitory income but the costs and discontinuities in actjustment may be the real reasons why empirical elasticities diverge from theoretical ones. Were this the case, no significant improvement in housing demand relationships is likely to result simply from better estimates of permanent income. True, a family does undoubtedly attempt to actjust its housing expenditures over a long horizon, but uncertainties, imperfect knowledge, and institutionalfrictions arise. No matter how certain one is of one's own future path, the confidence may not be shared by hard headed bankers or landlords. While those tests we have made of our data in relation to the permanent income hypothesis are not very conclusive, it is worthwhile to report their results. As part of our general analysis of covariance, it was simple to separate out those families who reported stable incomes in terms of but slight change from the previous y ear and about the same expected for the next y ear. When the income-expenditure regressions of these groups were compared to the main cells from which they were drawn, no significant statistical differences could be observed. In other words, the elasticity of housing demand was no different for the group which reported stable (more permanent) income.1 7 Another interesting experiment has been proposed by Eisner ,18 Eisner performed a test on total consumptian quite similar to one that we had already completed on housing expenditure data. Interestingly enough, our "within group" tests were designed to obtain more basic knowledge of consumptian patterns, whereas Friedman and Eisner sought to obtain more satisfactory measures of income. Our assumption was that, in comparisons of homogeneous minor 16The death of a husband, for example, may leave the widow with a sharply reduced permanent income without producing any change in housing arrangements for the remainder of her life span. 17 Cf. Friend and Kravis, "Consumption Patterns and Permanent Income," American Economic Review, May 1957. l8R. Eisner, "The Permanent Income Hypothesis: Comment," American Economic Review, Dec. 1958.

393

cells with heterogeneous major cells, as a result of differences in consumptian patterns, significant disparities should emerge in mean expenditures, cross-products, and weighted average coefficients of income elasticity. Although our objectives differed, the statistical methodology was the same with one exception: we based our test on individual observations rather than group means. Unlike Eisner, we found few significant differences between the coefficients of major and minor groups. We are not certain why our results differ so much from Eisner's. One obvious possibility is that housing data simply do not follow the same rules as general consumption. Certainly the residua! variance within groups was very high so that the differences in coefficients had to be large to be statistically significant. Another poesibility is (as noted earlier) that failure to differentiate tenure in the published data might lead to significant biases even for the over-all data. Finally, Eisner's use of the grouped data might weil have affected his results since, as he himself recognizes, "the averaging process invalved in working with group means may have 'washed out' many relevant variables ... "19 VII. The Prohability of Homeownership For many reasons, housing market analysts care not only about the dollar amounts of housing expenditures but also whether consumers choose to obtain housing services in the form of owned or rented dwelling units. The choice between owning and renting affects the level of consumer debt, the distribution of population between city and suburbs, and the efficacy of government housing programs. What are the variables which influence the aggregate rate of homeownership? Here again, while it is possible to design a multiple regression analysis by transforming a dichotomous tenure relation to, say, a O, l scale, our uneasiness about arbitrarily assigned numerical values led us to explore the factors making for homeownership by an examination of the differential ownership rates of subdivided groups of consumers. The variable which appears to be most consistently related to the homeownership rate is income: current, past, and future. The influence of current income shows up in virtually all crosstabulations. The influence of past income is suggested by the relatively high ownership rate of older families with low current income. The importance of anticipated income, though not readily 19 Eisner, ~- cit.,

p.

984. 394

discernible in SCE data, derives at least in part from the established credit rules of mortgage lenders and government agencies which require at least some evaluation of the homebuyer's income prospects for a considerable span of years in the future. As said before, even if homebuyers (the overwhelming majority of whom use mortgage credit) are imprudent enough to disregard the future income stream, the mortgage lender or guarantor is not. According to published tabulatians in the SCE, the homeownership rate rises from 35 percent for families with incomes of $2,000 to $3,000 to 82 percent for families with $10,000 or more. The relatively high ownership rate ( 42 per cent) for families with less than $1,000 income is explained by the high proportion of elderly heads in that class who become owners at earUer stages in the Iife cycle and who have ehosen to retain their ho mes despite subsequent declinesin money income. A seeond key factor is age of head. The relationship between tenure andstage in life cycle amongAmerican families is too wellknown to warrant much comment. The published data show a steady rise in homeownership from 13 percent for heads under 25 years old to approximately 60 percent for heads 55 or more. Ownership rates increase sharply (from 13 to 34 percent) at age 25-35 and again to 50 percent at age 35-45, with relatively little ris e thereafter. Strongly related to age of head is family size. Ownership rates rise from 25 percent for single consumers to 59 percent for families of four or more persons. A third factor is location. While ownership rates vary among regions, the most pronounced influence is residence in city or suburb. The ownership rate was considerably higher in suburbs campared to large cities but was approximately the same (65 percent) in all three major regions. Ownership Rates by 3-way Classifications To examine comparative ownership rates in greater detail, i.e., by three-way classifications, we have combined cells within the two most important classifications, income and age of head, against which other variables are crossed. Three income groups are used, under $3,000, $3,000 to $5,000, and $5,000 or more. Likewise, age of head has been retabulated into three groups, under 35, 35 to 55, 55 or over. The joint influence of age and income is brought out in the last columns of Tables 12 to 14. Withingiven age groups, homeownership increases steadily with income. For heads under 35, the ownership rate was 12.2 percent if income was under $3,000, 39.1 percent if income was between $3,000 and $5,000, and 51.4 percent if income was over $5,000. At age 35 to 55, the ownership rates 395

for the corresponding income groups were 31.1, 55.1, and 70.9 respectively, and for family heads 55 or over, 47.4, 63.2, and 75.0 respectively. Within given income groups, there were also consistent increases in ownership with age. Reflecting past levels of income, families with less than $3,000 in current income had an ownership rate of 47.4 percent if the head were 55 or older, 31.1 percent for heads 35 to 55, and 12.2 percent for heads under 35. In the $3,000 to $5,000 income group, the ownership rates for corresponding age groups were 63.2, 55.1, and 39.1 percent respectively and for the highest income group 75.0, 70.9, and 51.4 percent respectively. The chances we re nearly as great that a low-income old head would own his home as would a high-income young family. And, as far as can be judged from cross-sectional data, the sharpest increases in the ownership rate take place when young and middle-aged family heads rise into the middle-income group. The same data further subdivided by size of family (Table 12) demonstrate the upward pull on ownership rates which result from marriage and presence of children. Within given age and income groups, ownership rates were dramatically higher for two-person families (generally, married couples) than for single-person consumers. Even in the most "ownership-prone" group, elderly heads with high incomes, only a minority of one-person households were reported as owners. Regardless of income, young single-person consumers were rarely homeowners. The presence of additional persons in the household (usually children) was also accompanied by increased ownership rates, holding age and income constant. This was particularly true of young families with medium or high income, where ownership rates were nearly twice as high for three-person families as for twoperson families. With occasional exceptions, ownership rates were higher for each larger family-size class. While there is no valid way of ascertaining separately the quantitative influence on ownership of age, income and family size, it is clear from these data that (l) government-sponsored credit terms aside, the major eauses for the increase in the postwar national homeownership rate were higher income and higher marriage and birth rates for young households. The VA mortgage, which was airned at younger heads, offered, of course, a powerful reinforcement to "natural" demand factors. (2) Changes in the national ownership rate cannot be satisfactorily explained without standardizing the population for age. Another finding, confirmed by direct surveys of the urban apartment market, is that the rental market in central cities is becoming increasingly dependent on selected types of customers, the one- and two-personhousehold. Between 1940 and 1950 such households accounted for 75 percent of the net increase in renters. And 396

-;J

(O

w

o

17.9 12. 2 11. 8

37. l 29. 2 41. 2

55 and over 0-$ 3,000 $3,000-$ 5, 000 $5, 000 and over

l. 9o/o 7.0

l

0-$ 3,000 $3,000-$ 5,000 $5, 000 and over

35 to 55 --

35 and under 0-$ 3, 000 $3,000-$ 5,000 $5, 000 and over

A ge In come

64. o 65.4 69.6

35. o 44. s 52. 3

13. Oo/o 20.5 27. 5

2

62. l 63. 7 76.0

36. 2 59.4 68.8

20. 2o/o 41. 3 48. 7

53. 9 74. o 82. 8

40.0 63,3 76.5

l 7. 3o/o 50.7 67.3

Size of Family 4 3

72. 7 61. 3 79,0

41. o 55. l 80.9

10. 5o/o 48.7 78.7

5

Homeownership Rates by Income, Age, and Family Size (Owners as a percent offamilies in each class)

Table 12

83. 3 90. 9 81. o

34. l 58. 3 74.3

18. Bo/o 48.7 68,4

6

47.4 63. 2 75. o

31. l 55. l 70.9

12. 2o/o 39. l 51. 4

Total

a few limited surveys have shown that upwards of 80 percent of the tenants for new apartments in the center of large cities are comprised of childless adults, generally single persons and married couples. Table 13, a three-way classification of ownership rates by income, age, and occupation, again confirms the important role of age and income. The added information is the propensity of the self-emplayed and, to a lesser extent, skilled wage-earners to have higher ownership rates than other occupational groups with the same measured income and age of head. Even if no other evidence existed concerning the variability in income of the self-employed, the exceptionally high ownership rates for the young and middleaged self-emplayed in the lowest measured income group would bespeak the importance of a higher "permanent income" level. At the same time, the higher ownership rates of self-emplayed heads in most income and age groups also suggest that status factors play a role. With respect to location (Table 14), the chain of cause and effect is more difficult to determine. The higher ownership rates found for suburban families campared to large-city families in virtually all income and age groups is partly or largely the results of an association between type of structure, (the one-family house) and land values (low-density suburbs). Do families seeking a suburban location "automatically" become homeowners because, for many reasons, this is the predominant form of tenure available there? Or is it that families seeking the one-family owned home are pushed to the suburbs because the greatest apportunities and best bargains are to be found there? Doubtless both factors play a part. Other noteworthy findings on ownership rates by location are that higher ownership rates in the large cities of the West persist evenwithingiven age and income groups. Data on the role of education in relation to ownership rates show no pronounced or consistent influence after taking account of income and age of head. In summary, the prohability that a given family will be an owner or renter can be very largely determined by knowing its income, age of head, and size of family. For high-income families with a head of 55 or older and comprised of three or mor e persons, the ownership ratewas about 80 percent in 1950, leaving little to be explained by other factors. Foryoung single-person heads of any income, the prohability of ownership was close to zero. While current income is a powerful determinant of homeownership, its relative strength depends on size of family and age of head. Because of lags, the influence of age is, of course, considerably affected by previously attained levels ofincome and family size. The prohability of ownership also increases somewhat if a family head is self-employed, and further increases if the family 398

c.:>

(O (O

55.6 66.0 80.6

59.6 62.2 80.0

55 and over --0-$ 3,000 $3,000-$ 5,000 $5,000 and over

40. Oo/o 46.8 62.0

44.9 51. 6 74. 3

29.2 46.8 71.4

9. 6o/o 37.5 46.6

Salaried SelfProfesEmployed sionals

0-$ 3,000 $3,000-$ 5,000 $ 5, 000 and over

35 to 55

35 and under 0-$ 3,000 $3,000-$ 5,000 $5,000 and over

A ge In come

38.7 60.0 71.2

26.0 57.7 66.8

7. 6o/o 38.0 44.3

65.2 68.7 75.6

37.8 58.0 69.2

12. 4o/o 41.6 66.7

o

53.3 65. l 67 3

29.3 54.4 70.5

13. 9o/o 36.6 43.4

Occupation Clerical Skilled Semiand Sales Wage Skilled Workers Earner s

44.4 56.8 77.5

23. l 48.6 63.5.

11. 3o/o 32.3 25.0

Uns killed

Homeownership Rates by Income, A ge, and Occupation (owners as a percent of families in each class)

Table 13

55.0 69. l 74.4

31.1 52.3 54.2

10.6o/o 36.4 50.0

47.4 63.2 75.0

31. l 55. l 70.9

12. 2o/o 39. l 51.4

Not Gainfully Employed Total

o o

~

40.7 57 .s 66.9

Age 55 and over 0-$3,000 $3,000-$5, 000 $5,000 and over

7.0% 29.8 30.8

66.9 69.0 76.1

50.0 64.6 78.5

23.3% 46.2 61.5

Large

20.9 44.4 62.9

Nor t h Suburb

0-$3,000 $3,000-$5,000 $5,000 and over

Age 35 to 55

Age 35 and Under 0-$3,000 $3,000-$5,000 $5,000 and over

In come

51.8 60.0 92.9

34.5 59.4 75.0

18.9% 35.5 77.8

Small

58.9 61.0 73.4

24.6 51.1 63.5

10.3% 35.9 46.9

81.6 84.0 73.3

45.2 76.8 81.5

22.6% 66.7 53.4

Location south La r ge Suburb

67.4 73.3 100.0

51.5 52.5 75.0

50.0

~3.2

19.4%

Small

47.5 64.7 74.7

30.3 58.4 73.5

11.1/o 40.0 64.9

Large

Homeownership Rates by Income, Age and Location (Owners as Percent of Families in Glass)

Table 14

69.7 73.8 95.5

44.7 76.0 78.1

15.6/o 56.0 53.6

West Suburb

60.8 67.8 79.1

46.2 58.7 76.9

14.5% 39.6 63.9

Small

47.4 63.2 75.0

31.1 55.1 70.9

12.2% 39.1 51.4

Total

resides in suburbs or small cities. The "net" influences of occupation, location, and education, how ever, appear to be small after taldng inta account age, income, and family size. Interactions among the variables exist even in three-way tables so that finer tabulatians might show samewhat different results. It is unlikely, though, that even the most detailed analyses would greatly alter the combined weights of the three "key" variables in determining type of tenure. Because choice of tenure is limited to a binary scale, the problems of variance do not appear as camplex or difficult as in the analysis of expenditures. It apparently is far simpler to develop a model which will prediet whether a person will buy or rent his shelter than to prediet how much he will spend. The housing expenditure patterus of individual households are so camplex that for the time being it appears considerably simpler to prediet them in the aggregate than to find the specific factors which determine how much a particular family will spend.

401

Appendix A The Analy sis of Covariance 1 We have the reports x i i and y i . of in come and the related housing expenditures of a sample of elonsumer units in the population. b t is the regression coefficient for the se observations where the dispersion is from their grand means x and y. bi is the regression coefficient for a subgroup of these observations from the subgroup me ans xi and yi where the subgroups are based upon a classification by one or more independent variables. bw is the regression coefficient calculated from the total deviations within groups, Le., from the sum of the deviations from each of the subgroup means xi and y i. It is the weighted average (weights being based on variance) of the individual subgroup regressions b i. bm is the regression coefficient calculated from the among means sums of squares and products, i.e., from the dispersion of xi and yi from the grand means x and y. n = number of observations in subgroup. k = number of subgroups. SSD = sum of the squares of the deviations. S t = SSD Y - b~ · SSD x = the total sum of squares about the over-all regr~ssion line, t i.e., that with the coefficient bt. (nk- 2) d.f. 2 S 1 = l:SSDyi -bi· SSDx. =the total of the sum of the squares within each subgroup from their individual regression lines, i.e., those with the coefficient b i. k (n- 2) d. f. S 2 = l:(bi- bw)2 • SSDx. =the total sum of squares among regression coefficients. (k - 1) d.f. S 3 = SSD y - b 2 • SSD x = the sum of squares of the deviations of the means from the regression line of the means, i.e., that with the coefficient b m. (k- 2) d.f. 1

1For a mor e detailed exposition cf. A. Hald, Statistical Theory With Engineering Applications (John Wiley and Sons Inc., New York, 1952) pp. 571-584: W. J. Dixon and F. J. Massey, Introduction to Statistical Analysis (McGraw Hill, New York, 1951) Ch. 12.

402

84

_

-

2

(bw- bm) ·

· SSDxm _ -the sum of squares obtained 880 x,

~SSDx;

from the difference between bw and bm. lxd.f. 8t = S 1 + 82 + 83 + 84

The tests are:

83 + 84 l. For the difference in means: F= _---=-"'k'--....;;1::---8 l+ 82 k(n-1)- l

2. As a test of whether the slopes of the regression lines within the groups are the same: ~ F

= ----'k==:--_;::_1_ 81 k (n- 2)

3. As a test whether on e regression Une can be used for all the observations: 82 + 83 + 84 F = _2=-:('=:::k,--=1)'-Sl k (n- 2)

403

Appendix B Characteristics of Excluded Groups of Families As noted in the main discussion, we felt i t necessary to decide, before undertaking a large number of analyses of covariance, whether to use the reports of the entire sample or to restrict the study to a more homogeneous group. Though arguable, it seemed to us that the logic of testing general demand relationships, particularly for application to current demand analysis, required working with a more limited population. Several groups of families as reported by the SCE are not full y subject to housing market forces, i.e., their expenditures would not be expected to follow the path of income elasticities because of basic differences in social or biological characteristics. They tend to have either very high or very low income expenditure relationships. As a result, their inclusion in the analysis would lead to erroneous results. A brief description of the size and characteristics of the omitted group follows. Knowledge of these groups has been lacking in the past, as they were hidden in class averages. It is clear that they form an interesting study in and of themselves. l.

Nonwhites (1,354 families 1 )

Compared to the general population, nonwhites had lower incomes (37 percent reported incomes under $2,000 compared to 18.6 percent for the general population) and were more heavily Concentrated in lower status occupational groups. Nonwhites were somewhat more concentrated in the younger age groups (under 45). Educational attainment was lower; only 6.3 percent had 13 or more years of school compared to 18.3 percent for all families. With respect to location, nonwhites wer e much mor e heavily represented in the South, samewhat mor e in the North, and less in the West. Except in the South, urban nonwhites predominantly lived in large cities. The family size distribution of nonwhites was more heavily weighted with large families; campared to 13.9 percent of all 1The number of omitted families in each category is based on the full sample and includes families in the omitted income groups.

404

families, 17.6 percent of nonwhites headed f amilies with five or more persons. Nonwhites also had a "looser" family organization with lower proportions of "normal" families (husband-wife with children and no other adults), and with higher proportions of oneparent families as well as of families neither having children nor headed by a married couple. Only 30.9 percent of nonwhites were homeowners campared to 48.7 percent of all families. The level of housing was also lower, with 73.1 percent living in the two lowest housing braekets campared to 38.3 percent for all families. 2.

Families with white head 65 years or older (1,602 families)

The special characteristics of elderly families hardly need recounting. More than half had incomes below $2,000. Nearly 57 percent were not gainfully employed campared to lessthan 14 percent of all families. Educational attainment was also lower with 64 percent having eight years or less of school (all families, 40.4 percent). Reflecting pastand current migration patterns, older farnilies were relatively more frequently found in the West as well as in suburbs and small cities. Family size was smaller, with 80.9 percent made up of only one or two persons. A very high proportion (60 percent) of older families were homeowners. The current level of housing was surprisingly high; nearly 12 percent lived in housing in the highest four categories of mark et valu e or rent. The corresponding proportion for all families was only 3.9 percent. 3.

Rent-free families (487 families)

The reason for excluding this group from regression; analysis is obvious. These were typically families who were required to live at their job si te and were suppli ed with free living quarters as a supplement to income, i.e., income in kind. Had the housing and income accounts of the SCE been established on the basis of "real" rather than cash flows, the rental value of the housing occupied would have been added to both housing consumptian and income received. By definition, no rent-free families are homeowners. They have lower than average income. Data on age, family size and type, education and occupation, indicate that the rent-free group is made up largely of two types: (a) young professionals such as student doctors, nurses, etc., and (b) older unskilled workers such as janitors or caretakers, typically comprised of small households without children. Their geographical distribution is quite similar to that for all families, though slightly more Concentrated in the West. 405

4.

Nonhousekeeping families

(1,~27

families)

This group, which overlaps some of the groups already discussed, was removed from the deck for two reasons: (a) housing is not presurned to fill the same bundle of wants as for normal families, and (b) their housing expenditures were likely to be greatly affected by inclusion of charges for furniture, maid service, etc. Nonhousekeeping families were predominantly found in the lower in come groups and tended to be headed by younger, unskilled wage earners with higher than average educational attainment. A majority were one-person families and virtually 90 percent lived in housing with low value or rent. Their geographical distribution appeared to be the same as for the general population with no pronounced tendency to cluster more frequently in large cities. 5.

Atypical tenure groups (1,451 families)

This group also overlaps several of the aforementioned categories. It is made up chiefly of families who changed tenure during the year, thereby making it impossible to obtain a full year's rent or ownership expense. Moreover the housing expenditures of renters who became owners during 1950 or 1951 were unduly exaggerated because of the inclusion of large but nonrecurrent outlays for legal fees, mortgage fees and closing costs. Families in this group tended to be more often renters than owners. Their occupational distribution was fairly close to that of all families but income tended to be lower and educational attainment higher, both largely attributable to younger average age. Family size was below average, partly because families in this group were typically childless individuals or couples. In total (allowing for overlap) about 4,500 families were considered to be ineligible and were removed from the deck used for our main regression analyses. In addition, single-person consumers were omitted from regression on family size. The characteristics of the excluded familias relative to all families are shown in Table B -l.

406

.,..

o -:J

III.

II.

I.

Occupation Self-employed Salaried professional, etc. Clerical and sales

Income Under $1,000 $1,000-$2,000 $2,000-$3,000 $3,000-$4,000 $4,000-$5,000 $5,000-$6,000 $6,000-$7,500 $7,500-$10,000 $10,000 or more Total

Total Tenure Owner Renter Other Total

13 .l

13.6

9.8

6.3 12.3 18.7 24.0 16.9 9.5 6.4 3.5 2.4 100.0

48.7 44.0 7.3 100,0

4.9 3.2 4.3

10.2 26.8 29.9 18.2 9.8 3.0 1.2 0.7 0.2 100.0

30.9 67.4 1.7 100.0

9.8 5.4 5.6

\

2.1 1.8 100.0

h:

25.2 25.3 18.9 12.9 7.7

60.0 39.1 0.9 100.0

5.6 19.0 23.6

12.7 33 .lf 31.3 14.7 4.4 1.5 l. O 0.5 0.5 100.0

19.6 74.3 6.1 100.0

l Person All Nontfuite \Vhite Families w~ite Over 65 Under 65a 12, 489--~53---1,662 ____958 Rent Free

9.2 16.0 12.9

17.5 28.5 21.4 14.6 8.0 4.1 2.7 2.5 0.8 100.0

0.0 82.9 17 .o 100.0

487

Selected Characteristics of Excluded Groups of Farnilies in Gomparison with All Families (Percent Distribution)

Table B-1

7.0 15.8 17.4

9.3 5.0 3.1 1.6 1.7 100.0

17.4

10.6 25.3 26.0

12.6 71.5 15.8 100.0

1,228

--~~_p_ing

NonHouse-

_

7.2 14.3 14.5

11.1 21.0 23.1 20.1 12.3 5.9 3.4 1.3 1.7 100.0

28.3 54.8 16.9 100.0

_g_~ups

1,451

Atypica1 Tenure

00

... o

VI.

v.

IV.

III.

40.4 41.3 15.7 2.6 100.0 30.9 9.9

Location Nor t h: large cities sub urb s

3.8 21.8 23.1 20.4 16.4 10.4 4.1 100.0

Age of Head Under 25 25-34 35-44 45-54 55-64 65-74 75 or over Total

Education 8 years or less 9-12 years 13-16 years 16 or over Total

8.1 19.4 45.9 14.2 100.0

17.8 17 .l 14.9 13.1 100.0

Occupation Craftsman Operatives Unskilled wage earners Not gainfully employed Total

32.2 2.6

65.2 28.4 5.6 0.7 100.0

4.4 23.6 23.8 22.3 14.3 8.9 2.5 100.0

NonWhite

All Families

30.6 10.5

64.2 25.2 9.3 1.2 100.0

28.0 100.0

-72.0

6.7 4.8 10.9 56.8 100.0

White Over 65

Table B-l (continued)

32.8 5.7

32.9 39.6 23.6 3.9 100.0

100.0

--

7.7 16.2 16.2 25.0 34.9

7.7 12.5 20.5 11.1 100.0

l Person White Under 65a

24.4 6.2

35.7 38.8 22.0 3.5 100.0

12.7 28.1 16.4 15.0 12.1 11.3 4.3 100.0

11.3 12.7 23.4 14.4 100.0

Rent Fr e e

32.2 7.3

34.1 41.8 21.3 2.8 100.0

12.6 25.2 17.1 16.1 15.6 10.3 3.1 100.0

10.6 13.4 24.6 11.2 100.0

kee2i~

NonHouse-

30.6 7.4

34.0 43.8 19.7 2.5 100.0

10.7 31.0 19.4 13.6 12.6 9.7 2.8 100.0

14.2 17.1 21.1 11.5 100.0

Atypical Tenure Grou2s

i

Family size l person 2 persons 3 persons 4 persons 5 persons 6 or more persons Total

Family type H. W. only H. w. oldest child under 6 H. W. oldest child 6-15 H. W. oldest child 16-17 H. W. oldest child 18 and up l parent, oldest child under 18 Other adults, no child

VIII.

Location Nor t h: small cities south: large cities suburbs small cities large cities West: suburbs small cities Total

VII.

VI.

21.5 9.4 12.0 2.0 6.3 3.7 28.9

23.3 14.1 17.2 3.1 10.1 1.9 22.1

13.5 32.1 23.2 17.3 8.2 5.7 100.0

17 .s 32.0 20.0 12.9 7.6 10.0 100.0

0.2 47.2

0.3 0.5 8.3

o.o

38.7

30.8 50.1 12.3 3.7 1.7 1.4 100.0

6.6 10.1 1.9 2.4 20.7 5.4 11.7 100.0

0.3 39.9 4.5 8.6 8.2 1.0 2.7 100.0

15.4 4.0 3.5 17.6 5.1 8.5 100.0

s.o

White Over 65

NonWhite

All Families

Table B-1 (continued)

---

-

5.4 10.9 2.5 1.9 29.7 4.1 7.0 100.0

l Person White Under 6Sa

20.3 9.9 3.5 0.2 1.1 2.5 61.1

3.1 37.6

57 .l 30.3 8.4 2.9 1.1 0.2 100.0

4.2 16.8 3.3 2.4 23.0 3.3 7.6 100.0

keeei~

NonHouse-

24.2 18.3 7.6 1.6 3.7

33.9 33.4 15.6 10.7 4.7 1.6 100.0

5.1 15.0 3.7 3.7 22.8 8.0 11.1 100.0

Rent Fr e e

2.7 45.8

18.2 16.0 9.8 1.1 2.8

43.3 26.5 15.9 9.6 3.0 1.6 100.0

4.0 15.4 3.2 2.0 23.4 4.9 9.2 100.0

Atypical Tenure Groues

o

.,.. .....

