The Changing Distribution of Income in an Open U.S. Economy [1st Edition] 9781483296265

Table of contents :
Content:
Contributions to Economic AnalysisPage ii
Front MatterPage iii
Copyright pagePage iv
Introduction to the SeriesPage vThe Editors
PrefacePages vii-viii
List of FiguresPages xvii-xx
List of TablesPages xxi-xxiv
List of Conference SpeakersPages xxv-xxvi
Chapter 1 - The Scope, Growth, and Causes of Income Inequality in an Open U.S. EconomyPages 3-27Jeffrey H. Bergstrand, Thomas F. Cosimano, John W. Houck, Richard G. Sheehan
Chapter 2 - Levels of and Changes in the Distribution of U.S. IncomePages 29-63Charles T. Nelson
Chapter 3 - A Dominance Evaluation of Distributions of Income and the Benefits of Economic GrowthPages 65-103John A. Bishop, John P. Formby
Chapter 4 - The Growth in Male Earnings Inequality, 1973–1988: The Role of Earnings Capacity and UtilizationPages 105-144Robert H. Haveman, Lawrence Buron
Chapter 5 - Dimensions of Inequality in Labor IncomePages 145-179Finis Welch
Chapter 6 - Using Regional Data to Reexamine the Contribution of Demographic and Sectoral Changes to Increasing U.S. Wage InequalityPages 183-216Lynn A. Karoly, Jacob Alex Klerman
Chapter 7 - The Relationship Between Wage Inequality and International TradePages 217-241George J. Borjas, Valerie A. Ramey
Chapter 8 - A Macroeconometric Model of Income Inequality in the United StatesPages 243-278Nathan S. Balke, Daniel J. Slottje
Chapter 9 - Technological Progress and Income Inequality: A Model with Human Capital and Bequests*Pages 279-297Edi Karni, Itzhak Zilcha
Chapter 10 - Productivity and Income Inequality Growth Rates in the United StatesPages 299-327Kathy J. Hayes, Michael Nieswiadomy, Daniel J. Slottje, Michael Redfearn, Edward N. Wolff
Chapter 11 - Old Theories in New Bottles: Toward an Explanation of Growing World-Wide Income InequalityPages 331-342Barry Bluestone
Chapter 12 - General Economic Theory and Income InequalityPages 343-347Kenneth J. Arrow
Chapter 13 - Have we Underinvested in Education?Pages 349-353Orley Ashenfelter
Chapter 14 - The Changing Distribution of Income in an Open U.S. Economy: Findings and LessonsPages 355-360Robert H. Haveman
Chapter 15 - Summary and ConclusionsPages 361-379Jeffrey H. Bergstrand, Thomas F. Cosimano, John W. Houck, Richard G. Sheehan
IndexPages 381-385

Citation preview

CONTRIBUTIONS TO ECONOMIC ANALYSIS 223

Honorary Editor: J. TINBERGEN Editors: D. W. JORGENSSON J. -J. LAFFONT T. PERSSON

NORTH-HOLLAND AMSTERDAM · LONDON · NEW YORK · TOKYO

THE CHANGING DISTRIBUTION OF INCOME IN AN OPEN U.S. ECONOMY Edited by Jeffrey H. BERGSTRAND Department of Finance and Business Economics Thomas F. COSIMANO Department of Finance and Business Economics John W. HOUCK Department of Management Richard G. SHEEHAN Department of Finance and Business Economics College of Business Administration University of Notre Dame Notre Dame, Indiana U.S.A.

1994 NORTH-HOLLAND AMSTERDAM · LONDON · NEW YORK · TOKYO

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 RO. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN: 0-444-81559-7

© 1994 ELSEVIER SCIENCE B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V, Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science B.V, unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. PRINTED IN THE NETHERLANDS

INTRODUCTION TO THE SERIES This series consists of a number of hitherto unpublished studies, which are intro­ duced by the editors in the belief that they represent fresh contributions to economic science. The term "economic analysis" as used in the title of the series has been adopted because it covers both the activities of the theoretical economist and the research worker. Although the analytical methods used by the various contributors are not the same, they are nevertheless conditioned by the common origin of their studies, namely theoretical problems encountered in practical research. Since for this reason, busi­ ness cycle research and national accounting, research work on behalf of economic policy, and problems of planning are the main sources of the subjects dealt with, they necessarily determine the manner of approach adopted by the authors. Their methods tend to be "practical" in the sense of not being too far remote from appli­ cation to actual economic conditions. In additon they are quantitative. It is the hope of the editors that the publication of these studies will help to stimulate the exchange of scientific information and to reinforce international cooperation in the field of economics. The Editors

Preface The year 1992 marked the 150th anniversary of the University of Notre Dame. As one dimension in honoring the sesquicentennial, Rev. Edward A. Malloy, the university's president, invited and encouraged each of the university's colleges to hold one or more academic symposia. With the active support of John G. Keane, dean of the College of Business Administration and former director of the U.S. Bureau of the Census, the editors of this volume embarked on organizing a symposium to reflect on the emergence of dramatic changes in the distribution of earnings and income in the United States during the 1980s, the possible causes of these changes, and potential implications of and policy recommendations for such changes. On September 17-18, 1992, several of the nation's most prominent scholars on this topic and related areas gathered to present and discuss the original papers included in this volume. The list of contributors is on pages xxv-xxvi. The editors are deeply grateful to numerous people. First and foremost, we thank Dean John G. Keane for his early support and encouragement of a conference addressing important issues in the changing character of the U.S. economy's earnings and income. As former director of the Census Bureau, he actively fostered the interaction of academics and policymakers, which contributed to the stimulating discussion at the symposium. We are very indebted to the Chase Manhattan Bank for providing financial support for this conference. In honor of Rev. Theodore M. Hesburgh, C.S.C., former president of the university, the Chase Manhattan Bank generously donated a gift to the College of Business Administration, part of which was used to fund the conference. Numerous individuals in academia and government contributed significant time and ideas toward the organization of this conference. We are grateful to Barry Bluestone, John Coder, Gordon Green, Robert Haveman, Enrique Lamas, Charles Nelson, Tom Scott, and Dan Slottje for numerous planning discussions which contributed to the conference's success. Several scholars (whose names are among those on pp. xxv-xxvi) provided rich, thoughtful, and detailed discussions of the papers in this volume. We are deeply grateful for their time, efforts, and talents, which improved the quality of these papers significantly. Madeline Day, executive coordinator of the Notre Dame Center for Ethics and Religious Values in Business, did an excellent job coordinating

viii

Preface

the conference. We are indebted for her careful, professional, and cheerful handling of logistics. We thank Harriet Baldwin of the university's Center for Continuing Education for exceptional work in supporting the conference's activities in collaboration with Madeline Day. Several people contributed their talents toward the preparation of this volume. We are indebted to Sonia Grant and Anthony Sindone for excellent assistance in the editing of this volume. Diane Bandurski and Tammi Chapman provided outstanding technical typing; we are deeply grateful for their patience in this volume's preparation. We thank Assistant Dean Sam Gaglio for providing support for the manuscript's completion, and Joyce Happee for her prompt and clear editorial suggestions.

December 1993

The Editors

List of Figures Page Figure 2.1 Figure 2.2 Figure 2.3 Figure 3.1

Shares of Aggregate Household Income, by Quintile: 1970, 1980, and 1990 Percent of Persons with Low, Middle, and High Relative Income: 1964-1989 Median Relative Income of Persons 25-64 Years Old, by Years of School Completed First Order Dominance Comparisons of Three Hypothetical Income Distributions: X X , X Lorenz Dominance of U.S. Income Distributions, 1978 and 1989 First Order Dominance Comparisons of U.S. Income Distributions, 1980 and 1982 Second Order Dominance Comparisons of U.S. Income Distributions, 1980 and 1982 Lorenz Distributions of Luxembourg Income Study Per Capita Family Income Ordered by Statistically Significant Differences Pairwise Statistical Comparisons of Lorenz Curves Across Countries First Order Dominance Comparisons of Income Distributions in Six Countries The Lorenz Curve of 1949 Income and the Concentration Curve of the Distribution of the Benefits of Growth of the 1950s The Lorenz Curve of 1959 Income and the Concentration Curve of the Distribution of the Benefits of Growth of the 1960s The Lorenz Curve of 1969 Income and the Concentration Curve of the Distribution of the Benefits of Growth of the 1970s The Lorenz Curve of 1979 Income and the Concentration Curve of the Distribution of the Benefits of Growth of the 1980s Dominance Comparisons of the Distribution of the Benefits of Economic Growth Among American Families l5

Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5

Figure 3.6 Figure 3.7 Figure 3.8.a

Figure 3.8.b

Figure 3.8.C

Figure 3.8.d

Figure 3.9

2

3

33 37 40 70 72 73 80

83 84 85

91

91

92

93

94

xviii Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5

Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

List of Figures Trends in Real Earnings (1990 PCE-deflated) of White Men, Ages 25-34 152 Trends in Real Earnings (1990 PCE-deflated) of White Men, Ages 45-54 152 Interquartile Spreads in Annual Real Earnings of White Men, Ages 25-34 and 45-54 153 Percent of White Men Working Full Time Year Round (FTYR) by Age Group 154 Average Hours Worked Per Week for FTYR Working White Men by Earnings Distribution Location 155 Percent Working FTYR by Group, Ages 25-54 156 Relative Earnings of White Women to White Men, Ages 25-34, by Annual Earnings Quartiles 157 Relative Earnings of Black Men to White Men, Ages 25-34, by Annual Earnings Quartiles 158 Relative Earnings of Black Women to White Men, Ages 25-34, by Annual Earnings Quartiles 159 College Graduates' Earnings Relative to High School Graduates' Earnings Among Men, 1-10 Years Out of School, for Matched Centiles in Respective Distributions 162 College Graduates' Earnings Relative to High School Graduates' Earnings Among Men, 26-35 Years Out of School, for Matched Centiles in Respective Distributions 163 High School Graduates' Earnings Average Centile in College Graduates' Earnings Distribution, by Years Out of School 164 Earnings for High School Graduates 26-35 Years Out of School Relative to Earnings for High School Graduates 1-10 Years Out of School, for Matched Centiles in Respective Distributions 165 Earnings for College Graduates 26-35 Years Out of School Relative to Earnings for College Graduates 1-10 Years Out of School, for Matched Centiles in Respective Distributions 166 Relative Earnings of Young Men to Older Men, by High School Graduates and College Graduates 167

List of Figures Figure 5.16 Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Figure 5.21

Figure 5.22 Figure 5.23 Figure 5.24 Figure 5.25 Figure 5.26 Figure 5.27 Figure 5.28 Figure 6.1 Figure 6.2 Figure 7.1 Figure 7.2 Figure 7.3 Figure 7.4 Figure 7.5

Simulated Overlap Statistics Trends in Real Earnings (1990 PCE-deflated) of White Men, Ages 3 5-44 Trends in Earnings Inequality for White Men, Ages 25-34 Trends in Earnings Inequality for White Men, Ages 35-44 Trends in Earnings Inequality for White Men, Ages 45-54 Rank Correlation of Hourly Earnings and Annual Hours Worked Among FTYR Working White Men, Ages 25-54 Average Hours Worked Per Week Among FTYR Workers by Group, Ages 25-54 Relative Earnings of White Women to White Men, Ages 35-44, by Annual Earnings Quartile Relative Earnings of White Women to White Men, Ages 45-54, by Annual Earnings Quartile Relative Earnings of Black Men to White Men, Ages 35-44, by Annual Earnings Quartile Relative Earnings of Black Men to White Men, Ages 45-54, by Annual Earnings Quartile Relative Earnings of Black Women to White Men, Ages 35-44, by Annual Earnings Quartile Relative Earnings of Black Women to White Men, Ages 45-54, by Annual Earnings Quartile Inequality in Hourly Wages for Men By Census Region Inequality in Hourly Wages for Women By Census Region Trends in Returns to Skills, 1963-1988 Net Imports of Services as a Percent of GDP Net Imports of Nondurable Goods as a Percent of GDP Net Imports of Durable Goods as a Percent of GDP Actual and Fitted Values using Regression of College-High School Dropout Wage Premium on Durable Imports and Exports

xix 173 174 174 175 175

176 176 177 177 178 178 179 179 190 191 221 223 224 224

230

List of Figures

XX

Figure 7.6

Figure 7.7

Figure Figure Figure Figure Figure Figure Figure

8.1.a 8.1.b 8.1.c 8.1.d 8.1.e 8.2 11.1

Compensation of Employees in Durable Manufacturing (as a Percent of Aggregate Compensation, Inverted Scale) Compensation of Employees in Target Industries (as a Percent of Aggregate Compensation, Inverted Scale) The Lowest Income Quintile Over Time The Second Lowest Quintile Over Time The Middle Income Quintile Over Time The Second Highest Quintile Over Time The Highest Income Quintile Over Time The Gini Coefficient Over Time The Links from Global Competition to Growing Inequality

235

236 247 247 248 248 249 249 335

List of Tables

Table 2.1 Table 2.2

Table 2.3 Table 2.4 Table 2.5

Table 2.6

Table 2.7 Table 2.8 Table 2.9 Table 2.10 Table 2.11 Table 2.12 Table 3.1

Table 3.2

Table 3.3

Page Income Summary Measures 30 Mean Income of Households in Each Quintile and Top 5 Percent: 1970-1990 (in 1990 CPI-U-X1 adjusted dollars) 34 Percent of Persons With Low and High Relative Incomes: 1964-1989 39 Median Relative Income by Race, Hispanic Origin, and Age: 1964-1989 (1.00 = all persons) 41 Percent of Children Under 6 Years Old with Low and High Relative Incomes, by Family Type, Race, and Hispanic Origin: 1964-1989 42 Effect of Benefits and Taxes on Household Aggregate Incomes and Gini Indexes by Selected Characteristics: 1990 44 Gini Index of Income Concentration, by Definition of Income: 1990 46 Full-Time Year-Round Workers with Low Earnings, by Selected Characteristics: 1964-1990 50 Poverty Rates of Full-Time Year-Round Workers with Low-Earnings, by Relationship: 1964-1990 51 Effect of Standardization on Median Incomes and Gini Indexes: 1969-1989 54 Effect of Standardization on Median Incomes and Gini Indexes: 1979-1989 57 Effect of Standardization on the Black-White Median Income Ratio: 1989 58 Lorenz Dominance Comparisons of U.S. Income Distribution, 1978 and 1989: Lorenz Ordinates, Standard Errors and SMM Statistics 74 First Order Dominance Comparisons of U.S. Income Distribution, 1980 and 1982: Conditional Means, Standard Errors and SMM Statistics 76 Second Order Dominance Comparisons of U.S. Income Distribution, 1980 and 1982: Generalized Lorenz Ordinates, Standard Errors and SMM Statistics 78

xxii Table 3.4.a

Table 3.4.b

Table 3.4.c

Table 4.1

Table 4.2

Table 4.3

Table 4.4 Table 4.5

Table 4.6

Table 4.7

Table 4.8

Table 4.9

List of Tables The Distribution of Income and the Distribution of the Benefits of Growth in the 1950s and 1980s: The Level and Growth of Personal Income (1987 Dollars) The Distribution of Income and the Distribution of the Benefits of Growth in the 1950s and 1980s: Mean Income and Lorenz Ordinates The Distribution of Income and the Distribution of the Benefits of Growth in the 1950s and 1980s: The Benefits of Growth Variance of the Logarithm (VLN) of Earnings, Earnings Capacity, and the Utilization of Earnings Capacity, 1973 and 1988, Male Workers and All Males Aged 18-64 Comparison of the VLN and the Change of VLN of Earnings of Males from Various Studies, 1973 until Late 1980s Percentile Distribution of Total Earnings, All Males and Male Workers Aged 18-64, 1973 and 1988 (1988 dollars) Summary Measures of Earnings Inequality, Male Workers and All Males Aged 18-64, 1973 and 1988 Percentile Distribution of Earnings Capacity, All Males and Male Workers Aged 18-64, 1973 and 1988 (1988 dollars) Comparison of Inequality of Distributions of Earnings and Earnings Capacity, Male Workers and All Males Aged 18-64, 1973 and 1988, Various Indicators Summary Measures of Earnings Capacity Inequality, Male Workers and All Males Aged 18-64, 1973 and 1988 Distribution of Capacity Utilization Rates, Male Workers and All Males Aged 18-64, 1973 and 1988 Summary Measures of Inequality in Capacity Utilization Rates without Variance Adjustment, Male Workers and All Males Aged 18-64, 1973 and 1988

88

89

90

108

110

114 115

119

120

121

122

123

List of Tables Table 4.10

Table 5.1 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table Table Table Table

7.1 7.2 8.1 8.2

Table Table Table Table Table Table Table Table

8.3.a 8.3.b 8.3.c 8.3.d 8.3.e 8.3.f 8.4 8.5

Table Table Table Table Table Table Table Table Table Table

8.6.a 8.6.b 8.6.c 8.6.d 8.6.e 8.6.f 8.7 10.1 10.2 10.3.a

Source of Change in the Variance of Log Earnings, Male Workers and All Males Aged 18-64, 1973 and 1988 Simulated Changes in Distributional Overlap Real Median Hourly Wage By Region, 1973-1988 Decomposition of Inequality in Hourly Wages Men Decomposition of Inequality in Hourly Wages Women Regression Results for Variance of Logarithm of Hourly Wages: Males, 1973-1988 Regression Results for Variance of Logarithm of Hourly Wages: Females, 1973-1988 Cointegrating Regressions and Tests, 1963-1988 Estimates of Error Correction Model, 1965-1988 Level of Inequality in Different Sub-Periods Marginal Significance Levels for F-Tests of Hypothesis that Lagged Coefficients Are Jointly Zero Variance Decomposition for Income Inequality Variance Decomposition for Income Inequality Variance Decomposition for Income Inequality Variance Decomposition for Income Inequality Variance Decomposition for Income Inequality Variance Decomposition for Income Inequality Coefficient Estimates of Structural Model Equations Variance Decomposition for Income Inequality in the Structural VAR Historical Decomposition Historical Decomposition Historical Decomposition Historical Decomposition Historical Decomposition Historical Decomposition Historical Decomposition: Structural VAR Productivity, Inequality, and Macro Variables Phillips-Perron Unit Root Tests Bivariate Causality Model using BLSPROD as the Productivity Measure: Gini is the Dependent Variable

xxiii

125 172 188 192 194 206 208 226 229 246

252 254 255 256 257 258 259 263 264 266 267 268 269 270 271 272 304 307

310

XXIV

Table 10.3.b

Table 10.4.a

Table 10.4.b

Table 10.5

Table 10.6

Table 10.7.a

Table 10.7.b

Table 10.7.C

Table 10.7.d

Table 10.7.e

Table 10.8

Table 10.9

List of Tables Bivariate Causality Model using BLSPROD as the Productivity Measure: BLSPROD is the Dependent Variable Bivariate Causality Model using RLGNPEMP as the Productivity Measure: Gini is the Dependent Variable Bivariate Causality Model using RLGNPEMP as the Productivity Measure: RLGNPEMP is the Dependent Variable Multivariate Causality (Exogeneity) Test Results using the Gini Index Growth as the Inequality Variable and BLSPROD as the Productivity Variable Multivariate Causality (Exogeneity) Test Results using the Gini Index Growth as the Inequality Variable and RLGNPEMP as the Productivity Variable Multivariate Causality Model using BLSPROD as the Productivity Measure: Gini is the Dependent Variable Multivariate Causality Model using BLSPROD as the Productivity Measure: BLSPROD is the Dependent Variable Multivariate Causality Model using BLSPROD as the Productivity Measure: Transfers is the Dependent Variable Multivariate Causality Model using BLSPROD as the Productivity Measure: Tax is the Dependent Variable Multivariate Causality Model using BLSPROD as the Productivity Measure: Unemp. Rate is the Dependent Variable Impulse Response Functions of Productivity Growth to a One Standard Deviation Shock in Gini Growth Impulse Response Functions of Gini Growth to a One Standard Deviation Shock in Productivity Growth

