"schooling, experience, and earnings" by jacob mincer

SCHOOLING,EXPERIENCE, ANDEARNINGS

NATIONAL BUREAU OF ECONOMIC RESEARCH

Human Behavior and Social Institutions

1. Essays in the Economics of Health and Medical Care,Victor FL Fuchs, Editor

2. Schooling, Experience, and Earnings, by Jacob Mincer


JACOB MINCERNational Bureau of Economic Researchand Columbia University

NATIONAL BUREAU OF ECONOMIC RESEARCHNew York 1974Distributed by COLUMBIA UNIVERSITY PRESSNew York and London

NATIONAL BUREAU OF ECONOMIC RESEARCH

OFFICERS

Arthur F. Burns, Honorary ChairmanWalter W. Heller, ChairmanJ. Wilson Newman, Vice ChairmanJohn R. Meyer, PresidentThomas D. Flynn, TreasurerDouglas H. Eldridge, Vice President-

Executive SecretaryVictor A. Fuchs, Vice President-Research;

Co-director NB ER-West

Edwin Kuh, Director, Computer ResearchCenter

Hal B. Lary, Vice President-ResearchRobert E. Lipsey, Vice President-ResearchSherman J. Maisel, Co-director NBER-WestGeoffrey H. Moore, Vice President-ResearchEdward K. Smith, Vice President

DIRECTORS AT LARGE

Atherton Bean. International MultifoodsCorporation

Joseph A. Beirne, CommunicationsWorkers of America

Arthur F. Burns, Board of Governors ofthe Federal Reserve System

Wallace J. Campbell, Foundation f orCooperative Housing

Erwin 0. Canham, Christian ScienceMonitor

Emillo G. Collado, Exxon CorporationSolomon Fabricant, Now York UniversityEugene P. Foley, Monhrose Securities. Inc.Eli Goldston, Eastern Gas and Fuel

AssociatesDavid L. Grove, International Business

Machines CorporationWalter W. Heller, University of MinnesotaVivian W. Henderson, Clark College

John A. Meyer, Harvard UniversityJ. Irwin Miller, Cummins Engine Company,

Inc.Geoffrey H. Moore. National Bureau of

Economic Research,j. Wilson Newman, Dun & Bradstreet, Inc.James J. O'Leary, United States Trust

Company of New YorkAlice M. Rivlin, Brookings institutionRobert V. Roosa, Brown Brothers Harriman

& Co.Boris Shishkin, Washington, D.C.Arnold M. Soloway, Jamal caway Tower,

Boston, MassachusettsLazare leper, International Ladies' Garment

Workers' UnionDonald B. Woodward, RiverSide, ConnecticutTheodore 0. Yntema, Oakland University

DIRECTORS BY UNIVERSITY APPOINTMENT

Moses Abramovitz, StanfordGardner Ackley, MichiganCharles H. Berry, PrincetonFrancis M. Boddy, MinnesotaOtto Eckstein, HarvardWalter D. Fisher, NorthwesternA. A. Gordon, CaliforniaRobert J. Lampman, Wisconsin

Maurice W. Lee. North CarolinaAlmarin Phillips, PennsylvaniaLloyd G. Reynolds, YaleRobert M. Solow, Massachusetts Institute of

TechnologyHenri Thou, ChicagoWilliam S. Vickrey, ColumbiaThomas A. Wilson, Toronto

DIRECTORS BY APPOINTMENT OF OTHER ORGANIZATIONS

Eugene A. Birnbaum, American ManagementAssociation

Thomas D. Flynn. American Institute ofCertified Public Accountants

Nathaniel Goldfinger American Federationof Labor and Congress of IndustrialOrganizations

Harold G. Haicrow, American AgriculturalEconomics Association

Walter E. Hoadley, American FinanceAssociation

Philip M. Klutznick, Committee forEconomic Development

Roy E. Moor, National Association ofBusiness Economists

Douglass C. North, Economic HistoryAssociation

Willard L Thorp, American EconomicAssociation

W. Allen Wallis, American StatisticalAssociation

Robert M. Will, Canadian EconomicsAssociation

DIRECTORS EMERITI

Percival F. BrundageFrank W. Fetter

Gottfried HaberlerAlbert J. Hettinger, Jr.George B. Roberts

Murray ShieldsJoseph H. Willits

SENIOR RESEARCH STAFF

Gary S. BeckerCharlotte BoschanPhillip CaganStanley OilIerSolomon FabrlcantMilton FriedmanVictor R. FuchsJ. Royce Ginn

Raymond W. GoldsmithMichael GortMichael GrossmanF. Thomas JusterJohn F. KainJohn W. KendrickIrving B. KravisEdwin KuhWilliam M. Landes

Hal B. LaryRobert E. LipseySherman J. MaiselBenoit B. MandelbrotJohn R. MeyerRobert T. MichaelJacob Mincerlise MintzGeoffrey H. Moore

M. lshaq NadiriNancy RugglesRichard RugglesAnna J. SchwartzRobert P. ShayEdward K. SmithGeorge J. StiglerVictor Zarnowitz

Relation of the Directors to the Work and Publicationsof the National Bureau of Economic Research

1. The object of the National Bureau of Economic Research is to ascertain and topresent to the public important economic facts and their interpretation in a scientificand impartial manner. The Board of Directors is charged with the responsibility of en-suring that the work of the National Bureau is carried on in strict conformity with thisobject.

2. The President of the National Bureau shall Submit to the Board of Directors, orto its Executive Committee, for their formal adoption all specific proposals for researchto be instituted.

3. No research report shall be published until the President shall have submittedto each member of the Board the manuscript proposed for publication, and such in-formation as will, in his opinion and in the opinion of the author, serve to determinethe suitability of the report for publication in accordance with the principles of theNational Bureau. Each manuscript shall contain a summary drawing attention to thenature and treatment of the problem studied, the character of the data and their utilI-zation in the report, and the main conclusions reached.

4. For each manuscript so submitted, a special committee of the Directors (in-cluding Directors Emeriti) shall be appointed by majority agreement of the Presidentand Vice by the Executive Committee in case of inability to decide onthe part of the President and Vice Presidents), consisting of three Directors selectedas nearly as may be one from each general division of the Board. The names of thespecial manuscript committee shall be stated to each Director when the manuscript issubmitted to him. It shall be the duty of each member of the special manuscript com-mittee to read the manuscript. If each member of the manuscript committee signifieshis approval within thirty days of the transmittal of the manuscript, the report may bepublished. If at the end of that period any member of the manuscript committee with-holds his approval, the President shall then notify each member of the Board, request-ing approval or disapproval of publication, and thirty days additional shall be grantedfor this purpose. The manuscript shall then not be published unless at least a majorityof the entire Board who shall have voted on the proposal within the time fixed for thereceipt of votes shall have approved.

5. No manuscript may be published, though approved by each member of thespecial manuscript committee, until forty-five days have elapsed from the transmittalof the report in manuscript form. The interval is allowed for the receipt of any memo-randum of dissent or reservation, together with a brief statement of his reasons, thatany member may wish to express; and such memorandum of dissent or reservationshall be published with the manuscript if he so desires. Publication does not, however,imply that each member of the Board has read the manuscript, or that either membersof the Board in general or the special committee have passed on its validity in everydetail.

6. Publications of the National Bureau issued for informational purposes concern-ing the work of the Bureau and its staff, or issued to inform the public of activities ofBureau staff, and volumes issued as a result of various conferences involving the Na-tional Bureau shall contain a specific disclaimer noting that such publication has notpassed through the normal review procedures required in this resolution. The Execu-tive Committee of the Board is charged with review of all such publications from timeto time to ensure that they do not take on the character of formal research reports ofthe National Bureau, requiring format Board approval.

7. Unless otherwise determined by the Board or exempted by the terms of para-graph 6, a copy of this resolution shall be printed in each National Bureau publication.

(Resolution adopted October 25, 1926, and revised February 6, 1933,February 24, 1941, April 20, 1968, and September 17, 1973)

Contents

Acknowledgments xiForeword by Victor Fuchs xiii

Introduction 1

I. THEORETICAL ANALYSIS

1. Individual Acquisition of Earning Power 7

1.1 The Schooling Model 9

1.2 Post-school Investments: Individual Earnings Pro-files 11

2. Distribution Analysis 24

2.1 The Schooling Model 242.2 Comparative Analysis of Earnings Profiles 282.3 Distribution of Earnings 32

2.3.1 Variances 322.3.2 Aggregation of Variances 362.3.3 Skewness 37

2.4 Mathematical Note on Skewness 39

II. EMPIRICAL ANALYSES

3. Schooling and Earnings 43

3.1 Quantitative Analysis 433.1.1 Grouped Data 453.1.2 Ungrouped Data 51

3.2 Some Qualitative Implications 59

4. Age and Experience Profiles of Earnings 64

viii CONTENTS

5. The Human Capital Earnings Function 83

5.1 Empirical Specification 835.2 Regression Analysis of Individual Earnings 895.3 Major Findings of the Regression Analysis 92

6. Analysis of Residuals: Distributions of Earnings WithinSchooling and Age Groups 97

6.1 Variances 976.1.1 Experience Profiles of Dollar and Log Vari-

ances of Earnings 986.1.2 Analysis of Marginal Variances of Earnings 1026.1.3 Analysis of Log Variances of Earnings 103

6.2 Shapes of Residual Distributions 109

7. Random Shock, Employment Variation, and Aggregation 115

7.1 Human Capital Versus Random Shock Models 1157.2 Variation in Employment as a Factor in Earnings In-

equality 1197.3 Female and Family Distributions 121

7.4 Aggregation of Omitted Groups 125

8. Summary and Agenda 128

8.1 Summary of Findings 1288.1.1 The Earnings Function 1298.1.2 Accounting for Income Inequality 1338.1.3 The Earnings Structure 134

8.2 Some Questions and an Agenda for Further Research 1378.2.1 Ability, Opportunity, and Investment 1378.2.2 Family Investment in Human Capital of Chil-

dren 1408.2.3 The Distribution of Employment as a Com-

ponent of the Earnings Distribution 141

8.2.4 Further Elaboration of Earnings Functions 1428.2.5 Toward a Fuller Analysis of Income Distribu-

tion 143

Bibliography 145Index 149

Tables

3.1 Schooling, Average Annual Earnings, and Rates of Return,1959 48

3.2 Short-cut and Standard Estimates of Rates of Return,1939, 1949, 1958 50

3.3 Regressions in Overtaking Sets 533.4 Correlation of Log Earnings with Schooling Within Ex-

perience or Age Groups 573.5 Distribution of Years of Schooling, by Age Groups, 1959 603.6 Cohort and Cross-sectional Changes in Income Inequality,

AU U.S. Men, 1947—70 624.1 Estimates of Post-school Investments in Dollars and

Time-Equivalents per Person 734.2 Alternative Estimates of Post-school Investment Costs per

Person, 1939, 1949, 1958 74

4.3 Annual Growth Rate of Income of Men in Selected Age and

Schooling Groups, 1956—66 79

5.1 Regressions of Individual Earnings on Schooling, Expe-rience, and Weeks Worked 92Earnings of White, Non farm Men, 1959

6.1 Age Profiles of Dispersion 101

6.2 Age Profiles of Skewness 110

6.3 Inequality and Skewness in Marginal Distributions 1127.1 Panel Correlations of Male Earnings, Based on Consumers

Union Panel, 1959 Survey 117

7.2 Weeks Worked in 1959, by Age and Schooling 121

7.3 Earnings Profiles of Women and Men, by Schooling, 1959 1227.4 Husbands' Earnings and Family Income, 1959 126

Figures

1.1 Production of Human Capital1.2 Earnings Profiles2.1 Age Profiles of Investment Ratios 29

Charts(all charts are for white, nonfarm men)

3.1 Schooling and Average Earnings, 1959 464.1 Age Profiles of Annual Earnings, 1959 664.2 Experience Profiles of Annual Earnings, 1959 674.3 Age and Experience Profiles of Relative Annual Earnings,

1959 68

4.4 Age and Experience Profiles of Relative Weekly Earnings,1959 69

4.5 Experience Profiles of Average Hourly Earnings, 1959 71

4.6 Age Profiles of Decadal Percentage Changes in Income, bySchooling Cohorts, 1956—66, and in Cross Section, 1956 78

6.1 Experience Profiles of Variances of Annual Earnings, 1959 100

6.2 Experience Profiles of Log Variances of Annual Earnings,1959 104

6.3 Experience Profiles of Log Variances of Annual Earningsof Men Working Year-round, 1959 105

6.4 Profiles of Relative Skewness of Annual Earnings, 1959 106

6.5 Fit of Annual Earnings Distributions to Normal and Log-Normal 114

Acknowledgments

This study is a direct descendant of my doctoral dissertation "AStudy of Personal Income Distribution," Columbia University, 1957.A short version of the thesis appeared as "Investment in HumanCapital and Personal Income Distribution" in the Journal of PoliticalEconomy, August 1958. Since that time, the economic analysis ofhuman capital has grown into a large and vital field. The presentstudy is in part a replication, on the much richer 1960 Census data(1/1,000 sample), of the research on the 1950 data reported in mythesis. More importantly, it represents a feedback into the field ofincome distribution of developments in human capital analysis whichhave occupied my attention since 1957. Throughout this time I wasprivileged to work closely with Gary S. Becker whose thinking gaveform and direction to an entire field of economic analysis. I grate-fully credit much of the conceptual advance of the present study overthe 1957 vintage to this collaboration.