6 7 8 and 9 Total

5

Level of Housing l 2 3 4

Family type All other Total

100.0

(

( 3.9

(

11.7 26.6 28.0 17.7 12.1 29.8 43.3 19.4 6.3 0.6 0.4 0.1 O. l 100.0

16.1 100.0

8.1 100.0

aOmitted only from regressions on family size.

IX.

VIII.

NonWhite

All Families

18.9 28.5 20.3 17.4 3.5 4.9 2.2 2.6 100.0

4.9 100.0

White Over 65

Table B-1 (continued)

23.0 43.4 18.7 8.5 2.1 1.7 l. O 1.6 100.0

-

l Person White Under 65a

---

--

3.9 100.0

Rent Fr e e

24.8 40.5 19.6 8.2 2.7 1.5 l. l 0.9 100.0

1.2 100.0

keeEi~

NonHouse-

25.8 37.1 18.2 10.2 3.9 2.3 l. O 0.8 100.0

3.7 100.0

Atypical Tenure Grou12s

""'" ""'"

11\.

514 533 615 591

458

970

536

863

$5,000-$6' 000

$6,000-$7,500

$7' 500-$10,000

451

361

$3,000-$4,000

$4,000-$5,000

$ 391

$ 324

$2,000-$3,000

Income Class

629

556

624

571

455

$ 126

Owners without Mortgage Under 35 35-55 55-65 Years Years Years

894

803

674

650

543

$ 536

794

1,029

1,030

832

746

847

640

574

$ 504

722

642

583

$ 561

Under 35 Years

737

728

660

584

$ 509

Owners with Mortgage Under 35 35-55 55-65 Years Years Years

Average Housing Expenditures by Income, Tenure, and Age of Read

Table C-1

Appendix C

892

809

710

656

594

$ 522

Renters 35-55 Years

892

876

700

666

642

$ 561

55-65 Years

t.)

Ii'>....

545

555

583

603

645

$4, 000-$ s, 000

$5,000-$6,000

$6,000-$7,500

$7,500-$10,000

$414

$3, OOO-$L~, 000

$2,000-$3,000

Income Class

557 671

806

557

498

416

$364

729

549

512

474

$475

1,035

1,024

848

709

766 838

696

554

$572

694

631

$567

1,042

871

796 832

802

760

678

$566

606 642 775 676

766 820 985

551

$496

Wag e Earner s and not Gainfull y EmJ2lO;t:ed

667

628

$561

Renters Self-employed, Salarled Pro fessionals, Clerical and Officials, Sales etc, Workers

686

624

559

$511

Owners ~vithout Mortgas;e ~ers with Mortgage Self-emSelf-emWag e ployed, Wag e ployed, Salarled Earner s Salar i ed Earner s and ProfesProfesand sionals, Clerical not sionals, Clerical not and OffiGainOff iand GainSales full y full y cials, cials, Sales etc. Workers Em12lo~ed Workers EmJ2lo~ed etc.

Average Housing Expenditures by Income, Tenure, and Occupation

Table C-2

~

....

w

$ 405 446

$ 360

419

Income Class

$2,000-$3,000

$3,000-$4,000

574

519

596

678

$5,000-$6,000

$6,000-$7,500

$7,500-$10,000

679

605

537

$4,000-$5,000

494

Owners without 8 Years school 9-12 or Years Less school

664

619

554

515

536

$ 476

13 Years school or Mor e

Mort~a~e

880

698

668

627

564

$ 530

907

639

699

655

553

$ 510

1,049

888

789

691

646

$ 583

O>mers with Mortgage 8 13 Years Years school school 9-12 or or Years school Mor e Less

Average Housing Expenditures by Income, Tenure, and Education

Table C-3

807 935

692

701

649

598

$ 547

9-12 Years school

Renters

751

608

599

538

$ 466

8 Years School or Less

1,022

911

798

723

647

$ 567

13 Years school or Mor e

""'

..... ""'

Lf84

591

577

638

728

$3,000-$4,000

$4,000-$5,000

$5,000-$6,000

$6,000-$7,500

$7,500-$10,000

$2,000-$3,000

631

524

495

440

412

614

599

607

450

417

$ 370

$ 416

Income Class $ 380

Owners without Mortgage Large Cities and Large Small Suburbs Cities and Ci ties south Suburbs and All Nor t h West Regions

1,024

862

752

701

601

$ 597

867

726

668

614

558

$ 495

1,076

927

719

615

571

$ 431

Owners with Mortgage La r ge Ci ties and La r ge Ci ties Suburbs Small and south Cities Suburbs and All Nor t h West Regions

Average Housing Expenditures by Income, Tenure, and Location

Table C-4

789

877 1,025

801 862

989

706 702

721

610

$ 502

632

586

$ 506

659

651

586

$ 536

Ci ties and Suburbs Nor t h

La r ge

Renters La r ge Cities and Suburbs Small south Cities and All West Regions

C1J

.... ...... 582 558 736

363

465

2,484

$6,000-$7,500

$7,500-$10,000

548

$5,000-$6,000

318

443

631

$3,000-$4,000

$4,000-$5,000

$ 414

$ 416

$2,000-$3,000

Income Glass

2 Persons

624 779

606 617

532

557

-

593

546

499

$ 513 604

$ 258

l Person

819

762

727

668

552

$ 559

2 Persons

993

835

705

660

584

$ 520

3-5 Persons

872 912

982

684

656

603

$ 546

2 Persons

1,890

718

673

596

$ 507

l Person

634

648

958

802

816

743

615

556

586

737

$ 432

6 or mor e Persons $ 513

3-5 Persons

Renters

819

788

593

491

$ 414

6 or mor e Persons

Owners with Mortgage

469

436

$ 361

6 or mor e Persons

Mortg~

3-5 Persons

Owners without

l Person

c-s

Average Housing Expenditures by Income, Tenure, and Family Size

Table

oJ>. ..... O)

.477( .177)

Owners without mortgages Owners with mortgages Renters .452(.167)

• 533( .139)

.465(.038) .502(.028) .442 (. 020)

.465(.038) • 502(. 028) .44-2(.020)

Owners without mortgages Owners with mortgages Ilenters

0\iners without mortgages 01\ners with mortgages Renters

Vat:_~_!'l_b_les He~~~n_s_t_~t_ _ _ _(St~-~_r:_d_~ror)

bt

.451(.092) .493(.066) .413(.064)

.450(.038) • 504( .028) .4lf2( .020)

.448(.039) .457( .029) .411(.020)

w (Standard Error)

b

.0514 .0329 .0252

.0499 .0328 .0263

.3474 .5071 1.6638**

.2676 .1462 .2528

Among 3 Occupation Classes (Grouped Data)

l. 2874** .8534** .0010

Among 3 Location Classes (Individual Observations)

.1650* .7428** 1.8703**

Among 3 Education Classes (Individual Observations)

Mean Sguares of Residuals S3 and S1 and S4 S2

Regression Coefficients, Standard Errors, and Mean Squares of Residuals Derived from Analysis of Covariance

Table C-6

~

......

-J

,{:.67 ( .158) .605(.187) ,4Cf4(, 097)

Owners without mortgages Owners Hith mortgages Renters

.441(.004) .487(.007) . 552( .012)

Cities and suburbs North .4-37( .006) Cities and suburbs South and West .433(.012) Small cities all regions .505(.017)

*significant at the .05 level. **Significant at the ,Ql leve1.

.484( .085) . 597( .098) .448( .047)

.467(.158) .605(.187) .444(. 097)

Owners Hithaut mortgages Owners with mortgages Renters

.466(.078) . 601( .100) .442( .0Lf5)

(~tandard Error)

b

Variables Held eonstant

t

"' (Standard ~rror)

b

Table C-6 (continued)

.1%5 .3318 .1165

.2231 .3533 .1290

2.2120**

4. 68 54>'""'

2 .6732'''

.0011 .0022 .0034

Among 3 Tenure Groups (Individual Observations)

.0945 .2277 .1875

Among 3 Age Classes (Grouped Data)

.2944 .0281 .1254

Among 3 Family Size Classes (Grouped Data)

Mean Squares of Residuals S3 and S1 and S4 S2~--

""'

CXI

1-A

353 401 475 551 408

640

564

666

849

$4,000-$5,000

$5,000-$6,000

$6,000-$7,500

$7, 500-$10,000

$ 341

490

$ 400

$3,000-$4,000

$2,000-$3,000

Income Class

594

436

448

420

377

$ 314

708

587

628

52.0

464

$ 414

648

507

558

485

421

$ 368

Owners without

677 631

716 652

748 668 570

516 749

502

453

$ 427

393

402

617 519

590

$ 533 515

$ 433

13 Years school or More Large Ci ties La r ge and Suburbs Cities Small and south Ci ties Suburbs and All North West Regiom

644

446

448

$ 430

Mort~age

Average Housing Expenditures by Income, Tenure, Education, and Location 8 Years School or Less 9 to 12 Years School Large Large Ci ties Cities Large and Large and Suburbs Suburbs Ci ties Small Ci ties Small and south Ci ties and south Ci ties Suburbs and All Sub ur b s and All North West Regions North West Regions

Table D-1

~

.... co

507 499 660 656 698

620

721

676

758

949

$3,000-$4,000

$4,000-$5,000

$5,000-$6,000

$6,000-$7,500

$7' 500-$10,000

$ 494

$ 622

$2,000-$3,000

972

705

773

703

866

596

631

532

$ 465

621

679

564

$ 565

935

1,270

677

930

1,082

1,364

895

883

767 803

647

668

$ 413

662

596

$ 57 5

971

787

758

682

571 639

$ 622

13 Years school or More La r ge Cities Large and Suburbs Small Ci ties and south Cities and Suburbs All West Reg;ions Nor t h

$ 471

Owners with Mortg;ag;e

9 to 12 Years School Large Cities Lar ge and Small Ci ties Suburbs and south Cities and Suburbs All Nor t h West Regions

771

647

512

531

$ 385

8 Years School or Less La r ge Cities and Large Suburbs Small Cities and south Ci ties and Suburbs All Nor t h Regions West

Table D-1 (continued)

~

o

1\:1

583

703

$7,500-$10,000 74-3

884

809

773

744

$6,000-$7,500

738

722

578

649

595

608

$5, 000-$6' 000

591

$ 552

649

534

$ 436

560

$3,000-$4,000

$ 417

573

527

$2,000-$3,000

617

$ 508

Income _g]._ass

Small Cities All Regions

·~·------

1,040

800

656

664

583

$ 549

829 977 l, 082

864 977

814 1,010

707

818

645

637

714

$ 559

$ 558

l, 008

782

800

755

672

$ 6ll

13 Years school or More Large Ci ties Large and Cities Suburbs Small and Ci ties south Suburbs and All Regions North West

720 620

592

$ 531

12 Years ·--School-Large Ci.ties La r ge and Cities Suburbs Small and Cities south Suburbs and All Nor t h West Regions Renters

-----~------~····

9 to ------

$4,000-$5,000

La r ge Cities and Suburbs Nor t h

Large Cities and Suburbs south and West

---~--Y~_a!_~_s_c_h~o_l__o_r___l:E:.§.s__

Table D-1 (continued)

~

t~:)

.-

$2,000-$3,000 $3,000-$4,000 $4,000-$5,000 $s, 000-$6,000 $6,000-$7,SOO $7,500-$10,000

$2,000-$3,000 $3,000-$4,000 $4,000-$5,000 $5,000-$6,000 $6,000-$7,500 $7,500-$10,000

Income Class

-

465 524 402 363

217 -

$ -

l person

$33S 3S7 469 594 537 722

370 454 490 521 616 572

417 427 526 S66 623 57 s

3-5 persons

$350 395 378 441 535 399

2 persons

Under 35 Years of

293 489 486 591 600 741

1,306

-

582 293

~.2/+

$2llf

6 or mor e persons

~

2 persons 3-5 persons

6 or m'< .0479

.0793 .0177 .0171

.0273 .0449 .0316

Among 3 Occupation Classes (Grouped Data)

Mean Squares of Residua1s S3 and s1 and S4 S2

SERVICE EXPENOITURES AT MID-CENTURY by Robert Ferber University of Illinois

The objective of this paper is to examine expenditure patterns of urban families for services at the mid-Century mark and to suggest, on the basis of such an examination, hypotheses that might explain variations in such outlays. Mor e specifically, we shall focus on the following questions: l. What are service expenditures and how do they differ from other expenditures? 2. How important were the various categories of service expenditures at mid-Century, and how does this vary by population groups? 3. How important do various socio-economic variables seem to be in explaining variations in service expenditures? 4. To what extent are expenditures for different services intercorrelated? The scope of this investigation is restricted by data available from the 1950 Consumer Expenditures Study. This means that certain services cannot be included, notably personal business and domestic service, and that others are intermingled with related goods, as in the case of auto repairs. The omitted categories are of relative ly minor importance in the consumer budget, however, and the greatbulk of service expenditures 1 are covered in this study. It should be noted that our cancern here is with a static picture of consumer service expenditure patterns at a particular point in time, the year 1950. The dynamics of these patterns is a major subject in itself and is not treated in this paper. The Nature of Service Expenditures Goods vs. Services When a consumer buys a good, he is acquiring a tangible possession, if only for a brief period of time. When a consumer buys 1At least 75 percent, based on an estimate derived from the U. S. Department of Commerce data on aggregate consumptian expenditures in 1950.

436

a service, he is acqmrmg something intangible, something which he does not own but which nevertheless renders, in his opinion, some useful purpose or function. This function can vary from providing shelter, in the form of rent, to providing recreation, in the form of paying to see a rnavie or to take a trip, or to pay for medical care, etc. To be sure, goods also provide certain functions and would not be bought if i t we re not for the functions or services they perform. Thus, similar to renting accommodations, the purchase of a home provides shelter and would not be bought if it did not serve this purpose (excluding investment motives). In fact, essentially goods too are bought for the service that they provide and in this sense it could be claimed that the distinction between goods and services becomes rather vague. The distinction becomes sharper when we consicter these two forms of expenditure from the view of saving and investment. With the exception of purchases made for instantaneous consumption, such as restaurant meals, a certain proportion of the purchase price of a good can be retrieved, if necessary. Generally, this portion is small, though occasionally the resale value may exceed the original purehas e price, as dur i ng a sharp inflation or a war. To the extent that resale is possible, expenditures for goods represent saving as well as spending, and there is some evidence that acquisition of various durable goods is at times considered a substitute for saving. 2 When services are purchased, however, the re is clearly no element of saving.3 When the service is received, the money is fully spent and there is no question of possible resale. In the case of goods, this is only true when the good has been fully "consumed" rather than when it has been acquired. On the other hand, the distinction may lose much of its meaning when we consicter consumer choice. An expenditure is contemplated in order to fulfill a specific need or desire, whether real or imagined. In many, if not most instances, this need can be fulfilled either by acquiring a good, which is the n used to fill the need, or by obtaining the service directly. This is clearly true of such needs as shelter, recreation (e.g., TV versus movies), personal care and household operation. With the possible exception of food, where a good has to be purehas ed, or of medical care, where self treatment is hardly practicable, the consumer can generally ehoase to fulfill a given need or desire by purchasing a good or a service. Such canbe-and is at times-the case for clothing, for automobiles, for vacation trips, and for many other needs. In fact, our society conceivably could be organized in such a fashion that the great bulk 2 Particularly so during the last war. 3Except for the trivial case of refund of unusued prepaid services, e.g., tuition fees.

437

of consumer needs and desires are met through the purchase of services rather than through the purchase of goods (and probably much more efficiently than is currently the case! ). In any event, it deserves emphasis that the demand for many services even under current conditions has to be assessed not only in relation tothe needs or desiresfulfilled bythem butalso in relation to the availability of goods that canprovide essentially the same function. In many such cases, a decision one way or the other has important ramifications for outlays on other goods or services as well. Thus, the decision to build or purchase a house, instead of to rent one, automatically entraps the consumer inta an undetermined amount of future outlays on home maintenance. A decision to bu y a television set and to go to the movies less often commits the luckless purebaser to enriching the TV repair industry. The purchase of an electric appliance is automatically accompanied by the use of an associated service, electric power. In general, the purchase of a good will entail certain associated service expenditures to maintain the good in proper shape or operation. This is Iikely to be true of the purchase of a service only from an aggregative point of view, name ly, to the extent that the provide r of the service ma y himself have to incur e:xpenditures to maintain staff and equipment. Furthermore, the decision whether a good or a service should be purchased to meet a certain need may well depend on considerations other than the ability of the alternatives to meet the given need. Thus, there is little doubt that desire to "establish roots" has motivated many people in the past to buy rather than rent a house aside from the economics of the situation, and that the do-ityourself fad has led people into undertakinga on their own, when more level-headed thinking would have dictated otherwise. Fashions, fads, and the desire or distaste for tangible passessions all can influence the decision whether a good or a service should be purchased to fill a particular need. These factors become all the more important with the rise in standards of living and the growth of technology, both of whi ch act to increase the r ange of choice, one from the demand side and the other from the supply side. Types of Services Service e:xpenditures may be said to arise as a result of the following four ''basic" desires, or objectives, that appear to be characteristic of mid-Twentieth Century society: 4 There are some exceptions, however. Thus, the mere availability of electricity to a family formerly without it is likely to lead to the purchase of electric appliances and products.

438

Care and maintenance of a home-rent, household utilities, household operation, domestic service Adequate transportaHon-p u r c h a s e d transportation, auto operation Care and maintenance of other possessions-elotbing and jewelry services, business services, furniture and appliance repair Maintenance and improvement of self-personal care, medical care, recreation, education, gifts, and contributions This classification differs noticeably from the traditional triumvirate of basic consumer needs-food, clothing, and shelterpartly because of the fact that it refers to services only but largely be cause of the substantially increased levels of living in our "affluent society," which render this classical breakdown obsolete. The present classification recognizes that the aim of modern economic life is more than just survival and that most consumers are in a position to actjust their expenditures accordingly. 5 The above classification is clearlynot the only one of this type that could be prepared. However, i t does serve to compress the highly heterogeneous types of services into a small number of reasonably logical categories, perhaps the first time this has been tried, and potentially may be a useful analytical tool. The classification also serves to highlight on the one hand people's desires for a comfortable home and for material passessions and on the other hand for improving and maintaining the i r physical and mental beings as well as for adequate transportation for both work and play. In a traditional sense, the bulk of expenditures in the middle two categories would be classified as "luxuries'' but, again, given the present standards of living in this country these desires are generally felt to be fully as essential as the needs for material comfort. The classification of individual service components by category is admittedly somewhat arbitrary. Thus, one could question the inclusion of "gifts and contributions" or of "recreation" under "maintenance and improvement of self" if the latter category is defined in a rather narrow sense. In a broader sense, however, both of thesetypes of expenditures contributetc one's maintenance, and gifts to improvement as well from a metaphysical point of vie w. Similarly, repair of radio and TV could be listed under "maintenance and improvement of self" instead of "other possessions" except that in most instances the primary objective of the purchase would seem to be recreation. An analogous reason was used for classifying household operation under care and maintenance of a 5 It is perhaps needless to note that the same classification applies to goods as well as services, the only change required being removal of the prefatory phrases "care and maintenance of" in the first and third categories.

439

home, though part of this category undoubtedly pertains to "other material possessions" and would be so treated in an empirical study if data were available in sufficient detail. A certain degree of arbitrarine ss is inevitable in any such classification and any results obtained therefrom must be interpreted with proper care. It is of interest to note that onlytwo of the four objectives-care and maintenance of other passessions and maintenance and imp~ve­ ment of self-can be met almost solely through the purchase of services. With each of the other two objectives, the consumer is faced with the choice not only of allocating his resources among them hut also, in varying degrees, whether to fulfill that particular objective through the purchase of a good or through the purchase of services. It is also worth nating that each of the four basic desires includes both so-called luxury expenditures as well as so-called necessity expenditures, the latter being defined rather loosely as those expenditures essential for health and survival. This would include all or some of rent, utilities, household operation, equipment repair s, clothing services, purchased transportation, personal care and medical care. Possibly this dispersion of such expenditures reflects a deficiency in the classification scheme. More like ly, however, it illustrates once again the inapplicability of such definitions to mid-Twentieth Century conditions, a fact that is reinforced when we nate that virtually all of the so-called necessity expenditure categories include so-called luxury as well as necessity components. Even expenditures such as rent and personal care comprise for many, if not most, consumer units large components that could hardly be classified as necessities. Inasmuch as the distinction between necessities and luxuries has long been an arbitrary matter, i t seems all the more desirable to avoid using these concepts in discussing current expenditure patterns. As noted ear lie r, for the great maj or ity of the population, these distinctions passess little significance. If these concepts are used at all, they are best considered equivalent to income-inelastic and income-elastic properties of the expenditures concerned, hut in view of the semantic connotation associated with words "necessity" and "luxury," the more technical expressions would see m to be more appropriate. The se latter terms are also not without limitations, particularly with regard to the empirical estimation of elasticities, hut nevertheless passess considerable analytical value, as has been shown repeatedly in the past. In the following seetians of this study we shall examine the manner in which service expenditures for these basic purposes as well as for individual categories varied in 1950by population groups. Doing this and at the same time studying the extent to which such expenditures are interrelated by population groups and are affected

440

by different socio-economic variables should indicate the general pattern of consumer service expenditures at mid-Century. Expenditure Patterns The allocation of service expenditures by the classification advanced in the preceding section, and by major expenditure categories, is presented in Table l for urban families for 1950. As is evident from that table, the expenditure categories listed therein rep re sent about 40 percent of total urban family outlays for current living in 1950. This proportion varies in a U-shaped manner by income level rising to almost 44 percent at the highest and lowest income levels shown and dropping to below 38 percent for those within the $5,000-7,499 range. At the same time, in relation to income after ta.xes the proportion not surprisingly declines substantially as income rises, reflecting primarily the growing importance of saving at higher levels of income.6 Examination of the changes in outlays for different expenditure purposes indicates that the U-shaped pattern of expenditures for all services is the manHestation of opposing trends for these major categories. Service expenditures for the care and maintenance of a ho me decline in proportion to the total as income rises, while expenditures for transportation, self, and care and maintenance of other passessions rise with income. At the lowest income levels, outlays for the home ta.ke the largest proportion-more than half of total services at the lowest level-whereas among families earning $10,000 or more in 1950 outlays for one's self accounted for more expenditures than for the home. On the average, outlays for self and for the home accounted for three-fourths of urban family service expenditures in 1950, transportaHon an additional sixth, and other passessions the remainder. Considerable variation as income rises is evident in the relative importance of different services within each of the four basic classifications. Thus, for home-connected purposes, outlays for housing and utilities decline in importance with rising incomes while household operation expenses increase. For transportation, auto 6The proportion would probably decline less rapidly in relation to income and be higher in relation to total expenditures if data we re available for excluded services. The rnost important of these is business services, which can be expected to rise sharply with increasing income. On the other hand, the magnitude of the overall proportions shown in Table l as indicators of the importance of services in the household budget are biased upward because of the inclusion of outlays for various goods under such categories as auto operation, household operation, and medical care.

441

~

.,...,..

Housing Fuel, light refrig. Household operationt

Home

58.2%

Above services as pet. of income after taxes 42.6%

39.0%

l. l 0.3 3.2

0.8 0.2 3.8

1.2

2.0

4.0 2.0

12.4% 4.7 2.0

5. l 1.0

10.7

3.2

6.0

19.1%

5.6 1.0

1.1

2.3

2.5 2.0

15.8% 6.2 2.3

$2,000-2,999

o

39.2%

37.9%

11.

3.2

6.8

16.9%

l. l 0.5 3.4

5. l 0.9

2.0 1.2

1.5

5.3

10.9% 4.0 2.0

$3,000-4,999

36.5%

37.6%

11. 4

3.6

7.2

15.4%

l. l 0.7 4.0

4.7 0.9

1.4

2.2

1.7

5.5

9.8% 3.4 2.2

$5,000-7,499

35.0%

39.4%

13.3

3.9

7.0

15.2%

1.2 0.9 5.2

5.0 1.0

2.5 1.4

5.2 1.8

9.4% 3.2 2.6

$7,500-9,999

32.5%

43.6%

16.7

5.3

5.4

16.2%

0.9 1.4 9.8

3.7 0.9

1.3

4.0

3.8 1.6

2.5 4. l

9.6%

$10,000 & over

39.1%

39.0%

11.7

3.5

6.5

17.3%

1.0 0.6 4. l

5.0 1.0

1.3

2.2

4.8 1.7

11.0% 4.0 2.3

All families

•current family expenditures throughout this paper include gifts and contributions, which are listed Separately in the original source. tEach of these categories represents approximately half of the "household operation" total in each case in the original source. Thisallocatian was based on examination of the detailed expenditure breakdowns in Vol. 13 of tbe 1950 Consumer Expenditure Study. tActually, about 60 percent of this category represents purchases of goods connected with auto operation and maintenance, principally gas, oil, and auto parts. Nevertheless, the category is included in this study because of the substantial importance of services. Source: Derived from Study of Consumer Expenditures, Incomes and Savings, Vol. 18, Table l.

43.6%

11. 4

3.4

4.5

24.3%

Under $2,000

Total

Medical care Personal care Recreation (admissions) Education Gifts & contributions

IV. Self

Household i temst Clothing services

III. Other passessions

Au to operat i ont Pchsed. transp.

II. Transportatian

I.