311

312

313

314

314

315

316

317

318

319

320

322

List of Conference Speakers

Kenneth J. Arrow Stanford University

Orley Ashenfelter Princeton University

Nathan S. Balke Southern Methodist University

Michael R. Baye Pennsylvania State University

Jeffrey H. Bergstrand University of Notre Dame

David M. Betson University of Notre Dame

John A. Bishop East Carolina University

McKinley L. Blackburn University of South Carolina

Barry Bluestone University of Massachusetts-Boston

George J. Borjas University of California-San Diego

Stephen G. Bronars University of Texas-Austin

Lawrence Buron University of Wisconsin-Madison

Thomas F. Cosimano University of Notre Dame

David M. Cutler Harvard University

Carl Davidson Michigan State University

Greg J. Duncan University of Michigan

John P. Formby University of Alabama

James Foster Vanderbilt University

Joseph H. Haslag Federal Reserve Bank of Dallas

Jon D. Haveman Purdue University

Robert H. Haveman University of Wisconsin-Madison

Kathy J. Hayes Southern Methodist University

John W. Houck University of Notre Dame

Christopher Jencks Northwestern University

xxvi

List of Conference

Speaks

Sidney L. Jones Department of the Treasury

Edi Kami John Hopkins University

Lynn A. Karoly RAND Corporation

John G. Keane University of Notre Dame

Jacob A. Klerman RAND Corporation

Frank Levy Massachusetts Institute of Technology

Susan E. Mayer University of Chicago

Rev. Edward A. Malloy, C.S.C. University of Notre Dame

Kevin M. Murphy University of Chicago

Charles T. Nelson U.S. Bureau of the Census

Michael L. Nieswiadomy University of North Texas

Timothy O'Meara University of Notre Dame

Brooks Pierce Texas A & M University

Valerie Ramey University of California-San Diego

Michael Redfearn University of North Texas

Richard G. Sheehan University of Notre Dame

Daniel J. Slottje Southern Methodist University

Timothy Smeeding Syracuse University

George M. von Furstenberg Indiana University

Finis Welch Texas A & M University

Barbara Wolfe University of Wisconsin-Madison

Edward N. Wolff New York University

Stephen A. Woodbury Michigan State University

Itzhak Zilcha Tel Aviv University

The Changing Distribution of Income in an Open U.S. Economy J.H. Bergstrand et al. (Editors) © 1994 Elsevier Science B.V. All rights reserved.

Chapter 1 THE SCOPE, GROWTH, AND CAUSES OF INCOME INEQUALITY IN AN OPEN U.S. ECONOMY Jeffrey H Bergstrand, Thomas F. Cosimano, John W. Houck, and Richard G Sheehan University of Notre Dame

1.1

Introduction

One of the fondamental issues long studied by economists is the distribution of a nation's income. Numerous articles and books have presented evidence of a dramatic and persistent change in the distributions of earnings and income in the United States over the past two decades, cf. Harrison and Bluestone (1988), Burtless (1990), Levy and Murnane (1992), and Baily, Burtless, and Litan (1993). The evidence suggests that the distributions of earnings and income have become more unequal since the early 1970s in the United States, and in other industrialized countries as well. By contrast, investigations into the causes of increasing income inequality have yielded few substantive conclusions. Explanations for the growing income inequality commonly fall under microeconomic and macroeconomic categories. Typical microeconomic explanations consider both demand and supply effects. On the demand side, for example, long-run secular changes in consumer demand away from goods and toward services would tend to increase earnings inequality if services display greater earnings dispersion. On the supply side, for example, in an economy where young inexperienced workers are imperfect substitutes for older experienced workers, a rise in the relative supply of young workers — that is, a baby boom — will depress earnings of lower-paid young workers relative to those of higher-paid older workers and will create greater earnings dispersion. The typical macroeconomic explanation argues that income inequality increases during slow (or negative) growth periods. For instance, in a recession lower aggregate demand leads to a reduction in productionline worker hours and/or employment, while higher-paid middle and senior

4

J. H. Bergstrand, T. F. Cosimano, J. W. Houck, and R. G. Sheehan

managers are less affected. The reduction in demand for lower-paid lowerskilled production workers relative to higher-paid higher-skilled nonproduction workers tends to increase earnings inequality. While previous studies of the causes of income inequality often can be categorized as either "micro" or "macro," we emphasize at the outset that such factors may be complements, rather than substitutes, working in tandem to explain emerging income-inequality trends. Indeed, the increasing importance of international trade and competition for explaining changes in the distribution of U.S. income, as will be seen shortly, will further blur the distinction between "micro" and "macro" forces. The original papers in this volume attempt to contribute to a better understanding of the measurement and causes of income inequality and its changes. Despite an apparent consensus that the distributions of earnings and income have become more dispersed, several important issues remain unanswered in the description of earnings and income distributions. For example, the very definition of income has been challenged. Traditionally, annual family (or household) income has been employed in constructing income-inequality measures. In Chapter 2, Charles T. Nelson examines how income-inequality measurements are influenced by Census Bureau adjustments for family (or household) size, for federal, state and local taxes, for noncash transfers and benefits, and for returns on home investments. Changes over time in the level of income inequality have been estimated typically by examining changes over time in the shares of national income to various deciles, Gini coefficients, Theil indexes, or variances of the logarithm of income. In Chapter 3, John A. Bishop and John P. Formby discuss the merits of comparing income distributions intertemporally and internationally using the "dominance method," an approach resting upon explicit welfare criteria and subject to formal econometric testing. The method is adapted in this chapter to evaluate various decades' distributions of economic growth. Some analyses of changes in the distribution of earnings have attempted to decompose earnings changes into changes in the wage rate and changes in hours worked, to better understand whether increased earnings inequality is due to increased variance in labor market "opportunities" or in labor market "choices." In Chapter 4, Robert H. Haveman and Lawrence Buron provide a framework for decomposing changes in earnings into changes in "earnings capacity" (or potential human capital) and changes in "earnings capacity utilization" (or the utilization of human capital). Their results contrast sharply with previous estimates, finding that most of the

Income Inequality in an Open U.S. Economy

5

increased variance in male earnings appears to be in the utilization of human capital. In Chapter 5, Brooks Pierce and Finis Welch question the notion that the increase in income inequality is due largely to a secular rise in the demand for skilled versus unskilled labor, as though "skill" is unidimensional. Pierce and Welch employ "location statistics" to examine shifts in relative earnings distributions, that is, shifts in one group's earnings distribution relative to the earnings distribution of white males. They find that movements such as the declining wage of young college graduates relative to high school graduates in the mid 1970s, and the increasing relative wages of women generally, suggest that a simple convex monotonie transformation of the wage distribution is rejected. The five papers in the second part of this volume evaluate potential causes of the levels of and changes in income inequality. In Chapter 6, Lynn A. Karoly and Jacob Alex Klerman explore the relative importance of micro (sectoral) labor demand, micro (demographic) labor supply, institutional, macroeconomic, and international factors in explaining changes in earnings inequality, using time series of cross sections of male and female workers' earnings. They find some support for a variety of factors influencing earnings inequality between 1973 and 1988, including microeconomic, macroeconomic, international, and institutional causes. In contrast to the breadth of Karoly and Klerman's chapter, each of Chapters 7 through 10 focuses more narrowly upon microeconomic, macroeconomic or international influences on inequality trends. In Chapter 7, George J. Borjas and Valerie A. Ramey discuss theoretically and empirically why growing international competition, especially in concentrated durable goods industries, can have an important effect on a nation's distribution of earnings. They present convincing evidence that the growing U.S. trade deficit in durable goods can explain, even out of sample, much of the increased earnings premium for college graduates relative to high school graduates or dropouts. In Chapter 8, Nathan S. Balke and Daniel J. Slottje use recent timeseries techniques to explore the importance of various macroeconomic policy and performance variables for explaining expected and unexpected changes in the Gini coefficient for U.S. family income. The study departs from previous ones by accounting explicitly for feedback between income inequality and macroeconomic variables, and examines theoretical and structural vector autoregressions (VARs) to determine the relative importance of the macroeconomic policy and performance factors for

6

J. //. Bergstrand, T. F. Cosimano, J. W. Houck, and R. G. Sheehan

explaining increased income inequality. Higher unemployment plays a dominant role in explaining both expected and unexpected increases in income inequality. In Chapter 9, Edi Kami and Itzhak Zilcha discuss theoretically the potential impact of various types of technological progress on a nation's level of income inequality. Intergenerational decisions regarding investments in offsprings' human and nonhuman (physical) capital interact with technological change to influence w/ragenerational income distributions. This model provides a conceptual background to the next chapter. In Chapter 10, Kathy J. Hayes, Daniel J. Slottje, Michael Nieswiadomy, Michael Redfearn, and Edward N. Wolff examine empirically the relationship between productivity and income inequality growth rates, in both bivariate and multivariate econometric settings. There is evidence that higher productivity growth "Granger-causes" less income inequality growth, and that higher income inequality growth "Grangercauses" less productivity growth. The third part of this volume contains four shorter papers that generally focus upon policy implications and recommendations. In Chapter 11, Barry Bluestone examines the increasing openness of the U.S. economy as a factor influencing the U.S. distribution of income. The growing relevance of the standard assumptions of the neoclassical Heckscher-Ohlin model lends increasing credence to one of that model's implications — a tendency toward greater equalization of factor returns internationally (for like factors), but perhaps increased disparity zwiranationally between returns for skilled versus unskilled labor. He offers some policy choices. In Chapter 12, Kenneth J. Arrow considers some of the implications and deficiencies of general competitive equilibrium theory for understanding levels of and changes in income inequality. In particular, he discusses how the leisure-labor tradeoff, transactions costs, and dynamic considerations might influence the distribution of income. In Chapter 13, Orley Ashenfelter argues that the rate of return on investment in education might have been considerably underestimated. He offers some estimates of the return and describes an income-contingent loan program to support investment in schooling. In Chapter 14, Robert H. Haveman offers a perspective on the state of our knowledge concerning the measurement and causes of income inequality and its changes. He suggests some paths for future research and offers some policy recommendations. Finally, Chapter 15 offers a summary and conclusions, and focuses on key questions

Income Inequality in an Open U.S. Economy

7

remaining and on fruitful directions for future research. The present chapter is not intended to offer a comprehensive survey of the literature on the measurement and causes of income inequality. Comprehensive surveys can be found elsewhere; see Levy and Murnane (1992). In the remainder of this chapter, we provide an overview of each of the chapters in this volume and discuss how these studies are related and contribute to the income distribution literature.

1.2

Issues in the M e a s u r e m e n t of I n c o m e Inequality

Among several measurement issues, one must consider first the very definition of "income." The range of choices varies typically from pre-tax, pre-transfers-and-benefits earnings to post-tax, post-transfers-andbenefits income. Second, one must choose between an analysis of individuals versus families (or households); earnings or income distributions of families may move quite differently from those of individuals (for instance, as average family or household size changes over time). In Chapter 2, Nelson evaluates the impact on inequality measurement of alternative definitions of income and earnings. Nelson's paper is comprised of three parts. The first part addresses the inadequacy of "traditional" measures of income trends and inequality. Within this section, Nelson considers whether the slower rate of growth of real family (or household) income since 1973, and the greater dispersion of this income, overstates the true change in families' economic well-being since the average family size has shrunk. Nelson discusses the Census Bureau's relative income measure. The relative income measure illustrates the extent that the income of a person or a group of persons diverges from the median income of all persons. Persons may be categorized as having low relative income (less than half the median), high relative income (more than twice the median), or middle relative income (that in between low and high relative incomes). Even adjusted for family or household sizes, U.S. income inequality increased during the 1970s and 1980s. The share of persons with either low or high relative income increased from 29 percent in 1969 to 37 percent in 1989. Thus, the share of persons with middle relative income consequently fell from 71 to 63 percent. The remainder of the first part of Nelson's paper discusses the effects that various taxes, transfers, benefits, and imputed returns had on the level of inequality in 1990 U.S. household income. Nelson presents 14

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alternative definitions of income, ranging from pure "money income" to "fully-adjusted income." Several conclusions emerge. First, taxes tend to be redistributive, lowering the Gini index by 6 percent. Second, transfers tend to be even more redistributive, lowering the Gini index by 17 percent. Third, the redistributive impacts of these policy and nonpolicy adjustments are neither uniform by race, nor age, nor household-head status. The second part of Nelson's paper describes attempts at the Census Bureau to measure the rise in earnings inequality, in the number of workers with low-wage jobs, and in the share of workers with "low earnings." This topic also is addressed in Chapter 4 (Haveman and Buron). Low-earnings workers are considered those full-time, year-round (FTYR) workers with earnings insufficient to keep a four-person family above the poverty line. Not only did the proportion of low-earnings workers increase between 1979 and 1990, but the increase was shared by all races, genders, and ages. The sharpest increases in the proportion of low-earnings workers were among young FTYR workers and among high-school dropouts. Nelson also finds that the increase in earnings inequality in the United States was not unique. Australia, Canada, (West) Germany, and Sweden all experienced higher inequality between the early and mid 1980s. In international earnings comparisons using the Luxembourg Income Study data, the United States had the highest level of inequality, followed by Canada, Australia, (West) Germany, and Sweden, respectively. The third and final part of Nelson's paper addresses some of the potential causes of the rise in income inequality during the 1970s and 1980s using a "standardization" technique that simulates how the level of inequality would have changed over a period had a certain "characteristic" not changed. Summarizing some Census Bureau reports, Nelson shows that, between 1969 and 1989, changes in household types (e.g., fewer married-couple families versus single-parent families), work experience of householders, and industry employed (fewer workers in manufacturing) were among factors increasing the degree of income inequality. The standardization results suggest that, had these observed changes not occurred, the Gini index would likely have risen only half the amount official statistics indicate. By contrast, between 1979 and 1989 these same changes tended to have little impact on the degree of income inequality. However, further discussion of causes of income inequality changes is postponed until Section 1.3. A third measurement issue is the choice of the "metric" of income or earnings inequality. Nelson (Chapter 2), Balke and Slottje (Chapter 8),

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and Hayes et al. (Chapter 10) focus on the Gini index. Haveman and Buron (Chapter 4) and Karoly and Klerman (Chapter 6) use the variance of the natural logarithm of earnings. In Chapter 3, Bishop and Formby recommend the dominance method for analyzing levels of and changes in income distributions. The advantage of the dominance method is that it allows the researcher the potential to determine statistically whether one income distribution is "better" than another (on either efficiency or efficiency-equity grounds). This approach's appeal embodies three distinct features. First, the approach rests upon explicit welfare criteria that are widely accepted and allow rankings of entire distributions. Second, statistical inference procedures pioneered in Beach and Davidson (1983) permit dominance relationships between different income distributions to be subjected econometrically to rigorous hypothesis tests. Third, the dominance approach relies on ordinal measures of income distributions and of welfare, not cardinal ones. Using this method, Bishop and Formby find several strong results. First, the 1978 U.S. distribution of (family) income first order dominates — that is, is more equal than — the 1989 distribution. First order dominance is a pure efficiency criterion; it contains no preference for equity (i.e., the first order dominance theorem assumes only the class of anonymous, increasing welfare functions, whereas the second order dominance theorem restricts the class of admissible welfare functions to those that are "equality-preferring"). Second, in international comparisons using the Luxembourg Income Study data, the U.S. income distribution in 1980 first order dominated the distributions of the Netherlands and France, and crossed Sweden's, West Germany's, and the United Kingdom's. In 1986, the U.S. income distribution first order dominated those of the Netherlands, France and the United Kingdom, and crossed Sweden's and West Germany's. Third, in a comparison of the distributions of U.S. economic growth for the 1950s, 1960s, 1970s, and 1980s, Bishop and Formby demonstrate that the 1960s second order dominated — that is, were more income-equalizing than — the 1950s, which second order dominated the 1970s, which second order dominated the 1980s. They conclude that if growth and equity matter in evaluating U.S. welfare, the economic growth of the 1980s was unambiguously inferior to that of any of the previous three decades. While Nelson (Chapter 2) and Bishop and Formby (Chapter 3) focus on the emerging increase in income inequality using traditional and newer methodologies, respectively, Haveman and Buron (Chapter 4) and