Other friends and co-workers who helped to convert the firstdraft into the present manuscript were Orley Ashenfelter, YoramBen-Porath, Barry R. Chiswick, John C. Hause, Robert T. Michael,Carl Rahm, Sherwin Rosen, Theodore Schultz, and Finis R. Welch.

I owe special thanks to my students in labor economics atColumbia University. Though a captive audience, they have beenboth receptive to and critical of the materials first tried on themand eventually incorporated here.

I was particularly fortunate to have the competent and devotedresearch assistance of Masanori Hashimoto, Sara Paroush, andOdile Cornet.

Research here reported was initially funded by the EconomicDevelopment Administration of the U.S. Department of Commerce,and later by the Office of Economic Opportunity and the NationalScience Foundation. This support is gratefully acknowledged. Ofcourse, the opinions expressed here are my own, and should not beconstrued as representing the opinions or policy of these agencies.

XII ACKNOWLEDGMENTS

The book was edited and prepared for press by Ester Moskowitz,and the charts were drawn by H. Irving Forman.

Foreword

In 1957 Jacob Mincer completed his thesis, "A Study of Per-sonal Income Distribution," one of the pioneering works in the newand illuminating literature on investment in human capital. He di-rected our attention to the importance of training, both in schooland on-the-job, as a major explanation of income inequality.1 Sincethen Mincer has enriched our understanding of economic behaviorwith seminal studies of labor force participation, consumption, andopportunity costs. Unresolved problems concerning income distribu-tion were never far from his mind, however, and in recent years he hasattacked them with renewed vigor. The result is this volume, surelyone of the most important ever published on this subject and the mostsystematic one relying on the human capital approach.

In the pages that follow Mincer demonstrates his skill as awielder of Occam's razor. His objective is to explain a great deal witha little. The subject is earnings inequality, but the reader will look invain for references to unions, monopsonists, minimum wage laws,discrimination, luck, and the numerous other institutional factors thatare frequently introduced in such studies. Instead, Mincer fashions asimple but powerful theoretical model in which human capital is thecentral explanatory variable. Mincer does not deny that other factorsmay influence earnings. His position is, "Let's see how far the humancapital model can take us." And in his hands it takes us very far in-deed.

The two principal elements of human capital in the model areschooling and post-school investment. In the absence of specificmeasures of post-school investment, Mincer uses experience, whichhe estimates from age and the length of schooling. In the theoreticalsection Mincer shows in convincing fashion that it is years of ex-perience rather than age that should be emphasized in attempts to

1. See Jacob Mincer, "Investment in Human Capital and Personal tncome Distri-bution," Journal of Political Economy, August 1958.

XIV FOREWORD

explain variations in earnings. If one simply holds age fixed, estimatesof the return to schooling are biased downward because at a givenage those with less schooling have more experience, having leftschool earlier.

In highly simplified form, the story Mincer unfolds is the follow-ing: If you choose at random a group of white nonfarm men ofvarious ages and educational attainments, the differences in theireducation will explain only a small part (about 7 per cent) of the dif-ference in their earnings. This is also what other researchers havefound; unfortunately some have rushed to the conclusion that the re-maining difference must be the result of "luck" or "personahty."2Mincer notes that men who have the same amount of schooling mayhave very different amounts of labor force experience, and that theyalso will probably differ in the amount of post-schooling investmentthat they have. Those who engage in a great deal of post-school in-vestment (extreme examples would be medical residents or lawclerks) will have their earnings depressed (below what they couldhave earned) during the early portion of their working life. In lateryears, however, their earnings will be inflated by the return on thatinvestment.

The best time to measure the effect of schooling on the earningsof a cohort of men is about eight years after they leave school. Atthis point of "overtaking," there is minimum distortion from post-school investment because their return on previous investment isjust about equal to the cost of current investment. Mincer finds thatat this point differences in schooling explain, about one-third of theinequality in annual earnings. When account is taken of differencesin weeks worked the explanatory power goes to over 50 per cent!Mincer points out that if the quality of schooling could be controlled,3the explanatory power of the human capital model would be in-creased further.

Mincer shows empirically that schooling has more explanatorypower for groups with constant years of experience than for groupsof the same age, and that the explanatory power is at its peak forgroups with seven to nine years of experience. This result is pre-

2. See Christopher Jencks et al., Inequality (New York: Basic Books, 1972).3. See Lewis Solmon, "The Definition and Impact of College Quality," Working

Paper 7 (New York: NBER, 1973).

FOREWORD XV

dicted in the theoretical section. By contrast the "credentials" argu-ment of the effect of schooling does not yield such a prediction.

Mincer's insistence that experience matters more than age findsstrong confirmation in the data on female earnings—mentioned onlybriefly in this volume. The age-earnings profile for married women,whose work experience is often interrupted, is much flatter than thatof never-married women, who typically have at any given age a muchmore continuous attachment to the labor force and longer work ex-perience.4

When Mincer began his research, public interest in problems ofincome distribution was minimal. Economic growth was the vogue,and rapid growth was supposed to make life so much better foreveryone that relative shares would be of minor consequence. Notso today. A quarter century of rapid growth (real GNP per capita in1973 is almost double what it was in 1948) finds us more concernedthan ever about poverty and inequality.

Strong policy debates rage over whether and how the distribu-tion of income should be changed. In keeping with NBER policy,this volume takes no side in this debate, offers no policy recom-mendations. Instead, Mincer provides a logical, coherent, albeitincomplete explanation of why the distribution of earnings is whatit is—surely an invaluable contribution for anyone who wants to de-cide if or how to change the distribution.

I have stressed the book's positive contributions to economicscience; the inevitable qualifications and caveats that should ac-company such an ambitious work are amply provided by Mincer him-self. Indeed his own characterization of it as "an early and quiterudimentary effort toward a systematic analysis of personal incomedistribution," offers the promise that we can look forward to furtherinstalments in this lifetime of scholarship.

VIcToR R. FUCHSVice President-Research; Director, Center for

Economic Analysis of Human Behavior and Social Institutions

4. See Victor A. Fuchs, "Differences in Hourly Earnings Between Men andWomen," Monthly Labor Review, May 1971; and Jacob Mincer and Solomon Polachek,"Family Investments in Human Capital: Earnings of Women," Journal of PoliticalEconomy, March 1974.

Introduction

The positive relation between an individual's schooling and hissubsequent earnings may be understood to reflect productivity-augmenting effects of education. This relation is by no means director simple. Schooling and education are not synonymous: the educa-tional content of time spent at school ranges from superb to miser-able. The absorption of learning and marketability of knowledge andof skills acquired through learning also differ a great deal amongindividuals, places, and times. Moreover, school is neither the onlynor necessarily the most important training ground for shapingmarket productivities. Finally, nonpecuniary aspects of work, tem-porary and long-run deviations from equilibrium wage rates anddifferences in the amount of time spent in employment in the labormarket create additional differences among individual earnings,particularly when these are observed over a relatively short period.

It is not surprising, therefore, that observed correlations betweeneducational attainment, measured in years spent at school, and earn-ings of individuals, although positive are relatively weak. Still, whenearnings are averaged over groups of individuals differing in school-ing, clear and strong differentials emerge. The initial and simplestform of the human capital model elaborated in this study1 is ad-dressed to these schooling group differentials in earnings. The scopeof the model is then enlarged to deal with earnings differentialsamong age groups within the various schooling groups. This is ac-complished by relating earnings to training on the job and to otherhuman capital investments that follow the schooling stage of thelife cycle.2 Finally, by admitting into the model individual variations

1. As expressed in equation (1.1), this model was presented in Mincer (1957 and1958).

2. The conceptual framework for this part of the analysis originates in Becker's1-luman Capital (1964). Its empirical application to observed age-income profiles isshown in Mincer (1962b). The approach here is similar, though the focus is reversed.

2 INTRODUCTION

in investments and productivity within schooling groups and aftercompletion of schooling, some insights are obtained about the dis-tribution of earnings within age-education groups and in the ag-gregate.

The basic objective of this study is to gain some understandingof the observed distributions and structures of earnings from in-formation on the distribution of accumulated net investments inhuman capital among workers. The basic operational concept is thehuman capital earnings function, by which the two distributions—ofearnings and of net investment in human capital—are related. Theearnings function is fashioned in the theoretical analysis in Part I. Itis the major tool of the empirical analysis in Part II. An individual's"earnings profile" reflects his lifetime acquisition of human capital,and the aggregate distribution of earnings is viewed simply as adistribution of individual earnings profiles.

Clearly, this work is an early and quite rudimentary attempt at asystematic analysis of personal income distribution. Rapidly pro-gressing research in human capital and in various aspects of incomedistribution suggests that the foundations that emerge in this andrelated studies will be consolidated and built upon. The major limita-tion, at the present time, is the absence of adequate information onindividual investments in human capital. The accumulations of netinvestments that can be ascribed to individuals do not add up totheir total capital stock because "initial" capacities and investmentsprovided in and by the home environment are excluded. Still, the in-clusion in the earnings function of even crude measures of "post-school investments" in addition to schooling lends a great deal ofscope to the analysis of income distribution.

Individuals differ not only in the quantities of their accumulatedinvestments but also in the rates of return they receive. We have noindividual information on such rates. Variation in rates of return isprobably an important aspect of the distribution of earnings. I treatit as part of the residual variation in the analysis, which relates earn-ings to volumes of investment. Much of the residual variation, how-ever, is due to unmeasured quantities of human capital. It is not le-gitimate, therefore, to describe residual variation as a variation inrates of return, and even less so as a measure of risk in human capitalinvestment. The same ambiguity applies to one of the sources ofvariation in rates of return, namely, to ability: it is not clear to what

INTRODUCTION 3

extent, if at all, various "ability" measures represent unobservedcomponents of the human capital stock, or genuine efficiency pa-rameters.

Other limitations of the study are self-imposed. These are spelledout in the appropriate context, and discussed as subjects for futureresearch (see Chapter 8). The working model in the present study isstripped to bare essentials: the surprising scope of its empiricalpower is the major conclusion and promise to be drawn from it forfurther development.