Category

Percent of Total Current Family Expenditures• Spent for Particular Service, by Income Level, Urban Areas, 1950

Table l

operation increases relativelywith income while purchased transpartatian registers little change. The increase in service outlays on one's self is seen to be wholly due to sharp increases in educational expenditures and in gifts and contributions; outlays for medical care, personal care, and recreation either decUne or remain the same relativelyas incomes rise. To some extent, these differences reflect the substitution of one type of expenditure for another-as in the case of auto operation vs. purchased transportation-but in addition, and perhaps to a larger extent, they reflect the heterogeneous nature of the different services within as weil as between categories. This is particular ly true of the variety of expenditures relating to one's self but also holds for the other three in varying degrees as weil. As for goods, preferences for different types of services do not vary uniformly between income levels, or between other population groups. The extent to which these preferences vary by income level is brought out more clearly in Table 2, which presents estimates of the income elasticitybetween successive income intervals for each category of service expenditures listed in Table l. Each figure in this table shows the average percentage by which outlays for the given service increase for each unit percentage increase in income between the two income intervals.7 Thus, the last two lines of the table indicate that the elasticity of service outlays rises over the income scale, increasing from six-tenths of one percent for each percent rise in income at the low end of the scale to almost ninetenths of one percent at the upper end of the scale. At the same time, the elasticity of all other expenditures, excluding the categories Iisted in the table, declines from .84 at the lower income levels to .63 at the higher income levels. It therefore appears that the effect of a rise in income leads primarily to the purchase of goods at low income levels but shifts increasingly toward services at higher income levels. The body of the table indicates that substantial variations in income elasticity are evident among individual service categories as weil as among the four objectives of expenditures. Service expenditures for the home, for other passessions and for one's self are relatively inelastic to income changes at low income levels but become increasingly sensitive to income changes as the level of income rises. Outlays for the latter two purposes increase more 7 The income elasticities are computed from the expression:

where C i and Y i are the ave ra ge outlay and in come, respectively, at income level i.

443

""'""'""'

0.61 0.71 l. 90 l. 31 0.51

0.54 0.89

l. 31 0.75

0.40% 0.36 0.54

0.88 0.66 0.88 2.04 l. 00

0.88 0.86

l. 51

o. 20

0.91%

0.81%

0.94

0.88

1.16

0.58% 0.66 0.88

0.59%

$2-2,999 to 3-4,999

0.65 0.81 0.84 l. 66 l. 23

l. 07 l. 19

0.93 l. 15

0.86%

0.83%

0.93

1.11

0.98

o. 60% 0.47 l. 07

0.63%

$3-4,999 to 5-7,499

0.67%

0.88%

l. 19

l. 02

0.67

0.70%

0.93 l. 16 l. 00 l. 42 l. 50

l. 17

o. 76

0.59 0.91

0.63% 0.57 l. 17

$5-7,499 to 7,5-9,999

Derived from Study of Consumer Expenditures, Incomes and Savings, Vol. 18, Table l.

0.84%

All other expenditures

Source:

0.58%

o. 66

0.65

1.11

0.40%

Under $2,000 to 2-2,999

All services

Medical care Personal care Recreation (admissions) Education Gifts and contributions

IV. Self

Household items Clothing services

III. Other passessions

Auto operation Pchsed. transp.

II. Transportatian

Housing Fuel, light and refrig. Household operation

I. Home

Category

Income Interval

Income Elasticity for Particular Services, by Income Level

Table 2

--

0.63%

0.89%

l. 04

l. 18

0.33

0.83%

0.26 0.57 o. 28 l. 38 l. 61

l. 40 0.62

0.25 0.65

O. 77% 0.35 l. 40

$7,5-9,999 to 10,000 & over

than proportionately to a rise in i neo me above the $5,000-7,500 range. On the other hand, transportaHon exhibits an opposite trend, being highly e lastic at low income levels and be coming increasingly inelastic at successively higher levels. These trends in elasticities bythese four basic objectives are attributable to one or two types of service expenditures in each case. For transportation i t is auto operation: the purehas e and increased use of a ear were apparentlyprimary sources of additional expenditures as incomes rose from very low levels. Beyond the $5,0007,500 income leve l, however, marginal expenditure increases for auto operation decline sharply. The increasing sensitivity of outlays for housing operation and for housing at higher income levels is responsible for the rising elasticities of the se categories. 8 On the other hand, utility and clothing service outlays decUne at upper income levels, utility outlays being relatively insensitive to changes in income at all levels. Expenditures for education andgifts and contributions are generally highly elastic to income changes, the former particularly at middle levels of income. Medical and personal care we re s ornewhat less elastic, but followed the same generalpattern as education. Outlays for recreation (admissions) were elastic at the low income levels but became highly inelastic as incomes rnaved into fivefigures. It is therefore clear that as incomes increase beyond the middle range, an increasing share of each additional dollar is spent for housing, household operation, education, and gifts and contributions. These categories account for the rising sensitivity of service outlays as a whole over the income scale, and for the fact that services as a group appear to account for an increasing share of total expenditures as the level of income rises. It deserves to be emphasized that these results are purely descriptive in nature, showing how expenditures vary among different income levels. This variation is not necessarily indicative of the extent to which any particular consumer unit's consumptian pattern may change in moving from one income level to another or of the effect of income on consumptian patterns. This is not only because static camparisans cannot allow for dyrrarnie effects but also because different consumer units are invalved at each level, 8Because of the 50-50 split of the household operation category between "housing" and "other possessions," the elasticities for "household operation" and for "household items" are identical at all income levels. Actually, this is not likely to have been the case: examination of more detailed breakclowns of these expenditures, by income level by city group (Vol. 13, Table 2-l ), indicates that the elasticity of household items may have been somewhat higher at high incomes than that of household operation.

445

whose economic and social characteristics vary widely with income. These characteristics interact with income, as is shown at a later stage of this study, and "adulterate" the values of the elasticities shown in Table 2 because they too effect expenditure patterns. Some idea of the nature of the effect of some of these other characteristics on service expenditures is shown in Table 3 for each of the four basic types of consumptian categories. The table also presents the average income after taxes of the families in each population category so that some judgment can be made regarding the presence of an income interaction effect for each of the five characteristics included in the table. It is evident from this table that outlays on services are affected by variations in each of the five characteristics shown. Such outlays decUne in importance for larger families and for families with more wage earners, except for transpartatian in the latter case. At the same time, families headed by older people, by those with more education, or by those either not employed or in professtonal occupations tend to spend relatively more on services than other families. Here again, however, transportatton is an exception, being relative ly lessimportant in the expenditure pattern of the se famille s. It is further evident from Table 3 that although income does vary with each of these characteristics, these effects can hardly be explained by an income interaction effect except possibly for education. In fact, in most instances the relationship runs counter to the pattern one would expect from the data in Tables l and 2. This is particularly true of family size and of number of wage earners, where service expenditures generally decUne in importance as the values of these characteristics, and of income, rise. On the other hand, average income decUne s sharply as age of head moves beyond about 40, yet the share of service expenditures rises substantially. The one exception, transportation, is probably due as much to advance in age as to decUne in income, since people are not Iikely to spend as much on trave! as they be come older, particular ly after retirement virtually eliminates commuting expenses.

As in the case of income, the expenditure patterns exhibited in Table 3 for the four principal types of services do not necessarily characterize each of the component categories. Certain pronounced exceptions are apparent (the data are shown in Appendix Table 1), principally a tendency for the share going for actmissions and for education to increase among larger families and among those with more wage earners, and for these outlays to decline relatively for families with older heads. In addition, clothing services tend to decUne in importance among families with older heads and to increase with the number of full-time wage earners. These differences are not inconsistent with what would be expected on the basis of a priori reasoning. 446

Table 3 Percent of Current Family Expenditures Spent for Different Types of Services, by Selected Characteristics Object of Expenditure

Category

Characteristic Family size

l 2 3

4 5 6 or more

Avg. Income after Tax e s

Home

Transportatio n

$1,895 3,601 4,221 4,793 4,981 4, 948

22.6% 18.5 16.9 16.0 15.6 14.3

5.7% 7.0 6.8 6.5 6.0 5.7

Self

All Services

4.0% 3.5 3.4 3.5 3.5 2.9

14.6% 12. 6 11.4 10.8 11. l 10.0

46.8% 41. 6 38.5 36.8 36. 2 32.9

Other Possessions

Age of head

Under 25 25-35 35-45 45-55 55-65 65-75 75 and over

3,050 3,876 4,464 4,500 3,850 2,687 2, 161

16.3 17.0 16.8 15.6 17.5 20.6 24.5

7.7 7.0 6.2 6.7 6.8 5.9 4.6

3. l 3.5 3.6 3.5 3.4 3.4 4.3

9.9 9.9 10.7 12.6 13.0 14. 2 16. l

37.0 37.4 37.3 38.4 40.7 44. l 49.5

Occupation of head

Self employed Salaried, prof, official Clerical-sales Skilled wage earners Semi-skilled Unskilled Not employed

5,432

17.3

5.7

4.2

13.4

40.6

5,406 4,077

17.8 17.9

6.8 6.4

4.0 3.8

12.7 11.7

41.4 39.8

4,219 3,673 2,839 2,232

15.7 15.7 17.2 21. 7

7.5 6.6 6.0 5.2

3.0 2.8 3.1 3.5

10. 6 10.6 10.4 13.0

36.8 35.7 36.7 43.4

Non e

2,248 4,229 5,638 7,226

20. 3 17. l

3.4 3.5 3.6

11. g

14.9

6.2 6.5 7.0

11. 6 12.9

10.9

7. l

3. l

11. 3

41.8 38.7 38.4 32.5

3,191 3,976 5, 197 6,268

16.7 17.3 17.9 19. l

6. l 6.9 6.6 6.3

3.0 3.4 4.2 5.0

11.4 12.9 13.0

37. l 39.0 41.6 43.4

3, 910

17.3

6.5

3.5

11.7

39.0

Number of fulltime wage earners

2

3 or more

Education of h e ad

All families Source:

8 yrs. or less

9-12 13-16 Over 16 yrs.

11. 3

Derived from Study of Consumer Expenditures, Incomes and Savings, Vol. 18, Table l.

447

On the whole, these exceptions are not too frequent, certainly not as frequent as in the case of income, which would seem to indicate that the four main service categories may be relatively more homogeneous with respect to the se other population characteristics than with regard to income. In closing this section, it might be mentioned that variations in service expenditures we re al so computed by race, by ho me ownership and by city class. The only appreciable variation obtained for any of these characteristics was a tendency for nonwhites to spend less on self (particularly education and medical care), probably a manifestation of income differentials. Determinants of Service Expenditures The foregoing material, though largely exploratory, suggests a number of hypotheses regardingthe characteristics and determinants of service expenditures at mid-Century. Perhaps the most interesting ones are the following: 1. Expenditure patterns differ substantially both between and withinservice categories. Casual examination suggests that substantial differences also exist when the detailed expenditure categories shown in Tables 1-3 are subdivided further. This is likely to be particularly true of housing, household operation, purchased transportation, medical care, personal care and education. 2. Because of these differences, close interrelations between different types of service expenditures are not likely to be very frequent, particularly among detailed expenditure classifications. At this level, the classifications most likely to be related with each other are housing with housing operation, and education with gifts and contributions, using the proportion of total expenditures spent for that service as the variable of measurement. On a broader level, inter-relations do not seem likely either, with the possible exception of expenditures for the home and expenditures for other possessions. This is likely to be particularly true when income is held constant. 3. It is perhaps self-evident that certain service expenditures are dependent upon, and hence closely related to, ownership of the material or human resources giving rise to them, e.g., autos for auto operation, children for education. It is also possible that certaln service expenditure rates maybe related to spending rates for other purposes, e.g., clothing services to clothing purchases and, more broadly, education or auto operation to a high overall ratio of expenditures to income. 4. Because of the differences in service expenditure patterns, the principal determinants of such expenditures may vary substantially by category. These determinants will include in part certain 448

socio-economic characteristics, in part the availability of resources giving r i se to the se expenditures, and in part a ho st of miscellaneous factors. Since the latter are difficult to identify on an ex post basis, and since the availability of resources is itself to a large extent dependent on a family's socio-economic characteristics, the identification of the latter would seem to be the most fruitful means of approach to this problem. Though differences can be expected by category, the evidence presented so far indicates that one or more of the following three characteristics exert a major influence on all types of service expenditures: income of the consumer unit, age of head, and family size. Other socio-economic variables, such as education, occupation, and city size, appear to be of secondary importance. The first hypothesis is largely self-evident, given the results of the previous section, and is not pursued furthe r in this paper. Instead, the seeond and the fourth of these hypotheses are the primary focus of the empirical tests in the remainder of this paper. In the course of these tests, same additional light is thrown on certain aspects of the third hypothesis, though no attempt is made to test this hypothesis in any systematic manner for lack of facilities. Empirical Tests Two sets of empirical tests are carried out, one set to evaluate the relative importance of various socio-economic variables in influencing service expenditures, and the other set to probe the extent to which service expenditures are interrelated. Tests of Relative Importance The two principal means of evaluating the relative importance of a number of variables are by same form of multiple regression or by the analysis of variance. Multiple regression has the advantage of providing, among other things, direct estimates of the numerical effect of changes in each independent variable on the dependent variable. It has the disadvantage of a priori specification of the form of the relationship and of becoming unwieldy and subject to biases arising from ignored interaction effects as the number of variables is increased. Variance analysis has the advantage of flexibility but also can become unwieldy when many different variables are involved. In the present case, variance analysis seemed to be the better approach because estimation of relative importance of different variables was the primary objective and because the form of the relationship did not have to be specified. An additional consideration

449

was the relative ease with which different variables can be tested for significance. Because of the nature of the hypothesis, variance analysis was applied in two stages. In the first stage, the analysis of variance was carried out on four family income categories, four age-of-head categories, and four family size categories. 9 Three variables of measurement we re used: the proportion of total expenditures spent for services connected with the home and with other possessions, the proportion spent on transportation, and the proportion spent on services for self. Home-connected services and services connected with other passessions were combined partlybecause the two categories appeared to fluctuate with each other and partly because clothing service outlays was not included among the classifications available on punch cards. In the absence of this classification, the "other possessions" category contained only part of the household operation total for which separate treatmenf did not see m warranted. In effect, therefore, three separate analyses of variance were carried out on income, age, and family size. In each case, the significance of each variable and its associated interaction effects were assessed. The analysis was carried out with the individual family as the unit of observation. Since the number of families in the different cells was decidedly unequal, the analysis was carried out bythe method of fitting constants, samewhat tediousbut the only me ans of assessing accurately the significance of possible inte r action effects. 1 0 The seeond stage of the variance analys is consisted of treating the cell means for those characteristics found to be statistically significant in the first stage as norms for all families with those characteristics. In other words, the extent to which each family's share of spending on those services deviated from the mean for the appropriate cell was computed for the entire sample. The se deviations then served as the basis for ascertaining the extent to which additional variables may have affected service outlays. The variables tested in this fashion were: education of head, tenure (home ownership), city-size, and level of savings. 11 9The categories are, as follows: Income--Under $2,000, $2,000-4,999, $5,000-9,999. $10,000 and over. Age of head-- Under 35, 35-44, 4S-65, 65 and over. Family size--1, 2-3,4-5, 6 and over. 10 Goulden, L., Methods of Statistical Analysis, pp. 310 ff. 11 The categories are: Education--8 years or less, 9-12 years, over 12 years. Tenure--Home owner, renter and others. City-size-- Large cities, suburbs, small cities. Leve l of savings-- 5o/o or mor e of in come, between 5o/o and -5o/o les s t han -5%

450

Admittedly, this two-stage proeecture possesses limitations, since a certain amount of interaction is bound to exist between the variables listed above and income, age, and family size. To the extent that such interaction exists, spurious indications of significance are a danger. However, this approach nevertheless seems to be the best way of identifying possibly significant variables. Tests of Interrelation

.

The extent of interrelation between service expenditures was gauged by computing coefficients of earrelation between pairs of service expenditures at two levels: between the three broad categories of services used in the analysis of variance, and the individual expenditure classification shown in Tables 1-3, with the exception of clothing services. Correlations were computed both on an aggregative basis-all families combined-and for different strata of income- savings levels and tenure, as discussed later. As befor e, the unit of measurement was the share of total expenditures going to the particular category of services. Results F ratios obtained from the analyses of variance of income by age of head by family size are presented in Table 4. In accordance with prior expectations, all three variables are seen to influence substantially each of the service expenditure ratios not only directly but also through interaction effects as well. The general nature of the se effects is essentially the same as noted earlie r, but it ma y be useful to summarize them, as follows: expenditure expenditure expenditure share on share on home share on self and other goods transportatio n As income increases

falls, then ris e s

rises, then falls

ris e s

As age of head increases .....

falls, then rises

falls, then rises

rises

As family size increases •....

falls

rises, then falls

falls

The interaction effects are somewhat more complicated, but it would nevertheless see m useful to summarize the direction of the se 451

effects, for those which are statistically significant in Table 4. The following pertains to the first-order interactions: expenditure expenditure expenditure share on home share on share on and other goods transportaHon self Income by age

rises with age much more at low incomes than at high i neomes

is lowest at low incomes for older people, but for younger (35-45) people at high incomes

rises much more with rising income s am ong older people than am o ng younger people

Income by family size declines with rising family size much more at low incomes than at high income s

not significantly relate d

falls much more atlow incomes than at high incomes as family size ris e s

Age by family size

has a much sharper peak at 45-65 ages among middle family size, but little or no peak for same family size at other ages

falls uniformly at younger ages as family size rises, but exhibits an inverted-U patte r n amo ng older people as family size r i ses

rises with age for very small families, but falls with age for larger families

As is evident from Table 4, some of these interaction effects are substanHal and would clearly merit inclusion in any multivariate regression attempt to explain the variation in each of these ratios. Estimates of the relative importance of each of the three variables are presented in Table 5 on two bases, one using direct effects only and the other incorporating interaction as well as direct effects. 452

Table 4 F Ratios for Analysis of Variance of Income by Age by Family Size Home and other goods expenditures

Transportatian expenditures

Self expenditures

33.2**

152.3**

60.8**

Ag e

303.6**

14.6**

62.5**

Family size

174. 7**

30.4**

74.1 **

Income by age

9.8**

2.4**

4.0**

Income by family size

8.3**

1.1

4.9**

Age by family size

40.3**

4.1**

3.2**

9.9**

4.1 **

4.3**

Effect Income

Income by age by family size

**Significant at .01 level In either case, the estimate is obtained by subiraeting from the mean square for a given variable the mean square due to error and percentagizing the results. (Ordinarily, the residua! mean square would be divided by the number of levels used for that variable in the analysis, but that is unnecessary in the present case because this number is the same for all three variables.) Intaraction effects were allocated to variables in relation to the number of variables invalved in each instance. This table indicates that substanHal variation exists in the relative importance of the three variables with the category of services under consideration. Thus, income possesses the highest relative importance in influencing service outlays for transpartatian and home and other goods, but the least relative importance on self expenditures. Age is of relatively little importance for the first two categories but exerts substanHal effects on self expenditures. Family size exerts the greatest relative effect on self expenditures, iS of almost equal importance percentagewise on home and other goods-connected outlays but, samewhat surprisingly, is of much less relevance to transportaHon services. 453

Table 5 Estimates of Relative Importance of Age, Income and Family Size on Service Expenditure Shares Share of expenditures on Effects

Direct only

Direct and inte ractions

Variable

home and other goods

transpartatian

self

Ag e Income Family Size

7% 59 34

8% 75 17

33% 29 38

Total

100%

100%

100%

Ag e Income Family size

18% 46 36

9% 73 18

25% 34 41

Total

100%

100%

100%

As is apparent from Table 5, the foregoing results are affected only slightly if interaction effects are included in the analysis, at least by the method of allocation employed. From a more general point of view, it deserves to be stresaed that Tables 4 and 5 do not reflect the proportion of variance in the service shares which are not explained by these three variables. That this proportion is substantial is immediately evident if we campute an estimate of the (square of the) earrelation ratio by dividing the sums of squares attributed to these three variables by the total sum of squares for each ratio. The results are as follows: .17 Home and other goods Transportatian . 05 Self .07 In other words, at best the three variables account for onesixth of the total variance in the expenditure ratio, and at worst they account for one-twentieth. The high significance levels shown in Table 4, therefore, are in large measure attributable to the extensive degrees of freedom and do not obviate the need for searching for additional relevant variables. In a search for such additional variables, we turn to Table 6 whichpresents Fratios of the residua! effects of four other factors on the three service expenditure ratios. The residuals used in this analysis are the deviations of the individual family ratios from the 454

mean ratioforthe income-by-age-by-family-size cell inwhicheach particular family was classified. With one exception, all four variables are seen to exert significant effects on the residuals of all three ratios. The nature of the se effects may be summarized as follows: the residua! expenditure share on home and other goods transpartatian self As education rises ..

falls slightly

r i ses

rises

For home owners relative to renters

falls

r i ses

rises

rises (but lowest in suburbs)

falls (but highest in suburbs)

falls (lowest in suburbs)

rises, then falls

falls, then rises

falls, then rises

As city-size rises

As level of savings increases . . . . . . .

Particular ly noteworthy is the significance of the savings variable, an indication that, in this case at least, income is not sufficient to allow for the influence of financial considerations. Table 6 F Ratios for Residua! Effects of Additional Variables Facto r

Maintenance of home and other goods

Transportatian

Self

Education Tenure City size Savings

.9 52.6** 26.3** 24.9**

88.9** 51.5** 23.5** 74.8**

16.8** 34.5** 4.3* 27.1 **

*Significant at .05 level **Significant at .01 level As before, the high values of the Fratios in Table 6 may be samewhat mialeading since the proportion of residua! variation explained by each of these variables is very small. In no instance, does any of these variables explain more than two percent of the residua! variation, a figur e that is not like ly to be much higher even 455

allowing for possible furthe r contributions from omitted interaction effects. On the whole, therefore, it appears that if any appreciable proportion of the total variation is to be explained, a large number of explanatory factors will be needed. Interrelations Interrelations between service expenditures appear to be of relatively small magnitude. Among the three broad service categories, there is evidence of negative earrelation between expenditures for the home and expenditures for transpartatian as well as between transpartatian expenditures and self expenditures. In no instance, however, is as much as 10 percent of the variation in one variable associated with the other, as is shown by Table 7. Nevertheless, with the large sample sizes, the coefficients are highly significant in a statistical sense and maybe indicative of some substitution tendencybetween expenditures forthese different services, or purposes. This may be particular lytrue for ho me- connected expenditures and for transpartatian expenditures, for which highly significant, though still low, negative earrelations are apparent at all income levels. Intuitively too, this result seems reasonable,partlybecause people are often faced with the choice of reducing transpartatian expense by living closer to work but paying relatively more for housing than would be the case if they lived farther out. Table 7 Intereorrelation Between Service Expenditure Categories, by Income Level

Income level

Sample si z e

Under $2,000 $2,000-5,000 5,000-10,000 10,000 and over All

2,221 7,221 2,381 285 12,108

Coefficient of earrelation between shares of total expenditures spent on Home and transporta- Home and Transportaself tian and self tio n -.29** -.15** -.10** -.18** -.23**

*Significant at .05 level **Significant at .01 level 456

-.10** .10** .11** .05 .01

-.03 -.06** -.05* -.18** -.05**

The intereorrelations between individual categories of service expenditures provide scattered instances of statistically significant correlations (at the .05 level) between expenditure categories for different levels of income, savings and tenure. The following patterns appear to exist. The figures in parentheses are the highest values of the coefficient of determination obtained for that category, Positive correlation between housing and utilities (especially for home-owners) (.42) Positive correlation between housing and household operation (.58) Positive correlation between utilities and personal care (especially for renters) (.50) Negative correlation between utilities and auto operation (for home owners only) (.07) Positive correlation between household operation and medical expenses (especially for renters) (.67) Positive correlation between household operation and personal care (particularly at low income levels) (.22) Positive correlation between recreation and personal care (particularly at low income levels) (.20) Negative correlation between auto operation and other transportation (.25) Positive correlation between actmissions and other transportatian (especially for renters) (.69) Positive correlation between personal care and other transportation (.09) In some instances, these relationships are not unexpected, as between housing and household operation or between personal care and recreation (admissions). In the case of utilities vs. personal care, or of household operation vs. medical care, a meaningful interpretation of the relationship may or may not exist. Contrary to the previous set of intercorrelations, reasonably high degrees of association were encountered every now and then. This is brought out by the figures in parentheses in the above tabulation, which indicate that at times more than one-third the variation in expenditures for one category of services was associated with variation in outlays for another service. Such instances were clearly exceptions, but did occur with regularity. SummaryRemarks If there is one principal conclusion from this study, it is that service expenditures represent a highly heterogeneous conglomeration, the levels of which for particular purposes are influenced by numerous factors no one of which is of substantial importance by itself. It is not necessary to set up multiple regression functions

457

to see that all the explanatory variables tested in this study will account for only a small proportion of the variation in expenditure shares devoted to different classifications of services. This finding is not too surprising, for similar results have been obtained for other cross-section studies when the unit of observation was the individual consumer. Howeve r, i t does serve to emphasize all the more the desirability of extending work of this sort to take into account the growing substitutability of services for goods, and at times vice-versa. To be sure, this serves to introduce manyknotty problems in measuring consumer preferences, but only when these problems are solved are we likely to have a theory which will explain the bulk of the variation in consumer expenditures.