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Pierce and Welch (Chapter 5) investigate the recent rise in earnings inequality. Chapters 4 and 5 also differ from Chapters 2 and 3 by examining cross sections of individuals' earnings, rather than of families (or households) earnings. Chapters 4 and 5 additionally address an increasing tendency in the literature to attribute the growing earnings inequality to a rise in the return to "skill" as though — as Pierce and Welch state — skill is unidimensional. In Chapter 4, Haveman and Buron decompose the increase in earnings inequality into changes in inequality of earnings capacity and of capacity utilization. Earnings inequality is in part due to "opportunities" and in part due to "choices." Researchers frequently have interpreted the rising variance of real earnings as an increased dispersion in potential human capital — that is, in education, work experience, etc. (commonly summarized as "skill"). Increased variance in these factors would cause increased dispersion in the pure price of labor, or of "opportunities" (in Haveman and Buron's terminology). However, even if the variance in the pure price of labor was constant, earnings inequality could increase if there was growing dispersion in the distribution of time worked, or of "choices" (in Haveman and Buron's terminology). Note that increased dispersion of choices can reflect either increased variance in the supply of hours by workers, the demand for hours by firms, or both. Haveman and Buron note that previous empirical evidence has tended to confirm the conventional view that increased earnings inequality has stemmed from increased variance in the pure price of labor, or of opportunities. In fact, some studies have attributed all of the increased earnings dispersion to this phenomenon. However, Haveman and Buron's empirical work — using instruments for earnings capacity and earnings capacity utilization, rather than the (implied) wage rate and hours worked from monthly or weekly data samples — suggests the opposite. For FTYR male workers, Haveman and Buron find that only one-third of the increase in earnings variance can be attributed to increased inequality in their proxy for potential human capital services, and that the bulk of the remaining increase in earnings variance should be attributed to increased dispersion in time worked. Haveman and Buron address a fourth measurement issue as well. They investigate earnings inequality for FTYR male workers as well as for all working-age males. Changes in earnings inequality over time for the two populations may differ substantively, and the share of working-age males reporting no earnings or hours worked has increased sharply. Their

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empirical work suggests that less than 10 percent of increased earnings dispersion among all males can be accounted for by increased dispersion in potential human capital services with the bulk of the remainder accounted for by increased dispersion in labor market "choices." Thus, Haveman and Buron s paper suggests that changes in earnings inequality (and in its components) differs for FTYR male workers and all males (of working age). These results in Chapter 4 also corroborate Arrow's insight in Chapter 12 that the variance in earnings is much larger than that of abilities; Haveman and Buron's results suggest that the variance in potential human capital services is considerably smaller than that of earnings. In Chapter 5, Pierce and Welch also raise concern over interpreting the rise in earnings inequality simply as a higher return to "skill," or to potential human capital services. Like Haveman and Buron they examine distributions of U.S. FTYR individuals' earnings. Unlike Haveman and Buron, they do not employ descriptive statistics of inequality (Gini coefficient, variance of logarithm of earnings, Theil index), but rather examine the changing spread of one group's earnings rankings within the distribution of another group's earnings (in particular, that of white males). In general, Pierce and Welch find that there have been too many changes in wage differentials between groups for the notion of an increasing return to a single-dimensional pervasive "skill" to be maintained. The primary metric of relative inequality used in Pierce and Welch is an "average location" statistic. This statistic is the probability that a randomly chosen member of one group will have a higher income than a randomly chosen member of another group. Because the metric is ordinal, it is invariant to monotonie tranformations in earnings. Two additional measures supplement this statistic. Pierce and Welch draw several conclusions. First, for the distribution of white men, earnings at the high end of the distribution are expanding relative to those at the low end, suggesting that the return to skill has risen. Second, using hours worked data Pierce and Welch, like Haveman and Buron, find that there has been rising inequality in hours worked, with high-wage earners gaining hours relative to low-wage earners. Third, earnings of women, especially black women, improved systematically and dramatically relative to white men in the same quartile. For example, in 1963 the average white female (ages 25-34) drawn from the top quartile of this group's earnings distribution had earnings at the 40th centile of the white male (ages 25-34) earnings distribution. That is, a randomly chosen 25-34 year old white female drawn from the top quartile 5

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of this group's earnings distribution had only a 40 percent probability in 1963 of earning more than a randomly chosen 25-34 year old white male drawn from the top quartile of that earnings distribution. By 1990, that probability had risen to 75 percent. (If these two groups had identical earnings distribution, the probability would be 87.5, not 100, percent.) Fourth, despite this systematic relative improvement for women, the improvement in women's relative wages in this ordinal sense has not been uniform. Pierce and Welch note that the relative improvements have been only modest for the bottom two quartiles. Fifth, earnings of young (25-34 year old) black men improved systematically and dramatically relative to young white men in the same quartile between 1963 and 1978. The convergence stopped in 1978 for young black men, but not for older black men. Sixth, Pierce and Welch corroborate earlier well-known findings that the income premium for college graduates over high school graduates fell during the 1970s, but rose during the 1980s, and that earnings of older workers have risen relative to younger workers. However, they find that the timing of the latter change is different for college graduates than for high school graduates. A fifth measurement issue is the choice of methodology depending upon whether one is focusing upon the middle of an earnings distribution or on the tails. As Nelson (Chapter 2) and Haveman (Chapter 14) note, changes in the top five and top one percent of income earners represent a major policy concern. The "top-coding" of Current Population Survey data, however, arbitrarily alters the observed distribution, a concern of greater import when emphasis is placed on the distribution tails. Pierce and Welch's methodology allows scrutiny by individual centiles. In fact, they find no consistent pattern of movement in relative earnings of the most highly paid men, white college graduates at mid-career. They conclude that at the top end of the distributions "not much" is happening, whether comparing the highest paid high school graduates to the highest paid college graduates at mid-career, or the highest paid young college graduates to the highest paid mid-career college graduates. Although the five papers composing Part 2 of this volume focus upon the causes, rather than the measurement, of income inequality and its changes, four of those papers are largely empirical analyses of wage, earnings, or income inequality. Thus, those studies must address at least implicitly some of the issues discussed here. Moreover, some of those studies raise other measurement issues. Just as distributions of wages, earnings, or income may change

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differently for individuals and families, for men and women, for blacks and whites, inequality may change differently by geographic region within the United States. Bishop and Formby (Chapter 3) note that, while the South's level of inequality was tending to converge toward that of the Non-South in the 1970s, the income-inequality levels of the Northeast, Midwest and West were diverging from one another. In Chapter 6, Karoly and Klerman examine changes in hourly wages and wage inequality by nine U.S. geographic regions between 1973 and 1979 (henceforth, "the 1970s") and between 1979 and 1988 (henceforth, "the 1980s"). Karoly and Klerman find that wage differences between regions declined during the 1970s, but rose during the 1980s; this result held for men and for women. Yet they find that only about two (three) percent of male (female) wage inequality overall is explained by this regional diversity. Karoly and Klerman find that inequality (measured by the variance of the natural logarithm of hourly wages) within regions for men varied in the 1970s; wage inequality fell in some regions, was stable in others, and rose in still others. In contrast, during the 1980s within-region inequality for men generally rose in all regions, contributing to the aggregate rise in wage inequality. For women, within-region inequality declined in every region until 1979, and rose thereafter. Another measurement issue concerns the stationarity of the index of (wage, earnings, or income) inequality over time. Stationarity of a variable requires that it has no stochastic or deterministic trend. A variable is considered difference (trend) stationary if differencing (detrending) the data makes a variable stationary. A variable is considered integrated of order 1, or 1(1), if it requires first-differencing to achieve stationarity. Stationarity of an inequality measure is key to subsequent statistical analysis of its determinants because most regression analyses assume the underlying data, or linear combinations thereof, are stationary. Tests for stationarity of the data are performed in Borjas and Ramey (Chapter 7) and Hayes et al. (Chapter 10). In Chapter 7, Borjas and Ramey, employing MacKinnon's (1992) stationarity tests, find that their relative wage series (log of real weekly earnings for college graduates relative to the log of weekly earnings for high school graduates [or high school dropouts]) is stationary only after first-differencing. In Chapter 10, Hayes et al., using Phillips and Perron's (1988) stationarity tests, find that the Gini index of family income is stationary only after first-differencing. By contrast, in Chapter 8 Balke and Slottje find that the Gini index is stationary in level form. However, Balke and Slottje rely upon autocorrelation and partial

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autocorrelation functions solely to draw their conclusions, and do not employ recent stationarity tests as in the previous two chapters. With the exception of Balke and Slottje, the result that income inequality appears difference stationary suggests it contains a stochastic, rather than a deterministic, trend. This result is consistent with Pierce and Welch's inspection of inequality trends in Chapter 5. Whether other economies' levels of inequality have the same stochastic properties remains an issue for further research.

1.3

Issues in the Causes of I n c o m e Inequality

The literature on the causes of levels of and changes in income inequality is diverse. Chapters 6 through 10 focus on improving our understanding of the causes of income inequality and its changes over time. These potential causes may be categorized as: (i) micro (sectoral) labor demand, (ii) micro (demographic) labor supply, (iii) institutional, (iv) macroeconomic, and (v) international factors. In Chapter 6, Karoly and Klerman provide a fairly comprehensive analysis of these potential sources of earnings inequality changes. Their study has two parts. The first part uses a "shift-share" approach to determine the direct effects of sectoral and demographic shifts upon wage inequality. The second part uses regression analysis to determine the direct and indirect effects of all five factors mentioned above on the change in wage inequality. The shift-share analysis is based upon the notion that the variance of the logarithm of income can be decomposed into a "between-group" component (measuring inequality in mean incomes across population groups) and a "within-group" component (measuring inequality of incomes among individuals within population groups), where the latter is an employment-share weighted sum of inequality within each population group. In the shift-share analysis, Karoly and Klerman calculate the level of inequality that would have prevailed in 1988 had the percentage of people in each age group been held constant, first at the 1973 level and then at the 1979 level. The shift-share analysis is then conducted for industry groups. Karoly and Klerman find that for men the changes in the age structure served to dampen the rise in wage inequality. This result held using either the 1973 or 1979 weights and for almost all geographic

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regions. By contrast, equally dramatic shifts among women in the age composition of the work force had virtually no impact upon wage inequality. The authors find that the shift in employment of men out of manufacturing tended to exacerbate the rise in wage inequality. The change in this labor-demand factor increased inequality by 17 (13) percent using 1973 (1979) weights. For women, the changing structure of sectoral labor demand had virtually no effect upon the rise in this group's wage inequality. The second part of Karoly and Klerman's empirical evaluation is a regression analysis to determine the direct and indirect effects of changes in various factors on wage inequality. The pooled across state groupings and across years data sets allow testing for no fixed effects, year fixed effects, geographic fixed effects, or both fixed effects, separately for men and women. Sectoral labor demand effects are represented by. variables for shares of employment in durables and in nondurables. Demographic labor supply effects are represented by the share of 18-24 year olds. Institutional (wage-setting) effects are represented by the unionization rate. Macroeconomic effects are represented by state groups' unemployment rates. International effects are represented variously by the shares of GNP in merchandise exports, merchandise imports, durable goods exports, and durable goods imports. In their specification with the highest explanatory power, Karoly and Klerman find that interstate differences in business cycle activity, declines in unionization rates, and sectoral labor demand explain some of the interstate differences in wage inequality changes for men, although the estimated economic effects are usually small (with the exception of unionization). In contrast to men, these factors explain virtually none of the regional differences in wage inequality trends among women, similar to the shift-share analysis. When the international trade variables are included (and year fixed effects are necessarily excluded to avoid perfect collinearity), a higher share of imports of merchandise or durable goods in GNP generally increases wage inequality for men or women, and a higher share of exports generally decreases wage inequality for women. The influence of international competition on U.S. wage inequality is explored in detail, theoretically and empirically, by Borjas and Ramey in Chapter 7. In the first part of their study, Borjas and Ramey examine the intertemporal empirical relationship between annual trade deficits in services, in nondurable goods, and in durable goods (as percentages of GDP) and the "wage premia" for college graduates relative to high school

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graduates and college graduates relative to high school dropouts. Even though each wage premium, or relative wage, series is first-difference stationary, Borjas and Ramey argue that first-differenced data may not be appropriate in a regression analysis because first-differencing would obscure long-term persistent movements in relative wages. After determining that net imports of services and of durable goods (as percentages of GDP) are also first-difference stationary, they conduct cointegration tests to determine if relative wages and net imports share a common stochastic trend. Borjas and Ramey find that each wage premium series shares a stochastic trend with net imports of durable goods. In their extended empirical analysis of the intertemporal linkage of relative wages and trade, they find evidence that the import and export variables "Granger-cause" the wage premium, and find no evidence of the converse proposition. This linkage is not limited to the 1980s. In fact, the relationship can be predicted out of sample for the 1980s using pre-1980 historical data. The second part of their paper lays out a theoretical foundation for why increased international competition in durable goods especially may increase wage inequality. Durable goods industries are generally more concentrated than other industries, and workers in those industries tend to earn higher wages. In the model, the less-educated (high school graduate and dropout) workers in the concentrated durable goods sector share industry rents in the form of a wage premium (above the competitive wage in the competitive industry). When foreign firms enter the domestic durable goods market, the foreign firms capture a portion of the industry rents. This international competition raises the wage premium for college graduates relative to less-educated workers for two reasons. First, lower rents decrease the wage premium to the less-educated workers remaining in the concentrated industry. Second, since foreign competition reduces employment in the durable goods sector, workers move to the lower paying competitive sector, lowering the equilibrium wage for less-educated workers overall (relative to college-educated workers). In the third part of their study, Borjas and Ramey provide empirical support for their model. Selecting four target industries that are concentrated, unionized, and face international competition, they find that the college-high school graduate (dropout) wage premium is cointegrated over time with the share of aggregate employee compensation in these four industries. The smaller the share of aggregate employee compensation in these target industries, the larger is the college wage premium. Thus, as employment and wages in these concentrated, unionized, and traded durable

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goods industries has diminished, wage inequality has risen. Thus, Chapters 6 (Karoly and Klerman) and 7 (Borjas and Ramey) share significant empirical findings relating increased openness of the U.S. economy to higher income inequality. The results in both studies need to be viewed cautiously, however. For example, both studies find strong empirical evidence that increased imports as a percentage of GDP significantly increases inequality. Karoly and Klerman find that higher merchandise (goods) imports or durable goods imports significantly increase wage inequality. Their study correlates the level of the variance of the logarithm of hourly wages with the level of imports (as a share of GDP). Since Borjas and Ramey show that these two series are likely stationary only in first differences, the t-statistics in Karoly and Klerman's regressions may be unreliable. Yet Borjas and Ramey's results tend to confirm those of Karoly and Klerman. Borjas and Ramey uncover a "Granger-causal" relationship between higher durable imports and the college wage premium. Both studies also find a negative correlation between exports and wage inequality. Thus, increased "openness" need not cause greater inequality. Karoly and Klerman uncover significant relationships between exports and inequality for women, but not for men. Borjas and Ramey find a significant negative relationship between the college wage premium and exports. Both studies also find an asymmetry between the relationships of imports and inequality and of exports and inequality. A one percent increase in imports (as a share of GDP) raises inequality considerably more than a one percent increase in exports lowers inequality. By these estimates, balanced increased openness — that is, equal increases in exports and imports — will raise inequality. In addition to international trade being correlated with wage inequality in Chapter 6, Karoly and Klerman find that the unemployment rate has a positive, statistically significant, and economically significant effect on wage inequality. This result is robust across model specifications, with or without fixed year and fixed geographic effects. In Chapter 8, Balke and Slottje explore in more detail the relationship between income inequality and various indicators of macroeconomic performance and policy. The indicators of macroeconomic performance include the unemployment and inflation rates. The indicators of macroeconomic policy include the money stock (Ml), (real federal) defense expenditures, and (real federal, state, and local) transfer payments. Like Borjas and Ramey, Balke and Slottje are concerned with evaluating time series that are stationary. Unlike Borjas and Ramey, they examine autocorrelations and partial 1

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autocorrelations to determine variables' stationarity. Based upon these autocorrelations, their analysis uses first differences of logarithms of defense expenditures, transfers, M l , and the GNP deflator and levels of unemployment rates and Gini indexes. However, for robustness they also summarize their findings when all six variables are in levels and in first differences. Chapter 8's macroeconometric modeling of U.S. income inequality changes essentially has four parts. In the first part, Balke and Slottje conduct an atheoretical vector autoregression (VAR) analysis of the relationships among the six variables, using current and two lagged values of each variable. They find that current levels of income inequality are explained by past growth rates of transfers and past inflation rates, in addition to past levels of inequality. In contrast, lagged unemployment does not explain income inequality. Additionally, past levels of inequality only explain current growth rates of transfers and do not explain changes in other variables. In the second part, Balke and Slottje use the VAR results to conduct Choleski decompositions of the forecast error variance of income inequality to determine the portion of this variance due to "innovations" in the six variables. Variance decompositions of income inequality reveal the average amount of the (forecast) variance of income inequality from the VARs attributable to each of the (orthogonalized) "innovations." Aside from own innovations in inequality, Balke and Slottje find that innovations in the unemployment rate appear to be the most important factor explaining (forecast) variability in inequality. Only transfer payments ever explain a larger percentage than unemployment, and then only when transfers precede unemployment in the orthogonalization. Innovations in income inequality, however, do not appear to have much feedback on the other variables. Since the Gini index and unemployment rates are in levels while other variables are in first-difference logarithms, Balke and Slottje evaluate the robustness of their findings. The qualitative nature of their results is upheld whether all variables are in level or first-difference form. Because of some criticisms of atheoretical VARs, in the third part of Chapter 8 Balke and Slottje estimate a structural VAR and then conduct a variance decomposition of income inequality using forecasts from this VAR. The model's structure identifies contemporaneous relationships among the six variables. While defense expenditures and money growth are assumed exogenous, transfers payments are assumed to be countercyclical to economic activity. Conventional aggregate supply and 2

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demand functions are specified with aggregate demand a function of real transfers, real defense spending, and money, as well as prices. Income inequality is a function of all the other variables. The coefficient estimates of the structural VAR confirm that transfers are countercyclical and aggregate demand and aggregate supply have the expected relationships with prices. However, transfers and money have counterintuitive estimated coefficients in the aggregate demand equation. In the inequality equation, only unemployment has a significant (positive) effect on the Gini index. To determine both the direct and indirect effects of these variables on inequality, a variance decomposition of forecasts from the structural VAR model was conducted. Aside from own innovations to income inequality, aggregate supply and demand shocks explain about 40 percent of the forecast error variance of inequality. Money, defense expenditures, and transfer payments growth combined explain less than 15 percent of the variance. In the fourth part, Balke and Slottje conduct historical decompositions of income inequality. Inequality is decomposed during the period 1981-1990 into a forecast based on the estimated model (either theoretical or structural VAR) and actual values of variables through 1980, and the accumulated effects of current and past innovations of the variables. Using actual data through 1980, the model tends to underpredict the increase of income inequality during the 1980s. However, by 1990 there is little unexpected inequality. Thus, although shocks contributed to higher inequality in the 1980s, the level would have risen even in their absence. As was the case for the variance decompositions of the VAR forecasts, innovations in unemployment explain much of the unexpected increase in inequality using the atheoretical VARs. Using the structural VAR, innovations to aggregate demand and supply explain much of the unexpected increase in inequality. Balke and Slottje note that, although innovations in unemployment do not help to explain the trend in income inequality, these innovations do explain the unexpected increases in inequality in the 1980s. Using different methodologies, Chapters 6 and 8 both conclude that unemployment and income inequality are highly correlated. However, these results should be viewed cautiously. Even in Karoly and Klerman's regression with highest explanatory power (including year and geographic fixed effects), higher unemployment is statistically significantly positively correlated with higher inequality, but the "magnitude of the effect is not large." In Balke and Slottje's study, unemployment innovations explain

