Regional Economic Impact Analysis and Project Evaluation [1 ed.] 9780774853774, 9780774803502

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Regional Economic Impact Analysis and Project Evalu ion This book provides a non-technical introduction to the fundamental principles and techniques of regional impact and evaluation analyses. The book is written for readers who have a minimal background in mathematics and economics and so the materials listed in the bibliographies have been chosen for their accessibility to such readers. References to relevant papers of a more technical nature are indicated in notes for each chapter. Unlike existing texts, which usually concentrate on regional impact or evaluation analysis, Regional Economic Impact Analysis and Project Evaluation offers extensive introduction to both these subjects, since both are critical to the study and practise of regional economic analysis. Two case studies, intended as illustrations of practical applications, are included in each of the six chapters that deal with specific principles or techniques. While many of the case studies and much of the literature cited in the bibliographies is Canadian, a substantial portion is from the United States and Great Britain, emphasizing that the principles and techniques discussed in this book are universally applicable. H. CRAIG DAVIS is a professor in the Department of Community and Regional Planning at the University of British Columbia.

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Regional Economic Impact Analysis and Project Evaluation H. Craig Davis

UBC Press / Vancouver

© UBC Press 1990, 1993, 2001 All rights reserved Printed in Canada on acid-free paper @ ISBN 0-7748-0350-9

Canadian Cataloguing in Publication Data Davis, H. Craig Regional economic impact analysis and project evaluation Includes bibliographical references. ISBN 0-7748-0350-9 i. Regional economics - Evaluation. 2. Regional planning - Evaluation. 3. Economic development projects - Evaluation. 4. Canada - Economic conditions - 1971-* 5. Regional planning - Canada - Evaluation. 6. Economic development projects - Canada - Evaluation. I. Title HT388.D381990 338.9 C9O-09ii83-2

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(604) 822-5959 Fax: (604) 822-6083 E-mail: [email protected] www.ubcpress.ca

To Marjorie, D'Anne, Lauren, and Ethan

Contents

Preface xi 1 INTRODUCTION

3

PART ONE REGIONAL ECONOMIC IMPACT ANALYSIS

2 Economic Base Analysis 9 Case Study 1: An Economic Base Study of a Nova Scotia Region 23 Case Study 2: A Regression Base Multiplier Model for Kentucky Counties 25 3 Income-Expenditure Analysis 29 Case Study 1: An Income-Expenditure Multiplier for a Newly Locating Firm 45 Case Study 2: The Local Economic Impact of Kent State University 47 4 Input-Output Analysis 53 Case Study 1: An Input-Output Model of Metropolitan Vancouver 76 Case Study 2: An Input-Output Model of the Yukon Territory 77 Appendix 1: A Mathematical Summary of the Input-Output Model 81 Appendix 2: The Rectangular Commodity by Industry InputOutput Format 82 5 Regional Economic Impact Analysis: A Comparison of Approaches 89

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Contents PART TWO: PROJECT EVALUATION ANALYSIS

6 Cost-Benefit Analysis: The Evaluation of Social Costs and Benefits 95 Case Study 1: The Evaluation of Recreation Benefits at Graf ham Water 114 Case Study 2: Cost-Benefit Analysis in the Evaluation of STOL Air Transport 115 7 Cost-Benefit Analysis: Discounting Future Benefits and Costs 119 Case Study 1: A Cost-Benefit Analysis of an Urban Renewal Project 133 Case Study 2: A Cost-Benefit Analysis of a New Zealand Aluminum Smelter 135 8 Cost-Benefit Analysis: Risk Adjustment and Distributional Considerations 141 Case Study 1: Distributional Analysis and the Third London Airport 159 Case Study 2: An Evaluation of Alternative Uses for an Urban Land Parcel 160 9 Economic Evaluation Analysis: A Summary 165 Notes 171 Indexes 179

TABLES

1 Change in number of total jobs for county residents per added job in basic activity 27 2 Gross regional product 50 3 Measures of regional income 51 4 Hypothetical interindustry transactions table 54 5 Direct purchases per dollar of total output 57 6 Direct plus indirect purchases per dollar of final demands 58 7 Direct purchases per dollar of total output (closed I-O model) 60 8 Total requirements per dollar of final demands (closed I-O model) 61 9 Interindustry transactions, metropolitan Vancouver, 1971 70 10 Metropolitan Vancouver sales and employment multipliers 77 11 Interindustry transactions, Yukon, 1978 78 12 Yukon income multipliers 81 13 The make matrix of a two-commodity, three-industry input-

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output model of a hypothetical economy 83 14 Use matrix of a two-commodity, three-industry input-output model of a hypothetical economy 84 15 Accounting framework of the commodity-by-industry inputoutput model 87 16 Comparison of the principal approaches to economic impact analysis 94 17 Benefits and costs of a proposed STOL system 116. 18 Cost of investment funds in Canada 131 19 Tangible social benefits and costs of the East Stockton urban renewal project 134 20 Benefits and costs of the smelter energy project, 1981-2016, foreign financing of public capital expenditures 136 21 Benefits and costs of the smelter energy project, 1981-2016, domestic financing of public capital expenditures 136 22 Present discounted value of one dollar for selected discounted rates and time periods 138 23 Present discounted value of one dollar per period for selected discount rates and time periods 139 24 Incidence matrix of net present value 152 25 Illustrative PBS transactions for water pollution regulation 155 26 Illustrative goals achievement matrix 157 27 Summary of weighted costs of the third London airport 160 28 Evaluation matrix for decisionmakers: Harbour Park 164 FIGURES 1 Savings and consumption 30 2 Cash flows in a simple economy 31 3 The economic base and income expenditure models 40 4 Consumer surplus 97 5 Producer surplus 98 6 Consumer and producer surpluses and project net benefits 9 7 Production under imperfect competition 101 8 Taxation and price 102 9 Private and social marginal costs 106

Preface

My primary objective in writing this text is to provide the university student with a non-tech cal introduction to the fundamental principles and techniques of egional impact and evaluation analyses. The book has been developed over several years of teaching regional economic analysis to first-year graduate students in the field of city and regional planning. These students enter graduate school from a variety of academic disciplines. The book differs from similar texts in the area of regional economic analysis in at least three ways. First, it was written for the reader who has a minimum of training in mathematics and economics. Exposition in the text relies primarily on arithmetic and the simplest of algebraic expressions. Explanations involving matrix algebra are relegated to appendixes. The bibliography at the end of each chapter is the product of a selection process that has been undertaken by both the author and past students who have used earlier drafts of the book. The materials listed in the bibliographies are also generally accessible to readers with a limited economic background. References to relevant papers which are of a more technical nature are indicated in notes throughout the text. Second, the book is distinctive in that it offers extensive introductions to both regional impact and evaluation analyses. Existing texts pertaining to these subjects generally concentrate on one or the other. Since both are critical to the study and practice of regional economic analysis, there is an advantage in considering them sequentially in a single text. Third, the book has a decidedly Canadian flavour. Each of six chapters dealing with specific principles or techniques has two case studies which are intended as illustrations of practical appli-

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cations. Approximately half of these case studies are Canadian in content. Much of the literature contained in the bibliographies is also Canadian in content. The principles and techniques upon which the book is focused, however, are universally applicable, and a substantial portion of the literature cited is drawn from the United States and Great Britain.

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Regional Economic Impact Analysis and Project Evaluation

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CHAPTER ONE

Introduction

Individual citizens, businesses, community, and commercial organizations, as well as government agencies at various levels, have long been interested in the nature and magnitude of local economic changes that result from a variety of public and private sector initiatives. The effects of the vast majority of initiatives or projects are spatially concentrated. When, for example, a new firm locates within a particular region, a number of economic consequences occur within that region. An assessment of these consequences involves their identification and measurement, and a judgement as to their social value. In this regard, the purpose of this introductory chapter is threefold: to discuss the concept of the region, to define and distinguish between economic impact and evaluation analyses, and to present an overview of the contents of the book. D E F I N I T I O N OF A R E G I O N

A region is generally defined as a subset of the natio and may be an administrative unit such as a state, province, county, regional district, metropolitan area, or even a municipality. Conceptually, regions customarily take one of two principal forms: "homogeneous" regions or "nodal" regions. In practice, the analyst is often constrained to work with "administrative" regions. A homogeneous region may be defined as a set of contiguous "areas" (i.e., portions of the earth's geographical space) which are more like each other with respect to a particular characteristic than they are to other areas. In Canada, the Prairies (Alberta, Saskatchewan, and Manitoba) are a familiar example of such a region. The

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Regional Economic Impact Analysis and Project Evaluation

common economic characteristic of these three provinces is the production of wheat. The Maritimes (Nova Scotia, Prince Edward Island, and New Brunswick) are another example of a homogeneous region, in which the common economic characteristic is a reliance on fishing and agriculture as the principal means of livelihood. The characteristic which forms the definitional basis of a region need not be economic, however. Quebec is often thought of as a distinct Canadian region not because of any particular economic trait but because of its distinctively different culture and language. In the United States a particular portion of the southern and border states has been dubbed the "Bible Belt" because of a common affinity for fundamentalist religion. The "Solid South" is a name given to the southern Gulf states for their historic allegiance to the conservative wing of the Democratic party (a political loyalty which has considerably dissipated in recent years). "Resource regions" (those which share a common natural resource, such as a river basin or the geographic range of a mineral deposit) are also examples of homogeneous regions.1 A second approach to defining a region is based on the relative lack of homogeneity in the spatial economy. Nodal regions are those which are comprised of a set of functionally integrated areas characterized more by their interdependencies than by their homogeneity. The Canadian Census Metropolitan Areas (as defined by Statistics Canada) and the u.s. Statistical Metropolitan Standard Areas (as defined by the u.s. Bureau of the Census) are familiar examples of nodal regions. Municipalities and counties are included in these nodal regions largely on the basis of labor commutation patterns to and from the core of the region. In undertaking regional impact analysis, it is generally good practice to conceptualize the region prior to gathering data. Otherwise, considerable time and expense can be wasted in collecting information that is later found to be irrelevant to the analysis. A second rule of thumb is that the actual conceptualization of the region will depend directly on the nature of the impact and the units of measurement adopted. If the focus is on, say, the employment impact of a newly locating plant, the region may be defined in terms of the geographic labour pool from which the plant (and its potential suppliers) will draw its employees. If the emphasis of a comprehensive impact assessment is on socioeconomic effects, the region, at least during the construction phase, may be be defined in terms of the geographic range of social effects of, say, the

Introduction

5

migrant inhabitants of temporary construction camps. An impact analysis focusing on the environmental implications may dictate that the region be defined as a particular portion of a river basin or air shed. It is important to note that various components of a comprehensive impact analysis may result in different delineations of the region impacted. The definition of a region is not a product of regional analysis, but a methodological tool which can provide spatial boundaries for the various facets of the problem under study. In many cases, however, the region will be defined for the analyst at the outset of the study by the funding public agency as the region of the agency's political jurisdiction. The delineation of a region according to administrative boundaries constitutes a third avenue to defining a region. Given the difficulties of precisely circumscribing a region, regional analysts may be "relieved when they are forced to work with administrative regions on the grounds that policy considerations require it, or that data are not available for any other spatial units."2 IMPACT VS. EVALUATION ANALYSIS

Economic impact studies are based on conditional predictive models of economic analysis, that is, models which are designed to produce "If... then" statements of this type: If, under assumptions a, b, and c, a stimulus x is applied to the local economy, then impacts y and z are likely to result. Impact studies are generally designed to produce quantitative estimates of the effects or changes in the local economy resulting from a stimulus (positive or negative) to a particular segment of the economy. Because of the circulation of funds within the economy, the overall impact will be a multiple of the initial impact. By tracing linkages among the various elements of the local economy, the economic impact analyst arrives at an estimate of the multiplier effects of the initial stimulus. Although perhaps most commonly employed as an aid to estimating the impacts on a region of investment and public spending in a particular sector of the economy, economic impact analysis is also utilized to measure the effects of cross-sector stimuli such as taxation/subsidy policies, price changes, and regulatory measures. Impact analyses in practice are both ex ante and ex post. The principal benefits to be derived from such studies undoubtedly stem from the ex ante or pre-project variety. However, ex post or post-project studies are of importance for at least two reasons: to provide a standard by which the success of any ex ante analyses of

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Regional Economic Impact Analysis and Project Evaluation

the same project can be measured; and to generate information regarding the identification and measurement of impacts which may be useful in designing future ex ante impact studies. Unless explicitly otherwise directed, comprehensive economic impact analysis should appropriately distinguish between the construction and operation phases of the project to be analysed. For example, the construction of a dam may have enormous economic implications for the commercial sectors of nearby municipalities, while the impact of the dam's operational phase may be all but negligible. Whether ex ante or ex post, focused on the construction or operational phase, economic impact studies are designed to consider the economic effects beyond those of the first round of expenditures in order to determine the total economic impacts of the project or stimulus. In so doing, however, such studies say nothing about the social valuation of the results. As Waters (1976) has argued, economic evaluation analysis differs from impact analysis in that the latter is designed to estimate the effects of a particular stimulus or project while the former is designed to measure the value of a project, given the various impacts produced. If impact analysis results in "If... then" statements, evaluation analysis answers the question "So what?" Economic evaluation involves an examination and comparison of the economic benefits and costs attributable to the project. [Evaluation studies are intended to assess the relative merit of one project as opposed to another (and/or to assess the one project relative to what would have taken place in its absence). From the information contained in an impact study, items must be selected to be considered for evaluation purposes (e.g., cases of double counting must be eliminated). Next, it is necessary to assign weights or values to the various impacts in order to arrive at some measure of the net economic merit of this project that may be compared with alternatives. To do this it is necessary that the planning or policy objectives be quite explicit (along with the relative weights if multiple objectives are being pursued). Without a clear understanding of objectives it is not possible to identify which impacts are to be counted nor how they are to be weighted or valued. In contrast, one can proceed with impact studies with only limited knowledge of policy objectives. (Waters 1976: 100)

In the principal approach to economic evaluation analysis considered here, cost-benefit analysis, the goal is economic efficiency. Limited consideration is given, however, to the incorporation of

Introduction

7

the goal of equity within cost-benefit analyses, and to alternative approaches to economic evaluation. The second major way in which evaluation analysis is distinguishable from impact analysis lies in the necessity of evaluation analysis to estimate the true economic costs of the project in question, that is, the opportunities foregone as a result of the allocation of resources to the project. As with the process of determining the project's benefits, an examination of economic conditions within the region must be undertaken with and without the project in question. Such an examination may involve consideration of alternative means of attaining the relevant economic objective(s), or it may involve an assessment of the costs, as well as the benefits, of doing nothing. In sum, the information produced by an impact analysis is at most a subset of that required by an evaluation analysis. Evaluation analysis requires the regional economic objectives which the stimulus or project in question is designed to serve and information regarding the extent to which each of these objectives is served by the project's impacts. In addition, evaluation analysis necessitates information regarding the project's associated costs. SCOPE OF THE BOOK

This book is divided into two major sections. The first is concerned with the principal techniques of regional economic impact analysis: economic base analysis (Chapter 2), income-expenditure analysis (Chapter 3) and input-output analysis (Chapter 4). The structure of each of these chapters is the same. An exposition of the analytic technique is followed by a summary critique of the technique's principal theoretical assumptions. The major practical problems associated with the application of the technique are then addressed. In light of both its theoretical and practical shortcomings, each technique is evaluated and the appropriate conditions set forth under which it is most effectively applied. Selected modifications and extensions of the basic technique are then considered. The principal points in each chapter are summarized and all technical arguments requiring anything but the most rudimentary economics or algebra are relegated to footnotes and appendixes. Each chapter is concluded with two case studies presented as illustrative applications of the analytic technique discussed in the chapter. A cursory comparison of the three economic impact techniques with respect to a number of characteristics is contained in Chapter 5-

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Regional Economic Impact Analysis and Project Evaluation

The second section of the text consists of four chapters devoted to the fundamental principles and concepts of cost-benefit analysis. The focus of Chapter 6 is on the valuation of costs and benefits. The philosophical foundations of cost-benefit analysis are considered, and valuations are discussed under conditions of distorted market prices and in the absence of market values. Chapter 7 deals with the concept of discounting future costs and benefits, the difficulties of establishing an appropriate social rate of discount, and the alternative decision rules for public sector investment. Chapter 8 reviews various methods for incorporating into the analysis elements of risk and uncertainty and the economic goal of equity. As is the case with chapters 3 through 5 on impact analysis, each of the Chapters 6 through 8 on cost-benefit analysis contains sections on modifications and extensions of the basic techniques discussed in the chapter plus illustrative case studies at the end of the chapter. The advantages and potential weaknesses of cost-benefit analysis are then reviewed in the concluding chapter. SELECTED READINGS

Ashby, L.D. 1986. "The Region: Place or Process?", Review of Regional Studies, 16:1-5 Garreau, J. 1981. The Nine Nations of North America. Boston: Houghton Mifflin Waters, W.G. 1976. "Impact Studies and the Evaluation of Public Projects," Annals of Regional Science, 10:98-103

CHAPTER TWO

Economic Base Analysis

EXPOSITION OF THE MODEL

The Gross Regional Product (GRP)1 of a regional economy can be disaggregated into the customary national income accounting categories: The equation reveals to us that the source of regional economic growth can be found in any one of the above components of GRP. For example, a general tax cut will increase consumption (C) and raise GRP. Investment (/) may expand through, say, a residential housing boom within the economy. Local government spending (G) on sewer lines and roadways may be expanded and thus add to employment and income in the region. GRP may also be increased through the expansion of export sales (£) from the region and by the substitution of locally supplied commodities for import purchases (M). While each of these five components are indeed possible sources of regional economic stimuli, the economic base model explicitly recognizes only export expansion. The model implies that for a regional economy the importance of exports relative to the other components of GRP is such that we may ignore the latter four sources of possible economic stimuli without introducing significant error into the analysis. In short, export expansion is considered to be the sole or primary engine of regional economic growth. Given this predominant concern with the role of exports in the region, the base model conceptually divides the economy into two sectors, the export, or "base," sector and the non-export, or "ser-

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Regional Economic Impact Analysis and Project Evaluation

vice/' sector. The ba sector consists of all economic activity whose ultimate market lies outside the region, while the service sector is comprised of that portion of total economic activity whose ultimate market is local.2 Thus, if firm A sells its entire output locally to firm B and the latter exports all it produces, firm A is part of the base sector because its ultimate market is outside the region. A third hypothetical firm which sells 70 per cent of its output to B and the remainder to local final consumers would be appropriately classified as 70 per cent basic and 30 per cent service. Sales to local final consumers are sales to local purchasers who do not further process the commodity within the region. A quart of milk delivered to the door of a household in the region is a sale to a final consumer or purchaser. An identical quart of milk delivered to a local restaurant is a sale to an intermediate purchaser. Representing base or export activity as E and local or service activity as S, total activity Y in the region may be expressed as If we now assume that over the period of analysis the proportion of service activity to basic activity remains constant, we may define the proportion k as

Substituting (2.3) into (2.2) yields As can be seen from equation (2.4), total economic activity in the region is solely a function of export activity. However, it is also a multiple of that activity. That is, if export activity increases (decreases), total activity will increase (decrease) by the amount of the change in export activity times the multiplier, i + k. Since by definition k will always be positive (assuming some service activity to be present), the multiplier will always exceed one. The multiplier in equation (2.4) reflects the respending process that occurs when export expansion takes place within the region. For example, suppose a furniture manufacturer receives a substantial increase in orders from a wholesaler in another region. Further suppose that the fur iture manufacturer buys her lumber inputs from a local mill and her paints and varnishes from a local chemical plant. The increase in furniture exports will expand the wage bills (and profits) of all three local firms. A portion of the increase in these wages and profits will likely be expended on locally supplied goods and services. The incomes of the suppliers of these local commodities will correspondingly rise and the recipients of these

Economic Base Analysis

11

increased incomes will, in turn, spend portions of their incomes locally, and so on. For example, a wage earner in the lumber mill that sells to the furniture manufacturer may spend a portion of his increased income on a used car. In turn, the used car dealer may spend part of his increased income on a tailormade suit. The tailor will then spend a portion of her increased income locally and the respending process continues. The process eventually comes to an end, of course, because of leakages (taxes, savings, non-local expenditures) that occur with each transaction. Each recipient pays a fraction of his increased income to the public sector in the form of taxes and may choose, in lieu of spending money locally, to purchase goods and services outside the local economy or to place money in some form of savings. In addition, local suppliers of commodities, from the furniture manufacturer to the tailor, will generally purchase intermediate goods and services produced outside the region. The greater is the sum of all the leakages, the smaller is the multiplier. PRINCIPAL ASSUMPTIONS OF THE MODEL

The simple base model as described above has several fundamental assumptions which limit both its general applicability and usefulness. Perhaps the most obvious assumption is that exports are the sole source of regional economic growth. As was discussed at the outset of the preceding section, several alternative sourceshousehold consumption, investment, government spending, import replacement—are thus ignored. This assumption alone largely limits the appropriate application of the model to relatively smallscale economies which are highly dependent on exports. Mining and mill towns, fishing villages, agricultural and timber regions, and tourist-oriented areas such as ski and beach resorts are examples of regional economies which are in general appropriately represented by the base model. A second major assumption of the model is homogeneity of the export sector. That is, it is assumed that exports from the regional economy are homogeneous, or at least that a change in the magnitude of the flow of one export commodity does not vary in its impact on the regional economy from an equal change in magnitude of any other commodity which is exported. The impact on the economy is estimated by the base model to be the change in the volume of exports times the multiplier, i + k, regardless of the particular commodity exported. Obviously such is not always the case. An $x increase in the export of steel from a regional economy may well

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Regional Economic Impact Analysis and Project Evaluation

differ in its total impact on the economy from that of an $x increase in the export of wheat. The leakages associated with the two activities will likely differ (and thus so will the appropriate multiplier) because of differences in the proportions paid to local labour and suppliers of materials and because of differences in the expenditure patterns of the employees in the two activities. To the extent that such differences do indeed exist between export activities, the simple base model of equation (2.4) will be less than satisfactory as a general analytic model of the region for purposes of economic impact analysis. The constancy of the parameter k over the period of analysis is a third major assumption of the model. As the economy expands and the local markets for various commodities grow larger in volume, it becomes increasingly feasible for import replacement to occur. In a sparsely populated settlement, residents may journey to the nearest sizeable town to purchase commodities generally found in a department store. As the region's population grows, a catalogue store may be established. With continued expansion in the population, a small branch of a department store chain may locate in the region. Further, the increased size of the local market may bring larger establishments into the region. Continued economic growth may give rise to producers as well as suppliers of particular consumer commodities. Generally as the economy grows, the value of k will rise. The service sector will "fill in" as the local market expands, and the value of the multiplier will correspondingly increase. Thus, the shorter the period of analysis, the more accurate are likely to be the results of the prediction of changes in total activity, given the estimate of the increase or decrease in the level of the region's exports. A fourth assumption of the model is the absence of interregional feedback. That is, it is presumed that a c nge in the level of exports from the economy will not lead to f her changes in exports as a result of trade linkages between the region in question and other regional economies. For example, an increase in exports from region A to region B will increase income in region A via the multiplier expressed in equation (2.4). This increased income will lead to the increased purchase of imports by firms and households in region A. The imported commodities will possibly originate in part in region B. In such circumstances, region B's exports will expand, leading to increased income in the region via a similar multiplier process. As in region A, the increased income leads to increased imports. To the extent that the import expansion in B results in an

Economic Base Analysis

13

increase in exports from A, the export sector in A will have received a secondary stimulus via its trade linkages with region B. The secondary stimulus can lead in the same manner to a tertiary stimulus, and so on. Such interregional feedback effects can simultaneously occur between region A and several other regions. Empirical measures of such feedback effects tend to show that they have generally insignificant impacts relative to the impacts of the initial changes in export levels. However, to the extent that such feedback does occur, the impact of the initial change in the regional export level will be somewhat understated. A fifth assumption of the model is the existence of a pool of underutilized resources. It is assumed that an increase in export demand will result in a corresponding increase in the flow of export commodities. If, however, there are severe capital, labour, or resource constraints, the sole or primary result of an increase in export demand may be an increase in the prices of the exported commodities. SOME PRACTICAL DIFFICULTIES

In economic base analysis, the economy is presumed to be initially "at rest," or in equilibrium. Disturbances to this equilibrium occur in the form of changes in the level of external demand for the region's exports. The prediction of changes in equilibrium activity resulting from disturbances or exogenous stimuli to the economy is termed "comparative statics." The base model, a comparative static model, predicts the new static equilibrium state of the economy resulting from the old, given a change in exports. It tells us nothing, however, regarding how long the intervening period between equilibria will be or what conditions will prevail in that period. Regardless of the method employed to distinguish base from service activity within the economy, it is implicitly assumed that the initial allocations to the two sectors are made while the economy is in equilibrium. If the division between export and service activities were undertaken while the economy was in the process of adjusting to an increase in exports, the full impact on the service sector resulting from that increase would be incomplete. That is, at the time of measurement activity in the non-export or service sector would not have reached its new equilibrium level. Consequently, both the ratio, k, of service to base activity in the economy and the

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Regional Economic Impact Analysis and Project Evaluation

resulting multiplier would be understated. If the economy were adjusting to a decrease in exports during the period of measurement, there would be a tendency for k and the multiplier to be overstated. A second problem arising in practice is the choice of the unit of measurement of regional economic activity. The possibilities include physical production, personal income, sales, value added, and employment. There are several advantages to the use of employment data. Jobs are a continuous focus of public policy and the estimate of changes in total regional employment is more often than not the principal objective of economic impact analysis. Furthermore, compared to, say, value added, the concept of a job is one that is easily understood by all concerned with the results of impact analysis. Perhaps of most importance, however, is the fact that data on regional employment are usually readily available, since employment has long been a traditional source of official public concern. In comparison, data on other measures are generally obtainable only with varying degrees of difficulty. Because of these overall advantages, employment data are used in the great majority of applications of the base model. The adoption of employment as the unit of measurement of regional activity is not, however, without its disadvantages. First, there is the definition of a job. How, for example, does a seasonal job lasting five months and paying $1,000 per month compare with a year-round job paying $600 per month? Problems resulting from differing periods of employment and wage rates aside, there is the additional problem of handling changes in labour productivity. Suppose, for example, that the substitution of capital for labour in the export sector decreased employment in that sector but increased the total wage bill due to the increased productivity of the remaining work force. In this case the base model of equation (2.4) would predict a decline in service sector employment (since in employment terms AE < o), but in reality, because of the increased income generated in the base sector, one could reasonably expect that service sector employment would expand. Similar problems may arise when the flow into the region of money transfers such as unemployment and welfare payments is altered. Since there is no change in basic employment, the simple base model will fail to predict an increase (decrease) in total employment in the region resulting from the increased (decreased) flow of transfer payments. A third practical difficulty to be considered is the task of distinguishing between base and service activity in the region. Assuming that employment has been adopted as the measure of economic activity, the task is now one of identifying that portion of

Economic Base Analysis

15

regional employment whose production is ultimately for markets outside the region. There are at least four alternative methods to accomplish this task.3 Judgment

The most rudimentary method of base identification is the employment of judgment. If the economy is sufficiently simplistic and the analyst sufficiently knowledgeable about each firm's interactions with other firms in the economy and its ultimate market, the division between base and service employment within the economy presents little difficulty. In the absence of such knowledge, it is possible to adopt an ad hoc approach in which basic employment in the region is assumed to consist of all employment in, say, agriculture, mining, manufacturing, transportation, and non-local government. Service employment then consists of construction, communication, utilities, trade, services, and local government. The potential for misassignment with such an approach is only too evident.4 Survey

In the more general case in which the economic transactions within the region are sufficiently complex to preclude judgment or an ad hoc approach, the analyst must turn to other means. An obvious alternative or complement to judgment is to survey the various establishments in the region to ascertain the total employment of each and the division of sales to markets within and outside the region. The employment of each firm is customarily allocated to the base and service sectors in correspondence with the division of the firm's sales. Problems of sampling design aside, the survey method faces the potentially troublesome problem of yielding incorrect information because of confusion between immediate purchasers and ultimate markets. For example, in responding to a survey, a lumber mill may report that it sells its entire output locally to a furniture manufacturer, prompting the analyst to assign the mill's employment entirely to the local or service sector. However, it may be that the furniture manufacturer exports 80 per cent of his production. Under these circumstances, only 20 per cent of the mill may be appropriately assigned to the local service sector. Care must be taken in each case to identify the ultimate market. The severity of this problem generally increases with the size of the economy, since techni-

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Regional Economic Impact Analysis and Project Evaluation

cal linkages between establishments usually become more complex as the economy expands. In larger regional economies cases may well arise in which particular establishments do not have detailed knowledge of their markets beyond their immediate wholesalers. Location Quotient

It is likely that the most commonly employed approach to identifying the economic base of a region is the location quotient (LQ). The LQ for a particular sector i is defined as

where R r/ N/ are regional and national employment in sector i, respectively, and R and N are the regional and national employment totals. If the location quotient for sector / exceeds one, export employment is presumed to exist in the sector, since the regional proportion of total employment allocated to the sector exceeds that of the nation. In such cases basic or export employment, £,, is calculated as

where the term R (Ni/N) is an estimate of the amount of regional employment in sector i necessary to satisfy local demands based on the proportion of national employment allocated to sector i. To derive accurate estimates from the above equation of the amount of employment in regional sector i attributable to exports, several conditions must be met or at least closely approximated. First, the nation is implicitly assumed to be precisely selfsufficient in the production of sector i, that is, it is presumed that net exports of national sector i are zero. If, say, national sector i is a significant exporter, the ratio Nf/Nin equation (2.6) will overstate the proportion of regional total employment required for regional self-sufficiency and thus basic employment in the sector will be understated. If, on the other hand, the nation is a significant net importer of the output of sector i, equation (2.6) will tend to overstate £,-. The LQ approach also implicitly assumes identical consumption patterns between the region and the nation. Suppose, however, that consumption of the production of sector / were, say, higher in the region than in the nation. For self-sufficiency in the production of i in this situation, the region would need a proportion of total

Economic Base Analysis

17

regional employment somewhat higher than that of Nj/N. Without appropriate adjustment to this ratio, the estimate of E, yielded by equation (2.6) will be an overestimate of basic employment in sector i. A third implicit assumption of the technique is that of identical levels of labour productivity between the region and the nation. If labour productivity is, say, higher in regional sector i than in national sector /',(Nj/N)will be inappropriately large and, all other things equal, application of equation (2.6) would result in an underestimate of basic employment in the sector. Fourth, the LQ technique implies homogeneous commodity production in each sector. The higher the level of aggregation of the employment data, the more troublesome this assumption will prove to be. To illustrate, suppose we had the following data: Region Nation

Pulp mill RI = 100 NI = 50,000

Paper mill R2 = 200 A/2 = 300,000

Total employment R = 10,000 N = 10,000,000

With these data, base employment in the region's pulp mill would be estimated by equation (2.6) as fifty employees. Since the LQ of the paper mill is less than i.o (LQ = [2oo/io,ooo]/[3oo,ooo / 10,000,000] = 2/3), no base employment is presumed to be present. Now suppose that the regional pulp and paper mill data were available for only a single sector labelled "Pulp and Paper Mills." For this single sector, employment of 300 is recorded, the total employment of the pulp and paper mills in the region. The location quotient ([300/10,000] / [350,000/10,000,000]) would be less than one, and thus no export employment would be estimated. The fifty employees producing for export in the region's pulp mill no longer appear in the calculations because they are offset, or "absorbed," by the needs of the region for paper mill imports. In general, the higher the level of aggregation, the less the detailed information regarding the region's heterogeneity of production, and hence the greater will be the overall underestimation of basic employment in the region. Finally, cross-hauling—the simultaneous exportation and importation of the same commodity—also creates a problem for the LQ approach to base identification. The existence of cross-hauling implies that some portion of local needs is being met by imports instead of local production. Thus, to the extent that cross-hauling is present, the LQ estimate of base employment will be under-

i8

Regional Economic Impact Analysis and Project Evaluation

stated. For example, if regional sector i exports the entirety of its production, all sectoral employment would be appropriately designated basic. If, however, the economy imports an amount equivalent to or greater than its exports, equation (2.6) would estimate base employment to be nil. As in the above pulp mill/paper mill illustration of the effects of sector non-homogeneity, import employment offsets export employment, thus causing the latter to be underestimated.5 Violations of the LQ approach's first three assumptions discussed—identical consumption patterns, identical levels of labour productivity and zero net national exports—may result in either underestimation or overestimation of basic employment. However, for the last two assumptions—homogeneous sectoral production and no cross-hauling—violations result only in underestimation of basic employment. Given the importance of the last two assumptions, it can be expected that in most cases the location quotient approach will yield an understatement of total basic employment in the region and thus an overstatement of the regional economic base multiplier. These expectations are borne out by existing empirical studies.6 Minimum Requirements A fourth approach to base identification is the minimum requirements approach. To implement this approach it is necessary to collect sector employment data for regions similar in size and structure to the region of concern. For each sector i the regions are ranked according to the proportion of regional employment in that sector. As a hypothetical example, the regional rankings for sector i may appear as Region

R;

R

R{/R

1 2

5,000 4,500

25,000 35,000

.20 •13

n

3,000

30,000

.10

In this approach the lowest ratio of Rj/R, ra,, is assumed to be the minimum requirement necessary to satisfy local demands. Thus for region i above, the number of base employees in sector i would be estimated as £, = R, - ml R = 5,000 - .10 (25,000) = 2,500.