Use of the human capital approach does not imply that alterna-tive models of earnings distributions are invalid.3 In many respects,the various approaches are complementary rather than mutually ex-clusive. At any rate, the emphasis of the present study is not on thetesting of competing hypotheses, though some attention is paid tothat, but on a coherent interpretation of detailed empirical char-acteristics of earnings distributions. The usefulness of the humancapital approach lies in the extent to which such a unified interpreta-tion is possible.

The following is a brief guide through the contents of the study:Part I is a theoretical analysis of the relation between human

capital accumulation and earnings. In Chapter 1, this relation isanalyzed at the individual level, leading to a formulation of the in-dividual earnings profile. In Chapter 2, the analysis is extended to across section of individuals. The cross-sectional distribution of earn-ings is viewed as a distribution of earnings profiles of individualswho differ in accumulations of human capital acquired at school andin post-school work experience.

Part II is an empirical analysis of earnings of white, urban, non-student men4 observed in the 1/1,000 sample of the 1960 U.S. Cen-sus. Chapter 3 is an application of the 'schooling model," in whichhuman capital investments are restricted to schooling. This model isshown to be misleading, unless it is applied to a particular subset ofworkers, namely, those with somewhat less than a decade of con-tinuous work experience. In Chapter 4, age and experience profilesof earnings and wage rates are distinguished and compared among

3. Some of them are surveyed in Reder (1969) and Mincer (1970).4. For a corresponding human capital analysis of female earnings, see Mincer

and Polachek (1974).

4 INTRODUCTION

different schooling groups. Inferences about intergroup differencesin investment behavior and in wages flow from the analysis of ex-perience profiles.

Chapter 5 contains an empirical specification and applicationin regression form of a simple version of the human capital earningsfunction. This version includes only three independent variables:years of schooling, years of work experience, and weeks workedduring the year. Estimates derived from this earningsfunction showedsubstantial explanatory power in a statistical and qualitative sense.

Chapter 6 contains a study of residuals from the regressions ofChapter 5. Patterns of observed variances and skewness parameterswithin schooling-experience groups are analyzed in the light of thehuman capital model.

In Chapter 7, the human capital analysis is contrasted with "ran-dom shock" models. Tests of discrimination are performed on Con-sumers Union panel data. Further, there is an analysis of the effectsof intensive and extensive aggregation of data on earnings inequal-ity, 'intensive" referring to aggregation of personal into family in-come and "extensive" to wider coverage of pOpulation groups. Atthe level of detail in the current study, the empirical predictions ofthe human capital model are not substantially changed by such ag-gregations.

Chapter 8 contains a summary of major findings of the study, adiscussion of their limitations, and an agenda for more compre-hensive research.

Part I

THEORETICAL ANALYSIS

1

Individual Acquisition ofEarning Power

Investments in people are time consuming. Each additional pe-riod of schooling or job training postpones the time of the indi-vidual's receipt of earnings and reduces the span of his working life,if he retires at a fixed age. The deferral of earnings and the possiblereduction of earning life are costly. These time costs plus directmoney outlays make up the total cost of investment. Because of thesecosts investment is not undertaken unless it raises the level of thedeferred income stream. Hence, at the time it is undertaken, thepresent value of real earnings streams with and without investmentare equal only at a positive discount rate. This rate is the internal rateof return on the investment.

For simplicity the rate of return is often treated as a parameter forthe individual. This amounts to assuming that a change in an indi-vidual's investment does not change his marginal (hence average)rate of return. Another empirically convenient assumption is that allinvestment costs are time costs. This assumption is more realistic insuch forms of human capital investments as on-the-job training, butless so in others, such as schooling, migration, or investments inhealth. In calculating schooling costs, an equivalent assumption isthat students' direct private costs are exactly offset by their part-

8 THEORETICAL ANALYSIS

time earnings during the year.1 Like the preceding one, this assump-tion is not essential. Detailed information on direct costs can beincorporated into the model to yield a more precise empirical analy-sis. We forego precision, in order to gain in the simplicity of exposi-tion and analysis.

The first step is to analyze the effects of investments in schooling.This is done by assuming that no further human capital investmentsare undertaken after completion of schooling and also, at this stage,that the flow of individual earnings is constant throughout the worK-ing life. For this the cessation of net investment is a necessary, butnot sufficient, condition. Also excluded are economywide changesaffecting individual productivity and earnings during the life cycle.

Since changes in earnings are produced by net investments inhuman capital stock, the net concept is used in most of the analysis.In this section, zero depreciation is, in effect, assumed during theschool years and zero net investment during the working life. Theseassumptions are amended in later sections and in empirical interpre-tations.

In specifying the lengths of earning lives it is first assumed thateach additional year of schooling reduces earning life by exactly oneyear. An alternative, and mathematically simpler, formulation is onein which the span of earning life remains the same in all cases, withmore educated people retiring at correspondingly later ages. Em-pirically, this assumption is more nearly the correct one.2

1. This assumption was defended and used by Hanoch (1967, pp. 317—320).2. More educated men retire later. The length of working life is roughly constant.

Only after high school does an additional year of schooling reduce earning life some-what (by less than half a year).

The following table contains estimates of the average "retirement" age and lengthof working life of men classified by level of schooling. It is based on a March 1970BLS labor force survey (1970b, Table E, p. A-li). Very similar estimates are producedfrom data in years before 1970.

Estimated EstimatedYears of Average Re- Length of

Schooling tirement Age Working Life

8 65 479—11 66 4712 67 47

13—15 67 4516 68 45

l7ormore 70 45

(note continued)

INDIVIDUAL ACQUISITION OF EARNING POWER 9

When earning life is long, the alternative formulations cannotmake much of a difference. What matters is the deferral of earnings:The cost of currently postponing earnings by one year is much moresignificant than the present cost of reducing earnings by one year,four or five decades hence, An infinite earning life can, of course,be viewed as a special case of the equal-span assumption. The ad-vantage of the latter formulation is both its greater tractability andits flexibility in empirical interpretation.

1.1 THE SCHOOLING MODEL

In calculating the effects of schooling on earnings, it is first assumedthat postponement of earnings due to lengthier schooling is tanta-mount to a reduction of the earning span.

Let

n = length of working life plus length of schooling= length of working life for persons without schooling= annual earnings of an individual with s years of schooling= present value of an individual's lifetime earnings at start of

schoolingr=discount ratet= 0, 1, 2, .. . , n time, in yearsd = difference in the amount of schooling, in yearse = base of natural logarithms

Then

=rY'

(Note 2 concluded)Estimates of retirement age are obtained by adding to age 45 the product of participa-tion rates and years beyond the age of 45. The length of working life is the sum ofproducts of participation rates and age intervals.

Estimates of lengths of working life in eight broad occupational groups, based on1930—50 Census data, suggested larger differences in the earning spans among occu-pations. Note, however, that because of occupational mobility, length of stay in anoccupational class, even when that is broadly defined, is not coextensive with lengthof stay in the labor force. Compare Mincer (1958, p. 284, n. 12).

The finding that the length of earning life of more educated men is the same asthat of the less educated is not inconsistent with the observed positive relation be-tween schooling and labor force participation at the middle and older ages (Bowen andFinnegan, 1969): A negative relation holds when the more educated are still at school.


when the discounting process is discrete. And, more conveniently,when the process is continuous:

VS = YS=

Similarly, the present value of lifetime earnings of an individual whoengages in s — d years of schooling is:

VS_d = — e_rn).

The ratio, of annual earnings after s years to earnings afters — d years of schooling is found by letting V3 =

y —r(s—d) — —rn r(n+d—s) — 1I, S

— V — — a—rn —'s—d

It is easily seen that kS,R_d is (1) larger than unity, (2) a positivefunction of r, (3) a negative function of n. In other words, (1) peoplewith more schooling command higher annual pay; (2) the differencebetween earnings of individuals due to the difference in investmentof .d years of schooling is larger the higher the rate of return onschooling; (3) the difference is larger the shorter the general spanof working life, since the costs of schooling must be recouped over arelatively shorter period.

These conclusions are quite obvious. Less obvious is the findingthat k3,3_d is a positive function of s (d fixed); that is, relative incomedifferences between, for example, persons with 10 years and 8 yearsof schooling are larger than those between individuals with 4 and 2years of schooling, respectively. However, since the change in kS,S_dwith a change in sand n is negligible3 when n is large, it can be, forall practical purposes, treated as a constant, k.

The conclusion that k is constant holds exactly when spans of

ak — ak3. —= >0;—---.O,whenn—soo;

as — 1]2 as

—=an — 1]2 an

Both partial derivatives are numerically very small when rand n are in a wide neighbor-hood of 0.10 and 40, respectively.


earning life are assumed fixed, regardless of schooling. Redefine n asthe fixed span of earning life.

Then

(fl+8 YV8 = V3 I e_rtdt== — e_mn);

r

fn+8—d y= Ys_a I

= s—d (1 —Js—d r

and solving for k8,3_d from the equalization of present values, we get:

V

= = e—rs = erd. (1.2)

Here, in contrast to (1.1) the earnings ratio, k, of incomes differing byd years of schooling does not at all depend on the level of schooling(s) nor, more interestingly, on the length of earning life (n), when thatis finite, even if short.

Now, define k3,0= Y8/Y0=k3. By (1.2), In logarithms theformula becomes:

In Y3=ln Y0+rs. (1.3)

Equation (1.3) exhibits the basic conclusion that percentage in-crements in earnings are strictly proportional to the absolute dif-ferences in the time spent at school, with the rate of return as thecoefficient of proportionality. More precisely, equation (1.3) showsthe logarithm of earnings to be a strict linear function of time spentat school.

1.2 POST-SCHOOL INVESTMENTS:INDIVIDUAL EARNINGS PROFILES

The "schooling model" represented by equation (1.3) is the mostprimitive form of a human capital earnings function: Y3 in (1.3) is thelevel of earnings of persons who do not invest in human capital be-yond s years of schooling. Since most individuals continue to developtheir skills and earning capacity after completion of schooling, V3cannot be directly observed. Instead, an "earnings profile" is ob-served: the variation of earnings with age during the working life.


We proceed to a human capital analysis of the earnings profile, atfirst ignoring depreciation phenomena.

After entering the labor force in year j, the worker devotes re-sources C,, mainly in furthering his job skills and acquiring job-related information, whether in the form of direct dollar outlays oropportunity costs of time devoted to these purposes, on or off thejob. His "net" earnings Y3 in year j are obtained, therefore, by deduct-ing C, dollars from his "gross" earnings or "earnings capacity" E5,which he would earn if he did not continue to invest in himself.4

Accordingly, earnings during the first year of work experience,j = 0, are Y0 = — C0, where Y3 (= E8) is the initial earning capacityafter completion of s years of schooling.

If investment ceased earnings in the next year(and afterward) would be: Y1 = Y3 + r0C0. However, if investment inthat year is C1, then Y1 = Y3 + r0C0 — C1. More generally, net earningsin year j are:

i—I(1.4)

The generality of expression (1.4) is evident, since the start ofindex t is essentially arbitrary. In Becker's original statement of theaccounting equation (1.4), Y0 replaces and in instalments C,schooling and post-school investments are not distinguished. Infact, the expression for Y3, the schooling model, is a special case of(1.4), in which investments are restricted to time costs of schoolingand rates of return are the same in all periods. Then, with = E1:

Y0(1 +r)s, (1.5)

which is a discrete approximation of (1.3).Using equation (1.4) we can proceed to the analysis of variation

of earnings over the working life.5 On the assumption that working

4. Note that observed earnings, as they are usually reported, would equal "net"earnings if consisted of opportunity costs only. However, direct costs are includedin reported earnings. Thus observed earnings overstate "net" earnings, but sincedirect costs are much smaller than opportunity costs, observed earnings more closelyapproximate than E1.

5. At this point we are abstracting from variations in hours or weeks of labor sup-plied over the life cycle. Some consideration is given to this factor later.


life starts in the period following the completion of schooling, equa-tion (1.4) points to post-school investments as the variable whichtraces out the individual "age profile" of earnings. The initial earn-ing capacity Y3 acquired in years of schooling s is taken as constantfor a given individual, though it may vary among individuals. is

not readily observed, since most or all individuals are assumed toengage in post-school investment of one form or another.