458

t~>-

01

cc

Full-time wage earner s

head

of head

Occupation of

Age

Six or more person

Two person family Three per son f ami ly Four person family Fi ve person family

Category

Single consumer

Characteristics

Family size

Three or more fUlltime earnere

No full-time earnere one full-time earner Two full-time earners

Not gainfully employed

Self -employe d Salaried, professional, official Clerical and sales workers Skilled wage earners Semi- s killed wage earner s unskilled wage earnere

75 years and over

Under 25 years 25 - 35 years 35 - 45 years 45 - 55 years 55 - 65 years 65 - 75 years

family

A~ndix

Table l

3-3 4.} 4.6 4.4 4.6 4.9 7 .l

2.2 3-3 3-9 3-9 4.5 5.6 7-0

12.4 11.5 10.6 9-5 10.7 12.5 1).9

5-9

7,226

3-3

3.4

4.6 4.6 4.2

4.0 4.4 s. 7

10.0 10.9 1}.4

3,673 2,839 2,232 4.8 3.8 3-5

3-3 3-7 5.1

}.6 3-9

11.9 9-9

4,077 4,219

1}.2 11.0 9-3

4.8 3-7

3-3

11.8

5,4o6

2,248 4,229 5,638

5-3

3-9

10.4

6.0

3-3

5.0% 4.7 4.2 4.4 4.6

4.3

3-3% 3-9 4.0 4.1 4.2

~

8.3

16.8% 12.2 10.8 9-7 9-1 4.2

1.8

l.)

s.o 4.9

1.4

4.4 4.9

2.3

1.8 1.6 2.0

1.7 2.1 1.9

1.8 1.4

4.6 6.1 4.9 3-9 3-3

1.6

}.6

5-7 4.9 5.5

4.8 4.6 5.6

5.0 4.8

5.1 4.8

1.3

).2

1.8 1.4 1.4 1.9 2.2 2.0 1.6

1.6

4.4 4.6 4.5 4.9 5.4 6.5 6.3

4.0% 5-3 5-l 4.8 4.8

l.)

2.8% 1.8

4.4

5-9 5.6 4.8 4.8 4.6 3-9 3.0

3-9

2.9% 5.2 5. 3 5.0 4.4

1.1 1.2 1.5

1.2 1.3 1.0

1.4 1.2

1.4

1.2

1.5 1.4 1.3 1.3 l. l l. O 0.8

1.3

1.4% 1.2 1.3 1.3 1.2

1.0

l. l

0.9

l. O

1.0 1.1 0.9

1.1 0.9

0.9

0.9

1.0 0.9 0.7

l. O l. O

0.9

0.7

1.0

LO

0.9

l. O

0.9

l . l%

1.5

0.9 l. O 1.3

1.3 1.2 0.9

1.1

l. O

0.9

0.9

1.7 1.1 1.1 1.1 0.9 0.8 0.5

1.5

1.2

0.9% 0.9 l. l l. l

0.6

0.5 0.6 0.6

0.4 0.3 0.5

0.6 0.4

0.9.

0.9

0.6 0.3 0.6 l. O 0.6 0.2 0.1

0.9

O.J% 0.2 0.6 0.9 1.1

41.8 }8.7 38.4

35-7 36.7 4}.4

39.8 }6.8

41.4

40.6

37-0 37.4 37-3 38.4 40.7 44.1 49.5

32.9

46.8% 41.6 38.5 36.8 36.2

4.6 }2.5 (con't)

3-9 4.1 4.4

3-1 3.2 5.1

4.0 3.4

5.2

5.6

2.5 }.0 3-5 4.6 5-1 5.8 8.5

2.4

8-3% 5-3 ).6 }.l 3.0

Other Gifts and Au to transHousehold Clothing oper- porta- Medical Personal Recrecontrioperation ~ ~ tian ~ ~ ation Education ~ Total

5,432

3,050 3,876 4,464 4,500 3,850 2,687 2,161

4,948

$1,895 3,601 4,221 4,793 4,981

Ave. income arter taxes Housing

Percent of Total Family Expendi tures Spent for Differer.t Services, by Selected Cba.racteristics

"'o"

O)

3.3 3.0 4.0

11.0

ll.O

9.1 1:..4 1}.0 11.1

4,051 2,605 4,471 4,437 3,384 3,910

White Negro

Cwner all year OWner end of' year, renter earlier Renter end of year

3-9 4.9

4.0

}.l

4.5

4.3 4.2

1.3

1.2

1.3

l. l

1.2 1.6

4.6 3·9 4.8

1.5 1.3 1.1 1.1

4.8 4.4 4.4 4.o

l. O

4.2 1.6 1.4

1.3

5.0 4.8

1.2

1.2\1> 1.3 1.4 1.4

4.4 4.8

3-7% 4.2 5-7 1.2

4.9

5-5 4.4

5.2

5.0 2. 5

4.8 5.7 6.9 5.9

4.1 5.8

5.8

4.0 4.8

4.3% 5. 3 5.0 4.6

1.7

1.2 1.9

1.5

1.6 2. 5

1.3 1.8 1.2 l. O

1.9 1.5

0.9

2.1 1.6

1.8% 1.6 1.6 1.7

4.9

4.3 4.8

5.2

5.1 3.6

5.2 5 .} 5·3 5.2

4.6 4.8

4.7

4.9 4.8

5.0\l'. 4.9 4.8 4.7

0.9

l.O

0.8

l. O

0.9 1.6

0.9 0.8 0.8

l. O

0.9

l. O

0.9

0.9 0.8

0.9 0.9

l. O% l. O

l. O

0.9 1.2

1.0

1.1 1.1

1.2

l. O l. O l. l

0.8

l. O

1.2

l. O 0.8

1.2% l. l 0.9 0.9

0.6

0.3 0.4

0.8

0.6 0.3

0.5 0.6 0.4 0.5

0.6 0.6

0.4

0.6 0.6

0.4% 0.5 0.9 1.4

Other Auto transHousehold Clothing oper- porta- Medical Personal Recreoperation ~ ~ tian ~ ~ ation Education

D::!rived from Study s:!_~ Expenditures, Incomes and~~ Vol. 18.

l f'amil i e s

Source:

J.. l

4.9

9.4 11.5 9·9 10.2

Tcnur:2

).0

10.5

3,071 3,887 4,c66 3,894

Ra c e

3-7 3-9

11.2

}.l

5.8

10.9

3.8 4.4

4.7% 3-9 3.2 3.2

3,666

10.1\1> l l. 3 11.8 12.3

3,514 4,124

Lerge c i ties in the north Suburbs in the north Sreall c i ties in the ncrtb Large c i ties in the south Suburbs in the south Small c i ties in the south la r ge c i ties in the we st Suburbs in the west Srr.all c i ties in the we st

City Class

$3,191 3,976 5,179 6,268 11.5 10.8

8 years and under 9 through 12 years 13 through 16 years Over 16 years

Educatlon of head

~

3,958 4,690

Category

Cbaracteristics

Ave. il~comt arter texes Bou::.ing

(con't)

Appendix Table l Percent of Total Family Expenditures Spent for Different Services, by Selected Characteristics

Gif'ts

4.2

}.0 3.8

4.6

}.O

4.2

}.8 4.3 4.5 4.2

4.1 3-9

3·9

4.1 4.4

39.1

39.2 39.0

39.2

39.2 36.0

}8.5 39.9 }8.6 38.0

}8.8 }8.9

39.7

}8.6 39.0

3-7% 37-l'f, 39.0 3-9 41.6 5.4 5 .l 43 .•

contributions Total

and

COMMENTS by Janet Murray in collaboration with Faith Clark U. S. Department of Agriculture

Fi:rst, I want to comment on the helpfulness of having these analyses. Our knowledge has been extended not only with respect to the factors affecting consumptian that have been considered in the past, primarily income, family size, and/or family type (and less often by city-size, occupation, age, education, race, income change) but also by new characteristics such as holdings of assets. An extension is also being made in our experience with a variety of statistical techniques. In the four papers under review we have camparisans of means or other relevant measures for the families grouped by the characteristics under consideration, regression analysis, and an analysis of variance. Mrs. Crockett has developed some ingenious proeectures for her analysis first of the slopes and then the level of the income-expenditure and family-size curves. While I do not want to detract from the skills and contributions of the authors, I might comment that they have been aided by the modern electric computers which have permitted detailed bre;:tkdowns and camparisans not at all feasible 20 years ago. In spite of this commendable completeness, I might remindyou of one obvious gap in these studies, and that is the absence of urban-rural comparisons. This gap is, of course, not the fault of anyone here-it arises from camplex administrative causes. Although the rural segment of the population has been declining in importance in the overall picture, the urban-rural differences in expenditure patterns have historically been of greater importance than many considered in these papers. For information on urbanrural differences, we have to turn either to the 1935-36 or the 1941 • studies, or campare the 1950 Bureau of La bor Statistics data with the Department of Agriculture surveys-the Household Food Consumphon Survey, 1955, and the 1955 Survey of Farmers' Expenditures. Such camparisans are much tidierfor the analyst if they can be made for the same time period, and with data from the same study. Turning now to the individual papers; most of Mrs. Crockett's paper is taken up with the estimation of the various determinants of the demand for food that can be studied from the BLS 1950 survey. The effect of such characteristics as family size, age of head, 461

occupation, size of city and region on the level of expenditures and on the income elasticity has been calculated. The results appear reasonable. You may be interested in results of similar calculations made about 20 years ago based on data from the Consumer Purchases Study made in 1935-36 which show the same general relationships amongthe populationgroups as Mrs. Crockett's calculations. There was relatively little difference between the income elasticities for the several city-size groups; for several large cities in different regions; and for families of 2, 3-4, and 5-6 persons. Occupation did appear to affect the slope, with that for wage earners higher than for clerical, which in turn was higher than for business and professional. A slightly different result from that of Mrs. Crockett was found for the effect of race on the income-consumption slope. At the upper end of the income range in 1935-36, the slope was steeper for Negroes than for Whites; at the lower end, the slopes were about the same. In deriving these elasticities a much more limited amount of information was used than in the procedures reported by Mrs. Crockett and the other authors. Please remember that this was back in the thirties when we we re using our own or WP A labor instead of Univac or 650's or 705's! Income elasticities with their standard errors were computed at several different points on the curve but most of the comparisons were made at the mean income for all families. By and large most of the differences were not significant, supporting Mrs. Crockett's assumption that the elasticities are independentestimates of a single elasticity eonstant over city-sizes and family-sizes. Incidentally, the elasticity for the largest family-size group (7 and over) was noticeably higher than for other size groups though the difference was not statistically significant. This result is similar to Mrs. Crockett's and James Tobin's findings, and also those of Gregg Lewis and Paul Douglas in their analysis of BLS 1901 data. Significant differences in the food elasticities were found only in camparing occupational and urban- rural groups. This latter may als o be considered an occupational difference. In those days the lower elasticities for the farm families and the business and professional families wer e explained by the great er uncertainty of the income of those groups. Today, of cours e, we say that ttiere is alarger element · of the trans i tory as compared with permanent component of income. One other comment on these elasticities-the appropriateness of comparisons with those presented by Mrs. Crockett, as far as their absolute values are concerned, must be qualified by the fact that money plus non-money income before taxes, and the full range ofincome data, were used. Samewhat higher values would probably have been obtained if they had been more comparable with hers in these respects. 462

Table l. Income Elasticities for Food, 1935-36; All Families, Single Men and Single Women, and Gomparisons of Specified Type of Community, Regional, Family Size, Occupational, and Racial Subgroups (Elasticities l uniess otherwise specified at the mean income for all families, $1,622; figures in parentheses are standard errors) A. Family, single indi vi dual comparisons: All U. S. 1. All families of two or more 2. Single men 3. Single women

0.53 0.55 0.51

(0.003) (0.03) (0.07)

B. Type of community (city-size) comparisons: North Central Type of community

Business, professional, clerical 3-4 person

Metropolis (Chicago) Large city (Columbus) Middle-sized cities Small cities Villages Farms (Pennsylvania and Ohio) Money expense for food Home-produced food All food

0.58 (0.02) 0.53 (0.03) 0.48 (0.03)

-

0.50 (0.02)

-

2 person 0.53 0.52 0.50 0.45 0.42

(0.03) (0.05) (0.03) (0.02) (0.03)

0.20 (0.06) 0.17 (0.04) 0.18 (0.03)

Wag eearner, 2 person 0.56 (0.04) 0.48 (0.08) 0.44 (0.08)

-

-

-

C. Regional comparisons: Large city, business, professional, clerical, 3-4 person families inNew England (Providence) North Central (Columbus) South (Atlanta) Mountain and Plains (Denver) Pacific (Portland)

0.58 0.53 0.56 0.50 0.52

(0.03) (0.03) (0.02) (0.03) (0.02)

lElasticities cornputed from the incorne-expenditure curve: y = a + bx + c ..[x, where y = "expenditure" for food and x = incorne (rnoney plus nonrnoney incorne befor e tax e s).

463

Table l. Income Elasticities for Food, 1935-36; All Families, Single Men and Single Women, and Comparisons of Specified Type of Community, Regional, Family Size, Occupational, and Racial Subgroups-C ontinued D. Family-size comparisons: Large-city, North Central, business, professional, and clerical families of: 2 persons 3-4 persons 5-6 persons 7 or more persons

0.52 0.53 0.53 0.61

(0.05) (0.03) (0.06) (0.09)

E. Occupational comparisons: Large city, North Central, 3-4 person families: 0.49 (0.05) 0.56 (0.04) 0.66 (0.03)

Business and professional Clerical Wage-earner F. White-Negro comparisons:

Large-city, wage-earner, 3-4 person families: Region and income North Central (Columbus) $1,000 $1,622 South (Atlanta) $1,000 $1,622

White

Negro

0.62 (0.05) 0.66 (0.03)

0.57 (0.08) o. 72 (0.26)

0.60 (0.17) 0.51 (0.06)

0.61 (0.12) 0.61 (0.19)

G. Purchased food-at home and away from home, North Central families-type of community and family-size comparisons: .Purchased food Occupation, family size, city size

At home Away from home Total

Business, professional, clerical, 2-person families: Metropolis (Chicago) Large-city (Columbus) 464

0.37 0.33

1.65 1.46

0.57 0.52

Table l. Income Elasticities for Food, 1935-36; All Families, Single Men and Single Women, and Comparisons of Specified Type of Community, Regional, Family Size, Occupational, and Racial Subgroups- Continued G. Purchases food-at home and away from home, North Central families-type of community and family-size comparisonsContinued Occupation, family size, city size

Purchased food At home Awayfromhome Total

Business, professional, clerical, 2-person families-Continued Middle-sized cities Small cities Villages Farms (Pennsylvania and Ohio) 2 persons 3-4 persons 5-6 persons

0.41 0.33 0.33

1.28 1.44 1.39

0.51 0.45 0.39

0.24 0.17 0.32

1.05 0.49 1.34

0.26 0.18 0.38

Based on unpublished data from the Consumer Purchases Study, analyzed by Janet Murray. Parameters forthe income-expenditure curves were furnished by the National Resources Planning Board (see Family Expenditures in the United States, June 1941, p. 160).

Mrs. Crockett in her paper apparently has little cancern for the hypothesis that much of the difference observed among groups in expenditure-income relations is the result of variations in the mixture of the income components-the permanent and transitory components. Two pieces of evidence that support this hypothesis are offered here. In both sets, it was possible to identify and analyze separately those having such characteristics as would lead them to have "stable" incomes. The first piece of evidence is taken from the 1948 urban food consuroption survey of the USDA. For 2-person adult households with the head under 60 years, living in the North, we were able to exclude the schedules of those families likely to have temporarily high or low incomes. These included noncontinuous employment for the h e ad throughout the year, employment of the wife or other adult for so me bu t only a part of the year, and income in 1947 that was obviously not a part of the income in the spring of 1948 (the period of the 7-day food estimate). The results of this classification are shown in U. S. Department of Agriculture, Agricultural Information Bulletin No. 132. The 465

curve based on only the households with relatively stable incomes has a steeper slope than the one based on all households. We have not computed income elasticities for this relatively small set of households, bu t the coefficient would probably be significantly high er for the families with a relatively high share of their incomes that might be characterized as "permanent." The seeond piece of evidence comes from the 1955 food consumptian survey of the USDA. We ask ed a question on the schedule: "Was your family income in 1954 about the same as your family income in 1953?" For the set of the families reporting approximately the same income in the two years the income elasticity was slightly high er than that for the total group of families. The difference is not significant but is in the direction we might expect. If those that reported no income change can be assumed to have a relatively high permanent income component, this bit of evidence supports the hypothesis that the higher the permanent component of income, the greater the income elasticity. Another point to explore is the difference between the income elasticity obtained in the BLS 1950 survey and the USDA 1955 food consumptian survey. For all groups combined-and indeed for most of the separate subgroups studied-the income elasticity in the 1950 survey was 0.5, holding family size constant. In the 1955 survey, we have calculated an elasticity of 0.4 for urban households of 2 or more persons. Why such a large difference? Presurnably both surveys had the same representation of regions, races, occupation, and city-size groups. Margaret G. Reid (Journal of Farm Economics, Dec. 1958) has suggested two reasons for the difference. One is that the 1955 survey was limited to housekeeping families, thus excluding those families and single individuals who eat most of their meals in restaurants. As is weil documented, food away from home has a much higher income elasticity than food at home. In the 1955 survey, we obtained values of O. 77 for food away from home and 0.33 for food at home (urban households of 2 or more persons adjusted for family-size differences at each income class). The 1935-36 findings showed an even greater difference-about 1.5 compared with 0.35. We have not been able to discover any set of data we could use to calculate the difference between the income elasticity of a group of housekeeping families and a more inclusive group, but the elasticity for the housekeeping families would probably be lower than that of the total group. The other reason suggested by Miss Reid was that the 1955 survey c overed expenditures for the spring only, a period of the y ear when the expenditure for food away from horn e might be below the yearly average because it is not the common vacation season. The proportion of the total food expense that was spent on 466

away-from-borne food by families reporting in 4 seasons in 2 cities in 1948-49 was examin ed. The evidence is not el ear- cut that spring is below theyear average. In Birmingham, springwas a little below the 4-season average, chiefly because fall was such a high period. In Minneapolis-St. Paul, spring was about the same as the 4-season average. Let us turn now to Mr. Ferber's paper on Service Expenditures at Mid-Century. In both this paper and the paper on family housing expenditures, som e time is devoted to a discussion of classification problems. Problems of classification will probably always be with us, as lang as survey data are used to serve different purposes and types of analyses. The only solution as far as the mechanicaladaptation of survey data for various concepts is cancerned is for survey tabulatians to provide information on such item detail that recombinations can be made for different purposes (including comparabilitywith previous surveys). In the 1955 Household Food Consumptian survey, for example, we bad nearly 2,000 food item code s that permitted combinations inta 2 sets of food groups-one, meaningful for market analysts and the other for nutritionists-and even so, we're not sure that we made everyone happy. In this analysis of service items Mr. F er ber, quite understandably, did not go inta one aspect that is of particular interest to us in Agriculture, and that is the increasing amount of the service element in expenditures for food. This is invalved not only in restaurant and other meals bought away from home, but in the convenience built-in services that the bornemaker buys in her packaged foods, mixes, TV dinners, etc. Marguerite Burk who has studied food consumptian in almost all its aspects has made analyses along this line. To go back to services as defined by Mr. F er ber, som e earnparisons may again be made with 1935-36 findings. The National Resources Planning Board classified aggregate family expenditures inta four classes of goods and services: Durable goods (used over a period of 3 years or more); semidurable (ordinarily employed for from 6 months to 3 years); perishable goods (less than 6 months); and services. Housing was treated as a separate category to be thrown in with services as the analyst chose or not. Excluding housing, the "service" item amounted to 16 percent of expenditures in 1935-36 as againat Mr. Ferber's 28 percent. Because of differences both in coverage (all families as againat urban) and item classification this comparison might not be worth bringing up, although directionally the difference seems reasonable. The 1935-36 results do not exhibit the V-shaped variation in the proportion of expenditures going to services noted by Mr. F er ber, bu t increase consistently with income. This would seem more reasonable than Mr. Ferber's results. 467

Mr. Fe r ber' s technique for measuring income elasticities does not permit easy comparison with other estimates. In general, the level of elasticities that we found in 1935-36 for what he terms the "self" items-medical care, personal care, recreation and education-would appear to be fairly in line with his. The income elasticities derived from the 1955 Survey of Farmers' Expenditures (estimated from logarithmic linear regressions, excluding the lowest and highest income classes) were definitely lower. Table 2. Estimated Income Elasticities for Farm Family Expenditures, based on USDA 1955 Survey of Farmers' Expenditures 1 (All Family Sizes Combined) Coefficient of income elasticity Transportatian . . . . . . . . . . . . . Recreation, reading and education. Housefurnishings and equipment . Clothing . . . . . Personal care . Food . . . . . . Medical care . .

0.7

.6 .5 .5 .4

.4

.3

1 Estimated from logarithmic linear regression. Excludes incomes under $250, $250-499, and $7,500 and over (disposable family income). The average income for each classis not available. The expenditure data we re plotted at the midpoint of the classintervals used. A straight line was fitted visually to these observations. For the income interval between $500 and $7,500, the standard error would probably be quite small. Basic data in Farmers' Expenditures in 1955 by Regions, USDA Statistical Bulletin No. 224, table 21.

We have only a few observations on Mr. Hamburg' s paper on the Demand for Clothing, and even fewer on Mr. Maisel's and Mr. Winnick' s paper on Family Housing Expenditures. We question the value of the "Life" 1956 figures in light of the incompleteness of the total expenditure data which Mr. Hamburg describes. We were interested in nating the consistency .in the way the elasticity for clothing of clerical workers fell below other occupational groups. This was true in the 1935-36 findings as weil as for the 1950 and 1956 data presented by Mr. Hamburg. Clothing elasticity for farm families, based on the 1955 Survey of Farmers' Expenditures, was again relatively low-0.5

468

Mr. Maisel and Mr. Winnick c l ear ly brought out that housing expenditure analys is has so me especially difficult classification and conceptual problems. For this reason housing expenditures have often been handled differently in family expenditure studies from other categories of consumption. We should like to compliment the authors on their sparkling subtitle "Elusive Laws and Intrusive Variances." Picking up on this matter of variance as a final point, we should like to remark upon the surprise and cancern of some authors at how small a portion of total variation in ungrouped data was explained even by the large arsenal of facto r s affecting variability. In working with ungrouped data from the 1948 survey of food consumptian of urban families, we found that less than 30 percent of total variance in milk consumptian of families with no children and 45 percent of consumptian in households with children was explained by income, household size, and the age and education of the hornemaker, and practically all of this was attributable to household size. When the analysis was made on the basis of consumptian and income per person, only 4 or 5 percent of the total variance was explained. Some of this variation probably arises from reporting errors which are cancelled out in the averaging process when grouped data are used, hut a lot of the variation, we believe, will always remain as long as there are differences of opinions- "som e people like apples and so me like onions "-or as we say around our shop-sorne people like to eat more than others. It seems to us that the re may be two emulicting trends operating in family consumptian patterns. On the one hand, the averages for various population groups are no longer as different as they used to be. We have noticed, for example, that farm and city food patterus have become more alike over the last 20 or 30 years. On the other hand, as Dorothy Bradypointed out in 1938, variation about the mean is greater at higherthan at lower levels of expenditure. Thus today' s high er incomes provide mo re scope and leeway for the operation of individual tastes and preferences.

COMMENTS by Jacob Mincer City College of New York

The avowed purpose of the econometric analyses presentedin this session is to assess the influence of income and other family characteristics on four broad categories of consumption. This is accomplished by the authors in terms of a set of regression and/ or 469

variance analyses which in effect constitute a descriptive summary of the relevant parts of the 1950 survey data. Of course, a description of the behavior of data does not automatically lead to an understanding of the behavior of consumers. The authors of the papers on food and clothing recognize this problem explicitly by discussing possible sources of bias in the singleequation coefficients, by comparisons with time series, anq implicitly by listing a variety of ad hoc hypotheses whenever a particular finding is described. The authors of the other two papers show their awareness of the problem by expressing dissatisfaction with the heterogeneous and incomplete concept of the dependent variable which is dictated to them by the data to which they are restricted. This raises a question why the authors did not try to regroup detailed categories to provide more meaningful dependent variables, even if this meant a joint study of asset and service markets in some of the categories. If this was impossible or too costly, a more general question is this: Do we really want to study empirical constructs which have very little or veryunclear relations to the concepts we are interested in? Uniess we know how the two re late or use so me hypotheses about it, we are not abl e to interpret the results. I certainly do not agree with the statement of Maisel and Winnick that "ideally, the best definition of a dependent variable is one which yields the highest correlation with the explanatory variables." The purpose of the analysis should determine the choice of data and of the statistical procedures, and not vice versa. In general, we want an insight into structural economic relations and formulatians with (conditionally) predictive power. Now, if this is the case, I do not see why we should be disturbed by the low earrelation coefficients obtained when individual families are studie d as contrasted with grouped observations. To the extent that, in the aggregate, taste factors may be assumed eonstant or independent of economic factors over a reasonable span of time, little purpose is served in studying what, from the point of view of an economist, are idiosyncracies of individual families. Such study forces us to analyze a multitude of variables in order to eliroinate them. Cross-sectional grouping is clearly labor saving, but not entirely. The grouped data still reflect sizable distributional differences in tastes and intereorrelations among independent variables which often behave differently in time series. Also, the empiri ca! content of the variables is often different in cross-sections and in time-series. In the case of food, for example, more insightwould have been gained if food eaten at home, and food away from home, were separated in the analysis. As reported by previous investigators (Fox, Reid, Clark) the cross-sectional elasticity of food eaten away from home is about twice as high as the elasticity of food eaten at home. During the last two decades or so, 470

however, the consumptian of food away from borne did not increase more rapidly than that of food at home-which may to some extent explain the lower time-series elasticity of total food as campared to cross-sections. For food eaten at borne the discrepancy in elasticities is much smaller. I am not saying here that a correct estimate ofincome elasticity is obtained when both cross-seetians and time series yield similar figures. The income elasticity of .23 which Crockett got in the continuous cross-seetian is very close to the usual time-series elasticity found in previous studies. But bothare probably too low. The former is a short-run response to a change in income which is Iikely to be weaker than a long-run response. I doubt that this bias is much decreased by averaging incomes over a 3-year period. On the other hand, there is little doubt that the usual estimates from time series are biased downward for reasons discussed at length by Meyer and Kub in a recent article in the Review of Economics and Statistics. The higher elasticity (of .30-.45) obtained by Mrs. Crockett may, in part, be due to the greater length of the time series-a result predietable by the permanent income theory. In his study of clothing Hamburg also points out discrepancies between cross-seetians and time series. H e finds a cross-sectional grossincome elasticity of clothing expenditures near unity. Y et the percent ofincome spent on clothing has been declining. From this he infers that income elasticity is probably falling over time. But income elasticity has no bearing on shares of income spent, uniess relative price is held constant. It may well be, that the fall in the share of the consumer dollar is a reflection of decreased relative price 1 couples with a price-inelastic demand, while income elasticity remains near or even above unity. Westward migration and the movement to suburbs arefactors infavor of Hamburg's hypothesis, but I wonder if this is the most important part of the story. If only because of many elements of non-comparability the difference between the 1950 and 1956 elasticities cannot be interpreted as structural change. Returning to purely cross-sectional analysis, the effects of income and other variables on consumptian are studied either by a multiple regression technique, or by observing the effects ofincome within classifications by other variables. The proeecture reduces the net income coefficients relative to the gross ones, if the other variables are positively correlated with income. According to Crockett, this reduction brings the estimates closer to the true values. And, indeed, for food this works in the right direction if the right direction is toward values shown by time series. It does not work in the right direction, how ev er, for other categories where lShares in current dollars declined rnore than in eonstant dollars.