Economic Base Analysis

19

The minimum requirements approach suffers from the same problems that plague the location quotient technique but also from an important additional problem. If the nth, or lowest, Rt/R ratio is chosen as the self-sufficiency ratio, the implication is that each of the other n - i regions is exporting the output of its sector i. This logically raises the question of the destination of the exports. With the strict minimum requirements approach, no region will ever be designated as an importer. One might attempt to overcome this particular weakness by arbitrarily moving up the regional rankings to select a higher value of K//R to serve as the self-sufficiency ratio, but such a highly arbitrary and mechanistic approach could hardly be expected to yield consistently accurate results. In addition, compared to location quotients, the minimum requirements approach is considerably more demanding of data.7 EVALUATION OF THE MODEL

The economic base model is most representative of structurally simple regional economies such as those of settlements whose economic fortunes are entirely dependent on resource extraction (agriculture, mining, forestry, fishing) for export. The local or service sectors in such settlements are generally well-defined and easily distinguishable from the base activities. Among the severest limitations of the base model is the model's exclusive reliance on exports as the determinant of economic expansion and decline. This focus on production to satisfy external demands excludes from consideration other economic determinants such as residential construction, commercial capital investment, government spending in the region, personal consumption, and import replacement. A second shortcoming of the model which significantly limits its usefulness is the model's failure to distinguish between the linkages of different export activities. Changes of equal magnitude in different export activities may result in markedly dissimilar impacts on the local economy due to disparate sets of technical and consumption linkages between the export activities and the rest of the economy. The model also suffers from the limitation of an assumed stable relationship between base and service sectors. A significant increase in the base sector may bring about a more than proportional increase in the service sector due to import replacement, which results from the expanded local market. Similarly, a significant decline in exports may result in a more than proportional decrease in service activity.8 Additionally, there are in practice no methods for

2O

Regional Economic Impact Analysis and Project Evaluation

easily and accurately distinguishing between base and service activity. The more complex the economy under analysis, the more severe this limitation becomes. Despite its shortcomings, the base model is commonly employed in economic impact analysis. In large part this frequency of use is attributable to the model's theoretical simplicity and relative ease of application. However, in view of the model's deficiencies, its application is appropriately limited to the analysis of short-term impacts on small-scale economies of changes in export production which do not result in significant alterations of economic structure. MODIFICATIONS AND

EXTENSIONS

The above simple version of the base model may well appropriately reflect the short-run economic circumstances of a number of the nation's smaller regions. The model is both inexpensive and easy to construct. However, the complexity of many regional economies is such that the model's theoretical shortcomings and practical difficulties may prove to be too severe for the basic model to be successfully applied. In several cases the model has been modified in some fashion in an effort to overcome one or more of its weaknesses. Some of the more interesting of these modified approaches are discussed below. The Differential

Multiplier

In order to overcome the particular shortcoming of the model attributable to the assumption of a homogeneous export sector, Weiss and Gooding9 identified three separate export activities in their base study of Portsmouth, New Hampshire. In addition to the aggregate of private sector export activities, a U.S. Air Force base and a naval shipyard were distinguished. A separate employment multiplier was estimated for each of the three export subsectors from the following multiple regression equation: where S is total service employment in the region, X, = basic employment in export activity i, and a, are constants. The value of the base employment multiplier for each export subsector is simply i + a,-, since fl, is the change in S resulting from a unit (one man-year) change in X,. The regression utilized eleven years of employment data which were assigned to base and service sectors on the basis of judgment, location quotients, and "special studies." In the analysis it was assumed that the local expenditure pattern

Economic Base Analysis

21

of the employees in the three export activities were identical. It was further assumed that sales-purchase relationships (i.e., technical linkages) between the three export subsectors were negligible. (The existence of technical linkages between the export activities would have presented difficult statistical problems.) Although these assumptions are presumably well-founded in the context of the Portsmouth study, they severely limit the general applicability of the overall approach. An Econometric Approach

Another approach to base multiplier analysis utilizing time series data is that of Mathur and Rosen.10 To identify the basic portion of each sector's employment by the Mathur-Rosen approach, it is first necessary to hypothesize that employment (R,) in each sector will vary to some degree in accordance with changes in employment (W) in the rest of the world (i.e., in the region's major export markets). Assuming a linear relationship between R, and W, where boi and b-n are constants whose values may be estimated by regression analysis, given time series observations of R, and W. (Where non-linear relationships between R, and W were observed, a semilog relationship was assumed in which In R,- = In boi + bi; W.) Once the estimates b0j and b-a have been derived, the average estimated value for R/, R,*, can be obtained from average world employment, W*, as Division of both sides of the above equation by R* yields two proportions, b0i/R* and b-n W*/R*. "The first expression represents the proportion of localized employment, that is, employment which is insensitive to changes in outside employment, and the second expression is the proportion of non-localized employment in the z'th industry" (Mathur and Rosen 1974:93). The amount of local and export employment for any observation R, may now be estimated by multiplying R/ by the above two proportions. Thus, base employment in sector i = R,b1;W*/Rr*). Service employment in sector i = R, - Base employment = R/(b0;/R/*). As Isserman11 argues, the above approach to the identification of basic employment is likely to result in consistent overestimation. By assigning to the base sector all employment that is "sensitive," that is, correlated with national employment in the regression, the analysis will assign to the base sector local, non-basic employment that is statistically correlated with base employment and hence

22

Regional Economic Impact Analysis and Project Evaluation

with national employment. A portion of non-basic employment will thus be incorrectly assigned to the base sector, resulting in an overestimation of basic employment. This tendency toward an artificially large base sector may be exacerbated by recent secular growth trends among the various sectors of the economy. For example, in recent years employment in local government, a generally non-basic activity, has grown more rapidly than employment in basic activities. Regression equation (2.9) is therefore likely to mistakenly assign some of this growth in local employment to the export sector, since it will allocate to this sector employment which is simultaneously expanding in both the region and the nation. The Bracketing Approach

Since the above econometric approach to base analysis tends to overestimate basic employment in the region and, as previously argued, the location quotient approach tends to underestimate regional base employment, a bracketing approach has been proposed by Isserman12 which combines the two approaches to establish upper and lower bounds for the multiplier. Two principal problems arise with this approach. First, there is the problem of choosing a value for the multiplier between the two bounds. This is particularly troublesome if the difference between the two bounds is significant. That such may indeed be the case ca.n be seen from Isserman's empirical estimates of lower and upper bound multiplier values—1.18 and 3.54 for Washington, and 1.80 and 3.28 for Kansas. Although the upper and lower estimates for the base employment of individual sectors were not reported, the overall multiplier estimates clearly imply that the differences between the bounds for at least some sectors were substantial. A second problem which may arise is the possibility that the econometric analysis "lower" bound multiplier may for particular sectors exceed the location quotient "upper" bound value. Indeed, Isserman experienced this problem, and "Murphy's law" assures us that in practice such situations will continually arise. SUMMARY AND

CONCLUSIONS

The regional economic base model consists of two sectors: the "base," or "export," sector, which is comprised of economic activity whose ultimate market lies outside the region; and the "service," or "local," sector, which is composed of all other activity. According to the model, the sole engine of regional economic

Economic Base Analysis

23

growth is export activity, that is, the level of activity in the base sector. In addition to excluding from consideration potential sources of economic stimuli other than exports, the model's principal theoretical weaknesses are its assumptions of a constant ratio of service to total activity and sector homogeneity. The major practical difficulties of empirically implementing the model are associated with the tasks of choosing a unit of measurement for economic activity and of assigning activity to the base and service sectors. Alternative techniques adopted to accomplish this latter task include judgment, survey, location quotients, minimum requirements, and linear regression. While each has its advantages and disadvantages, the location quotient method is probably the most frequently employed. The base model is continually employed in regional analysis, despite widespread criticism of it in the literature on economic analysis (see, e.g., Lane 1966; Lewis 1976). In part this is because the model is structurally simple and inexpensive to construct. However, given its assumptions, the model as described above is most appropriately applied to analyses of short-run economic impacts on small-scale, single-export economies. CASE STUDIES

Case Study i: An Economic Base Study of a Nova Scotia Region

To illustrate the application of techniques of economic base identification, Schwartz13 in his discussion of regional multiplier estimation sets forth an economic base analysis of a hypothetical project to be located in Cape Breton County, Nova Scotia. To simplify the construction of the base employment multiplier, it was assumed that the labour supply for the project would be drawn entirely from the county, and that the project's suppliers of inputs were all located outside the county. The objective of the study was to assess the project's impact on employment in the county, which includes Sydney, the province's second largest city. Data for the county's experienced labour force by industry and by place of residence were obtained at the three-digit sic14 level from the 1971 census. These data were supplemented by published sources and telephone interviews. For the vast majority of industries the simple location quotient was used to distinguish base from service activity. However, several other approaches were also adopted. For example, in determin-

24

Regional Economic Impact Analysis and Project Evaluation

ing the basic labour force in the non-defence federal administration, it was argued that activity in this sector can be divided into three categories: the first consists of those services which the region would have to provide in the absence of the federal presence; the second, those services which are associated with the export commodities produced by the sector by virtue of the fact that the region may serve as a regional federal administrative centre); the third, those services associated with the injection of funds into the region on the basis of external political decisions. The author argues that while all three categories of federal administration in the region are supported by external sources of funds, the first category is dependent on local demand and is therefore more appropriately treated over the long run as non-basic. The problem is to separate it from the other two so that federal activity in the region can be divided into its basic and non-basic components. This involves adjusting the benchmark to include only the federal administration related to the local administration of federal programs. Since most federal administration related to the administration of federal programs is in the Ottawa-Hull metropolitan area, the national benchmark could be defined to exclude this area as well as the region, (ibid., 62)

The general form of the adjusted location quotient is (Ri/R) I [(N{ - Ri)/(N - R)]. It is generally employed when the region R is of significant size in relation to the nation N. In dealing with the labour force in the federal administration above, however, the author netted out the Ottawa-Hull metropolitan area as well as the region itself. Similarly, for provincial administration the provincial benchmark was apparently modified to exclude the capitol metropolitan area of Halifax as well as the Cape Breton region. The agricultural and forestry labour force was assigned on the basis of judgment. Under the presumption that primary activity is generally basic, all forestry activity was designated as basic. Given the small size of the region's agricultural sector, however, and its heavy concentration in dairy farms, it was judged that economic activity in this sector was tied primarily to local demand. In some sectors all employment was designated as basic due to the specialized nature of the sector. The Cape Breton fishing industry is such a case. The region is noted for its comparative advantage in fishing and is obviously heavily reliant on the export market. In this sector the standard location quotient approach is particularly unreliable because a large share of Canada's employment in the industry is directly linked to external markets. Where no regional em-

Economic Base Analysis

25

ployment was found in the designated sector (e.g., crude petroleum, asbestos mines, rubber, and plastics), the resident labour force was presumed to work outside the region and was hence designated as entirely basic. In other sectors (e.g., kindergarten, elementary and secondary schools, shoe repair, barber and beauty shops, and non-university education) the labour force was assigned entirely to the non-basic sector because the output of the sector was assumed to be consumed entirely in the region. Finally, unemployment in the region was estimated primarily on the basis of census data and, since unemployment benefits are deemed to originate outside the region, the unemployed were added to the estimate of employment in the basic sector. The resulting ratio of non-basic to basic employment for the county was 1.24. Assuming this ratio constant over the period of analysis, the base employment multiplier for the county was 2.24. That is, for every job created in the base sector, a total of 2.24 jobs were created in the regional economy. Case Study 2: A Regression Base Multiplier Model for Kentucky Counties

In their Kentucky study Smith et al.15 explicitly recognize that the "usual applications of base theory involve rather heroic assumptions," but argue that a regression approach such as the one constructed for this analysis involves fewer untested assumptions than does the customary base model built on a single, homogeneous export sector. The regression model employed is where TE = total regional (county) employment, E} = export (basic) employment in the ;th endogenous sector, and a0 is a constant. The sector export multipliers are a\,...,an. As formulated above, the regression model "implicitly assumes that the categories of basic employment (and income) included as independent variables are exhaustive of all possible sources of export income." The authors hold this assumption to be questionable and seek to improve the above regression base model by explicitly incorporating into the analysis consideration of commuting patterns and transfer payments. It is the authors' view that the pre-project residents of a region are the appropriate focus of concern in local public investment decisions pertaining to job creation programs. Given this view, it is argued that the base model will produce biased results when ap-

26

Regional Economic Impact Analysis and Project Evaluation

plied to projects which result in substantial flows of in- or outcommuting. For example, if basic employment increases by 100 jobs, half of which are absorbed by in-commuters (or former outcommuters), the unmodified regression model above will count all 100 jobs as additions to local base employment. If the pre-project residents are held to be the analyst's appropriate concern, then the. inclusion of increased in-commuting and diminished out-commuting as additions to local employment is unwarranted. In addition to a commuting pattern bias, a second potential shortcoming of customary economic base analyses, the authors argue, is the failure to allow for the employment impact of transfer payment income which is received in varying amounts as public welfare assistance, unemployment compensation, retirement and disability benefits, veterans' pensions, and the like. Such payments increase local spending and result in an expanded ratio of service to base employment. There is thus a measure of service employment in the economy which is not directly tied to the consumption spending of those employed in the base sector. The result is to bias the base multiplier estimate upward. A modified regression model was thus constructed which contains, in addition to the private-sector export industries, variables representing in-commuting, out-commuting, and transfer payments. 1970 census data for no non-metropolitan Kentucky counties were used to calibrate the model. The task of identifying export employment in the various counties was a relatively simple one since, in the authors' view, practically all extractive and manufacturing activity in the Kentucky rural communities is exclusively export-oriented. In the remaining sectors (e.g., construction; government; transportation, utilities, services, and finance; wholesale and retail trade) location quotients were applied. The authors lacked sufficient confidence in this base-identification technique, however, to interpret the resulting regression coefficients as multipliers. A partial list of the empirical results of the study are shown in Table i. From the income transfer regression coefficient or multiplier of 226.00 jobs per million dollars of transfers, it is assumed that on the average one job is created per $4,425 of income transfers (4,425 = 1,000,000 / 226). The authors note, however, that this result tends to be overstated, since the transfer payments identified do not include associated transfers of in-kind income such as food stamp and medicaid benefits. The coefficient for in-commuting is appropriately negative, since the in-commuter takes a job that would otherwise have gone to a

Economic Base Analysis

27

TABLE 1

Change in number of total jobs for county residents per added job in basic activity Agriculture Mining Heavy machinery (fabricated metals, non-electrical mach., & transport equipment) Light machinery (electrical mach., instruments, & related products) Food and kindred products Wood (lumber, wood furniture, and other wood products) Misc. manufacturing Transfer payments (jobs per million dollars) In-commuting Out-commuting

1.31 1.02 2.76 1.22 2.57 1.86 1.76 226.00 -0.65 0.87

Source: ibid., 19

local resident. (The effect of in-movers in the study was ignored for lack of data.) That the multiplier is -0.65 rather than -i.o leads the authors to conclude that the local spending of each in-commuter results in 0.35 of a job in the service sector. For out-commuting, the authors admit that the minimum rational value is i.o, since there can be no leakage of primary employment from this source. The coefficient of 0.87 obtained from the regression is thus judged to be "spuriously low." SELECTED

READINGS

Coffey, W.J. and M. Polese. 1987. "Trade and Location of Producer Services: A Canadian Perspective," Environment and Planning A, 19:597-611 Gibson, L.J. and M.A. Worden. 1981. "Estimating the Economic Base Multiplier: A Test of Alternative Procedures," Economic Geography, 57:146-59 Greytak, D. 1969. "A Statistical Analysis of Regional Export Estimation Techniques," Journal of Regional Science, 9:387-95 Isserman, A.M. 1977. "The Location Quotient Approach to Estimating Regional Economic Impacts," Journal of American Institute of Planners, 43:33-41 —. 1980. "Estimating Export Activity in a Regional Economy: A Theoretical and Empirical Analysis of Alternative Methods," International Review of Regional Science, 5:155-84

28

Regional Economic Impact Analysis and Project Evaluation

Lane, T. 1966. "The Urban Base Multiplier: An Evaluation of the State of the Art," Land Economics, 42:339-47 Lewis, W.C. 1976. "Export Base Theory and Multiplier Estimation: A Critique," Annals of Regional Science, 10:58-70 Moore, C.L. and M. Jacobsen. 1984. "Minimum Requirements and Regional Economics, 1980," Economic Geography, 60:217-24 Norcliffe, G.B. 1983. "Using Location Quotients to Estimate Economic Base and Trade Flows," Regional Studies, 17:161-8

CHAPTER THREE

Income-Expenditure Analysis

EXPOSITION OF THE MODEL

The Keynesian multiplier or income expenditure model offers an alternative approach to constructing an economic impact analysis appropriate to a small-scale regional economy. To illustrate a simple form of the model, let us imagine a small band of settlers who have established a self-sufficient commune in a relatively remote rural region. One of the inhabitants of the settlement decides to withdraw $1,000 from her savings in order to build a barn. By how much will the income of the settlement rise as a result of this investment expenditure? Assuming no government and a completely closed economy (i.e., no imports or exports), the resulting increase in local income will depend entirely on how the population of the settlement divides its newly received income between current consumption and savings. Let us assume that each member of the community is likely to save 20 per cent of any addition to his or her income. The marginal propensity of the community to save (the change in savings resulting from a change in income) is .2. The marginal propensity to consume in this case is i - .2 = .8. The carpenter who contracts to build the barn (and supply the lumber) will save $200 of his $1,000 fee and spend the remaining $800 locally on food, household goods, and the like. The recipients of this $800 of local expenditures will in turn collectively spend .8 x $800 or $640, and so on. Each time a dollar is spent in the community, the income of the recipient (and hence the income of the community) rises by precisely one dollar. The chain of increases in local income thus occurs

30

Regional Economic Impact Analysis and Project Evaluation

as $1,000 + 800 + 640 + 512 + 409.60 + . .. In mathematical terms this series of numbers is a "converging" series. That is,

We can now calculate the increase in local income resulting from the original $1,000 investment stimulus to the local economy as $1,000(1 + .8 + .82 + .83 + . . . + .8") = 1,000 x i/(i - .8) = $5,000. The multiplier in this case is seen to be i/(i - .8) = 5.0. In algebraic terms we might describe or "model" the above multiplier process by beginning with the equation which states that income Y is the sum of local consumption expenditures C and investment 7. Consumption in turn may be expressed as a linear function of income, where c0 is the autonomous portion of consumption (i.e., that portion of consumption which is independent of income—the level of consumption that would occur if income were zero) and c\ is the marginal propensity to spend (c\ = AC/AY). An increase in local income is divided between consumption and savings, as shown in Figure i.

Figure i Savings and consumption Assuming the flow of investment expenditures to be constant, substitution of (3.3) into (3.2) yields

From equation (3.4) the multiplier is seen to be i/(i- c\), identical to the sum of the converging series of (3.1). With a marginal propensity to consume of 0.8, the multiplier is again readily calculated to be 5.0. If either regional investment expenditures or autonomous consumption rises by $X, total regional income will correspondingly increase by $5X.

Income-Expenditure Analysis

3i

To move conceptually towards a more realistic regional economy, let us relax our assumptions of no government and a closed economy. Our illustrative local economy might now be conceived as a small resource community with a general store and a restaurant/bar which serves as the local entertainment centre. The local consumption pattern may be as shown in Figure 2.

Figure 2 Cash flows in a simple economy Twenty per cent of each additional dollar of local income goes to senior government taxes; 10 per cent is saved; 30 per cent is expended on goods and services purchased outside the regional economy; and 40 per cent is spent locally, divided between the general store and the restaurant/bar in the manner shown in Figure 2. To keep the example simple, taxes on businesses are ignored. Each dollar of new income is assumed to filter through the local economy according to Figure 2, subject to the various leakages as shown. The amount of income generated at the end of the first round of this "filtering process" can be determined from the Figure as 4[(.2 x .3) + (.8 x .1)] = .056, which is the r of equation (3.1), that is, the community's marginal propensity to spend locally. Assuming each succeeding round of spending from the local income generated from the wages and salaries paid by the general store and restaurant filters through the economy in the same fashion (i.e., that the marginal propensity to spend locally is constant), the multiplier is determined as i/(i - .056) = 1.06. This multiplier is substantially less than the self-sufficient settlement multiplier of 5.0, since in our second resource-community illustration the economy is open to trade and is linked with a senior level public sector.

32

Regional Economic Impact Analysis and Project Evaluation

In this latter case, the regional economy is subject to leakages of imports and taxes as well as savings. Algebraically, local income1 Y in the resource community can be defined as Disposable income Yd is that income left after income taxes are paid at rate t. Consumption is now defined as a linear function of disposable rather than gross income. Imports may be similarly treated as a linear function of disposable income. Substituting (3.8), (3.7), and (3.6) into (3.5), and simplifying,

The magnitude of the regional income multiplier, i/[i - (i - t)(ci mi)], is seen to be inversely dependent on the leakage rates, that is, the tax rate (t), and the marginal propensities to import (mi) and to save (i - Ci}. With the values given in Figure 2, the multiplier of equation (3.9) can again be shown to be i/[i - (i - .2)(.875 -.805)] - i/(i - .056) = 1.06, where Ci = AC/AYd - (.4 + .3)7(1 - .2) = .875 and ml = AM/AYd = .3 + 4(.2 x .7 + .8 x .9)7(1 - .2) = .805. Compared to the expression of equation (3.9), the regional income multiplier may of course become considerably more complex (as can be seen from several of the references at the end of this chapter), but the process for determining its form and magnitude is identical to that discussed above. One can elect to trace the money flows through and leakages from the regional economy as was done in Figures i and 2 to determine r. Alternatively, one can construct the multiplier in algebraic terms, as was done in equations (3.1) to (3.9). As shown above, given the same set of assumptions, the two approaches yield identical results. PRINCIPAL ASSUMPTIONS OF THE MODEL

There are at least four principal assumptions of the Keynesian income-expenditure analysis, as discussed in the preceding section. First, it is assumed that the coefficients of the multiplier, however formulated, are constant. Thus for the income multiplier of equation (3.9), it is assumed that the tax rate t, the propensity to

Income-Expenditure Analysis

33

consume c\, and the marginal propensity to import m\ are unchanged over the period of analysis. This is indeed a simplifying assumption, since there is substantial empirical evidence, primarily at the national level, to indicate that the values of these coefficients are dependent on the level of income. The constant-coefficients assumption further implies that the first-round pattern of expenditures is identical to that of succeeding rounds. Obviously this is not always the case. For example, the pattern of consumption expenditures from additional income accruing to, say, temporary residents in a construction camp in the region will likely differ from that resulting from additional income received by long-established residents in the region. Second, as is the case with the regional economic base model, it is assumed that each producing sector is homogeneous. That is, it is assumed that the product mix problem is negligible. As discussed in the preceding chapter, this assumption does not always hold in practice. For example, in the resource-community illustration of the previous section, it might well be that some of the items sold in the general store are made locally, while others are produced outside the region. A dollar of sales of externally produced commodities will have a smaller impact on local income than will a dollar of sales of locally made commodities, since the former involves greater leakages (imports). Third, it is assumed that there are no capacity constraints on the producing sectors of the model. Thus, the general store and restaurant/bar of the resource-community example meet the increased demands from additional income with increased production of goods and services rather than increases in prices resulting from an inability to expand short-run output. Fourth, in the examples discussed above it was assumed that interregional feedback is negligible. The data necessary to incorporate interregional feedback effects within the multiplier are difficult to obtain. This matter is discussed more fully in the following section. SOME PRACTICAL DIFFICULTIES Marginal and Average Propensities

Since regional impact analysis is generally applied to economic stimuli that result in additional income for local residents, it is appropriate in formulating a regional income multiplier to associate with the local residents marginal propensities of consumption,

34

Regional Economic Impact Analysis and Project Evaluation

savings, imports, and taxes. It is frequently the case, however, that data are available for only a single time period, or pertain to a geographical unit other than the region under study. Given the difficulty of constructing estimates of marginal propensities under these circumstances, it is common practice for analysts to adopt average rather than marginal propensities and to assume the differences to be negligible. One alternative to adopting average propensities is to make educated guesses of marginal propensities. Family expenditure data2 which yield rates of taxation, consumption, and savings for various income classes are useful for constructing such estimates. Although they are usually difficult to construct empirically, marginal propensities are theoretically appropriately associated with established local residents. For in-migrants, however, it is generally held that average propensities are relevant. This is because all spending in the community by an in-migrant is "new" spending. That is, the in-migrant's direct contribution to local spending is not the increment to his present spending level, as is the case with the established resident, but the entirety of his spending, since his previous expenditures in the community were zero. The local income impact is thus the in-migrant's average rather than his marginal propensity to spend locally. On this basis, Sinclair and Sutcliffe (1978) argue that at least in the first round of expenditures, in-migrants and locals should be distinguished in order to allow the appropriate propensities to be associated with each group. Unemployment

If a portion of the newly created positions resulting from the economic stimulus to the regional economy is taken by the formerly unemployed in the region, the loss of the flow of unemployment benefits into the region must be taken into account to avoid overstatement of the economic impact. In recognition of this circumstance, it is common for regional analysts to estimate coefficients representing an inverse relationship between a change in regional income and a change in monetary transfers to the unemployed. (Because of the possibility of variation of this relationship between regions, particularly due to variations in regional average earnings, it is advisable to avoid whenever possible the construction of estimates of such coefficients from national data.) It may be argued, however, that under particular conditions the

Income-Expenditure Analysis

35

assumption that changes in unemployment benefits are inversely proportional to changes in regional income may be inappropriate. If the jobs created by the stimulus are taken by in-migrants (and/or new local entrants into the labour force), regional income will rise, but unemployment benefits will decrease only to the extent that the local unemployed fill any spin-off positions in, for example, local supplying activities, trades, and services. To the extent that these latter jobs are also taken by in-migrants and new labour force entrants, there is little reason to anticipate a decrease in the flow of unemployment benefits to the region. Alternatively, if the newly created jobs are taken primarily by the region's unemployed, the estimation of the income multiplier by determining only unemployment benefits and average regional earnings may prove to be overly simplistic. The unemployed are likely to have propensities to consume and to import, rates of taxation and savings, and consumption patterns which are quite different from those of the rest of the regional population. Hence the multiplier effects attributable to the spending of the previously unemployed may differ significantly from those of the remainder of the regional population. Where the previously unemployed constitute a substantial portion of those newly employed by the stimulus, it may be appropriate to construct a distinct multiplier for the unemployed as a regional subgroup. This possibility is further discussed in the section entitled Modifications and Extensions. Induced Investment

If the nature of the economic stimulus under examination is such that substantial in-migration will result, it is likely that significant capital investment will be induced. In-migration frequently results from projects for which the requisite occupational skills within the region are in short supply; projects in regions with low rates of unemployment and underemployment; and particular cases such as secondary educational institutions, specialized housing projects, and certain recreational projects in which the stimulus by its very nature attracts consumers as in-migrants.3 Capital investment induced by in-migration will be provided both by the public sector in the form of expanded social infrastructure (e.g., schools, hospitals, streets, sewers) and by the private sector (housing and commercial expansion). As an alternative to attempting to include within the multiplier a coefficient for the marginal propensity to invest, and thus to create

36

Regional Economic Impact Analysis and Project Evaluation

a "super-multiplier" along the lines of Wilson (1968), one may choose to estimate the impact of induced investment by incorporating the induced component of investment into the multiplicand. (The multiplicand is that expression which when multiplied by the multiplier yields the impact estimate.) In his study of the impact of a university, Brownrigg (i973)4 found that the effect of incorporating into his analysis induced investment due to in-migration was to expand the conventional multiplicand by 20 per cent. Yannopoulos (1973) also considered the induced investment effects of in-migration within the multiplicand in his study of the regional impact of new office locations. As might be expected by the nature of an office compared to that of a university, the multiplicand in this case was expanded by only 9 per cent. However, Yannopoulos also considered the induced investment effects attributable to new office location linkages with other economic activities: "The entry of additional offices within the area will increase the demand for a host of services which are used as inputs to their production functions... Perhaps the most important factor here is that the additional demand for professional, financial, physical and business services which may lead to the enlargement of the local infrastructure of these services, will generate considerable external economies of proximity and will thus induce further office development in the town" (Yannopoulos 1973:37). The amount of induced investment for office construction was estimated to expand the original multiplicand, which consisted of the direct plus indirect (interindustry) components, by 39 per cent. Taken together then, the two components of induced investment increased the original multiplicand by almost half its original value. Several points emerge from consideration of induced investment in the regional impact analyses cited. First, induced investment effects of a significant magnitude are most likely to be associated with regional economic stimuli that result in substantial inmigration or in considerable satellite economic activity. In the former case, the induced investment (particularly public sector investment) is more likely to be a function of the expansion of population than of the increase in income. Second, the increase in regional income due to induced investment will generally be temporary and thus will not persist throughout the operational phase of the stimulus. Third, to the extent that the effects of induced investment considered by the regional analyst are indeed temporary, induced investment is more appropriately introduced into impact analysis via the multiplicand than the multiplier.5

Income-Expenditure Analysis37

Interregional Feedback As discussed in the previous chapter, if an economic stimulus in the form of increased exogenous spending arises in region A, the region's income will increase and so also will its imports from, say, region B. As region B's exports rise, its income will increase and so, possibly, will its imports from region A. The original stimulus to region A may thus lead via interregional trade linkages to a further stimulus to the region. While a number of explorations of interregional income interdependence, or feedback effects, based primarily on international trade theory, have been undertaken, Brown6 appears to be the first to estimate empirically the differences between regional income multipliers with and without interregional feedback effects. Working with a two-region model representing the developing areas (geographically, 1/5) of the UK and the rest of the UK respectively, Brown found that the income multiplier for the areas as a whole increased only marginally from 1.28 to 1.29 with the consideration of interregional feedback effects. On the other hand, Steele7 argues that the feedback effect is significant for a number of UK regions, particularly in the presence of a regional export surplus. It appears, however, that the differences between the two sets of results are attributable more to the differences in data used than to the formulations of the models.8 In general, the magnitude of the interregional feedback effects will be positively related to the region's share of national income, and inversely to the region's degree of self-sufficiency. For small regions, and in particular those which are geographically isolated, interregional feedback effects are generally not likely to be significant, particularly if the concern of the impact analyst is with a general measure of the region's economic activity rather than with one or more specific sectors. Employment Multipliers The employment multiplier associated with a particular regional economic stimulus is designed to yield an estimate of the total employment attributable to the stimulus per job or man-year of employment directly created. Employment multipliers can be derived from income multipliers by appropriately applying to the latter the increase in income necessary to create an additional unit of employment. Depending on the nature of the income multiplier, these employment/income ratios may be constructed for the sector stim-

38

Regional Economic Impact Analysis and Project Evaluation

ulated and the rest of the regional economy, for the first and subsequent rounds of expenditure, or for a range of economic sectors. Whatever the approach selected, it is generally assumed that the marginal and average employment/income ratios are equal. The simplest estimations of employment multipliers from income multipliers are those made under the assumption of no significant differences between the propensities to spend and the expenditure patterns of the employees in the sector directly stimulated and those in the rest of the economy. Assuming the sector directly stimulated to be sector i, an employment multiplier, Me, can be approximated from the income multiplier, My, as follows:

The first term in the equation represents the income generated in the local service sector (total income generated less one dollar of income in sector i) per dollar of income in sector i. The first term multiplied by the numerator of the second yields the number of dollars induced in the service sector by one job in sector i. This product divided by the denominator of the second term is an estimate of the employment generated in the local service sector by a job in sector i. Finally, the addition of one to the product of the first two terms is the addition of the job created in sector i to those generated in the service sector. The three terms thus represent total employment in the economy resulting from one new job created in sector i. As an example, suppose the income multiplier is 1.50, and that average wages in sector i and the commercial sector of the regional economy are $40,000 and $20,000 per person-year, respectively. A job created in sector i will thus result in an increased income of $60,000 (40,000 x 1.50) in the economy, $40,000 in sector i and $20,000 in the region's commercial sector. The $20,000 of income in the commercial sector roughly translates into one job. One job created in sector i thus results in two jobs created overall in the economy and hence an employment multiplier of 2.0. Alternatively, from the above equation the employment multiplier can be calculated as Me = (1.50 - i.o) (40,000/20,000) + i.o = 2.0. In a study9 of the impact of a steel mill on a region of 60,000 population, the average wage in the steel sector was found to be approximately three times that of the wage in the local service sector. This wage ratio was used to convert an income multiplier of 1.35 to an employment multiplier of 2.06, which states that total man-years of employment in the economy can be expected to slightly more than double for every man-year increase in the steel mill.

Income-Expenditure Analysis

39

In his study of the impact of the location of a pulp and paper mill in the Scottish Highlands, Grieg10 first estimated the employment increase in the region's forestry and transportation activities that result from the location of the mill. The previously constructed first- and subsequent-round income multipliers were converted to employment multipliers by dividing the first- and subsequentround income generated by the weighted average of income increases necessary to create an additional job in the private and public service sectors. Lower and upper ranges were determined and the employment multiplier was estimated to be 2.1 to 2.4. The same approach to multiplier conversion was adopted by Brownrigg (1973) in his study of the impact of the University of Stirling on a population base of just under 100,000.n The resulting employment multiplier was estimated to be within the range 1.9 to 2.5. McGuire (1983), adopting the multiplier approach formulated by Grieg and Brownrigg, assessed the local impacts of two nuclear establishments in Scotland. For the operational phase, the employment multipliers were within the range 1.2 to 1.7. EVALUATION OF THE MODEL

In common with the economic base model of the previous section, the income expenditure model is most appropriately applied to small-scale regional economies whose intersectoral relationships are sufficiently simplistic to be modelled without the gathering of substantial data. The two approaches to regional economic impact analysis are substitutable. Each is designed to facilitate the estimation of the amount of induced economic activity associated with a new or expanded activity within the local economy, as is shown in Figure 3. However, the income-expenditure approach to regional multiplier formulation offers a number of advantages over an economic base approach using employment data. First, income as a unit of measurement provides a more sensitive indicator of change in economic activity than does employment. Suppose, for example, that with an unaltered employment level, a regional export industry were to experience an increase in productivity. Since such increases generally result in higher wages, application of the incomeexpenditure multiplier model will appropriately reflect the increased income in the service sector resulting from the rise in productivity of the export sector. As earlier argued, such is not the case with the simple economic base model. Although an increase in service sector employment is likely to result from expanded consump-

4O

Regional Economic Impact Analysis and Project Evaluation

New economic activity

Economic base model

Income-expenditure model

Direct & indirect »• employment

Direct & indirect •• income

Employment multiplier

Income multiplier

Induced employment

Induced income

Total employment

Total income

Figure 3 The economic base and income-expenditure models tion expenditures, the relationship between consumer expenditures and service sector employment would first have to be established before appropriate changes could be made in the base multiplier through an adjustment in the base/service ratio. Also related to the unit of measurement is a definitional problem. A dollar of income is a relatively unambiguous concept. Difficulties arise, however, with the concept of employment, the customary unit of measurement of the economic base multiplier. It is difficult to calibrate the base model with a mixture of full-time, part-time, and seasonal employment data. Additionally, there is the problem of how to treat jobs associated with a wide range of wage rates. (In fairness to base analysis, however, it should again be noted that although the base model is customarily calibrated in terms of employment, there is nothing inherent in the model that requires the adoption of employment as the unit of measurement.) Second, the income-expenditure model offers a greater degree of flexibility in impact analysis. In addition to its application to changes in exports, the model can be applied with equal facility to changes in other components of gross regional product, such as household consumption, investment, and government spending. The model also readily lends itself to the analysis of import replacement. Third, in contrast with economic base analysis, the incomeexpenditure multiplier model can easily incorporate consumption patterns which deviate from the community average (e.g., those of commuters from outside the local economy and, possibly, in-migrants). In large measure the impacts resulting from such devia-

Income-Expenditure Analysis

41

tions can be estimated by distinguishing the first-round income effects as previously noted. This is particularly advantageous when one is attempting to estimate, as is discussed further in the section following, the impact of expenditures of transient construction workers on a regional economy or, say, those of tourists. Fourth, in the area of public finance there is a further relative advantage to the income expenditure model in that the fiscal operations of the local government can be explicitly treated in the model. Information regarding changes in flows of tax revenues, local government expenditures, or transfers from senior government agencies to the local government or to the local populace directly can be readily introduced into the analysis. (See Case study i at the end of this chapter.) Since in impact studies, the effect of a new economic activity on local finances is often an integral part of the analysis, the ready incorporation into the model of local government fiscal operations is a distinct advantage. In addition to the specification of intergovernmental transfers mentioned above, the explicit treatment of local government in the model both facilitates an analysis of the impact of an economic stimulus on local municipal finances, and assures that such a financial analysis will be consistent in its results with those of related income and employment analyses. Finally, there are obvious advantages to the greater elaboration of the economic structure of the local economy displayed by the multi-sector, diagrammatic version of the income-expenditure multiplier model (see, e.g., Figure 2) vis-a-vis that provided by the two-sector, economic base model. In addition to the general advantage of providing a more detailed overview of the operations of the local economy, the income-expenditure model explicitly details the spending leakages from the economy and thus reveals particular areas of potential stimulation to local income generation through import replacement. As a related point, the model also offers a greater potential for explicit accounting of the impacts of increased investment in particular sectors of the local economy. Such investment not only generates local income directly and indirectly, but is likely to affect the value of the multiplier by reducing to some degree one or more of the leakages associated with local consumption expenditures. In contrast to the base model, the income-expenditure model explicitly sets forth these leakages. In sum, the income-expenditure model significantly expands the scope of economic growth and development possibilities beyond that of export expansion.

42

Regional Economic Impact Analysis and Project Evaluation MODIFICATIONS AND EXTENSIONS

As implied by the flexibility in formulating the income-expenditure model, there exist a number of variations of the basic approach outlined here. In the first of the multiplier models to follow, an attempt is made to distinguish between the short and long run and to incorporate into the multiplier model the relationships between sectors of the local economy. In the second, it is argued that the local economic response to an external stimulus will vary with the economic sector to which the stimulus is applied; accordingly, an effort is made to distinguish economic sectors in order to produce not one but several income multipliers. In the third, several local income multipliers are estimated by disaggregating the economy not by economic activities, but by social cohorts. Intersectoral Flows Model

Tiebout12 has argued that for many regional economies all sectors except consumption can be assumed to be determined in the short run by forces other than local income. The following seven categories of final sales were considered as exogenous: private exports, exports to the federal government, local consumption, local business investment, local housing investment, local government investment, and local government operations. The total increase in local income resulting from an economic stimulus to the region was estimated as the total combined increase in the above spending categories (other than consumption) times the multiplier i/(i - cs), where c is the marginal propensity to consume locally and s is the income created per dollar of local consumption sales. In the long run (say, five to ten years or longer) several of the exogenous categories are considered to be functions of local income. In turn, the region's income is presumed to be determined by the levels of private sector exports and sales to the federal government. The appropriate multiplier now takes the form i/(i - Sc,s/) where c, is the marginal propensity of final sales category i to spend locally and Sf is the income created per dollar of sales in category i, where category i ranges over local consumption, the three categories of local investment, and local government operations. The multiplier thus becomes "i / {i - [(propensity to consume locally x income created per dollar of local consumption sales) -I- (propensity to invest in local business x income created per dollar of local business investment sales) + (propensity to invest in local housing x income

Income-Expenditure Analysis

43

created per dollar of housing sales) + (propensity to invest by local government x income created per dollar of local government investment) + (propensity to spend on current operations of local government x income created per dollar of local government current operations spending)]}" (ibid., 74). As can be seen from the components of the multiplier, the data requirements for this particular variant of the income-expenditure model are considerable. They are made even more so by Tiebout's attempt to include within the model a measure of the intersectoral transactions between producing sectors of the local economy. The model thus requires data pertaining to sales between producers. Because of this particular requirement the model has subsequently become known in the literature as a "rows only" input-output model. (The input-output model is the focus of the next chapter.) Differential Sector Multiplier Model

Brownrigg and Grieg13 use the income-expenditure approach to construct a set of differential sectoral multipliers. The authors explicitly recognize that the impact of tourist expenditures on a local regional economy will depend not only on the magnitude of these expenditures but, as well, upon which particular sectors of the local economy the expenditures are initially made. Hence, the multiplicand is disaggregated in order to analyse the differential effects of the various tourists' expenditures. It is argued that each sector will have its distinct set of leakages due to different patterns of local ownership and employment, different sales-purchase linkages with the rest of the local economy, and different patterns of imports of goods and services. The contribution to local income (AY) generated through tourist expenditures is estimated by the expression where L, is the addition to local value added by tourist expenditures in sector i of the local economy and k is the regional multiplier. The multiplicand L, is then disaggregated to analyse the differential effects of the various aspects of tourist expenditures. For example, for subsector s, the local value added, Ls, is given by the expression where £7 is tourist expenditure at establishment /. Aj is the proportion of the ;th establishment's turnover, which comprises wages, salaries, and profit, and B; is the proportion of the establishment's other input purchases; a;- is the proportion of establishment ;'s

44

Regional Economic Impact Analysis and Project Evaluation

wages, salaries, and profit retained in the region; fi, is the zth local input purchased by establishmentj; and -y,- is the local value added generated per dollar on input i purchased by establishment;'. This approach enables the analyst to construct a set of sectoral multipliers yielding the direct, indirect, and induced income effects without constructing a full-scale input-output transactions table. As can be seen from the above equations, however, the approach, like that of the Tiebout model, is quite data-demanding. Differential Demographic Cohort Model

In contrast to the Brownrigg and Grieg disaggregation of the local economy into various production components in order to construct differential sector multipliers, Davis14 disaggregates the local economy into different socio-demographic groups and estimates a distinct multiplier for each. For purposes of estimating the impact of a federal fisheries program on a sparsely populated coastal region, the regional population was divided into three groups: residents employed prior to the stimulus or program, residents previously unemployed, and in-migrants to the region. It was argued that among the three groups there would be significant differences in the impact on the local economy of a dollar received from employment under the program because of differences in the savings rates, local to non-local consumption ratios, and the pattern of local expenditures. The multiplier, kj, for the group, or cohort j, was defined in terms of the additional local income generated in the economy per dollar of income received by a member of the cohort /.

wh e for cohort;', w, = the average dollar of public assistance lost per dollar of wage/salary gained; Cj = the marginal propensity to consume locally of cohort j and the average propensity for inmigrants; and Sj = local income generated per dollar of consumption spending for cohort;'. The results were k\ = .078, k2 = .044, and k3 = .117, where the subscript i refers to the local residents employed prior to the stimulus, and subscripts 2 and 3 refer to the previously unemployed and in-migrants, respectively. Estimates of the corresponding employment multipliers were then derived from the income multipliers.