The variation of earnings with experience is best observed byconsidering the annual increment of earnings in (1.4):

(1.6)

According to (1.6), earnings grow with experience so long as netinvestment (Ci) is positive and its annual instalments either diminish

— <0] or increase at a rate lower than the rate of return:

Note that if investments increase sharply (at a faster rate than r),net earnings will decline, presumably temporarily. However, grossearnings always increase, so long as investment is positive, since

= r,C3. (1.7)

If both rj and investment are the same in all periods (C, = C,÷1; =net and gross earnings grow linearly. Henceforth we shall assumethat all

While constant or linearly increasing investment is conceiv-able for some stages of individual work experience, these assump-tions cannot be expected to hold over any long periods of the work-ing life. Such assumptions are inconsistent with the theory of optimalallocation of investment in human capital over the life cycle. Rationalallocation requires that most of the investment be undertaken atyounger ages. Thus schooling, a largely full-time activity, precedesjob-training, a largely part-time activity, and the latter diminishes withage, terminating years before retirement.

According to Becker (1964 and 1967) this tendency is due to thefollowing incentives for shifting from learning to earning activitiesas soon as possible: (1) With finite lifetimes, later investments pro-duce returns over a shorter period; so total benefits are smaller. (2)To the extent that investments in human capital are profitable, their


postponement reduces the present value of net gains. (3) A person'stime is an important input in his investment, but the consequence ofhuman capital accumulation is an increase in the value of his time;thus investments at later periods are more costly, because forgoneearnings (per hour) increase. However, these incentives would beoverridden in the special or temporary cases where productivity inlearning grows as fast or faster than productivity in earning.

Should we then not expect an early and quick accumulation ofall the desired human capital even before individuals begin theirworking life? The answer of human capital theory to this question istwofold: Investments are spread out over time because the marginalcost curve of producing them is upward sloping within each period.They decline over time both because marginal benefits decline andbecause the marginal cost curve shifts upward.

Specifically, the argument (Ben-Porath, 1967; Becker, 1967)visualizes individuals as firms which produce additions (Q) to theirown human capital stock (H) by combining their human capital withtheir own time (T) and with other market resources (R) in a productionfunction:

Q= f(H, T, R).

Attempts to increase investments Q within a given period run intodiminishing returns: Costs rise with the speed of production. Thusthe marginal cost curve in Figure 1.1 is upward sloping.

The marginal revenue obtained by adding a unit of investment tothe capital stock is the discounted flow of future increases in earningpower. For reasons indicated, the benefits of later investments de-cline. The MR curve slides downward with increasing age, tracing outa declining pattern of investment over the life cycle.

The decline is reinforced if the MC curve shifts to the left withadvancing age. As already mentioned, this. is not a logical necessity:MC would remain fixed if earning and learning powers increased atthe same rate. A recent attempt by Ben-Porath (1970) to test for such"neutrality" empirically suggests that investments decline over earn-ing life faster than would be predicted by the mere downward slideof MR on a fixed MC curve in Figure 1.1. By implication, marginalcosts rise over the life cycle.

Investments, however, need not decline throughout the lifecycle. Ben-Porath (1967) has shown that the optimization process

INDIVIDUAL AcQuIsITIoN OF EARNING POWER 15

FIGURE 1.1PRODUCTION OF HUMAN CAPITAL

Dollars

0

may lead to an increase in investment during the early stages becauseof 'corner solutions": The initial stock (H0) may be so small that evenan input of all the available time, other resources not being highlysubstitutable, produces less than the optimal amount of output. Asthe stock increases, investment output will increase for a while untilan optimum is reached with an input of less than the total availabletime. At this point investments and the time devoted to them begin todecline. The initial period of complete specialization in the produc-tion of human capital is devoted to full-time schooling. It is identifiedby the absence of earnings, a condition which may end before thecompletion of schooling.

The optimization process described above applies explicitly(Ben-Porath, 1967) to gross investments in human capital. Note,however, that the predicted decline in gross investment applies afortiori to net investment if depreciation is constant or increases withage.

Two major conclusions can be drawn from the Ben-Porathanalysis:

1. The higher the marginal revenue curve and the lower the mar-ginal cost curve (cf. Figure 1.1), the larger the investment in humancapital in any given period. Marginal revenue is higher the lower thediscount rate and the depreciation rate, and the longer the expectedlength of working life. Marginal cost is lower, the greater the learning

MC

MR1

MR2

Q2Q1 Q


ability of the individual. Since the nature and conditions of individualswhich these factors describe change rather slowly, the size of single-period investments is likely to be an index of lifetime investments.Longer schooling is likely to be followed by greater post-school in-vestment, and generally, the serial correlation of instalments of in-vestment is likely to be positive.

2. While the preceding inference is significant for a distributionalanalysis, the major implication of Ben-Porath's optimization analy-sis for the individual investment profile is that investment costscan be expected to decline after the schooling stage. As a result, bothgross and net earnings slope upward during the positive net invest-ment period. Moreover, the age profile of gross earnings is concavefrom below. From (1.7), we have the second difference:

< 0, (1.8)

since < 0. Net earnings need not be concave throughout. Theprofile is concave if the decline of investments (Ci) is a nonincreasingfunction of j, i.e., if

<0. (1.9)

If investments decline at a strongly increasing rate for a while, sothat the inequality sign is reversed, age profiles may rise at an ac-celerating rate for a while; but eventually they become concave asnet investment terminates.

The profile of net earnings has a steeper slope than gross earn-ings, since = — and <0. The peak of both gross andnet earnings is reached when positive net investments equal zero.6

Figure 1.2 indicates the shape of gross earnings and net earn-ings Y, during the post-school investment period OP. Of particularinterest are the initial earnings capacity Y8 and peak earningsThe former, Y8, isthe earnings concept used in the schooling model.Its estimate is particularly useful for the empirical analyses in thisstudy. Estimates of and of Y,, would make possible quick andsimple methods of estimating rates of return and amounts of invest-ment costs.

During the early years of experience, earnings of continuing in-

6. I abstract from depreciation and from changing hours of work.

Y;=

Otosoo

1

r

To illustrate, if r exceeds 10 per cent, it takes lessthe trained person to overtake the untrained one,working life with the same initial earning capacity.

than a decade forif both start their


FIGURE 1.2EARNINGS PROFILES

EarningsY

Vp

Ys

V0

0

vestors are smaller than the Y8 earnings that can be obtained after syears of schooling without further investments. But earnings of in-vestors continue to grow and, before long, exceed In Figure 1.2,J is the overtaking year of experience. Knowledge of/permits one toread off the value V3 from the profile of observed earnings It turnsout that J is an early stage of experience, and its upper limit can beestimated from equation (1.4):

i—I i—i

C3 = Y3, when = C3.

t=Jare equal, then rJC,, = C3; soI= hr.ner; therefore, assume is not increas-

(1.10)

JP Years of work experience

If instalments C from t =If Cg declines, jis reacheding. Then,


Even for the rough estimate of V8 by (1.10) it is necessary to knowthe value of the rate of return to post-school investment. If r,, isknown, can be more precisely determined, since at the start ofworking life the present value of the constant earnings streammust equal the present value of the observed earnings profilewith as the discount rate. If, as is perforce assumed in empiricalcalculations of rates of return to "education," the rate of return topost-schOol investment (rn) equals the rate of return to schooling,the conventionally calculated rates can be applied to estimate Y8. Inturn, estimates of Y8 at two levels s1 and s2 make it possible to apply acheck of internal consistency to the hypothesized equality r8 =since, by (1.3) In — In Y81 = — s1). Further applications of the"overtaking" or "crossover" point of the earnings profile to short-cutestimation of changes in rates of return and to distributional analysisare elaborated in Part II of this study.

At the end of the net investment period,

(1.11)

The total volume of post-school investment costs can beestimated, once hence are known,7 since

(1.12)

Similarly, the costs of rising from schooling level s1 to level s2 are:

—

r(1.13)

Si

The above analysis of dollar profiles of earnings is easily trans-lated int&an analysis of logarithmic earnings profiles. This is notonly useful but necessary, for two reasons: (1) Relative (percentage)variation in earnings is of major interest in the study, of incomeinequality; and (2) for empirical analysis, post-school investmentsmust be expressed in the same "time" units as schooling. Indeed, theconversion of investment costs into time-equivalent values trans-

7. In Figure 12, total post-school investment costs are given by the areaYoY$Yp.


forms the earnings equation (1.4) into its logarithmic version. This isaccomplished by the following device:

Let k3 be the ratio of investment costs C) to gross earnings E) inperiod j. This ratio can be viewed as the fraction of time (or "time-equivalent," if investment costs include direct outlays as well as timecosts) the worker devotes to the improvement of his earning power.His net earnings in year / are, therefore, smaller by this fraction thanthey would be if he did not invest during year j:

C3 = k,E,,

andE3 = + rC,....1 = E,_1(l + rk3_1).

By recursion, therefore:i—i

E5= E0 fl (1 +

r relatively small, this is approximately:

In (1.14)

and since V,, = E3(1 — k5), we get

i—IIn Y3=In (1—k3). (1.15)

The assumption that = 1 during the school years shows (1.15) to bean expansion of the schooling model:

In (1.16)

The assumption that r3 is the same for all post-school invest-ments simplifies matters. Let

i—i

the cumulative amount of "time" expended in post-school invest-ments before year j. Then

In (1.17)

8. This device was applied by Becker and Chiswick (1966) to schooling invest-ment. Here it is extended to cover post-school investments.


If = we have, denoting (S + K,), the simplest generaliza-tion of the schooling model:

In E,=ln E0+rh,. (1.18)

When the investment period is completed, K,. is total "time" de-voted to post-school investment. It can be calculated from (1.17), if

is known:In

(1.19)

The earnings profiles under these assumptions provide info rma-tion on the number of "years" of post-school "training," a statisticthat is impossible to obtain in surveys of workers or firms, and onethat is bound to be greatly underestimated if it is based on reportedapprenticeship periods or other formal training programs in firms.9

The shape of the log-earnings profile is upward sloping so longas k, > 0. Its rate of growth and concavity are given by the first andsecond derivative of (1.15) with the same conclusions as in the dollarprofiles, with replacing C,.

Note that the decline in k, with experience follows a fortiori fromthe assumption of declining dollar values of post-school invest-ments, and that consequently concavity in the logarithmic profile isto be expected more frequently, that is, even when the dollar profileis linear or S-shaped.

In the foregoing analysis it was assumed that (1) net investment isnever negative, that is, the formulation abstracts from depreciationphenomena; and (2) changes in earnings over the life cycle representchanges in earning capacity rather than changes in hours of worksupplied to the labor market (rncluding the hours spent in on-the-jobtraining).

The first assumption is not seriously misleading in the life-cyclecontext if the second is maintained: As Chart 4.4 in Part II shows,"fuJi-time" earnings or wage rates reach a peak and remain on aplateau until men reach an age near retirement. On average (the dataare mean earnings classified by years of education), net investmentmay be viewed as non-negative through most of the working life.Still, the finiteness of life, the increasing incidence of illness at older

9. Cf. discussion in Mincer (1962). Of course includes forms of investment otherthan post-school training. Information and job mobility are examples.

INDIVIDUAL AcoulsmoN OF EARNING POWER 21

ages, and the secular progress of. knowledge, which makes oldereducation and skill vintages obsolescent, are compelling facts sug-gesting that as age advances, effects of depreciation eventually beginto outstrip gross investment.