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unexpected inequality changes in the 1980s, but do not explain the trend rise in inequality. These results suggest, as Balke and Slottje note, macroeconomic performance may have more to do with the "timing" of inequality increases than with their trend. This result suggests further research is necessary to distinguish between "short-run" and "long-run" sources of rising inequality. In Chapters 9 and 10, the focus shifts to long-run macroeconomic factors — bequests, technological change, capital accumulation, and productivity growth — and their relationships with income inequality. In Chapter 9, Kami and Zilcha present an intertemporal model of technological change with human capital and noncapital bequests to consider the impacts of such change on w/ratemporal distributions of income. The authors consider an overlapping generations economy where parents choose between bequeathing offspring with human capital (through investment in education) or nonhuman capital. In the model, parents are informed of their offspring's (random) native abilities prior to the education investment decision. The parents' investment in the offspring's education in conjunction with the offspring's random native ability determines the offspring's human capital stock. The dependence of human capital upon random native abilities introduces heterogeneity in the model, which — coupled with inequality in intergenerational transfers — results in intragenerational income dispersion. In this paper, technological change affects the intragenerational distribution of income through its effects on factor prices directly (via productivity) and indirectly (through its effect on factor accumulations). Hicks-neutral technological change (biased neither toward labor nor capital) has no theoretical impact upon the intragenerational income distribution because such change does not affect factor prices, and the only factors affecting the evolution of inequality in their model are those affecting relative factor prices. Native abilities, while altering the intragenerational distribution, have no effect with respect to the evolution of the dispersion over time. By contrast, Harrod-neutral (or labor-biased) and Solow-neutral (or capital-biased) technological change will affect the intragenerational income distribution, unless the elasticity of substitution in production between labor and capital is unity. Harrod-neutral technological change will augment the effective labor supply and the productivity of labor, reducing the relative price of labor — and increasing (decreasing) income inequality — if the elasticity of substitution in production is greater (less) than unity. On the

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other hand, Solow-neutral technological change will augment the effective capital stock, reducing the relative price of capital — and decreasing (increasing) income inequality — if the elasticity of substitution in production is greater (less) than unity. Induced factor-price changes interact with random abilities to alter the income distribution. Since the preference structure causes investment in education to be proportionate to that in capital, the intragenerational income distribution effects persist over time. Kami and Zilcha's model in Chapter 9 identifies a potential "longrun" source of the rise in income inequality in the United States and other countries. In their model, the presence of either Harrod-neutral or Solowneutral technological change will alter relative factor prices, influencing the accumulations of physical and human capital relative to labor. But the study leaves for empirical researchers the issue of whether productivity growth — which arises generally from growth in physical and human capital per worker — tends to raise or lower income inequality. In Chapter 10, Hayes et al. address empirically the relationship between income inequality and productivity growth. The authors are interested in more than just the effect of productivity growth on income inequality. They also examine potential "feedback" effects from income inequality growth to productivity growth. If income inequality growth "causes" a decline in productivity growth, the usual "equity-efficiency tradeoff would be called into question in policy discussions. In the first part of Chapter 10, Hayes et al. discuss the time-series properties of the variables. Since estimation of bivariate systems sometimes can suggest feedback owing to the neglect of some important variables, the authors consider also a multivariate model that includes several macroeconomic variables. All tests employ two alternative definitions of productivity, output per worker-hour and real GNP per employee. Using tests from Phillips and Perron (1988), Hayes et al. conclude that time series for both indexes of productivity, the Gini index, the marginal tax rate, transfer payments per person, and the unemployment rate are all stationary in growth rates, i.e., first-difference logarithms. Hayes et al. next examine the bivariate relationship between income inequality growth and productivity growth. Using either productivity measure, their results suggest that higher productivity growth "Grangercauses" lower income inequality growth. There is weaker evidence that higher income inequality growth "Granger-causes" lower productivity growth.

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In the third part of their study, Hayes et al. examine the multivariate causality model, including all five variables mentioned above. They find strong support for including the other three measures. The growth rates of taxes, per capita transfers, and the unemployment rate each significantly affect productivity growth. The multivariate model estimates confirm the strong negative effect of productivity growth on growth in the Gini coefficient. Moreover, the results in the multivariate model for the effects of inequality growth on productivity growth are less ambiguous than in the bivariate model. Higher income inequality growth leads to lower productivity growth. The last part of Chapter 10 summarizes the results of estimating a VAR of the five growth rate variables to investigate the responses of changes in the growth rate of income inequality to changes in the growth rate of productivity, and vice versa. Impulse response functions are used to analyze the estimated dynamic relationships among the variables. Impulse response functions measure the response of endogenous variables in a system to "innovations" with a Choleski decomposition used to generate orthogonal errors. This decomposition eliminates common movements from error terms. The ordering of equations, however, necessarily affects the impulse response functions estimated. Irrespective of the ordering, an innovation in income inequality growth usually leads to a short-run (no more than two-year) increase in productivity growth, but a decrease in later years. For innovations in productivity growth, the results are even stronger. Innovations in productivity growth lead to decreases in income inequality growth beginning in the second year. The empirical findings summarized in this section suggest that sectoral, or industry, shifts in labor demand (away from manufacturing), declining influence over wage-setting institutions by unions, higher unemployment rates, lower productivity growth, and growing international trade competition especially in durable goods all appear to have contributed to rising wage, earnings, and/or income inequality in the 1970s and 1980s. Although each study carefully examines alternative potential explanations of income inequality and its changes, the studies collectively suggest several potential causes of inequality and areas for further research.

1.4

Policy Implications and R e c o m m e n d a t i o n s The last section of this volume includes four shorter papers by

Income Inequality in an Open U.S. Economy

23

Barry Bluestone, Kenneth Arrow, Orley Ashenfelter, and Robert Haveman, each based upon a speech presented at the conference. These papers reflect upon issues addressed in the preceding papers, raise topics often ignored in the distribution of income literature, and suggest some alternative policy prescriptions. In Chapter 11, Bluestone re-examines the importance of "factor price equalization," a theorem based on the Heckscher-Ohlin model of international trade. The Heckscher-Ohlin framework typically is presented as a two-country, two-good, two-factor model. The two countries are assumed to share identical, homothetic tastes for the two substitutable goods and identical, constant-returns-to-scale technologies with some factor substitutability. Perfect competition prevails in each market with zero transport costs and no artificial barriers to international trade in goods, although factors are internationally immobile. In this framework, each country will (incompletely) specialize in production and export the good using intensively in production the factor that the country has in relative abundance. Bluestone notes that, even a quarter of a century ago, countries differed considerably in tastes and production functions, transport costs and tariffs were nontrivial, and numerous important markets were monopolistic or oligopolistic. However, in the last quarter century the world has moved substantially closer to the Heckscher-Ohlin framework. An important implication of the Heckscher-Ohlin model is that international trade's shifting of each country's production toward the good that uses intensively the factor in relative abundance will increase (decrease) the demand for and price of the relatively abundant (scarce) factor. For the United States, greater international trade will tend to increase the wage rate of skilled labor and decrease the wage rate of unskilled labor (creating greater wage inequality and higher college wage premia), consistent with empirical results presented in Chapters 6 (Karoly and Klerman) and 7 (Borjas and Ramey). Bluestone discusses three policy alternatives. The "first-best" solution to this seemingly "natural" trend toward greater wage inequality in the United States is to equalize labor inputs through improved education and training. This solution lacks empirical support, however. For instance, between 1963 and 1987 the variance in years of schooling declined while the variance of earnings rose. The "second-best" solution is more vigorous use of traditional tax and transfer policies to redistribute income. However, Bluestone argues that even the Clinton Administration's income tax initiatives to shift a greater share of the tax burden toward the highest

24

J. H. Bergstrand, T. F. Cosimano, J. W. Houck, and R. G. Sheehan

income earners will be insufficient to offset the trend toward increasing inequality introduced by international trade and changing labor demands. Bluestone's "third-best" solution is direct intervention in product and labor markets to redress inequality in the pre-tax-and-transfer distribution. Of course, he notes, among most economists the first-best and second-best solutions are clearly superior to any policy aimed at increasing market intervention. In Chapter 12, Kenneth Arrow addresses some of the implications and deficiencies of general competitive equilibrium theory for understanding levels of and changes in the distributions of earnings and income. In the first part, Arrow addresses the implications of general competitive equilibrium theory for the distribution of income. The theory suggests that people are paid what they are worth, i.e., their marginal product. Consequently, wages are equalized up to workers' "net advantages," in the words of Adam Smith. However, the theory is simultaneously weak and implausible, according to Arrow. The theory is weak because of an absence of any independent measures of abilities or net advantages. These factors tend to be inferred from the wage distribution. The theory is implausible since an intuitive assessment of abilities suggests that its variance is narrower than the variance of earnings (which Haveman and Buron corroborate empirically). Arrow next considers some deficiencies of general competitive equilibrium theory for explaining observed earnings and income inequality. He notes that prior papers indicate that income inequality increases during recessions. Real fluctuations in effective demand should imply proportionate layoffs of skilled and unskilled workers. That unskilled workers bear a disproportionate share of layoffs during recessions suggests that the transactions costs in hiring and firing the two types of workers differ. Yet transactions costs are usually ignored in general equilibrium theory. In the third part, Arrow notes that the literature on the causes of income inequality generally has ignored the role of dynamic choices and processes. For example, even in the structural VARs in Chapter 8 (Balke and Slottje), the structure is imposed only upon contemporaneous relationships. He discusses some alternative ways of considering the distribution of income as the outcome of a dynamic sequence. In Chapter 13, Orley Ashenfelter argues that there is convincing evidence that the United States as a nation has underinvested in education. First, Ashenfelter argues that there is virtually no evidence that the

Income Inequality in an Open U.S. Economy

25

economic return to schooling has been overestimated by attributing erroneously to education increased earning power caused, in fact, by ability. Based on a series of studies, Ashenfelter contends that: (1) when the incomes of two sons who have equally well-educated fathers are compared, the son who is better educated has a higher income; (2) when the incomes of two brothers (from the same family) are compared, the better educated brother tends to have a higher income; (3) when the incomes of genetically identical twins are compared, the better educated twin has a higher income. Ashenfelter then suggests that the United States has underinvested in education. He argues considerable empirical evidence indicates that the economic return to schooling has been underestimated. The additional economic return for each extra year of schooling may be as high as 16 percent. If the return to schooling is so high, why are school completion rates so low? First, individuals may not know that the economic return to schooling is so high. Second, this is an average return, and an individual may choose to avoid concentrating investment spending in education since that strategy works against the notion of "diversification" of investments. These results lead Ashenfelter to suggest an income-contingent loan program for raising investment in education. He discusses the creation of a quasi-governmental agency to package loans and sell them in the private market, much like housing mortgages. In Chapter 14, Robert Haveman summarizes some of the important results contributed in the conference, discusses some avenues for future research, and offers some policy recommendations. Haveman suggests that the role of international trade and competition forms "a most worthwhile avenue for further research." His sense of the findings regarding international trade's importance is that it explains at most 30 percent of the rise in inequality, but that the verdict is still out. He also suggests that the potential role of ill-measured changes in the underlying distributions of skills, motivations, and abilities in affecting earnings distributions needs further attention. While some papers have examined the impact of transfer payments on the trend in inequality, more work needs to be done investigating the processes by which such programs have altered inequality and the economic disincentives these programs create. Additionally, while most papers have examined indexes of inequality, or distributions of earnings, little attention has been paid to changes in the "tails" of the distributions (with the exception of Chapter 5). Along policy lines, Haveman suggests first that the nation's statistical agencies should consider procedures for measuring permanent

26

J. H. Bergstrand, T. F. Cosimano, J. W. Houck, and R. G. Sheehan

household income, due to the seemingly low signal-to-noise ratio from annual income measures. Since Haveman believes changes in inequality are influenced heavily by movements in the tails of the distributions, he argues that additional resources should be devoted toward measuring the "economic well-being" of individuals in these tails. To address the lowskill, low-wage earners that apparently have suffered the most in the past two decades, he recommends policy measures that might influence both the supply of and demand for these workers: a wage-rate subsidy to increase low-wage labor supply and a targeted employment-tax credit for employers to encourage low-wage labor demand.

1.5

Conclusions

In the concluding paper, Chapter 15, we attempt to put the volume's papers in perspective in terms of their contribution to the income inequality literature. We conclude this chapter by discussing very briefly four issues raised by the papers in this volume. First, U.S. income inequality increased substantially during the 1980s, and arguably even before the 1980s. This result holds regardless of measure: wages, earnings, income, earnings capacity, or capacity utilization. This result is not peculiar to the United States, nor even localized within the United States. Yet there is considerable variation among demographic, geographic, and industrial "groups" regarding the degree of the change. Second, increasing import competition in international trade — notably in durables — may explain some of the trend increase in inequality in the past two decades. Traditional theories of trade predict that international goods exchange will tend to raise the average level of a nation's per capita income, but also tend to redistribute its income. Policies to compensate for such redistribution need to be explored further. Moreover, the income inequality correlated with the industrial reorganization associated with internationalization needs to be more carefully isolated from that associated with (secular) economic growth. Third, the level of income inequality and the "business cycle" are related empirically. However, the reasons behind such a correlation remain vague. Moreover, it remains unclear whether the business cycle affects the trend of income inequality, the timing of income inequality, or both. Fourth, income inequality and productivity growth appear to be negatively related. Moreover, the direction of causality appears to run

Income Inequality in an Open U.S. Economy

27

"both ways." Further theoretical and empirical work needs to examine these simultaneous influences.

Endnotes 1. Standard t-statistics have been shown to be unreliable in cointegrating regressions. Karoly and Klerman note that the correlation between the import and wage inequality variables may simply indicate a common trend. They are "less confident that this result indicates a true causal relationship." 2. For a recent straightforward discussion of these techniques, see Keating (1992).

References Baily, Martin Neil, Gary Burtless, and Robert E. Litan (1993). Growth with Equity. Washington, D.C.: The Brookings Institution. Beach, CM., and R. Davidson (1983). Distribution-free Statistical Inference with Lorenz Curves and Income Shares. Review of Economic Studies, 50, 723735. Burtless, Gary, ed. (1990). A Future of Lousy Jobs? Washington, D.C.: The Brookings Institution. Harrison, Bennett, and Barry Bluestone (1988). The Great U-Turn. New York: Basic Books. Keating, John W. (1992). Structural Approaches to Vector Autoregressions. Federal Reserve Bank of St. Louis Review, 74, no. 5, 37-57. Levy, Frank, and Richard J. Murnane (1992). U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations. Journal of Economic Literature, 30, 1333-1381. MacKinnon, James G. (1992). Critical Values for Cointegration Tests. In Robert Engle and Clive W.J. Granger (eds.), Long-Run Economic Relationships: Readings in Cointegration. Oxford, England: Oxford University Press. Phillips, P.C.B., and P. Perron (1988). Testing for a Unit Root in Time Series Regression. Biometrica, 75, 335-346.

The Changing Distribution of Income in an Open U.S. Economy J.H. Bergstrand et al. (Editors) 1994 Elsevier Science B.V.

Chapter 2 LEVELS OF AND CHANGES IN THE DISTRIBUTION OF U.S. INCOME Charles Τ Nelson U.S. Bureau of the Census

ABSTRACT This chapter provides an overview of recent Census Bureau research on income distribution issues. The study addresses three topics in particular. First, the alleged inadequacy of traditional measures of income trends have given rise to "relative" income measures and to adjustments of income trends for the effects of taxes and noncash benefits, which are explored here. Second, since earnings are a dominant component of incomes, trends in distribution of earnings are explored with a particular focus on characteristics and trends of "low-earnings" U.S. workers and on emerging trends in the distribution of earnings in four other industrialized countries. The third part of this paper examines the contribution of certain social, demographic and economic factors for explaining changes in the level of median U.S. household income, in the degree of U.S. income inequality, and in Black-White income ratios.

2.1

Introduction

Much of the recent literature on the distribution of income has focused on two trends. First, in the short run, the United States is experiencing for the first time in almost a decade declining real incomes and increasing poverty rates. Second, in the longer run, the slowdown in the growth of family and of household incomes and the growing inequality of the income distribution has been persistent.

*None of the views expressed in this paper necessarily represent those of the Bureau of the Census or the U.S. Department of Commerce.

30

C.T. Nelson

Table 2.1

Income Summary Measures* Year-round full-time workers

Year

Median family income

Gini ratio

Median house­ hold income

1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975 1974 1973 1972 1971 1970 1969

$35,353 36,062 35,565 35,632 35,129 33,689 33,251 32,378 32,037 32,476 33,386 34,595 34,156 33,107 32,913 31,905 32,491 33,370 32,722 31,189 31,226 31,292

0.396 0.401 0.395 0.393 0.392 0.389 0.383 0.382 0.380 0.369 0.365 0.365 0.363 0.363 0.358 0.357 0.355 0.356 0.359 0.355 0.353 0.349

$29,943 30,468 30,079 29,984 29,690 28,688 28,197 27,581 27,577 27,669 28,125 29,074 29,168 28,067 27,913 27,442 28,197 29,108 28,545 27,377 27,640 27,828

Gini ratio 0.428 0.431 0.427 0.426 0.425 0.419 0.415 0.414 0.412 0.406 0.403 0.404 0.402 0.402 0.398 0.397 0.395 0.397 0.401 0.396 0.394 0.391

Male/ female Male Female ratio of median median median earnings earnings earnings $27,678 $19,822 28,912 19,793 29,450 19,451 29,852 19,457 30,118 19,357 29,389 18,978 29,207 18,592 28,713 18,260 28,816 17,792 29,389 17,409 29,558 17,782 30,050 17,929 30,458 18,104 30,247 17,822 29,606 17,821 29,670 17,451 29,940 17,553 17,542 30,975 30,032 17,377 28,502 16,961 28,374 16,845 28,047 16,510

0.716 0.685 0.660 0.652 0.643 0.646 0.637 0.636 0.617 0.592 0.602 0.597 0.594 0.589 0.602 0.588 0.586 0.566 0.579 0.595 0.594 0.589

Traditional income measures have shown that, since the early 1970s, there has been little overall growth in real incomes. Real median family income more than doubled between 1947 and 1973, for an average annual growth rate of 2.8 percent. In contrast, over the 17-year period from 1973 to 1990, real family income grew 5.9 percent, or 0.3 percent per year (see Table 2.1). Household income, which differs from family

31

The Distribution of U.S. Income Table 2.1 (continued) Year-round full-time workers

Year

Median family income

1968 1967 1966 1965 1964 1963 1962 1961 1960 1959 1958 1957 1956 1955 1954 1953 1952 1951 1950 1949 1948 1947

$29,926 28,563 27,967 26,587 25,477 24,527 23,733 23,064 22,812 22,405 21,174 21,281 21,106 19,843 18,652 19,118 17,654 17,130 16,557 15,679 15,899 16,370

Gini ratio

Median house­ hold income

Gini ratio

0.348 0.348 0.349 0.356 0.361 0.362 0.362 0.374 0.364 0.361 0.354 0.351 0.358 0.363 0.371 0.359 0.368 0.363 0.379 0.378 0.371 0.376

$26,844 25,719 (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA)

0.388 0.399 (NA) NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA)

Male/ female Male Female ratio of median median median earnings earnings earnings $26,570 $15,452 25,859 14,942 14,652 25,457 24,413 14,629 14,230 24,057 23,471 13,835 22,928 13,596 13,331 22,501 21,789 13,220 (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA)

0.582 0.578 0.576 0.599 0.591 0.589 0.593 0.592 0.607 (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA) (NA)

"Median incomes are in 1990 dollars using the CPI-U-XI (1967 to 1990) and the CPI-U (1947-1966). NA denotes not available.

income in that its universe includes persons living alone and those living with nonrelatives, showed an even slower rate of overall income growth between 1973 and 1990; over this period, real median household income grew 2.9 percent, or 0.2 percent per year.