Income-Expenditure Analysis SUMMARY AND

45

CONCLUSIONS

Construction of regional income-expenditure multipliers can be undertaken in either diagrammatic or algebraic expressions. The structure of the particular multiplier developed depends on the relationships posited by the analyst between regional income and its components of consumption, investment, government spending, and exports. The principal assumptions of the analysis consist of constant coefficients and homogeneous sectors. In addition, the basic approach assumes the absence of capacity constraints and of interregional feedback. One of the primary difficulties in empirically developing an income-expenditure multiplier is the scarcity of data necessary to estimate the values of marginal rather than average propensities. Additional issues include the incorporation of interregional feedback, unemployment, and induced investment into the analysis and the conversion of income multipliers to employment multipliers. Compared to the economic base employment multiplier of the previous chapter, the income-expenditure approach arguably possesses the advantages of a more economically sensitive and unambiguous unit of measurement, and the potential for easier accounting of intergovernmental transfers and differing expenditure patterns of various socio-demographic cohorts within the community. Further, within the income-expenditure multiplier formulation it is generally easier to develop a more detailed overview of the economic flows within the community and to link income and employment impacts with studies of fiscal and socio-environmental effects. As was the case with the economic base model, there exist a number of approaches that modify or extend the basic incomeexpenditure model. CASE STUDIES

Case Study i: An Income-Expenditure Multiplier for a Newly Locating Firm

The purpose of this study15 was to formulate a regional multiplier which would serve to determine the impact of the location of a new firm on regional income. Income generation attributable to the enterprise was conceptually divided into three components:

46

Regional Economic Impact Analysis and Project Evaluation

direct income: local income associated with the firm itself; indirect income: the increase in income generated by firms (existing and new) which are linked through supply relationships with the new enterprise; and induced income: the local income generated by the consumption spending from the direct and indirect income generated by the enterprise.

Given estimates of the first two components of regional income, the multiplier is designed to yield an estimate of the third component. The proposed multiplier was derived from five basic equations. As a first step, it was assumed that consumption C of local commodities varies linearly with disposable income. where c0 is a constant, c\ is the marginal propensity to consume locally supplied commodities, and tn and fy are the non-local and local tax rates, respectively. Imports (M) were considered to be a function of the levels of local consumption and local government spending (G). where mc and mg are the marginal propensities to import of the local consumer goods sector and the local government, respectively. Local government spending is in turn functionally related to revenues raised from residential property taxes, business taxes, and senior government transfers (R). where tb is the business tax revenue as a proportion of regional disposable income. The flow (R) of public funds into the region from senior governments was assumed proportional to the population of the region in view of the fact that the major portion of funds transferred from the province to the municipalities were allocated on a per capita basis. Finally, it was assumed that population varies linearly with regional income. where p0 is a constant and pi is the marginal propensity for local population to increase with income. On the basis of equations (3.14) to (3-18) the local income multiplier can be written as

Income-Expenditure Analysis

47

Once there is an injection of new funds into the region by a newly locating firm and its associated suppliers, the multiplier provides a means for for estimating the total amount of income retained within the community after several rounds of local private and public expenditures. One of the features of the above multiplier is the explicit incorporation of the fiscal operations of the local government sector. The impact of a new firm on local public finances is often a principal concern of the community's public officials. Empirical estimations of the multiplier for the base year 1973 are 1.35 for Prince George, a metropolitan region of approximately 60,000 inhabitants; 1.24 for the northern BC coastal region of Kitimat, with an approximate population of 30,000; and 1.08 for Hat Creek, a rural region of about 4,000 residents. Case Study 2: The Local Economic Impact of Kent State University

Kent State University is located in the Ohio municipality of Kent, a community of approximately 28,000 people in 1970. The objective of this study16 was to obtain an estimate of the economic impact of the university on the Kent community. The estimation of the local income (value added) multiplier of the university as an economic sector was undertaken in two steps. First, the percentage of total university expenditures in each of fourteen major spending categories was determined. These percentages at were constructed directly from survey data. Second, estimates of the ratios fo, of payroll to sales in the local economy were made for each of the same fourteen categories. Payrolls in this case were used as a proxy for local value added. The net effect on the multiplier of the use of the payrolls proxy is not immediately evident. On the one hand, the adoption of only one component (wages and salaries) of value-added will result in an understatement of the multiplier (but less so for a non-profit institution than the customary commercial corporation). On the other hand, it is likely that a portion of the university payroll accrues to individuals residing outside the local community. A priori, it is difficult to judge which of the two opposing effects is the greater. Given estimates of «/ and b;, a total university spending of x dollars would generate b(«,j dollars of local value added in category i. The total dollar amount Z of first round spending in the local economy would thus be Dividing each side of equation (3.19) by x yields the proportion 2bj0,- of the first round spending which stays in the local economy.

48

Regional Economic Impact Analysis and Project Evaluation

Designating this proportion as m, the total local impact T on the local community is The local multiplier is thus i/(i-m).17 From the survey data pertaining to a, and bi an empirical estimate of this multiplier was determined as 1.09. As the authors point out, this multiplier was constructed on the assumption that the propensity to spend locally and the distribution of expenditures are the same for both the university and the service sector of the local community. If this assumption did not hold, and k represented the value for the service sector corresponding to m, the total local impact T of x dollars of expenditures by the university would be(3.21) and the local multiplier would be (i-fc + m)/(i-fc). If m < k, the multiplier would be greater than that [i/(i-m)] of equation (3.20); if m > k, the multiplier would be smaller. Differences in m and k can result from differences in average propensities to consume by university and local service sector personnel and by different expenditure patterns between the two. The authors hold the former to be the more important, and recalculate the multiplier under the extreme assumptions of zero and i.o average propensities to consume by the employees in the local service sector. The resulting multipliers are 1.08 and 1.10, respectively, and the authors conclude that any violation of their assumption that m = k is not significant. Finally, for purposes of comparison, the authors construct an economic base multiplier by adopting employment as the unit of measurement and using the unmodified location quotient approach to identify the economic base of the community. The resulting multiplier is 2.9. Since the location quotient approach is known to overstate the multiplier in the presence of cross-hauling, a modified approach is adopted in which all manufacturing employment is assumed to be basic. The multiplier yielded by this modified approach is 1.82. Given the difference in this case between the income multiplier (1.08) and the employment multiplier (1.82), a general warning is given against calculating one of the two multipliers and assuming the other is similar in magnitude.

Income-Expenditure Analysis

49

SELECTED READINGS

Haughton, G. 1987. "Constructing a Social Audit: Putting the Regional Multiplier into Practice," Town Planning Review, 58:255-64 Lewis, P.M. 1986. "The Economic Impact of the Operation and Closure of a Nuclear Power Station," Regional Studies, 20:425-32 McGuire, A. 1983. "The Regional Income and Employment Impacts of Nuclear Power Stations," Scottish Journal of Political Economy, 30:264-74 Sinclair, M.T. and C.M.S. Sutcliffe. 1978. "The First Round of the Keynesian Regional Income Multiplier," Scottish Journal of Political Economy, 25:177-86 Sinclair, M.T. and C.M.S. Sutcliffe. 1988. "The Estimation of Keynesian Income Multipliers at the Sub-National Level," Applied Economics, 20:1435-44 Wilson, J.H. 1977. "Impact Analysis and Multiplier Specification," Growth and Change, 8:42-6 Wilson, T. 1968. "The Regional Multiplier: A Critique." Oxford Economic Papers, 20:374-93 Yannopoulos, G. 1973. "Local Income Effects of Office Relocation," Regional Studies, 7:33-46 APPENDIX

Regional Income and Product measures On the national level in both Canada and the United States, the most prominent measure of economic activity is Gross Domestic Product (GDP).IS GDP may be measured over the year as the sum of all factor payments in the economy (i.e., as the aggregate of value added). Alternatively, GDP for the year may be determined as the dollar volume of final sales in the economy. The "final" sale of a commodity is a sale of a good or service which does not undergo any further processing within the economy. For example, a sale of flour to a local household is a final sale, while the sale of flour to a bakery in the economy would constitute an intermediate sale. The sale of building materials to a domestic construction firm is an intermediate sale; the sale of the materials to an external construction firm is a final sale. The regional counterpart of GDP is gross regional product, which may also be measured by either the value-added or final sales approach. The composition of the alternative measures, defined according to their national accounting counterparts, is shown in Table 2. Again, the two measures are merely alternative ways of measuring the same aggregate monetary flow and always yield the same numerical result.

50

Regional Economic Impact Analysis and Project Evaluation

TABLE 2

Gross regional product Value added Employee compensation Rental income Profits Net interest Depreciation charges Indirect business taxes

= Final sales Personal consumption expenditures Gross private investment Government purchases of goods & services Net exports

Employee compensation represents all payments to and on behalf of employees of firms in the region. The category includes wages and salaries, taxes withheld, social security, and pension fund contributions. Rental income is composed primarily of rents paid to regional residents plus the imputed rents of owner-occupied housing. Profits are the pre-tax net income of both incorporated and unincorporated enterprises in the region. Net interest is the interest payments received by regional residents less consumer interest payments. Depreciation, or capital consumption allowances, represents an estimate of the depletion of the region's capital stock during the accounting period, and indirect business taxes refers to all taxes which are not levied on income, such as excise taxes, customs duties, and property taxes. The second set of GRP components—the sales or expenditure components—are the familiar national accounting categories of final sales. Household consumption expenditures includes the purchases of locally supplied commodities (other than houses) by individuals in the region. The three principal components of gross private capital formation are new construction (including residential construction), equipment, and inventory expansion. The category of government purchases of goods and services includes government expenditures on both current and capital accounts but excludes transfer items such as unemployment compensation, social insurance, veteran's pensions, and interest payments on the basis that such payments do not directly contribute to current production. Net exports is simply the difference between exports and imports of goods and services. While gross regional product is the most commonly used measure of regional income in income expenditure analysis, there are in the literature references to other measures of income, most notably regional personal and disposable income. The relationship between the measures is shown in Table 3.

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51

TABLE 3 Measures of regional income Gross regional product less depreciation charges less indirect business taxes less corporate taxes and undistributed corporate profits plus government interest and other transfer payments equals regional personal income minus personal income taxes equals regional personal disposable income

Regional personal income is seen to be gross regional income less those factor payments that do not directly accrue to people as income, plus interest income and transfer payments such as unemployment compensation, welfare, and veterans' benefits. Regional disposable income is equal to regional personal income less income taxes, and is not be confused with "discretionary income," which is disposable income less fixed financial commitments (e.g., rent, utilities, and personal loans).

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CHAPTER FOUR

Input-Output Analysis

EXPOSITION OF THE MODEL

In 1973 Professor Wassily Leontief of Harvard University was awarded the Nobel prize in economics for his development of input-output (I-O) economics. As a direct result of Leontief's work, a number of detailed I-O models of the U.S. and Canadian national economies have been prepared. I-O models of numerous other national economies are now routinely prepared on an annual basis. At the subnational level the input-output approach has rapidly developed to become a cornerstone of regional economics (Miernyk 1967; Richardson 1972). A regional I-O model provides a sharply focused still-life picture of the regional economy. It reveals, as no other approach does, the ways in which the various sectors of the region's economy are meshed together and are linked to the potential sources of economic stimuli: the "final demands" of household consumption, private capital formation, government purchases, and exports. To a large extent the I-O model resolves "The dilemma of having to choose between the micro- and the macro-economic approach—that is, between inspecting individual trees and looking at the general outline of the forest... [the I-O model] describes the entire forest in terms of all the trees of which it is comprised."1 The number of sectors into which the regional economy is divided depends on several factors, including the purpose to which the model is to be put and the resources at the disposal of the analyst constructing the model. For example, an early I-O model of the metropolitan St. Louis region contains fewer than 30 sectors while an I-O model of greater Philadelphia possesses approximately 500.

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Regional Economic Impact Analysis and Project Evaluation

To gain a better understanding of the basic I-O model, let us focus our attention on the simple, hypothetical three-sector model of Table 4, keeping in mind that for practical purposes no analyst would set out to construct an I-O model of so few sectors, since at such a high degree of aggregation too much information regarding the structure of the economy would be lost. TABLE 4

Hypothetical interindustry transactions table ($ million) Ag

Man

Ser

C

I

G

E

Total

Ag Man Ser

10 20 5

5 30

5 25 10

10 5 35

5 5 5

10 5 10

25 10 5

70 100

Imp VA

5 30

15 40

Total

70

100

where Ag Man Ser C I

10

80

5 35 80

= agriculture = Manufacturing = Service = Consumption = Investment

G = government purchases E = exports Imp = imports VA = value added

Note that the production sectors in this model (in this case, agriculture, manufacturing, and services) encompass the entirety of economic activity in the region. In practice, I-O sectors are customarily defined in terms of standard industrial classification (SIC) codes,2 with the sector definitions covering the full range of the codes. Each sector in the model is represented as both a seller and a purchaser. Potentially, each sector buys inputs from, and sells its output to, each of the other sectors. It is from this double-entry accounting feature that the model derives the name "input-output." The transactions data in the I-O model, such as those of Table 4, represent the sales and purchases between sectors that occurred over a particular period, generally a calendar year. These data yield significant information for each sector's backward (purchases) and forward (sales) linkages with the rest of the economy. Reading along the row of, say, the manufacturing sector of the model in Table 4, we see that during the year for which the model was constructed, the manufacturing sector sold $20 million to agriculture (e.g., farm machinery), $30 million to manufacturing (e.g., frames from the metal fabricating industry to the auto industry), and $25 million to services (e.g., electronic computers).

Input-Output Analysis

55

In addition to these intermediate sales (sales of product which will undergo further processing within the region), manufacturing also made significant final sales (sales which will not undergo further processing within the region). The sector sold $5 million to households (e.g., autos), $5 million to investment (e.g., increased inventory, sales on capital account), $5 million to government (e.g., office equipment) and $10 million to exports (e.g., construction equipment to the rest of the country and to foreign countries). Total sales (intermediate plus final) of the manufacturing sector add up to $100 million. The rows reveal the sales distribution of each of the sectors, while the columns reveal the purchase patterns. Again looking at manufacturing, it can be seen that this sector purchased $5 million from agriculture (e.g., raw foodstuffs), $30 million from manufacturing (e.g., steel frames by the auto industry), $10 million from services (e.g., accounting services), $15 million from imports (e.g., forest products produced outside the region), and $40 million from value added (e.g., wages). Total inputs to manufacturing were $100 million, a figure identical to the total output of the sector. Total output (sales) is equal to total input (purchases) for each of the three sectors because of the following identity: Total sales revenue = total costs + profit For each productive sector the transactions data of Table 4 account for all sales revenue and costs and for the residual, balancing item of profits, which is part of value added. (As seen from the appendix, chapter 2, Value added is composed principally of wages and salaries, rents, profits, interest, and dividends.) In the above manner the input-output transactions table presents a snapshot of the structure of the economy, highlighting the interrelationships between the various sectors of the economy. Although this picture by itself adds significantly to our understanding of the workings of the economy, the usefulness of the I-O model extends considerably beyond this contribution. For purposes of impact analysis the model allows us to predict the effects throughout the economy of changes in the final demands for the output of any one sector. Suppose at the national level there is an increase in the demand for Chevrolets. To fill this order (or to replace inventories if the order is filled from existing stocks), General Motors will have to purchase the necessary inputs, which include steel, glass, and rubber. To deliver these particular inputs to GM, the steel sector will have to purchase inputs from the coal mining and iron ore mining sectors; the glass sector will have to increase its inputs from the stone &

56

Regional Economic Impact Analysis and Project Evaluation

clay and primary non-ferrous metals sectors, and the rubber sector must increase its purchases from the chemicals and fabricated metals sectors. (Of course, the I-O model would tell us that each sector affected by the initial GM order would require inputs of power, transportation, and warehousing, as well as a variety of other goods and services.) In turn, each of these sectors supporting the increased production of steel, glass, and rubber will have to buy a wide range of inputs, which will initiate further rounds of transactions between sectors. Added to these reverberations of intersectoral sales and purchases is the increased consumption of households, which results from the increased wage payments in the economy. Moreover, among the increased purchases by households may well be additional automobiles, which would initiate the particular chain reaction just described all over again. However, these reverberations or rounds of spending attributable to the original stimulus will eventually end because in each round portions of the money circulating will flow out from the economy as import purchases, savings, and taxes. In short, each purchase from a particular sector by a firm or by a final consumer initiates a chain reaction throughout the economy. What the input-output model does is to trace through the resulting maze of economic reverberations or interactions to show, when the rounds of spending have come to an end, what the increased output of each sector will be, given the initial increase in one of the final demand categories. (If final demand decreases, the I-O model will reveal the decreased output for the economy sector by sector.) To illustrate how the I-O approach performs the system analysis of a change in one of its sectors, let us look again at our hypothetical three-sector model. Let's assume that the government purchases of the output of the manufacturing sector increase by $10,000, and trace the effects on the sales of each of the three sectors of the regional economy. As a first step in the analysis, let us construct from the transactions table of Table 4 a table of direct purchases, as shown in Table 5. The table shows the percentage of total inputs purchased by each sector at the top of the columns from each sector at the left of the rows. Each column of coefficients is determined by dividing the first three elements in the corresponding column of the transactions table (Table 4) by the total input figure of that column. For example, the coefficients in the agriculture column were calculated as 10/70 = .14, 20/70 = .29 and 5/70 = .07. Each of these coefficients shows the amount of input required from the row sector to enable the column

Input-Output Analysis

57

TABLE 5

Direct purchases per dollar of total output

Ag. Man. Ser.

Ag.

Man.

Ser.

.14 .29 .07

.05 .30 .10

.06 .31 .12

sector to produce a dollar of output. Hence, on the average, manufacturing requires five cents of inputs from agriculture for every dollar of output produced. The coefficients in each column together represent the "recipe" for each column sector's output.3 If we make the critical assumption that these recipes do not change over the period of analysis (a point to which we shall later return), we can perform the systems analysis described above, which reveals the accumulated effect on each sector of a stimulus (positive or negative) to any one of the sectors. In our illustrative case of a $10,000 increase in government purchases of output from manufacturing, the table of direct purchases of Table 5 reveals that in order to expand its production by $10,000, the manufacturing sector will have to purchase $500 of inputs from agriculture, $3,000 of inputs from manufacturing activities, and $1,000 of services. In turn, each of these sectors will have to purchase inputs in order to deliver the supporting production to the manufacturing sector. Again, from the table of direct purchases, these purchases are as follows:

AgMan. Ser.

Ag.:$5oo

Man.:$3,ooo

Ser.:$i,ooo

Total

50o(.i4) = !$ 70 50o(.29) = 145 50o(.07) = 35

3,ooo(.05) = $150 3,ooo(.3o) = 900 3,ooo(.io) = 300

i,ooo(.o6) = $ 60 i,ooo(.3i) = 310 1,OOO(.12) = 120

$280 i,355 455

In the above second round of spending, it can be seen that the total increases in production for the three sectors of agriculture, manufacturing, and services are $280, $1,355 and $455, respectively. These production increases will cause a third round of spending as follows: These rounds of spending will continue with each round becoming increasingly weaker in its impact because of the leakages from the local respending process attributable to imports, savings, and taxes. The total increase in sales for each sector resulting from the

58

AgMan. Ser.

Regional Economic Impact Analysis and Project Evaluation

Ag.:$28o

Man.:$i355

Ser.:$455

Total

28o(.i4)= $39.20 28o(.29) = 81.20 28o(.07) = 19.60

i/355(-05) = $ 67.75 i/355(-•30) = 406.50 i/355( .10) = 135.50

455(.o6)= :$ 27.30 455(-3i) = 141..05 455(-!2) = 54 .60

$134-25 628. 75 209,.70

initial stimulus to the manufacturing sector of $10,000 in government purchases can be estimated from the model by summing the increases in sector sales in each round: Ag.: Man.: Ser.:

$500 + 280 + 134.25 + ... = $ 1,000 $10,000 + 3,000 + 1,355 + 628.75 + • • • = $15,500 $1,000 + 455 + 209.70 + ... = $ 1,900

Although the approach is straightforward, it is a tedious and time-consuming one, but one which the computer does quickly and efficiently. With the aid of a computer-generated matrix inversion, as described in Appendix i to this chapter, a table of total requirements can be constructed. From this table we may read directly the total (direct plus indirect) impact on each sector of a unit change in the final demand for any one particular sector. The table of total requirements for our hypothetical example is shown in Table 6. TABLE 6

Direct plus indirect purchases per dollar of final demands

Ag. Man. Ser.

Ag.

Man.

Ser.

1.21 o.io 0.12

0.57 1.55 0.60

0.16 0.19 1.22

Reading across the manufacturing row of the table, we may note that for a one-dollar increase in the final demands for manufacturing, agriculture's sales increase by $0.10, manufacturing sales increase by $1.55, and sales by the service sector increase by $0.19. To ascertain the impact on the economy sector by sector of a $10,000 increase in the final demands for manufacturing, we have only to multiply the figures in the manufacturing row of this table by $10,000.

Input-Output Analysis

59

The Closed I-O Model

The open I-O model described above traces the increased flow of commodities between sectors in the regional economy which results from increases in final demands. However, the open model does not take into account the increased spending in the economy via the consumption expenditures of households. In short, the open I-O model considers only intersector sales/purchases linkages within the regional economy and ignores consumption linkages. This particular characteristic of the open I-O model immediately distinguishes it from the previously discussed economic base and income-expenditure models in that the latter two approaches explicitly account for the induced or consumer respending effect and ignore the indirect or intersector sales/purchases linkage effect. In the base and expenditure models the indirect effect must be determined exogenously, that is, outside the model. The induced effect is incorporated into the I-O model's results by "closing" the model with respect to the household sector. That is, the household sector is brought into the endogenous transactions matrix as a column from the exogenous final demands, and the personal income portion of the value-added row is incorporated into the transactions matrix as an additional row. The household sector is now treated as a producing sector, selling its "product," labour, to other producing sectors and to final demands, and purchasing "inputs" from other sectors in order to maintain the flow of its product. At this point an objection might be raised. Households don't buy directly from most other sectors; the vast bulk of household purchases are made from the retail trade sector. This objection might be extended to the other producing sectors as well, since many firms make the bulk of their purchases not directly from the producers of the commodities but from wholesalers. However, to uncover the actual structural linkages between the various sectors in the regional economy, and at the same time to avoid doublecounting the value added by the trade sectors, only the mark-ups or value-added margins are included in the entries in the wholesale and retail trade rows of the transactions table. Having closed our model with respect to ho seholds in order to incorporate into each sectoral multiplier the induced as well as the indirect effects, we may return to our hypothetical model, which has now been expanded to four sectors. The new, four-sector direct purchases table appears as Table 7. It can readily be seen that the Table is merely the table of direct purchases of the three-sector,

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Regional Economic Impact Analysis and Project Evaluation

"open" model (see Table 8) augmented by the household row and column. TABLE 7

Direct purchases per dollar of total output (closed I-O model)

AgMan. Ser. H.H.

Ag-

Man.

Ser.

HH.

.14 .29 .07 .14

.05 .30 .10 •25

.06 •3i

•15 .08 •54 .00

.12 .38

If again we consider the economic impact on the region of a $10,000 increase in final demands for manufacturing, the direct impact will now be estimated as: Man.: $10,000 10,000 10,000 10,000 10,000

AgMan. Ser. H.H.

x .05 = x .30 = x .10 = x .25 =

$ 500 3,000 1,000

2,500

Again, to produce the supporting output, each of the four sectors will require the following inputs: Ag.: $500

Ag. Man Ser. H.H.

AgMan. Ser. H.H.

5oo(.i4) 50o(.29) 50o(.o7) 50o(.i4)

= :$ 70 = H5 = 35 = 70

Man.: $3000 30oo(.o5) 30oo(.3o) 3ooo(.io) 30oo(.25)

= = = =

Ser.: $1000

H.H.: $2500

iooo(.o6) = $ 60 iooo(.3i) = 310

250o(.i5) = !$ 375 250o(.o8) = 200 2500054) = 1350

120 iooo(.38) = 380 10OO(.12) =

2500(.OO) =

$150 900 300 750 Total

oo

$ 655 1555

1805 12OO

Input-Output Analysis

61

These requirements will lead to a third round of spending, and so on. Comparing the successive rounds of spending as shown below for the closed version of the I-O model with the previous rounds of spending associated with the open version, it is clear that the estimates of the total impact on each sector have now been expanded by household purchases, that is, the induced impact. If we were to sum each successive round of spending, the new total increases (to the nearest $100) would be Ag.: Man.: Ser.: H.H.:

$ 500 + 655 + 457.75 + $10,000 + 3000 + 1555 + 1312.00 + $1000 + 1805 + 1065.95 + $2500 + 1200 + 1166.35 +

• • • = $ 3/2oo .. . = $19,900 • • • = $ 7/700 • • • = $ 8,300

If the table of total (direct + indirect + induced) requirements of our closed or expanded model were to be constructed by the mathematical process described in Appendix i, it would appear as shown in Table 8. TABLE 8

Total requirements per dollar of final demands (closed I-O model)

AgMan. Ser. H.H.

Ag.

Man.

Ser.

H.H.

1.38 0.32 0.41 0.46

0.92 1.99 1.17 0.93

0.62 0.77 1.99

0.66

1.22

0.83 1.1O

1.76

Reading along the manufacturing row, we see that if the final demands for the output of the manufacturing sector were to increase by one dollar, the estimated sales impacts on the agriculture, manufacturing and services sectors would be, respectively, $0.32, $1.99 and $0.77. Further, the resulting generation of regional household income is $0.83. The closed I-O model yields both the sales and income impacts on the regional economy of a final demand increase in any one of the three productive sectors. Because of the relative importance of the induced impact component in regional economic analysis, the closed version of the I-O model is generally preferable to the open version.

62

Regional Economic Impact Analysis and Project Evaluation

As a final point in this section, note that the model was closed only with respect to households. Additionally, the local government portion of the final demand sectors might be similarly incorporated into the transactions matrix, since the expenditures of this economic agent are in most cases entirely local and closely related in volume to the local revenue raised. Closing the model with respect to local government would be accomplished by the transfer into the processing matrix of the transactions table of the column of local government purchases from final demands and the row of local government taxes from value added. PRINCIPAL

A S S U M P T I O N SO F T H E M O D E L

The assumption generally considered to be the most crucial of the model is that of fixed direct purchase coefficients. The proportions in which each sector purchases its inputs from all other sectors are assumed to be invariant over the period of analysis. There are, however, a number of reasons why this particular assumption may not hold in reality. A fixed pattern of inputs implies unchanged technology. Any technological advances in a particular sector will likely alter both the proportions and kinds of inputs that are combined to produce the sector's output. Second, the proportions of inputs may be altered by changes in the relative prices of the various inputs. If, for example, steel becomes increasingly expensive relative to aluminum, any activity which purchased steel as an input in the past may now consider using aluminum as a substitute. A third source of change in the I-O direct purchases coefficients can be found in the model's organization and classification of data. If a sector includes heterogeneous activities, shifts in the proportions of these activities over time will adversely affect the accuracy of the coefficients. For example, suppose the model contains a sector labelled "marine construction," which includes the construction of both small pleasure craft and ocean-going ships. Obviously the two activities will have significantly different input patterns. The input pattern of the single sector marine construction will be a weighted average of the two activities. If these two activities expand over time at different rates, this weighted average, and thus the input pattern of the marine construction sector, will be altered. Finally, the direct purchases coefficients of the model may be changed by the location of a new firm in the region. A new firm of significant size will alter the coefficient matrix by changing the in-

Input-Output Analysis

63

put proportions of the sector into which it is introduced. The death or out-migration of a firm of significant size will similarly alter the coefficient matrix. As was the case with variations in the growth rates of activities aggregated into a single sector, the entry or exit of a firm of significant size will alter the weighted average input pattern of the relevant sector. A second major assumption of the I-O model is that of linearity. All inputs into a particular sector are assumed to be proportional to the output of that sector. With such a fixed, linear production function, an x per cent increase (decrease) in the output of any sector i will necessitate an x per cent increase (decrease) in each of the sector's inputs. Such an assumption rules out internal economies of scale in which an x per cent increase in output necessitates less than an x per cent increase in at least one input. It further excludes external economies in which the firm's unit costs are lowered not through changes in the volume of its output, but by the actions of other firms. For example, firm B might experience an external economy in the following way: Suppose firm A, a supplier to firm B, experiences significant economies of scale because of expanding output and lowers the price of its product. The production costs of firm B have now been lowered through no action of its own. Accounting for such external economies within the I-O model is precluded by the linearity assumption. Similarly precluded by this assumption is the existence of discontinuities, threshold effects, irreversibilities, and other violations of smooth linear functions. The third major assumption of the I-O model has already been touched upon. It is the assumption of homogeneous sectors. The model assumes that an $x increase (decrease) in the final demands for sector i will always have the same impact on the economy. However, given that for practical purposes many, if not all, sectors in the model are an aggregate of heterogeneous activities with different input patterns, such an assumption will be violated in varying degrees in reality. To return to the marine construction sector, an $x increase in demand for pleasure craft will not have the same impact on the economy as will an $x increase in shipbuilding. To the greatest extent possible, the model is designed to aggregate activities of similar input patterns to minimize errors of this kind. Finally, in the closed version of the model there is the assumption of a household consumption function that is linear and homogeneous to the first degree. That is, it is assumed that the marginal propensity to consume is equal to the average. As was discussed in the preceding chapter on income-expenditure analysis, regional

64

Regional Economic Impact Analysis and Project Evaluation

data necessary for the construction of localized consumption functions are difficult to obtain. (However, there are a number of empirical studies on the national scale which show that the MFC is less than the APC.) SOME PRACTICAL DIFFICULTIES

The construction of a regional I-O model may proceed from the bottom up or from the top down.4 There are practical difficulties associated with each. If the bottom-up approach is adopted and primary data are gathered via a survey, there are several potential problems in the interpretation of the data collected. Fundamental among these problems are conflicts between responses from buyers and sellers regarding the same set of transactions. For example, firm A may report that during the given year it sold $x to firm B. Firm B, on the other hand, may state that within the same period it purchased from firm A $y. The analyst is essentially left to his judgment as to which report is the more reliable. In other cases the firm surveyed may sell its output to, or purchase inputs from, a wholesaler and may thus be somewhat uncertain of the final destination of its production or of the origin of several of its inputs. Difficulties can also arise in distinguishing between current and capital transactions. Current, or non-capital, commodities are those which are consumed within one year of purchase, while capital goods are those with economic lives in excess of one year. Capital goods produced in the base year and sold to business users are not entered into the processing matrix but appear in the final demand category, investment. Capital goods may also be exported, placed in inventory, or sold to the public sector. Care must be taken in designing and conducting the survey to distinguish capital transactions and to record the appropriate final demand destinations. Another difficulty that arises in the construction of a regional I-O table from primary data is the treatment of secondary products. Each firm in the economy is placed in an I-O sector according to its primary product. However, a firm may produce subsidiary or secondary products which are not appropriate to its sector classification. For example, in addition to its principal product, a manufacturing firm may produce and sell electrical energy. Within the I-O model a secondary product may be treated as being sold from the producing industry to the sector for which the product is primary, or the product may be essentially redefined as part of the output of

Input-Output Analysis

65

the appropriate sector. In the latter case, the secondary production is subtracted from the total output of the industry which produced it and added to the output of the sector for which the production is the principal activity.5 If the collection of primary data is foregone in favor of constructing the regional I-O model from the top down by modifying national I-O coefficients, a new set of difficulties must be faced. These difficulties or problems center around the "regionalization" of the coefficients. How can the national coefficients best be adjusted to reflect the economic structure of the regional economy? I-O analysts are continuously investigating methods of coefficient modification in order to lessen or avoid the costs of primary data collection.6 EVALUATION OF THE MODEL

Compared with economic base and income-expenditure analysis, the I-O model offers considerable advantages. As did incomeexpenditure analysis, I-O analysis represents a significant improvement over economic base in that it explicitly recognizes as sources of economic growth and decline not only exports but personal consumption, capital formation, and government spending.7 Unlike income-expenditure analysis, however, the I-O model disaggregates each of these exogenous determinants among the producing sectors of the model. Since the I-O model is designed to represent transactions between producers as well as those between producers and final demands, the model affords the impact analyst considerably more detail regarding the economy than either of the two previous models. Instead of producing a single aggregate multiplier for the economy, the I-O model yields a multiplier for each of the producing sectors represented in the model. Further, because of the model's incorporation of producer-to-producer transactions, the indirect effect is determined by the model in each multiplier calculation. In the base and income-expenditure models, any indirect effect must be calculated outside the model as part of the change in exogenous demands. In common with the two previous models, however, the I-O model suffers from the limitations of constant coefficients, linear relationships, sector homogeneity and the absence of capacity constraints. Each of the entries in the model's direct purchases coefficients matrix is taken to be unchanged over the period of analysis.

66

Regional Economic Impact Analysis and Project Evaluation

It is thus assumed that within this period there are no shifts in the pattern of input purchases due to changes in technology, the relative prices of inputs, product mix, or the configuration of producing units within the economy. Since the I-O model is fundamentally a set of simultaneous linear equations, it does not readily incorporate non-linear relationships such as economies of scale or external economies. Such phenomena, if incorporated at all, must be done so in a piece-wise linear fashion. Additionally, the I-O model suffers, as do the base and incomeexpenditure models, from sector homogeneity, although to a considerably lesser degree. The I-O model avoids the failure of the base and expenditure models to distinguish explicitly between producing sectors in the exogenous final demand categories. Nevertheless, because its costs of construction are more than proportional to the number of sectors represented, the model is not entirely free from product-mix problems resulting from sector aggregation. Overall, the regional I-O model is a substantial theoretical improvement over the base and income-expenditure models, but the advantages in theory are not without their associated costs in practice. The I-O model is relatively data demanding. If surveys to establish primary data are necessary, the model can take up to several months to construct and can be considerably costly in dollars as well as time. Because of the richness (and cost) of the detail yielded by the I-O model, applications of the models are generally limited to economies with a substantial degree of economic complexity as measured by the interrelationships between producing units within the economy. For the most part the I-O model is not competitive with the base and income-expenditure models. As discussed in previous chapters, the latter models are appropriately applied to relatively small-scale resource regions; the I-O model is most relevant to the more diversified economies of metropolitan regions. MODIFICATIONS AND

EXTENSIONS

The literature on regional science and economics is rich in modifications and extensions of the basic input-output model discussed above.8 In the text that follows, examples are given of studies which illustrate, respectively, the development of specialized I-O coefficients; attempts to reduce the costs of constructing regional I-O models; and the incorporation of I-O information into the construction of income-expenditure multipliers.