471

the time-series values are generally higher or similar to crosssections. According to the permanent income theory, even when this reduction works in the right direction, it does i t for the wrong reas on. By that theory, the other variables like age, occupation, family size, etc., are often in part proxies for permanent income, and the more of these we hold eonstant the less comparable the measured income with the long-run concept of income. As parameters of consumptian behavior the resulting net coefficients may therefore be inferior (i.e., less meaningful) to the gross ones. This difference in views about specifications puts question marks on interpretations: Is the higher income elasticity of food consumptian for Negroes than for Whites a reflection of greater importance of permanent components of income among the former? If planning of family size is more widespread among Whites than among Negroes, so that family size reflects permanent income among Whites more stronglythan among Negroes, could this not explain the higher family size elasticity of Whites? Clearly, the lower intercepts of the regressions for Negroes than for Whites, for small cities than for large ones, and the parabalic intercepts by age conform to the permanent income theory. Similarly consistent are the lower elasticities of food, clothing, and housing expenditures for self-emplayed as campared to wage-earners. Hamburg's classification by income change-income expectation groups shows the largest elasticity for the eonstant income group-which is als o consistent with the permanent i neo me theory. Again we find in the study by Maisel and Winnick that in a given income braeket Whites spend more on housing than Negroes, professional and selfemplayed more than wage-earners, people with higher education more than people with less education, etc. To what extent are these phenomena to be interpretedas genuine behavioral differences, and to that extent are they optical illusions implicit in the nature of the data-as the permanent income theory asserts? Unfortunately, no real effort is made in the studies to come to grips with such questions. Maisel and Winnick point out that the concept of income bas ed on a one-year accounting period is probably less adequate for the study of housing than for other categories. In other words, the discrepancy between measured and permanent income is likely to be much s tronger for housing than for other categories. If the income harizon relevant for housing decisians is a rather long one, as we would think, it is not surprising that a 3-year eonstant income group shows elasticities statistically indistinguishable from those of other groups. Another phenomenon which deserves more treatment, particularly in connectionwith the study of food and clothing demand, is the interaction of numbers of earners in the family with income, family size, and age of head. Since the percentage of income spent 472

on food and on clothing increases with numbers of earners, this interaction is Iikely to reflect itself in the following findings which are reported: increasing with age family size elasticities of food consumption; and increasing with ag e and with length of homeownership status gross income elasticities of clothing expenditure. Hamburg's table 25 is rather suggestive in this connection: the increase in clothing elasticity with ag e is mor e pronounced in the wage earner grolips, particularly the unskilled than in the upper occupational groups. In the former, family size and number of earner s are likely to expand with age of head more than in the latter where higher incomes permit undoubling. Incidentally, Hamburg's finding that Negroes spend more on clothing than Whites in the same income braeket should be supplemented by figures showing that both family size and number of earners are substantially larger for Negroes than for Whites in the data. Finally, on the same subject, I tend to differ with Crockett's suggestion that the effect of earners on consumptian reflects the desire for more consumptian which motive pushed the earners to work in the first place. This may or may not be true for total consumption, bu t in the case of food and clothing i t is mor e of an occupational expense than a desired expenditure. The fact that this interaction does not seem to be important in the other categories of consumptian is, I think, evidence in favor of my interpretation. In contrast to the other papers, the approach taken by Ferber is more akin to a partial earrelation than to a partial regression analysis. The study is based on individual family units, and as I mentioned before I doubt that, from an aggregative point of view, the size of cross-sectional earrelation coefficients is of any great importance. Ferber summarizes his findings with four conclusions: (l) Expenditure patterus differ between and within categories of services; (2) Determinants of these expenditures differ from item to item; (3) Interrelations between types of services are not very frequent; and (4) Consumptian of same services are related to ownership of some goods. I find it difficult to visualize the meaning of these findings from the standpoint of economic analysis. Do (l) and (2) mean that demand functions differ for different services? This scarcely surprising finding, I gather, is revealed in tables 4 and 5. Is the existence of earrelations between 2 types of expenditures to be interpreted as a relation of substitutability when the coefficient is negative, and complementarity, when it is positive? Since the camparisans are in terms of shares of total expenditures spent onthese services, there is a danger that the negative earrelations largely reflect camparisons of two items, one of whi ch has an (expenditure) elasticity less than, the other more than unity. Similar ly positive earrelations may arise when both elasticities are on the same side of unity. That som e 473

of the results in table 7 may be explainable in these terms is suggested by the information on elasticities in table 2. The signs of these earrelations may also be explained by interactions between socio-economic variables. Taketheincome braeket below $2000: it is inhabited primarily by the old with less education, and the young with more education. According to the information in table 3 this could very well lead to a negative earrelation between expenditure onhome and on self, and between expenditure onhome and ontransportation, as reported in table 7. I suspect, therefore, that this approach is unlikely to yield clear answers to the question whether the individual consumer unit considers the particular two categories of services to be substitutes or complements in consumption. To summarize my impressions: we have got a wealth of empirical results. Some of the information produced by this research effort was hitherto unavailable. But we are far from knowing how to interpret the findings in terms of consumer behavior. The sparadie and ad hoc theorizing is often suggestive, but it is no substitute for a careful theoretical model specification and rather extensive testing.

COMMENTS by Margaret G. Reid

In the selection of the title of their paper the authors were truly inspired. They have indeed presented an array of intrusive variances and clearly demonstrated the elusiveness of many basic tendencies. It .may be, however, that they were unduly ambitious in their goal. For example, there seeros little likelihoad that explanatory variables will ever be identified to account for all variation in relative preferences for housing campared to other consumer goods. Furthermore, in understanding economic processes and making predietians, such information is probably unimportant. With a lesser goal, such as estimating the effect of income, household type, occupation, race and city size, for example, preferences can be ignored to the extent that they tend to be randoro with respect to explanatory variables, and undoubtedly preferences have a large randoro component with respect to other variables. On the other hand, if relative preferences or any other unidentified conditions are systematically related to an explanatory variable, such as income, their effect cannot be ignored in an interpretation of the slope and levels of regressions observed. Their effect will manifest itself in the relative level of the regressions. If the estimate is free from error, then a high leve! of housing at a given

474

income will presurnably indicate the presence of another variable, perhaps a relatively high level preference for housing campared to other consumer goods. However, if the role of preferencesis to be revealed in this manner, it is essential that other conditions associated with such levels be held eonstant and that the explanatory variables be free from error. It is a well-known fact that error in an independent variable tends to lower the slope of a regression. This tendency occurs because such error introduces randoroness in the distribution of the dependent variable. This affects the leve! of the curve observed as well as the slope. If there is a randoro error in income, housing at a given family income will tend to be correlated with the average of the dependent variable. The authors observed such a direct relationship. This they laid to difference in standard of living among occupations and to discrimination in the market amongraces. Theymayboth be the manifestation of a common condition, namely errors in the income variable. My analysis points to this likelihood. The authors in table 4 report log-log regressions of housing expenditures with respect to income ranging from .44 to . 75. Many other sets of data show similar coefficients. However, in my opinion the downward bias in these coefficients from error in incomes is very great so that they greatly understate the differences in housing associated with normal income. My analysis indicates that the elasticity of housing with respect to normal income may be as high as 2.0. This suggests to me that high quality housing may, in fact, be one of the im portant luxuries of our economy, a principal consumptian item distinguishing the rich from the poor. My analysis further indicates that much, if not all, of the difference in level of housing at a given income among various strata is the result of such error, and that, when normal income as well as household type and employment level are held constant, there is a marked similarity among cities and occupation, home tenure, race and city size groups in the housing at a given income. I ha ve investigated housing- income relations using a great many sets of survey data, going back to those of 1890 and including the censuses of housing and the large-scale housing survey of 1934. The 1950 BLS data have been included in spite of the difficulty involved in the heterogeneous character of the housing variable, which heterogeneity has been spelled out in some detail by the authors. All the sets of data exaroined tell the same story. Am o ng households or families the elasticity of housing with respect to income is low and varies a good deal among groups. However much of this variation can be explained by conditions Iikely to be associated with the mixture of errors with normal income in the income distribution: e.g., the larger number of earners at high than at low incomes as reported in the BLS data. Furthermore, when an instrumental variable is used that is correlatedwith normal income anduncorrelated 475

with error, housing is found to increase relatively more than income, so that the elasticity of housing with respect to income exceeds 1.0. I have used many types of instrumental variables. For example, one of these used for the BLS data is occupation of the head. Inter-elass regressions between occupations in log form were exaroined for 30 cities. With importance of owner-occupancy held eonstant the elasticity of housing with respect to average income is about 1.5. This is samewhat lower than the elasticity of value of owner dwelling units with respect to average income among census tracts as reported in the 1950 census.! The samewhat lower coefficients from the BLS than the census data may be wholly the result of the heterogeneity of housing expenditures in the BLS data, describing owners in various stages of paying for their dwellings and tenants with various amounts of services included in rent. Indication of a very high elasticity of housing with respect to incomes also comes from a recent estimate using time series for years between 1914 and 1942. Using such data and taking inta account relative price of housing and other explanatory variables Muth 2 observed, at average income, an elasticityof stock of housing with respect to income of 1.68. The similarity between the coefficients from cross section data when an instrumental variable is used and the time series is of great interest in indicating a considerable stability of relative preference and the cross elasticities of price between housing and consumer products in general. Even though this stability may not be present for other consumer products nor for housing of all periods, the use of instrumental variables in the analysis of cross-section data may prove very fruitful in isolating the factors affecting trend. It may indeed be the only way to reduce appreciably the intrusive variances and elusive tendencies characteristizing the stock of regression coefficients describing housing.

1 For preliminary reports on these see Journal of the American Statistical Association, J une 1954, pp. 337-38 and Journal of Political Economy, April 1958, pp. 150-151. 2Richard F. Muth, The Demand for Non-farm Housing, unpublished doctoral dissertation, University of Chicago Library, 1957.

476

REJOINDER by Robert Ferber

The following comments re late to Professor Mine er' s remarks on my paper: l. The four conclusions mentioned we re advanced as hypotheses and not as definitive results. These hypotheses were not meant to summarize the findings of the paper. 2. The first two hypotheses do not necessarily me an that demand functions vary for different services. Though this is not unlikely, it would depend on much mo re extensive work than has been presented here. It is perhaps needless to note that the implications of the first two hypotheses go beyond the interpretation of demand functions al one. 3. As Professor Mincer points out, negative earrelations between shares and expenditures do not necessarily reflect substitution effects nor do positive earrelations reflect complementary effects. At the same time, it might be worth nating that some of the same earrelations were carried out using amounts of expenditures rather than shares and the diraction of earrelation was invariably the same. In any event, the results cannot be conclusive since a number of other possibly relevant factors have not been taken into account. To do so would entail extensive multi-variate analysis, which was beyond the scope of this exploratory study. The data grouping problem to which both of the discussants of my paper refer is indeed a basic one and in many ways a most perplexing one. Almost any grouping of data is not Iikely to provide me aningful concepts for a variety of analytical purpose s. The problem in any single case, therefore, would seem to be first to see what can be done with the existing data in an attempt to provide more meaningful classifications. Such an attempt was made in the present case by classifying the various categories of service expenditures into four groups. These groups, it was felt, provideda system of classification that was more relevant to modern conditians and at the same time helped to provide more of a functional rather than a commodity definition of expenditures. To the extent that such a classification scheme is useful, the more difficult and far more expansive task of reclassifying primary data in numerous alternative ways is avoided.

477

REJOINDER by Morris Hamburg

The discussants of my paper have perhaps been too generous and, therefore, I find that there are not many points which require a rejoinder. Janet Murray and Faith Clark made two observations: (l) they questioned the value of the Life 1956 figures because of the incompleteness of the total expenditure data which I described; and (2} they were interested in nating the consistency of the lower income elasticity coefficients for clothing of clerical workers as campared to the coefficients for other occupational groups in the 1935-36, 1950 and 1956 data. On the first point, it is clear that if we were to wait for perfeet data, no research would get done. This is particular lytrue in the consumer expenditures field. If the point of the Murray-Clark remark is that to confront rather uncertain hypotheses with imperfect data is a proeecture which makes one uneasy, I agree. In statiatics courses, students are taught how to reject or accept hypotheses through the use of sample data. I think it would be a good idea in all such courses for the instructors to emphasize that there are times when the data should be rejected rather than the hypotheses. If one were to observe a human being moving in an upward direction away from the earth and this person had no visible means of propulsion, one would not reject the validity of the law of gravity. Clearly, something is amiss in the observation. In the United States, there have been only a few !arge scale cross section consumer expenditures studies covering recent periods, namely, those for the years 1935-36, 1941, 1950 and 1956. It is certainly a worthwhile pursuit to attempt to squeeze as much information out of these studies about consumer behavior patterns as is possible. The fact that in one of the studies a definition of total expenditures was used which was an understatement relative to the concepts used in the others is clearly not a sufficient reason for concluding that results obtained from the former study are without value. A sensible procedure would seem to be to examine what the effects of this deficiency are upon the measures one computes and if possible to actjust for them. The expenditures e lasticity coefficients in my paper, derived from the 1956 Life data, were the slopes of double-logarithmic linear regression lines fitted to averages of clothing expenditures and total expenditures by income classes. If total expenditures were understated by the same percentage in all income classes, the elasticity coefficients remain unchanged. Small differences among income classes in the percentage understatement of total expenditures would have relatively little effect on the elasticity coefficients. 478

There is som e e viden c e that this is, in fact, the situation with respect to the overall expenditures elasticity coefficient for clothing. A rough test performed on the 1950 BLS data, actjusting total expenditures to the 1956 Life concept by actding improvements on owned dwelling and mortgage on owned clwelling and subtracting other housing and education, resulted in no change in the first two decimal places in the calculated expenditures elasticity coefficient for clothing. Furthermore, there was no cb.ange to two decimal places in the corresponding marginal propensity. With regard to Murray-Clark's seeond comment on the consistency of the pattern of lower clothing elasticity coefficients for clerical workers than for other occupation groups, I assume they would take this evidence to be one strike in favor of the Life data. That is, if an hypothesis seems to make sense on a priori grounds and data appear to confirm the hypothesis, we tend to feel reassured with respect to both the hypothesis and the data. Parenthetically, it might be noted that those who have worked with the Life data would probably not consicter the problem of the definition of total expenditures the most important deficiency in this body of data. Professor Mincer's comments are somewhat more concerned with methodology and inferences drawnfrom the analys is. He points out that a decrease over time in the percentage of income going to clothingwould not necessarily mean that income elasticity is falling over time. He states that "it may well be that the fall in the share of the consumer dollar is a reflection of decreased relative price coupled with a price-inelastic demand, while income elasticity remains near or even a bo ve unity." Howeve r, the data certainly see m to suggest otherwise. Time series regressions of per capita deflated clothing expenditures on per capita deflated disposable income and relative price of clothing indicate a decline in the income elasticity of clothing from a level of about 1.0 in the pre-World War II period to about O. 7 in the post war period. To the extent that income elasticity coefficients derived from time series and cross section data measure similar phenomena, it is not surprising that the cross section elasticity, which had been fairly eonstant at about a level of 1.1 in earlier studies, was observed to be about 0.6 in 1956. Professor Mincer's suggestion that interactions of such variables as number of earners, family size, age of head and income are deserving of fuller treatment is certainly a worthy one. This fuller treatment will be much more possible with the aid of Univac runs than with the more limited tabulation resources primarily used in the preparation of this paper. However, the utility of taking into account !arge numbers of independent variables depends somewhat on the purpose of the analysis. One interestingfinding was the fact that the gross marginal propensities and income elasticities for clothing changed very little, even when many variables other 479

than income were held constant. For example, a gross marginal propensity to spend on clothing of 0.119 changed to 0.114 when the tabulations were controHed for the effects of eight other variables. This suggests that it would have made little practical difference whether these other variables were taken account of, if the purpose were (say) to obtain a cross sectional propensity for insertion into a complete structural system utilizing time series data. A final point raised by Professor Mincer isthat he questions, "To what extent are these phenomena to be interpreted as genuine behavioral differences, and to what extent are they optical illusions implicit in the nature of the data-as the permanent income theory asserts?" Since an answer to this question would only be repetitious of comments in other rejoinders (see, e.g., that by Friend and Crockett), no response will be attempted here.

480

STUDY OF CONSUMER EXPENDITURES INCOMES AND SAVINGS

Proceedings of The Conference on

CONSUMPTION AND SAVING Volume II Edited by lRWIN FRIEND

and RoBERT JoNEs

Wharton School of Finance and Commerce University of Pennsylvania

University of Pennsylvania 1960

ADVISORY COMMITTEE NEIL H. BORDEN Harvard University

WASSILY LEONTIEF Harvard University

RAYMOND T. BOWMAN Bureau of the Budget

PEYTON STAPP Bureau of the Budget

REAVIS COX University of Pennsylvania

GEORGE J. STIGLER University of Chicago

NEIL H. JACOBY C. R. WHITTLESEY University of California at Los Angeles University of Pennsylvania DEXTER M. KEEZER McGraw-Hill Publisbing Co.

ARYNESS JOY WICKENS U. S. Department of Labor

BUREAU OF LABOR STATISTICS STAFF HELEN HUMES LAMALE

ABNER HURWITZ

DOROTHY S. BRADY, Consultant WHARTON SCHOOL STAFF Irwin Friend, Director of Study Jean Crockett

Robert Jones

Morris Hamburg

Irving Kravis

@Wharton School of Finance and Commerce, University of Pennsylvania, 1960 Manufactured in the United States of America By McGregor & Werner, Inc., Washington, D. C.

TABLE OF CONTENTS Page Introduction, Volume I . . . .

iii

Part 4 General Saving Relations: Permanent lncome and other Theories Consumer Expenditures and the Capita! Account Harold W. Watts and James Tobin . . . . . . . The "Permanent lncome" and the "Life Cycle" Hypothesis of Saving Behavior: Comparison and Tests Franco Modigliani and Albert Ando .. Windfall Income and Consumptian Ronald Bo:i, is the partial earrelation 34

between the same two variables, account having been taken of the remaining n-2 variables. The general schema of this earrelation matrix is shown in Figure l. For each set of stock variables, two Fi8Ure l For~at

of

eor~Plation

Matrices

G2neral eas;:c n ;: n lt1ltiple Simple earrelation Cor:--elo.tion -...,--e:..:o:...:e=fficients Coefficients

Example (n=3)

-r-----

rart :i. al earrelation Coefficicnts

Rl·23

rl2

rl3

rl2•3

R2•13

r23

rl3•2

r23·1

R3•12

n)

r 1 j" (all kfi,j} (i,j,k=l,2 ••• n)

matrices are shown for home-owners and two for renters. One matrix of each pair represents the earrelations of deviations from the over-all mean, the other represents the earrelations of deviations from regressions of Type I as shown in Table 3.2. The purpose of presenting both matrices is to see in what way the common dependence of the stock variables on the demographic and economic explanatoryvariables alters their association with each other. The four matrices are presented for the following two sets of variables: l. 12 stocks (A 11 A 2 , A 3 , A 4 , A 5 , A6 , A 7 , T, M, I, C, Z) in Tables 3.4.1 and 3.4.2 2. 5 stocks (Ah T, M, I, C) in Tables 3.4.3 and 3.4.4 Two general impressions, confirmatory of the basic hypothesis, emerge from inspection of these earrelation matrices: l. In general, the earrelations are positive between assets and negative between assets and debts. The exceptions have fairly obvious specific explanations; for example, the negative earrelation between radio-phonograph and television holdings indicates substitutability between these recreational goods. The general pattern is that those who have more have more of all assets-households advance on all fronts togethe r, keeping some balance among accumulations of different assets and reductions of debt. The same impression, with the same type exceptions, is given by the regressions themselves. As between demographic and socio-economic groups, as well as within groups, those who have more tend to have mo re quite generally. 35

Table 3. 4.1. Home owners - earrelations Among stocks before regression T

A1 ~ A3 A4 ~

~ ~

'-~49

1}6

204

o7'b'--.._g 150 130 l~~ -o- -o117 091 l4o 076 055 -039

T

-o-

-o-

M I c z

110

034* 052 -o-o-

-o012 o61

041

-o-

o8l -o-oo69

079 187 o34* 139

192 123 loB o88

-o-o-0-o040 122

031* -oo69 -o-0-o-

-094 -o-0o62 -0011

078 -oo69 -0048

M

036* -o-o034* -0-o049

162 011 139 029* 121 o66 102 o48

T

M

I

051 012 039 -0038* 071 035* -o130

c

z

074 -o-o057

122 -o117

-o-

058 099 113 -o105 -030* 073

11~7

039 -oo4~ -o--.... 017 039"·-~li -111 035* -o- 109"-~ -074 -o- -0- -126 -o63 -.._l8Ji: o96 -o- o8o -o48 ~2'-.....~7

-~9

after regression

Al

A2

Al

A2 A3 A4

~

~

~

T

M I

c

z

-o101 113 043 -0044

-0072 056

-o-

-o-0-o- -0036* -0-0- -0-

~

A6

~

134 099

130 o8o 038* 011.6

040 -o-o- -0032* -o-

-o-

049 -0031* -o- -031*

·O·

-o-0-o-

o4o ·O·

-o-

-o- -o-o- ·033* 032* -o- -o- -o-o- -o- -o-0- Olf-2 -o-

I

-o-

051

031~*

-0-

-o-o-

·0-

·O·

097 -154

-o-

-o-

·O·

·O·

z

041 032* -0033* -0- -o-o- -o- -o-0- -o- 045

-o-

-o-

052 -0031* -o·O·

-o-

c

-o-

-156 3~Q49

o2'·---~

-o-o-o-o-0-0-

~45 ',

-o- -048

78'·

'

Nate: In matrices above -o- has replaced earrelations not significant at .05, asterisks denote non-significance at .01.

36

Tabh 3.4. 2. Renters • Correlations Among Stocks before regression

-\

-'2

A3

A4

-\

~

"6

Ar,

T

M

I

c

z

213

1Bo 115

173

047

o66

-o-o-

-oo46

097 149 o81

-o-o-

136

-o-

-'2 A3 A4

~

"6 Ar,

070 -o137 -o127 044 153 -o82

T

-o-

M

042* 045 115

I

c z

-o-

-o-o-o-

oa·r -o-

091 048 145 047 o67

-o-o-

-o-

-o-

-o-

037* 042 034* -042 -o-o- -o- -0-o- -o- 058

-o-o-

-o-

079

-o-

-o-

-o-

o48

097

-o-

-0- 052 032* 045 -o- 032* Olf3 -0- o61 037* -o- 101 -o- 103 -o- 071 -o- -0- 04o* 128 -o- -o- o6o -o- -o99 o62 -o-o-o- -o- -059~ 74 049 -o- -o- 169'--....g_66

arter regression

-\ Al

A2

A3

A4

~

090

169

~ k~

A4

~

~

Ar T M

I

c

z

Note:

o67 -o115 -o- 122 122 037* -o112 .056 062 039* -0- -o- -o- -o037* -o- -o- 035* o56 098 -o- -038 -o- -o- -0- -o-o- 036* -0- -o-

"6

Ar

T

M

I

c

z

-o-o-0-0-

055

103 129

-o-o-

032* o48

034* o6o -o04o* -o- -o048 033* -o-o- 093 -o-o- -o- -o-042

038*

l6o

120

098

-o-

070

078 049

-o048 -0-

-o-

o36• -o-0-0-

073 -o-

-o-

-o-

-0-0-o-o-

-o-

-o044 -o-

-o-oo46

-0-042 -o-

-o-

-o-

042

In matrices above -0- has rep1aced corre1ations not significant at .05, asterisks denote non-significance at .01.

37

00

c:.:l

!-054

c

057

M

-0-

1 o:.9

1 -o-

I

c

-o-

212

c

c

-o-

-o-156

-0-

130 -035*

I

-o-

c

T

126

-oc

o46

01;9

M

128 -034*

I

c

-0- -059'~?

after regression

-o-

:::'~

1,140-~0-

Af

l -o-

l 127

Q5l}

-o-

-o-

-o-

~

Ao40

I

130 -035*

M

----------057

T

-o-

-.146

Af

before regression

Renteres - earrelations Among stocks

-I

M

T

Af

c

I

M

T

Af

Table 3.4.4.

In matrices above -0- has replaced earrelations not significant at .05, asterisks denote non-significance at .01.