32

C.T. Nelson

Real median earnings of foil-time, year-round (FTYR) men declined significantly between 1973 and 1990. After rising 42.2 percent from 1960 to 1973, male FTYR median earnings fell 10.6 percent in real terms from 1973 to 1990. In fact, 1968 was the last year in which the real median earnings of FTYR men was lower than the 1990 median ($27,678). In contrast, the median earnings of FTYR women increased between 1973 and 1990. The real median earnings of FTYR women in 1990 was 13.0 percent higher than in 1973. The female-male earnings ratio for FTYR workers, which was the same in 1980 as it was in 1960 (0.60) rose fairly steadily throughout the 1980s to its 1990 level of 0.72. As the earnings of women have risen substantially in comparison to those of men, women are composing an increasing proportion of all FTYR workers. In 1960, women accounted for 24.3 percent of the FTYR work force. The corresponding percentages in 1970, 1980, and 1990 were 30.0 percent, 35.3 percent, and 39.2 percent, respectively. Significant increases in income and earnings inequality have also occurred over the last two decades. One commonly-used method of measuring the extent of inequality in the income distribution is the Gini index of income concentration. This index ranges from 0 (indicating perfect equality) to 1 (indicating perfect inequality). Over the 20-year period from 1970 to 1990, the household Gini index rose from 0.394 to 0.428, an increase of 8.6 percent. Most of this increase took place between 1980 and 1990, as the overall change in the Gini index between 1970 and 1980 was only 2.3 percent (from 0.394 to 0.403). Most of the change in income inequality in the 1980s was concentrated in the 1980-86 period; over this period the Gini index for households rose from 0.403 to 0.425 (a gain of 5.5 percent). The Gini index in 1990 was not statistically different from the 1986 index. White, Black, and Hispanic-origin households have all experienced increases in their respective Gini indexes over the last two decades. For Whites, the Gini index increased from 0.387 in 1970 to 0.419 in 1990 (8.3 percent); for Blacks, the increase was from 0.422 to 0.464 (10.0 percent). Hispanic-origin data was not available prior to 1972; the Gini index for these households rose from 0.373 in 1972 to 0.425 in 1990 (13.9 percent). As will be discussed later in this paper, there is certainly a relationship between the rise in the proportion of single-parent families and the rise in overall income inequality. However, it is also true that, within household types, income inequality has grown over time. For example, the Gini index for married-couple households rose from 0.331 to 0.368 (11.2

33

The Distribution of U.S. Income

percent) between 1969 and 1989. For single-parent households, the rise was from 0.410 to 0.448 (9.3 percent) over this period. Another frequently-used inequality measure is the share of aggregate income received by each quintile of the population. The proportion of aggregate income received by the highest quintile of households grew over the 1970-1990 period from 43.3 to 46.6 percent, while the share of the aggregate going to the middle 60 percent of households declined from 52.7 to 49.5 percent. Those in the lowest quintile did not experience a statistically significant change in their share of the aggregate between 1970 and 1990 (see Figure 2.1). None of the quintiles experienced real declines in mean incomes over the 1970-1990 period, as shown in Table 2.2. Rates of growth in the lowest four quintiles ranged from 6 percent (in the second quintile) to 16 percent (in the fourth quintile). The reason for the change in shares over time is the large increase in the mean income of those in the highest

• • •

1970 1980 1990

it 20% Lowest

Figure 2.1

Middle 60%

Highest 20%

Shares of Aggregate Household Income, by Quintile: 1980, and 1990

1970,

34

C.T. Nelson

Table 2.2

Year 1990 1985 1980 1975 1970

Mean Income of Households in Each Quintile and Top 5 Percent: 1970-1990 (in 1990 CPI-U-X1 adjusted dollars) Lowest Quintile

Second Quintile

Third Quintile

Fourth Quintile

Fifth Quintile

Top 5 Percent

$7,195 6,819 6,845 6,765 6,304

$18,030 17,281 17,035 16,619 17,079

$29,781 28,685 28,111 27,266 27,494

$44,901 43,148 41,414 39,619 38,757

$87,137 80,598 73,842 69,950 68,622

$138,756 124,328 110,347 106,151 105,329

quintile. Between 1970 and 1990, the mean income (in 1990 dollars) of households in the highest quintile rose 27 percent, from $68,622 to $87,137; for those in the top 5 percent, the increase was 32 percent. Since earnings account for about 80 percent of all money income, changes in the distribution of wages represent an obvious starting point in examining growing inequality in the income distribution. In fact, the growing inequality of the earnings distribution has been a well-documented trend. Ryscavage and Henle (1990) found that, while earnings became more dispersed during both the 1970s and the 1980s, this trend accelerated and became more widespread in the 1980s. Between 1978 and 1988, the Gini index for the earnings of FTYR men rose from 0.296 to 0.337. For women, the rise was from 0.240 to 0.296. Increasing Gini indexes were also evident among Whites (both men and women), Blacks (men only), and Hispanic-origin FTYR workers (both men and women). Grubb and Wilson (1992) found increasing wage and salary inequality over the 1967-1988 period, "with two spurts of increasing inequality (1967-72 and 1980-86), and a period of relative stability (with some cyclical variation) during most of the 1970's" (p. 33). They also detected a decline in inequality after 1986. These trends indicate some fundamental changes in the income distribution, changes that have been the subject of a significant amount of recent research. The purpose of this paper is to summarize recent Census Bureau research efforts dealing with income distribution issues. This research may be roughly divided into three major areas: 1

2

The Distribution of U.S. Income

35

(1) Methodological Issues Researchers have raised legitimate questions about the adequacy of "traditional" measures of income trends and income inequality. A recent report on relative income answers some of those concerns and in doing so provides an improved picture of the changing distribution of income and of differences in economic well-being between subgroups of the population. The money-income concept itself is an area of controversy. Research on the effect of taxes and noncash benefits on the distribution of income have resulted in reports that provide a far more complete picture of overall economic well-being than one based simply on the traditional pre-tax, prenoncash-benefit definition that has been the source of most income statistics since the 1940s. (2) The Distribution of Earnings The growth in earnings inequality is commonly cited as a major contributor to the changing distribution of income, since earnings is by far the single largest component of household income. Two recent studies have examined U.S. earnings trends from quite different perspectives. One looked at the growth of low-earnings workers, which were basically defined as FTYR workers with earnings below the poverty threshold of a fourperson family. The other study compared wage inequality levels and trends in the United States with those in four other industrialized countries. (3) Social, Demographic, and Economic Factors Related to the Changing Distribution of Income Researchers have pointed to such trends as the growth in singleparent families, the changing age structure of households, and the growth in the proportion of working wives as contributing factors to shifts in the income distribution. Two recent studies examined the effects of these and other factors on income and inequality trends and on Black-White income differences. The main goals of this paper are to provide brief descriptions of the issues associated with these new studies, summarize their major findings, and provide a notion of how these reports fit into Census Bureau research plans. This paper will also attempt to predict, from the Census Bureau's standpoint, the emerging income research issues of the 1990s.

36

C.T. Nelson

2.2

Methodological Issues

2.2.7

Relative Income No single income measure provides a perfect picture of economic well-being. Researchers have raised legitimate concerns about the adequacy of traditional household-based income and inequality measures to accurately examine income trends and differences in economic well-being between subgroups of the population. A basic problem with most household-based income measures is that they fail to account for the fact that household size has changed over time (and very often differs between subgroups of the population). To compare incomes while ignoring the effect of the size of the income unit can lead to misleading results. For example, average household size declined from 1973 to 1990 from 2.97 to 2.63 persons, while real median household income grew by a total of 2.9 percent. One could certainly argue that this rate of change of household income understates the true change in economic well-being over this time, since the lower average household size in 1990 implies a lower level of household needs and thus a higher level of economic well-being even if there was no real change in income. The same argument holds true for subgroup comparisons of income. The elderly-nonelderly household income ratio in 1990 was 0.50. One could certainly argue that this ratio significantly overstates the true difference between these groups in economic well-being, since average household size differs so much between the two household types. McNeil (1991) uses a relative income measure to make income differences more comparable over time and across different subgroups of the population. The steps associated with calculating relative income are: 3

(1) (2)

Each person was assigned the income of his or her family. Those incomes were then adjusted for differences in family size, using an equivalence scale. The median equivalence-adjusted income was calculated for all persons. A relative income value was assigned to each person which represents the ratio of his or her equivalence-adjusted income to the median level of equivalence-adjusted income. 4

(3) (4)

Thus, the relative income measure shows the extent to which the income of a group of persons diverges from the median income of all

The Distribution of U.S. Income

37

persons. Relative incomes are used to examine inequality issues through the characterization of persons into three groups: (1) (2) (3)

Low relative income denotes persons whose equivalence-adjusted incomes are less than one-half of the overall median; High relative income denotes those whose equivalence-adjusted incomes are more than twice that of all persons; Middle relative income denotes everyone else (those between onehalf and double the overall median).

Results were tabulated at five-year intervals over the period from 1964 to 1989. The major, but not surprising, finding of the report was that over the period from 1969 to 1989 there was an increase in overall income inequality, as the proportion of persons with either low or high relative incomes increased from 29 to 37 percent (see Figure 2.2). The proportion 5

I

1964

Figure 2.2

1969

1974

1979

1984

Low

0

Middle

•

High

1989

Percent of Persons with Low, Middle, and High Relative Income: 1964-1989

38

C.T. Nelson

with low relative incomes rose from 18 to 22 percent, while the proportion with high relative incomes rose from 11 to 15 percent. During the period from 1964 to 1969, there was a decline in inequality, as the proportion of persons with low or high relative incomes dropped from 31 to 29 percent. Whites, Blacks and those of Hispanic origin all experienced increases in inequality over the last two decades (see Table 2.3). Among Whites, the proportion with high or low relative incomes grew from 27 to 35 percent from 1969 to 1989. The proportion with high incomes grew from 12 to 16 percent, while the proportion with low incomes grew from 15 to 19 percent. For Blacks, the proportion with low relative incomes grew slightly from 1969 to 1989 (from 43 to 44 percent), after a substantial decline from 1964 to 1969 (from 49 to 43 percent). The percentage of Blacks with high relative incomes was also slightly higher in 1989 than in 1969 (3 percent in 1969 versus 5 percent in 1989). Data for those of Hispanic origin are not available for 1964 and 1969. However, data over the 1974-1989 period show increased percentages with high or low relative incomes. The proportion with high relative incomes grew slightly (from 4 to 5 percent), while the proportion with low relative incomes rose from 34 to 40 percent. The statistics presented in McNeil (1991) offer stark evidence of the increasing disadvantage of not obtaining a college education. Between 1964 and 1989, the median relative income of persons without a high school diploma declined steadily from 0.93 to 0.65 (see Figure 2.3). For those who had completed high school but had not completed at least one year of college, the median relative income dropped from 1.23 to 1.08. The median relative income of those who had completed one to three years of college also declined (from 1.43 to 1.29). The median relative income of persons with four or more years of college was 1.75 in 1989, not significantly different from the 1964 median. Thus, college graduates were the only educational attainment group to avoid a decline in relative economic status between 1964 and 1989. The study found a marked difference between the trends in economic status between the young (those under 18) and the elderly (those over 64); see Table 2.3. In 1969, 19 percent of young persons had low relative incomes; by 1989, that figure was 29 percent. For the elderly, the proportion with low relative incomes declined over this same period from 42 to 32 percent. The median relative income of the elderly grew from 0.59 in 1969 to 0.73 in 1989, while the median for children dropped from 0.91 to 0.84 (see Table 2.4).

The Distribution of U.S. Income Table 2.3

39

Percent of Persons With Low and High Relative Incomes: 19641989

Characteristics Race and Hispanic Origin White Black Hispanic Origin" Age Under 18 In MarriedCouple Family Not in MarriedCouple Family 18 - 64 65 and over

Characteristics Race and Hispanic Origin White Black Hispanic Origin Age Under 18 In MarriedCouple Family Not in MarriedCouple Family 18 - 64 65 and over

Low Relative Incomes 1974 1979 1984

1964

1969

15.5 48.5 (NA)

14.7 42.6 (NA)

15.5 43.3 34.1

16.7 44.1 34.2

18.6 41.1 38.4

18.8 43.9 40.1

21.2

19.4

22.3

24.5

28.7

29.1

16.3

13.0

13.8

14.9

18.2

17.6

60.0 14.5 39.4

63.4 12.9 42.0

62.6 13.9 35.6

60.3 15.1 36.2

62.0 17.5 29.3

63.0 17.3 31.5

1964

1969

High Relative Incomes 1974 1979 1984

1989

12.9 2.3 (NA)

11.9 3.1 (NA)

12.0 2.9 3.6

13.1 3.2 4.3

15.4 4.6 8.0

16.0 5.0 5.0

6.3

6.0

5.9

6.6

7.7

8.4

6.8

6.6

6.9

8.1

9.6

10.6

1.8 15.9 9.2

1.3 14.7 6.7

1.0 14.5 6.8

1.0 15.4 6.4

1.6 17.7 9.9

1.6 18.3 9.4

"Persons of Hispanic origin may be of any race. ΝA denotes not available.

1989

40

C.T. Nelson

1964

Π I

Figure 2.3

1969

1974

Completed college Completed high school, no college

1979

[Γ] |

1984

1989

Completed 1 to 3 years of college Did not finish high school

Median Relative Income of Persons 25-64 Years Old, by Years of School Completed

The declining relative economic status of children is, of course, a matter of great concern. Over the 1964-1989 period, the proportion of children living in families that did not include a married couple more than doubled (from 11 to 25 percent). Over that same period, a slight increase in the median relative income of children in married-couple families, from 0.95 to 1.00, occurred while the median declined slightly for those not living in married-couple families, from 0.41 to 0.35. Thus, one may view the declining economic status of children as the result of a combination of the worsening relative economic status of single-parent families and the increasing number of children living in single-parent situations. In 1989, 63 percent of the children under 18 not living in married-couple families had low relative incomes; for children under 6, the figure was 72 percent (see Table 2.5). Young children not living in a married-couple family had an extremely high probability of having low relative incomes, regardless of race or Hispanic origin. Sixty-six percent

41

The Distribution of U.S. Income Table 2.4

Median Relative Income by Race, Hispanic Origin, and Age: 1964-1989 (1.00 = all persons)

Characteristics Race and Hispanic Origin White Black Hispanic Origin" Age Under 18 In MarriedCouple Family Not in MarriedCouple Family 18 - 64 65 and over a

1964

1969

1974

1979

1984

1989

1.06 0.52 (NA)

1.05 0.58 (NA)

1.05 0.59 0.69

1.06 0.58 0.69

1.06 0.58 0.66

1.06 0.60 0.63

0.90

0.91

0.89

0.88

0.84

0.84

0.95

0.97

0.98

1.00

0.98

1.00

0.41 1.14 0.63

0.38 1.14 0.59

0.38 1.13 0.65

0.39 1.14 0.64

0.36 1.13 0.76

0.35 1.13 0.73

Persons of Hispanic Origin may be of any race. NA denotes not available.

of young White children living in single-parent families had low relative incomes in 1989; the comparable figures for Blacks and those of Hispanic origin were 80 percent and 79 percent, respectively. (The latter two percentages were not significantly different.) The relative income concept is intended to supplement our traditional income measures, and provides a better basis for comparing incomes across time and between groups (through the use of equivalence scales). Obviously, the use of equivalence scales and the sensitivity of results to other types of equivalence scales are prime areas for further research. The Census Bureau will also explore ways to incorporate our relative income findings into official annual income statistics series. 2.2.2

The Effect of Taxes and Noncash Benefits on the Distribution of Income The pre-tax, pre-noncash-transfer income concept has been used as the basis for income comparisons since the Census Bureau began collecting

42 Table 2.5

C.T. Nelson Percent of Children Under 6 Years Old with Low and High Relative Incomes, by Family Type, Race, and Hispanic Origin: 1964-1989

In Married-Couple Family: Total White Black Hispanic Origin Not in MarriedCouple Family: Total White Black Hispanic Origin

In Married-Couple Family: Total White Black Hispanic Origin Not in MarriedCouple Family: Total White Black Hispanic Origin

a

Low Relative Incomes 1974 1984 1979

1964

1969

18.4 13.7 50.0 (NA)

14.5 11.7 36.6 (NA)

15.8 14.1 30.4 33.9

17.6 16.0 29.9 34.5

21.7 20.2 35.0 41.3

20.7 19.1 35.6 45.1

68.0 58.0 82.0 (NA)

74.2 68.8 80.0 (NA)

72.9 68.6 79.1 83.9

71.7 64.5 81.0 80.9

71.2 66.0 79.4 81.6

71.6 65.5 80.3 79.4

1964

1969

High Relative Incomes 1984 1974 1979

1989

4.2 4.6 0.6 (NA)

0.8 1.5 (NA)

1989

3.9 4.2 1.3 (NA)

3.9 4.1 1.3 1.9

5.3 5.5 1.9 2.1

7.2 7.7 3.2 2.6

9.1 9.5 3.1 2.2

0.3 0.6 (NA)

0.5 0.7 0.2 0.3

0.4 0.6 0.1 -

0.9 1.6

1.0 1.2 0.8 0.5

-

0.5

^Persons of Hispanic origin may be of any race. NA denotes not available and "-" denotes less than 0 . 1 .