Input-Output Analysis67

An Input-Output Analysis of Air Pollution As was shown in this chapter, I-O multipliers derived directly from the table of total requirements are measured in dollars of sales. It was also shown that for the closed version of the model, one can obtain income multipliers from the table. In addition, employment multipliers can be constructed by converting the change in sales of each producing sector into the corresponding change in employment by application of the sector's ratio of employment to sales. Multipliers and impacts using other units of measurement can be similarly constructed. For example, in their study of air pollution in California, Davis and Lofting9 devised I-O multipliers for suspended particulates, sulfur oxides, nitrogen oxides, hydrocarbons, and carbon monoxide. The multipliers are measured in tons of pollutant emission per million dollars of sales. An objective of the study was to compare the amount of air pollution resulting directly and indirectly from service activities with that produced by manufacturing activities. When input-output analysis was employed to look at the indirect pollutant impacts as well as the direct impacts, it was found that in several cases service activities did not pollute significantly less than many industrial activities. The results varied with the selection of the individual service activity, the particular pollutant, and the California regional air basin. To the extent that a general pattern emerged, it was found, as might be expected, that the transportation and utilities sector constitutes the major emittor of pollutants per dollar of final sales, followed by manufacturing and all other services. Short-Cut Method of Estimating Regional I-O Multipliers Because of the considerable costs of constructing regional I-O models from primary data, a great deal of attention among I-O analysts has been directed to means of reducing these costs. One such method, suggested by Drake,10 focuses on the use of existing national and regional input-output models. The first step in this shortcut methodology is to estimate the direct-effect component by regionalizing u.s. national I-O direct purchases coefficients. This is done in two steps. First, for each regional sector, the u.s. County Business Patterns (CBP) four-digit sic county data are utilized. When a particular four-digit input is required at the national level but is shown by CBP data not to be produced locally, that input is

68

Regional Economic Impact Analysis and Project Evaluation

deleted from the column of direct coefficients. Second, the edited column is further reduced, where appropriate, by application of the location quotient method, by which arij = anij LQ, where LQ, < i.o where ar^ and an^ are the matrices of direct input coefficients of the regional and national I-O models, respectively. Secondary impact components—the direct component (for open models) and the indirect plus induced components (for closed models)—are then predicted from regression analysis, using a sample of seventeen regional I-O models as a source of observations. For both the open and closed models the secondary components were regressed upon the direct component, the size of the economy relative to the u.s. economy (as measured by total nongovernmental earnings), and the agricultural and manufacturing proportions of total non-governmental earnings in the region. The tests for accuracy of this approach are encouraging and provide the analyst in need of "ballpark" estimates of I-O sector multipliers with a computerized procedure for obtaining such results. Income-Expenditure Multipliers Incorporating I-O Analysis

In an effort to estimate the regional economic impacts of the wage and salary expenditures of public- and private-sector employers in British Columbia, Davis11 constructed a set of income and employment multipliers for each of seven different regions in the province. The seven regions were an aggregation of the province's twenty-nine regional districts delineated by the BC government for purposes of regional economic analysis. Income multipliers were constructed by first estimating for each region marginal rates of taxation, savings, consumption, and imports. An attempt was made to incorporate explicitly into each income multiplier an indirect impact component by utilizing an existing input-output model of the most populous region (the Vancouver metropolitan region) of the province. For each sector considered in a particular region, the indirect effect was estimated as a proportion of the indirect effect produced by the corresponding sector in the Vancouver region. The proportion adopted was the ratio of total employment in the region to that in Vancouver on the assumption that the complexity of the regional economy (and thus the size of the indirect income effect generated) is roughly proportional to the region's total employment. Income multipliers were defined as total local value added per dollar of wage and salary. Estimates of the seven multipliers

Input-Output Analysis

69

ranged from 1.19 for the Cariboo region, a relatively sparsely settled region in the provincial interior, to 1.49 for the Lower Mainland, which is composed largely of metropolitan Vancouver. Employment multipliers were derived from the income multipliers and were designed to reveal the person-years of employment per million dollars of wages and salaries. The estimates ranged from 44.8 for the Cariboo region to 54.5 for the Lower Mainland. SUMMARY AND

CONCLUSIONS

Like economic base and income-expenditure analyses, standard input-output analysis is based on a demand-oriented model of Keynesian heritage.12 However, unlike the former two impact models, each of which is generally composed of a single equation, the I-O model is a set of linear simultaneous equations equal in number to the model's producing sectors, as determined by the analyst. Although the number of sectors varies considerably from one model to the next, a typical regional I-O model might consist of twenty-five to forty. Once the set of equations is solved via matrix inversion, it is then possible for the analyst to estimate the output or sales impact on the regional economy, sector by sector, of a stimulus to any one of the sectors. Further, in contrast to the two previous models, each of which yields a single overall multiplier for the economy, the I-O model yields an individual multiplier for each sector represented. The I-O model explicitly takes into account not only the relationships between producers in the economy, but also those between producers and consumers. Thus, for example, if a regional steelproducing sector receives a stimulus to sales, the model estimates the increase in sales of the suppliers to the steel sector, the suppliers to the suppliers, and so on; as well, it estimates increases in local sales in each sector attributable to the increased wages and salaries resulting from the increased economic activity in the region. For all its advantages in representing the highly interdependent metropolitan economy, the I-O model has serious weaknesses. The model is based exclusively on linear economic relationships and the dollar volume of inputs to any sector is directly proportional to the output of that sector. The model thus assumes away externalities, and increasing returns to scale. Unfortunately, metropolitan economies are often characterized by precisely these elements. The most notorious shortcoming of the model, however, is the assumption of unchanged input coefficients, which implies that

70

Regional Economic Impact Analysis and Project Evaluation

the proportions of inputs to produce a dollar of output in any sector are unaltered over time. In reality, however, such proportions are changed, for example, by technological progress and by changes in the relative prices of substitutable inputs. In addition to these theoretical shortcomings, the I-O model is both expensive and time-consuming to construct. Yet for complex metropolitan economies it is commonly considered to be the most powerful tool of economic impact analysis available. Furthermore, its richness of applications has long made it a cornerstone of regional economics. CASE STUDIES

Case Study i: An Input-Output Model of Metropolitan Vancouver

The Vancouver Census Metropolitan Area (CMA) serves as the basis for this study.13 Geographically, the area of the Vancouver CMA is less than .2 of i per cent of that of the Province of British Columbia. However, the metropolitan area, Canada's third most populous, contained approximately 45 per cent of EC'S 1971 population of 2.3 million. The base year of 1971 was selected because it was the year of the most recent census data. Questionnaires were sent to major employers in the region and to a random sampling of smaller business establishments. 332 usable returns were received, which represented approximately 26 per cent of the total non-government employment in the region. The data collected from this survey were used to construct the final demands, final payments, gross outputs and interindustry transactions. However, for the trade and transport sector, which relies upon gross margins, modified national coefficients from the unpublished 1966 national table were adopted. All transactions were recorded in producers' prices. The transactions table for the Vancouver region is shown in Table 9. The model was aggregated from the original twenty-seven sectors used in the construction process to the eighteen sectors shown in the table. There are seven final demand sectors, of which four are export sectors, and three final payment sectors. The importance of service activities to the metropolitan economy is immediately obvious from the table. Of the gross regional product of $5.3 billion, the service activities (sectors 11-18) contributed 64 per cent in terms of value added. They also accounted for 71 per cent of the region's total employment and a surprising 50 per cent of the region's exports. A little more than half of the Vancouver

Input-Output Analysis

7i

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices)

Sector i Agriculture, forestry, fishing, & mining 2 Construction

1 795

1,920

4

3

2

5

304

12,923

0

o

592

243

258

205

3 Food & beverages

824

O

20,935

i

4 Wood industries

21,909

505

2

230

17,408

o

5 Paper & allied products

29

2

19,523

223

19,497

6 Chemicals & petroleum

1,013

329

1,085

2,364

2,689

7i

20,070

11,705

112

O

116

12,558

19,824

2,132

451

712

76

231

7 Non-metallic products 8 Metal fabricating 9 Printing & publishing

369

347

10 Manufacturing, n.e.c.

1,585

5,022

468

103

639

11 Trade & transport

L389

10,647

10,385

4,173

3,716

12 Communications

451

2,339

932

1,562

558

1,221

1,642

5,886

3,229

2,730

755

n,255

2,710

2,788

3,3«

19

o

9

O

O

16 Education

129

42

421

250 7,590

693

17 Business services

1,400

3,372

484

232

1,838

13 Utilities 14 Finance, insurance, & real estate 15 Health & welfare

18 Other services

31

Total intermediate purchases

11,368

90,839

109,680

44,129

Imports

18,744

93,680

172,598

140,771

8,651

300,257 87,942

89,712

123,453

76,596

54,96l

35,590

388,199

166,308

178,414

65,702

572,718

448,586

363,314

Wages & salaries Other value added Total value added TOTAL INPUT

26,939

327 2,291

1,675 38,865 54,484 41,403 37,167 78,570 171,919

72

Regional Economic Impact Analysis and Project Evaluation

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices) continued

Sector i Agriculture, forestry, fishing, & mining

6

7 0

718

9

8

10

494

11

o

o

682

300

580

314

3 Food & beverages

o

30

O

o

o

4 Wood industries

o

162

0

3,012

17,488 2,148

1,488

2 Construction

5 Paper & allied products

1,067

888

2,139 1,082

6 Chemicals & petroleum

7,367

2,893

1,332

7 Non-metallic products

173

7,441

0

o

370

8 Metal fabricating

909

2,295

18,613

614

17,852

7,364

1,045

245

7,285

1,222

9 Printing & publishing

518

97

10 Manufacturing, n.e.c.

2,073

3,825

11 Trade & transport

1,614

4,397

137 16,953 3,079

12 Communications

450 17,134

301

1,164

2,028

7,022

817

1,992

1,512

2,438

1,880

2,018

2,993

6

o

o

o

o

o

1,318

3,835

7,043

13 Utilities 14 Finance, insurance, & , real estate 15 Health & welfare 16 Education 17 Business services 18 Other services

43

o

767

o

3/149

1,155

19

o

183

37,513

29, 126

55,219

2,608 1,841

138

182,722

5,379

77,863

40,785 52,301

Wages & salaries

25,516

22,001

69,865

50,720

Other value added

26,098

2O,47O

Total value added

51,614

42,471

39,879 109,744

12,217

62,937

495,167

76,976

242,826

156,023

Imports

TOTAL INPUT

2,112

1,227

406,040

Total intermediate purchases

10,410

57,276 173,115 89,674 262,789 502,787

Inp

Output Analysis

73

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices) continued

Sector i Agriculture, forestry, fishing, & mining 2 Construction 3 Food & beverages

11

366

14

13

12

15

o

o

o

o

14,206

1*739

1,212

1*413

1*507

645

o

0

49

157

600

46

O

o

177

5 Paper & allied products

5,820

251

O

16

i

6 Chemicals & petroleum

14*653

1,960

3,462

229

2,152

159

196

345

o

0

639

4 Wood industries

7 Non-metallic products 8 Metal fabricating

2,056

4,069

1*730

0

9 Printing & publishing

23*307

1,832

33

8,696

4,440

530

1*417

10 Manufacturing, n.e.c.

1*385

379

1*413

11 Trade & transport

40, 189

1*344

1,646

9*203

6,320

12 Communications

24,176

742

1,663

7'925

15*837

893

13 Utilities

643

6*445

1,581

2,474

14 Finance, insurance, & real estate

33*091

4*335

2,079

32,646

765

30

o

15 Health & welfare

o

o

o

16 Education

o

20

o

H

645

5*129

4*158

5*44i

i*555

276

0

468

895

209,128

23,112

68,090

21,010

122,124

29*541

24,158 64,245 39*142

31*790

22,360

182,132

169, 185

17 Business services 18 Other services Total intermediate purchases Imports Wages & salaries Other value added Total value added TOTAL INPUT

27,631 1*952

800,608 586,462

89*373 76,727

113,700

375*374

86,767

1,387,070

166,100

152,842

557*506

255*952

1,718,322

218,753

241*245

657*386

299*322

74

Regional Economic Impact Analysis and Project Evaluation

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices) continued

Sector i Agriculture, forestry, fishing, & mining

17

16

18

o

o

2 Construction

520

3 Food & beverages

837

4 Wood industries 5 Paper & allied products

0

1,017

C

TIS

281

15/174

45

1,212

27,666

0

1,6O2

25,082

217/381 2,633

10,819

9,188

0

992

47, 180

298

786

69,210

10,533

6 Chemicals & petroleum

343

116

208

45/831

52,790

7 Non-metallic products

738

0

14O

41,520

1,021

o

73

132

84,063

7/879

8 Metal fabricating 9 Printing & publishing

59/3H

18,766

1,029

49,664

12,560

614

789

114/379

531/187

2,482

3/7i8

5/817

59/126

65,834

13 Utilities

4/577

1,630

3/791

80,679

92,168

14 Finance, insurance, & , real estate

1,251

5/393

4/825

116,045

394/432

o

o

0

107

82,902

4,609

27/495

5,122

10 Manufacturing, n.e.c.

2,208

11 Trade & transport

1,856

12 Communications

15 Health & welfare

7/613 82

398

16 Education

1,689

33

O

17 Business services

7,308

10,997

2,239

96,032

31,212

o

572

6,667

16,657

293,049

29,948

31,184

30,908

952,338

1,861,849

22,079

52,62O

1/567/976

995,811

193/655

2,683,052

46,710

Other value added

153/437 78,691

150,827 142,712

H7/526

2,079,902

Total value added

232,128

293/539

341,181

4,762,954

384,968

280,711

346,802

424,709

7,283,268

3,242,628

18 Other services Total intermediate purchases Imports Wages & salaries

TOTAL INPUT

TIS = Total intermediate sales C = Household consumption

18,635

338,258

Input-Output Analysis

75

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices) continued

Sector

I

i Agriculture, forestry, fishing, & mining 2 Construction

E,

E2

E3

0

3

11,197

7,465

3H,495

208,087

10,847

2,418

17

0

7,662

39,574

70,735

49,531

3 Food & beverages 4 Wood industries

G

21,043

8,364

1/532

21,990

43,663

123,593

5 Paper & allied products

0

3,448

27,068

61,252

229

6 Chemicals & petroleum

0

3,448

27,068

61,252

229

7 Non-metallic products

o

192

30,021

o

4,222

2,328

8,896

82,426

42,142

9,294

1,724

54,664

15,883

O

18,772

170,792

234,438

9,348 209,811

8 Metal fabricating 9 Printing & publishing 10 Manufacturing, n.e.c.

o

3/197

11 Trade & transport

27,381

14,901

357,535

309,647

12 Communications

0

1,864

64,347

27,582

O

13 Utilities

o

9,335

59,063

o

o

6,574

9,203

94,960

17,272

13,032 o

14 Finance, insurance, & real estate 15 Health & welfare

o

201,707

14,395

211

16 Education

o

213,123

11,075

22,635

17 Business services

o

27,744

153,208

24,971

5,284

18 Other services

o

2,298

39,729

54,290

16,714

362,339 394,611 —

741,984

1,609,818

949,852

47,873

—

—

148,936

—

—

Total intermediate purchases Imports Wages & salaries

847

465,285 — —

Other value added

_

_

_

_

_

Total value added

_

_

_

_

_

756,950

938,793

-

-

-

TOTAL INPUT

EI = Exports to rest of B.C. E2 = Exports to rest of Canada E3 = Exports to u.s.

76

Regional Economic Impact Analysis and Project Evaluation

TABLE 9

Interindustry transactions, metropolitan Vancouver, 1971 ($1,000—producers' prices) continued

Sector i Agriculture, forestry, fishing, & mining 2 Construction 3 Food & beverages 4 Wood industries 5 Paper & allied products 6 Chemicals & petroleum 7 Non-metallic products 8 Metal fabricating 9 Printing & publishing

E

E4

TFD

o

13,282

50,528 545-052

38,621

198,461

114-359 179

303,605 88,728

423-504

o

385-053 34-243

5-798

o

558

39,706

316,134

102,709

449-336 35-456

x 65,702 572-718 448,586 363-3M 171-919 495-167 76,976

139,660

158,763

242,826

5-672

76,219

96,709

156,023

4,016

453-123 1,603,943

I,7l8,322

11 Trade & transport

153,481

12 Communications

o

418-594 1,030,474 91,929

159,627

218,753

13 Utilities

0

59,063

160,566

241,245

5,868

131-132

541-341

657-386

o

14,606

299,215

299,322

927

35-484

276, 1O2

280,711 346,802

10 Manufacturing, n.e.c.

14 Finance, insurance, & real estate 15 Health & welfare 16 Education 17 Business services 18 Other services Total intermediate purchases Imports Wages & salaries Other value added Total value added TOTAL INPUT

E4 = Exports to rest of world E = Total exports TFD = Total final demand X = Total sales

8,351

502,787

191,814

250,770

1-972

112,705

408,052

424-709

339,802

3,364,758

6,330,930

7,283,268

Input-Output Analysis77

CMA'S $7.3 billion of sales were made locally, while 22 per cent went to the rest of BC, 13 per cent to the remainder of Canada, and 6.4 per cent to the United States. Sales and employment multipliers derived from the inverse matrix (table of total requirements) with the household sector endogenous are shown in Table 10. The sales multipliers show for each sector the estimated total sales generated within the economy by an increase of $1 in final demands for that sector's production. The employment multiplier for a particular sector shows the estimated total person-years of employment generated within the economy per million-dollar increase in the sector's final demands. TABLE 1O

Metropolitan Vancouver sales and employment multipliers

i Ag., for., fish., mining 2 Construction 3 Food & beverages 4 Wood inds. 5 Paper & allied products 6 Chemicals & petroleum 7 Non-metallic products 8 Metal fabricating 9 Printing & publishing 10 Manufacturing, n.e.c. 11 Trade & transport 12 Communications 13 Utilities 14 FIRE 15 Health & welfare 16 Education 17 Business services 18 Other services

Sales multiplier

Employment multiplier

1.61 1.68 1.63 1.49 1.64 1.18 1.97 1.63 1.67 1.50 1.69 1.64 i-54 1.69 1.64 1.68 1.67 1.61

155.2 90.1 61.8 70.7 60.7 15.0 91.1 69.4 76.8 74-3 160.7 89.2 53-3 86.0 138.4 136.2 93-4 145.0

Source: Davis, 26-7

Case Study 2: An Input-Output Model of the Yukon Territory The Yukon territory is a geographically isolated region in northwest Canada. It is sparsely settled with a 1981 population of 23,153 and a population density of 0.048 (pop/km2). The Yukon economy is almost entirely dependent on the export of natural resources and on government spending. The Yukon I-O model was constructed for the base year 1978.14

TABLE 11

Interindustry transactions, Yukon, 1978 Industry Hard rock mining Placer mining Oil and gas Forestry Hunting, trapping, fishing, and subsistence Transportation Construction Utilities Wholesale trade Retail trade Services Finance, insurance and real estate Manufacturing Total processing Indirect taxes less subsidies Other operating surplus Depreciation Net income of unincorporated business Labour income* Imports Total final payments Total outlays

2

3

4

5

6

7

8

9

10

11

— — —

— — —

— — -

— — —

— — —

— — 182

— — —

— 864 — -

—

—

— —

— —

347

6

80 130

— — -

1,412 11,812 685 2,383 1/588 3/285

8,549 19/074 621

1

i

—

2

-

3 4

—

5 6 7 8 9 10

11 12 13

14

17O

-

H,i93 584

100

11

7,177 2,584 56 9/304 36 9'403 43/507 840

730

63

—

1,350

19 21

37/053 20,863 107,086

22

150,593

20

1,352

1,032

1°

— — 218

1,032

3/300 93 24,558

3/940 28 38,718

7 -193 —

76 8,178 9,832

4

1/757 -23/397 35/578

3,016 7,602 4,602

1,352 220

-

10 1,096 13 1,849 3,067

13/543 6,278

660 21,636

13 47 57

3/594 3/598 4,630

33/759 58,317

-

18

1,867 4/569 6,425

220

2/354 1,160 2,810

— -

82 17

—

17

1

-

1,857

5 3

2

507

35/234 13,096

15 16

1

—

-

5/597 43/«2 81,830

2,7H 4/H9 788 209 —

3/291 3/091 186 M,399

17/155 13/444 748 2,607 81 1,408

-

1,116

1,784 436 1,058

179

1,775 1,766

9,186

15,396

7,857 8,091

4,248

8,287

35 40,591

1,046

51,158

i

211

—

1,995

2,328

—

122

HI

99 11,130

13,874

-2

21O

2,482 4/469 7/159

21/559

17/973

31/318

71,909

915

8,379 25,847 77,005

5/724 7/215 59 19,817 2/344 13/150 4/659 3,068 23,864 3,872 50,958 70,755

TABLE 11 (cont.)

Industry Hard rock mining Placer mining Oil and gas Forestry Hunting, trapping, fishing, and subsistence Transportation Construction Utilities Wholesale trade Retail trade Services Finance, insurance and real estate Manufacturing Total processing Indirect taxes less subsidies Other operating surplus Depreciation Net income of unincorporated business Labour income* Imports Total final payments Total outlays

12

2,580 2,302 238 24,486 7-183 2,H3

GDP

Total prod.

19

2O

21

22

— -

— -

11,398

3,696 —

24,961 — -

7,187 37,57i 21,027

-

724 25,687 12,983

9,403

49 4,165

33,900 10,934 249,434

17,378

1,309 179,607

635 39,686

— 36,359

3,891 29,070 181

43 2,139 196

12,187 58,749 68,406

— —

-

9,861

558 3,527 389 37,6i5 47,oi9

46 i,33! 3,649 7,404 11,569

10,509 131,108 73,363 354,322 603,756

— — 225 225 17,603

179,607

-

7 8

3,030

9 10 11

1,869

12 13

3,291 18

M

15

21

934 —

17

M

— -

5 6

22

— «9

C

55,737 68,131 13,410 22,463 6,565 34/622

-

2O

133,213 4,700 57 -

GFCF 18

284

3 4

19

G

i7'378 -

-

18

X 16

1,725 1,948

—

2

17

VPIC 15

— 861 i,596

i

16

13

Total int. prod. 14

-

26

932

124

"3

4 268 89 516 89 409

*Column and row entries may not sum precisely to totals because of rounding. Source: Stabler 1984:115-23

-

50,226 6,969 67,056 106,742

-

150,591

-

4,700

-

57 119

150,591 6,425 57 2,067

— -

4,630 2,580 13,700 8,149 49,447 70,441 36,153

4,630 58,317 81,831 21,559 71,910 77,006 70,775

11,810 81,291

-

-

13,H9 635 354,322

47-019 11,569 603,756

-

3,240

—

13,101

12,187 58,749 81,507

78,244 78,244 114,603

7,047 7,181 17,468 98,759

— — -

7-047 50,226 92,619

i7'556 181,334 165,982

517,315

1,121,071

&&

8o

Regional Economic Impact Analysis and Project Evaluation

The final demand columns and the final payment rows were developed from the income and product accounts for the region which are prepared annually by the Department of Indian Affairs and Northern Development. The interindustry transactions were constructed from survey data obtained from questionnaires sent to the approximately 1,360 business firms in the territory. The questionnaire data were for 1981 and ratios between these data and the 1981 total final demand and payments data were calculated in order to scale the interindustry transactions to 1978. The Transactions table of the Yukon territory is shown in Table 11. The model contains thirteen industries, five final demand categories and six final payment sectors. The model is constructed on a gross-domestic-product basis and thus focuses on production within the region regardless of the ownership of the productive factors. Contrary to the common practice of representing the wholesale and retail trade sectors by their respective gross margins rather than actual transactions in order that final demands may be traced directly to the producing sectors, actual transactions were used for these sectors in the Yukon model rather than gross margins. The reasoning was that this method would provide the opportunity for tracing a more accurate picture of the transactions within the economy "with little loss, since most of the products sold into final demand in the Yukon were produced elsewhere." From Table 11 the dominance of the economy by the hard rock mining industry and by government is obvious. Between them they account for 48 per cent of the direct labour income paid to the household sector. Further, hard rock mining accounts for 76 per cent of the region's exports with the remainder attributable to sales by the trade and services sectors to tourists and temporary residents. Type i and Type n income multipliers for various sectors are shown in Table 12.15 Type i income multipliers reveal the direct plus indirect income per dollar of direct income. Type n multipliers reveal the total (direct plus indirect plus induced) income per dollar of direct income. As the author points out, the magnitude of the multipliers reflects both the extent of the linkages within the economy and the labour intensiveness of the indirect and induced interactions.

Input-Output Analysis

81

TABLE 12

Yukon income multipliers

Industry Utilities Wholesale trade Retail trade Manufacturing FIRE

Construction Transportation Placer mining Hard rock mining Services Forestry

Direct income change

Direct + indirect income

change

0.07

O.22

O.1O 0.11

0.23 0.27 0.17 0.09 0.28 0.25

0.07 0.05 0.17 0.15 0.13 0.15 0.21 0.33

O.2O 0.22 0.27 0.36

Total income change

Type I income mult.

Type II income mult.

0.27 0.29 0.33

3.09 2.41 2.36 2.33 1.84 1.72 1.71. i-53 1.43 1.26 1.09

3-79 2.96 2.90 2.86 2.26

O.21 0.11 0.35 0.30 0.25 O.27 0.33 0.44

2.11

2.10 1.88 1.76

1.54

1.33

Source: West, 121

SELECTED

READINGS

Hewings, G.J.D. and R.C. Jensen. "Regional, Interregional and Multiregional Input-Output Analysis," in P. Nijkamp, ed., 1986. Handbook of Regional and Urban Analysis. New York: North-Holland, vol. 1:295-355 —. 1988. "Emerging Challenges in Regional Input-Output Analysis," Annals of Regional Science, 22 spED:43-53 Hoover, E.M. 1975. An Introduction to Regional Economics. New York: Knopf Leontief, W. 1966. Input-Output Economics. New York: Oxford University Press Miernyk, W.H. 1967. Elements of Input-Output Analysis. New York: Random House Miller, R.E. and P.O. Blair. 1985. Input-Output Analysis: Foundations and Extensions. Englewood Cliffs, NJ: Prentice Hall Richardson, H.W. 1972. Input-Output and Regional Economics. Trowbridge, UK: Redwood Press Schaffer, W.A., E.A. Laurent, G.F. Floyd, E.M. Sutter, jr., C.K. Hamby, and R.C. Herbert. 1976. On the Use of Input-Output Models for Regional Planning. Leiden: Martinus Nijhoff

82

Regional Economic Impact Analysis and Project Evaluation APPENDIX 1

A Mathematical Summary of the Input-Output Model In the standard, demand-oriented I-O analysis, total sales (Xj), of any sector (i) of an n-sector model can be expressed as where x,y = the value of output of sector i purchased by sector/, and y, = the final demand for the output of sector /'. The economy is thus conceptualized by n linear equations, each expressing the transactions of a particular sector with the processing sectors and with final demands (sales). Equation (4.1) represents the row equations of the input-output model's transactions table. The second table of the input-output model, the table of direct purchases, can be expressed as the matrix a,-,, where

Substituting (4.2) into (4.1) yields which may be expressed more compactly as where X = Xj, A = a,y, and Y = y,. Given the exogenous or final demands on the economy, equation (4.4) may be solved to yield the changes in total outputs, where / is an n-order identity matrix. The Leontief inverse, (I-A)~l, is the third table of the standard inputoutput model, the table of total requirements. The element r,y, in the zth row andyth column of the (I-A)~l matrix represents the change in gross output of sector i per unit change in the final demand for the production of sector j. Thus we may write the final-demand multiplier 'for sector / as 2 r,y, which yields the change in aggregate production in the economy per unit change in the final demand for sector;'. The inverse matrix is often transposed to facilitate reading along rows rather than down columns. In such cases the final-demand multiplier for sector i is where r',y is an element of the transposed inverse matrix.

Input-Output Analysis

83

APPENDIX 2

The Rectangular Commodity by Industry Input-Output Format Rationale for Rectangular I-O Models To this point in the discussion of I-O analysis, the data on sales and purchases have been organized on the basis of producing units, and the input-output model has been developed in an industry-by-industry format. It has been assumed that the producing units comprising an industry, as defined in terms of SIC codes, collectively produce a single, homogeneous output. It has further been assumed that in the process of producing their outputs, the producing units in each industry purchase their inputs in identical, fixed proportions. When constructing interindustry models, attempts are thus made to define industries in such a way as to minimize the violations of these assumptions. As mentioned earlier in the text, these attempts are often made difficult by the existence of secondary products. Within the industry-by-industry format, I-O sectors are defined in SIC codes and each firm in the economy is placed in a sector according to the SIC code of its primary product. However, a number of firms produce subsidiary or secondary products which are not appropriate to the firm's sector classification. As an alternative to the means of handling secondary products within the interindustry transactions table, the problem may be avoided altogether by abandoning the interindustry format in favor of a commodity-by-industry format. Since the construction of its first national I-O model in 1961, Canada has consistently adopted this latter format; the United States switched to this format beginning with its 1972 table. In the commodity-by-industry format there is no reason why the number of commodities represented in the model must be equal to the number of industries in the model. In the illustrative model below of a hypothetical economy, there are two commodities (goods and services) produced by three industries (primary, secondary, and tertiary). A Simple Illustrative Rectangular I-O Model The proportions of the two commodities produced by each of the three industries are shown in the so-called make matrix of Table 13. Each row of the make matrix shows the commodity composition of the industry's total output, that is, the amounts of each of the commodities listed at the top of the matrix produced by the industry appearing at the left. Each column of the matrix reveals the industry origins of a particular commodity, that is, the amounts of each commodity appearing at the top of the matrix produced by the industries listed at the left. In short, the make matrix reveals "who produces what."

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TABLE 13

The make matrix of a two-commodity, three-industry input-output model of a hypothetical economy

Primary Secondary Tertiary Total commodity production

Goods

Services

60 80 10 150

10 20 70 100

Total industry Output 70 100

80

While outputs are the focus of the make matrix, inputs are the basic entries in a complementary table, the use matrix. This matrix for our hypothetical economy is shown in Table 14. TABLE 14

Use matrix of a two-commodity, three-industry input-output model of a hypothetical economy

Primary Goods Services Value added Total industry inputs

15 5 5« 70

Secondary 35 25 40 100

Tertiary 10 40 30 80

Final demand

Total commodity output

90 30

150 100

Strictly speaking, the use matrix (sometimes called the "absorption matrix") comprises only the first two rows and three columns of Table 14. The final-demand and value-added matrixes (columns and rows or "vectors" in this case) are shown in order to illustrate the balance of the system. The first two rows of Table 14 reveal the distribution of the commodities among purchasing industries and final demand. The first three columns reveal the input purchase patterns of the three industries in the model. The total production figures of each commodity and each industry are the same as in the make matrix. Thus, the use matrix reveals "who buys what." Given the two matrixes above, a summary of the accounts may be presented, as is done in Table 15, which will facilitate the discussion of the derivation of the tables of total requirements. In Table 15 the following notation is adopted: U = use matrix; E = vector of final demand for commodities; Q = vector of total commodity outputs; V = make matrix; X =

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85

vector of total sector outputs; W = vector of final payments to industries; W2 = vector of final payments to final demand categories. Construction of Tables of Total Requirements As with the interindustry purchase coefficients (a,y), which show the amount of industry i's output required to produce a dollar of industry j's output, a set of commodity-by-industry coefficients (&/,-) may be constructed from Table 14, using the above notation.

or

The matrix B = [bjj] is of dimension m commodities by n industries and is known in the literature as the industry technology matrix. A coefficient in the /th row and /th column of this matrix reveals the proportion of industry j's total inputs accounted for by commodity i. It is assumed that these coefficients remain unchanged during the period over which an impact analysis is undertaken. X in equation (4.7) is a matrix whose principal diagonal consists of the elements of the X vector and whose off-diagonal elements are zeros. The industry technology matrix may now be used to write where Q and E are, respectively, the vectors of total output and final demands for the commodities produced by the economy. In terms of the values recorded in Table 14:

As the B matrix was constructed from the use matrix, a matrix D = [d,y] may be constructed from the make matrix:

or

The coefficient in the zth row and /th column of the D matrix, the market share matrix, reveals industry i's share of the economy's total production of commodity /. As was the case with the B matrix, it is assumed that the elements or coefficients of the D matrix are unchanged over the period of analysis, that is, that each industry will maintain its market share of each domestically produced commodity regardless of the levels of commodity production.

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This equation which states that the values for industry outputs may be determined as the product of the market share matrix and the vector of commodity outputs. In terms of the values displayed in Table 14, equation (4.10) may be shown as

As a first step in constructing the table of total requirements, equation (4.8) is substituted into equation (4.10) to yield Using ordinary matrix algebra procedures we may write

where the bracketed quantity in equation (4.12) is the matrix or table of total requirements.16 The z/th element in this matrix represents the amount of output from industry i required for the delivery of a dollar of commodity j to final demand. In terms of the values in Table 14,

From the commodity and industry data of Table 15, it is also possible to construct a table of total requirements in the interindustry format. As a first step, final demands for commodities must be translated into final demands for industry outputs. This task is accomplished by the following equation: From the values of Table 15, equation (4.13) may be written as

The transformation of commodity final demands to industry final demands is accomplished by apportioning commodity final demands on the basis of the ratio of industry to total outputs of each commodity. For example, the final demand for primary output is determined as 0.4 (production of goods) *9O (final demands + o.i (production of services) *3O (final demands

goods by the primary sector / total production of for goods produced by all sectors) services by the primary sector / total production of for services produced by all sectors)

Input-Output Analysis = 36 + 3 = 39

87

(final demands for goods produced by the primary sector) (final demands for services produced by the primary sector) (final demands for the production of the primary sector)

Substitution of equation (4.13) into (4.12) yields The z/th element of the (I - DB)"1 matrix reveals, in customary interindustry fashion, amount of output of industry i required for industry / to deliver on dollar of output to final demands. In terms of the values in Table 15, equation (4.14) may be expressed as

TABLE 15

Accounting framework of the commodity-by-industry input-output model COMMODITIES

Goods

Services

INDUSTRIES

Primary

Secondary

FINAL DEMAND

TOTAL OUTPUT

E

Q

Tertiary

COMMODITIES

Goods

U

Services INDUSTRIES

Primary Secondary

V

X

Tertiary W,

FINAL PAYMENTS

TOTAL INPUTS

Q'

X'

W,

CHAPTER FIVE

Regional Economic Impact Analysis: A Comparison of Approaches

SIMILARITIES AMONG THE THREE MODELS

There are several ways in which the three economic impact models —economic base, income-expenditure, and input-output—are similar in characteristics. All three models, for example, can be classified as conditional predictive models, models designed to predict changes in the economy resulting from particular stimuli. The three models may also be classified as comparative static models in that there is no explicit consideration of time in the models. Each of the models assumes that prior to the economic stimulus, the economy is essentially in an equilibrium state. That is, it is assumed the economy is not in the process of adjustment to a previous stimulus. The economic model then predicts the new equilibrium state of the economy, but reveals nothing about the length of time necessary to attain this state. Thus each of the models compares, under a particular set of assumptions, the pre- and poststimulus static equilibrium states without regard to the intervening time period between the two states. All three models are based on linear relationships. Consequently the models are generally constrained from readily incorporating economic phenomena such as externalities, internal economies of scale, joint production, threshold effects, and discontinuities in the relationships of sector outputs to inputs. DIFFERENCES AMONG THE THREE MODELS

With respect to a number of elements, each of the models differs to a degree from the other two. Comparisons of the three models with

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respect to several associated features and assumptions are drawn below from discussion of the models in the previous chapters. Units of Measurement

The economic base model is formulated in terms of a division of "economic activity" between the export and local markets and makes no specification of how economic activity should be measured. In practice, however, the overwhelming majority of base models are calibrated in terms of employment. This is largely because of the relative availability of employment data, the political importance of employment, and the common understanding of the concept of a job compared with other measures of economic activity such as value added and gross regional product. As the name of the model implies, the unit of measurement of the income-expenditure model is regional income. Although income may be measured in several different ways, value added is the commonly adopted unit of measurement for the model. For any particular firm, value added is primarily the sum of its factor payments (e.g., wages and profits). Since an input-output model of a region focuses on the interactions between the different sectors of the regional economy, the dollar volume of sales is the most convenient method by which to record these transactions. As discussed in the previous chapter, however, the "closed" input-output model also readily yields impacts measured in terms of value added. Sources of Economic Stimuli

The economic base model conceptually divides the local economy into two sectors: export and non-export. The driving economic force of this model is exports. Increases in non-export or service activity occur primarily as responses to increases in the volume of goods and services sold externally. Changes in the level of service activity resulting from import substitution can be accommodated indirectly in the model, however, by changing the value of the ratio of service to base activity. Economic expansion in the income-expenditure model relies on an injection of external funds into the economy. As is the case with the economic base model, these funds may be revenue gained from the sale of exports. In contrast to the base model, however, the funds may also flow from the remaining Keynesian categories of

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household consumption, investment, and government spending. Economic expansion can result in the model if local households decide to draw down their savings to consume locally supplied commodities. Growth will result also from an increase of capital spending in the local economy. The injection of funds into the region from senior levels of government in the form of purchases of goods and services or as transfer payments will stimulate local economic activity. Finally, as with base analysis, an estimate of the impact on the local economy of import substitution can be gained from the model by changing the coefficients of the model to reflect the new pattern of cash flows through the local economy. The sources of economic stimuli in the input-output model are the same as those in the income-expenditure model. The driving force of the model is composed of the final demands of household consumption, investment, government spending, and exports. However, while these categories are generally treated in the aggregate in the income-expenditure model, the input-output model considers the final demands for the output of each individual producing sector. With regard to import substitution, input-output is similar to the other two impact models in that significant import substitution necessitates a change in coefficients, in this case the direct purchase coefficients. Constancy of

Coefficients

The assumption of constant coefficients is common to all three economic impact models. In the economic base model, it is assumed that k (the ratio of service to base activity) remains constant over the period of analysis. In the income-expenditure model, it is assumed that there is no change in the model's various marginal propensities. That is, among consumers in the regional economy it is assumed that there are no variations in the marginal propensity to save, the marginal propensity to import, the marginal propensity to consume locally, and the marginal rate of taxation. To the extent that various producing sectors or industries are identified in the model, it is assumed that for each the marginal propensity to import and to generate local income are unchanged. In the input-output model the assumption of constant coefficients pertains to the industry's direct purchase coefficients. That is, for each sector it is assumed that the input requirements are unaltered. This assumption of constant coefficients implies that over

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the period of analysis there are no significant changes in technology, commodity price patterns, or consumer purchase patterns, and no new locations or closures of significant firms in the region. Sector Homogeneity

Like the assumption of constant coefficients, sector homogeneity is an assumption common to all three impact models. For the economic base model it is assumed that the base (export) and service (non-export) sectors are each composed of homogeneous activities. As a result of the sector homogeneity assumption, the base model will not distinguish the impact on the regional economy produced by an increase in exports of one activity from the impact resulting from an equivalent increase in exports of any other sector. In the income-expenditure model the sector homogeneity assumption implies that for each producing sector identified in the model there is no product-mix problem. That is, it is assumed that all firms in a particular sector have the same propensity to generate local income per dollar of local sales. It also implies that the tax rates, savings rates, propensities to import and local consumption patterns do not vary among community groups such as the unemployed, in-migrants and long-time residents. Sector homogeneity in the input-output model means that each sector in the transactions matrix of the model contains a number of firms with identical input patterns. In reality, of course, the column of direct input coefficients for any particular sector is more likely to represent a weighted average of the various input purchase patterns of the firms included in the sector. The assumption pertains also to the household consumption sector in that it is assumed that all consumers in the regional economy have the same purchase pattern. Impact Components

As earlier discussed, the direct impact of a project is the economic activity (employment, factor payments, or sales) generated directly by the project itself. Indirect impacts are measured by the economic activity generated by suppliers to the project, suppliers to the suppliers, and so on. Indirect impacts thus encompass the entirety of economic activity created in the economy through the chain of input purchases initiated by the inputs purchased by the project. The induced impact is the volume of economic activity generated by the consumer purchases resulting from the increased income in the economy.