-o-

-o-

105

-o-~

r~-0-

T

l

Note:

o48

I

078 -073

a.fter regression

M

T

Af

l

Ar

l 057

I

-o-o-

048

j 133

M

l

057

T

M

'Ä~l49

T

l-o-

Af

Af

before regression

Table 3.4.3, Home owners - Correla.tions Among stocks

2. Much, but by no means all, of the interdependence among stocks when expressed as deviations from over-all means turns out to be due to the common dependence of stocks on the explanatory variables of the regressions. The flow calculations The analysis of the flow variables is almost paraHel to the stock analysis. The same types of calculations have been made except that the flows take the role of the stocks, and five stock variables (Ar, T, M, I, C) are added to the list of independent or explanatory variables. The F-Ratios for five analysis of variance tests are shown in Table 4.1. The regression coefficients, standard errors, Su and R 2 for the "pooled" regression of each flow on the whole list of independent variables are shown in Table 4.2. A cursory glance at Table 4.1 disciases many more nonsignificant relationships than were found for the stocks. In general the demographic dummyvariables are of less importance for flows than for stocks, although there are several notable exceptions. It is worth painting out that the factors represented by Age and Education, where those variables are significant, are not at all well represented among the other independent variables. A comparison of tests (3) and (4) shows that the significance of A and E is almost always enhanced by controlling Family Size, Region, Community Size, Income, Housing Level, and the five stock variables. Furthermore, test ( 5) shows that even where the re is no significant additive effect of A and E, there is evidence of significant interaction with at least some of the other independent variables. The specific nature of such interaction has not yet been explored. The R2 's for flows in Table 4.2 are samewhat higherthan those found for stocks. Values below .20 are almost the exception instead of the rule; some are as high as .70. Apparently flows are easier to prediet than stocks partly be cause stocks themselves can be used as predictors. Turning to the regressions and examiningthe education coefficients, one nates at all age levels a tendency to dissave more by borrowing as education is increased. In the discussion of stocks it was proposed that the generally high levels of observed assets attributed to education was evidence of higher past saving by the relatively highly educated. A possible reconciliation is that the saving measure adopted does not include purchases of durables and automobiles while the high asset position noted above included the stocks of such goods. Among renters the re was a furthe r significant tendency for the higher education classes to purchase more autos at the expense of C and I. The main effect of Age on the flows is to diminish the rate of purehas e of T and A f, entirely consistent with the smaller stock of

39

~

'

'

~

Note:

u sed

4567

5

3822

5 4555

12

** denotes significance at .01 1eve1 * denotes significance at .05 1eve1

remaining

Degrees of Freedom: 3810

l2

4562

5

3817

5

4550

5

2.'71*

2.10

6.14**

1.22

11.50**

(S)

Ssvillb

l51.6o** 503.91**

43.87**

30.23**

4.34**

.79

1.45

1.93

.43

134.76** 261.20** 17 .63**

l.8o

6o.22** 14.46**

291.!~7**

1.67

81.51**

1.34

41.62**

47 .66**

.51

1.18

17.93** 2.95**

1.69**

2.60**

1.56**

9.o8**

3.84** 21.57**

2.18**

3.03**

2.93**

2.79**

185 4365

5

3805

5-95** 3.58**

3620

185

4.71**

5.72** 2.66** 15-95**

1.34

6.20**

1.98

1.39

6.12** 15.83** 1.29*

1.78**

1.03

.34

126.41** 19l.o6*':}

36.10** 850.56** 24.70**

8.ll**

6!~.::.3**

(LID)

.93

Change in Cash (CC) Balances

1.25

1.99

1.58

u.64**

Change in Debts

1.04

(6.1)

Inatallment Debt Change

8.0?.**

2.81*

Mortgage Debt (cM) Change

l0.6o** 1057·30** 598.10**

479.61** 571.57** 20.58**

(DA}

10.75**

Auto FUJ;·chase (6T}

10.6511-"

Change in Assets

14.33**

Variable J.)UrS Ol.e GOOQS Pureheses (Ef}

Additive Effects Interaction of Age & Effects of' N,R,L, Additive Effects of Age & EducaEducation with O,N, of Age & Ell.uca··· tian when added R,L,Y,H,E minus the Simple Effects Y,H, and E when tion when added to O,N,R,L,Y,H&E Additive age, educaadded to occupation of Occupation to Occutation tian ef.fects owners renters owners renters owners renters renters owners renters owners

,-,

Table 4.1. "F'' •tests for Flov Regreasions

Table 4.2.1 F1ov Regression Coefficients for Ef and Independent Variable

~

Auto Purchase

Durable Good Purchase (Ef)

(~)

Home ow:ners

Renters

Home ovners

E-2

14.62 (20.42)

1.05 (13.09)

39.24 (25.74)

40.42 (22.30)

E-3

27.78 (28.95)

10.31 (18.86)

7-52 (36.49)

82.52 (32.12)

A-2

-81.15 (24.34)

-37.70 (13.22)

10.16 (30.69)

- 8.1q (22.50)

A-}

-198.18 (26.!10)

-79.88 (15.31)

6.34 (33.28)

-31.68 (26-07)

A-4

-272-50 (28.32)

-131.55 (17 .16)

-34.70 (35.70)

-101.72 (29.22)

O-l

-35-30 (36.49)

26.02 (23.76)

25.83 (46.00)

27.92 ( 40 .l:''i)

0-2

- 1.37 (29.98

- 1.8o (17 .98)

8.68 (37. 79)

47.50 (30.62)

0-3

-13.41 (27.55)

- 9.86 (17.89)

-46.37 (34.72)

.68 (30.47)

0-5

-17-36 (25.63)

-19.04 (15.61)

-61.73 (32 .31)

-41.04 (26.58)

o-6

-38.58 (30-07)

-52.91 (17.22)

-123-95 (37-91)

-84.1lh (29.32)

l

68o.01 (42.79)

322.28 (25.07)

147.95 (53·94)

159.61 (42.69)

N

1.14 (6.15)

2.99 (3.94)

-25.12 (7.76)

-25.23 (6.72)

R-2

-10.67 (21.54)

-26.55 (13.o6)

35-39 (27.15)

.65 (22.25)

R-3

6o.36 (19.o8)

-15.83 (13.04)

86.77 (24.o6)

9().14 (22.21)

L-2

- 7-47 (19.50)

3.16 (14.67)

45.12 (24.58)

6lf.26 (24.98)

L-3

-19.77 (22.70)

-15.76 (14.95)

40.58 (28.62)

45.57 (25.45)

Y/1000

42.74 (3 .16)

20.41 (1.91)

44.72 (3.98)

21.55 (3.26)

H/1000

9-74 (1.81!)

82.76 (22.30)

10.50 (2.32)

87.42 (37.98)

-.6143 ( .0138)

- .2143 ( .OJ.l1)

.0662 ( .0174)

.0783 ( .0189)

.oo86 ( .0094)

.0153 ( .0075)

Renters

-.6591 ( .0118)

-.6246 (.0128)

-.0004 ( .0033)

.0172 (.0072)

-.Olll ( .0042)

.0142 ( .0124)

I

.1226 ( -0790)

.1616 (.0446)

- .1256 ( .0996)

-.0796 ( .076o)

c

.0100 ( .0033)

.0079 ( •0035)

.oo82 ( .0042)

.0217 ( .0059)

M

Note:

550.20

319.76

693.57

544.49

.6o2

.184

.740

.665

All coefficients are in dollars.

Estimatederrors in parentheses.

41

Table 4.2.2 Flow Regressions Coefficients for Independent Variable E-2

E-3

Mortgage Debt Change

~

and 6I

Inatallment Debt Change (al)

{~)

Home owners

Renters

9().61 (72.19)

4.20 (29.71)

5.72 (11.6o)

8.23 (12.26)

-39.49 (42.79)

11.70 (16.44)

34.34 (17.66)

223.25 (102.32)

A-2

-649.6o (86.05)

-13.28 (29.98)

A-3

-1250.19 (93.32)

7.89 (34.74)

A-4

-1}87.62 (100.11)

0-1

Home owners

Renters

4.01 (13.82)

3.62 (12.37)

- 4.30 (14.99)

7.68 (14.33)

8.20 (}8.93)

- 6.6o (16 .o8)

-13.53 (16.06)

243.40 (128.98)

}8.66 (53.90)

-14.71 (20.72)

.98 (22.24)

0-2

-12.83 (105.97)

.29 {4o.8o)

40.09 (17.03)

26.10 (16.84)

0-3

-58.19 (97.37}

20.31 (4o.6o)

29.93 (15.64)

22.55 (16.75}

0-5

-33.00 (9Q.6o)

15.51 (35.42)

22.07 (14.56)

6.12 (14.61)

o-6

-17.82 (106.31)

-11.63 (39.06)

•72 (17-oB)

6.80 (16.12)

l

1588.21 (151.26)

44.88 (56.87)

22.53 (24.30)

1.64 (23.47)

N

-15.61 (21.75)

- 1.00 (8.95)

R-2

-16.48 (76.13)

- 2.76 (29.64)

16.04 (12.23)

- 8.77 (12.23)

R-3

2o6.o8 (67.45)

-12.25 (29.59)

9.77 (10.84)

14.84 (12.21)

- 3.16 (3.49)

- 7.45 (3.69)

L-2

-30.16 (68.91)

25.25 (33.28)

10.62 (11.07)

- 7.70 (13.73)

L-3

-187.88 (8o.25)

-13.50 (33.91)

-11.43 (12.89)

19.63 (13.99)

Y/1000

-61.61 (11.15)

3.30 (4.3l,)

.25 (1.79)

·93 (1.79)

H/1000

6o.l0 (6.51)

-74.71 (50.59)

1.55 (1.05)

73.59 (20.83)

-.4664 (.0489)

-.0193 ( .0252)

.0093 ( .0078

.0094 ( .QlOl,)

.0443 ( .0332)

-.0019 ( .0171)

-.1787 ( .0053)

-.2661 ( .0071)

M

-.2174 ( .0117)

-.8569 ( .0165)

.0025 ( .0019)

.0052 ( .oo68)

I

.6348 (.2794)

-.0009 ( .1012)

.0317 ( .0449)

.0115 ( .0418)

c

.0500 ( .0117)

-.0004 ( .0079)

-.0019 ( .0019)

-.0035 ( .0032)

1944.89

725.41

312.47

299.34

.153

.730

.251

·378

42

-

Table 4.2.3 Flov Regression Coefficients for Independent Variable

Change in Cash Balances (~) Home owers Renters

be

and

M

Change in Assets (6 A) Home ovners Renters

E·2

- .38 (69.45)

-148.06 (75.83) l

E-3

45.72 (98.45)

A-2

26.86 (82.79)

-249.68 (l09.2lf) : 168.81 (169.98) i -149.39 (76.53) -754.63 (142.95)

A·3

271.29 (89. 78)

-232.05 (88.68)

-1528.49 (155.02)

69.05 (88.30)

A-4

294.70 (96.32)

11.19 (99.38)

-1492.05 (166.32)

131.56 (98.96)

l

43.20 (119.92)

l

16.52 (75.51) l7lf.)l (loB. 77) 102.11 (76.21)

0-l

2.84 (124.10)

-113.14 (l37.6o)

0-2

-82.69 (101.96)

0-3

54.51 (93.69)

0-5

- 4.18 (87.17)

103.19 (90.41)

122.61 (150.51)

-12.61 (90.03)

o-6

-38.59 (102.29)

249.94 (99.71)

216.85 (176.61)

81.96 (99.29)

l

-430.24

(145.5!~)

410.42 (214.27)

272.75 (137.01)

-295.61 (104.15)

6o.95 (176.05)

93.66 (103.71)

7.92 (103.63)

-17.74 (161.76)

-966.32 (145.17) 1127.21 (251.29)

36.74 (103.19)

347.27 (144.56)

-51.51 (20.93)

-75.18 (22.84)

R-2

86.86 (73.25)

174.94 (75.67)

64.49 (126.47)

-68.37 (75.35)

R-3

- 2.01 (64.90)

71.82 (75.53)

279.26 (ll2.o6)

35.61 (75.21)

L-2

-14.38 (66.30)

-29.o8 (84.96)

-lo8.82 (114.48)

- 6.69 (84.6o)

L-3

6.67 (77.22)

157.10 (86.56)

-194.97 (1)3.32)

-98.87 (86.19)

Y/1000

117.32 (10.73)

479.15 (11.09)

282.34 (18.53)

-34.45 (11.04)

H/1000

-3!.48 (6.27)

-845.45 (129.15)

- .41 (10.82)

-671.64 (128.6o)

-.2983 ( .o813)

.1578 ( .o64o)

N

-139.29 (36.14)

- 2.88 (22.74)

Af

.2414 ( .0471)

- ·0252 ( .o643)

T

.1300 ( .0320)

.1659 ( .0437)

.3974 ( .0552)

.1612 ( .0435)

M

.0078 ( .0113)

.1028 ( .0421)

-.2176 (.0194)

-1.1485 ( .0419)

I

-.2105 ( .2688)

-.4377 ( .2585)

.4619 (.4641)

.4o94 ( .2574)

c

-.2199 ( .0113)

- .2020 ( .0201)

.0563 ( .0194)

-.o28o (.o2oo)

su

1871.29

1851.83

3231.01

1843.95

R2

.116

·523

.135

.227

43

Table 4.2.!:. F1ou Regression Coefficients for M and S Independent Variable

Change in Debts (M) Renters Home owners

l

Saving Home owners

(S)

l

Renters

E-2

138.61 (98.30)

171.15 (92 .16)

-95.41 (73.80)

-154.63 (70.99)

E-3

306.59 (139-34)

411.87 (132.76)

-137.78 (104.61)

-237.57 (102.27)

A-2

-686.51 (117.18)

183.80 (93.02)

-68.12 (87.98)

-81. 70 (71. 65)

A-3

-1358.66 (127.o6)

269.20 (107.78)

-169.82 (95.41)

-200.15 (83.02)

A-4

-1534.51 (136.33)

115.09 (120.78)

42.46 (102.36)

0-1

278.69 (175.64)

267.48 (167.23)

131.73 (131.87)

0-2

53-32 (1411.31)

299.6o (126.58)

0-3

-32.21 (132.6o)

118.)6 (125.95)

14.47 (99-56)

0-5

-32.48 (123.38)

-61.50 (109.88)

155.o8 (92.63)

0-6 l N

l

16.46 (93.04)

l

5.26 (128.82) -205.91: (97 .50)

7.63 (1o8.35)

-81.62 (97 .02) 48.89 (84.61) !

176.65 (93-35)

258.61 (121.18)

239-22 (1o8.69)

1928.63 (2o6.oo 11017.39 (176.44)

-8ol.42 (154.66)

-670.13 {135-91)

76.61 {27.76)

-186.21 {22.24)

-79.48 (21.38)

-153.14 (91.96)

78.61 (77.84)

84.77 (70.84)

-22.37 (144.77) 46.92 (29.62)

R-2

-14.13 (103.67)

R-3

246.04 (91.86)

43.34 (9L8o)

33.22 (68.97)

- 1·13 (70.71)

L-2

-85.8o (93.85)

71.00 {103 .25)

-95.02 (70.46)

-77.70 (79-53)

L-3

-316.20 (109.29)

-211.48 (105.20)

121.23 (82.05)

112.62 (81.03)

-83.89 (15.19)

-505.77 (13 .48)

)66.23 (11.40)

471.32 (10.38)

-64.21 (6.66)

-1614.17 (120.91)

Y/1000

63.8o (8.87)

942.53 (156.97)

-.6903 ( .0666)

.1573 (.0782)

.3921 (.0500)

.0005 ( .o6o2)

-.1377 ( ,01152)

--3701 (.0531)

-5351 ( .0340)

-5313 ( .0409)

-.2203 (.0159)

-.8968 ( .0511)

.0027 ( .0120)

-.2517 ( .0394)

I

.2868 ( .38o5)

.1822 ( .)ll11)

.1751 (.2857)

.2272 ( .2420)

c

.0576 ( .0159)

.0724 ( .0244)

-.0013 ( .0120)

-.1005 (.0188)

H/1000

M

2648.55 .073

2250.64

1988.50

1733.62

.485

.326

.617

44

these items noted in the preeecting section. Older home owners seem to pay off mortgage debt more rapidly, as well as increase cash balances. No similar behavior is apparent for renters-perhaps their balances are nearer to a stationary equilibrium. The only significant coefficients in the saving equations are the negative ones for the 45-54 age class. The reasons for the unusually high spending in that age class are obscure. Among the Occupation coefficients there are few significant relationships. Between wage and salary groups (all but 0-2) there is same tendency for the blue-collar end of the scale to refrain from purchases of durables and to increase assets of other kinds, including cash, as evidenced })y the saving coefficients. Businessmen seem to raise funds by increasing debts and reducing cash. Since there seems to be no offsetting increase in the observed assets, it is possible that the funds were spent on business investment. Most of the effects of Region and Community Size that were noted in the stock seetian are substantiated by the flow relations. Where smaller stocks were observed before, smaller flows tend to maintain stocks at a relatively low level. An exception to this appears for T in the case of suburban dwellers. They did not show significantly higher auto stocks than metropolitan households, but they appear to be increasing at a faster rate. The Income and Housing Level coefficients again are highly significant, accounting in large measure for the relative ly high R2 's. The only exception is for Change in lustallment Debt-it appears to be as unrelated to Y and H as was the stock of installment debt. The long- and short-run income coefficients have been computed for the flows exactly as they were for the stocks. The calculations are shown in Table 4.3. It is interesting to note the implication that for home owners short-run increases of income result in debt reduction while long-run changes result in debt expansion. For renters, both kinds of income change reduce debt but the effects of short-run changes are more marked. The negative income effect on asset change for renters may indicate same substitutability betweenpresent wealth and future income; in the case of home owners, the same effect may operate but, if so, it is offset by home investment. The differences between short- and long-run coefficients for saving are definitely in the direction, if not in the amount,predicted by the permanent income hypothesis. Finallythere are the five stock variables, Au T, M, I, and C, which we re introduced in the flow regressions. The hypothesis was that the re is a balance among stocks whi ch households ten d to maintain; that, in other words, when an asset is above its equilibrium level changes will t end to reduce it and/or increase other assets. Reduction of debt will, of course, imply reduction of assets. This should show up in negative coefficients for an asset when it appears in "its own" flow regression and positive coefficients in other 45

Table4.3 Computations of Long- and Short-Run Income Coefficients for Flows

De penden t Variables

Home owners

Er

~T

~M

41

AC 6A

,6D

s

Housing Coefficient

$

9.74 10.50 60.10 l. 55 - 31. 48 . 41 63.80 - 64.21

Renters

Er

6T

6M 61

AC

b. A AD

s

82.76 87.42 74. 71 73.59 -845.45 -671.64 942.53 -1614.17

"Adjusted" H ou sing Coefficient

$

20. 16 21. 73 124.40 3.20 - 65. 16 • 85 132.06 -132.91

12.41 13. 11 - 11. 20 11. 03 -126.81 -100.73 141. 37 -242. 12

Long-Run Short-Run !neo me lncome Coefficient Coefficient (per $ 1000 of income)

$

42.74 44.72 - 61. 80 .25 117.32 282.34 - 83.89 366.23

20.41 21.55 3.30 . 93 479.15 - 34.45 -505.77 471.32

$

62.90 66.45 62.60 2.95 52. 16 281. 49 48.17 233.32

32.82 34.66 7.90 11.96 352.34 -135.20 -364.40 229.20

regressions. Making necessary allowances for the negative nature of debts, one can derive apattern of signs for the five stock coefficients. The estimated coefficients show little statistically significant divergence from this pattern of signs. Indeed, for home owners there is only one exception to the pattern-the positive effect of cash balances on mortgage debt change. For renters, there are three exceptions, but two of the m re late tomortgage debt and the hypothesis really is barely applicable in this case. The third exception indicates a positive effect of iostallment debt on durable purchases. Correlation matrices we re computed as before; Table 4.4 shows a set for variables E f, å T, å M, ål, åC, and s. The lower part of each table shows earrelations between residuals from regressions listed in Table 4.2. In most cases the interrelationships among the flows have been substantially reduced by allowing for their common dependence on a set of independent v~riables. In the case of saving, however, the exclusion of E f and åT from the saving concept is strongly underlined by the negative earrelations between Sand both E f and å T. This substitutability between purchases of durable goods and autos and other forms of investment is even more apparent when considering the earrelation of residuals. Furthermore, after 46

""'

-:J

l

f

-119

--

-o- -119 -092

230

032*

-034 o and

cov(e'V'} = cov(e'X) = O The regression coefficient e is a measure of the elasticity of consuroption with respect to transitory income. Substituting (2.44) into (2.10*), we obtain C= K+ mX +U'= K +MX + eo +eV' +e'

(2.45)

Notice that according to (2.45) the elasticity of consumptian with respact to transitory income is constant, which implies, since e is presurnably less than unity, that the marginal propensity to consume 104

out of transitory income decreases with the size of the transitory component. This would seem a more reasonable hypothesis than to assume a eonstant marginal propensity, and meets some of the objections raised by Friedman [7] in his comment on Bodkin's paper. Remembering that V == Y - X, we can rewrite (2.45) as C == (K + ,; 0 ) + mX +,;(Y - X} + e' ==

(K+ eo) + (m -,;)X+

(2.46}

e Y+ e'

oralsoas (2.46'} We can see from this equation that, if (2.44) holds, then in effect consumptian is a function of both current and permanent incomeunless of course ,; == m in which case the coefficient of X (or the exponent of x) vanishes. It follows that even if we discard (2.19) and replace it with the much weaker proposition < m, the Friedman and M-B-A mode l still imply a consuroption function quite different from the accepted form (2.22}. Let us next examine the implications of replacing (2.19) with (2.44) on bY, the regression coefficient of C on Y. This question is most easily answered by referring back to equation (2.21'), and using (2.44) to evaluate cov(U,V). We have

e

(2.44a)

U= U' - E(U') =ev+ e; e= e' - E(e') and hence E(UV) =E [(N+ e)V] =

evar(V)

(2.47a)

Substituting this result in (2.21')-and remembering that in the numerater of this equation var(X) must be replaced with m var(X) because we have replaced (2.10) with (2.10*)-we obtain _ m var(X} + ,; var(V) _ ( 2 2 byvar (X) +var (V) - mrXY +,; 1-rxy

)

.

(

O, f"

~

O

Hen c e w+a-q

=w+a-f(w+a) =g(w+a) =g(x),

g' = 1-f' >

o,

g"

= -f" ::5 o

(2.49a)

Here g(x) expresses the relation between (the present value of) lifetime consumptian and lifetime resources. Accordingly g' (x) might be labeled the "over life marginal propensity to consume" and we might expect that g' (x) :::; g (x) x

'

(2.49b)

i.e., the over life marginal propensity to consume will be no larger than the average, or equivalently the elasticity of over life consumptian with respect to total resources willnot exceed unity.

( Continued) families reporting that their purpose for saving was "to bequeath money" amounted to only 2o/o; and while the proportion rises with income, even in the income class over $10,000, it was but 5o/o. Similar results have been reported by Katona and Mueller [13b], Table 34. On the other hand in an interim report recently issued by the Inter- University Committee for Research on Consumer Behavior (Interim Report No. l, January 1959), the proportion of families giving as one of the reasons for saving "to leave an inheritance to children" was reported to be 29o/o. This much higher percentage might reflect the "disproportionately high representation from the upper income groups" in the sample, although the data provided are insufficient to test this conjecture.

107

Equations (2.49} and (2.48) imply (2.50} et =kig(x) and the right hand side is preciselythe function F(x) of equation (2.1). Substituting (2.51} into (2.2} and assuming again a multiplieaU ve er ror term, we can further write C t = C + U' = K~ + ln g( x) + U'

(2.50')

lt is apparent from (2.50} that even if we recognize the estate motive, the consumptian function implied by the M-A-A model does not reduce to the conventional form (2.22), for it asserts that consumptian is determined by total resources x and not by current income y. Furthermore, the various propositions about the behavior of k* over the life cycle discussed in II. 7 should still apply. On the othe~ hand, the independence of k* from w+ a- q no longer enables us to conclude that the ratio of \i>ermanent) consuroption C' to total resources x is independent of x or, equivalently, that the elasticity of permanent consuroption with respect to total resources is unity within a homogeneous cell. In fact, from (2.50} we find

d log et_ det_ g'(x) d log x - dX - g(x)/x which, according to (2.49b), is smaller than unity-unless the equality holds in (2.49b). But the equality cannot hold for all x, except under the assumption of the simplest model that g(w + a) is proportional to (w + a). Suppose, for the sake of illustration, that g(w + a) can be approximated by g(w + a)

=(w+ a) m = x m ,

(2.51}

Then, (2.50') becomes C= K*+ mX +U' t

(2.50")

which is precisely of the form (2.10*), instead of (2.10). Now, we have shown that, through the test based on regression on cell means, we should in principle be able to discriminate between (2.10) and (2.10*),at leastforlarge samples, becauseBY is a nearly unbiasedestimate of the coefficient m. Even U (2.51) is not strictly valid, the regression of Ch on Yh should provide some information on the nature of the function g(x); in particular, U the inequality in (2.49b) holds within the range of incomes covered by the sample, we should expect to find that By is decidedly less than unity. It appears therefore that the regression over the cell means can provide not only a test of the M-B-A model as against the traditional 108

ones, but can also shed light on the tenability of the estate motive hypothesis underlying the simplest version of the model.64 III - TESTS OF THE FRIEDMAN AND M-B-A MODELS BASED ON THE RELATION BETWEEN CELL MEANS FOR BLS-WHARTON SCHOOL DATA65 III.l. Restatement of the Tests in Terms of the Relations among Arithmetic Cell Means

Most of the testable implications of the Friedman and M-B-A models, derived in Sections II.8 and II.9, are stated in terms of the relation between ch and y h> i.e., the mean logarithms of consumptian and income in each cell, or, equivalently, the logarithm of the geometric rueans of consuroption and income. Now, there is no difficulty in principle in working with the logarithm of the individual observation or with geometric rueans thereof. There are, however, some actvantages to be gained by transforming our propositions in terms of the relation between the arithmetic cell means, In the first place the published results of budget studies almost uniformly

64Although in this paper we are concerned with the individual and

not with the aggregate, time series, consuroption function, it may be appropriate to stress at this point that there is, in general, no simple relation between the two. In particular, even if the bequest motive is important and individual consuroption is not proportional to individuallife resources within a homogeneous cell, it is still possible for the aggregate consuroption within a cell to be proportional to aggregate life resources. As shown elsewhere, [2], [18], such a time series proportionality will hold for instance if (l) the proportion of total resources devoted to bequest depends on the relative position of the individual' s resources in the distribution of resources over individuals but not on the absolute level of total resources, and (2) the wealth distribution remains fairly 65 stable over time, except for a scale factor. The tests carried out in this section are similar in purpose and, to some extent in methods, to the ingenious battery of tests developed by Watts [23]. As far as purpose is concerned, the main difference is that Watts was interested primarily in testing the first three propositions of the models and only incidentally the fourth, whereas in our case the opposite is largely true. With respect to methods, one important difference is that he relies on the sa vingincome ratio and the mean value of this ra tio for various groups, whereas we shall be working with the relation between mean consuroption and mean income over groups. Mr. Watts basic data are those collected by the Survey Research Center in their Survey of Consumer Finances, and cover in addition to the year 1950, also the years 1947, to 1949.