The Distribution of U.S. Income

43

family income statistics in the 1940s. The growth in the importance of noncash benefits to economic well-being and the growing interdependence of our tax and transfer systems has made the traditional money-income concept less relevant over time. In 1980, the Census Bureau began supplementing the annual Current Population Survey (CPS) income questionnaire with questions on the receipt of noncash benefits. After developing techniques for valuing these benefits, the Census Bureau in 1982 began publishing a series of reports on the effect of government noncash transfers on the poverty rate. That year, the Census Bureau also began a series of reports on the after-tax distribution of income. These tax estimates were the result of a tax simulation methodology developed at the Census Bureau in the early 1980s. In 1988, the Census Bureau started a new report series in which the noncash benefit valuation techniques first developed in the early 1980s were refined and expanded to include private sector noncash benefits (such as employer contributions to health insurance). In addition, this new report series showed the combined effect of taxes and noncash benefits on both income and poverty estimates. These reports are now scheduled for release annually on the same day as the Census Bureau's official income and poverty statistics. Table 2.6 shows the importance of taxes and benefits not included in the money-income definition to different types of households. The aggregate value of benefits measured by the Census Bureau in 1990 that were not included in the official money income definition was $527.3 billion, or about 13 percent of aggregate pre-tax, post-benefit income. Aggregate taxes totaled $730.8 billion (18 percent of pre-tax, post-benefit income). Thus, aggregate household income that had been fully adjusted for the effect of benefits and taxes was slightly lower than the money income aggregate. The redistributive power of taxes and benefits is apparent from a comparison of Gini indexes before and after their inclusion. The index based on a fully-adjusted income concept was 0.383, 10 percent lower than the Gini index based on the official money income definition (0.426). Our analysis has continually shown that government transfers (both cash and noncash) are significantly more important to income redistribution than taxes. Table 2.7 shows the individual effects in 1990 of government cash and noncash transfers, other noncash benefits, and taxes on the Gini index. Taxes lowered the Gini index by a total of 6 percent, from 0.490 to 0.463. Transfers lowered the Gini by 17 percent, from 0.463 to 0.384. The 6

7

C.T. Nelson

44 Table 2.6

Effect of Benefits and Taxes on Household Aggregate Incomes and Gini Indexes by Selected Characteristics: 1990

Income Components

0

All White Black Households Households Households

HispanicOrigin Households

Money Income $264.8 $174.0 $3527.5 $3150.6 (official definition) Additions and Subtractions from Money Income: 3.4 101.2 2.8 109.9 Capital Gains Employer-provided Health Insurance 134.9 118.5 11.8 7.8 Means-tested Noncash 12.4 5.4 23.2 37.2 Transfers Nonmeans-tested 2.6 68.0 5.3 24.5 Noncash Transfers 15.0 9.4 198.5 220.8 Return on Home Equity (22.9) (14.2) (416.2) (379.5) Federal Income Taxes (111.1) (7.6) (4.1) (123.7) State Income Taxes (170.4) (14.0) (10.8) (190.9) Payroll Taxes Additions and Subtractions as a Percent of Total Pre--tax, Post-transfer Incom 1.4 1.1 2.8 2.7 Capital Gains Employer-provided 3.3 3.2 3.8 3.8 Health Insurance Means-tested Noncash 4.0 2.7 0.6 0.9 Transfers Nonmeans-tested 1.9 1.7 1.3 1.8 Noncash Transfers 5.4 4.8 4.6 5.4 Return on Home Equity (10.1) (10.4) (7.3) (7.0) Federal Income Taxes (2.4) (2.0) (3.0) (3.0) State Income Taxes (4.5) (5.3) (4.7) (4.7) Payroll Taxes Gini Index: Money Income 0.42: 0.426 0.417 0.463 (official definition) Fully-Adjusted* 0.37' 0.383 0.375 0.399 Income Definition

The Distribution of U.S. Income

45

Table 2.6 (continued)

Income Components

Households with a Female Households with Married-Couple Householder, No One or More Households with Husband Present, Members 65+ Children with Children

$146.6 $1222.6 $593.8 Money Income (official definition) Additions and Subtactions from Money Income: 41.3 1.5 17.2 Capital Gains Employer-provided Health Insurance 8.5 57.5 6.6 Means-tested Noncash 4.5 14.9 6.4 Transfers Nonmeans-tested 1.3 10.0 67.6 Noncash Transfers 6.8 57.9 76.9 Return on Home Equity (142.4) (6.6) (50.9) Federal Income Taxes (45.7) (2.8) (14.0) State Income Taxes (7.6) (70.0) (13.4) Payroll Taxes Additions and Subtractions as a Percent of Total Pre-tax, Post-transfer Income: .8 3.0 2.2 Capital Gains Employer-provided Health Insurance 1.1 4.1 3.7 Means-tested Noncash 8.4 0.3 0.8 Transfers Nonmeans-testes 0.7 0.7 Noncash Transfers 8.8 3.8 4.2 10.0 Return on Home Equity (10.2) (3.7) (6.6) Federal Income Taxes (1.8) (3.3) (1.6) State Income Taxes (4.3) (1.7) (5.5) Payroll Taxes Gini Index: Money Income (official definition) 0.465 0.342 0.451 Fully-Adjusted Income Definition 0.397 0.317 0.370 Aggregate incomes are in billions of dollars. *Fully-adjusted income includes the effects of all taxes and benefits shown.

a

46 Table 2.7

C.T. Nelson Gini Index of Income Concentration, by Definition of Income: 1990

Definition of Income Gini Index Income before taxes: 1. Money income excluding capital gains (current measure) 0.426 2. Definition 1 less government cash transfers 0.480 3. Definition 2 plus capital gains 0.491 4. Definition 3 plus health insurance supplements to wage or salary income 0.490 Income after taxes: 5. Definition 4 less Social Security payroll taxes 0.492 6. Definition 5 less Federal income taxes (excluding the EITC) 0.471 7. Definition 6 plus the Earned Income Tax Credit (EITC) 0.469 8. Definition 7 less State income taxes 0.463 9. Definition 8 plus nonmeans-tested government cash transfers 0.412 10. Definition 9 plus the value of Medicare 0.402 11. Definition 10 plus the value of regular-price school lunches 0.402 12. Definition 11 plus means-tested government cash transfers 0.394 13. Definition 12 plus the value of Medicaid 0.392 14. Definition 13 plus the value of other mean-tested government noncash transfers 0.384 15. Definition 14 plus net imputed return on equity in own home 0.383

component with the single largest effect on the Gini was nonmeans-tested cash transfers (principally Social Security). In 1990, the inclusion of these benefits lowered the Gini index by 11 percent, from 0.463 to 0.412. The redistribution of income resulting from the inclusion of taxes and noncash benefits was not uniform by race. Although the fully-adjusted Gini index for Whites was 10 percent lower than the official index, for Blacks the difference was 14 percent, probably a reflection of the relatively greater importance of means-tested noncash benefits to Black households. These benefits composed 4.0 percent of the aggregate pre-tax, post-benefit income of Black households; the comparable figure for White households was 0.6 percent. A comparison of households with one or more members 65 years old or over shows that taxes and benefits are more important to the redistribution of income in these households than they are for households in general. The fully-adjusted Gini index for these households was 0.397, 15 percent lower than the official money income index of 0.465. In this

The Distribution of U.S. Income

47

case, the greater redistribution of income is probably a reflection of the importance of nonmeans-tested noncash transfers (principally Medicare) and net return on home equity. The importance of means-tested noncash benefits to income redistribution becomes particularly apparent in a comparison of households with a female householder with children (no husband present) to marriedcouple households with children. In 1990, means-tested noncash transfers accounted for 8.4 percent of the aggregate pre-tax, post-benefit income of family households with children maintained by women. The comparable percentage for married-couple households with children was 0.3 percent. The fully-adjusted Gini index for family households with children maintained by women was 0.370, 18 percent lower than the official Gini index for these households of 0.451. For married-couple households with children, the comparable difference in Gini indexes was only 7 percent (0.317 versus 0.342). One of the drawbacks of the current noncash report series is the lack of an adequate time series to examine income trends under alternative definitions of income. The Census Bureau released a report in 1992 showing the effect of taxes and noncash benefits on income and poverty estimates over the entire 1979-1991 period. This is as far into the past as this series allows since, prior to March 1980, there were no questions on the receipt of noncash benefits on the CPS. Future research at the Census Bureau will certainly be aimed toward further improvements and refinements to our tax simulation and noncash valuation techniques. The Census Bureau will also work toward transferring the CPS tax simulation and noncash valuation techniques to another Census Bureau income survey, the Survey of Income and Program Participation (SIPP). The SIPP has several advantages over the CPS as a source of tax and noncash benefit analysis, though the Census Bureau has thus far lacked the resources to create and maintain two tax and noncash benefit valuation models. These advantages include: 1) a shorter recall period, which improves the reporting of program participation; 2) a longitudinal survey design; and 3) questions that ask respondents directly about tax filing status and taxes paid. The Census Bureau hopes to exploit these advantages into the creation of a new tax and transfer model over the next few years.

48 2.3

CT Nelson The Distribution of Earnings

2.3.1

Workers with Low Earnings Much literature over the past decade has centered on the rise in earnings inequality and the growing number of workers in low-wage jobs. McNeil (1992) adds to that literature by bringing together CPS income data over the 1964-1990 period to provide information on the number and characteristics of workers with low earnings, and trends in the prevalence of low-earnings workers over time. Unlike poverty, there is no official definition of low earnings. Thus, the choice of a low-earnings threshold is by definition a subjective one. The threshold used in McNeil (1992) was the poverty threshold for a family of four with two children. This choice was guided in part by: (1) the notion that a desirable goal for a society might be one in which all FTYR workers have sufficient earnings to keep a four-person family above the poverty line; and (2) the fact that other studies, including another Census Bureau report, have used a similar definition. Shown below are the lowearnings thresholds over time. Most of the analysis in the report is based on FTYR workers, since the concept of low earnings has little meaning for those without a fairly strong attachment to the labor force. Perhaps the major finding of this study was the sharp rise in the proportion of FTYR workers with low earnings between 1979 and 1990 (see Table 2.8). The rate rose from 12 to 18 percent over this period. This is in contrast to the decline in the proportion of low-earnings workers during the 1964-1974 period; over this period the proportion of workers with low earnings dropped from 24 to 12 percent. The most striking characteristic about the increase in low-earnings workers over the 1979-1990 period is the fact that it was so universal. Increases were experienced by FTYR Whites (from 11 to 17 percent), Blacks (from 19 to 25 percent), and those of Hispanic origin (from 20 to 31 percent). There were also increases in the proportions of both male and female FTYR workers with low earnings (from 7 to 13 percent and from 20 to 24 percent, respectively). A particularly sharp increase occurred in the proportion of FTYR workers between the ages of 18 and 24 with low earnings over the 19791990 period (from 23 to 43 percent). Increases were also evident among workers 25 to 34 (from 9 to 18 percent), 35 to 54 (from 10 to 13 percent) and 55 to 64 (from 12 to 16 percent). 8

9

10

11

The Distribution of U.S. Income

49

Low-Earnings Thresholds: 1964-1990

Year 1964 1969 1974 1979 1984 1989 1990

Threshold for low annual earnings $3,144 3,676 4,843 6,905 9,694 11,570 12,195

Corresponding hourly rate for person working 40 hours a week for 50 weeks $1.57 1.84 2.42 3.45 4.85 5.79 6.10

Comparisons by years of school completed also show an upward shift over the 1979-1990 period in the proportion of FTYR workers with low earnings. In 1979, persons without a high school diploma had a lowearnings rate of 21 percent. In 1990, the rate was 36 percent. Over this period the low-earnings rate for persons with a high school diploma who had not completed at least one year of college rose from 13 to 22 percent; the rate for those with one or more years of college increased from 6 to 11 percent. However, the great majority of FTYR workers with low annual earnings are not in poverty. The poverty concept is based on total family income, not merely the earnings of a FTYR worker. In 1990, 13 percent of FTYR workers between the ages of 16 and 64 with low earnings were in poverty (see Table 2.9). That percentage is lower than the comparable 1979 rate (16 percent), and is about one-half of the 1964 poverty rate (27 percent). An area for further research would be to examine whether the decline in the poverty rate of FTYR low-earnings workers is the result of a growing number of workers in these families, the changing composition of the poverty population, or the effect of nonwage income. The poverty rate for all FTYR workers in 1990 was 3 percent. The poverty rate of workers with low earnings varied by family relationship. In 1990, the poverty rate of husbands with low earnings was 21 percent; for wives with low earnings, the poverty rate was only 6 percent. In contrast, for female family householders (no husband present) with low earnings, the poverty rate in 1990 was 28 percent.

C.T. Nelson

50 Table 2.8

Full-Time Year-Round Workers with Low Earnings, by Selected Characteristics: 1964-1990 1964

1969

1974

1979

1984

1989

1990

All workers

24.1

14.4

12.0

12.1

14.6

16.3

18.0

Sex: Men Women

14.7 42.4

7.6 25.3

6.9 21.8

7.2 19.8

9.9 20.7

11.5 22.5

13.0 23.6

Race and Hispanic Origin: White Black Hispanic Origin"

21.9 48.4

12.7 30.5

11.4 18.1

11.4 18.5

13.8 21.5

15.7 21.2

17.1 25.3

(NA)

(NA)

18.3

19.7

22.9

27.6

31.4

Years of Schooling: Less than 12 12 13 or more

(NA) (NA) (NA)

21.4 12.4 6.5

19.7 12.0 5.4

21.3 13.0 6.2

28.1 16.7 8.0

32.1 19.5 9.3

36.1 21.6 10.5

Age: 18-64 18-24 25-34 35-54 55-64 65 and over

23.1 39.6 17.7 20.8 27.8 47.9

13.5 25.6 9.8 11.5 16.4 39.0

11.4 22.3 8.2 9.8 12.8 33.6

11.6 22.9 8.8 9.9 12.0 28.9

14.2 33.4 11.9 11.4 13.6 32.1

16.0 39.2 15.8 12.0 14.5 26.6

17.8 43.4 18.4 13.2 16.4 28.8

°Persons of Hispanic origin may be of any race. NA denotes not available.

While this study represents a large step forward for the Census Bureau as a method of measuring an important economic trend, it provides only one view of the changing U.S. earnings distribution. Future Census Bureau research will explore ways to incorporate these and other findings into a broader overview of the entire earnings distribution, how it has changed over the past two decades, and, perhaps more importantly, the reasons for these changes. The effect of nonwage compensation, which is

The Distribution of U.S. Income Table 2.9

51

Poverty Rates of Full-Time Year-Round Workers with LowEarnings, by Relationship: 1964-1990 1964

1969

1974

1979

1984

1989

1990

All Workers

26.9

18.6

15.6

15.8

17.6

12.7

12.9

Husbands Wives Female family householder, no husband present Male unrelated individual Female unrelated individual

44.0 7.9

37.9 4.8

36.3 4.7

38.7 4.3

34.3 7.0

22.3 5.5

21.4 5.5

33.8

28.4

25.5

26.7

30.2

28.5

27.8

44.8

36.2

30.3

30.8

27.3

15.1

17.4

38.3

28.1

14.4

17.0

17.3

15.1

14.1

certainly growing over time, should also be incorporated into future studies on the changing distribution of earnings. 2.3.2

International Comparisons of Earnings Inequality The literature on growing earnings inequality in the United States is quite extensive. The question of whether this trend is unique to the United States has received much less attention. In order to gain a more complete understanding of the nature and causes of earnings inequality in the United States, it is important to examine how the recent experience of a changing U.S. earnings distribution differs from that of other industrialized countries. A problem with most international income or earnings comparisons is a lack of comparability across countries. The Luxembourg Income Study (LIS), a collection of microdata from various countries, was designed to minimize these comparability problems. The LIS data was used in Green, Coder and Ryscavage (1992) for international income comparisons. In this study, the countries selected for comparison with the United States were Canada, Australia, Sweden, and West Germany. The universe for this study consisted of male householders between the ages of 25 and 54 who worked FTYR and received no social insurance or private pensions. The study had two parts: (1) it examined differences

C.T. Nelson

52

in earnings inequality between workers in the five countries in the mid 1980s, and (2) it examined differences in earnings inequality for these workers between the early and mid 1980s. Measures of several different inequality measures indicated that the U.S. distribution of earnings exhibited the highest level of inequality in the mid 1980s. Canada was the country with the second most unequal earnings distribution. Of the other three countries, Australia's earnings distribution exhibited the highest level of inequality, followed by West Germany's, and then Sweden's. The most important finding of the study was that all of the countries exhibited, to some extent, increases in earnings inequality between the early and mid 1980s. Both the United States and Canada exhibited strong increases in earnings inequality over this period. Earnings in Sweden also showed a significant increase in inequality, though not as large as the two North American countries. Earnings in West Germany and Australia also exhibited more inequality, though the evidence was not as strong in these countries as in the other three. These findings, which indicate that the United States was not alone among developed countries in experiencing increasing earnings inequality in the 1980s, suggest that it may be wise for researchers who wish to explore the reasons for rising U.S. inequality to broaden their perspectives and examine the structural changes taking place in the labor markets of other developed countries as well. The study suggests that increasing dispersion of earnings may be related to more general phenomena (such as the effect of changing technologies or the transmission of business cycles) that occur across countries, rather than circumstances that may be unique to the United States. 12

13

2.4

Social, D e m o g r a p h i c , and E c o n o m i c Factors Related to the C h a n g i n g Distribution of I n c o m e

The change in the distribution of income and the slowdown of income growth in the United States discussed at the outset is the product of many factors. Two recent papers produced by Census Bureau analysts attempted to examine the relationship between changing income distributions and the social, demographic, and economic changes that took place in the 1970s and 1980s. Ryscavage, Green and Welniak (1992) use a standardization methodology to quantify the impact of several

The Distribution of U.S. Income

53

demographic, social and economic factors on income distribution measures. Green, Ryscavage and Welniak (1992) use the same methodology to examine Black-White income differences. Ryscavage, Green and Welniak (1992) examined seven specific demographic, social, and economic factors for their possible effects on income measures. Two demographic factors were considered: the changing age structure of the population and changes in distribution of the population by race. Two social factors were included: changes in living arrangements and educational attainment levels. The three economic factors included in the analysis were work experience of householders, work experience of wives in married-couple families, and the industries in which workers are employed. A standardization technique was employed in this study to attempt to answer the question: What would happen to 1989 income and inequality measures if households had the same set of demographic, social, and economic characteristics that existed in 1969 and 1979? Essentially, the March 1990 CPS file was reweighted to reflect the social, demographic, and economic characteristics of the March 1980 and March 1970 CPS files. After reweighting the files, it was possible to derive a variety of income measures, thus allowing an examination of the possible effect of these factors on the changing distribution of income over time. Table 2.10 shows the results of the standardization procedures on median household income over the 1969-1989 period. Changes in the age distribution of the population had a relatively minor negative effect (-$264) on median household income. The more rapid growth in the Black population relative to the White population also had a small negative impact on median household income. The standardization indicated that, without this difference, the median income would have been $194 higher than the actual median in 1989. Changes in household type and educational attainment of householders are associated with dramatic changes in household income over the 1969-1989 period. Controlling for changes in the distribution of households by type (the declining proportion of married-couple families and rising proportions of single-parent families and nonfamily households) indicates that median household income in 1989 would have been $3,226 higher had these changes not occurred.