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For both the economic base and income-expenditure models, the analyst must supply the multiplicand consisting of the direct and indirect impact components. The base and income-expenditure models then yield, via their consumer spending multipliers, the total (direct + indirect + induced) component. In contrast, the inputoutput model, with its focus on interdependencies between producing sectors of the economy, provides the indirect impact. Given the direct impact as the multiplicand, the I-O multiplier constructed from the open model yields the direct plus indirect impact; the closed model multiplier provides the total impact. Number of Multipliers With rare exceptions, the economic base and income-expenditure models yield single aggregate multipliers for the regions represented. In the economic base model, economic activity is generally apportioned between export and non-export activity on a sectorby-sector basis. The two categories are then summed for the purpose of determining an determine the overall multiplier for the region. In the income-expenditure model, analysis at the sector level is customarily undertaken only to obtain a weighted average of an appropriate regional economic propensity at the aggregate level, such as propensity to spend locally or the propensity of businesses to generate local income per dollar of sales. In contrast to the economic base and income-expenditure models, the input-output model is specifically designed to reveal the linkages between sectors and to yield a distinct multiplier for each economic sector of the model. Thus, the number of multipliers derived from the model is equal to the number of producing sectors in the model's transactions matrix. Appropriate Application

Of the three approaches to economic impact analysis, the economic base model has the most severely limiting set of assumptions. It is most appropriately applied to small-scale economies heavily dependent on a single export. Settlements which owe their continued existence to mining or forestry operations are prime examples of such economies. Compared with economic base analysis, the income-expenditure approach recognizes a wider range of sources of economic stimuli. It is thus arguably more readily applicable, for example, to a smallscale economy whose immediate growth is attributable to, say, a housing boom or an increase in consumer spending. The income-

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expenditure model also offers a greater degree of flexibility in distinguishing the first round from subsequent rounds of expenditures. It is thus generally the more appropriate model with which to analyse the impacts of projects with prolonged construction stages or projects which attract significant in-migration into the region, cases in which there are likely to be significant differences between the expenditure patterns of newcomers to the community and those of long-time residents. Finally, the income-expenditure model offers greater flexibility for the inclusion of more than one producing sector and is thus generally more applicable to an economy dependent on more than one exported commodity. In all such cases, however, the analyst must weigh the advantages of the income-expenditure model against its generally greater costs of construction. Compared with the input-output model, both the economic base and income-expenditure models are limited in application to smallscale economies in which the interdependencies between producing sectors are relatively insignificant. It is precisely these interdependencies or sales/purchase relationships which are the focus of the input-output model. Hence, the more complex the economy is in terms of intersector linkages, the more appropriate is the I-O model for the purpose of impact analysis. For larger urban-centered regions, particularly metropolitan areas, the input-output model is decidedly the more appropriate model. Again, however, the analyst is forced to weigh the advantages of the model against the associated costs in both time and money. Table 16 summarizes the characteristics of the three impact models. TABLE l6

Comparison of principal approaches to economic impact analysis

Static/dynamic Linear/nonlinear Unit of measurement Source of stimulus Constant coeffs. Sector composition Impact components No. of multipliers Appropriate application Construction costs

Economic base

Income expenditure

10

static linear employment E

static linear income

C,I,G,EM

static linear sales C,/,G,E,M

homogeneous induced one small-scale economy very low/low

propensities homogeneous induced one small-scale economy low

«.; homogeneous indirect + induced n large-scale economy high/very high

k

CHAPTER

SIX

Cost-Benefit Analysis: The Evaluation of Social Costs and Benefits

Cost-benefit analysis (CBA) involves the systematic enumeration and evaluation of the socially desirable and undesirable effects of public sector projects or programs. The objective of CBA is to assist decisionmakers in choosing among alternative means for attaining public goals. In many respects CBA is to the public sector what profit analysis is to the private sector. However, whereas the latter focuses on the cash flows of revenues and costs of a particular project from the viewpoint of the firm, the former is concerned with the project's associated benefits and costs from the viewpoint of society. In general the private sector considerations regarding a particular project are but a subset of public sector concerns. ENUMERATION OF SOCIAL COSTS AND

BENEFITS

Once a project or set of projects has been clearly defined, the immediate task of the cost-benefit analyst is to identify and evaluate the relevant social consequences, that is, the social costs and benefits. These effects may be classified as direct or secondary. The direct benefits of a project are measured by the social value of the project's output. The associated direct costs are the social value of the resources necessary to produce that output. The direct net benefits of a dam, for example, would be the value of the electricity produced minus the dam's construction and operation costs. Apart from consideration of the project's direct effects is the issue of indirect or secondary effects. Secondary effects reflect the impacts of the project on the rest of the economy in terms of the project's various sales and purchase linkages within the economy.

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Secondary effects are further classified in the literature as "stemming" and "induced." Stemming effects are associated with the forward or sales linkages of the project under consideration. For example, stemming benefits might appear in the form of the increased production of an electroplating firm made feasible by the lower-cost power emanating from a hydroelectric project. Another illustration might be the increased value of agricultural production attributable to an irrigation project. A project's induced benefits are measured by the increased value of production attributable to the project's backward or purchase linkages with the rest of the economy. Induced secondary benefits relate, in the terminology of input-output analysis, to the indirect and induced sales attributable to the project. (Note that the word "induced" in cost-benefit analysis is more broadly conceived than it is in input-output analysis.) For the hydroelectric project one might consider as induced secondary benefits the increase in production of iron, cement, and other materials that went into construction of the dam and, as well, the increase in output of consumer commodities attributable to the wages and salaries generated by the project and its suppliers. It can readily be seen that any consideration of secondary effects is very much dependent on the application of economic multiplier analysis discussed in previous chapters. The incorporation of secondary costs and benefits within CBA is generally discouraged by economists because of the potential for double (or multiple) counting. For example, in the case of the hydro project, if the value of the output of the electroplating firm were counted as stemming secondary benefits, double counting of the value of electricity would ensue. First, the output of electricity by the hydro project would be counted as a direct benefit of the project. Second, since the value of the output of the electroplating firm includes the value of all its inputs, including electrical power, a portion of the output of the hydro project would again be counted as a benefit. The same reasoning applies to the incorporation of induced secondary costs. For example, once the value of the electrical output of the hydro project has been determined, the value of the iron and cement that went into the construction of the dam has already been taken into account. The cost of the materials is included in the value of the electricity in the same way that the value of electricity is included in the value of output of the electroplating firm. To include as costs the value of intermediate products in addition to the value of the final product amounts to double-counting. (The limited

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97

circumstances under which secondary effects are defensible, and the use of input-output analysis to estimate these effects, are discussed in the later section entitled Modifications and Extensions.) M A R K E T PRICES AND

SOCIAL VALUES

Projects considered by the CBA analyst generally involve the valuation of commodities produced (and displaced) by the projects. These valuations are made on the basis of consumers' willingness to pay for the goods and services received (or lost). Market Prices and Consumer Surplus

In Figure 4 below, the demand curve AC for commodity x shows the the prices consumers are willing to pay for various amounts of the commodity. At the market price OP for the commodity, amount OD is produced and sold to consumers, who pay OPBD. OPBD is not, however, the value of the commodity x produced, since consumers are willing to pay an amount greater than this. All consumers pay price OP for units of x sold in the market, but it is clear from the demand curve that they are willing to pay prices higher than OP for units of x fewer than OD. If a supplier (in this case a "discriminating monopolist") could charge for each unit produced what consumers are willing to pay, the amount paid for OD of x would be OABD. The difference between what consumers are willing to pay for a particular commodity and what they actually pay is termed "consumer surplus."

Figure 4 Consumer surplus

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Regional Economic Impact Analysis and Project Evaluation

In the above figure consumer surplus is PAB, the area below the demand curve and above the price line. The value in cost-benefit analysis of any commodity is measured by the consumers' willingness to pay for the commodity, as determined by the demand schedule for the commodity. Value (willingness to pay) is thus the sum of the amount actually paid by consumers plus consumer surplus. In the above figure, OABD (willingness to pay) = OPBD (amount paid) + PAB (consumer surplus).1 Social Valuation and Producer Surplus

The concept of producer surplus is closely related to that of consumer surplus. For a particular commodity, producer surplus (sometimes referred to as "economic rent") is the difference between what suppliers actually receive and the minimum they would be willing to receive to supply the commodity. In Figure 5 below, producer surplus is APB, the area under the price line and above the supply curve.

Figure 5 Producer surplus As is the case with consumer surplus, increases and decreases in producer surplus are appropriately recorded in CBA as effects of a project under analysis. Social Valuation and Consumer/Producer Surpluses

The concepts of consumer and producer surplus allow the analyst to establish a project's net benefits in terms of these concepts. The benefits of a project, as has been discussed, are measured by the consumers' willingness to pay for the output of the project. The

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99

costs of the project are the costs to society of producing the project's output. Consumer surplus (CS) for a commodity is defined as the consumers' willingness to pay (WTP) for the commodity less what they actually pay (CTC: cost to the consumer). Producer surplus (PS) is the amount received by suppliers of the commodity less their costs of supply (CTP: cost to the producer). Since what consumers pay and what producers receive are identical, the sum of the changes in consumer and producer surpluses attributable to a project represents the net benefits of the project. In summary,

To illustrate the application of the concept of surpluses to establish the net benefits of a project, let us look at a general case in which the project under study is predicted to shift the supply curve of the commodity that the project produces.

Figure

Consumer and producer surpluses and project net benefits

When the supply curve shifts from S0 to Si, the change in consumer surplus is clearly areas a + b in Figure 6. At price PI, producer surplus is c + d; at P0 it is a + c. The change in producer surplus is thus d - a. The change in total surplus is thus (a + b) + (d - a) = b + d. While the change in surplus, or net benefits of a project, is easily established conceptually, it is obvious that in practice the estimation of this change can be formidable. Construction of demand curves is generally time-consuming and can involve substantial statistical difficulties. Similar problems arise in the construction of

ioo

Regional Economic Impact Analysis and Project Evaluation

supply curves; moreover, under market conditions of imperfect competition, the supply curve is theoretically undefined. In practice, the change in net income of the producer is frequently adopted as a measure of the change in producer surplus. As for the change in consumer surplus, it can readily be shown that the area a + b in Figure 6 can be computed as 1/2 (P0 - PI) (Qi + Qo).2 However, the volume of the project's output in many cases is not sufficiently large to change the existing price. In this circumstance the change in consumer surplus can be ignored and the project's (total) benefits can be measured as the project's output valued at the existing market price. At this point two general questions regarding market prices may be raised: Under what conditions do market prices reflect social valuations? If market prices for the commodities in question do not exist, how can social valuations be made? Each of these questions will be considered in turn. VALUATION WHEN MARKET PRICES DO NOT REFLECT SOCIAL VALUES

Social valuations may or may not be reflected by existing market prices. Unadjusted market prices are useful in CBA under the following conditions: (i) a high degree of competition in the economy, so that commodity prices closely reflect their costs of production; (2) market prices free from distortion by government policies, so that for any given output the price at which producers are willing to sell is equal to the price at which consumers are willing to purchase; and (3) reasonably full employment of the economy's labour and capital stock, so that returns to these productive resources are accurate indicators of what society gives up by diverting the resources from alternative productive activities. Obviously, for many cases considered by the cost-benefit analyst these conditions will not prevail, and "accounting" or "shadow" prices will have to be substituted for the prevailing market prices. The principle of shadow pricing in the absence of each of the above three conditions is briefly considered below under the headings of imperfect competition, taxes and subsidies, and unemployed resources. Imperfect Competition

In highly competitive markets no producer has control over the price of his output and each maximizes profits by producing that

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101

output which equates marginal cost (the cost of producing one additional unit) to the existing price. In this situation, market prices can be appropriately regarded as indicators of social valuations, since they reflect the value of resources required for production. If imperfect competition prevails, however, market prices and marginal production costs are no longer equated. As shown in Figure 7 below, the imperfect competitor faces a downward sloping demand curve, since by definition he is able to influence market prices by producing at various levels of output.

Figure 7 production under imperfect competition The particular level of output that results in maximum profits is Q0, where marginal cost MC is equal to marginal revenue MR. The producer sells Qo not at price PI, which reflects marginal costs, but at the higher price P0 determined by demand (consumer willingness to pay). Let us now consider two cases of imperfect competition in the context of cost-benefit analysis: the purchase by the project of an input produced under conditions of imperfect competition, and the sale of the project's output in an imperfect market. In the case in which the project purchases an input produced in an imperfectly competitive market, there arises the question of whether the cost-benefit analyst should value the input produced by the imperfect competitor at the input's market price or its marginal cost (i.e., the cost of supplying the input). The answer depends on the input's supply conditions. If the input supplied to the project is new production, that is, if it results from production additional to that previously undertaken, the appropriate unit value of the input is the marginal cost (i.e., the cost of supply, or

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PI). The supply cost represents the cost of resources necessary to produce the input to the project. If, on the other hand, the input were supplied to the project by a diversion from other uses of the input, the appropriate social valuation is the market price P0, since this is the value placed upon the input in the uses from which it was diverted. Thus, under conditions of imperfect competition in the supply of inputs to a project, adjustment of the market price to a new, shadow price may or may not be appropriate depending on whether the inputs result from new or diverted production. To the extent the input comes from new production, shadow pricing is appropriately considered. In our second case the project's output is sold in an imperfect market. Should the output in this circumstance be valued at price P0, the price consumers are willing to pay, or at Pl7 the marginal cost of producing the output? Again, the appropriate valuation depends on supply conditions. If the project output displaces existing production, the resources that were used to produce the displaced production are now released. The benefit to society is the cost of these resources, PI. Alternatively, if the project's output adds to existing production without displacement, the appropriate valuation is what consumers are willing to pay for the output, P0. Taxes and Subsidies

A tax or a subsidy levied on a commodity results in two prices for the commodity, the price at which the producer is willing to sell (the producer price) and the price consumers are willing to pay (the purchase price). The difference between the two is the tax or sub-

Figure 8 Taxation and price

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103

sidy. For example, suppose a tax is levied on a consumer commodity. In Figure 8, S and S' are the supply curves for that commodity without and with the tax, respectively. Pc is the purchase price paid by the consumer and Pp is the producer's price, the amount received by the supplier. The difference (Pc - Pp) is the tax revenue per unit which accrues to the government. Parallel to our discussion in the previous section on imperfect competition, let us consider two cases involving taxation: valuation of an input to a project under analysis when a tax has been levied on the input, and valuation of the project's output when it has been taxed. (In each case the analysis of a subsidy can be similarly undertaken, with opposite results.) In the case of a tax levied on an input to a project, the social valuation of the input depends on whether the input is from new supplies or from a diversion of resources from other uses. If the input comes from new supplies, that is, from marginal increases in production, the proper valuation is the supply cost, which is equal to the price paid by other users of the input less the tax, that is, Pp. On the other hand, if the input comes from a diversion from other uses, the appropriate valuation is the value of the input in its alternative uses, that is, the market or consumer price, Pc. For the case of a tax levied on the output of the project, the analysis again follows that of imperfect competition in the preceding section. If the output displaces other production, the social economic benefit is the value of the resources released. Output is thus valued at Pp. If, on the other hand, the project output adds to existing production without displacement, it should be valued at Pc, the consumers' willingness to pay. In both cases direct consideration of the tax (Pc - Pp) is excluded from the valuations, since it involves no additional resource costs but is merely a transfer of funds to the government from both the producers and consumers of the commodity in question. Unemployed Resources

Unemployed resources are resources that are in excess supply at existing market prices and are thus not currently utilized in commodity production. The opportunity costs of the use of such resources in a particular project are nil, since no production is foregone by their use. In other words, the appropriate valuation for each of these resources is a shadow price of zero rather than the market price. While the argument of a zero shadow price for, say,

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Regional Economic Impact Analysis and Project Evaluation

unemployed labour is basically sound, there are a number of concerns with this approach. First, there is the matter of the variation of the level of unemployment over time. Assuming labour is unemployed at the time the analyst undertakes the CBA, can he be certain that labour will continue to be unemployed by the time the project is initiated? Further, there is the question of how far into the future unemployment can be projected. Labour unemployed in the first year of the project may well have job opportunities in the second and third years. Unemployment is notoriously difficult to predict. Moreover, particular political problems may arise if the analyst who projects existing unemployment into the future is an employee of the government responsible for the reduction of unemployment. A second problem associated with placing a zero shadow price on unemployed labour is that it implicitly assumes that there are no psychic benefits of leisure. If the opportunity cost of returning to work is the sacrifice of leisure on which a positive value is placed, the proper shadow price is neither zero nor the market wage rate but the "reservation" price of labour, that is, that wage which would be just sufficient to induce labour to forego leisure. If, on the other hand, workers attach a negative value to the leisure that is "forced" upon them by the lack of employment opportunities, the shadow price of labour could be arguably set at a level less than zero. Given the difficulties of measuring psychic values, benefits and costs associated with leisure are frequently ignored by practitioners. A third area of concern is unemployment benefits. From the individual unemployed worker's point of view, such benefits are part of his opportunity costs of returning to work, since the individual will have to forego these payments. From society's viewpoint, however, unemployment benefits are merely transfer payments between its members and should not be considered a part of the social opportunity costs of hiring unemployed labour. Foregoing these payments involves no social sacrifice of commodity production. Hence, such payments should not be accounted for in any CBA with a viewpoint that extends beyond the local economy. The feasibility of assigning shadow prices to unemployed labour is generally relevant only to a single project, or possibly a limited number of projects. In the case of several projects, each drawing on unemployed labour with a zero shadow price, it is quite possible that in sum they would more than exhaust the pool of unemployed labour. In assigning a zero shadow price for labour in a particular project, analysts should attempt to divide the manpower require-

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ments of the project into various occupational categories and either assure themselves of the number of workers that will come from the ranks of the unemployed or attempt to attach probabilities to their estimates. Given the uncertainties, particularly over time, as to just what portion of the project's wage bill can be associated with formerly unemployed labour, it is appropriate for analysts to investigate their results for sensitivity to variations in the unemployment rate. The principles of setting a shadow price on unemployed capital are similar to those relating to labour. If capital would otherwise be unemployed, its use in a proposed project involves no sacrifice of current production. If the analyst can be reasonably certain that specific capital (or land) used by the project would be otherwise idle over several periods, a shadow price of zero is appropriately assigned. There is, however, one particular difference between unemployed capital and labour that is of relevance in constructing the shadow price. Frequently, a machine will have a fixed amount of productive capacity. Employing the machine now will diminish its future productive life. In such cases, where real depreciation is a function of usage (rather than time), the opportunity cost of using the otherwise unemployed capital is not zero but the foregone value of its future employment. For example, suppose a machine that will be totally obsolete in five years and would be otherwise unemployed is used in the project for one year. Its shadow price is zero. If, however, the productive life of the machine is five years extending into the indefinite future, its present use diminishes its future use by one year, and the shadow price of the machine is the discounted value of its future services. (Discounting future monetary flows is the subject of the next chapter.) VALUATION WHEN MARKET PRICES DO NOT EXIST

The focus of the previous section was upon measures to establish accounting prices in situations in which existing prices are judged not to reflect social valuations. The present section deals with the even more difficult task of establishing means of social valuations in situations in which no market prices exist. The two major instances in which this circumstance occurs are the cases of externalities and public goods. Externalities

Externalities are non-market effects and can be either negative or positive. Negative externalities arise when one party imposes

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Regional Economic Impact Analysis and Project Evaluation

costs upon another for which the latter is not compensated through the marketplace. For example, a pulp mill may discharge wastes into a stream whose water is used for processing by a downstream brewery. The treatment costs are involuntarily borne by the brewery and are not the result of the brewery's activities in the market. The treatment costs are external to the pulp mill in that they do not appear in the mill's financial accounts. Positive externalities or external benefits in cost-benefit analysis are generally much less significant, and examples are hard to come by. The standard illustration is still that of the beekeeper whose bees pollinate his neighbour's orchard. The pollination process increases both the productivity of the orchard in bearing fruit and of the bees in producing honey. The beekeeper receives no reward in the marketplace for the benefit he confers upon the orchard owner and, likewise, the orchard owner receives no payment from the beekeeper. While positive externalities associated with productive economic activities continue to be relatively scarce,3 negative externalities are becoming increasingly important as economic activity continues to expand within relatively fixed environmental limits (see, e.g., Daley 1977; Boulding 1981). The incorporation into CBA of external effects is as.essential to the appraisal of a project as is the accounting of the marketed outputs of the project. The discharge of sulphur oxide into the regional airshed, for example, is just as much a real output of a public utility as is the electricity that it generates. When negative externalities are present, private costs are less than total costs to society. In Figure 9 below, negative externalities are present and social marginal costs (SMC) exceed private marginal costs (PMC).

Figure 9 Private and social marginal costs

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At output Q area ABC represents the total costs external to the producer, that is, those costs borne by society but not by the producer. The problem with most externalities, particularly with those associated with environmental damage, is that they are characterized by a lack of market prices and thus fall into the category of "intangibles" (e.g., residual discharge into airsheds and commonly used water courses, the loss of scenic views, the creation of noise). To place dollar values on environmental damages, the analyst must first have an acceptable estimate of the cumulative effects of the project upon the environment. It is then necessary to assess the social valuation of these effects. Both tasks can pose substantial analytical difficulties. We are only beginning to appreciate the complexities and uncertainties involved in estimating the environmental consequences of economic activities. Natural communities or ecosystems are composed of many interwoven chains of interdependencies. These interdependencies are frequently nonlinear, continuously subject to influences external to the ecosystem, and often link together trophically distant species. Further, a number of the interrelationships are mutualistic or symbiotic. Change, in terms of probability, sign, and magnitude, is frequently difficult to predict. However difficult the task of determining a project's biophysical consequences, it is likely to be no more formidable than the problem of assessing the social valuation of these consequences.4 In attempting this valuation the cost-benefit analyst may be appropriately led to consider non-market phenomena such as option and preservation values. Option values pertain to the worth of an environmental amenity to those who are not presently "consuming" the amenity but who wish to preserve the option of doing so in the future. Preservation values refer to the psychic benefits received by those who are rewarded by the mere knowledge of the existence of particular environmental amenities regardless of any intention to consume them either now or in the future. The difficulties of constructing quantitative estimates of such values in practice are obvious. Public Goods

Public or collective goods have two distinguishing characteristics: non-rivalry—the consumption of the commodity by one consumer in no way diminishes the supply available to others; and nonexcludability—if the commodity is supplied to one member of society, it is jointly supplied to all. It is difficult to present examples of

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pure public goods, but strong "public good" qualities are exhibited by many commodities, for example, national defence, lighthouses, non-cable radio and TV signals, pest control, urban beautification, flood prevention, parks, street lighting, and open space. To see why market failure is associated with the provision of public goods, let us consider the example of a lighthouse. If two or more shipowners decide to construct a lighthouse, it is in their interests to get as many other shipowners as possible to share in the construction and operation costs in order to minimize the costs of each individual owner. Because of the characteristic of non-rivalry, the consumption of the services of the lighthouse by additional users does not, at least up to a point, interfere with the consumption of these services by any other user. Thus the greater the number of users, the greater is the net social benefit of the lighthouse. Because of the lighthouse's characteristic of non-excludability, however, the services of the lighthouse provided to one ship are provided to all ships. It is thus in the interests of each shipowner to refrain from paying his share of the costs of the lighthouse in the hopes of obtaining a "free ride." The greater the number of potential consumers of a particular public good, the greater is the freerider problem and the less likely the good will be provided by the free market.5 Social Valuation of Non-Market

Effects

The problems of socially valuing intangibles and public or collective goods are similar: there are no observable market prices and the problems of determining shadow prices are substantial. Fundamentally, attempts to incorporate into CBA the social values of intangibles can be grouped into three categories. Surveys One method of determining individuals' willingness to pay for particular non-market amenities is simply to ask them. However, the task of simulating the marketplace in a questionnaire or interview can be difficult. If respondents assume that the system of financing the intangible amenities or of paying for reduction of the intangible costs will be based on some form of direct levies, they may be inclined to consciously or subconsciously reduce their individual estimates of willingness to pay. On the other hand, if the intangible benefit or cost reduction is assumed to be provided out of general revenue with no increased direct charge to the respondents, the stated willingness to pay may possibly be exaggerated.

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The accuracy of the response may also be substantially shaped by the ability of the respondent to conceptualize the intangible effect. In addition to the innate capacity of the respondent, his ability in this context will depend on the accuracy and completeness of the information provided as well as the time and effort expended by the respondent. For various reasons, the respondent's willingness to pay may also be influenced by his knowledge or estimation of the responses of others. Finally, responses may significantly depend on the time frame over which the hypothetical payments would be made. This latter factor involves conceptualizing the present worth of future expenditures, a problem to be discussed in the following chapter.6 Proxies for social values In some situations, values for intangible elements may be inferred. For example, some idea for the valuation of a scenic view may be gained from the differentials in charges between units with and without views in hotels and condominiums. Valuations placed on airport noise may be statistically established under certain conditions by analysing rent differentials and sale prices between houses located near the airport and similar residences distant from the airport. Valuations of commuters' time are often established through analysis of travellers' preferences for faster but more expensive modes of transportation. Publicly provided recreational facilities are frequently valued through the analysis of travel cost data, that is, by the analysis of consumers' willingness to pay the costs necessary for the consumption of the recreation amenities. In cases in which the public sector provides an unpriced commodity, a social valuation may be inferred from a similar or competitive commodity provided in the private sector. In sum, there exists a variety of approaches to inferring social valuations, each with its own set of individual problems. No universally applicable, general-purpose methodology has yet emerged. Qualitative analysis Given the difficulties of assessing the social worth of intangibles, there arise situations in which the most appropriate approach to incorporating intangible effects into CBA is to attempt to assess the characteristics of each effect (e.g., magnitude, duration, spatial extent, incidence) in non-economic or qualitative terms. Under such circumstances the analyst might still attempt to establish a "critical" monetary value for the amenity by determining what dollar value would have to be placed on the intangible(s) in order for an

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accept/reject decision based solely on monetary values to be reversed. MODIFICATIONS AND

EXTENSIONS

In this section modifications and extensions of the previous discussion of the social valuation of economic effects are focused on further consideration of the role of secondary benefits within costbenefit analysis, an extended methodology for the estimation of the social opportunity cost of labour, and the use of hedonic prices for the valuation of non-market environmental effects. Input-Output and Secondary Benefits

Discussion of secondary benefits and costs in the first section of this chapter generally supported their exclusion from cost-benefit analyses. Stabler et al.7 observe that in practice, however, the increased availability of both regional I-O models and computers has "facilitated the development of an increasingly comprehensive approach now regularly used in regional benefit-cost assessment studies. Applied analyses, which once focused almost exclusively on direct benefits and costs, now routinely attempt to measure a variety of 'indirect benefits' as well" (ibid., 13). The use of I-O analysis has prompted a replacement of "stemming" and "induced" benefits and costs with the interindustry notions of "forward" and "backward" linkages. The authors point to a number of recent studies in which particular indirect or secondary effects are treated as benefits. However, "there is a substantial difference between secondary or indirect "effects" and indirect "benefits." We argue first that indirect effects, as measured by changes in value added calculated with an input-output model, are largely income transfers. It is therefore seldom correct to include them, and never without modification, in a benefit-cost analysis" (ibid., 15). In the authors' view it has become only too customary to use an I-O model to calculate the increase in value added resulting from the purchase/sales linkages of the project within the region and to count this increase as a benefit. However, the value added measure is not a benefit. It is an upper limit on the value of the opportunity costs of the resources generating the value added, and is at best the basis for calculating secondary benefits under special circumstances.8 From a national viewpoint indirect effects created by a project in

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region A constructed with foregone expenditures in region B cannot generally be considered to be social benefits. The secondary effects produced in region A can be assumed to be substantially the same as those foregone in region B unless it can be shown that the linkages in A are characterized by a significantly greater potential for capturing the advantages of declining long-run average cost curves or of hiring unemployed and immobile resources.9 The case in North America for secondary benefits on the basis of either declining costs or extended unemployment, the authors conclude, is weak. The best case for secondary benefits in CBA occurs from the regional viewpoint in a situation in which funding of a specificpurpose nature leads to an increased output in linked industries in the region while the loss of output through indirect activity occurs outside the region. (Specific purpose transfers are those transfers made by senior government agencies for exclusive use in a specific activity, and would not otherwise be forthcoming.) If funding of a project is of a general-purpose nature, that is, funding that might well be otherwise allocated to alternative projects in the region, secondary benefits can arise only from differences in levels of activity between the linkages associated with the project and those resulting from the best alternative. With either specific or generalpurpose transfers, payments (e.g., profits and interest) to factors non-resident in the region must be subtracted from local value added in the calculation of any secondary benefits. Social Opportunity Cost of Labour

When new employment is generated in the presence of unemployment, the social opportunity cost of labour, as previously argued, will be less than the market wage. In a study of newly constructed factories in the eastern Scottish borders in and around Berwick upon Tweed, Hodge10 attempts to estimate empirically the magnitude of this differential and its variation over time. At the basis of this estimation of the social opportunity cost of labour (SOCL) are the various states (e.g., employed, registered unemployed, unregistered unemployed, employed outside the region, retired, preparing to emigrate) and the proportions in which the new project draws employees from these various states. The value of lost output attributable to the project is represented initially as

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where ptji the probability that newly hired employee i was previously in employment state ;', and W7,y is the annual wage of employee i in state /. To the above costs are to be added the costs of migration (which might include psychic costs) for those who have moved into the region to take the newly created jobs, less the possible avoidance of costs of those local successful job seekers who would have otherwise emigrated. The costs to employers of hiring and training new workers must also be considered. When new job opportunities are created, a portion of those taking the new jobs give up previously held employment. This creates job vacancies which in turn are likely to be filled in part by those already employed, and so on. Hodge incorporates estimates of these "chain effects" of employment into the analysis by means of a Markov chain approach, a probabilistic model in which the "state" of the system in any time period is dependent only on the preceding states. Constant transition probabilities between employment states are used, as are probabilities that are judged to reflect more accurately the prevailing labour market conditions in the region. As a result the analysis yields one estimate of the social cost of labour for the first year of the project and another for subsequent years. These estimates are then reformulated under differing assumptions regarding various factors such as adjustment costs, migration costs, and the proportion of those hired drawn from the locally employed. Hedonic Prices

The hedonic price approach to the monetary evaluation of nonmarket phenomena is based on the assumption that a particular commodity may be resolved into a number of constituent characteristics which determine its market value. If a statistical relationship can then be established between the market value of a commodity and its various attributes, the contribution of each of the attributes to the commodity's value can be estimated. This contribution is the hedonic or shadow price of the attribute. The most general application of this approach is the valuation of environmental variables through their relationships with house prices. Such an approach is adopted by Anderson and Crocker11 in their study of air pollution and residential property values, in which it was posited that particular air pollutants have a negative effect on house prices. Three metropolitan areas (Washington, Kansas City, and St. Louis) were selected on the basis of the availability of com-

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parable data on mean ambient air concentrations of sulphur oxides and suspended particulates. Regression equations were constructed using measures of property values and rents as dependent variables. The explanatory variables included measures of the above-mentioned pollutants as well as more traditional variables such as family income, age of housing structures, distance from the central business district, and median number of rooms. The results of the regression analysis confirm the hypothesis that property values and rentals tend to be inversely correlated with air pollution. For an additional 10 |xg./m3 per day of suspended particulates plus an additional o.i mg./ioo cm2/day of sulphation, property values fell by $300 to $700 per property and rents decreased by $2 to $4 per month. SUMMARY AND

CONCLUSIONS

Secondary costs and benefits reflect the project's indirect impact and result from the project's sales and purchase linkages with the rest of the economy. Their inclusion within the cost-benefit framework is generally discouraged by economists because of the potential for double-counting. In cost-benefit analysis the social benefits of a project are measured by the consumers' willingness to pay for the output of the project. The project's costs are the opportunity costs of the resources required to produce the output. Net social benefits were shown to be the sum of consumer and producer surpluses. Measurement of these surpluses relies heavily on the assumption that existing market prices accurately reflect social valuations. If the economic conditions underlying this assumption do not prevail, adjustment of market prices, that is, the institution of shadow prices, may be considered. Three cases in which shadow pricing may be appropriately considered are imperfect competition, unemployed resources, and taxes and subsidies. While the problem of distorted market prices poses significant problems for the analyst concerned with social valuations, the task is even more demanding when there exist no market prices at all. Such is the situation when the analyst is faced with valuing externalities and public goods. In such cases one of three general approaches is generally adopted: surveys, associated market prices, or qualitative analysis. Evaluation of costs and benefits under conditions of distorted market prices and the absence of prices poses significant problems

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for the cost-benefit analyst. In such cases, guidelines that can be clearly established in theory are frequently difficult to apply in practice and the analyst must approximate the ideal. CASE

STUDIES

Case Study i: The Evaluation of Recreation Benefits at Graf ham Water

In order to estimate the consumer surplus or benefits associated with an unpriced recreation site, a demand curve must first be estimated. In his attempt to evaluate the benefits of trout fishing at Grafham Water in the UK, Smith12 adopts the travel-cost, or Clawson, method13 for deriving a demand curve by showing how many visits would be expected at the site at various hypothetical admission charges. The method consists of three fundamental steps. First, data are gathered on the geographic origin of each visitor according to "distance zones," which are generally defined by concentric circles with the site at the centre. Second, a relationship between distance zones and visits per given size of population is determined from the data. By adopting a cost per mile for travel to the site, the relationship between distance and visits/population size is converted to travel costs and visits/population size. It then becomes possible to obtain estimates of changes in visits resulting from changes in travel costs. The third step is to derive a demand curve from the above relationship. This is undertaken by assuming that population sizes of the zones are equal and that a change in admission to the site will have the same impact on the number of visits as will an equivalent change in travel costs. Once the demand curve has been constructed in this fashion, the economic benefits of the recreation site are calculated as the total area under the curve, that is, as the consumer surplus associated with the site. In constructing a demand curve in the above manner for the trout lake at Grafham Water, the author posits an exponential relationship between costs per visit (travel costs + fishing fee) and visits per 100,000 population. Travel cost estimates were constructed on three different bases: fuel costs only, fuel costs plus depreciation, and "running costs" as provided by the UK Automobile Association. The results were found to vary sufficiently widely to convince the author to undertake a questionnaire survey of anglers visiting the site. Adjustments were made regarding the average number of visitors per vehicle. Distances from zones were also adjusted, in accordance with the mean actual road distances from each zone's

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settlements. The distance of each settlement was weighted by its population. Among the other problems with which the author attempted to deal were "those variables which influence visit rates and which are correlated with distance, the two most important such variables almost certainly being travel time and the existence of alternative fishing facilities" (Smith 1971:97). The costs of the time spent in travelling to the site are additional to the travel costs discussed above, and the exclusion of these costs will result in an underestimate of the site's benefits. Consideration of alternative sites, which was judged by Smith to be of little significance in this study, can be of importance in other circumstances and may require a respecification of the relationship between travel costs and the number of visits to the site of concern. In concluding that the approach adopted produces useful results, the author mentions, however, that the estimated benefits are for users only and not for society as a whole. As Schofield (1987) points out, non-user benefits may be substantial depending on the site and the nature of the recreational experience. Although such benefits are difficult to measure, they may include increased producer surplus, positive externalities (such as reduced crime rates, increased health) as well as option and preservation values. Case Study 2: Cost-Benefit Analysis in the Evaluation of STOL Air Transport

In 1979, several air carriers applied to the Canadian Transport Commission to provide a STOL (short take-off and landing) service connecting Toronto, Montreal, and Ottawa. Hearings concerning the requests were held in the following year, and in 1982 a licence for the air service between the three cities was approved. As Hettich14 reports, during the 1980 hearings two cost-benefit analyses were submitted, each focusing on a limited STOL service between Toronto and Montreal. A major benefit was presumed to be a savings of time by passengers. This savings was attributable to a shorter flight duration, but more importantly, to the time saved in getting to and from the more centrally located STOLports. A second presumed benefit was derived from lessened impact on existing airports, where reduced congestion and fewer delays were expected to result from traffic diversions to the STOLports. The lower volume of traffic might also be expected to result in further benefits by delaying planned construction of new facilities at the existing airports. Finally, it was argued, an operating STOL system using

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Canadian aircraft would provide a demonstration effect which would benefit the Canadian aircraft industry through increased sales. A major cost of the STOL system is, of course, the resources required to construct terminal facilities, air control systems, and access systems. In addition there are to be considered the opportunity costs of land used to establish the ports. Since few new journeys can be expected, the increased costs of transporting passengers drawn from conventional flights must be considered. Given the proposed sitings, an additional cost of rerouting existing power lines was also a factor to be considered. Finally, the analysis might also be expected to include costs imposed on users of land near the new ports (other than the rerouting of power lines), such as increased noise and height restrictions on buildings. The results of the two CBAS, one done for the city of Toronto and one undertaken by Transport Canada, are shown in Table 17. The figures are in present values of millions of 1980 dollars. In each report a social discount rate of 10 per cent was used. TABLE 17

Benefits and costs of a proposed STOL system Toronto study

Transport Canada

42

38.7

3

2-3

45

41.0

Infrastructure Opportunity costs of Toronto airport site Increased transportation costs Increased costs of power line rerouting Total costs