To accommodate these phenomena the formulation is amendedby positing a rate at which the human capital stock H1 depreciatesin time period t. Then

E1 = E1_1 + rC_1 — (1.20)

where denotes gross investment, as C1 denoted net investment.Letting the gross investment ratio k = C/E1, we get:

Et— 1

thus k1 = — and

In E1 = In E1_1 + In (1 + —

by recursion, and assuming (rk — is small, we have:

In E1= In (1.21)

and

InY1=InE1+In(1—kfl (1.22)

as an amendment to (1.14). It is clear that the peak of earning capacityE1 is reached when k1 = 0, i.e., when k = call it k*(E max). It isalso clear that observed wage rates reach a peak some time there-after, since from (1.22):

In Y=ln (1 (1.23)

only when < i.e., when net investment is negative. It can beshown 10 that if is fixed and if the gross investment ratio declines

10. From (1.23) Yg reaches a maximum when, approximately

L.* L..*— — —

Then

— k*(E max)] = k7 —

and

max)— k_11,_* ,_* r


linearly over time, the (unobservable) peak of earning capacity pre-cedes the (observed) peak of wage rates by t= 1 Ir, that is, by about adecade or even earlier if the rate of decline of diminishes over thelife cycle. Note, also, that while the net investment period terminatesbefore peak earnings (wage rates) are observed, the gross investmentperiod continues beyond it.

In a few recent human capital analyses in which depreciation istaken into account, the rate is assumed to be fixed purely for mathe-matical convenience.'1 Yet, the depreciation rate on human capital islikely to be related to age, experience, and size and vintage of stock.If descriptions in developmental psychology can serve as a guide, thelife-cycle pattern of after the individual matures is plausiblydescribed as flat and very low, beginning to rise in the fifties.'2

To the extent that hours of work vary over the life cycle, the pro-file of annual earnings is affected. Under conditions of certainty, forexample, individual wealth can be considered fixed, while the costof time grows with experience until peak earning capacity is reached.If so, the growth and decline of earning capacity is likely to induce acorresponding pattern of hours of work supplied to the market.Hence, the growth of observed annual earnings leads to overesti-mates of investments in human capital or of rates of return. Hours of

11. Cf. Johnson (1970), Rosen (1974), and Koeune (1972).12. Health statistics show the proportions of workers with some limitations of

work activities during the year to be rising slowly to 13 per cent of those in the 45—54age range, and accelerating to 55 per cent at age 75. However, in a survey of thepsychological literature, Birren (1968, pp. 180—181) states: "Except for individualswith cumulative injuries or problems of health, worker performance up to age 60should be little influenced by physiological changes in aging." In discussing agechanges in learning capacity, the same author states: "There has been a generaltendency since the work of E. L. Thorndike in the 1920's to advance continually theage at which subjects in learning research are regarded as aged. At the present timethere is little evidence to suggest that there is an intrinsic age difference in learningcapacity over the employed years, i.e. up to age 60."

Psychologists note, of course, that it is difficult empirically to isolate intrinsic agepatterns in productivity, that is, changes that are not affected by the individual'sadaptation, such as health care and training—gross investment, in our terminology.Hence, their observations of time changes in "productive capacity" often show system-atic differences when individuals are stratified by education, social background,ability measures, and so forth. [See Mincer (1957, Chap. 1, n. 1).] To the extent thatthese patterns reflect differential patterns of "adaptation," the analysis of humancapital investment behavior is likely to contribute to an understanding of these find-ings, rather than conversely.


work may peak before observed wage rates because, as noted above(Cf. note 10), capacity wage rates decline before observed wage ratesdo, given human capital depreciation.'3

Variation in hours (weeks) worked is taken account of in theempirical analyses. The analysis of the relation between hours ofwork and human capital investments is not theoretically integratedinto the present model. Though the problem is discussed in severalplaces below, its fuller development is relegated to a future study.

13. Recent analyses of optimal allocation of consumption and work over the lifecycle by Becker and Ghez (1967 and 1972) suggest that hours of work are likely to peakbefore earning capacity, a fortiori before observed wage rates decline.

2

Distribution Analysis

2.1 THE SCHOOLING MODEL

The analysis of individual earnings is now adapted to a cross sectionof workers. I begin with schooling, that is, I restrict human capitalinvestment to schooling alone. In equation (2.1) a subscript i is nowattached to the variables Y (earnings) and s (years of schooling) inorder to distinguish individual differences in them. For simplicity, I

initially disregard individual differences in the (average) rate of re-turn r and in original earning capacity Y0. The symbol denoteshypothetical earnings of an individual who does not continue toinvest in human capital after the completion of S years of schooling.

In Y0+rs1. (2.1)

Even at this primitive stage, several important and rather real-istic implications follow for the personal distribution of earnings:

1. The positive skewness that is almost always exhibited bydistributions of income or earnings may be partly due to the effectof the logarithmic transformation, which converts absolute differ-ences in schooling into percentage differences in earnings. Clearly,

DISTRIBUTION ANALYSIS 25

a symmetric distributiondistribution of earnings.

schooling.Assume first a

S2 — s,,, = — s1 = d.ings distributionrelative dispersion(V1 + Y2)/2> A

of schooling implies aIndeed, a positive skew

positively skewedof earnings cannot

Sk= +(Y2 — 2Ym + Y1) = .k(e2rd — + 1)Y1

> 0.

Using Bowley's formula, relative skewness is defined as,

(Y2 — Y1)RSk=

Y2— V1

Sk

= V2 — V1) — — 1 —

— 1 >0. (2.3)

Both measures ofmeasures of dispersion and skewnessdispersion in the distribution of schooturn on investment in schooling (r).

These conclusions remain unchanged whenschooling is not symmetric, except that the degreeearnings distribution is now additionally affected

the distribution of schooling, theskewness in the distribution of

to schooling, the larger the earn-

V0 and rto be fixed:

be avoided unless the distribution of schooling is strongly skewed inthe negative direction.

2. The larger the dispersion inlarger the relative dispersion andearnings.

3. The higher the rate of returnings inequality and skewness.

The implications for inequality are shown by taking variances inequation (2.1), assuming both

o2(ln = r2cT2(s).

The implications for skewness are shown most simply in a non-parametric formulation: Let V1 be a lower percentile level of earningscorresponding to an s1 level of schooling; Y2, symmetric upper per-centile corresponding to s2; median earnings; and Sm, median

symmetric distribution of schooling, so thatThe absolute (dollar) dispersion in the earn-

is D=Y2_Yj=(e2Td_1)Y1; so TheRD = = e2Td. Positive skewness exists whenmeasure of it is

(2.2)

skewness are necessarilyare positiveling (d) and

positive, andfunctions ofof the rate of

allthere-

the distribution ofof skewness in theby the degree of


skewness in the distribution of schooling. Let s2 — s,,, = d2; andSm — = d1; d2 d1. Then

= — + Y1 = {e — 2erdl + 1]Y1. (2.4)

Let d2.= d1 +Let relative skewness in the distribution of schooling be defined

by sks = Then it can be shown (by approximation 1) that evenwhen sks is negative, the distribution of earnings remains positivelyskewed when the absolute value of sks does not exceed rd1 and thelatter is less than unity:

d1 — d2< rd1 < 1. (2.5)

The empirical usefu'ness of the schooling model formulated inequation (2.1) may be questioned on two grounds: The initial earn-ings level Y0 and the rate of return r cannot be assumed to be thesame at all levels of schooling and for all persons. It is merely a con-venient simplifying assumption. But if individual values of rare inde-pendent of s, and (2.1) is used as a statistical estimating equation,then r must be thought of as an average over all schooling levels and

1. Skewness in the distribution of earnings is positive when

— + 1 > 0

or

— 1)2 + — 1) > 0; — 1)2 > —

Taking square roots:

— 1 > Vi — erdi 1

1 — Vi —

Taking logs: rd1 > —In (1 — Vi — This condition holds when rd1 > Vi —since for x < 1, x > —In (1 — x), by the Taylor expansion. Hence > 1 — is asufficient condition for positive skewness in earnings when < 0.

Again, assuming sufficiently small, and taking logs, > and so< rd1 < 1 is a sufficient condition for positive skewness in earnings, when

This condition can also be written as rd2 > rd1(1 — rd1). It is always fulfilled whenrd2 > 0.25, so long as rd1 < 1. Skewness was defined with respect to a particular(S1 — s2) interval in the distribution of schooling. Therefore, so long as an s2 can befound such that r(s2 — > 0.25, where srn is median schooling, the distribution ofearnings must be positively skewed in that interval.


persons, and individual differences in r (and in In Y0) are impoundedin the statistical residual.

Let rates of return differ by schooling level. Then equation (2.1)becomes

In Y0+?s,

where is the marginal rate of return for a particular level of school-ing, and 7 is the average. If ? is not the same for all individuals (i), then

In (2.6)

Now the inequality of earnings in a group is affected not only by thedispersion in schooling and by the average size of the rate of return,as indicated by equation (2.2), but also by the dispersion in the ratesof return and by the average level of schooling. This is clearly seen inthe case where and s, are independent.2 Ignoring variation, in Y0:

o2(ln Y8) = r2o-2(s) + + o2(s)cr2(r). (2.7)

Here is the average of across individuals.Should it not be assumed that and s, are positively related?

Presumably, persons who can benefit more (get larger returns) fromgiven amounts of investment will invest more. However, the averagerate of return of an individual, 1, ceases to be an index of his abilityto benefit from schooling investment when individuals with differingamounts of investment are compared, because ?, depends, in part, onthe level of investment. As spelled out by Becker (1967), the conditionfor a positive correlation between and s, in a cross section is thatthe dispersion of "abilities" (levels of demand curves for investmentfunds) exceed the dispersion of "opportunities" (levels of investmentfund supply curves).

There are no a priori reasons for specifying which dispersion isgreater, and the empirical evidence3 suggests there is little if anycorrelation between rates of return and quantities invested across

2. By a theorem of L. Goodman (1960).3. See Tables 3.3 and 4.4 in Part II. In bodies of data in which and sj are cor-

related, empirical estimates of the coefficient of ? will be biased. In that case the ex-pression for the inequality of earnings (2.7) will contain additional variance and co-variance terms.


individuals. Hereafter, the symbol ? will not be used. Instead, unlessit is otherwise stated, r will denote the average rate of return.

By definition, the schooling model described in (2.1) applies tothe earnings of individuals who do not make post-school investmentsin human capital. Because such individuals are rare, these earningscannot be directly observed. They can be rather crudely estimated, asexplained in Chapter 1, by earnings at the overtaking stage of the lifecycle (see Figure 1.2). In the following section, the earnings model isexpanded beyond schooling to take account of variation in earningsdue to life-cycle and individual differences in the distribution of post-school investments.

2.2 COMPARATIVE ANALYSIS OF EARNINGS PROFILES

Figure 2.1 portrays investment profiles of three individuals whosegross investment at each age is measured in "time-equivalent"units (k*), that is, as a ratio to earning capacity. The three investmentprofiles = and a common depreciation curve D = aredrawn schematically. Here I denotes the individual, j his age, thedepreciation rate.

Individuals who invest more than others have their investmentprofiles shifted upward. describes investment behavior of an indi-vidual with the same level of schooling (s1) as but larger post-school investments while '2 describes the investment profile of a per-son wi.th more schooling (s2) than but the same level of post-schoolinvestment as 1. and '2 need not be parallel, but they are plausiblynear-parallel, given that the expected period of gross investment Textends over most of a lifetime.

Consider now the two comparisons, and define experience aschronological time (1) since the start of post-school investments.Note that the net investment ratio k, is given by the vertical dif-ference between I and D, and recall that the growth rate of earningcapacity in period j is given by nc,.