109

provide information only for the values of arithmetic means of variables within cells. Hence, propositions relating to arithmetic means, and only such propositions, can be tested directly from published data, whereas tests based on geometric means require access to the original individual observations. The seeond advantage is that propositions stated in terms of relations between arithmetic means are easier to understand in common sense terms and their aggregative implications are much more readily visualized, Let us then examine the implications of our original propositions concerning the relations among arithmetic cell means. Suppose that the relation between logarithmic cell means is of the form (3.1) We wish tq establish what (3.1) implies as to the relation between the arithmetic means, c h and Yh. Remembering that Ch and ch denate sample cell means and since E(Ch) =E( C l h), andE((\) == E(c l h), we can make use of (2.8) to obtain the relation (3.2)

This equation states a relation between arithmetic and logarithmic population cell means; a similar relation will hold between sample means except that we must now allow for the effect of sampling fluctuations. Thus (3.3) Applying the same reasoning to the income variable we have

Y h = ln Yh - 1/2 var (Yl h)+ T/h

(3.4)

Substituting now from (3.3) and (3.4) inta (3.1), we obtain

solving for ln ch, and properly regrouping terms, we obtain

66 This relation hold s exactly if the distribution of c in cell h is lognormal; otherwise it holds onlyto a firstapproximation. Whether or not c is log normall y distributed is a question that can be tested explicitly from the original observations. We maynote that when the criterion of classification is current income, with income classes narrowly defined then c 1y may be expected to be lognormally distributed if the error terms in (2.6) and (2.17) are themselves log normally distributed.

110

ln ch = [B 0 + 1/2 var( C l h) - 1/2 By var(Y l h)]

(3.5)

Now let us assume first that the within cell variances of C and Y are the same in all cells, or var(C[h)=var(C),var(Y[h)=var(Y),h=1,2, ... , H

(3.6)

Then from (3.5) we obtain the following relation between the arithmetic cell means:

(3.7) where B 0 = B0 + 1/2 [var( C) - B y var(Y)]

eh = vh -

E h+

B y 7Jh

We may also expect E(eh ln yh) =o67, We havethus established that if (3.6) holds, then (3.1) implies (a) that the relation between the arithmetic cell means is linear in the logarithms, and (b) that the regression coefficient of ln ch on ln yh is the same as the regression coefficient of Yh on C\, except for sampling fluctuations. The common sense of this result is not far to seek. If (3.6) holds, the arithmetic mean in each class is proportional to the geometric mean, and therefore the logarithm of the arithmetic mean differs from the logarithm of the geometric mean only by a constant. Actually for conclusion (b) to hold we do not need (3.6) but only the much weaker condition that [var( C 1 h) B Y var(Y l h)] should be uneorrelatad with ln yh. In those c ase s were this condition-referred to hereafter as (3.6')-may be expected to hold-at least approximately-the propositions derived in Part II can be restated and tested by replacing everywhere Ch and Yh by the logarithm of the arithmetic cell me ans, ln c h and ln yh ,68 67 Since the re is no reason to expect ln y h to be corre1ated with sampling errors in (3.3) and (3,4), this property follows from (3.1). 68 u we express the quantity [var(C [h)- By var (Y [h)] in terms of X, U and V, by making use of (2.10*) and (2.18), we find that it is equal to (a) m

2

var (X l h)+ var(U' [h)-

BY

111

[var(X [h)+ var(V'

l h)]. ( Continued)

III.2. The Relation Between Consumptian and Income When Fami!!~~~!'.~- Classified_ By Current Income We have seen in Part II that the Friedman model plus the assumption of multiplicative error terms implies a relation between measured income and consumptian of the form (2.22), and that the same is true for the M-B-A model within homogeneous cells and al so approximately, for a sufficiently heterogeneous cross-seetian of households. In particular, if we group the households into, say, H current income classes, and denote by CY and YY the mean value ( Continued} Similarly, making use of (3.4) and (2.18), we find that {b} ln (yh} = Xh

+ (1/2) var (X l h}.

Now, if in fact m ~ l and B is a good estimate of m, then (a) will reduce approximate1y to v~r(U' l h) - B var( V' l h), which is uncorre1ated with Xh if conditions (2.40) hÖld. Since there is no reason to expect any appreciab1e earrelation between var (U' l h) or var( V' l h) and var (X l h), we can conclude that, if the hypothesis m~ l is correct, and if we have a good classification criterion, then condition (3.6 1 ) will hold. Hence the regression coefficient of ln ch on ln yh, just likethat of ch on Yh, should be close to unity, except for sampling fluctuations. In f act we sus pect t hat under these conditions the test based on the arithmetic means will be more reliable than that based on the geometric means, because it is less likely to be affected by a possible earrelation between var(v* l h) and Xh. This conjecture, which we shall not try to prove here, is actually not unreasonable since our original hypothesis (2.6) and (2.17) arestatedin terms of the relationbetween arithmetic values, and the logarithmic transformation was introduced only to deal with multiplicative er ror terms. But once we deal with means of cells with large frequencies the error terms should become negligible and we can go back to the use of arithmetic means. On the other hand if m is in fact appreciably lower than unity, then the use of arithmetic means will not provide a good estimate of the true value of m, uniess var(X l h) is uncorrelated with Xh, as can be seen from expression (a) above. The common sense of this result is not far to seek: If m is less than one, and therefore consuroption is not a linear function of x, then the mean consumphon in a cell, en, does in fact depend on the var{X) in the cell. In this case, to estimate m, we can rely on the arithmetic means only if var(X l h) is uncorre1ated with h' a condition that to a first approximation can be tested from the observed earrelation of var( Y l h) with Yh' If this condition does not hold we have no choice but to rely on the geometric cell means. But in choosing our classification criterion we mustmake sure that the re is no significant earrelation between var(v* l h) and Xh - see on this point footnote 58, p. 98. One can readilythink of criteria that would not satisfy this condition, e.g., occupation; indeed the self-emplayed are like ly to have both a higher value of X and a higher value of var(v*).

x

112

of C and Y, respectively, in income class y, then (2.22) implies Cy = b0 +by YY + wy; E(wy) =O for all y. Making use of the results of the last section, we have log cY

= b0 +bY

log Yy + eY, E(eY) =O for all y,69

(3.8)

if (3.6') holds.

Thus, according to both models, the relation between mean consumptian and mean income over the income classes should be linear in the logarithms and its slope should provide an unbiased estimate of the slope of the basic equation (2.22). This implication of our models is not without interest since the relation between consumptian and income is frequently regarded as adequately approximated by a straight line. However, before we test it against available data we need to ask ourselves whether condition (3.6) is in fact likely to be satisfied. For this purpose let us note that (2.22) implies var( C l y) =b; var(YI y)+ var(wl y) Thus, in order for (3.6) to hold, it is sufficient that var(Y) and var(w) be roughly the same in all income classes. The consequences of the se conditions failing to hold can be analyzed by making useof (3.5} toexpressb~ of (3.8} intermsof var(YI y) andvar(wl y), We find b~ =

b0 + 1/2 [var(wj y) -bY (l-b) var(YI y)]

From this result, and the fact that b Yis lessthan one, we can deduce that, if in a given in come class var( w) is abnormally high, or var(Y) is abnormally low, the observation for this class will tend to fall above the overall regression line, and conversely. Now var(YI y) will tend to be eonstant over the income classes if the range of each income class is very narrow or if the width of the classes is roughly eonstant in logarithmic terms. For the BLSWharton published tabulatians the latter condition seems roughly satislied with the probable exception of the first and last open-ended classes. In these two classes var(Y) may tend to be abnormally !arge and on this account the corresponding observation might tend 6 9In this equation and in later ones in this section, we shiit from natural logarithm to logarithm to the bas e l O, denoted by log, because in the computations necessary to carry out the tests it was found more convenient to use the latter base, Since natural logarithms differ from logarithms to the bas e l O only by a proportionality factor, the substitution though it affects the eonstant term, does not effect the slope of the regression equation, which is what we are concerned with.

113

to fall below the overall line of relation. 70 In the first income class, however, this tendency is likely to be more than offset by an abnormally large value of var(w). As indicated earlier, the lowest income class appears to contain a large number of households in exceptional circumstances, so that the variance of "permanent income"-which is one of component of var(w)-may well be a good deal larger than the average. As a result the observation for the lowest class may well tend to be appreciably above the average line of the relation. 71 In summary, if we plotlog cy againstlog Yy for the nine income classes reported in volume 18 of the Consumer Expenditures Study, we should expect to find that, except for sampling fluctuations, the point will fall in a straight line. However, the dot representing the lowest income class may lie above the line, and that representing the last el ass may lie somewhat below. The results of a test of this proposition are summarized in Table III.l and figure III.l. The tests were carried out for all households combined and al so for each of three major tenure group s. The tenure groups we re ehosen be cause in several of the tests presented later we find it necessary to deal separately with owners and renters and it is desirable to have an overall view of their comparative behavior.72 In this and the following tables, unless the 70The common sense of this conclusion can be seenfrom the following alternative reasoning: in the open-ended classes the abnormally large coefficient of variation of y will cause the arithmetic mean to be disproportionately large in relation to the geometric mean and hence the observation forthese classes will tend to be pulled to the right and therefore below the regression line. 7lrn terms of the reasoning of the footnote above, the large value of var (~ will result in an abnormally large coefficient of variation of c, eausing ln c h to be abnormally la r ge relative to C\, pulling the observation above the regression line. These conjectures can of cours e be explicitlytes te d from the original data by computing var (Y) and var (C) in eachincome class. Such a test is presently being carried out, and the result will be reported in a later paper. There is also a reason to believe that there is an exceptional amount of underreporting of income in the lowest income class, which would bias the result in the same direction. (See H. Lubell). This bias is at least partially eliminated for the BLS- Wharton data if we adjust reported income by the amount of the "Account Balance" item, as we shall generally do in what follows. 72Five tenure groups are distinguished in Volume XVIII, Table 6, namely: (l) Owner all year: Bought home in 1950; (2) Bought home in 1949-46; {3) Bought home before 1946; (4) Owner end of year, renter earlier; and (5) Renter at end of year. We leave out tenure groups {l) and (4) from our consideration both because they are small in size-1.2 per cent and 3.2 per cent of total sample respectively-and because they exhibit a behavior quite different from that for other households.

114

..... ..... 01

---···--

-

-

.86 .78 .80 .75 .96 .91

.72 .49 .63 .46

.91 .85

.47 .30

.52 .37

.87 .88

.87 .92

.85 .87

.85 .88

.61 .67

.66 .74

.69 .76

.65 .72

.57 .72

.57 .72

.63 .77

.59 .74

.89

.83

.82

.85 (. 74)4

*

1 Marginal propensity to consume =!:J.c/ !:J.y. 2 Elasticity of consumption with respect to income =!:J.C/ !:J.Y 3 Regression of the logarithm of mean consumption on the logarithm of mean income weighted by class frequencies, and ornitting the first income class. 4 computed as explained in 3, but including the first income classes. Study of Consumer Expenditures, Vol. 18, Table 6.1. •::'Consumption is defined as "Current Consumption Expenditure" t "Gifts and Contributions," and income as "Money Income After Taxes" - "Account Balance Difference."

--

l. All Families a~ Marg. Pr'f.l b Elasticity 2. Bought Home before '46 a) Marg. Prop. b) Elasticity 3. Bought Home after '46 ~~.Marg. Prop. b Elasticity 4. Renters a) Marg. Prop. b) Elasticity

"Marginal Propensity to Consume" and "Elasticity of Consumptian With Respect to Income" Between Income Classes.** Study of Consumer Expenditures - Urban U. s., 1950* Between Income Classes 1,000 3,000 6,000 7,500 Estimated Average under over to to to to Elasticity 3 1,000 10,000 4,000 7,500 10,000 2,000 (by)

TABLE III.I

O)

.... ....

lO

9

8

3.9

3. 3

3.7

5

If

3

2

l

3.4

3.3

3.2

3.1

3.0

3.5

3.6

6

11

o

o

~F

12

000

c

l,. l

Loc; C

l

2.9

o

2.8

l•

3.0

2

3.2

4

3.3

5

3.4

6

lO Y2 (Thousands of Dollars) 3.5 3.6 3.7 3.8 Log Yz

8

3.9

11

4.0

12

4.1

13

Figure III.l Relation between consuroption and income -- Home owners (pre-1946)

3.1

3

4.2

14

4.3

c

4.4

16

contrary is stated, consumptian is defined as "current consumptian expenditure" plus "gifts and contributions" and income as "money income after ta.xes" adjusted for the "account balance difference." In figur e l we show for one of the tenure group s -t ho se who bought the home before 1946-a scatter diagram of c1 against y and also of logcY against logyY. An examination of the flrst mentio~ed scatter shows el early that the relation is not linear. Furthermore, if we disregard the first class, it is apparent that the curve joining the points gets progressively flatter, i.e., the slope falls steadily with income. This visual impression is confirmed by the figures in row 2.a of Table ill.l, which show, for this tenure group, the "marginal propensity to consume"-the ratio of the increment in consumpHon tothe increment in income-between selected income classes.73 1t is apparent that, beginning with the seeond income class, the marginal propensity tends to fall with income. It is also clear from the Table that this tendency prevails equally for each of the remalning tenure groups and for all families combined. 74 Let us inspect next the relation between the logarithm of mean consumptian and income, which is again shown graphically in Figure l for tenure group 3. If we leave aside the first dot, the relation appears to be extremely close to a linear one as expected. While the slope of the Une joining successive points- "the elasticity of consumptian with respect to income" between successive braekets-is of course subject to some variation, it tends to hover in the neighborhood of .8 without any appreciable tendency to rise or fall as income increases. This conclusion is again confirmed by the figures in row 2.b of Table III.l, which shows the elasticity between selected income classes. It is also seen from this table t hat very similar results hold for the remaining ho me owner group. On the other hand, for renters even the elasticity seems to fall with income. As a result some declining tendency is visible also for all families combined. However, this tendency is certainly not pronounced when allowance is made for sampling fluctuations, and in any event the elasticity appears a good deal more stable than the marginal propensity. Returning to Figure 1, it will be noted that the black dot for the last income class is somewhat low in relation to the other. Howeve r, it is not appreciably out of line with the remaining point s. Furthermo re, this tendency is not at all clear for the other tenure groups. 73we refer to this slope as the marginal propensity to consume in accordance with the prevailing practice, but it should be remembered that, if our models are correct, this slope bears very little relation, if any, to the Keynesian concept. 74 As explained later in this section, the figures for renters presented in this table have been corrected slightly for the highest income class by omitting one familywhich is way out of line havingreportedan income net of taxes of over $130,000.

117

On the other hand, the dot for the first income class is distinctly out of line, being much too high. This statement holds equally well for the remaining tenure groupsand for all families combined as evidenced by the extremely low elasticity between the first and the seeond income class shown in the first column of Table III. l. As we have suggested earlier, this phenomenon is probably due to the fact that the coefficient ofvariation of consumptian in this class is considerably larger than in the remaining ones, distorting the relation between the geometric and the arithmetic mean. It would seem, therefore, that if we are interestedin estimating the slope b of cy on YY by fitting a regression equation to the logarithm of thl arithmetic means, it would be advisable to disregard the first observation, since failure to do so would impart a downward bias to the estimate. This is the proeecture we have followed in estimating the value of by for each tenure group, shown in the last column of Table III. l. For all famili~s combined we also show in parentheses the regression coefficient estimated using all observations, including the lowest income class. The inclusion of this class is seen to lower the coefficient to an appreciable extent. We do not bother to present standard er rors of the regression coefficient or earrelation coefficients, since the latter run consistently around .99, and therefora the standarderrors are negligibly small. The fact that the logarithmic fit is so remarkably good is encouraging, though only of limited significance in view of the deficiencies of the basic data. Of much greater significance would be to test whether such good fits are obtained for other budget studiesafter proper allowance for differences in sample size-and whether the logarithmic fit is consistently superior to the arithmetic one. Although we do not propose to provide here an exhaustive answer to this question, we present in Table III.2 the result of calculations similar to those of Table III.l for a number of other recent American budget studies. In order to facilitate comparison, for each study the income classes have been so ehosenthat the first five intervals are roughly comparable to those used in Table l, when allowance is made for changes in the over-all average income. In Table Ill.2 particular interest attaches to the result obtained for the Family Expenditure study of the National Resource Planning Board, shown in Part C, be cause the estimates are based on unusually large samples, with the exception of the last two intervals. The results shown in this table broadly confirm the impressions gained from Table III.l. With very minor exceptions the marginal propensity falls continuously with income from the seeond income class on. 7 5 For the elasticity on the other hand, the re is no such 7 5 The only conspicuous exception occur s for SRC 19 50 Surv e y in which the marginal propensity rises in the last interval. This ( Continued)

118

co

.... ....

.90 .92

3,000 to 4,000 .77 .85 -

------··

--

5,000 to 7,000 .41 .52

Under 500 .92 .80

500 to 1,000 .89 .88

1,500 to 2,000

Between Income Classes

.86 .92

3,000 to 5,000 .65 .76

B-Bureau of Labor Statistics, Non Farm Families, 19412

.65 .55

1,000 to 2,000

1 Data from l. Friend and S. Schor [l l] Table 2. zH. Lubbeli [14] Table l.

(a) Marg. Prop. (b) Elasticity

(a) Marg. Prop. (b) Elasticity

Under 1,000

Between Income Classes

A-Survey of Consumer Finances, SRC-FRB, Total U.S., 19501

---

.61 .89

--

.62 .83

--------

5,000 to 10,000

-

7,500 to 10,000

"Marginal Propensity to Consume" and "Elasticity of Consumptian With Respect to Income" Various U. S. Budget Studies

TABLE III.2

over 10,000

over 10,000

o

.... t-.:1

m. 2 (Continued}

.80 .63

500 to 1,000 .85 .83

1,500 to 2,000 .73 .81

3,000 to 4,000 .62 .76 ---

4,000 to 5,000

- ----------

.61 .77 --

5,000 to 10,000

- - - - - - - - - - - --

.44 .74

10,000 to 15,000 .56 .86

15,000 to 20,000 .29 .68

over 20,000

3 Data from National Resource Planning Board, Family Expenditures Study in the United States, Statistical Table s and Appendixes, In come, w hi ch includes certain imputed consuroption item s, from Table l, les s personal taxes, Table 17. Consumption, including gifts, was obtained by subtracting Saving, Table l, from Income net of personal taxes.

(a) Marg. Prop. (b) Elasticity

Under 500

Between Income Classes

C-National Resources Planning Board, Family E:xpenditure Study, Total U. S., 1935-363

"Marginal Propensity to Consume" and "Elasticity of Consumptian With Re spe et to Income" Various U. S. Budget Studies

TABLE

tendency, or at most it is very slight. Also, the elasticity between the first and seeond income classes is uniformly quite low, being lower than for every other interval almost without exception. The fact that from Survey to Survey there are appreciable fluctuations with no systematic pattern in both the elasticity and the marginal propensity between roughly equivalent income intervals is not inconsistent with the implications of our models that these slopes have little to do with the structure of individual behavior and reflect primarily errors of measurement and random components in both measured consumptian and measured income. A final comparison is presented in Table III.3, in this case with the British data collected by the Oxford Institute of Statistics. The falling tendency of the marginal propensity from the seeond classon is again unmistakable. Both the marginal propensity and the elasticity are again rather low between the first and seeond income class, even though the upper limit of the lowest income class is much higher in relative terms than for the American surveys presented earlier-about one-half of average income as against about 25-30 per cent for the American studies. For this study, we can exhibit at !east some indirect evidence in support of our explanation for this phenomenon; it is represented by the coefficient of variation of consumptian in each in come class, reported in the last row of the table. Unfortunately the published data enable us to campute this coefficient only for families classified by income before taxes rather than by net income. As a result the coefficient exhibited in the table isprobably somewhatupward biased. However, the biasis notlikely to be large or very different for the first few income classes, and therefore the fact that, as expected, the coefficient for the first income class is very mu ch larger thanfor the neighboring ones is not without significance. Unfortunately, however, Table III.3 does not agree with our previous results and with the predietlon of our models on the most important point. It is seen that even the elasticity exhibits an unfnistakable tendency to fall with income be y ond the seeond income class, even though less markedly than the marginal propensity. In the light of the large fluctuations found in Table III.2, however, it will be necessary to carry out more extensive and systematic tests before we take this disturbing result too seriously. For the moment it seems safe to conclude that, at least for the United States, the proposition that the relation between consumptian and income for a broad cross section of families should be approximately linear in the logarithms is reasonably well supported. For the BLS- Wharton School data the over-all e lasticity may be ( Continued) results from a suspiciously high saving estimate for the income class $7,500 to $10,000, whlch may be reasonably attributed to sampling error.

121

~

t-.) t-.)

.28

200 to 400

.28

.99

.99

.23

400 to 600

.23

.32

.41

.41

.76 .84

.95

.32

.63

.78

1,000 to 1,500

.94

600 to 800

.72

over 1,500

1 Data from H. F. Lydall. Net income from Table 75; Consumptian is net income minus Saving Table 75. The coefficient of variation of c beT· Z• if bez·TbzT is zero or negative, as seems probable in the case of the income change-income expectation variable, and if r TZ is large, the n the bia s in u sing b ev . z as an e stim ate of b CP will be much lessthan the biasin using bey for this purpose. Ohserve that if we !et Z be simply an income change variable, this should be positively correlated with T and negatively correlated (if at all) with C given T be cause of lags in the actjustment of consumptian to changes in permanent income.

Regressions Grouping by Family Characteristics Other Than Income We next consicter universe regressions of the form -

Cz = a

G

G

-

+ bey y z,

(18}

where Cz and Yz are mean consumptian and mean income for groups corresponding to particular values of Z. For a fixed number of groups G b

G

_~(C z -C) (Yz -Y) ~(Yz - Y)2

ev -

where the summations extend over the G groups. If the structural equation is given by (3) with beT= O and if the residua! from this equation is U

Since T and U are both uncorrelated with Z, T2 = T and Uz = U for each group and we have bG = b CY

ep •Z +

b

ez ·P

~(Pz -P) (Zz - Z)

220

~(Pz - P)2

(19)

G

Thebiasin using bcy as an estimate of bep.z is given by the last term in (19) and willapproach zero only if rcz·p approaches zero. Nate that Z will ordinarily be ehosen so that rzp is at leJist of moderate size, since otherwise sample estimates of bcy may be come indeterminate. An analogous result follows from the double log medel: G

bc'y' = b c'p' .z' + bc'z'.p'

~(P'z -P') (Z'z -Z)

~(P'z- P') 2

(20)

Between group regressions of this type have been fitted by Franco Modigliani and Albert Anda in the paper presented at this Conference and earUer by Robert Eisner. 6 Conclusions The choice between the two approaches - that which attempts to fit (1) or (2) and thatwhich attempts to fit (18) or its logarithmic counterpart- appears to depend partly on the direction of interest, which in the seeond case is Concentrated on the effects of "permanent" income to the exclusion of those of "temporary" income and of other family characteristics, and partly on presumptians as to the size of certain parameters of (4) or (12 ). If b PZ. y (or b P' z' . y') is small, the first approach permits estimation of the effects of family characteristics other than income. In addition it yields an estimate of the effect of "permanent" income if bpy . .z is close to one, and an estimat e of the effect of "transitory" income if bpy. z is close to zero. It is possible to make bpy· z approach more closely to unity by eliminating the income extremes as in the CrockettFriend paper and same of the other demand studies, since this probably reduces the variance of "transitory" income relative to the variance of "permanent" income without particularly affecting the earrelation r zp. The seeond approach yields an estimate of the effect of permanent income if b cz· P is small. It is not clear that this should be so, however, either for the housing variable used by Modigliani-Anda or the age, occupation, and city class variables used by Eisner. It may be argued, of course, that (3) or (11) with Z representing the classifying variable is not a correct mode l. Howeve r, it is incumbent on the users of this approach either to present same empirical or a priori argument that the classifying variable has no significant effect on consumption, holding permanent income constant, or else

6Robert Eisner, "The Permanent Income Hypothesis: American Economic Review, Dec., 1958.

221

Comment,"

to specifythe nature of its influence in such a waythat bcr or be' v' becomes an unbiased estimate of the desired parameter. In the Modigliani-Anda study it may reasonably be argued that Z should be taken to be the relative rather than the absolute value of house (H/P rather than H). This solves the problem only if it can be shown either that the effect of H/P on consumptian is insignificant or that H/P is not correlated with H. Both arguments are questionable if only because of family size effects, since large families are likely to have more expensive houses (or pay higher rent) than small families both in absolute terms and relative to permanent income and are also likely to have high consumption. It is suggested that in the absence of a variable which is correlated with "permanent" income but clearly does not affect consumptian in its own right, serious consideration should be given to the introduction into income-consumption relationship of variables which may be correlatedwith transitory but not permanent income. (See Case IV.) Preferableto the income change-income expectation variable used by Crockett and Friend from the point of view of eliminating earrelation with P might be the difference between current and expected income (under the assumption that the permanent component of expected income is equal to that for current income). Alternatively, such a variable as H/Y, where H is housing leve!, might be used for this purpose. It seems likelythat this variable is negatively correlated with T, and probably not significantly correlated with P.7 Furthermore it is reasonable to assume that a high leve l of H/Y either tends to raise consumptian in its own right, or has little effect on consumptian and in this case the last term in (17) will be negative or zero. It follows that an improved estimate of the effect of P should result from including the variable H/Y in the regression analysis. This variable is to be used as a qualitative variable in an analysis of the Life 1956 data analogous to the Crockett-Friend study of the B.L.S, data reported here.

7 Let H= a H -y=

9

+ hp 9 P

be the regression of H on P.