42 4i 43 13 139

27.5 42.2

Total benefits— total costs

-94

-28.7

BENEFITS

Travel time savings Benefit to existing airports Reduced congestion Delay in expenditure for new facilities Industrial benefits (not estimated) Total benefits COSTS

69.7

Source: Adapted from ibid., 492

Differences between the estimates of benefits and costs between the two analyses can be expected, in light of the difficulties of making estimates of the impacts produced by the STOL system. Disparities between the two studies undoubtedly also resulted from

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differences in perspectives between the two sets of analysts undertaking the studies. Differences between the two reports aside, it is readily seen that they concur in showing the STOL system to be economically infeasible. However, as mentioned, the project was approved. From his review of the CTC hearings regarding the STOL system, Hettich draws, two major hypotheses to explain why the actions of decisionmakers may differ from the recommendations of cost-benefit analysts. The hypotheses also shed light on the disparities between the two CBA studies. The first pertains to the differences between social costs and an agency's financial outlays. "The larger the share of non-budgetary costs in total economic costs, the more likely it is for a project with a negative net present value to be undertaken. The discussion suggests furthermore that costs external to an agency may be prevalent in situations where publicly-owned land or other publicly-owned assets constitute a significant input into the project," (ibid., 494). The author's second hypothesis relates to possible differences between the objectives of CBA and those of an agency. "If output or performance of the department is measured primarily by the extent to which it succeeds in satisfying its public or traditional 'clients/ the decision-maker will be interested mainly in producing benefits for this group" (ibid., 494). SELECTED

READINGS

Anderson, L.G. and R.R Settle. 1977. Benefit-Cost Analysis: A Practical Guide. Lexington MA: Lexington Books Boulding, K.E. 1981. Evolutionary Economics. Beverly Hills: Sage Publications Daley, H.E. 1977. Steady-State Economics. San Francisco: W.H. Freeman and Company DeLong, J.V. et al. 1981. "Defending Cost-Benefit Analysis: Replies to Steven Kelman," Regulation, 5:39-44 Kelman, S. 1981. "Cost-Benefit Analysis: An Ethical Critique," Regulation, 4:33-40 Montador, B. and H. Baumann. 1977. Government Intervention in the Marketplace and the Case for Social Regulation. Ottawa: Treasury Board

Secretariat, Planning Branch Moore, T. 1978. "Why Allow Planners to Do What They Do?: A Justification from Economic Theory," Journal of the American Institute of Planners, 44:387-98

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Prest, A.R. and R. Turvey. 1965. "Cost-Benefit Analysis: A Survey," Economic Journal, 75:685-705 Sassone, P.G. and W. A. Schaffer. 1978. Cost-Benefit Analysis: A Handbook. London: Academic Press Schofield, J. A. 1987. Cost-Benefit Analysis in Urban and Regional Planning. London: Allen and Unwin

CHAPTER SEVEN

Cost-Benefit Analysis: Discounting Future Benefits and Costs

For the vast majority of projects, or developmental stimuli, that the analyst is likely to consider, associated benefits and costs will extend beyond the initial year. For example, while the construction costs of a dam are generally limited to the immediate present, the benefits and operating costs (and perhaps the environmental costs) attributable to the dam will in all likelihood extend a significant number of years into the future. How then do we go about comparing future costs and benefits with those of the present? THE DISCOUNT

RATE AND

NET PRESENT V A L U E

If offered the choice of the receipt with absolute certainty of a specific cash sum either immediately or one year from now, no rational person would select the latter alternative. A dollar one year from now is obviously not the same as a dollar now—it is worth something less. The relevant question at this poin is precisely how much less. To simplify the calculations involved in answering this question, let us assume that the rate of interest is 10 per cent and is compounded annually. We shall also adopt temporarily the simplifying assumption that at the 10 per cent rate one can borrow or lend as much as one wishes. Put another way, money is assumed to be worth 10 per cent. Under these conditions, what is the value now of, say, $1,100 to be received one year hence; that is, what is its "present worth" or "present discounted value"? Let P0 represent the amount one would have to part with in order to obtain $1,100 one year from now at 10 per cent interest. If one

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were to invest P0, at the end of one year he would have accumulated the original principal, P0, plus the interest, 10 per cent of P0. We may thus determine P0 as follows: Given the opportunity of earning 10 per cent on his money, the rational individual is indifferent between receiving $1,000 now and $1,100 one year hence. The present discounted value, P0, of $1,100 in this case is $1,000. Having established the present value of the receipt, or benefit, of $1,100 a year from now, what is P0 of a cash outlay, or cost, of $1,100 in a year's time? Again we find that the answer is $1,000, since one would be indifferent between paying $1,100 a year from now and investing $1,000 now at 10 per cent in order to obtain $1,100 to fulfill the financial obligation one year later. In general, if the market rate of interest is z and the cash flow (benefit or cost) one year hence is Pl7 the present value, P0, of this flow (i.e., the amount that would have to be put into the bank in order to obtain PI one year hence) is calculated as

The present discounted value of a cash flow two years hence can be similarly calculated as

Generalizing, P0 of a cash flow, Pn, n years hence is For example, if money is worth 9 per cent, the present value, P0, of a series of cash flows of $800 one year from now, $1,000 two years hence and $1,200 three years into the future can be calculated as In sum, we can now compute the present worth or "net present value," NPV, of any stream of costs and benefits as

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Discount Tables

It is immediately obvious from the above equation that the calculation of NPV can in many cases be quite a tedious exercise. To facilitate the determination of NPV, appropriate tables have been prepared. For example, from Table 22 of the appendix, it can be seen that the present value of $100 five years hence discounted at 15 per cent is $497, which is the result of $ioo/(i.i5)5. From this table one can readily see the substantial effect of the discount rate. One thousand dollars ten years hence discounted at 5 per cent is $614; discounted at 20 per cent it is $162. Appendix table 23 shows at various discount rates and time periods the present value of an annual cash flow of $1.00. From the table it can be seen that the present value of, say, $100 each year for twenty-five years discounted at 10 per cent is $907.70. The present worth of $1,000 per year for fifteen years at a discount rate of 20 per cent is $4,675. Both tables are frequently useful in determining the NPV of a stream of costs and benefits, as is illustrated in the following example. It should be pointed out, however, that use of these tables is rapidly declining as a new generation of preprogrammed calculators, which can readily generate values for discounted monetary streams, has come into common usage. Numerical Example

Suppose that a homeowner is faced with the necessity of replacing her old furnace. She is considering two new models, of which the more fuel-efficient costs an extra $1,000 but is guaranteed to result in an average annual savings of $200 in her fuel bill. The fuelefficient model requires no extra maintenance, has a life of twenty years (as does the alternative, standard model), and Will not affect the selling price of the home. If the homeowner would have to borrow the extra $1,000 at 15 per cent (i.e., the value or cost of money is 15 per cent), would it be economic for her to purchase the fuelefficient model? To answer this question we have only to compare the present additional cost ($1,000) of the fuel-efficient furnace with the present value of the savings of $200 at 15 per cent over twenty years, the life of the furnace. From Table 23 the present value of this stream of benefits is $1251.80 ($200 x 6.259). Since this figure exceeds the extra cost ($1,000) of the furnace, the additional expenditure is seen to be economically worthwhile. Another way of looking at the situ-

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Regional Economic Impact Analysis and Project Evaluation

ation is to recognize that in order to get a benefit stream of $2oo/year for twenty years, one would have to invest $1251.80 at 15 per cent; however, the homeowner can secure this benefit stream at 15 per cent for only $1,000. In addition to the previous assumptions we may note that in utilizing the above tables, we are implicitly assuming that the annual savings in fuel bills occur at the end of each year. Since in reality these savings are likely to occur on a monthly or bi-monthly basis, the present value of our benefit stream in this example is somewhat understated. Let us now slightly alter our set of assumptions by supposing that our homeowner plans to move from her present house in five years. Further, she has been assured by her real estate agent that the more fuel-efficient furnace will increase the sales value of her home at that time by $500. Is the more fuel-efficient furnace still worthwhile? The discounted costs and benefits are now determined as

In this case Table 22 was used to obtain the present value of $500 five years hence at 15 per cent and Table 23 was employed to find the immediate worth of $2OO/year over five years, again at 15 percent. Because the NPV is negative, the extra expenditure on the more fuel-efficient furnace cannot under these circumstances be economically justified. As a final observation regarding this example, we might note that we have, in addition to our previous assumptions, assumed that the homeowner obtains no benefits from the "pride of ownership" of a more technologically advanced heating unit that is relatively conserving of fossil fuels. It is further assumed in this case that there are zero transactions costs, that is, there are no costs involved in arranging a loan (other than the 15 per cent interest rate).

Discounting Future Costs and Benefits THE APPROPRIATE

123

DISCOUNT RATE

Because of its obvious importance in determining whether or not a particular project is considered economically desirable, the discount rate must be chosen with considerable care. In the theoretical literature on the subject there have been two fundamental approaches to the designation of the appropriate discount rate: the social opportunity cost (soc) of capital and the rate of social time preference (STP). SOC

The social opportunity cost of capital is a measure of what society is giving up by diverting investment funds from the private to the public sector. For purposes of cost-benefit analysis, soc is expressed as an annual rate of return. The argument in support of the soc measure rests primarily on a concern for economic efficiency. In economic terms, the flow of investment funds between economic projects should be channelled into the private and public sectors according to their respective rates of return. If the rate of return to capital in the private sector is r and a discount rate r* is used for public sector projects, a socially inefficient allocation of resources will result if r* is not set equal to r. For example, if r = 10 per cent and r* is set at 6 per cent, the risk is run of using resources to undertake public sector projects that yield rates of return of 6.1 per cent to 9.9 per cent while foregoing the higher 10 per cent return in the private sector. A net loss to society results. Rate of return in public sector 9.9 per cent Funds for projects earning these 9.0 rates of return in the public sector 8.0 would be diverted from the private 7.0 sector where they would earn an 6.1 average return of 10 per cent. If, on the other hand, r* is set at a rate higher than r, say 15 per cent, the risk is run of foregoing projects in the public sector that would yield rates of return of 10.1 to 14.9 per cent, which exceed 10

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Regional Economic Impact Analysis and Project Evaluation

per cent average return in the private sector. Again, a net social loss occurs. Rate of return in public sector 14.9 per cent Funds for projects that would earn 14.0 these rates of return in the public 13.0 sector are retained in the private 12. o sector where they earn an average 11. o return of 10 percent. 10.1 In both cases we are left with an r* that differs from r and a resulting inefficient allocation of funds between the private and public sectors. The obvious conclusion is to apply to public sector projects a discount rate equal to the social opportunity cost of the resources employed. To this point in the analysis it has been assumed that the social cost of public projects has been solely the cost of displaced investment in the private sector. This assumption is relaxed in discussion to follow. STP The social time preference is that rate of return necessary to effect the sacrifice of present for future consumption. Proponents of the social time preference approach to the discount rate argue that the rate of return to resources invested in the private sector significantly understates the value society places, or should place, on future compared with present consumption.1 Arguments for adopting a rate of discount lower than the prevailing soc rate as determined by market rates of return generally proceed along two complementary lines. One position is that there is a human tendency to discount the future too greatly. Half a century ago, the economist Pigou asserted that individuals are myopic in their consideration of the future, as if they viewed the future through the wrong end of a telescope. This myopic bias toward a higher than optimal discount rate results, according to the argument, in the rejection of projects that yield disproportional shares of benefits to future generations. A second argument in support of a discount rate lower than market-revealed rates is that each individual's willingness to sacri-

Discounting Future Costs and Benefits

125

fice current for future consumption is dependent to a significant degree on the willingness of everyone else to do the same. Proponents of this position argue that society's willingness to forego present for future benefits would be greater if the government would co-ordinate the process by insuring that the sacrifice of present benefits is shared by everyone. At the root of both of these positions is an equity consideration: the distribution of net benefits between the present and the future. STP proponents generally hold that the discount rate should be lower than that dictated by the soc of capital in order to pass on to future generations greater economic benefits stemming from public sector investment. This argument is not universally accepted, however. Schofield (1987) points out two counterarguments in favour of higher than market-revealed rates. Both rest on the central issue of equity. If it is judged that future generations are likely to be economically better off than the present generation, then the lower the discount rate used in CBA calculations the greater will be the tendency to approve projects which provide for the relatively rich (future generations) at the expense of the relatively poor (the present generation). At the heart of the second argument is the proposition that market rates do not reflect in any democratic fashion the weighted average of individual time preferences. It is the relatively better off members of society who are active in financial and investment markets and who thus exercise a disproportionate amount of influence on market rates. Further, the rich, so the argument goes, tend to have lower rates of time preferences than do the less well off. Again, the conclusion is for a rate of discount higher than one determined on the basis of market conditions.2 Measurement of the Discount Rate As earlier argued, if investment funds for the project(s) under analysis are presumed to be diversions from investments in the private sector, the soc is the relevant measure of the discount rate. However, if the funds are presumed to be diversions from private consumption, the STP is arguably the relevant rate.Let us discuss each of these propositions in turn and then proceed to a situation in which funds are presumed to be diverted from a variety of sources. A decision to adopt the rate of return on investment in the private sector as the appropriate discount rate immediately raises at least two questions. The first is whether to adopt the pre-tax or post-tax rate of return. The answer to this question is straightfor-

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Regional Economic Impact Analysis and Project Evaluation

ward. Government taxation of returns to investment merely involves a redistribution of the returns and does not in any sense alter the volume of the returns. The pre-tax rate of return is thus the relevant measure of the full returns to investment and hence the appropriate rate at which to discount public sector projects. A second question which arises is not as easy to answer. There exist several rates of return in the private sector and these rates differ substantially between industries or sectors of the economy. Which is the appropriate rate(s) to apply to the public sector? One answer would be a weighted average of the rates of return in the industries from which the private investment funds were diverted. However, the practical difficulties of identifying these industries for any particular public sector project can be substantial. If it can be determined that the dollars diverted from private investment would have been channeled into one particular industry, it is appropriate to apply to the diverted funds the pre-tax rate of return prevailing in that industry. Strictly speaking, since we are evaluating the full social costs and benefits of the public sector project, the valuation of the social costs and benefits of the operations of the industry should also be considered. For example, if the industry in question generates significant negative externalities, the industry's rate of return should be appropriately adjusted downward. With regard to funds diverted from private consumption, it is appropriate to apply as the STP rate the post-tax return on savings. The argument for so doing is based on the assumption that in a given time period individuals allocate their disposable incomes between consumption and savings such that the "returns" on the last dollars allocated to the two categories are equal. Under this assumption the yield or return foregone on the last dollar spent on consumption is the post-tax return that would have been obtained from savings. Finally, let us suppose a situation in which funds for the project^) under consideration are presumed to be diverted from several industries, from private consumption, and from private savings. If we represent the proportion of total funds to be diverted from source i as «,- and the appropriate rate of discount from that source as rif the appropriate discount rate, r, to be employed in the analysis is .

If i in the above equation represents an industry from which investment funds are diverted, r, may be taken to be the average rate

Discounting Future Costs and Benefits

127

of return to investment in that industry adjusted for any significant externalities. If i pertains to the diversion of funds from private consumption as a source of financing, rf is the post-tax return on savings. If the source of financing is funds diverted from personal savings, it might first be thought that r, is the post-tax return on savings, since this is what savers would forego through a diversion or loss of their savings. However, in a fully or near-fully employed economy, it may be assumed that savings are channeled into productive investment projects by the financial intermediaries holding the savings. Under these circumstances the appropriate opportunity costs are again a weighted average return of pre-tax rates of return in the private sector, since it is ultimately these investment returns that are foregone by society through the loss of personal savings. The difficulties of applying these guidelines in practice, however, are not to be underestimated. As Prest and Turvey observed some time ago, "Discussions about social rates of time preference, social opportunity cost, etc., do not cut very much ice in most empirical work and we have not been able to discover many cases where there was any convincingly complete application of such notions. . . The truth of the matter is that, whatever one does, one is trying to unscramble an omelette, and no one has yet invented a uniquely superior way of doing this" (1965:699-700). Two areas remain to be included in our discussion: the importance of the viewpoint adopted in the analysis and the advisability of sensitivity analysis regarding the discount rate, that is, the examination of the effect of changes in the discount rate on the net present value of the project. To this point, in consideration of the discount rate, we have consistently adopted the national viewpoint with respect to all costs and benefits generated by a regional public-sector investment project. Were we to limit ourselves to a regional perspective or viewpoint, it is arguable that the selection of an appropriate discount rate would be substantially altered. From a strict regional perspective it would not be unreasonable to adopt the regional/municipal government's long-term borrowing rate as the appropriate rate of discount. Such a selection would imply that resources used for public sector investment projects in the region would otherwise be employed outside the region and would produce no direct regional benefits. Under these circumstances the only opportunity costs of the borrowed funds are the associated interest payments, regardless of what rate of return the funds might have earned outside the region.4 In view of the continuing debate and of the importance of the in-

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fluence of the selection of the discount rate on the results of the analysis, it is generally recommended that analysts perform calculations to see how sensitive their results are to variations in the discount rate. For example, if r = 10 per cent, one might choose a "lower bound" (e.g., 5 per cent) and an "upper bound" (e.g., 15 per cent) to determine the effects of different discount rates on the project's economic desirability.5 It is then left to the policymakers to use their own judgments regarding the appropriate measure of the discount rate, taking into account any equity considerations they deem to be relevant. ALTERNATIVE INVESTMENT CRITERIA

Cost-benefit analysis is applied both in cases where a single project is to be accepted or rejected and in situations where several competing projects must be considered. The three most commonly employed criteria for assessing the relative desirabilities of proposed projects, or investment opportunities, are the net present value, the benefit cost ratio, and the internal rate of return. The net present value (NPV) of a time stream of benefits (Bt) and costs (Ct) is determined by valuing the net benefits (Bt - Ct) in any period t by the factor i/(i + r)1 where r is the appropriate discount rate. In general, for a project whose economic life extends over a number of years, The decision rule is to consider undertaking the project only if NPV > o. The benefit cost ratio B/C for a particular project is simply the present value of the project's benefits divided by the present value of the project's associated costs. It can be readily calculated from the above information as

The decision rule is to consider undertaking the project only if B/C > i.o. A project's internal rate of return (IRR) is that discount rate which equates the present value of the project's benefits with the present value of its costs. Alternatively, it can be expressed as that dis-

Discounting Future Costs and Benefits

129

count rate which equates the net present value of the project to zero. It is determined by solving the following equation: The decision rule is to consider undertaking the project if the IRR > the opportunity cost of capital. Compared with the two previous criteria, the IRR suffers from two serious disadvantages. The first, which is immediately obvious, is the difficulty of calculating IRR. While tables of discount factors are readily available to aid in the determination of NPV and the benefit cost ratio, there are no standard counterpart tables to assist in the calculation of IRR and one must generally rely on trial and error methods or a computer program. A second and perhaps less obvious shortcoming of the IRR ranking criterion is that the solution to the above equation may yield multiple values for IRR. Solving the above equation for IRR will involve finding roots to satisfy a polynomial expression. For the above n period project there will be n-i values for IRR (assuming n >2).

These two shortcomings preclude further consideration of this particular criterion. For investment decisions, the IRR "is not an intrinsically correct rule," but merely a procedure that often yields the result produced by the NPV criterion. Unfortunately, at times the two remaining criteria, NPV and B/C, give apparently conflicting guidelines. For example, among the five projects listed below, project D has the highest net present value while project B has the highest ratio of discounted benefits to discounted costs. In choosing among projects, the fundamental rule is to select those projects which result in the largest net present value. If there are no financial or physical constraints upon the selection of projects listed, only project C would be rejected. Let us consider, however, cases in which such constraints are relevant. Project

A B C D E

Discounted Discounted benefits costs $400 600 325 675 500

$300 400 350 500 350

NPV

$100 200 -25 250 150

B/C 1.33 1.50 0.93

i-35 1.43

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Regional Economic Impact Analysis and Project Evaluation

When selection occurs under the constraint of a specified budget, the general rule is to choose those projects with the greatest return per dollar cost, that is, those with the highest B/C ratios, until the budget is exhausted. For example, under a budget constraint of $750, project B would be first chosen, followed by project E. The combination would just exhaust the budget (400 + 350 = 750) and would yield a total net present value of $350. No other project or combination of projects within the budget constraint can be chosen which will exceed this value of NPV. Suppose now the budget constraint is raised to $850. If we attempt to add project D, the project with the third highest B/C, the budget constraint is exceeded. The procedure for selecting projects according to B/C ratios until the budget is exhausted breaks down when the selection of an additional project violates an otherwise non-binding budget constraint. Under this condition, various combinations of projects must be examined. With the present financial constraint of $850, projects D and E yield the highest total NPV ($4OO).

In addition to budget constraints, the analyst must at times consider the physical constraints of dependency and exclusivity. Suppose, for example, that with a budget constraint of $750, there is also the constraint that project B is dependent on C, that is, project B cannot be undertaken unless project C is first put in place. Under this circumstance, project D is to be selected. With the same budget and the constraint that projects B and E are mutually exclusive, NPV will be maximized by selecting B and A. Again, the basic rule is to select those projects, given financial and physical constraints, which result in the greatest net present value.7 MODIFICATIONS AND

EXTENSIONS

Discussion in this section is directed first to the rationale for the use by Canadian federal agencies of a social discount rate of 10 per cent and a critique of this value. Attention is then turned to a discussion of the influence of inflation on the discount rate. Determination of the Social Discount Rate for Investment Projects in Canada8

As stated earlier in the chapter, the Treasury Board of Canada recommends a real, inflation-free discount rate of 10 per cent for public investment projects in Canada, with a sensitivity analysis to be

Discounting Future Costs and Benefits

131

undertaken with rates of 5 per cent and 15 per cent. The 10 per cent figure is based on empirical analysis of data pertaining to the period 1965 to 1974, in which it was determined that 10 per cent was the weighted average cost of investment funds. TABLE l8

Cost of investment funds in Canada Sector Domestic investment Domestic consumption Foreign borrowing

Social rate of return 11.45% 4.14 6.11

Social cost of capital

Proportion of borrowing x x x

Weighted cost of capital 8.59%

o-75 0.05

==

0.20

=1.22

=0.21

1O.O2%

Source: Government of Canada 1985

As shown in Table 18, it was assumed that for every investment dollar in Canada seventy-five cents comes from displacement of other private investment, five cents is drawn from postponed domestic consumption, and twenty cents comes from foreign sources. The cost of displaced investment is taken to be the pre-tax rate of return on capital in the private sector. The social cost of postponed consumption is taken to be the post-tax rate of return on savings, and the cost of foreign borrowing is determined as that rate of return necessary to attract funds from foreign sources. A number of criticisms of the above analysis have been made, most of which point to an overestimation of the appropriate discount rate. Among the contrary arguments advanced have been: —The social rate of return earned by a number of private firms is overstated because they benefit from subsidized energy inputs from the public sector. —The rates of return to firms in the private sector are based on average rather than the lower marginal returns. —The rate of return in the private sector is overstated because the income tax adjustment (tax liabilities were added to accounting profits to determine the pre-tax, social rate of return) is based not on the current tax code but on an amalgam of outdated and generally harsh fiscal measures. —The inclusion of sales taxes as benefits contributes to the exaggeration of the social rate of return because a portion of these

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Regional Economic Impact Analysis and Project Evaluation

taxes (e.g., taxes on cigarettes and alcohol) are levied simply to offset social costs. —The portion of incremental funding of private investment in Canada that comes from foreign sources, which has a lower social opportunity cost, is underestimated. —The proportion of funding contributed by the relatively low cost domestic savings is understated. These points, as well as the proper methodology to account for risk in both the public and private sectors, continue to be subjects for debate for government and academic analysts concerned with the social discount rate to be applied to public investment projects. In the meantime more recent empirical work on the social discount rate has tended on balance to support a rate slightly lower than the 10 per cent standard. Inflation and the Discount Rate Inflation is a persistent and significant increase in the general price level. To see what adjustments to the discount rate are necessary under conditions of inflation, let us initially assume complete price stability and a stream of net benefits n years into the future. In the absence of inflation our hypothetical discount rate is taken to be r. The NPV of our net benefit stream is determined as

Suppose now an annual rate of price inflation of p per cent is foreseen for the next n years. That is, the general price level is expected to increase p per cent per year. Our net benefit stream may be expressed in nominal (inflated) dollars as B^i + p) one year hence, B2(i + p)2 two years hence, and so on. If the benefit stream is left unadjusted for inflation, the NPV determined with an unchanged rate of discount will obviously be higher. There is good reason, however, to expect the rate of discount to rise. Realizing that debts will be paid in inflated dollars, lenders will demand a higher rate of return to compensate for the inflation factor. The increase in r will approximate (i + p) in order to maintain returns at the same real (uninflated) rate. In short, NPV can be recalculated in nominal terms as

It can now be seen that the (i + p) terms in equation (7.12) cancel and equation (7.12) reduces to equation (7.11). We thus have two approaches to handling inflation in the determination of NPV. Ei-

Discounting Future Costs and Benefits

133

ther all costs, benefits, and the discount rate are valued in real dollars (equation (7.11)) or all are valued in nominal dollars (equation (7.12)). The results are identical. In practice, it is common to adopt the first approach, that is, to ignore the inflation factor by projecting costs and benefits in constant prices and using a real rate of discount.9 SUMMARY AND

CONCLUSIONS

Estimates of monetary flows of costs and benefits that are predicted to occur in the future do not have the same value as flows of the same magnitudes that are scheduled to occur in the present. Formulas for discounting future flows have been established that permit the comparison of costs and benefits occurring at any point in time. As these formulas are somewhat cumbersome to apply, analysts generally turn to published discount tables (such as those shown in the appendix), to pre-programmed calculators, or to specifically designed computer programs. In the discounting procedure, the choice or construction of an appropriate social rate of discount is a contentious one among economists. The debate between those favouring rates reflecting the social opportunity cost of capital, and those favouring a social time preference rate, or some synthetic rate, remains unresolved. If the opportunity cost rate is adopted, as is common practice, then it becomes appropriate to weight the various rates of return on the foregone uses of the funds acquired. Given the importance of the discount rate in establishing the rankings of public investment projects, empirical efforts to construct the appropriate rate are ongoing. Of the three criteria—net present value, the benefit-cost ratio and the internal rate of return—for deciding the relative social desirabilities of investment projects, the use of net present value is the generally recommended procedure. Inflation is customarily accounted for in cost-benefit analysis by estimating costs and benefits in constant prices and adopting a real rather than nominal rate of interest. CASE STUDIES

Case Study i: A Cost-Benefit Analysis of an Urban Renewal Project

In July 1959 a i89-acre urban renewal plan for East Stockton, California, was approved by the federal government. Clearly, as Mao10 observed, the government expected significant social benefits to

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result from the redevelopment project. "Lots in the area were all undersized—25 x 50 feet. There were no curbs, gutters, sidewalks, or sanitary and storm sewers. About 90 percent of all the dwelling units in the area were unfit for human habitation. There was a lack of recreational facilities for adults and children, compared with the city as a whole, the area experienced above-average rates of crime, disease, fires, and juvenile delinquency" (ibid., 100). By 1964 82 per cent of the cleared land had been sold. In his ex post analysis of the redevelopment project, Mao constructed the following table of tangible benefits and costs associated with the project. TABLE 19

Tangible social benefits and costs of the East Stockton urban renewal project BENEFIT Increase in value of project land Increase in value of nearby land Value of public improvements Cost reductions in muni, services Fire protection Health protection Police protection

Amount $ 227,631 415,500 822,980

Date of reckoning June 30, 1960 June 30, 1964 June 30, 1966

700,000 425,000 1,167,000

Jan. i, 1964 Jan. i, 1964 Jan. i, 1964

$ 113, 190

Dec. 31, 1958

201,535 113,800 387,466 93^35 59,228 32,731 2,342,418 701/315 551,980 84,715

June 30, 1961 Dec. 31, 1960 Dec. 31, 1960 June 30, 1961 June 30, 1964 Dec. 31, 1962 June 30, 1961 June 30, 1964 Dec. 31, 1967 June 30, 1961

COST

Survey and planning Project execution expenditures administration, travel, office furniture legal services acquisition expenses site clearance disposal & retention costs project inspection value of improvements demolished Site improvements Public and supporting facilities Relocation payments Source: adapted from ibid., 104

The iSg-acre redevelopment plan was approved by the federal government in July 1959 and by 1964 82 per cent of the cleared land had been sold. The dates of reckoning for the benefits were established at points in time in which it was judged that the major share of benefits were captured by the project. (Benefits which accrued after the dates were estimated on the basis of benefits already generated.) Dating of costs was done on the basis of expenditure data supplied by the redevelopment agency. To simplify the analysis, it

Discounting Future Costs and Benefits

135

was assumed that real costs were incurred when payments were made by the agency. The costs and benefits in Table 19 were discounted at 6 per cent. Two-thirds of the redevelopment funds were supplied by the federal government. The social opportunity cost of these funds was set at 5.5 per cent, based on previous work by Eckstein,10 who experimented with two alternative models of incidence. One model was burdensome to low-income families, the other to high-income families. In both cases the social cost of capital was found to be between 5 and 6 per cent. The local share of project funding was money borrowed at 4.4 per cent. Assuming a marginal tax rate of 40 per cent, purchasers of the tax-exempt securities received the equivalent of a 7.3 per cent corporate bond. With two-thirds of the funding at a social cost of 5.5 per cent and the remaining one-third at 7.3 per cent, an approximate weighted average of 6 per cent was taken to the overall social cost of capital. At a discount rate of 6 per cent, it was determined that the present value of the project's tangible costs exceeded the present value of tangible benefits by $1,098,723. However, it was also determined that the project produced considerable intangible benefits as well. Indeed, 85 per cent of the relocated former residents who were surveyed indicated that they had benefited from the project. The following method was proposed by Mao for treating the intangible benefits: First, discount all project expenditures to the present at the social cost of capital. The sum of the present values is the total tangible cost of the renewal project. Next, discount all tangible benefits to the present at that [same] rate. The sum of the present values is the total tangible benefit of the renewal project. Now, if total tangible cost exceeds total tangible benefit, the difference is the value which society must assign to the intangibles in order for the project to break even, (ibid.: 99-100)

It was thus concluded that for the redevelopment to be socially beneficial, the intangible benefit of increased welfare of former residents had to exceed in dollar terms $1,098,723. The subjective valuation of the intangibles was left for each interested party to undertake. Case Study 2: A Cost-Benefit Analysis of a New Zealand Aluminum Smelter

In 1980, the New Zealand government gave initial approval to the construction of a world-scale aluminum smelter. Total investment

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Regional Economic Impact Analysis and Project Evaluation

over a decade was to be well in excess of a billion dollars and funding was to be provided by an international consortium proposing the smelter. Since the government did not release the results of the expected costs and benefits of the project, Wright and Mansell,12 in their critical examination of the government's evaluative process, attempted to reconstruct the official analysis. The results of this effort revealed an estimated net present value of the scheme of $110 million. This result was produced by adopting a social discount rate of 10 per cent and assuming the cost of foreign funding to be 3 per cent. TABLE 2O

Benefits and costs of the smelter-energy project, 1981-2016, foreign financing of public capital expenditures (millions of 1980 NZ$) Benefits: net additions to foreign exchange reserves

$927

Costs: resources used

817

Net benefits

110

Source: ibid., 55

Again using a discount rate of 10 per cent, the authors proceeded to demonstrate that a very sizeable portion of the benefits of the project were derived from the proposition that it would be externally funded. The difference between the present value of the inflow of capital from foreign borrowing and the subsequent outflow was estimated by the authors to be $253 million. If this benefit, attributable solely to foreign financing and the willingness to discount the burden of repayment at a relatively high rate, is subtracted from the determination of total benefits, the project shows a NPV of -$143 million, as shown in Table 21. TABLE 21

Benefits and costs of the smelter-energy project, 1981-2016, domestic financing of public capital expenditures (millions of 1980 NZ$) Benefits: net additions to foreign exchange reserves Costs: resources used

$674 817

Net Benefits:

-143

Source: ibid., 58

Discounting Future Costs and Benefits

137

The factor of foreign funding alone is the difference between an attractive and socially unacceptable project. The authors argue, however, that the benefits associated with foreign financing were calculated in a questionable manner. The cost of the borrowed capital (soc) in the government calculations was the estimated real interest rate of 3 per cent. As mentioned, however, a social discount rate of 10 per cent, which the authors assume to be the public sector's estimate of the social time preference, was employed to determine net present value. This difference between soc (the return foregone on displaced alternative projects) and the social time preference (society's preference for present benefits over future benefits) is the critical determinant of the large net benefits associated with foreign borrowing. Most analysis of the soc for public projects assumes that they are financed domestically. Given this, the theoretical dilemmas revolve around the fact that public funds normally come from a variety of sources and it is difficult to identify which opportunities are being displaced. There is an additional constraint that the rate should not be such that it diverts funds from preferred alternatives in the private sector. However, both these dilemmas can be avoided if the project is financed externally. All that is needed is the reasonable assumption that implementation will not influence the interest rate on future loans and the social opportunity cost is identical to the real interest rate on the loan, (ibid., 59)

If such a procedure is adopted, it becomes relatively easy for the public sector to justify projects by simply resorting to foreign funding. The authors deplore this possibility and recommend that in the evaluative process for any project the soc and discount rates be identical. Further, the authors suggest that governments may be myopic in always assuming that a high discount rate implies prudence in the evaluative process. In the present case, "it may have been implicitly assumed that the cost stream would precede the benefit stream and that a high STP [discount] rate would therefore lead to a conservative evaluation. In actuality, this practice has just the opposite effect if the project is financed by foreign borrowing and if, as in the present case, net benefits are positive in the early years. It would have been ironic if the approval of this major development proposal was based on a misunderstanding about the implications of using a supposedly conservative social discount rate" (ibid., 61).

138

Regional Economic Impact Analysis and Project Evaluation SELECTED READINGS

Baumol, WJ. 1968. "On the Social Rate of Discount," American Economic Review, 58:788-802 Dasgupta, A.K. and D.W. Pearce. 1972. Cost-Benefit Analysis: Theory and Practice. New York: Barnes and Noble Government of Canada. 1976. Benefit-Cost Analysis Guide. Ottawa: Planning Branch, Treasury Board Secretariat, catalogue no. BT 35-2-1976 Prest, A.R. and R. Turvey. 1965. "Cost-Benefit Analysis: A Survey," Economic Journal, 75:685-705 Province of British Columbia. 1977. Guidelines for Benefit-Cost Analysis. Victoria: Environment and Land Use Secretariat Sassone, P.G. and W. A. Schaffer. 1978. Cost-benefit Analysis: A Handbook. London: Academic Press Schofield, J.A. 1987. Cost-Benefit Analysis in Urban and Regional Planning. London: Allen and Unwin Sugden, R. and A. Williams. 1978. The Principles of Practical Cost-Benefit Analysis. Oxford, Eng.: Oxford University Press

APPENDIX

Tables of Discount Rates TABLE 22

Present discounted value of one dollar for selected discount rates and time periods Year

1%

3%

5%

.952 .907 .864 .823 .784 .614 .481 •377 .295

1

.990

.971

2

.980

3 4 5 10 15

.971

•943 •915 .889 .863 •744 .642 •554 .478

.961 .951 .905 .861

20

.820

25

.780

Rate of discount 10% 15%

.909 .826 •751 .683 .621 .386 .239 .149 .092

.870 .756 .658 •572 •497 .247 .123 .061 .030

20%

25%

.833 .694 •579 .482 .402 .162 .065 .026 .010

.800 .640 .512 .410 .328 .107 .035 .012 .004

Discounting Future Costs and Benefits

139

TABLE 23

Present discounted value of one dollar per period for selected discount rates and time periods Year

1%

i

O.99O

2

1.970

3 4 5

2.941

10

3.902 4.853

15

9-471 13.865

20

18.046

25

22.O23

Rate of discount 10% 15%

3%

5%

0.971 1.913 2.829 3-717 4.580 8.530 11.938 14.877 17.413

0.952 1.859 2.723 3.546 4.329 7.722 10.380 12.462 14.094

0.909 1.736 2.487 3.170 3-791 6.145 7.606 8.514 9.077

0.870 1.626 2.283 2.855 3.352 5.019 5.847 6.259 6.464

20%

25%

0.833

O.SOO

1.528

1.440

2.1O6

1.952

2.589

2.362

2.991

2.689

4.192

3-571 3.859

4.675 4.870 4.948

3-954 3-985

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CHAPTER EIGHT

Cost-Benefit Analysis: Risk Adjustment and Distributional Considerations

This chapter is concerned with two primary issues in cost-benefit analysis: the valuation of costs and benefits in the face of risk and uncertainty, and the incorporation into the analysis of distributional considerations. RISK AND

UNCERTAINTY

There are two primary sources of uncertainty and risk associated with an investment project. First, there are the unforeseen changes in the project's external environment. For example, the economic value of the project may be substantially affected by changes in consumer tastes, production technology, government policy, and prices of the project's inputs and outputs. With no change in external conditions, uncertainty may still exist with regard to the project's actual outcome. There may be, for example, significant variation between the project's design specifications and its actual performance, or between the project's production requirements in the initial and final stages of the project. Although the terms risk and uncertainty are sometimes used interchangeably in the practical cost-benefit literature, economists generally distinguish one from the other. Risk is present in situations in which information about the probabilities of various outcomes of the project in question is available. Uncertainty prevails when the lack of information precludes reasonable determination of such probabilities. In the sections to follow, general approaches to risk and uncertainty are first reviewed. Methods are then discussed for handling risk and uncertainty, respectively.