If the increase in investment (from to 1) is restricted to post-school investment, meaning that schooling (si) is the same in bothcases, then net investments (k,) are larger for each additional year ofexperience and of age, and peak earning time (P1) is shifted to a laterage (P2) and to a later year of experience. Earning capacity risesmore rapidly at each age and for a longer period, reaching a higherlevel at P2. Even if the increase in investment includes also an in-

Gross investment ratio

k*=I


FIGURE 2.1AGE PROFILES OF INVESTMENT RATIOS

crease in schooling (shift from to 12), the conclusion for the age-earnings profiles remains the same. This is not necessarily true, how-ever, for the description of experience-earnings profiles, since thesame age no longer represents the same year of experience as it didbefore. For example, if the shift from to '2 is, indeed, parallel, as inFigure 2.1, meaning that post-school gross investment ratios remainunchanged, net investment ratios (k,) will not be greater for each yearof experience. In fact, they will actually be somewhat smaller if D hasan upward slope; and peak earnings will be reached at an earlier yearof experience. With D relatively flat, the (log) experience-earningsprofiles are nearly parallel, though the age-earnings profiles di-verge.4

4. This is exact when D is horizontal and the same in all schooling groups. Thenthe parallel shift of gross investment implies the same parallelshift in net investments

In that case, the logarithmic experience-earnings profiles would be exactly alike inthe two cases, except for a difference in levels. At a given year of experience the ratioof earnings would be equal to Thus, relative differentials in earningsbetween the two schooling groups would be the same at any level of experience, withor without post-school investments.

0

0 S1 S2 P1 P2 Tj T2Age


This analysis underscores the importance of distinguishing be-tween age profiles and experience profiles of earnings. In the specialcase just discussed, shapes of experience profiles of (log) earningsare the same in all schooling groups, though shapes of age profilesare not. While relative intergroup differentials in earnings do notchange with experience, they grow with age! This is because at givenages, earnings rise less rapidly (and decline more rapidly at ad-vanced ages) for the lower profiles. For groups with more schoolingearnings peak at the same or earlier years of experience, but at laterages.

If an increase in investment ratios results from both longerschooling and more "time" spent in post-school investments, that is,s2> s1 and k23> for each j, then log earnings profiles for both ageand experience will be steeper and peak later than if either schoolingor post-school investment are the same, though this behavior will beless evident in the latter profiles than in the former.

Note also that the steeper the upward slope of D in the neighbor-hood of its intersection with I, the less the difference in age at whichearnings begin to decline in all schooling groups. If retirement age isrelated to the time of onset of declining earning power, this analysismight well explain why persons with more schooling retire later inlife, and yet have a somewhat shorter earnings span.

So long as gross investment extends over the working life andretirement age is not earlier for the more educated, 12 is likely to ex-ceed at each age. This is the simplest interpretation of the uni-versally observed divergence ("fanning out") of age profiles of earn-ings. Note that if '2 declines more steeply than (without intersect-ing), logarithmic age profiles will still diverge ("fan out"), but logexperience profiles will converge: earnings of higher schoolinggroups will grow at a somewhat slower rate. Dollar age profiles willfan out, a fortiori, and so may5 dollar experience profiles, eventhough log experience profiles converge.

A positive correlation between dollar investments in schoolingand at work does not constitute evidence against the possibilities for

5. A convergence of log experience profiles would mean that the more schooledpersons spend less "time' in post-school investment. However, they clearly spendmore in dollar terms, if '2 > at each age. The sufficient condition for a positivecorrelation between schooling and post-school investments in dollars is even weaker:C2 > C1 in each year of experience.


substitution between the two forms of investment in human capital.Rather, it reflects the dominance of individual differences in factorsdetermining the scale of total human capital accumulation. Individ-uals who invest more in human capital, invest more in both forms ofit. Evidently, abilities to learn on the job are positively, though farfrom perfectly, related to abilities to learn at school, and so arefinancial opportunities to incur such investments. Indeed, given im-perfect markets for human capital, it would not be surprising to findthat just as schooling investments are positively related to personal(family) income, so are post-school investments to personal earningcapacity, that is, to the preceding schooling investments.

As already noted, a positive correlation between dollar school-ing and post-school investments does not imply a positive correlationbetween these investments in "time" units. If individuals with dif-fering amounts of schooling all have the same post-school invest-ment ratios, as indicated by the parallel investment profiles inFigure 2.1, then the correlation between "time" spent in school andin post-school investments is zero. However, dollar post-school in-vestments are larger in proportion to the larger earning capacity(initial gross earnings) of the more schooled. This case can bedescribed as one of unitary elasticity of post-school investmentswith respect to earning capacity. The positive elasticity is less than1 when dollar post-school investments are larger at higher schoolinglevels, but less than in proportion to the higher earning capacity.

We may now summarize our conclusions concerning compara-tive earnings profiles for different schooling groups, and the impli-cations of these comparisons for earnings differentials by schooling,age, and experience. So long as the elasticity (or "marginal propen-sity to invest") is positive with respect to earning capacity (correla-tion between dollar schooling and post-school investments is posi-tive), dollar earnings grow faster in upper schooling groups, at givenyears of experience and—a fortiori—of age. Logarithmic profiles fanout with age, so long as '2 > I, but not necessarily with experience.They converge with experience if the "income elasticity of invest-ment" is less than 1, that is, when the correlation between "time" inschooling and in post-school investment is negative.

Hence "skill differentials" in dollar earnings which are attribu-table to schooling differences can be expected to grow with age andexperience, and relative (percentage) differentials to grow with age.


The latter also grow with experience, but only if the elasticity of post-school investments with respect to earnings capacity exceeds 1.They decline with experience if the elasticity is less than 1, and re-main fixed at all stages of experience when the elasticity is 1.

2.3 DISTRIBUTION OF EARNINGS

Thus far I dealt with intergroup differences in earnings of personsdiffering in schooling and age.

However, within groups of workers of the same schooling andage, earnings inequality is far from negligible. There are severalreasons for this: (1) differences in accumulated human capital,despite the same length of schooling, because of differences inschooling quality or rates of return to schooling; (2) differences inpost-school investment behavior; 6 and (3) differences in rates of re-turn to post-school investments.

2.3.1 VARIANCES

Assume first that individuals who complete a given level of school-ing have the same gross earnings (earning capacity) Y3 and rates ofreturn r3, but differ in their post-school investment behavior.

Individual differences in post-school investments were illustratedin Figure 2.1. The conclusion was that earnings of individuals who in-vest more in each year j rise more rapidly with experience and for alonger period. This means that relative (as well as absolute) disper-sion of gross earnings within a schooling cohort rises with experienceuntil peak earnings are reached by the largest investors.

Note, however, that the change in dispersion of net earningswith age is not monotonic: Assuming, as I have thus far, that Y,,and r are fixed within schooling groups, earnings of investors areinitially smaller than those of noninvestors. Only after the over-taking year of experience (I) do their earnings surpass those of non-investors. In this case, earnings profiles of individuals with the sameschooling but differing in post-school investments will cross in the

6. Such as job training, job search, or investment in hea'th. Effects of differencesin job search behavior have been analyzed by Stigler in his pioneering work on infor-mation in labor markets (1962).


neighborhood of J reaching the smallest dispersion in that neighbor-hood. More generally, f is not the same for each investor, but it has astrong central tendency, if, in the period preceding J the rate of de-cline of investments, is similar even though its volume differs amonginvestors.

In the special case, where and fare the same for all, dispersionfirst diminishes, reaching zero at time J and increases thereafter. IfI differs, a minimum but nonzero dispersion is reached at someaverage 1.

The assumption that initial post-school earning capacities arethe same among persons with the same schooling is not tenable. Forthe moment, let us keep r the same for these individuals and for alltheir investments. Let i indicate individual differences in the earningsfunction:

= + r

Then,

= + r2o-2 + 2prcr(Y8jcr (2.8)

where p is the correlation between dollar post-school investmentsand (dollar) earning capacity. If this correlation is nonnegative, thedollar variance of gross earnings must rise with experience (j), since

increases with j. This is because the variance of a sum mustincrease when the sum is generated by positively correlated incre-ments.

If the positive correlation p is not too weak, the monotonic growthin dollar variances will also be observed in net earnings,7 sincecr2(Y0) = — C0), and o-2(Y0) <o2(Y3), so long as p(C0, >o(Yj. That is, the initial (first-year) variance in net earnings will besmaller than the variance at overtaking, which will, in turn, be smallerthan subsequent variances, according to (2.8). The size order of thevariances is changed if p is small. By the same token, if p is negativeand sufficiently large, a monotonic decline occurs.

7. An example of the effects of such a positive correlation is the growth in the dis-persion of earnings due to better recognition of differences in productivity of workerswhose initial wages were similar. This may be viewed as worker investment in em-ployer information about their quality. Cf. Stigler (1962).


Exactly the same arithmetic applies to variances of logs. Theirprofiles depend on the correlation between initial post-school earn-ing capacity (In and investment ratios A strong positive corre-lation leads to monotonic growth of relative (log) variances with ex-perience, a strong negative correlation produces a monotonic de-cline, while a weak correlation creates U-shaped experience profilesof log variances. The bottom of the U-shaped profile is found at theovertaking period only when the correlation is zero. Negative correla-tions shift it to later periods; positive correlations, to earlier periods.

If, as is suggested by Figure 2.1, positive and near-unitaryelasticities hold, we would expect to observe dollar variances mono-tonically increasing with experience but U-shaped profiles of relativevariances.

According to the same kind of analysis, the dollar variance ofearnings within a schooling group at the "overtaking" stage of ex-perience is larger the higher the schooling level. Since

Y,=

therefore,

cr2(Y8j = o2(Yo) + r2a'2 (2.9)

and grows with increments of schooling. Other things equal,particularly rand the correlation parameterp, expression (2.9) impliesthat dollar variances of earnings increase with level of schooling ateach stage of experience.

The relation between relative (log) variances and level of school-ing would be the same if similar assumptions could be made aboutcorrelations between time-equivalents of investment components.This is not the case, however, as the empirical analysis in Part IIindicates.

Thus far I have neglected individual differences in rates of re-turn. Once differences in r• are assumed, age changes in dispersioncan be generated, provided post-school investment is assumed aswell, since variations in rates of return alone are not sufficient togenerate age changes in the dispersion of earnings. However, it isnot necessary in this case to assume that post-school investmentdiffers among persons.

—I


For simplicity, look at gross earnings:

E), = + r1

Assume o-2(r2) > 0, and C,, C3 for all 1. If C, = 0, o-2(E31) remains fixedthroughout earning life. But if C3 > 0, o-2(E31) increases with j, assum-ing that r, and are not negatively correlated:

= + + 2p(ZC3)ci(Y3)cr(r). (2.10)

Note that variances of net earnings are the same as variances of grossearnings when investments are the same for all. A similar monotonicgrowth of relative variances can be derived from the logarithmicformulation. If reversals or declines in profiles of variances are ob-served, the hypothesis that post-school investments do not varyamong individuals must be rejected. In the logarithmic case the impli-cation is that > 0. This test is of some importance, because thedispersion in earnings of persons with the same schooling representsan exaggerated index of risk if it is attributed solely to variation inrates of return. A general approach is to assume both > 0 anda2(rj) > 0. The empirical implications remain qualitatively the sameas when only > 0.

I conclude that the fanning out of dollar variances and the pos-sible reversals or declines in profiles of relative variances of earn-ings within schooling groups reflect systematic age increments andindividual differences in the scale of human capital investments,rather than random increments ("shocks") in earnings, as the ex-clusively stochastic theories of income distribution would have it.8

Finally, the conclusions about the determinants of earnings dis-persion that were expressed for the schooling model by (2.7) can bedirectly generalized by earnings function (1.4). The logarithmic ver-sion is required for studying relative inequality, and a simplifiedformulation parallel to (2.7), in which correlations among terms areignored, is derived as follows:

In = In +where

j—i

8. See Part II, Table 7.2, for empirical evidence against random shock models.9. Section A, above.


Then

cr2(ln E,) = o2(ln Y3) + kfr2(r3) + (2.11)

The positive determinants of Y8) in (2.7) were initial capacitylevels and dispersions in schooling investments S and in rates of re-turn r8. Now (2.11) adds the corresponding parameters of the distribu-tion of post-school investments as parameters of inequality of grossearnings in an experience group j. Incidentally, the inequality deter-mined in the schooling model, ff2(ln Y8j, can be seen, under simpli-fied assumptions, as the inequality in a particular experience group,when j=/ The overall inequality, however, is of a distribution ofearnings of workers who are at different levels of experience in theirworking life.