Standardized $29,146 29,170 29,100 32,132 25,896 30,469 30,124 30,669

Actual

$28,906 28,906 28,906 28,906 28,906

28,906

28,906

28,906

All Age Race Household Type Education Work Experience of Householder Work Experience of Wife Industry of Householder

1989 Median Income

-1763

-1218

-1563

$-240 -264 -194 -3226 3010

Difference

.429

.429

.429

.429 .429 .429 .429 .429

Actual

.415

.420

.419

.410 .432 .427 .411 .430

Standardized

1989 Gini Index

Effect of Standardization on Median Incomes and Gini Indexes: 1969-1989

Variables

Table 2.10

.014

.009

.010

.019 -.003 .002 .018 -.001

Difference C.T. Nelson

The Distribution of U.S. Income

55

This large negative change was offset by the positive impact that increases in educational attainment had on median household income over this 20-year period. The median income in 1989 would have been $3,010 less had these educational attainments not occurred. Standardizing for differences in householders' work experience (based on the percentage of householders working and, if working, the percentage that worked full-time year-round) shows that these changes had a negative effect on median household income of $1,563. This reflects the fact that the percentage of working householders has declined slightly over time and that their composition has shifted. The net effect of differences in the level of work attachment among wives in married-couple households also had a net negative effect on median household income. It is difficult to measure the effect of this change alone, since, at the same time, dramatic shifts were taking place in the composition of households. The decline in the proportion of households that were married couples over this period served to offset the effect of working wives on overall median household income. While the effect of working wives had a large positive impact on the income of married-couple households, the effect on total household income, when coupled with the large compositional shifts that were taking place at the same time, resulted in a net negative impact. As one might expect, the decline of the proportion of jobs in goods-producing industries (and the corresponding increase in serviceproducing jobs) resulted in a net decline in household income. The percentage of all nonagricultural payroll jobs in service-producing industries rose from 65 to 77 percent from 1969 to 1989. According to the standardization results, this shift resulted in a net decline of $1,763 in median household income. Overall, the combined effect of the social, demographic, and economic changes covered in this study was to slow the growth of median household income by $240. The increase in median household income over the period of 1969 to 1989 was 9.4 percent based on official income figures; the standardized rate of growth over the same period was 10.3 percent. Table 2.10 also shows the effect of standardization on the Gini index of income concentration. Using the change in the Gini index, the effect of these trends on income inequality is observed. Changes in age, race and educational attainment level over time had a minimal impact on income inequality. Changes in the composition of households, on the other

56

C.T. Nelson

hand, appear to have had a significant impact. The Gini index after standardization for changes in household composition was 0.411, compared with the official index of 0.429. Each of the economic variables had the effect of increasing income inequality over time. The Gini index (officially 0.429) would have been 0.419 had there been no change in the work experience of householders, 0.420 had there been no change in the work experience of wives, and 0.415 had there been no shift between goods- and service-producing industry jobs. The net effect on the Gini index of all of these changes was significantly more profound than their effect on median household income. The standardization results indicate that, had these changes not occurred, the Gini index would have increased only half as much as the official statistics show. The standardization also allowed an examination of the possible effect of social, economic, and demographic changes over the 1979-1989 period. The major finding of this standardization was that the impact of these factors was significantly different over this period (see Table 2.11). Over the 1969-1989 period, social, economic, and demographic changes tended to restrain income growth and promote inequality. In contrast, these changes over the 1979-1989 period tended to promote income growth, while they had a very minor effect on the Gini index. The major implication of this finding was that the "negative" impact of social, economic, and demographic changes over the 1969-1989 period (lower incomes, a higher Gini index) was mainly a product of changes that occurred in the 1970s rather than in the 1980s. In 1967, the Black-White household income ratio was 0.58. In 1990, 23 years later, this ratio was only slightly higher (0.62). In an effort to better understand the relationship between the large and sustained differences in income between Whites and Blacks and the social, demographic, and economic changes that have taken place over the last two decades, Green, Ryscavage and Welniak (1992) used the same standardization techniques just outlined to examine Black-White income differences over time. As Table 2.12 shows, shifts in the demographic, social, and economic characteristics between 1969 and 1989 appear to have had a much larger impact on Black household income. A standardized median income of White households in 1989 would have been virtually the same as the actual median ($30,384 versus $30,413), while a standardized Black

57

The Distribution of U.S. Income

m

(Ν

1

^

1

ο ο ο ο ο ο ο ο

ο ο

ο ο ο

(Ν

ο ο

ο ο

Effect of Standardization on Median Incomes and Gini Indexes:

1979-1989

Τ3

χ

-α

OO O Os CN (N • Os »n (N

© ^ o^ o ^ oo" ON" oo" o" t-" λ

00^

r

(Ν (Ν (N m (N

ON

00 ON

5


0. t

t

t

t

K K

L L

9.2.2

Equilibrium In each period the economy features three markets: two factor markets (labor and capital), and one commodity market. To define a competitive equilibrium, we begin by considering the state of the economy at the outset of period t. Each family ω G Ω consists of two members, the "old" member belonging to G and the "young" member belonging to G . Suppose that the distribution of the bequests received by individuals of generation G is given by the function b \il —> [0, m], where m < °o. The human capital distribution in G is h (co), where the initial b.^co) and h (co) are given. Clearly, both functions b^co) and h (co) depend upon the history up to date t. Let the bequest transfer, b^co), the stock of human capital, h (co), the effective wage rate, w , the interest rate, r , the wage rate, w , and interest rate, r , at date t + 1, and the realization θ (ω) of θ (ω) be given. An individual ω G G chooses the levels of savings, s (co), bequest transfer, b (co), and investment in his offspring's education, e (co), so as to maximize t l

t

t

iA

t

t

0

t

t

t

t

t+1

t+1

ι+1

ι+1

t

t

t

t

c (œ) ic (œ) 2[(b (œ)(l + a

lt

a

2t

t

subject to constraints

r

)] 3[(h a

t + 1

t + 1

(œ)w

] 4 a

t + 1

(9.2)

284

Technological Progress and Income Inequality

c (co) = (1+ r^b^Cco) + w h (co) - s (co) - b (co) - e (co) > 0

(9.3)

c (co) = (1+ r )s (œ).

(9.4)

h (co) = e (co)0 (co)

(9.5)

lt

t

2t

t+1

t+1

t

t

t

t

t

t

t+1

Definition 1. Given the capital stock at the outset of period 0 ( K q ) and [bjico), h (co)] for all ω e G , a competitive equilibrium is a sequence of functions {c (co), c (co), s (co), b (co), e (co)}~ and a sequence of prices {w , r } ~ such that for t = 0, 1, 2, ... : 0

0

lt

t

t

2t

t

t

t

0

0

(a)

for all ω e G , [c (co), c (co), s (co), b (co), e (co)] is the solution to maximization problem (9.2)-(9.5);

(b)

U (co^(co) = θ ^ ω Μ μ ί ω ) = L = Fj^K,, w );

(c)

K

(d)

K

t

lt

2t

t

t

t =

t+1

t

t

t

f

=

(L>

k

t

t>

r

Jjs(co) t

t

+ b (œ)]dji(œ). t

where F£* and F * denote the inverse functions corresponding to F and F . K

L

K

Condition (a) asserts that the various demand functions in the economy are derived from optimal consumer behavior assuming that all consumers are price takers. Conditions (b) and (c) are the equilibrium conditions in the labor and capital markets, respectively. The specification of the demand functions is based on the assumption that firms are price takers in the factor markets. In (b), we used the fact that 9 (co) is independent of t and ω. Condition (d) describes the dynamic adjustment of the aggregate nonhuman capital stock in the economy assuming full depreciation of the capital stock in each period. Note that the aggregate capital stock is determined by aggregate saving and nonhuman capital transfers, while the aggregate labor supply depends only on the intergenerational transfers of human capital in the form of education. These conditions, in conjunction with constraints (9.3) and (9.4), imply the material balance condition: t

Jk(œ) + c _ (co) + e (cû)]d^co) + 2(t

1}

t

K

T + 1

= F(K ,L ) T

T

for t=0,l,...

(9.6)

Ε. Kami and I. Zilcha

285

Next consider the first-order (necessary and sufficient) conditions for the optimization problems (9.2)-(9.5):

(9.7)

(9.8)

(9.9)

From (9.7) and (9.9), we also obtain that (9.10)

Given the realization of θ(ω), the lifetime income of ω G G , y (co), is t

t

y (co) = (1+ r ^ i œ ) + w ^ ^ c o ) ] t

(1 + ^ ( c o )

(9.11)

Using equation (9.9), the aggregate stock of human capital in period t is given by: (9.12)

where B = ί ^ό _ (ω)άμ(ω) is the aggregate transfer of nonhuman capital to generation t. Similarly, using equation (9.10), the aggregate of physical capital stock in period t is: t Λ

{

ί

ι

286

Technological Progress and Income Inequality ί

\

(9.13)

K. =

9.3

Income-Distribution Effects of Technological Innovations

9.3.1

The Measurement of Income Inequality A formal analysis of the distributional effects of technological changes requires a formal measure of income inequality. To define such a measure we introduce the following notation. Let X and W be two random variables with values in a bounded interval in R, and let vc^ and denote their respective means. Define & = X/m and W = W / n v Denote by F and F the cumulative distribution functions of & and \V, respectively. Let [a, b] be the smallest interval containing the supports of and \V. x

x

w

t

Definition 2. F is more equal than F J [F (s)-F (s)]ds < 0. x

w

if, for all t G [a, b],

t

a

x

w

This definition, due to Atkinson (1970), is equivalent to the requirement that the Lorenz curve corresponding to X is everywhere above that of W. Thus, if F is more equal than F , according to Definition 2, then it has a lower Gini index. We say that X is more equal than W if the c.d.f. of & and W satisfy: F is more equal than F . Henceforth the relation X is more equal than W is denoted X > W. We say that X is equivalent to W, and denote this relation by X « W, if X > W and W > X . The following result concerning the relation > between two random variables will be needed in the sequel. x

w

x

w

Lemma 1. Let X and Y be random variables taking values in compact intervals in R. Let Ζ be a positive random variable with compact support and suppose that Ζ is independent of X and Y, then: (i) X - Y (ii) X > Y

implies XZ - YZ, implies XZ > YZ.

Proof. See Appendix A for the proof.

Ε. Kami and I. Zilcha

287

9.3.2

Technological Improvements To examine the effects of improved technology on income inequality, we conduct the following comparative dynamics analysis. We take the distribution of incomes at the point at which the technological innovation is introduced as given. We also assume that the new technology is unanticipated. We consider three kinds of exogenous changes in period t = 0 representing permanent shifts in the production technology. These shifts are represented parametrically by pairs ( γ , γ ), t > 0, and are defined by F(y K , y L ), where F(-,) is the production function. A Hicks-neutral technological improvement is characterized by γ = y = y , y = 1 for t < 0, and y = γ > 1 for t > 0. A Harrod-neutral technological improvement is characterized by y = 1 for all t, y = 1 for t < 0 and y = γ > 1 for t > 0. A Solow-neutral technological improvement is characterized by y = 1 for all t, y = 1 for t < 0 and y = γ > 1 for t > 0. η

lt

t

2t

2ι

t

η

t

2t

t

t

lt

2t

2t

2t

lt

lt

9.3.3

Income-Distribution Effects of Hicks-Neutral Technological Changes Let Q = FiyKjjLt), γ > 1. Then the competitive equilibrium t

implies (9.14) Consider the effects of a Hicks-neutral technological improvement on the equilibrium intragenerational income distribution. Henceforth, we denote by superscript prime the value of the respective variable following the introduction of the technological improvement under consideration. Proposition 1. Given the above economy, a Hicks-neutral technological improvement will have no effect on the inequality in income distribution in equilibrium during the period it occurs and in every period thereafter, ie> y't Yt t = 0, 1, 2,... . β

f o r

Proof. See Appendix Β for the proof. The only factors that affect the evolution of the income inequality in the economy are factors that affect the factor-price ratio. Hicks-neutral technological improvements do not affect the factor-price ratio. In the

288

Technological Progress and Income Inequality

context of the present model, this means that native abilities, while affecting the intragenerational dispersion of incomes, are neutral in so far as the evolution of this dispersion over time is concerned. The situation is quite different in the case of Harrod-neutral and Solow-neutral technological improvements. 9.3.4

Income-Distribution Effects of Harrod-Neutral and Solow-Neutral Technological Improvements The following Lemma will be used to obtain the main result of this subsection.

Lemma 2. Let Ζ be a random random variable defined on the probability space (S, S , ν) with Ζ = | Ζ(ζ)άν(ζ) < «>. For each λ s [0, «>), define the random variable W(-; λ) by 8

W(C; λ) = [1 + λΖ(ζ)]/[1 + λΖ] Then λ > λ implies \¥(·; ί ) > W(-; λ). Proof. See Appendix C for the proof. Let σ denote the elasticity of substitution, i.e., let r = F / F . Then L

K

= Constant For more details see Allen (1938). Proposition 2. (a) A Harrod-neutral technological improvement results in a decrease (no change, increase) in income inequality during the period it occurs and in every period thereafter if the elasticity of substitution is smaller than (equal to, larger than) one, i. e., y{ > y if σ < 1, y[ ~ y if σ = 1, and y > y[ if σ > 1 for t = 0, 1, 2,... . (b) A Solow-neutral technological improvement results in a decrease (no change, increase) in income inequality during the period it occurs and in every period thereafter, if the elasticity of substitution is larger than (equal to, smaller than) one, i. e., y[ > y if σ > 1, y^ ~ y if σ = 1, and y > y[ if σ < 1 for t = 0, 1, 2,... . t

t

t

t

t

t

Ε. Kami and L Zilcha

289

Proof. See Appendix D for the proof. In view of the conclusions of Hicks-neutral technological progress, the conclusions of Proposition 2 are readily understandable. Harrod-neutral technological improvements increase the aggregate effective labor supply and the marginal productivity of labor. These changes increase or decrease the price of labor relative to that of capital depending on whether the elasticity of substitution in production is smaller or larger than one. Similarly, Solow-neutral technological improvements increase the effective capital stock at the same time that they increase the marginal productivity of capital. These changes increase or decrease the price of labor relative to that of capital depending on whether the elasticity of substitution is larger or smaller than one. Given the elasticity of substitution, the effects of Harrod-neutral and Solow-neutral technological changes on the factor-price ratio are opposite to one another. The induced changes in the factor-price ratio interact with the random native abilities to decrease or increase the intragenerational dispersion of incomes the period in which they occur. Since the structure of preferences is such that the investment in education is proportional to that in physical capital, the effects of the new technologies persist in every period thereafter.

9.4 C o n c l u d i n g R e m a r k s This paper examines the effect of technological changes on the distribution of incomes in the context of a competitive overlapping generations economy with human capital. The specification of the economy involved assumptions which were introduced for expository convenience and entail no essential loss of generality. For instance, although the model contains a random individual's native ability which implies a nondegenerate income distribution in each period and in the steady state, each individual's decision making is under certainty. This is due to the assumption that each parent is informed of his offspring's native abilities prior to making his decisions regarding investment in the offspring's education. This assumption is for expository convenience and entails no essential loss of generality. In fact, one may think of a model in which the parent faces uncertainty regarding the offspring's talents and abilities. The decision regarding how to split the bequest between education and nonhuman capital

290

Technological Progress and Income Inequality

becomes a portfolio decision in which the expected rates of return must be weighted against the corresponding risks. In general, risk-averse parents will choose a diversified portfolio, dividing their bequest between investment in their offsprings' education and in nonhuman capital. This effect is captured in our model by assuming that the offspring's human capital and nonhuman capital are imperfect substitutes and enter the parent's (concave) utility function as two distinct arguments. Another implicit assumption is that technological changes are unanticipated. Our analysis indicates that if a new technology becomes anticipated, it will affect income inequality through its effect on the factor-price ratio prior to its actual implementation. In the present model, since the investment in education is proportional to the level of saving and production displays constant returns to scale, an anticipated technological change will have no effect on the factor-price ratio and therefore on the distribution of incomes prior to its implementation. However, in a more general setup, anticipated technological changes may affect the aggregate stock of capital and the aggregate supply of labor prior to the implementation of the change. In this case, the nature of the change in the income inequality depends on the nature of the anticipated technological improvement.

References Allen, R. G. D. (1938). Mathematical Analysis for Economists. New York: St. Martin's Press. Atkinson, A. (1970). On The Measurement of Inequality. Journal of Economic Theory, 2, 244-63. Azariadis, C , and A. Drazen (1990). Threshold Externalities in Economic Development. Quarterly Journal of Economics, 105,501-26. Bishop, J.Α., J.P. Formby, and P.D. Thistle (1992). Explaining Interstate Variation in Increase Inequality. Review of Economics and Statistics, 74, 553-557. Diamond, P. (1965). National Debt in a Neoclassical Growth Model. Economic Review, 55, 1126-50.

American

Ε. Karni and L Zilcha

291

Eckstein, Ζ., and Zilcha I. (1991). The Effects of Compulsory Schooling on Growth, Income Distribution, and Welfare. Journal of Public Economics, forthcoming. Karni, E., and Zilcha, I. (1992). Technological Progress and Income Inequality. Manuscript. Loury, G. (1981). Intergenerational Transfers and Econometrica, 49, 843-67.

Distribution of Earnings.

Lucas, R. E. Jr. (1988). On the Mechanics of Economic Development. Journal of Monetary Economics 21, 3-42. Persson, T., and G. Tabellini (1991). Manuscript.