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GENERAL APPROACHES TO RISK AND UNCERTAINTY

In dealing with risk and uncertainty, the task of the analyst is to explicitly acknowledge the problem and to present quantitative evidence of its importance wherever feasible. Since the future cannot be predicted with certainty, and uncertainty implies risk, various methods of accounting for the elements of risk and uncertainty in cost-benefit analysis have evolved. There are three general approaches to the measurement of costs and benefits which are relevant to the conditions of either risk or uncertainty: the introduction into the analysis of an uncertainty or risk premium to the discount rate; adjustment of the estimated life of the project; and compensating valuation. Uncertainty or Risk Premium

This approach attempts to incorporate uncertainty or risk into CBA through the addition of a "premium" to the discount rate. If r is the discount rate and r' is a risk factor, or premium appropriate to the project, the project's NPV would be determined as The rationale for this approach is the argument that forecasts of costs and benefits become more speculative the further into the future they occur. The risk premium insures that the more distant in time are the predicted monetary flows, the more heavily are they discounted. Since a major share of the costs of investment projects frequently occurs in the early periods of the project's life, while the benefits extend well into the future, the addition of a risk premium tends to reduce the number of projects accepted on the basis of economic efficiency and eliminates, one hopes, the more risky of the projects considered. On theoretical grounds the approach is difficult to justify. The approach requires the addition of two numbers that are conceptually distinct. The discount rate reflects the social opportunity cost of capital, while the risk premium is intended as a quantitative measure of the uncertainty of the project's outcome. Addition of the two in order to evaluate future costs and benefits is arguably not the most satisfactory approach to determining a project's net present value. The addition of a risk premium to the discount rate implicitly assumes that risk is compounded over time at a fixed rate, an argument with no empirical basis and limited intuitive appeal.

Risk Adjustment and Distributional Considerations

143

Project Life

Another way to deal with risk is through adjustment of the project's life to its "payback period"—the period over which accumulated net benefits of the project become equal to the project's capital costs. The weakness of this approach is obvious. Its application to public sector projects with substantial net benefits extending far into the future could easily lead to the rejection of investment alternatives with NPVS considerably higher than those of projects accepted. A similar approach is to adjust the economic life of projects uniformly downward. The rationale is to eliminate those net benefits which extend into the distant future, that is, the more "uncertain" benefits. The approach suffers the same weakness as does the payback period. Both completely ignore relevant information beyond an arbitrarily established cutoff date. Further, in the case of shortening the economic life of a project, particularly one with a high discount rate, the approach may also be somewhat superfluous, since future net benefits are already so highly discounted. It might be noted that the fifty-year cutoff period often associated with water resource projects is generally adopted more for computational ease than for risk adjustment. Range of Valuations of Benefits and Costs A third general approach to dealing with risk or uncertainty is to construct conservative or, alternatively, various estimates of the costs and benefits in each period. As an example of the latter variant of this approach, one might choose to construct "high," "likely," and "low" estimates of each period's project effects. Three values of NPVS for a project would then be determined. In addition to producing a most-likely estimate of NPV, analysts can state with some assurance that the project's true NPV lies between their high and low estimates. Analysts may also choose to examine the extent to which their results are sensitive to the upper and lower estimates of each period's benefits and costs. Such a procedure can reveal which of an analyst's estimates are more influential on the final results of his analysis and should thus be the focus of any further efforts towards refinement. RISK

AND

EXPECTED

VALUES

If the analyst is confident that he can estimate the probabilities of the various feasible outcomes of the projects under consideration,

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risk can be treated in CBA by calculating the expected value of the NPV of each project. In general, if project outcome i in a particular time period t has an associated net gain of (B, - Q) and a probability of occurring of pi, then the expected value E(Bt - Q) of the project's net benefits in period t is

where there are n possible outcomes and 2P/ = i.o. By calculating the expected value of the project in each time period, the expected net present value of the project may be determined as

To illustrate, suppose the probabilities of the outcomes of projects A and B have been estimated in such a way as to yield the following results: A

B

Potential

Potential

NPV

Probability

NPV

Probability

$200,000 $300,000 $400,000

•3 •4 •3

$100,000 $600,000

0

.1 •4 •5

Simple arithmetic will show that the expected value of project A is $300,000 (.3 x 200,000 + .4 x 300,000 + .3 x 400,000) and that of Bis $340,000 (.1 x o + .4 x 100,000 + .5 x 600,600). On the basis of expected values project B is preferable to project A. It is difficult, however, to ignore the variance of the expected net benefits. For project B the chances that the NPV will be $100,000 or less are fifty-fifty. Further, the odds are one in ten that the project will yield no benefits at all. In contrast, the lowest expected NPV of project A is $200,000. Decisionmakers with significant aversion to risk-taking, may well choose project A over B. Thus no general recommendation can be made by the analyst, since each decisionmaker must make his individual trade-off between the higher expected value of project B with the "safer," but lower, expected return of project A.

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In sum, the expected value approach is to be recommended in that it overcomes the arbitrary nature of the preceding approaches. However, as illustrated by the above example, the variance of the outcomes can also be an important factor to be taken into account. UNCERTAINTY AND

GAME THEORY

If information necessary to construct the probability distributions of the various project outcomes is unavailable, the analyst must forego the above recommended approach to accounting for risk and contend with the more general problem of uncertainty. In such circumstances one might choose to rely on one of the various strategies evolved by game theorists. To illustrate, suppose that for three competing projects (A, B, and C), three states (Si, Sz, and 53) of the external environment are likely. (For example, three approaches to flood control might be considered under conditions of no flooding, partial flooding, and severe flooding.) Assume that the net present values of the three projects under the differing external conditions are as follows:

A B C

Si

82

83

400 500 450

300 100 150

o 50 75

An optimistic decisionmaker might be led to choose the project with highest potential payoff in terms of present net values. Under this "maximax," or Hurwicz, strategy, project B would be selected because of its potential return of $500 under condition Si. On the other hand a pessimist might be inclined to adopt a "maximin," or Wald, strategy, that is, to maximize the minimum return. Since the minimum returns for A, B, and C are o, 50, and 75 respectively, project C would be selected. If it were strictly the case that even rough estimates of the probabilities of the three environmental states could not be made, then one might assign equal probabilities to each and consider the present values. On this basis, the "Laplace" strategy, one would be led to choose project A (.33(400 + 300 + o] = 231) over project B (.33(500 + 100 + 150] = 214.5) and project C (.33(450 + 150 + 75] = 222.8). (Under conditions of equal probabilities, it is unnecessary to multiply each outcome by its probability of occurrence—one has only to add the three outcomes: A:joo; 6:650; 0675.)

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As a final illustration one might adopt the "Savage" strategy of attempting to minimize the maximum "regret" (maximum potential benefits foregone minus benefits captured) associated with one's choice. The table below is a summary of the maximum regrets resulting from choosing one project over the others. It is constructed from the preceding matrix of net present values. Thus, if one chooses project A and environmental state Si prevails, the gain is $400 but the net benefits foregone by not selecting project B are $500. The regret is therefore $100.

A B C

Si

Sz

100 o

2OO

75 25

150

0

50

0

83

The remainder of the table is constructed in similar fashion. With this strategy, project B is selected, since the maximum regret is $200 compared with $150 for project C and $100 for project A. EQUITY

As discussed in Chapter 5, a fundamental postulate of cost-benefit analysis is that the value of a project is dependent on consumers' willingness to pay for the project's output. An individual's willingness to pay for a commodity is directly dependent on his income. Hence, the sum of individual valuations is dependent on the existing distribution of income within society. The importance of this point should not be underestimated. In traditional cost-benefit analysis, a dollar of benefits (costs) is a dollar of benefits (costs) regardless of incidence. The social valuation process within CBA, and thus ultimately the rejection or acceptance of proposed projects, is based on the prevailing social income distribution. To illustrate the point, suppose a proposed social centre for the elderly is subjected to CBA. The discounted present value of construction and operation costs is $250,000. With memberships at $100 a year, the present value of estimated benefits is less than $250,000. Strictly on the grounds of economic efficiency the social centre cannot be justified. However, if the income distribution were changed in favor of the older segment of society (e.g., by increased social insurance benefits), the estimated consumer surplus, which is based on consumers' willingness to pay, might be

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147

increased to the extent that the centre would be economically justifiable. In conducting cost-benefit analyses, economists have traditionally focused on the criterion of economic efficiency and have either ignored the resulting distributional consequences or have chosen to assume that such consequences fall well within the responsibility of the decisionmaker. In the early years of CBA it was generally agreed that a dollar of benefits was a dollar of benefits regardless of "to whomsoever it may accrue." While as a society we generally believe that an extra dollar received by a poor man generates greater satisfaction than an extra dollar accruing to a rich man, economists (or anyone else) have yet to construct any scientific basis for verifying this belief. Consequently, the problem of equity is frequently left to the politician. Given that value judgments are necessary in dealing with questions of equity, it is sometimes argued that efficiency and equity considerations should be sequential. All projects should be designed with regard only to the criterion of economic efficiency. If the income distribution that results from the project is socially unacceptable, then changes can best be made through fiscal policy. If we represent that portion of a project's discounted net benefits accruing to individual i in society as B;, we may express the change in economic or social well-being, AW, of society as the sum of the individual net benefits. where 0, is the relative weight assigned to individual i. If the analyst chooses to ignore the project's effect on income distribution, he is effectively assigning unitary weights to the individual net benefits in the above equation (i.e., a\ = a2 = . . . = an = i.o). The adoption of such an assumption implies acceptance of the existing income distribution. There are two primary arguments advanced in support of this position. First, it is argued that while a particular group may bear the major share of the costs of a given project, over time the costs and benefits of a large number of projects will be distributed in such a way as to leave the social income distribution essentially unchanged. The argument is difficult to accept on a priori grounds, particularly from a regional viewpoint. What assurances have people who, say, lost their access to wilderness through the construction of a dam that their diminished well-being will be offset by subsequent public investment projects? A second argument in favor of ignoring the distributional

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changes of public projects is that such projects are not the appropriate instruments for producing a socially satisfactory income distribution. As argued above, investment projects should be selected solely on the basis of economic efficiency and any unsatisfactory distributional consequences should be corrected via the transfer powers of the public sector. There is much to be said for this argument, in that it attempts both to secure the maximization of economic output and to redress any negative distributional consequences. Again, however, there is no assurance that those who suffer the costs of the public sector's investment projects will receive the benefits of the public sector's transfer policies. There is nothing in the political system to insure such compensation. The argument also assumes that fiscal policy is the preferred means of redistributing income. One might counter that given the work ethic that either prevails or should prevail in society, redistribution through the creation of employment rather than by taxes and transfer payments constitutes a socially more satisfactory means of redistribution. That is, one might raise the question: If jobs are lost in a region, are unemployment benefits and welfare payments appropriate forms of compensation? Finally, implicit in both of the above arguments favouring the status quo is the notion that considerations of efficiency and equity are independent. They may, of course, be very much interrelated. The distributional consequences of public sector projects affect the demand patterns of consumers and the patterns of supply of inputs (including labour) by resource owners. The resulting changes may affect in turn the economic efficiency of the project in question as well as that of other projects. The problems of efficiency and equity cannot always be neatly separated. In the following sections five methods for explicitly incorporating equity considerations into cost-benefit analysis are reviewed: income weights, public sector decision weights, constrained maxima, variable project design, and incidence exposition. Income Weights

As discussed above, it is common practice for cost-benefit analysts to implicitly adopt unitary weights with regard to the social welfare function by omitting from the analysis any consideration of distributional consequences. One method of departure from this stance is to adopt an arbitrary set of weights biased towards those

Risk Adjustment and Distributional Considerations

149

with lower incomes. As an example, Foster1 suggests the following weighting scheme: where Y is the average income of the community and Y, is the net income of income class i. The lower is the income of group i, the greater is the weight a, attached to the net benefits received. Alternatively, income weights which favour the poor may be assigned in accordance with the following formulation where Y is the lowest income group, b is an arbitrary coefficient and a,- is the weight applied to the higher income groups Y,. Once the assumption of unitary weights is dropped in favour of an arbitrary weighting scheme, there is, of course, any number of possible weighting formulations. Since economic science has no way of empirically establishing the social welfare function of equation (8.4), economists have no foundation for offering advice regarding the socially "best" set of weights. The problem then is to find not the optimal weighting scheme, but one that is politically acceptable. The greater the number of persons who must agree on the selection, the more difficult the task becomes. Given the difficulty of constructing a consensus regarding a weighting scheme, the possibility of introducing inconsistencies into the analysis as weights change, and the potential for obscuring the efficiency aspects of the analysis, it is not surprising that a number of economists concerned with CBA (e.g., Mishan 1974; Cutt and Tydeman 1976; Harberger 1978) oppose the introduction of such weighting schemes. Public Sector Decision Weights

A second approach to a weighting scheme is to find that set of weights that has been implicitly adopted by the public sector. One suggestion as to how this might be done is to adopt the marginal income tax rates of the federal government.2 Following this argument, the weights might take the following form: where b, is the marginal tax rate associated with income class i. However, if one is truly attempting to apply the weighting scheme or distributional preferences of the federal government, one must consider how closely the marginal tax rate corresponds with the government's concern for income redistribution. Within the tax system itself, there is a multitude of deductions that also serve to

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redistribute income. Moreover, to be comprehensive one would additionally have to take into account the various sales and excise taxes and the many transfer payments that are specifically designed to redistribute income. Weisbrod3 recommends an alternative method of estimating the set of weights implied by, or consistent with, past government policies. To establish such weights, he recommends careful study of the acceptance of past government projects, particularly those that have been accepted over competing projects with higher NPVS. This approach requires a considerable amount of research and must cope with substantial empirical difficulties. There are additional objections to this approach that may be raised. In a society in which changes in attitudes as well as in the tax and transfer systems are nearly continual, there can be no guarantee that future policy with respect to acceptance of proposed public sector projects will be consistent with the past. Further, projects accepted in the past over competing projects with higher NPVS may have been chosen for reasons other than distributional (e.g., political logrolling or trade-offs, or possibly qualitative environmental effects). Another potential weakness of the approach is the possible gap between what legislators originally wished for or designed and the actual outcome. Generally, only data pertaining to the latter will be available to the researcher. Finally, Layard4 raises the following general argument in response to all attempts to ascertain a set of weights consistent with government policy. If the government has been consistent in the past in its weighting of socioeconomic classes, why be concerned about assisting it in continuing to be consistent? On the other hand, if it has not been consistent, how can one reasonably expect to devise a weighting system that consistently accords with government policy? Constrained Maxima

A third approach to incorporating distributional consequences into CBA is to forego the previous approaches to developing a set of weights in favour of reformulating the investment decision problem as one of a constrained maximum. That is, the decision rule for choosing the most desirable project would be the maximization of NPV subject to the constraint of meeting some special criteria with regard to one or more target groups in the project region. For example, one might set as a constraint on the maximization of NPV the requirement that x per cent of the total net benefits (or $y, or z

Risk Adjustment and Distributional Considerations

151

jobs) must accrue to a particular target group. Alternatively, the constraint might be formulated in terms of requiring that a specific proportion of the target group population be aided by the project(s) in question or that a specific proportion of particular needs of the group be met. The approach might be taken one step further. If equity considerations are thought to predominate over considerations of efficiency, the decision criteria might be formulated as the maximization of net benefits accruing to a particular group under the constraint that some minimum level of NPV for the regional population as a whole must prevail. As a simple illustration, suppose the task is to choose among projects A, B, and C, given the following information: Project NPV (society) NPV (poor)

A

B

C

100

200 50

300 -10

70

Ignoring distributional considerations, one would be led from the above estimations of discounted net present values to choose project C in order to capture the highest NPV. If, however, the objective were to select that project which maximizes NPV subject to the constraint of a minimum level of net benefits (say 50) for the target group, project B becomes the most desirable of the three projects. If, as discussed above, the objective is to maximize the net benefits accruing to the poor subject to some minimum level of overall social benefits (say 100), the analyst is led to choose project A. Measurement difficulties aside, the central problem here is to establish agreement as to the target group(s), the objective function, and the relevant constraint(s). Variable Project Design

Yet another approach to the incorporation of distributional considerations into CBA, relevant to single project analyses, is that of variable project design. Co-operation between the cost-benefit analyst and, say, the project's engineering staff might result in several project designs, each meeting the project's equity objectives in varying degrees. As a variant of this approach, the project might be designed for maximum efficiency, and then cost estimates be produced of the modifications to project design necessary to meet vari-

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ous sets of distributional considerations. Such approaches, it is argued, can sensitize all project participants to both efficiency and equity needs and provide the decisionmaker with a greater range of choice than that afforded by the usual "accept/reject" situation. Depending on the nature of the particular project, however, this approach can add substantially to the project's costs. Incidence Presentation

Perhaps the most satisfactory approach to the distributional question one can adopt in the context of cost-benefit analysis is to focus solely on the estimation and exposition of the incidence of each project's benefits and costs. For example, the matrix shown in Table 24 represents a scheme for displaying the incidence of discounted net benefits for n different social groups over m regions. TABLE 24

Incidence matrix of net present value Population group A

Population group B•

Population • grouP n

Region i Region 2 Region m Total

Total XXX XXX XXX

XXX

XXX

XXX

XXX

The social groups may include particular segments of society (e.g., native groups, single mothers, the unemployed, the physically handicapped) to which the analyst wishes to draw particular attention. Alternatively, the groups may comprise a range of income classes. The regions shown in the figure add a spatial component to the analysis of incidence. A total is determined for each social group across regions (the row sums of the table) and for each region across social groups (the column sums of the table). The incidence of costs and benefits can be ignored altogether, of course, by focussing only on the grand total (the xxx in the southeast corner of the table). Once estimates of incidence in the project region have been recorded, it is the responsibility of the decisionmaker to determine how the information is to be utilized. It should be recognized, however, that this process is not value-free, since selection of the

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153

groups to be considered can be very much a function of the biases or values of the analyst who must define the groups according to a number of criteria such as age, sex, race, ethnic background, education, wealth, employment status, and so on. There are two practical difficulties which limit the number of criteria used. First, the number of cells in a matrix or table, such as Table 24, increases very quickly with the criteria used to define the categories for which impacts are to be estimated. Doubling any one criterion (e.g., increasing the number of regions) doubles the number of cells in the table and may well require a disproportionate research effort to fill the cells of the table, although many may be zero. As an interrelated constraint, the greater the number of cells in the table, the more difficult it may become to convey the information to the decisionmaker in an easily digestible form. The primary advantage of the incidence exposition approach is that it separates, to the greatest extent possible, efficiency and equity considerations but gives the decisionmaker the information necessary to incorporate distributional considerations should he so desire. The approach thus presents a number of options regarding equity concerns. These options range from ignoring the data altogether (i.e., assigning unitary weights) to assigning an explicit set or sets of weights to the net benefits received by various cohorts in the economy, distinguished by criteria such as location, income, age, ethnic background, and so on. MODIFICATIONS AND

EXTENSIONS

Discussion in this section focuses on a step-by-step procedure for the incorporation of distributional considerations into the costbenefit framework and into two evaluation frameworks which are extensions of, or alternatives to, CBA: the planning balance sheet and the goals achievement matrix. Each of these three efforts was undertaken largely to give more explicit emphasis to the issue of equity in the economic evaluation process. Trade-Off between Efficiency and Distribution

As discussed earlier, a project is deemed to be economically efficient if the social gains resulting from the project exceed the social costs. If the project or set of projects subjected to cost-benefit analysis results in small changes in the economy, or if the benefits and costs produced are widely spread throughout the economy, the traditional disregard in CBA of distributional consequences of projects

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is readily defensible. If these conditions are not fulfilled, however, the analyst must consider the two objectives of efficiency and equity and the potential conflicts between them. In most instances of competing projects, improved efficiency is gained at the expense of equity considerations. The question thus arises as to what procedure should be followed within a cost-benefit analysis with respect to distributional considerations. In their consideration of CBA as applied to air transport projects, Hettich and Swoveland recommend the following six-step process: 1 Determine at the planning stage whether or not the distributional effects of the project(s) considered will be consequential and important to the principal policy questions. If possible, consult in advance with the policymakers to ascertain whether or not they are concerned with the distributional aspects of the project(s). 2 If distributional consequences are considered to be important, sketch a framework for dealing with them. Judgments must be made as to what groups will receive benefits and what groups will bear the costs. Consideration must be given to how these groups can be broken down by income group and how benefits and costs can be correspondingly allocated to each group. 3 Determine what type of formal distributional analysis to conduct. In general, tabular or matrix presentation of costs and benefits by income group is the most acceptable. The nature and extent of the table will depend on the principal distributional questions to be answered and the availability of relevant data. If the necessary data are too costly to collect, formal distributional analysis may have to be abandoned in favour of a summary discussion of what the principal distributional questions are, and why fully satisfactory answers to these questions cannot be produced. 4 If a distributional weighting system is employed, care should be taken to insure that the weights are not designed to reflect the value judgments of the analyst. Various systems and the data requirements of each should be discussed with the policymakers. It is the responsibility of the latter to decide which system or systems to employ. 5 Distributional analysis should be considered as an adjunct to the conventional cost-benefit analysis. CBA without distributional considerations (i.e., with the traditional single goal of efficiency) should first be presented. Tabular material on the distributional consequences, or the results of calculations using distributional weights, should be added as supplementary material. 6 If important benefits or costs cannot be quantified and formally included in the distributional analysis, the possible biases of

Risk Adjustment and Distributional Considerations

155

the exclusion of these effects on the distributional results should be discussed. The Planning Balance Sheet

The planning balance sheet (PBS) was developed by Lichfield6 primarily in response to two perceived shortcomings of conventional CBA: the absence of explicit consideration of the incidence of costs and benefits, and the tendency to emphasize those costs and benefits that can be assigned monetary values. In the PBS, the analyst attempts to record all (economic, social, and environmental) impacts regardless of the unit of measurement. If a particular impact cannot be readily monetized, it may be expressed in physical units. A change in noise level, for example, might be calibrated in decibels; a transport improvement might be measured in terms of probabilities of accident preventions. If physical measurement is not possible—as it would not be, for example, in accounting for a loss of aesthetics—then a qualitative description of the impact is made. All benefits and costs recorded in the balance sheet are to be assigned to "producers" (those who create the benefits and those who are responsible for generating the costs) and to "consumers" (the recipients of the benefits and the bearers of the costs). The entries are generally made in double entry form, recording for each producer and consumer the relevant benefits and costs. For example, an assessment of proposed water pollution regulations might take the following form in a PBS. TABLE 25

Illustrative PBS transactions for water pollution regulation Sector

Benefit

Cost

Possible increased revenues Tax receipts

Expenditures to reduce effluent Expenditures to support actions

Higher quality activities Improved aesthetics Better-tasting water Higher yields

Tax Tax Tax Tax Tax

PRODUCER

Industries causing water pollution Regulating agency CONSUMER

Recreationists Sightseers Water-consumers Fishermen Other taxpayers

Source: adapted from McAllister 1980:153

payments payments payments payments payments

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Regional Economic Impact Analysis and Project Evaluation

Unlike CBA, which records real costs (i.e., social opportunity costs), PBS, with its emphasis on incidence, includes both real costs and transfers. For example, unemployment or welfare benefits foregone by a newly employed individual who was formerly without a job would be explicitly recorded in a PBS as a cost to the individual and a benefit to taxpayers. In CBA, as previously discussed, such entries are not made, since they do not reflect net social costs or benefits but merely a transfer between groups within society. PBS does recognize that some costs and benefits will have a onetime effect, while others will be continuing. To equate the two, it is recommended that where possible these effects be monetized and capitalized or expressed in terms of annual equivalents by means of an appropriate discount rate. In utilizing the completed PBS, decisionmakers must use their own weighting systems in considering all the recorded costs and benefits and their incidence. The Goals Achievement Matrix

Like the planning balance sheet, the goals achievement matrix (GAM) is an evaluation matrix designed to overcome the tendency of conventional cost-benefit analysis to ignore or downplay the incidence of costs and benefits and those impacts which can't be readily monetized. The GAM was developed by Hill7 largely in response to what he perceived to be the major shortcomings of both CBA and PBS. Within CBA, costs and benefits are measured in order to choose a course of action based on the objective of economic efficiency. "A major danger inherent in this approach is that if the primary emphasis is on efficiency, other objectives may get 'short shrift' because of the manner in which the problem is structured. Efficiency can perhaps be measured more precisely and reliably than other objectives, but this does not entitle it to an honored status" (ibid., 21). In Hill's view, PBS improves upon CBA by including costs and benefits, measured in various ways, for a range of social objectives. However, there is no explicit identification of objectives in PBS, and benefits and costs have meaning only in relation to well-defined objectives:8 "Whereas benefits can be computed referring to different planning objectives, the benefits and costs are not necessarily additive or comparable. It is meaningful to add or compare benefits and costs only if they refer to a common objective. Furthermore, since benefits and costs can legitimately be compared only in terms of an objective, if the objective is of little value both for an entire community and for any sections within it,

Risk Adjustment and Distributional Considerations

*57

then the benefits and costs referring to the objective are irrelevant for the community in question" (ibid., 21). An illustrative goals achievement matrix in which goals (limited to two in the illustration) are explicitly stated and weighted is shown in Table 26. TABLE 26

Illustrative goals achievement matrix Goal Relative weight

Incidence Group a b c d e

2

Relative weight i 3 i

3

Costs A

Benefits D

H

L

J

sum

Costs E -

Benefits R S

T

~~ U

2

2 1

Relative weight 3 i

K sum

4 5

Source: adapted from Hill 1968:23

In Table 26 various groups (a... e) are identified and a relative weight is determined for each. The letters A, B, and so on are the costs and benefits that may be defined in monetary, non-monetary or qualitative measures. Dashes indicate that no cost or benefit would accrue to the group listed at the left in attaining the goal shown above. Braces indicate that certain impacts cannot be disaggregated among the social groups. For some impacts (e.g., those pertaining to goal a) summation may be possible, while for others (e.g., those related to goal P) the summation process may be precluded by the different measures in which the impacts are made. SUMMARY AND

CONCLUSIONS

The focus of this chapter has been on two important issues in costbenefit analysis: risk and uncertainty, and equity. Risk is present in situations in which information about the probabilities of various outcomes of the initiative in question is available. Uncertainty prevails when the lack of information precludes reasonable determination of such probabilities. Three general approaches to the the consideration of uncertainty and risk within cost-benefit analysis are the addition of a premium to the discount rate, an adjustment to the estimated life of the project, and the construction of a range of

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valuations of costs and benefits. In addition to these general approaches, expected value estimations may also be considered for the purpose of incorporating the specific element of risk into CBA. To contend with the more general problem of uncertainty, the costbenefit analyst may choose to draw upon the various strategies developed in game theory. Equity issues pertain to the question of the incidence of costs and benefits. Traditionally, cost-benefit analysts have ignored such issues. The arguments for so doing have been varied. One such argument is that over time the distributional consequences "wash out," that is, in the long run with the institution of many projects, no one group suffers significant disadvantages relative to other groups in society. Alternatively, it has been argued that decisions regarding equity should involve explicit transfers and should not be embedded in projects whose principal focus is appropriately on economic efficiency. Opponents to these arguments point to the lack of a mechanism to insure compensation for losses resulting from investment projects and, in specific cases, question monetary transfers per se as an appropriate form of compensation. Implicit in all such arguments concerning the exclusion of equity issues from cost-benefit analysis is that considerations of equity are independent from those of efficiency. It is evident, however, that the two sets of concerns are not so readily separated in theory or in practice. To incorporate equity considerations explicitly into the costbenefit framework, a number of weighting schemes have been developed. Because of the element of subjectivity inherent in these approaches, however, none has gained wide acceptance. Additional options include reformulating the approach to ranking investments as one of a constrained maximum, and introducing variable project design into the analysis. Perhaps the most appropriate approach for the analyst to adopt is to undertake the estimation and exposition of the incidence of each project's impacts in tabular form so as to facilitate the application of explicit weighting schemes by decisionmakers as well as other interested parties. Dissatisfaction with the focus of traditional CBA on the contribution of quantifiable impacts towards the single goal of economic efficiency has led to the development of approaches to the evaluation process which take the form of matrix presentations of project consequences. Prominent among these extensions of, or alternatives to, CBA are the planning balance sheet and the goals achievement matrix.

Risk Adjustment and Distributional Considerations CASE

159

STUDIES

Case Study i: Distributional Analysis and the Third London Airport

In 1968 the UK government established the Roskill Commission to investigate the relative merits of four potential sites for a third London airport. On the assumptions that total benefits, if measured, would exceed total costs for the airport and that benefits would not vary among the sites, the commission essentially limited its analysis to the relative costs of the sites. From the analysis the sites were ranked as follows according to suitability: Cublington, Thurleigh, Nuthampstead, and Foulness.9 Subsequent to the commission's work, Nwaneri10 undertook a further analysis to determine if the application of distributional weights would alter the results of the commission's work. The "beneficiaries" of the new airport included: the British Airports Authority and its employees; the British and foreign airline operators and their employees; UK-resident and foreign leisure air travellers; British and foreign business air travellers; British and foreign air freight operators; industries attracted by and dependent on the airport. The "sufferers" included the communities living in the areas affected by the airport, and the people who would bear the burden of any additional drain on public funds (by taxation, inflationary financing, or reduced public expenditure) as a result of the project. In his analysis, Nwaneri considered two types of equity issues —intra-site and inter-site differences. The former were judged to arise at any one of the airport sites because of differences in incomes and in the levels of depreciation in house prices from a given level of nuisance from the airport. Inter-site differences would arise from differences between sufferers at the four sites, in particular because of the numbers of households affected. These latter differences were also attributed to differences in the "social standing" of the four communities as determined by income, occupation, social class, education, and tenure. In an effort to account for the differences in equity, Nwaneri devised five sets of weights based on varying marginal income tax rates, levels of depreciation in house prices, proportions of households affected, disruption factors derived from social standing of the communities, and marginal utilities of income. A table containing five sets of weighted costs was then constructed for each of the four sites. A summary of the results is shown in Table 27.

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TABLE 27

Summary of weighted costs of the third London airport (millions of pounds; 1968 prices discounted to 1975) Cublington 2733.8 2930.9 3111.5 2812.6 2791.2

Ui U2

U3 U4 U5

Foulness Nuthampstead (intersite differences in brackets) 2929.3 2984.7 3295.6 3025.3 2955.0

2742.1 2987.6 3142.8 2756.4 2799.6

Thurleigh 2830.8 2800.7 3014.1 2702.4 2788.1

Ui: costs weighted by marginal tax rates only U2: costs weighted by marginal tax rates and size of community 1)3: costs reflecting combined weights based on marginal tax rates, size of community, and depreciation in house prices 114: costs reflecting marginal tax rates but biased by degrees of community disruption U5: costs weighted by marginal utility of income factor Source: ibid., 247

Consideration of the above results led Nwaneri to conclude first that Foulness is indeed the least preferred site. However, the use of distributional weights resulted in a significant reordering of the three remaining sites. As seen from the table, the positions of Cublington and Thurleigh were reversed in four of the five weightings. In view of this reordering by the distributional analysis, Thurleigh arguably becomes the overall least-cost site. Case Study 2: An Evaluation of Alternative Uses for an Urban Land Parcel

In his review of a number of evaluation methods, Poulton11 poses seven criteria for comparison purposes: 1 maximization of decisionmaking value of inputs 2 matrix or diagrammatic format 3 intelligibility to laymen 4 compatibility with the decisionmaking process 5 recognition of all significant objectives 6 recognition of all significant interest groups 7 openness to all influential values. According to these criteria, Poulton found both the planning balance sheet and the goals achievement matrix to be superior to cost benefit analysis as methods of evaluation. However, with the

Risk Adjustment and Distributional Considerations

161

above criteria in mind, the author argues that there is scope for further improvement in the evaluation process, and accordingly proposes an evaluation matrix for decisionmakers (EMDM). The EMDM consists of four related but independent submatrixes. The column headings for all four submatrixes are the options facing the decisionmaker. The row headings of the first two submatrixes are values and objectives, respectively, that are of importance in that they are, or are widely held to be, of major importance to a number of individuals. Since fiscal impacts and administrative requirements are often of significant importance to decisionmakers, the third submatrix is concerned with such effects. The row headings are those of fiscal objectives. The primary concern of the last submatrix is the incidence of the impacts of the various options. The row headings are those groups which have a significant interest either in the options considered or in the decisionmaking process itself. The author provides an illustrative application of the EMDM to the Harbour Park issue in Vancouver. The fourteen-acre site is located adjacent to Stanley Park, a large and attractive urban park. It is also on the waterfront and close to the central business district. Controversy regarding the form of development for the site has been ongoing for a number of years, and in the late 19705 Vancouver City Council was in the process of reviewing several options. An abbreviated version of the Harbour Park EMDM is presented in Table 28 below. Two of the five major options are shown and in some submatrixes only representative row entries are shown. Although EMDM lacks the rigour of PBS and GAM, Poulton argues that this rigour is more than real and is often more of a straitjacket than a support. EMDM, he concludes, satisfies the concerns of parties to the decisionmaking process better than either PBS or GAM.

TABLE 28

Evaluation matrix for decisionmakers: Harbour Park ALTERNATIVES

Large scale development

Park only

ITEM

COMMENTARY

VALUES

General values exerting influence on final decision

Fairness

Concern with unusual confiscation of property rights

—

Site zoning changed

Transfer of benefits from few people to many or vice versa

Many —* few (park acquisition)

Few —* many (revenues to city)

OBJECTIVES

Synthesized by City Planning Dept., reflect all major concerns

public use

% area in public use

100%

20%

Yacht marina

number of berths provided

350

?

Large surplus

FISCAL OBJECTIVES

Revenue to the City

Break-even on commercial operations

Revenue from operation of marina and developments covers costs (min. position)

$30,000 p.m. surplus on marina

All costs covered

All operating and site preparation costs covered; substantial contribution to site acauisition costs

$252,000 p.a. deficit Large surplus on operations and site preparation costs

AFFECTED PARTIES

Includes all groups on behalf of which strong pleas have been made

Site users Park users

Park is small and disturbed by traffic, excellent substitutes are available

AFFECTED PARTIES

Largely consist of the adjacent community and passing road traffic

Non-users Local residents

Threatened with extra noise, pressure on street parking space, loss of views

Source: Adapted from ibid., 94-5

Slight benefit

Noise/parking View loss Foreground Distance

o Noise/parking o View loss + Blocked for 97 apts o Foreground Distance View transfers to new properties

— 40% — — ++

Risk Adjustment and Distributional Considerations SELECTED

163

READINGS

Cutt, J. and J. Tydeman. 1976. A General Approach to the Analysis of Public Resource Allocation. Canberra: Australian National University Press Dorfman, R. 1972. "Decision Rules under Uncertainty," in R. Layard (ed.), Cost-Benefit Analysis. New York: Penguin Books, 360-92 Harberger, A.C. 1978. "On the Use of Distributional Weights in Social Cost-Benefit Analysis," Journal of Political Economy, 86:887-8120 Lichfield, N., P. Kettle and M. Whitbread. 1975. Evaluation in the Planning Process. New York: Pergamon Press McAllister, D.M. 1980. Evaluation in Environmental Planning. Cambridge, MA: MIT Press Mishan, E.J. 1974. "Flexibility and Consistency in Project Evaluation," Economica, 41:81-96 Pearce, D.W. 1983. Cost-Benefit Analysis. 2nd ed. London: Macmillan Ray, A. 1984. Cost-Benefit Analysis: Issues and Methodologies. Baltimore, MD: Johns Hopkins University Press for the World Bank

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CHAPTER NINE

Economic Evaluation Analysis, A Summary

Cost-benefit analysis is unquestionably the principal technique— or as might be argued, the principal set of techniques—for economic evaluation analysis. Its purpose is to bring about a more efficient allocation of resources in society, particularly those resources under the management of the public sector. In accomplishing this purpose, the approach has a number of strengths and weaknesses, which are summarily reviewed below. A D V A N T A G E S OF

C O S T - B E N E F I T - A N A L YS I S

Social Viewpoint

CBA is designed to extend the analysis of project effects beyond those pertaining to the parties directly involved in the project to the impacts upon all segments of society. It provides a framework for considering the cash flows as well as other ramifications of a proposed project, and thus affords a comprehensive social view of the competing demands on society's resources. Systematic Enumeration and Valuation

Although several of the effects of projects under analysis may be difficult to quantify, they are at least identified in a comprehensive cost-benefit analysis and incorporated into the analysis in qualitative terms. CBA forces the analyst to estimate the social worth of all project inputs and outputs or to explain why data availability or lack of technical knowledge does not permit such valuations.