2.3.2 AGGREGATION OF VARIANCES

The aggregation of variances of overall years of experience in aschooling group is visualized by the well-known aggregation formulafor variances:

(2.12)

where T is an aggregate of several j groups; the within-groupvariances; d3 = — the differences between the means of group jand the overall mean; the number of observations in j; and n, thetotal number of observations.

The size of is clearly a positive function of the rate of growthof mean earnings with experience. In dollar terms, therefore, weshould expect variances of earnings to increase with length ofschooling, if relative frequencies of numbers of workers are similarby years of experience. However, because of upward secular trendsin schooling, these frequencies are not similar: there are relativelytewer older workers in the upper schooling groups. Consequently,the increase in dollar variances of earnings with schooling is some-what attenuated. The conclusions about relative variances of earn-ings classified by schooling cannot be determined a priori. A discus-sion of findings based on empirical data is deferred to Part II.

Formula (2.12) is equally applicable to an aggregation of vari-ances over all years of schooling in a given experience group. Be-cause and in dollar terms increase with experience, increases in


the dispersion of earnings by experience and (a fortiori) by age arepredictable. Relative variances are not expected to grow monotoni-cally with experience, because reversals are likely to arise some timeduring the working life. In a classification by age, the growth of rela-tive variances with age is likely to dominate, but reversals may stilloccur. The attenuation of inequality which is due to secular trends inschooling holds for schooling, experience, and age aggregations, aswell as for total inequality observed in the cross section.'°

2.3.3 SKEWNESS

Positive skewness is a well-known feature of income distributions.Human capital models can explain skewness in several different, notmutually exclusively ways:

a. It will be recalled that the distribution of investment time-equivalents, h, = S, + tends to impart positive skewness to thedistribution of earnings, even when investments are symmetric. Sup-pose, therefore, that without investments, the distribution of earn-ings V0 would be symmetric. In that case, the distribution of In V0would be negatively skewed and so would the distribution of Ingiven a symmetric distribution of investments. Thus, unless the dis-tribution of investments has a strong positive skew, the logarithmicdistribution of earnings will be negatively skewed. At the same time,unless the distribution of investments has a substantial negativeskew, the distribution of dollar earnings will be positively skewed. Anormal distribution of "raw abilities" is, therefore, likely to producea positively skewed distribution of earnings with a shape intermediatebetween normal and log normal. The larger the investment com-ponent r(S + K) in earnings, the better the log normal rather thannormal approximation.

b. Assume that the distribution of r, is symmetric, and ignorevariation in VOL. In that case, even for fixed h, the distribution of earn-ings would be positively skewed. As before, positive skewness wouldbe accentuated at higher levels of investment h.

10. To state that inequality in the cross section is, in part, affected by the rate ofchange of secular trends in schooling is to ignore possible feedbacks of such trends onrates of return. Such effects depend on the nature of the trends, a subject outside thescope of this study.


c. An important conclusion emerges from the analysis of within-group variances: systematic allocations of individuals' investments inhuman capital over their life cycle and systematic differences amongindividuals in the scale of their investments show up as positive cor-relations among instalments of investment within and between theschooling and post-school stage. Consequently, dollar variances ofearnings are positively related to experience (age within schoolinggroups) and to schooling (at given years of experience). Sinceaverage earnings must grow with schooling and experience, the allo-cation of human capital investments produces a positive correlationbetween means and variances across subgroups of workers definedby schooling and experience. The positive correlation between meansand variances of subsets of the distribution leads to positive skew-ness in the aggregate. This explanation of skewness is additional andindependent of assumptions about the shape of the distribution ofschooling which were emphasized in the schooling model.'1 It is theonly explanation inherent in the human capital model of individualbehavior.

The conclusions about positive skewness in the aggregate do notapply to the logarithms of earnings, because, as the previous discus-sion suggested, log earnings are likely to be negatively skewedwithin groups, and an a-priori case for a positive correlation be-tween logarithmic means and variances in subgroups is not clear.12

The effects of secular trends in schoohng on the distribution ofearnings is an important example of the distinction between observa-tions in cohorts and in cross sections. Though the theoretical analysisis carried out in longitudinal (cohort) terms, empirical analysis andinterest focus on the distribution of earnings in a cross section in agiven period of time. The possible consideratio,ls impinging on thisdistinction are too numerous for a useful a-priori analysis, given thelimited information available. However, the distinction between co-horts and cross sections receives attention, where possible andappropriate, in the empirical analysis of Part II, below.

11. See the mathematical note at the end of this chapter.12. Both in dollars and in logs, aggregate skewness in the cross section is also

affected by secular trends in schooling in a manner analogous to the effects onvariances, as discussed above.

—


2.4 MATHEMATICAL NOTE ON SKEWNESS

Let

N = population of an aggregate; M, its mean; a-, its standard devia-tion; and a, its third moment (skewness).

= population of component I; its mean; its standard de-viation; and aj, its skewness.

M.

Then+ +

2 13Na-3

(.)With the help of this relation we can (1) investigate the conditionsunder which a combination of symmetric distributions of the com-ponents results in a positively skewed aggregate, (2) show that thetheoretical model ensures such a result.

Let = 0, hence

+Ncr3

+2 14

Ncr3 (.)Since the denominator is positive, aggregative skewness will be posi-tive (a > 0), if and only if:

+ > 0.

A. If no intragroup dispersion exists = 0), or if all componentdispersions are the same (a-, = C), the second term vanishes:

= — M) = 3C(NM — NM) 0.

In this case aggregate skewness is positive, if and only if

> 0. (2.15)

This expression is, in fact, the third moment in the distribution ofcomponent means around the aggregate mean. When the i's areinterpreted as schooling groups, expression (2.15) measures skew-

13. For derivation, see Bates (1935, pp. 95—98).


ness introduced by the distribution of schooling alone. In the school-ing model this is positive, provided the skewness of the schoolingdistribution is not excessively negative.

B. If intragroup dispersion does exist > 0), and differs fromgroup to group, the factor can be interpreted as the contri-bution of intragroup differentials to aggregate skewness. The condi-tion for

> 0 (2.16)

is

Dividing both sides of the inequality by NM we get:

zniIn other words, in order for (2.16) to hold, the weighted average

of the intragroup variances weighted by must exceed the aver-age of these variances weighted by nj. Clearly, this occurs when the

are positively correlated with the Mi's. This condition holds inthe complete model, in which intragroup dispersion is expected toincrease with the average accumulated investment (S + K), hencewith average earnings.

Part II

EMPIRICAL ANALYSIS

3

Schooling and Earnings

3.1 QUANTITATIVE ANALYSIS

Human capital models have been employed in empirical analyses ofincome distributions in attempts to explain differences in level,inequality, and skewness of earnings of workers who differ byschooling and age, to interpret shapes of age-earnings profiles ofindividuals, and to explain differences in earnings distributionsamong regions and countries.' Though sketchy in many respects,these studies tend to provide at least qualitatively consistent inter-pretations of some of the apparently bewildering variety of featuresof income distributions.

There is as yet no evidence of quantitative explanatory power ofthe human capital model to match the promise indicated by thequalitative or comparative analyses. As yet, no serious attempts havebeen made at a full quantitative accounting of the effects of the dis-tribution of investment in human capital on observed earnings in-equality. The only available empirical estimates of the extent of in-

1. Mincer (1957, 1958, 1962), Becker (1964, 1967), Ben-Porath (1967), Chiswick(1967), LydaIl (1968).

44 EMPIRICAL ANALYSIS

come inequality2 that can be attributed to investments in humancapital are limited to investments in schooling, measured by years ofschooling.

Applying the "schooling model" (equation 1.3) in a simple re-gression of 1959 log earnings of men aged 25—64 in the experiencedlabor force on their years of schooling, Chiswick found coefficientsof determination varying between 10—20 per cent within U.S. regionsand states. The coefficients are 10 per cent and 18 per cent for earn-ings of white men in the non-South and South, respectively. Withinstates, Chiswick applied regressions to incomes of men aged 25 andover, instead of earnings, which were not available in the published1960 Census data.

Low as they are, the coefficients of determination are overstated,because they are based on data grouped by income and schoolingintervals. Application of the same regression to individual observa-tions of 1959 earnings of all U.S. white, nonfarm, nonstudent males,3aged 15—64 yields a coefficient of determination of barely 7 per cent.

The inadequacy of the schooling model as an explanation of in-equality, which is measured here by the variance of log earnings, isapparent not only in the low coefficients of determination but also inthe small slope coefficients of the regression. According to equation(1.3) these coefficients are supposed to' represent estimates of aver-age rates of return on investments in schooling. But as Chiswick'sdata and my Table 4.4, below (first row) show, the regression slopesare substantially lower, almost half the size of internal rates calcu-lated directly from age profiles by Becker, Hansen, and Hanoch.

The disappointing performance of the schooling model need notcast doubt on the relevance or importance of human capital analysis.As the discussion in Part I indicates, the schooling model repre-sents an incomplete specification of human capital theory of thedistribution of earnings. The model cannot adequately explain in-

2. Though the human capital model applies strictly to labor incomes, the empiri-cal literature often describes total incomes rather than earnings.

3. These were males with some earnings in 1959. Earnings were defined as wagesand salaries plus self-employment income, provided wages and salaries were themajor source of earnings. The 1/1,000 sample of the 1960 U.S. population Census,used in this study, contained 31,093 men in this category. The earnings of over 95 percent of them consisted of wages and salaries alone. This is the basic body of dataused in our empirical analyses.

SCHOOLING AND EARNINGS 45

equality of earnings among individuals who differ not only in school-ing but also in other behavioral characteristics including, in particu-lar, other forms of investments in human capital. In the empiricalanalyses that follow, it will be seen that when the human capitalmodel is expanded to include post-school investments its explana-tory power is greatly increased. In the expanded model biases in theregression estimates of the schooling model are removed. Althoughthe inclusion of an undifferentiated and indirect concept of post-school investments constitutes only an initial step toward a morecomplete analysis, it provides a unified interpretation for a variety ofqualitative and quantitative aspects of the structure of earnings.

3.1.1 GROUPED DATA

Before proceeding to incorporate post-school investment behaviorinto the empirical analysis, it is useful to consider the applicabilityof the schooling model somewhat more closely. As we have seen, theschooling model is too blunt an instrument for analyzing the un-grouped distribution of earnings. Evidently, variation in earningswithin schooling groups is a major part of total inequality. Withgrouped data, the positive relation between schooling and earningsdoes, of course, emerge clearly. Still, the model does not fit properlyin one respect: The slope of line 1, Chart 3.1, that is, the regressionslope of average earnings (in logs) on years of schooling, is again tooflat, as it was in the ungrouped regression. Apparently, grouping doesdoes not eliminate the problem of within-group variation of earnings.These earnings have been averaged in each schooling group, but theaverage depends on the age distribution in the groups, given theexistence of pronounced age-earnings profiles. As is well known,earnings at later stages of work experience are substantially higherthan at early stages. Because of strong secular trends in schooling,average age is older in the lower schooling groups, younger in thehigher schooling groups (Table 3.1, column 2, below). Consequently,earnings differentials among schooling groups, shown as the slopeof line 1, Chart 3.1, are understated. But, even it earnings of a fixedage group (e.g., age 32—33, line 2, Chart 3.1) are compared, thedownward bias in the slope is still not removed.