Is Inequality Harmful to Growth?

292

Technological Progress and Income Inequality

Appendix A Proof of Lemma 1 It is sufficient to show one part of Lemma 1. We shall prove part (ii). Let F (0), F (9), and G(9) denote the cumulative distribution functions of X, Y, and Z, respectively. Let [a, b] be the support of F and F and [α, β] the support of Ζ ( a > 0). Define x

y

x

y

Since θ > 0, we get Η(ξ) = J£F (cy0)dG(9). Similarly, let Η(ξ) = j£F (èye)dG(e), the cumulative distribution function of YZ. Let [a', b'] be the support of Η(ξ) and Η(ξ). Then x

y

For any fixed θ G [α, β], performing a change of variables, we get

But, by definition 2, X > Y implies /a[F (s) - F (s)]ds < 0 for all a < τ < b. Since θ > α > 0, this implies / ^ ( ξ / θ ) - ¥ (ξ/θ)]άξ < 0. Hence, T(t) < 0 for all t G [a', b']. Thus, by definition 2, XZ > YZ. • x

y

γ

Ε. Karni and L Zilcha

293

Appendix Β Proof of Proposition 1 Let Q = F(yK ,yL ), γ > 1. In this case, using equations (9.12) and (9.13): t

t

t

Thus X does not depend on γ or on B . Let t

t l

(9.15)

In view of Lemma 1, we need to show that b ^ i œ J / B ^ « \ {(υ)ίΒ for all t. Since b^co) is given, this is true for t = 0. By Lemma 1 b[ ((ù)IB[_ « b ^ c o y B ^ implies that y (co) - y^(co). We proceed by induction. Assume that y (co) « yi(co). By equation (9.3) and the optimality conditions (9.7)-(9.9), for all ω: χ

A

x

ιΛ

0

t

(9.16

y (co) = c (co) + s (co) + b (œ) + e (co) t

lt

t

t

t

Hence, y (co) - y[(co) implies b^(œ) « b (co). Lemma 1 and equation (9.11) imply that ; (o>) - y (co). • t

t

y

+1

t+1

294

Technological Progress and Income Inequality Appendix C Proof of Lemma 2 Differentiating \ ν ( ζ ; λ) with respect to λ, we get:

W,(C; λ) = Hence, sgn \ ¥ ( ζ ; λ) = sgn[Z(Q - Ζ]. Thus, for λ > ί for every ζ if Ζ(ζ) < Ζ then \ ν ( ζ ; ί) > \¥(ζ; λ) and if Ζ(ζ) > Ζ then Λ¥(ζ; λ) < \ ¥ ( ζ ; λ). Let w ( , λ)(δ) =/ c|w(C;X) 1 F ..^(s) > F . (s). Hence F ^ is more equal than λ

F

{

W(;X)

W(

F

W ( - ; λ)·

w(

; X)

W(

w ( ;

D

Appendix D Proof of Proposition 2

(a)

Let Χ / ( γ ) =

Hence,

/dCKZ/yL/)

1- d - V

/[d(K /yL V(K /YL )]| /

/

t

l

/

t

/

t

;X )

Ε. Karni and L Zilcha

295

Hence, by the definition of σ:

(9.17)

= 0 σ = 1.


1. We proceed by induction. Consider the case σ < 1 and assume that, for some t, y{ > y . By equation (9.16), bj(cD) > b (co). Using Lemmas 1 and 2 and equation (9.18), we obtain: 0

0

0

t

t

296

Technological Progress and Income Inequality

Λ

b>)

b (co) t

K m

Β.

Β.

(

Thus, by definition, y' > y , which completes the induction step. Similar arguments apply to the cases σ = 1 and σ > 1. t+1

l+1

(b) Consider a Solow-neutral technological improvement. Then

F (YK/,L/) L

χ/(γ) =

YF^YK/A')'

Using the same procedure as in part (a), it is readily verifiable that




= 0 σ = 1. >


σ = 1.


X implying y > yj. Similarly, σ = 1 implies y ~ yj, and σ > 1 implies > y. We proceed by induction. Consider the case σ < 1 and assume that for some t, y > y' By equation (9.16), this implies b (co) > bj(œ). As in part (a), we use this fact together with Lemmas 1 and 2 and equation (9.20) to derive that Y (co) > Y[ , thus y > y[ . The cases σ = 1 and σ > 1 are proved similarly. • 0

0

0

0

t

v

t+1

t

+1

t+1

+x

The Changing Distribution of Income in an Open U.S. Economy J.H. Bergstrand et al. (Editors) © 1994 Elsevier Science B.V. All rights reserved.

Chapter 10 PRODUCTIVITY AND INCOME INEQUALITY GROWTH RATES IN THE UNITED STATES Kathy J. Hayes Southern Methodist University Michael Nieswiadomy University of North Texas

Daniel J. Slottje Southern Methodist University Michael Redfearn University of North Texas

Edward Ν. Wolff* New York University

ABSTRACT This paper examines the relationship between the size distribution of income and productivity. We are particularly interested in whether or not exogeneity tests indicate that the inequality and productivity relationship runs both ways. Bivariate and multivariate causality tests and impulse response functions from a vector autoregression are calculated. There is considerable evidence that productivity growth rates and inequality growth rates are inversely related. The main lesson from this study is that policies designed to affect productivity growth or income inequality should be considered simultaneously.

10.1

Introduction

Much has been written about the slowdown in the growth rate in productivity in the United States since the 1970s. The 1992 Economic Report of the President states, "The major long-run challenge confronting

*We thank John Formby, Frank Levy, Kevin Murphy, Robert Haveman, and Kenneth Arrow for comments. The usual caveat holds.

300

K.J. Hayes et al.

the American economy is to increase the Nation's rate of productivity growth — that is, growth in output per worker" (Council of Economic Advisors, 1992, p. 29). Having become accustomed to a quarter century of rapid productivity growth following World War II, the collapse in productivity growth between 1973 and 1981 shocked many Americans. Productivity growth has partially improved since 1981, but mainly in the manufacturing sector. If the United States is to have the highest standard of living in the world, its citizens cannot become apathetic about the fundamental relationships between economic growth and productivity. As noted in Hayes et al. (1993), there are many alleged causes for the decline in the U.S. productivity growth rate. The Council of Economic Advisors (1992) and Denison (1985) attribute the slowdown to pollution and worker-safety regulations (some of which may be useful), inexperienced youth and women entering the work force, dishonesty and crime, and problems with American business management. The Council of Economic Advisors (1992) and Bishop (1989) accuse public school education. The United States spends more per pupil than any other country except Switzerland. Yet we continually rank below other countries on standardized tests. Boskin (1988) blames the present tax system for discouraging saving. Fischer (1988) and Wolff (1985) note a number of possible reasons for the productivity growth rate slowdown: a decline in the level of human capital, a reduction in investment and saving rates, increased employment in the service sector, and the increasing size of the government sector (Olson, 1988). Dertouzos et al. (1989) argue that there are at least six reasons for slow productivity growth: outdated strategies, short time horizons, technological weaknesses in development and production, neglect of human resources, failures in cooperation, and government and industry working at cross purposes. The above factors are certainly culpable parties in this sluggishness. It is surprising, however, that no study has analyzed the role that income inequality has played in explaining the slowdown in productivity growth, even though rising income inequality has itself recently received considerable study. The relationship between income inequality and productivity growth is of paramount importance today since there appears to have been a structural change in the level of income inequality in the United States starting around 1968. Nearly one-third of this increase in income dispersion occurred between 1979 and 1982. Academicians and policy makers have noted this disturbing upward trend in measured U.S.

Productivity and Income Inequality

301

inequality. Levy (1988), Formby et al. (1989), Bishop et al. (1991), and Slesniek (1990) all presented empirical evidence to substantiate the claim that there is an upward trend in the level of U.S. income inequality. Juhn et al. (1993) and Ryu and Slottje (1993) argue that this increase in inequality is due to a change in the distribution of skills in the economy and a rise in the return to skill for highly skilled workers. Ryu and Slottje (1992a,b) find empirical evidence corroborating these arguments. Slottje (1989) notes that changes in female labor force participation, in the composition of the economy (service-sector growth versus manufacturing-sector decline), and in the labor supply behavior of older white males all may have affected the income distribution. Levy and Murnane (1992) survey in more detail the potential causes of increased income inequality. This brief review of the literature suggests that the causes of changing income inequality and of productivity growth stagnation are still being debated. It appears clear, however, that income inequality (as measured by the Gini coefficient and using family income as the income-recipient unit) has seemingly increased while productivity growth has decreased (and even has been negative) in the United States in the 1980s. The purpose of this paper is to examine the relationship between changes in productivity in the U.S. economy and changes in U.S. income inequality from 1948 to 1990. To our knowledge, no study has analyzed the impact of income inequality on productivity. We are especially interested in possible "feedback" between productivity change and income inequality. If income inequality both affects and is affected by productivity change, social welfare policies and national productivity policies should be modeled simultaneously. This approach would represent a significant change in analyzing the productivity dilemma. Moreover, the usual equity-efficiency trade-off would be called into question. Policies designed to ameliorate inequality may also increase productivity growth. To examine these issues, we first analyze naive bivariate causality models relating a measure of income inequality and a measure of productivity change. We initially estimate the bivariate causality models to see if "naive" feedback exists. Even if it is not present, the existence of a relationship cannot be dismissed. On the other hand, if feedback is present, the existence of a causal relationship is not certain, since feedback between variables of a bivariate system may be due to neglect of important variables (Lutkepohl, 1982). This argument suggests that other relevant

302

K.J. Hayes et al.

economic variables should then be included in the model. Therefore, we also utilize a "Wiener-Granger" multivariate causality model to search for feedback. The signs of the coefficients in these models, however, generally do not have any specific interpretation. Thus, a dynamic simultaneous equations vector autoregression (VAR) model is also developed to analyze these relationships. Impulse response functions from the VAR estimation allows us to determine empirically if productivity and income inequality have feedback on one another in future periods. In Section 10.2, theoretical reasons for expecting relationships between income inequality and productivity changes are discussed. Section 10.3 presents the models used for testing these relationships. Unit root tests are conducted to ascertain the temporal behavior of the series. The naive bivariate, multivariate "Wiener-Granger," and VAR models are discussed. The results of various models are discussed in Section 10.4. Section 10.5 concludes the paper.

10.2

Relationships Between Income Inequality and Productivity

Consider a given distribution of productivity levels, where some industries have higher levels of productivity than others. Economic theory suggests that in competitive markets the distribution of productivity levels should generate a distribution of wages related to the marginal revenue product of those resources (see also Arrow, Chapter 12 in this volume). Ignoring regulations and unions, which cause deviations from this equilibrium, the income distribution could be mapped from the distribution of productivity levels. As just discussed by Karni and Zilcha in Chapter 9, technological change is one source of productivity growth. Yet how the distribution of income changes depends upon the bias, or lack thereof, in the technological improvements. Jorgenson et al. (1987) demonstrates that productivity growth in agriculture, nonmetallic mining and quarring, construction, and rubber and wood industries has increased while that in metal and coal mining, textiles, and telecommunications has decreased. One might expect, therefore, that changes in wages in those industries reflect these changes in productivity, leading to a change in the overall income distribution. However, the causal direction of the relationship might be reversed. Increased income inequality may cause greater dispersion in the distribution of investments into human capital. Referring again to Chapter 9, widening

Productivity and Income Inequality

303

income inequality may lead to increased dispersion in parents' "bequests" of human capital to offspring. As the distribution of human capital becomes more skewed, labor may become less productive. In particular, as the variance of skills of heterogeneous labor increases, workers may not "mesh" as efficiently, reducing labor productivity. This argument is consistent with the empirical results in Juhn et al. (1993) and papers in this volume that document an increased dispersion in the distribution of skills. Separately, as incomes become more unequal, workers may become more resentful of the status quo and less cooperative and effective in the workplace. In both cases, the quality of the inputs used in the production process has been diminished, reducing productivity. The analysis here is based on highly aggregated data. For example, we aggregate income to look at total family income. Public policy must be conducted ultimately with an awareness of the entire income distribution of a targeted income-recipient unit. Thus, we believe that our focus on total family income and on macroeconomic aggregates is an appropriate research strategy.

10.3

D a t a and Methodology

All data in this study are annual observations for years 1948-1990. To test the robustness of the model, the productivity growth rate is defined in two ways. First, it is defined as the percentage change in output per hour of all persons in the nonfarm business sector as defined by the Bureau of Labor Statistics and reported in the 1992 Economic Report of the President (BLSPROD). Second, it is defined as the percentage change in real GNP per employee (RLGNPEMP). Employment data are collected from the Bureau of Labor Statistics' Labor Force Statistics Derived from the Current Population Survey: A Data Book. The Gini coefficient (Gini) is used as our inequality measure since it is economically intuitive and frequently cited in the literature. While it violates the principles of transfers in the middle of the income graduation, it still is considered an acceptable measure, cf., Cowell (1977) and Slottje (1989). The Gini coefficients are constructed from data reported in the Current Population Reports. The income units are families. Table 10.1 shows time series of the two measures of productivity growth rates, the Gini coefficient, and other macroeconomic variables described below. The Gini coefficient gradually declines from 1948 to 1969, and then slowly rises through

304 Table 10.1

K.J. Hayes et al. Productivity, Inequality, and Macro Variables

Year

BLSPROD

RLGNP /EMP

Gini

Tax

Transfers

Unemp. Rate

1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969

0.038 0.017 0.064 0.030 0.022 0.022 0.015 0.029 0.006 0.019 0.024 0.032 0.010 0.032 0.031 0.036 0.038 0.023 0.021 0.021 0.029 0.000

0.018 0.025 0.054 0.041 0.017 0.011 0.012 0.019 -0.013 0.008 0.022 0.022 0.005 0.030 0.040 0.004 0.025 0.013 0.005 0.001 0.009 -0.013

0.4315 0.4410 0.4390 0.4210 0.4265 0.4190 0.4320 0.4230 0.4150 0.4075 0.4130 0.4195 0.4230 0.4335 0.4225 0.4215 0.4210 0.4155 0.4050 0.4055 0.4065 0.4065

0.337 0.380 0.359 0.437 0.392 0.278 0.297 0.288 0.253 0.203 0.230 0.258 0.261 0.248 0.300 0.282 0.298 0.296 0.285 0.321 0.320 0.225

3.06 3.34 3.96 2.98 3.04 3.16 3.57 3.63 3.69 4.06 4.76 4.75 4.93 5.50 5.57 5.63 5.70 5.95 634 7.33 8.01 8.37

3.8 5.9 5.3 3.3 3.0 2.9 5.5 4.4 4.1 4.3 6.8 5.5 5.5 6.7 5.5 5.7 5.2 4.5 3.8 3.8 3.6 3.5

1990, particularly during the 1980s. As noted above, there exists a potential bias in using bivariate causality models. Thus, to analyze the relationship between our inequality indicator and changes in productivity, we must control for other macroeconomic phenomena which influence these variables. Tax policy, as reflected by marginal tax rates, affects the effective rate of return received by investors and should influence investment and productivity gains. We expect the marginal tax rate to show feedback because of its impact on income and perhaps productivity. Following Nieswiadomy et al. (1991) to measure the marginal tax rate (Tax), we use: [1 - (yield on Aaa municipal bonds/yield on Aaa corporate bonds)]. This variable is constructed from data compiled by Moody's Investor Services, Inc. This

Productivity and Income Inequality

305

Table 10.1 (continued)

Year

BLSPROD

RLGNP /EMP

Gini

Tax

Transfers

Unemp. Rate

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

0.009 0.035 0.027 0.025 -0.020 0.023 0.027 0.014 0.007 -0.014 -0.009 0.009 0.001 0.024 0.021 0.008 0.019 0.008 0.009 -0.009 -0.001

-0.008 0.022 0.015 0.010 -0.026 0.005 0.016 0.008 0.002 -0.011 -0.007 0.010 -0.007 0.028 0.020 -0.002 0.011 0.005 0.009 0.003 -0.003

0.4140 0.4150 0.4190 0.4165 0.4150 0.4185 0.4185 0.4260 0.4265 0.4265 0.4275 0.4345 0.4465 0.4470 0.4490 0.4545 0.4580 0.4565 0.4605 0.4615 0.4610

0.239 0.294 0.301 0.329 0.313 0.273 0.330 0.352 0.368 0.388 0.343 0.264 0.211 0.269 0.244 0.244 0.229 0.241 0.242 0.244 0.268

9.50 10.52 11.11 11.83 12.76 14.50 14.74 14.67 14.61 14.86 16.02 16.44 17.04 17.49 17.16 17.63 18.07 18.20 18.66 19.24 19.95

4.9 5.9 5.6 4.9 5.6 8.5 7.7 7.1 6.1 5.8 7.1 7.6 9.7 9.6 7.5 7.2 7.0 6.2 5.5 5.3 5.5

measure, Tax, is somewhat limited in information about the distribution of tax liabilities. Although tax progressivity measures have been developed (see, for example, Suits, 1977), these measures, like the marginal tax rate used here, are summary statistics. Neither measure provides information about the impact of tax changes on the tails of the income distribution. We also include transfers per person (Transfers) and the overall unemployment rate (Unemp. Rate) in the analysis to control for the impact of the state of the economy and to control for cyclical affects in the economy. Transfer data and unemployment rate data are from the 1992 Economic Report of the President. As noted in Haslag et al. (1988), these are the primary variables that have been found to affect inequality. We expect the unemployment rate to exhibit feedback into the system, since it is likely to influence both income inequality and growth in productivity. We expect the average

306

K.J. Hayes et al.

marginal tax rate to show feedback because of its impact on income inequality and perhaps changes in productivity as well. However, we are not certain if income inequality exhibits feedback. To our knowledge, this hypothesis has not been tested before. The analysis begins with an examination of the orders of integration of the time series. A time series is integrated of order one, 1(1), if it requires first differencing to attain stationarity. A series is 1(0) if it is stationary. Stationarity is important for our subsequent analysis since conventional asymptotic distribution theory applies to vector autoregressions of stationary variables. Tests from Phillips and Perron (1988) are employed (using the same notation). The Phillips-Perron tests involve running the following three regressions using ordinary least squares:

y

=

à

t

y -i t

+

û

y = μ* + α* y t

y = μ

(10.1)

t

(10.2)

+ u/

M

+ p(t-T/2) + fty

t

M

+ û

(10.3)

t

where Τ is the sample size and u , u * and u are regression disturbances. In model (10.1) the null hypothesis of a unit root (H : α = 1) is tested against the stationary alternative (H :oc