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Comparison of Future with Present Effects

While it is clear that a dollar tomorrow is less valuable than a dollar today, the central question for evaluative analysis is: How much less? Until this question is answered, flows of monetary costs and benefits extending into the future cannot be readily compared. The discounting procedure within CBA enables the analyst to undertake such comparisons. Sensitivity Analysis The results of any evaluative analysis are sensitive in varying degrees to the various inputs. Because of the quantitative nature of much of CBA, the approach permits the systematic measurement of the sensitivity of the analysis's outcome to changes in the estimates of the various components of the analysis (e.g., the values of particular costs and benefits, the social rate of discount, the allowance for risk or uncertainty, and equity weightings). Explicit Assumptions Because procedures for identifying, valuing, and discounting so many of the project costs and benefits are prescribed by costbenefit analysis, a considerable number of the assumptions made by the analyst are made evident in the analysis. By forcing analysts to "put their cards on the table," that is, by making explicit many of the assumptions employed in the analyses of projects, CBA potentially focuses and sharpens the debate between a project's promoters and opponents. POTENTIAL WEAKNESSES OF COST-BENEFIT ANALYSIS

As has been stressed throughout the preceding three chapters, there are a number of areas which render cost-benefit analysis less than fully satisfactory as an aid to decisionmakers concerned with choices among alternative allocations of public monies. In summary form, these areas are as follows: Secondary Benefits

With the apparent increased tendency to use the input-output model to calculate secondary benefits, the issue of secondary impacts remains a contentious one. Under most circumstances, however, the incorporation of secondary benefits in CBA involves an

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167

overestimation of total net benefits. Inclusion of secondary effects within the analysis should therefore be explicitly and fully justified. Measurement of Surpluses As we have seen, the measurement of benefits in CBA is based on the concept of willingness to pay. Thus, CBA often demands the estimation of consumer and producer surpluses. Without empirically established market demand and supply functions, this task can prove to be difficult indeed. Furthermore, in estimating consumer surplus in situations in which the income effect is significant, the task of constructing the appropriate consumer demand function compounds the difficulties of measurement. Prices

The economic underpinning of cost-benefit analysis is the model of perfect competition in which government intervention in the economy is at a minimum and full employment of resources prevails. In these circumstances prices are taken to represent simultaneously social valuations by consumers and social marginal costs by producers. Deviations from this model (taxes, subsidies, imperfect competition, and unemployed resources) call for appropriately adjusted market prices to be used in CBA. The task of constructing these "accounting" or "shadow" prices is generally not an elementary one. Treatment of Intangibles As regional populations and population densities continue to increase in conjunction with environmentally insensitive technologies, we are likely to witness increasingly serious adverse ecological consequences. These consequences are often difficult to monetize and yet must occupy a central role in cost-benefit analysis. The incorporation of intangible environmental impacts into CBA is perhaps the most challenging problem currently facing costbenefit analysts. Rate of Discount The appropriate rate of discount to be adopted in CBA remains an area of debate among economists. Resolution of the disagreement between those who favour the social opportunity cost rate, those

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Regional Economic Impact Analysis and Project Evaluation

who hold to the social time preference rate, and analysts who have proposed various forms of synthetic rates, does not appear to be imminent. Additionally, even when there is agreement in theory regarding the proper discount rate, there is often considerable argument concerning the empirical estimation of the rate. Risk and Uncertainty

As is the case with several other aspects of CBA, there is no general agreement on the appropriate adjustments to be made within the analysis for either risk or uncertainty associated with a project. Approaches in this area range from adjustments to the discount rate to attempts to incorporate investor attitudes via various applications of game theory. Equity Considerations

In its infancy, cost-benefit analysis scrupulously avoided matters of equity. A dollar of benefits was a dollar of benefits regardless of its recipient. Currently it would be unusual for cost-benefit analysts not to include in their analyses in some fashion the incidence of costs and distribution of benefits. A general consensus on just how such considerations should be incorporated into CBA, however, has yet to be reached. It is precisely this problem of accounting for goals other than economic efficiency in combination with the difficulty of incorporating intangible effects that has led to the construction of the planning balance sheet, the goals achievement matrix and other broader approaches to project/program evaluation. In addition to the above problem areas within CBA, which have been emphasized in the preceding chapters, one might also add to the disadvantages of the analysis the technical knowledge it demands of its practitioners and the consequent difficulties of the untrained in understanding and critiquing it. CONCLUSION

In sum, as an approach to economic evaluation, cost-benefit analysis takes both a "wide" and "long" view. It adopts a wide view in that it accounts for social and environmental effects with economic implications. Ideally, all relevant costs and benefits are considered in the CBA evaluative process. CBA also adopts the long view in that

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169

it considers the costs and benefits which extend into the future. Moreover, a procedure is adopted to enable the analyst to compare the present values of the monetized future effects. At its best, CBA can be "systematic, quantitative and communicable, and hence an improvement upon the casual, implicit and possibly capricious evaluation that can so easily be concealed if such matters are left to informal judgement 'on their merits'" (Williams 1972:210). Improperly employed, it can be an instrument for lending "technical" support to a vested interest. When the analysis is objectively employed, however, even critics of CBA concede that the approach may be of critical importance in eliminating from further consideration the weakest of the projects proposed. If the limitations of CBA prevent us from consistently choosing the optimal projects, "avoiding the worst when one can't get the best is no small accomplishment" (Wildavsky 1966:298). Cost-benefit analysis has, as does any evaluative approach, a number of weaknesses or, stated more sympathetically, a number of areas in which significant improvements can be made. As is the case with any form of analysis, CBA is not a substitute for decisionmaking. It can be, however, a significant aid if properly employed in full and explict recognition of its limitations.

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NOTES

CHAPTER ONE: INTRODUCTION 1 A recent attempt to divide the North American continent into nine homogeneous regions (the Bread Basket, the Foundry, MexAmerica, Ecotopia, etc.) can be found in Garreau 1981. 2 H.W. Richardson, Regional and Urban Economics (Harmondsworth: Penquin 1978), 17. For other discussions of the concept of the region and regional economic problems, see W. Isard, Introduction to Regional Science (Englewood Cliffs, NJ: Prentice-Hall 1975); E.M. Hoover, Introduction to Regional Economics (New York: Alfred A. Knopf 1975); A.J. Brown and E.M. Burrows, Regional Economic Problems: Comparative Experiences of Some Market Economies (London: George Allen & Unwin 1977); J. Friedmann and C. Weaver, Territory and Function: The Evolution of Regional Planning (London: Edward Arnold 1979); C. Gore, Regions in Question: Space, Development Theory and Regional Policy (London: Methuen 1984); and D.J. Savoie, Regional Economic Development: Canada's Search for Solutions (Toronto: University of Toronto Press 1986). CHAPTER TWO:

ECONOMIC BASE

ANALYSIS

1 GRP is a measure of the volume of economic activity in a region. Its development and components are discussed in the appendix to Chapter 3. 2 It must be kept in mind that this definition of service activity in the context of the economic base model differs from the standard meaning of a service activity as one which produces an intangible commodity. 3 For empirical comparisons of these methods, see Greytak 1969; Isserman 1980; and Gibson and Worden 198. 4 For a discussion of interregional trade in service (i.e., intangible commodity) activities, see Coffey and Polese 1987. Empirical estimates of the service activity exports from Edmonton, Vancouver, and the Puget Sound region can be found, respectively, in W.Z. Michalak and K.J. Fairbairn, "Producer Services in a Peripheral Economy," Canadian Journal of Regional Science 11 (1988), 353-72; D. Ley and T. Hutton, "Vancouver's Corporate Complex and Producer Service Sector: Linkage and Divergence within a Provincial Staple Economy," Regional Studies 21 (1987), 413-24; and W.B. Beyers and M.J. Alvine, "Export Services in PostIndustrial Society," Papers of the Regional Science Association 57 (1985), 33-45.

172

Notes to pp. 18-35

5 Since cross-hauling results from geographical, commodity, or temporal aggregation, the above cross-hauling and aggregation problems can be considered essentially the same. See H.C. Davis and H.A. Cherniack, "Some Considerations and Empirical Evidence of Regional Commodity Cross-Hauling," Canadian Planning Issues 17 (Vancouver: School of Community and Regional Planning, University of British Columbia 1985). 6 See, for example, R. Leigh, "The Use of Location Quotients in Urban Economic Base Studies," Land Economics 46 (1970), 202-5; and H.C. Davis, "Economic Base and Input-Output Multipliers: A Comparison for Vancouver, BC," Annals of Regional Science 9 (1975), 1-8. For suggested modifications to the location quotient, see Isserman 1977. 7 There is, however, a "short-cut" approach to minimum requirements that reduces the necessary data to only the population of the region. This is accomplished by accepting the equation relating minimum employment/total employment to population as established by others through the regression analysis of a large number of regions. See, for example, Moore and Jacobsen 1984. 8 For a discussion of the influence of aggregate income, population, economic diversity, and the level of exogenous demand on the stability of the economic base multiplier, see R.C. Martin and H.W. Miley, jr., "The Stability of Economic Base Multipliers: Some Empirical Evidence," Review of Regional Studies 13 (1983), 18-25. The authors conclude from empirical tests that the usefulness of base multipliers is limited to relatively short periods of time. In a test of the base model for four timber-dependent communities in the Pacific Northwest, Polzin et al. found the model to yield acceptable results in five-year forecasts but to persistently underestimate non-export activity in the longer run. See P.E. Polzin, K. Connaughton, C.H. Schallau, and J.T. Sylvester, "Forecasting Accuracy and Structural Stability of the Economic Base Model," Review of Regional Studies 18 (1988), 23-36. 9 SJ. Weiss and E.C. Gooding, "Estimation of Differential Employment Multipliers in a Small Regional Economy," Land Economics 44 (1968), 235-44. 10 V.K. Mathur and H.S. Rosen, "Regional Employment Multiplier: A New Approach," Land Economics 50 (1974), 93-6. 11 A.M. Isserman, "A Bracketing Approach for Estimating Regional Economic Multipliers and a Procedure for Assessing Their Accuracy," Environment and Planning 9 (1977), 1003-11. 12 Ibid. 13 H. Schwartz, A Guide To Regional Multiplier Estimation (Ottawa: Ministry of Supplies and Services 1982). Prepared for the Project Assessment and Evaluation Branch, Department of Regional Economic Expansion. 14 Standard Industrial Classification. For Canadian sic codes, see Statistics Canada, Standard Industrial Classification, catalogue no. i2-5oiE (Ottawa: Minister of Supply and Services Canada 1980). For u.s. sic codes, see Executive Office of the President, Office of Management and Budget, Standard Industrial Classification Manual (Springfield, VA: National Technical Information Service 1987). 15 E.D. Smith, M.M. Heckbert, and J. Van Veen, "A Modified Regression Base Multiplier Model," Growth and Change 12 (1981), 17-22. For adjustments to baseline data for transfer payments as well as sectoral wage differentials and outcommuters, see also Gibson and Worden 1981; Norcliffe 1983.

CHAPTER THREE: INCOME-EXPENDITURE ANALYSIS 1 In income expenditure analysis local income is generally defined as local value added. See the appendix to this chapter for a discussion of value added and other measures of regional income. 2 See, for example, Statistics Canada, Family Expenditures in Canada: Selected Cities, 1984, catalogue 62-555 (Ottawa: Minister of Supply and Services 1986). 3 For an attempt to integrate the in-migration process into the income multiplier,

Notes to pp. 36-54

173

see H.C. Davis and D. Webster, "A Compositional Approach to Regional Socieconomic Impact Assessment," Socio-Economic Planning Sciences 15 (1981), 159-63. 4 M. Brownrigg, "The Economic Impact of a New University," Scottish Journal of Political Economy 201973), 123-39. 5 For an extensive discussion concerning the appropriate means of incorporating into regional multiplier analysis the effects of induced investment, as well as those of interregional trade, see P.A. Black, "Injection Leakages, Trade Repercussions and the Regional Income Multiplier," Scottish Journal of Political Economy 30 (1981), 227-35; M.T. Sinclair and C.M.S. Sutcliffe, "Injection Leakages, Trade Repercussions and the Regional Income Multiplier: An Extension," Scottish Journal of Political Economy 30 (1983), 275-86; and P.A. Black, "The Regional Income Multiplier: A Comment," Scottish Journal of Political Economy 31 (1984), 199-201. 6 A.J. Brown, 1967. "The 'Green Paper' on the Development Areas," National Institute Economic Review (1967), 26-33. 7 D.B. Steele, "A Numbers Game or the Return of the Regional Multipliers," Regional Studies 6 (1972), 115-30. 8 M. Brownrigg, "The Regional Income Multiplier: An Attempt to Complete the Model," Scottish Journal of Political Economy 18 (1971), 281-97. 9 H.C. Davis, "Assessing the Impact of a New Firm on a Small-Scale Regional Economy: An Alternative to the Economic Base Model," Plan Canada 16 (1976), 171-6. 10 M.A. Grieg, "The Regional Income and Employment Effects of a Pulp and Paper Mill," Scottish Journal of Political Economy 18 (1971), 31-48. 11 See note 4 above. 12 C.M. Tiebout, The Community Economic Base Study (New York: Committee for Economic Development 1962). 13 M. Brownrigg and M.A. Grieg, "Differential Multipliers for Tourism," Scottish Journal of Political Economy 22 (1975), 261-75. 14 H.C. Davis, "Income and Employment Multipliers for a Small BC Coastal Region," The Canadian Journal of Regional Science 3 (1980), 227-36. 15 Davis, "Assessing the Impact." 16 J.H. Wilson and R. Raymond, "The Economic Impact of a University upon a Local Community," Annals of Regional Science 7 (1973), 130-2. In estimating the impact of the university, the authors limited their analysis to the spending of faculty, staff, and students, thus excluding factors such as university operating and capital expenditures, and commercial investment attributable to universityrelated sales. 17 It is not clear from the authors' discussion why the first round spending is x (total university spending) rather than mx (the portion of university spending in the local economy). If indeed mx were the first term on the right-hand side of equation (2), the resulting multiplier would be m/(i - m). 18 An alternative measure of economic production is Gross National Product (GNP). While Canadian national economic accounts have traditionally focused on GDP, the u.s. national accounts have only recently been reoriented from GNP to GDP. GDP differs from GNP in that GDP consists of income to all factors in the economy regardless of citizenship. Thus, the profits earned by a Japanese-owned auto plant in Ontario contribute to Japan's GNP and to the Canadian GDP. The wages earned by a Canadian who lives in Windsor but commutes daily to work in Detroit contribute to the Canadian GNP and the u.s. GDP. C H A P T E R F O U R : I N P U T - O U T P U TA N A L Y S I S 1 WW. Leontief, J.C.M. Koo, S. Nasar, and I. Sohn, The Future of Minerals in the U.S. and the World Economy (Lexington, MA: Lexington Books (1983), 4. 2 See Ch. 2, note 14.

174

Notes to pp. 57-80

3 The direct purchases coefficient matrix is sometimes referred to imprecisely in the literature as the "technical" coefficient matrix. Strictly speaking, technical coefficients define the sector's technology. That is, technical coefficients represent those inputs, locally and externally produced, that are required to produce the sector's output. For this reason, a distinction is frequently made between national and regional direct purchase coefficients. The former are labeled "technical" coefficients and the latter "trade" coefficients. (It must be noted, however, that to the extent that the national inputs in the transactions table are exclusive of imports, the corresponding direct purchase coefficients are only approximations to true technical coefficients.) Thus, the regional input-output table of total requirements is somewhat inaccurately titled. 4 For a discussion of both survey (bottom-up) and non-survey (top-down, i.e., modification of national coefficients) approaches to the construction of inputoutput models, as well as hybrid methods, see R.E. Miller and P.D. Blair 1985, 266-316; and Hewings and Jensen 1986, 307-16. 5 Largely to avoid the problem of accounting for secondary products in an interindustry matrix, both Canada and the u.s. produce I-O tables at the national level in a rectangular, commodity-by-industry format. To date, regional input-output models constructed in the commodity-by-industry format are rare. Because of the future potential of such models, however, the format is discussed and illustrated in Appendix 2. For a more extensive discussion, see Miller and Blair 1985, 159-178. 6 For an overview of these efforts, see H.W. Richardson, "Input-Output and Economic Base Multipliers: Looking Backward and Forward," Journal of Regional Science 25 (1985), 607-62. 7 For empirical and mathematical comparisons, respectively, of input-output and economic base multipliers, see J.A. Kuehn, M.H. Procter, and C.H. Braschler, "Comparisons of Multipliers from Input-Output and Economic Base Models," Land Economics 61 (1985), 129-35; and J- Merrifield, "A Note on the General Mathematical Equivalency of Economic Base and Aggregate Input-Output Multipliers: Fact or Fiction," Journal of Regional Science 27 (1987), 651-4. 8 For an overview of the extensions of regional and interregional input-output analysis into areas such as regional growth and development, demographic projections, social accounting, and the linkage of input-output models with econometric, ecologic, linear programming, and labour market models, see Hewings and Jensen 1986, 325-42; 1988. 9 H.C. Davis and E.M. Lofting, "Air Pollution in California: Manufacturing vs. Services," Environmental Management 6 (1982), 337-42. 10 R.L. Drake, "A Short-Cut to Estimates of Regional Input-Output Multipliers: Methodology and Evaluation," International Regional Science Review i (1977): 1-17. 11 H.C. Davis, "Income and Employment Multipliers for Seven British Columbia Regions," Canadian Journal of Regional Science 9 (1985), 103-15. 12 Like the economic base and income-expenditure models, the input-output model is "demand-driven," that is, it is designed to reveal the effects of changes in demand. At times, however, the model has been reformulated to emphasize supply constraints and shortages and forward linkages between sectors. See J. Oosterhaven, "On the Plausibility of the Supply-Driven Input-Output Model," Journal of Regional Science 28 (1988), 203-217. 13 H.C. Davis, An Interindustry Study of the Metropolitan Vancouver Economy, report no. 6 (Vancouver: University of British Columbia, Faculty of Commerce, Urban Land Economics 1976). 14 J.C. Stabler, "Interindustry Relations of a Frontier Economy," The Canadian Journal of Regional Science 7 (1984), 115-23. 15 While Type i and Type n multipliers are standard multiplier formulations in the input-output literature, there is considerable inconsistency in the definitions of

Notes to pp. 80-107

175

"direct" and "indirect" effects between the two types of multipliers. For a discussion of this problem and a proposed solution, see G.R. West and R.C. Jensen, "Some Reflections on Input-Output Multipliers," Annals of Regional Science 14 (1980), 77-89. 16 For the purpose of keeping the illustration simple, the model ignores leakages from domestic industries in the form of imports, inventory reductions and purchases of government-produced competitive commodities. For a mathematical treatment of the incorporation of these elements into the commodity-by-industry input-output model, see Statistics Canada, The Input-Output Structure of the Canadian Economy 1971-1980, catalogue i5-2OiE (Ottawa: Ministry of Supply and Services 1985), 29-32. CHAPTER SIX! COST-BENEFIT ANALYSIS: EVALUATION OF SOCIAL COSTS AND BENEFITS 1 In a more refined construction of the concept of consumer surplus, the demand curve is adjusted for an "income effect." The reasoning is that if consumers were indeed required to pay what they were fully willing to pay for each unit of the commodity purchased, their real income would be reduced to the extent that their demand for the commodity would be reduced. See, for example, E.J. Mishan, Cost-Benefit Analysis (London: George Allen and Unwin 1971), 325-38. 2 This can be demonstrated as follows:

The increase in consumer surplus in the above diagram can be seen to be

3 Positive externalities are arguably associated with educational activities, public health programs, and other planning functions (Montador and Baumann 1977; Moore 1978). 4 Discussions of the ethical concerns underlying cost-benefit analysis in such matters as the evaluation of environmental intangibles can be found in Kelman 1981 and DeLong et al. 1981. See also A.V. Kneese and W.D. Schulze, "Ethics and Environmental Economics," in A.V. Kneese and J.L. Sweeney, eds., Handbook of

176

Notes to pp. 108-125

Natural Resource and Energy Economics, vol. i (New York: North-Holland 1985), 191-220; and M. Sagoff, The Economy of the Earth (Cambridge: Cambridge University Press 1988). 5 If the decision to provide the public good, or any other commodity, has been clearly established, benefits may be ignored and the task becomes one of "costeffectiveness," that is, the problem of finding the least-cost means of providing the good. For example, alternative means of effecting a specified increase in, say, recycling, crime prevention, voter registration, public health, or civic volunteers, may be matters for cost-effectiveness. In each of these examples the output (and hence the associated benefits) is fixed and the problem is one of attaining these benefits at the least cost. Aside from benefit valuation, the principles of costeffectiveness are the same as those of CBA. 6 A general defence of the use of survey questionnaires in cost-benefit analysis can be found in D.S. Brookshire and T.D. Crocker, "The Use of Contingent Valuation Methods for Cost-Benefit Analysis," Public Choice 36 (1981), 235-52. 7 J.C. Stabler, G.C. Van Kooten, and N. Meyer, "Methodological Issues in the Evaluation of Regional Resource Development Projects," Annals of Regional Science 22 (1988), 13-25. 8 For further discussion of the difference between secondary benefits and economic effects or impacts, particularly as established through input-output analysis, see R.A. Young and S.L. Gray, "Input-Output Models, Economic Surplus, and the State or Regional Water Plans," Water Resources Research 21 (1985), 1819-23; and J.R. Hamilton and R.L. Gardner, "Value Added and Secondary Benefits in Regional Project Evaluation: Irrigation Development in the Snake River Basin," Annals of Regional Science 20 (1988), 1-11. 9 Differential social and environmental effects between the two regions might also be considered in this context. 10 I. Hodge, "The Social Opportunity Cost of Rural labour," Regional Studies 16 (1982), 113-22. 11 R.J. Anderson and T.D. Crocker, "Air Pollution and Residential Property Values," Urban Studies 8 (1971), 171-80. 12 R.J. Smith, "The Evaluation of Recreation Benefits: The Clawson Method in Practice," Urban Studies 8 (1971), 89-102. 13 M. Clawson, Methods of Measuring Demand for and Value of Outdoor Recreation, reprint 10 (Washington, DC: Resources for the Future 1959). 14 W. Hettich, "The Political Economy of Benefit Analysis: Evaluating STOL Air Transport for Canada," Canadian Public Policy 9 (1983), 487-98.

CHAPTER SEVEN: DISCOUNTING FUTURE BENEFITS AND COSTS 1 See, for example, S.A. Marglin, "The Opportunity Costs of Public Investment," Quarterly Journal of Economics 77 (1963), 274-9; and A. Maass, "Benefit-Cost Analysis: Its Relevance to Public Investment Decisions," Quarterly Journal of Economics 80 (1966), 208-26. 2 There is an additional argument for high discount rates, one that might be advanced by resource conservationists. If it is assumed that most of the public projects submitted to the CBA process involve the extraction or harvesting of natural resources, an environmentalist might logically argue for rates higher than the soc over the normal range of capital investment projects to allow for greater stocks of environmental resources to be preserved for future generations. This argument must be weighed, however, against the tendency of a higher discount rate to accelerate the harvesting of resources. For further discussion of the environmental implications of discount rates, see D. Pearce et al., Blueprint for a Green Economy (London: Earthscan 1989).

Notes to pp. 125-149

177

3 It should be noted, however, that a consensus has not emerged from the debate in the literature. The topic remains one of the most controversial issues in the area of public sector economics. For an argument in favor of the adoption of the soc rate, see, for example, P.A. Diamond and J.A. Mirrlees, "Optimal Taxation and Public Production," American Economic Review 61 (1971), 8-27. A defence of the STP rate can be found in J. Kay, "Social Discount Rates," Journal of Public Economics i (1972), 359-78. D. Morawetz, in "The Social Rate of Discount, Targets and Instruments," Public Interest 27 (1972), 370-3, cautions against the adoption of a single rate, and V.L. Broussalian, in "Discounting and Evaluation of Public Investments," Applied Economics 3 (1971), 1-10, questions the application of discounting altogether. 4 From the preceding discussion it can be seen that the process of determining the appropriate social discount rate is a complex one and that we have only touched upon a few of the major issues. Fuller treatment of the subject can be found in Sugden and Williams 1978; and Sassone and Schaffer 1978. For examples of efforts to establish empirically the social discount rate, see D.F. Burgess, "The Social Discount Rate for Canada: Theory and Evidence," Canadian Public Policy 7 (1981), 383-94; G.L. Jenkins, "The Public-Sector Discount Rate for Canada: Some Further Observations," Canadian Public Policy 7 (1981), 400-7; and T. Munroe, "The Question of the Social Discount Rate," Economic Forum 12 (1981), 226-50. 5 For a discount rate of 10 per cent, application of a low of 5 per cent and a high of 15 per cent is recommended by the Canadian Treasury Board (Government of Canada 1976) for purposes of sensitivity analysis. For the same median value of 10 per cent, the Province of British Columbia 1977 recommends a range of 8-12 per cent to be employed. 6 R. Layard, "Introduction," Cost-Benefit Analysis (Markham, ON: Penguin 1972), 5i7 Mishan has developed a procedure to ensure a unique ranking of alternative investment projects, irrespective of the investment criteria (NPV, B/C, or IRR) employed. The approach is based on adjustments to fulfill three conditions: a common capital outlay, a common period of investment, and the accounting of reinvestment opportunities open to each benefit. See E.J. Mishan, Cost-Benefit Analysis, 3rd ed. (London: George Allen and Unwin 1982), 235-57. 8 This section summarizes several of the arguments reviewed in Government of Canada, "The Social Discount Rate: Is 10 Percent Too High?", Economics Branch, National Energy Board (unpublished staff paper 1985). 9 A more formal development of the argument can be found in S.H. Hanke, P.H. Corner, and P. Bugg, "Project Evaluation during Inflation," Water Resources Research 11 (1975), 511-14. Note that the analysis presented above pertains to a persistent and general increase in prices, a situation in which a significant change in relative prices is not expected. If, however, a marked shift in prices of commodities relevant to the project(s) being evaluated is anticipated within the period of analysis, this shift must be incorporated into the analysis. 10 J.C.T. Mao, "Efficiency in Public Urban Renewal Expenditures through BenefitCost Analysis," Journal of the American Institute of Planners 32 (1966), 95-106. 11 J. Krutilla and O. Eckstein, Multiple River Development Baltimore: Johns Hopkins University Press 1959). 12 R.W. Wright and R.L. Mansell. "Myopic Project Evaluation: New Zealand's Second Smelter," New Zealand Economic Papers 15 (1981), 50-64.

CHAPTER EIGHT: RISK ADJUSTMENT AND DISTRIBUTIONAL CONSIDERATIONS 1 C.D. Foster, "Social Welfare Functions in Cost-Benefit Analysis," in J. Lawrence, ed., Operational Research and the Social Sciences (London: Tavistock Publications 1966), 305-18. 2 O. Eckstein, "A Survey of the Theory of Public Expenditure Criteria," in J.M.

178

3 4 5 6 7 8 9

10 11

Notes to pp. 150-160

Buchanan, ed., Public Finance: Needs, Sources and Utilization (Princeton, NJ: Princeton University Press 1961). B.A. Weisbrod, "Income Redistribution Effects and Benefit Cost Analysis," in S.B. Chase, ed., Problems in Public Expenditure Analysis (Washington: Brookings Institution 1968), 177-209. R. Layard, "Introduction," Cost-Benefit Analysis (Markham, ON: Penguin 1972), 60. W. Hettich and C. Swoveland, Benefit-Cost Analysis for Air Transportation Projects (Ottawa: Transport Canada 1983). N. Lichfield, "Cost-Benefit Analysis in City Planning," Journal of the American Institute of Planners 26 (1960), 273-9. M. Hill, "A Goals Achievement Matrix for Evaluating Alternative Plans," Journal of the American Institute of Planners 34 (1968), 19-28. Objectives can, of course, be readily incorporated into PBS. For further discussion of PBS and GAM, see Lichfield et al. 1975 and McAllister 1980. Commission on the Third London Airport: Papers and Proceedings, vol. vn, parts i and 2, stage n, Research and Investigation: Assessment of Short-Listed Sites (London: HMSO 1970). For criticism of the commission's research methods, see A.D.J. Flowerdew, "Choosing a Site for the Third London Airport: The Roskill Commission's Approach," and E.J. Mishan, "What Is Wrong with Roskill?" in R. Layard, Cost-Benefit Analysis (New York: Penguin Books 1972). V.C. Nwaneri, "Equity in Cost-Benefit Analysis: A Case Study of the Third London Airport," Journal of Transport Economics and Policy 4 (1970), 235-54. M.C. Poulton. "A Land Use Evaluation Technique for Decision-Makers," Regional Studies 16 (1982), 85-96.

Author Index Alvine, M.J., 15 n Anderson, L.G., 117 Anderson, R.J., 112 Ashby, L.D., 8 Bauman, H., 117 Baumol, W.J., 138 Beyers, W.B., 15n Black, P.A., 36n Blair, P.D., 64n, 65n, 81 Boulding, K.E., 106, 117 Braschler, C.H., 65n Brookshire, D.S., 109n Broussalian, V.L., 125n Brown, A.J., 5n, 37 Brownrigg, M., 36, 39, 43, 44 Buchanan, J., 14gn Bugg, P., 133n Burgess, D.F., 127n Burrows, E.M., 5n Chase, S.B., 15on Cherniack, H.D., 18n Clawson, M., 114 Coffey, W.J., 15n, 27 Commission on the Third London Airport, 159n Connaughton, K., 19n Corner, PH., 133n Crocker, T.D., 109n, 112 Cutt, J., 163 Daley, H.E., 106, 117 Dasgupta, A.K., 138 Davis, H.C., 18n, 35n, 44, 45n, 68, 76n DeLong, J.V., 107n, 117 Diamond, PA., 125n Dorfman, R., 163 Drake, R.L., 67 Eckstein, O., 149n

Fairbairn, K.J., 15n Flowerdew, A.D.J., 159n Floyd, G.F., 81 Foster, C.D., 149 Friedman, J., 5n Gardner, R.L., lion Garreau, J., 4n, 8, Gibson, L.J., 15n, 25n, 27 Gooding, E. C., 20 Government of B.C., 128n, 138 Government of Canada, 128n, i3on, 138 Gore, C, 5n Gray, S.L., non Greytak, D, 15n, 27 Grieg, M.A., 39, 43, 44 Hamby, C.K., 81 Hamilton, J.R., l10n Hanke, S.H., 133n Harberger, A.C., 163 Haughton, G., 49 Heckbert, M.M., 25 Herbert, R.C., 81 Hettich, W., 115, 117, 154 Hewings, G.J.D., 64n, 66n, 80, 81 Hill, M., 156 Hodge, I., 111, 112 Hoover, E., 5n, 81 Hutton, T., 15n Isard, W., 5n Isserman, A.M., 15n, 18n, 21, 22, 27,

Jacobsen, M., 28 Jenkins, G.L., 127n Jensen, R.C., 64n, 66n, 80, 80n, 81 Kay, J., 125n Kelman, S., 107n, 117

18o

Index

Kettle, P., 163 Kneese, A.V., 10711 Koo, J.C.M., 53n Kuehn, J.A., 6511

Ray, A., 163 Raymond, R., 47n Richardson, H.W., 5n, 65n, 81 Rosen, H.S., 21

Lane, T., 23, 28 Laurent, E.A., 81 Layard, R., 129n, 150, 159n Leigh, R., 18n Leontief, W., 53, 53n, 81, 82 Lewis, P.M., 49 Lewis, W.C., 23, 28 Ley, D., ijn Lichfield, N., 155, 156n, 163 Lofting, E.M., 6yn

Sagoff, M., 1o7n Sassone, P.G., 118, 127n, 138 Savoie, D.J., 5n Schaffer, W.A., 81, 118, 127n, 138 Schallau, C.H., 19n Schofield, J.A., 115, 118, 125, 138 Schulze, W.D., 107n Schwartz, H., 23 Settle, R.F., 117 Sinclair, M.T., 34, 36n, 49 Smith, E.D., 25 Smith, R.J., 114, 115 Sohn, J., 53n Stabler, J., 77n, no Steele, D.B., 37 Sugden, R., 127n, 138 Sutcliffe, C.M.S., 34, 36n, 49 Sutter, jr., E.M., 81 Sweeney, J.L., 107n Swoveland, C, 154 Sylvester, J.T., 19n

Maas, A., 124n McAllister, D.M.,156n, 163 McGuire, A., 49, 39 Mansell, R.L., 136 Mao, J., 133, 134, 135 Marglin, S.A., 124n Martin, R.C., 19n Mathur, V.K., 21 Merrifield, J., 65n Michlalak, W.Z., 15n Miernyk, W.H., 53, 81 Miley, jr., H.W., 19n Miller, R.E., 64n, 65n, 81 Mirrlees, J.A., 125n Mishan, E.J., 98n, 13on, 159n, 163 Montador, B., 117 Moore, C.L., 28 Moore, T., 117 Morawetz, D., 125n Munroe, T., 127n Nasar, S., 53n Norcliffe, G.B., 25n, 28 Nwaneri, V.C., 159, 160 Oosterhaven, J., 69n Pearce, D.W., 125n, 138, 163 Polese, M., 15n, 27 Polzin, P.E., 19n Poulton, M.C., 160, 161 Prest, A.R., 118, 127, 138 Procter, M.H., 65n

Tiebout, C.M., 39n, 42, 44 Turvey, R., 118, 127, 138 Tydeman, J., 163 Van Veen, J., 25 Waters, W.G., 6, 8 Weaver, C., 5n Webster, D., 35n Weisbrod, B.A., 150 Weiss, S.J., 20 West, G.R., Son Whitbread, M., 163 Williams, A., 127n, 138 Wilson, J.H., 47, 49 Wilson, T., 36, 49 Worden, M.A., 15n, 25n, 27 Wright, R.W., 136 Yannopoulos, G., 36, 49 Young, R.A., l10n

Subject Index accounting prices. See shadow prices backward linkages, 54 benefits, defined, 95, 98-9 benefit-cost ratio, 128, 130 bracketing approach, 22 budget constraint, 129-30 capacity constraints, 13, 33, 45, 65 closed economy, 29, 31 closed input-output model, 59-62, 63, 67, 68, 90, 93 commodity by industry inputoutput tables: make table, 83, 87; use table, 84, 87; industry technology table, 85; market share table, 85; table of total requirements, 85-6, 87 comparative static models, 13 conditional predictive models, 89 coefficients: constancy, 12, 32-3, 57, 62-3, 91-2, 94; regional vs. technical, 57n construction phase: vs. operation phase, 6 consumer surplus. See surplus cost effectiveness, 108n cross-hauling, 17, 48 current vs. capital transactions, 64 differential multiplier model, 20-1 differential sector model, 43-4 differential cohort model, 44 discount rate: Canadian 130-2; effect of inflation, 132-3; measurement, 125-8; net present value, 119-22, 121-2, 128-30, 135, 136-7, 142, 143-5, 145-6, 150-1; social opportunity cost, 123-4, 125, 137; social time preference,

124-5, 126, 133, 137; tables, 121, 138-9 double-counting, 6, 59, 96-7, 113 environmental effects, 5, 45, 107, 110, 112, 119, 145-6, 147, 167 equity, 7, 146-63, 168 evaluation analysis: vs. impact analysis, 5-7 evaluation matrix for decision makers (EMDM), 137-9 existence value. See preservation value externalities, 69, 89, 104-7, 115, 126, 127 factor payments, 49, 51, 90, 92 feedback effects, 12-13, 33, 37, 45 final production (sales): vs. intermediate production (sales), 10, 49, 55 forward linkages, 54 free rider, 108 game theory, 145-6 goals achievement matrix (GAM), 132-4 gross (total) product, 9, 49-51 hedonic prices, 112-13 homogeneity of sectors, 11-12, 17-18, 33, 62, 63, 92, 94 impact analysis: vs. evaluation analysis, 5-7 impact components, 46, 92-3 imperfect competition, 100-2, 103, 113, 167 import replacement, 19, 40, 41, 90, 91 incidence. See equity income: discretionary, 51;

182

Index

disposable, 32, 50-1; personal, 50-1 input-output model: open vs. closed, 59-62; and secondary benefits, 110-11 intangibles, 107, 167 interindustry input-output tables: transactions table, 54, 56, 59, 62, 70-5, 78-9, 82, 93; table of direct purchases, 56-7, 58, 59-60, 82; table of total purchases, 58, 61, 77, 82 internal rate of return, 128-9 investment decision criteria, 128-30 leakages, 11, 32, 41, 43, 56, 57 location quotient, 16-17, 22, 23, 24, 48, 68 minimum requirements, 18-19 multiplicand, 36, 93 multiplier employment: economic base, 10, 14; income-expenditure, 37-9; input-output, 67 income: income-expenditure, 29-32; input-output, 61 sales: input-output, 58, 61, 82 net present value. See discount rate operation phase: vs. construction phase, 6 opportunity cost, 7, 103, 104, 105, 111-12, 116, 123-4, 125-8, 133, 135, 142, 156 option value, 107, 115 physical constraints, 129-30 planning balance sheet, 132-3, 155-6 pollution, 67, 112-13, 155 preservation value, 107, 115 producer surplus. See surplus product-mix problem. See homogeneity of sectors propensities (marginal vs. average), 33-4

public good, 107-8 regions: administrative, 3, 5; homogeneous, 3-4; nodal, 3, 4; resource, 4 regression analysis, 20-1, 21-2, 25-7, 68, 113 risk, 141-5, 168 secondary products, 64-5, 83 secondary costs and benefits, 95-7, 110-11, 166-7 sensitivity analysis, 127-8, 143, 166 shadow prices: hedonic prices, 112-13; imperfect competition, 100-2; taxes and subsidies, 102-3; unemployed resources, 103-5 social opportunity cost of capital, 123-4, 135, 136, 137 social time preference. See discount rate standard industrial classification (sic) codes, 54, 67 surplus: consumer, 97-8, 98-100, 114, 167; producer, 98, 98-100, 115, 167

tax, 5, 9, 11, 31, 32, 34, 35, 41, 46, 50, 56, 57, 62, 68, 91, 92, 100, 102-3, 113, 125, 126, 127, 131, 132, 135, 148, 149, 150, 159, 160, 167 tourism, 11, 41, 43-4 transfer payments, 14, 25-6, 41, 45, 46, 50, 51, 91 travel cost method, 109, 114-15 uncertainty, 141-3, 145-6, 168 unemployment, 14, 25, 26, 34-5, 44, 45, 50, 51, 92, 100, 103-5 value added, 14, 43, 44, 47, 49, 50, 54, 59, 62, 68, 76, 90, 110, 111 weighting of benefits and costs, 148-50 willingness to pay, 97-9, 101-3, 108-9, 113, 146, 167