Then

P+ T

This is negatively correlated with T, hut not substantially so with P if a 9 and T are both small relative to P.

222

WHO SAVES?* Irwin Friend and Stanley Scho r University of Pennsylvania

Recent years have witnessed the dissemination of a wealth of saving data and the appearance of widely publicized "new" theories of saving (or consumption) which are stated to explain all or most of the important saving phenomena. One of the most interesting aspects of these developments is that in spite of the new data and theories we know pathetically little about who save s what and therefore about the degree of confidence to place in various theories of saving behavior. We probably do have from 1929 on fairly reliable annual data on individuals 1 , corporate, and government saving (the latter defined as surplus or deficit on income or product account). Individuals 1 or personal saving-defined in the national income accounts, largely by statistical necessity, to include saving by noncorporate farm and nonfarm enterprises, nonprofit organizations, private pension, welfare and trust funds, as well as by consumers-has accounted for some two-thirds of the total, with corporate saving accounting for most of the remainder. The data prior to 1929 are much more dubious than the later data, but more important even after 1929 we are not in a position to break down individuals 1 savings with an y confidence in to the economic group s responsible. In other words we cannot really say what part of saving is accounted for by the upper, middle, or lower in come classes or any other e conomically significant group of individuals (e.g., entrepreneurs). This paper will attempt to highlight what we do and do not know about the relative importance of the different income groups in the total of individuals' or personal saving. This concentration on *This paper is bas ed on research undertaken in connectionwith the Wharton School Study of Consumer Expenditures, Incomes and Savings The authors wish to acknowledge the helpful comments by Ho mer Jones, Tynan Smith, and Dorothy Projector of the Federal Reserve Board and James N. Morgan of the Survey ResearchCenter of the University of Michigan. The paper, but not the comments on it or the rejoinder to the se comments, was published in The Review of Economics and Statistics, Part Z, May, 1959.

223

distribution of saving by in come as against its distribution by other economic characteristics is based, first, on the central role of income in saving allotted by almost all saving theories; second, on the potential policy implications of saving propensities of different income classes; third, on the rash of papers in recent years which have assumed that existing data show either that the marginal propensity to save out of current income is eonstant over all or most of the rang e of in come l or that the average propensity to save out of "permanent" (average, discounted, expected) income is constant; 2 and finally, on the fact that another major, economically relevant classification of savers-into entrepreneurs and nonentrepreneurs-has recently been treated elsewhere. 3 Though a number of different approaches have been experimented with, virtually all of our information on saving by income class has been obtained from sample surveys of individual consumer units or families (including single persons). In the period after World War II, there have been two sources of such data-the Federal Reserve Board-Michigan Survey Research Center Survey of Consumer Finances which collected annual data on saving and income for 1946 to 1950 from a total U. S. sample of some 3,500 spending units, and the Bureau of Labor Statistics' Survey of Consumer E.xpenditures in 1950 which collected saving, income and detailed expenditure data for 1950 from an urban U. S. sample of 12,500 families. The estimated distributions of total family saving by income class for the years 1946 to 1950, based on the Federal ReserveMichigan data, were published some time ago, but it has not previously proved possible to assess satisfactorily the reliability of these estimates, largely because the absence of data on the earnposition of saving-i.e., on the changes in individual items of assets and liabilities-precluded adequate comparison with externa! statistics.4 Such data for 1950 have been made available to us by the

1E.g., Everett E. Hagen, "The Consumptian Function--a Review Article," this Review, XXXVII (February 1955); M. Bronfenbrenner, T. Yamane, and C. H. Lee, "A Study in Redistribution and Consumption," this Review, XXXVII (May 1955). 2Milton Friedman, A Theory of the Consumptian Function, National Bureau of Economic Research, 1957; Franco Modigliani and Richard Brumberg, "Utility Analysis and the Consumptian Function," Post Keynesian Economics, ed. K. K. Kurihara (New Brunswick, N. J., 1954). 3rrwin Friend and Irving B. Kravis, "Entrepreneurial Income, Saving and Investment," American Economic Review, XLVII (June 1957). 4rrwin Friend with the as sistance of Vi to Natre lla, Individuals 1 Saving: Volume and Gomposition (New York, 1954), 57-68.

224

Federal Reserve Board (in the form of punch cards for each spending unit) and are analyzed in this paper. In addition, the results from the B.L.S. 1950 survey, including detailed data on saving by income groups recently published as part of the joint Wharton School-B.L.S. Study of Consumer Expenditures, Incomes and Savings, are al so analyzed in this paper. 5 The availability of these two bodies of detailed information on saving by income class permits first a comparison of the income distribution of family saving implied by the B.L.S.-Wharton and Federal Reserve-Michigan survey data; second, a comparison of the estimates of different components of saving from the survey data with externa! statistics; third, an assessment of deficiencies in the survey estimates of sa ving by in come class; fourth, the presentation of tentative, adjusted distributions of family saving by in come class; and fifth, a rough allocation of "non-family" saving (including earparate saving) to the appropriate income classes. As a concomitant of this analysis, the paper willpresent new information on the estimated income distribution of key components of saving giving same insights inta the forms saving takes for different income groups. Income Distribution of Family Saving from Survey Data According to published Federal Reserve-Michigan data, the highest tenth of spending units ranke d by size of in come befor e taxes accounted for 73% of the net saving of the nation's spending units in 1950, the last year for which data are available.6 The highest tenth of spending units had income before taxes in excess of $6,210 and received 29% of the total of such income. The high proportion of saving effected by the upper 10% income groupwas notpeculiar to 1950. Thusthe Federal Reserve-Michigan data attribute a slightly higher proportion of total saving to this group in 1947 and 1948, two other years of expanding economic activity, and a much higher proportion (105%) in 1949, a year of very mild recession. Similar proportions to that indicated for 1950 seem to have characterized the earlier budget studies startingwith the turn of this century-for which data are admittedly spotty-except for 1935-36 which seems closer to 1949 (and is of course also a period of recessionary tendencies). 7

5study of Consumer Expenditures, Incomes and Savings (Philadelphia, 1957), Vols. XI and XVIII. 6These data on saving and income are summarized in the Federal Reserve Bulletin, September 1951 and August 1951. 7see Raymond W. Goldsmith, A Study of Saving in the United States (Princeton, 1955), Vol. I, 161- 3. -

225

The historical survey data do not point to any clear seeular trend in the proportion of saving accounted for bythe upper income groups but this may reflect the margin of error in the data, and there is some presuroption that the apparent decline in the proportion ofincome received bythese groups since the 1920's mayhave been associated with some decline in their share of saving. 8 The survey data do suggest that the upper income groups account for a higher proportion of saving in a recession than in a boom. Before considering new data hearing on the relative importance of saving by upper income groups, it should be pointed out that the results obtained will depend to some extent on the definition of sa ving used and on the time period covered. Virtually all the survey data discussed in this article exclude from saving (i) net investment in consumer durable goodsother than hou sing; (ii) all (F .R.B.-Michigan) or part (B.L.S.-Wharton) of the change in equity in social insurance (notably old-age and survivors' insurance); (iii) the change in equity in corporate pension funds as a result of employer contributions; (iv) part of the change in equity in private trust funds; (v) the change in equity in non-profit institutions; (vi) sa ving by persons living outside the U. s., on military reservations, or in institutions; and (vii) undistributed earparate profits; but include in saving (viii) gross (rather than net or depreciated) investment in housing and (ix) unincorporated business saving. As discussed subsequently, a change in the treatment of several of these items (i, ii, and ix) would decrease the relative importance of the upper in come group s in saving, while a change in the treatment of other items (iv, vii, and perhaps viii) would increase the upper income share. The time period covered by a survey affects the results obtained for the relative importance of upper income saving in two ways. First, it is possible that people with high current income in any year tend to have higher income than normal for them and hence to save more than they do customarily, while people with low current income have lower than normal income and hence save less than customarily. 9 Annual surve y data would as a result tend to show too high a concentration of saving among upper income groups as 8 Such a decline in their share of saving is implied by estimates presented by Simon Kuznets in Shares of Upper Income Groups in Income and Savings (National Bureau of Economic Research, 1950), 45 ff. 9The B.L.S.- Wharton data for 1950 show relatively small differences between the consumption-income ratios of families with a three-year spanof relatively constantineornes and withnonconstant incomes for the middle and upper income classes but significant differences for the lowest income groups. See Irwin Friend and Irving B. Kravis, "Consumption Patterus and Permanent Income," American Economic Review, XLVII (May 1957), 545.

226

campared with the situation over a longer period of time. Second, there is some reason to believe that the survey data in a prosperous year like 1950 tend to understate the concentration of saving among upper income group s in economically depressed periods and therefore over the business cycle as a whole. New Data on Income Distribution of Saving A more adequate picture of the income distribution of saving implied by survey data for 1950 can be presented by analyzing and camparing the F .R.B.-Michigan saving data for individual spending units (from which mean and aggregate saving for various income groups can be obtained), and the corresponding B.L.S.-Wharton saving data covering a much larger sample but confined to urban families only.l 0 Table l shows thepercentagedistributionof saving by after-tax income class for the U. S. as a whole derived from F.R.B.-Michigan data for individual spending units by applying the same weights used in their published tabulatian s; for the urban U. s. again derived from F .R.B.-Michigan data for direct comparison with the B.L.S.-Wharton results; and for the urban U. S. from B.L.S.-Wharton data by applying internal (unadjusted) and external (adjusted) weights. 11 The F .R.B.-Michigan data, unlike the B.L.S.Wharton data, include imputations and are internally adjusted for nonrespon&e and for missing income and asset information. l 0Families include one person families or single individuals. While no adjustment will be made in this article for the differences between the F .R.B. -Michigan "s pending unit" and the B.L.S. "family ," it should be noted that the two concepts imply somewhat different income distributions of saving. (See Study of Consur:!_ler Expenditures, Incomes and Savings, Vol. XVIII, xxxiv.) 11Personal insurance is included in B.L.S.- Wharton saving unlike the treatment in the volumes of statistical data published by the Studyof Consumer Expenditures, Incomes and Savings, University of Pennsylvania, 1956 and 1957, where it is shown separately. The externa! weights applied to the average saving by income class indicated by the B.L.S. 1950 survey were obtained from the income distribution of urban families estimated by Hyman G. Kaitz in Dewhurst andAssociates, America' s N e ed and Resources: A New Survey (New York, 1955), 961-64. The Kaitz weights were used to correct for the understatement of the numbers offamilies at the extremes of the income distribution, particularly at the upper end, in the B.L.S. sample data. The use of these weights results in increased e s timates offamilysaving for the urban U .S., hut do e s not markedly affect the income distribution of saving. (See Table I and Study of Consumer Expenditures, Incomes and Savings, Vol. XVIII. Vol. XVIII also discusses the nature and limitations of the B.L.S. sample, response, treatment of the data, and interna! as well as externa! weights applied.)

227

NI NI 00

52.0

100.0 $14,463

100.0

-14.7 - 0.2 0.2 14.3 18.0 27.6 19.9 34.9

%

Savings

. %

32.9

100.0

8.5 17.6 21.1 21.7 14.5 11.7 2.8 2.1

Spe n ding units

%

$10,775

100.0

- 8.0 0.8 - 1.1 11.3 15.1 27.3 21.6 33.0

Savings

Urban

31.5

100.0

8.9 14.2 16.5 18.3 15.2 17.2 5.6 4.0

%

Spending units

$5,653

100.0

31.5

100.0

6.3 12.3 18.7 24.0 16.9 15.9 3.5 2.4

%

-32.2 -16.4 -11.7 - 2.4 6.5 29.9 32.4 93.9

%

Spending units

$3,282

100.0

-39.3 -24.5 -22.9 - 5.3 12.5 47.5 35.0 97 .o

%

Savings

Unadjusted

Savings

Adjusted~·

B.L.S.-Wharton (Urban)

~·Adjusted

on basis of incorne distribution of urban farnilies prepared by Hyman B. Kaitz for Arnerica's Needs and Resources (see text).

Amount (millions)

Total (per cent)

12.9 19.4 20.7 20.3 12.4 10.3 2.2 1.8

Under $1,000 $1,000-1,999 $2,000-2,999 $3,000-3,999 $4,000-4,999 $5,000-7,499 $7,500-9,999 $10,000 and over

%

Spe nding units

lncome after taxes

Total U. S.

Federal Reserve-Michigan

Table 1.-Percentage Distribution of Aggregate Federal Reserve-Michigan and B.L.S.-Wharton Savings Estimates by Income Class, 1950

According to the Federal Reserve-Michigan data the 2% of spending units with incomes (after taxes) over $10,000 accounted for one-third of total saving by all spending units in 1950, with not much difference in this respect between the total and urban U. s. Clos e to 5% of the spending units with incomes over $7,500 effected 55% of saving; and 10% of the units were responsible for 75% of saving. The B.L.S.-Wharton data, however, point to a significantly greater concentration of saving in the upper income groups. Here, it is found that the 4% of families with incomes over $10,000 accounted for nearly 95% of saving, and the highest 10% ranked by income for over 125%.12 The proximate reason for the differences in the income distribution of saving implied bythese two bodies of data is the consistently lower average saving indicated by the B.L.S.-Wharton estimates for each income group (Table 2). Thus, while the average income for each group is about the same, the average saving-income ratio is roughly 5% lower for the B.L.S.-Wharton than for the Federal Reserve-Michigan data, with the notable exception of the lowest income group where the difference is much greater. (The difference is also considerably larger in the $7,500-$9,999 group but this seems to reflect a discontinuity in the Federal Reserve-Michigan series.) Such a difference in estimated saving behavior, in conjunction with the more rapid rise in saving than in income common to both series, explains the greater concentration of saving found in the B.L.S.-Wharton data as well as the lower estimate of total saving. The difference in concentration of saving indicated by the two surveys is not changed much when families headed by selfemplayed or not gainfully employed persons are excluded (to eliminate the two groups which have a special impact on the income distribution of saving), and the difference in average saving estimates persistsover the entire income range (Table 3). Associated with this difference in average saving, there is a very substanHal disparity in the two estimates for total U. S. urban saving, with the Federal Reserve-Michigan figure fully $5 billion higher than B.L.S.-Wharton. It appears that only a small part of this disparity could be attributable to conceptual differences in the definitions of savingused in the two surveys. The Federal ReserveMichigan data exclude from saving two components included by the B.L.S.-viz., change in charge accounts and in currency-resulting in a comparative overstatement of saving in 19 50 amounting roughly

12In view of the greater concentration of sa ving shown by the B.L.S.Wharton data, it may be noted that these results are presurnably mor e comparable to the prewar surveys than are the F .R. B.Michigan data.

229

o

(..:l

N

'~Adjusted

All

3,233

574 1,510 2,497 3,486 4,438 5,862 8,837 16,290

Average income $

%

8.6

-55.2 - 0.2 0.1 5.6 9.1 12.7 28.4 33.1

Savingincome ratio

s.

on basis of Kaitz income distribution.

Under $1,000 $1,000-1,999 $2,000-2,999 $3,000-3,999 $4,000-4,999 $5,000-7,499 $7,500-9,999 $10,000 and over

Income after taxes

Total U.

3,549

633 1,531 2,504 3,479 4,458 5,918 8,536 17,586

Average income $

Urban

Federal Reserve-Michigan

9.2

-48.9 0.9 - 0.7 4.9 7.7 12.9 30.1 29.6

%

Savingincome ratio

-105.5 - 13.5 - 5.0 - 0.7 1.7 5.2 12.3 26.4 4.3*

4,147>:
!:oJr:

0.4 1.2 2.5 8.8

of saving in form of cash and deposits allocated proportional to externa! estimates of cash and deposits holdings in each income class adjusted by Kaitz income distribution. ~.!.:)

--1,206 393 699 503 488 53 778 266 4,504

1,068 1,687 2,490 3,333 4,068 5,286 6,488 7,095 15,644

Self emElo~ed business personal personal sav i ng income

-

--

183 516 90 354 630 85 228 613 3,801

Other self personal sav i ng

1 These figures are unadjusted and are the same as those in Table V.

Under $1,000 $1,000 - 1,999 $2,000 - 2,999 $3,000 - 3,999 $4,000 - 4,999 $5,000 - 5,999 $6,000- 7,499 $7,500- 9,999 $10,000 and over

Income after taxes

--

516 139 90 l 107 201 365 978 2,840

s avi ng

603 1,537 2,492 3,441 4,414 5,394 6, 585 8,393 14,457

income

EmElo~ees 1

They are presented for comparison.

1,727 1,478 2, 527 3,496 4,359 5,369 6,477 8,618 14,944

personal income

emElo~ed

Mean Personal Savings and Personal Income by Classes of Total Income after Taxes for Entrepreneurial Groups 1950 Survey of Consumer Expenditures

Table VI

above, we subtract the net change in business investment from total savings, we get an estimate of personal savings. This shows the change in personal net worth (exclusive of capita! gains) and is a meaningful measure of personal saving. The measure of personal income obtained by subtracting net change in business investment from the conventional definition of income is perhaps less meaningful, but it does satisfy the accounting identity consumer expenditure + change in personal net worth = personal income. The results of so defining and computing personal savings and income from the 1950 Study are given in Table VI. As can be seen from the graph of these data in Figure II, the entrepreneurial personal savings-income curves come very close to the employees' curve. The marginal coefficient is higher for the entrepreneurial curves eausing them to lie below the employee curve at the bottom range and above it at the top. This comparison has specifically excluded the retired group and is on this account superior to those made in earlier studies. Fi(. II

Engel Curves of Personal Saving for Occupational Groups 1950 Survey of Consumer

Expenditures

6,000

+ .. +++ self-employed businessmen

other self-employed

employees

4,000

8,000

12,000

16,000

income ofter taxes (dollars)

325

20,000

Since we have not totally excluded the significance of income variability, it is plausible to believe that the slight discrepancies remaining between the entrepreneurial and nonentrepreneurial curves could be accounted for in !arge measure by this factor. The alternative hypothesis being considered in this section, namely, that differences in income variability account for the occupational differences in savings, can be exaroined by changing the usual way of classifying families in the Engel curve presentation. The average relationship between savings and income after taxes is still the type of pattern desired, but the classifying variable instead of being braekets of current income is changed to braekets of some variable more closely related to long run income position. Two measures are selected, food expenditure and housing expenditure. It is assumed that families are not likely to make short run alterations in either of these two types of basic expenditure as a result of fluctuations in current income. Within a class of, let us say, food expenditure an average of savings and an average of current income will tend to long run or permanent values if temporary variations are randomly distributed about the means. The relationship between average savings and average income after tax within braekets of food expenditure isthus put forward as a direct estimate of the permanent savings-income pattern. If variability of income explains the occupational savings differentials, we should find that the permanent Engel curves for the different groups are indistinguishable from one another. Friedman has suggested a mo re extreme version of this theory in which he claims that the permanent curves should be straight line rays from the origin, Le., that the savings-income ratio is eonstant for alllevels of income. In Table VII and Figure III we see the outcome of using food expenditure as a classifying variable. The different propensities for the four occupational groups are brought doser tagether than in Figure I, but the higher position and steeper slope of the entrepreneurial curves are unmistakable. Possibly, the relationship for employees could be considered as a straight linerayfrom the origin, but there is decided curvature in the permanent savings-income curve for entrepreneurs. As can be seen in Table VII, some of the results for the entrepreneurial group are erratic, but the basic pattern is clear. Apart from one of these erratic values, the upper classes of food expenditure definitely show consistently greater sa vings a verages for the entrepreneurial groups. On balance, businessmen's savings outstrip those of other self employed. The savings-income ratio can be seen to vary with permanent income levels for all but the employees. A further compilation of data along the same lines is provided by using housing instead of food expenditure as a classifying variable more closely related to permanent income status than is current income. Renters and homeowners must be treated separately in 326

c,., t-.:1 -:J

Under 499 500 - 999 1,000 - 1,499 1,500- 1,999 2,000 - 2,L>99 2, 500 or more

($)

Food expenditure

12 30 489 686 75 3,830

-

-

($)

l, 536 3, 083 5,026 6,803 6, 770 17' 186

($)

- 0.8 l. O 9.7 10.1 - 1.1 22.3

(/,)

Self emp]2yed businessmen savi.ne;s in come ra.tio

47 177 211 287 5, 219 1,850

($)

l, 207 2,836 4,964 6,896 13,329 17. 111

($)

- 3.9 6.2 4.3 4.2 39.2 10.8

(/,)

Other self employed sa vings income ra tio 55 96 92 87 259 366

l, 711 2,965 4,119 5,238 6,709 9,906

EmJ2lo:zees sav i ng s income ($) ($)

3.2 3.2 2.2 1.7 3.9 3.7

(%)

ra tio

Mean Savings and Mean Income for Classes of Food Expenditure by Occupational Groups 1950 Survey of Consumer Expenditures

Table VII

-

167 287 238 654 421 1,414

--

($)

886 1,981 3,414 4,602 7,294 11,607

($)

-

- 18.8 - 14.5 7.0 - 14.2 5.8 12.2

( ')',)

Retired and unem12loyed savings income ra tio

Fig.m Saving -Income Relationship Classified by Levet of Food

Expenditure for

Occupational

Groups

1950 Survey of Consumer Expenditures 6,000

en

~ >

2,000

o

!/l

o +-t+++

-2,000

self-employed businessmen other self- employed employees retired & unemployed

,------,-0

4,000

8,000

income after

l 2,000

16,000

eo,ooo

taxes (dollars)

order to get measures of housing status that are comparable among families. This separation, in itself, has the extra advantage of isalating a variable that is, in any case, related to savings behaviour, namely, home ownership. The separation into two groups, however, drastically reduces the sizes of the individual sample s within which we study the savings-income relation. The patterns naturally become considerably more erratic, especially for the self employed units. For homeowners, the level of housing expenditure is taken to be represented by the estimated market value of the dwelling. For renters (technically non homeowners) the annual payment for rent, fuel, light, and refrigeration determines the classification scheme for the proxy measurement of permanent income. The results, displayed in Table VIII and Figures IV- V, show the same pattern of savings superiority among the self employed units, but occasionally the employee group show a higher figure for savings at the middle or upper range of incomes. Employee home owners have a fairly steep and rising savings curve by this method

328

w

t-.:1 CP

Under 250 250-499 500-749 7 50-999 1,000-1,249 l, 250-1,499 1,500 and over

($)

119 298 148 426 - 1,729 - 417 6,843

-

Annual rent - Renters

-

2,229 2,903 4,088 5, 187 4,304 7,389 20,658

5.3 -10.3 3.6 8.2 -40.2 - 5.6 33.1

Market value of home - Homeowners ($) -11.2 Under 5,000 295 2,642 15 0.5 5,000-7,499 3,314 331 4, 553 0.7 7, 500-9, 9)ff9 10,000-12,!•99 534 5, 565 9.6 9.2 540 5, 889 12,500-14,999 6,269 14.9 934 15,000-17,499 988 7,213 13.7 17,500-19,999 7, 591 22.9 20,000-24,999 1,740 9,194 11.0 25,000 and over 1,014

Self emEloled businessmen savings income ratio ($) (/'o) ($)

72 66 196 996 - 2, 154 2,617 412

--

168 2,448 1,465 1,007 2,849

- 10286 666 - 1,800

2, 17 5 2,524 3,446 5,962 5,640 9,167 12,760

2,195 3, 354 3,891 6,878 7,100 9,475 6,767 8,708 14,600

3.3 - 2.6 - 5. 7 16,7 -38.2 28.5 3.2

- 3.9 3.0 -17 .l 26.2 2.4 25.8 21.6 11.6 19.5

Other self emEloled income ratio (%) ($) ($)

savings

-

68 3 20 - 23 - 139 27 5 -1,343

--

119 152 149 230 27 5 393 645 1,047 1,093

2,151 2,908 3, 677 4, 571 5,096 6, 781 7,826

3,181 3,818 4, 252 4, 723 5,309 5, 511 6,859 6, 594 10,957

EmElolees sav i ng s in come ($) ($)

- 2.7 - 4.1 -17.2

- o.s

3.2 - 0.1 - 0.5

3.7 4.0 3.5 4.9 5.2 7.1 9.4 15.9 10.0

(to)

ra tio

-

---

-

---

85 99 149 546 591 42 873

109 289 263 448 771 409 206 417 206

933 1,503 2,629 3,062 4,629 4,317 6,122

l, 719 2,005 2,405 2,456 2,765 3,162 3,304 3,593 8,335

- 9.1 - 6,6 - s. 7 -17.8 -12.8 l. O 14.3

- 6.3 -14.4 -10.9 -18.2 -27.9 -12.9 - 6.2 -11.6 - 2.5

Retired and unemEloled savings in come ratio (to) ($) ($)

-

Hean Savings and Mean Income for Housing Classes by Occupational Groups 1950 Survey of Consumer Expenditures

Table VIII

Fig'.IV

Sav i ng -In come Relationship C l as sified by Leve l of Housing for Occupational Groups Homeowners 1950 Survey of Consumer Expenditures 4,000

~ 1..

2,000

()

.....

.....

o

~ III

a>

c

o

> .,o +++++ - 2,000

o

4,000

income

self-employed businessmen other self-employed employees retired /le. unemployed 8,000

12,000

16,000

after taxes (dollars)

of classification, but after an income leve! of about $4,000, their savings are consistently surpassed by one of the two entrepreneurial groups. The fact that they sometimes save mo re, at a given income leve!, than one of the entrepreneurial groups, may well be a chance result following from the thinness of the sample size on the subdivisions used. In the renter group, employees have a persistent dissaving at nearly all income levels. Apart from some erratic movements the entrepreneurs have the usual positive savings gradient. The outcome of the exploratory computations attempting a socalled permanent income classification leave the basic hypotheses of this study intact. In a negative sense, income variability is not an overwhelming factor which explains away the occupational savings differentials. We must look to other factors, possibly those put forward in the hypotheses about the imperative demands for business capita! funds placed upon the personal financial lives of entrepreneurs. 330

Fig-. V

Soving- Income Relationship Classified by Level of Housing for Occupational Groups

Renters 1950 Survey of Consumer Expenditures

6,000 +++++

self-employed b