The basic reason for the persistent bias becomes intuitively ap-parent if it is assumed that the individual growth curve of earnings is


CHART 3.1SCHOOLING AND AVERAGE EARNINGS, 1959

(schooling groups of white, nonfarm men)

Annual earnings(thousand dollars)9

8

7

6

5

4

3

6 7 8 9 10 11 12 13 14 15 16

NOTE

Years of schooling completed

Curve 1: average earnings of all workers, age 15—64.Curve 2: average earnings at age 32—33.Curve 3: average earnings with 10 years of experience.Curve 4: average earnings with 7—9 years of experience.SOURCE: 1/1,000 sample of U.S. Census, 1960.

Table 3.1.Estimates are shown in

2


largely a function of post-school investment, such as on-the-job andother forms of training and experience. The earnings profile is a func-tion of work experience rather than of age: Since less schooled per-Sons enter the labor force earlier, they spend more time acquiringwork experience; at a given age, they will reach higher relative levelsof their earnings profiles than persons of the same age, but with moreschooling. This is why earnings differentials are still understated inline 2. On this post-school investment hypothesis, the more appro-priate standardization is for years of experience rather than age.Empirical support for the argument is found in line 3 of Chart 3.1,where earnings are shown at ages corresponding to a decade aftercompletion of schooling. The slope of line 3 is almost double that oflines 1 and 2, and is indeed well within the usual range of directlycalculated internal rates of return (about 12 per cent).

In the absence of direct information in the 1960 Census, years ofwork experience were measured by subtracting the age of comple-tion of schooling from reported age. Average ages of school leavingwere estimated by Hanoch (1968) from the same data (cf. Table 3.1,column 2). Conceptually, age is not irrelevant, since it is a factor inthe depreciation of human capital stock. Separate estimates of ageand experience effects on earnings require individual data on jobexperience. Such estimates as are available indicate that experience,rather than age, is the dominant factor in earnings.4

The intuitive argument in support of a standardization by yearsof experience does not indicate the particular stage of experience atwhich earnings of different schooling groups should be compared.But the decade of experience chosen for line 3 is not entirely arbi-trary. The argument and evidence can be more rigorously stated,paying closer attention to the concepts implicit in the schoolingmodel (1.3):

In Y8 = In V0 + rs.

Implementation of this model is a problem not only because thevariation in earnings within schooling groups is omitted, but alsobecause data for the (dependent) earnings variable are not available.According to the derivation of the schooling models, represents ahypothetical concept of earnings a person would receive after com-pletion of schooling, if he did not incur any further growth-producing

4. See discussion in Chapter 4, below.


TABLE 3.1SCHOOLING, AVERAGE ANNUAL EARNINGS, AND RATES OF RETURN, 1959

(U.S. white, nonfarm men)

Me-

Age atFirstYearof Ex-

Average Annual EarningsAt Overtaking

Rate ofReturn

Im-In 10thYear of Earn-

Years of dian pen- All At Age Experi- ings Used plicitSchooling Age ence Ages 32—34 ence (Va) Year (r) (r8)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

0—4 52 14 $3,350 $3,390 $ 2,520 $1,910 7

5—7 48 14 4,000 4,070 2,740 2,130 7 (17)

8 45 16 4,520 4,600 3,580 2,830 7 16 19.69—11 36 18 4,660 5,250 4,360 3,660 7—8 (14)12 34 20 5,330 5,870 5,280 4,800 8 13 13.2

13—15 33 23 6,240 6,850 6,520 6,100 8—9 (11)

16 35 25 8,020 8,160 8,600 7,950 8—9 10 10.1

17+ 37 28 9,200 8,710 10,200 9,900 9 (9) 7.3

NOTE:

Col. 3: Estimates of Hanoch (1967): Mean age at the terminal school year plus1. These estimates were modified in the lowest two groups by the as-sumption that boys did not enter the labor force before the age offourteen. Also, an average of five rather than six years was estimatedas the average duration of college studies.

CoIs. 4—7: 1/1,000 sample of U.S. Census, 1960.Cols. 7—8: Uses estimate of r in column 9 to equate the present values of V, in

column 7 with the present values of the observed profiles.Col. 9: Values in parentheses are extrapolated.Col. 10: (In — In

self-investments. Values of V, are not observable, but as was shownin Chapter 1, they can be approximated if certain assumptions areaccepted.

The two basic assumptions are that rates of return to schoolingare not very different from rates of return to post-school investment,and that earnings profiles Y5 with no further (net) investment remainlargely flat far most of the working life. Both assumptions are em-pirical, and some evidence in their support is considered in laterdiscussion.

Recall the expanded earnings function (1.4):

i—i= + (r —


Here denotes net earnings of person i with s years of schoolingwho is in his jth year of work experience; C,, dollar costs of post-school investments; and r, rates of return to post-school investments.Since the first expression on the right is gross earnings after com-pletion of schooling, it equals the observed earnings at the stageof experience / = J, when the second right-hand term is equal to zero.

As was demonstrated in equation (1.10), J< hr. If r is not verydifferent from the rates of return as usually calculated, the "over-taking" year of experience at which observed earningsshould be a decade or less. As a rough guess, earnings at ten yearsafter completion of schooling were used in line 3 of Chart 3.1.

A more direct approach is to estimate Y. as that amount of annualearnings in a constant income stream whose present value equals thepresent value of the actual earnings profile. The present values mustbe taken at the start of working life, and the rate of return is used asthe rate of discount. Such estimates of earnings V3 are utilized in line4 of Chart 3.1. Its slope is somewhat steeper than that of line 3, be-cause higher rates of return, hence earlier "overtaking" years of ex-perience and lower earnings than in line 3, were assigned to the lowerschooling groups.5 The overtaking years of experience run from 7 inthe lower to 9 in the higher schooling groups.

The earnings figures (Y3), the estimated years at overtaking (j),internal rates (r) used for estimating them,6 and the slopes of thelines (r3), are shown in Table 3.1 (columns 7, 8, 9, and 10, respec-tively). Note that the slope r3 in the schooling model (1.3) is an esti-mate of the rate of return to schooling only, while the rate as usuallycalculated (r) from age profiles, although often called a rate of returnto education or schooling, is a rate on a mix of schooling and post-

5. The causes of the differences in slopes of the four lines in Chart 3.1 are per-haps best visualized by inspection of Chart 4.3 in Chapter 4, which shows the ageprofiles of log earnings in the several schooling groups. The slope of line 1 cor-responds to the vertical distance (per school year) between points at mean ages; theslope of line 2 corresponds to the distance ABC at age 33; while the slopes of lines 3and 4 correspond to the distances between the estimated overtaking points(A'B'C'). The last is the best estimate. It is necessarily the steepest.

6. These rates were calculated from the earnings profiles shown in Charts 4.1 and4.2. Direct costs and student earnings were conveniently ignored in the calculation,on the assumption of their rough cancellation at higher levels and unimportance atlower levels. In this I follow Hanoch (1968). The assumption is not tenable in general,but rough estimates suffice for the present analysis.


TABLE 3.2SHORT-CUT AND STANDARD ESTIMATES OF RATES OF RETURN a

TO ScHooLING, 1939, 1949, 1958(U.S. white, nonfarm men)

Year •

High School College b

Short Cut(1)

Standard(2)

Short Cut(1)

Standard(2)

193919491958

15.1%13.514.4

12.5%11.815.1

12.8%10.610.2

11.0%10.611.5

SOURCE: Mincer (1962).a. For 1939, data are based on earnings; for 1949 and 1958, based on

income.b. For 1939 and 1949, refers to persons having more than sixteen years

of schooling; for 1958, sixteen years.

school investment. It is a weighted average of the rates on schooling(rd) and on post-school investments In constructing lines 3 and4 of Chart 3.1, it was assumed that r3 and r, hence r8 and do notdiffer. A rough check of consistency appears in the results in Table3.1. A comparison of estimated by the slopes of line 4 and of the rutilized for its construction shows them to be very close at the collegeand high school levels (Table 3.1, columns 9 and 10). The small dis-crepancy at these levels suggests that it is not misleading to labelinternal rates of return calculated from earnings profiles as 'rates ofreturn to education." Lines 3 and 4 are not only steeper, but alsostraighter than line 1. Evidently, the closer the correspondence of thedata to the concepts of the model, the better the empirical f it.8 Ac-tually, linearity is not required by the model, since r may differ bylevel of schooling. Nonetheless, the broken shape of line 1 is morelikely to reflect a bad fit than erratically different values of r.

The experiments reported above indicate that although theschooling model is incomplete, it is relevant to the analysis of

7. Cf. Becker (1964, p. 42).8. LydaIl (1959) attempted to test the "goodness of fit" of the semilog form of the

schooling model, using line 1. This, as we have seen, is not the most appropriate test.Nevertheless, he would not have relected the model had he not mistakenly used adouble-log form in his test (p. 95).


earnings differentials. Moreover, its proper empirical implementationgives rise to a useful by-product: a quick and easy, though rough,method of assessing rates of return to schooling. Data for fewer thanthe first ten years of earnings are needed for the purpose, a majoradvantage in up-to-date analysis, compared to procedures which re-quire information on a whole working life of earnings.

Table 3.2, column 1, shows estimates of rates of return to school-ing calculated by assigning ages 23, 28, and 33—34 as the periods ofovertaking to elementary school, high school, and college graduates.The ages are taken from Table 3.1 (column 3 + column 8). This calcu-lation, the same as in column 10 of Table 3.1, utilizes only one earn-ings figure in each schooling group. In contrast, the rates of returnshown in column 2 of Table 3.2 were calculated from complete ageprofiles of earnings. The similarity is rather close, a strong sugges-tion of the feasibility of "short-cut" estimation.

3.1.2 UNGROUPED DATA

The schooling model will now be explored in ungrouped, individualdata. Overtaking values of earnings which were estimated forschooling groups can also be estimated, under somewhat strongerassumptions, for individuals whose schooling is known. Since, at I,

= c1/

if all individuals in a schooling group are assumed to have the samerate of return to, and proportionate time distribution of, post-schoolinvestments, the overtaking year of experience (j) would be the samefor all. On this assumption we may select a set of individuals in oursample whose years of work experience correspond to the over-taking years which were used in the grouped data. The distributionof earnings of these individuals can be viewed as an estimate of thelatent distribution of earnings that would be received if no furtherhuman capital were invested after completion of schooling.

As indicated in Table 3.3, below, I selected several subsets of thesample to approximate the distribution of earnings at overtaking.The findings in Table 3.3 do not vary much among the samples. Asexpected, earnings inequality in the overtaking sets is smaller thanaggregate inequality. Indeed, the earnings at this stage of the life


cycle are an estimate of lifetime earnings, since the present value ofapproximates the present value of the observed earnings profile.

The variance of log earnings in this group is about 0.50 (Table 3.3,column 6) compared to 0.68 in the aggregate. Thus, at the start ofworking life, expected lifetime inequality measured in relative terms(in logs), is about 25 per cent less than aggregate inequality. The dif-ference in dollar dispersions is greater. The dollar variance of theaggregate cross-sectional distribution of annual earnings is abouttwice the size of the dollar dispersion in the overtaking set.

The earnings distribution at overtaking serves two purposes: Assuggested above, it provides a base for assessing the contribution ofpost-school investments to aggregate inequality. More directly, itserves as a testing ground for the schooling model, since the lattercan be directly applied only to earnings of this particular populationgroup. However, for several reasons, the inequality estimated in theovertaking set cannot be fully explained by differences in years ofschooling alone:

a. The distribution of schooling investments is only partly meas-ured by the distribution of years of schooling. The dispersion inyears of schooling fails to reflect variation in initial earning capacityand in expenditures of time and money of students attending schoolsof the same quality, as well as schools of differing quality.9

b. The empirical definition of the "overtaking"set is quite rough.In the absence of specific information each individual was assignedthe average age of school-leaving in his schooling group. Actualdispersion in those ages is not negligible.'0

c. Overtaking years differ among people with the same amountof schooling and experience, if their rates of return differ, and if theirdollar investment profiles are not proportional. The observed residualvariances in the regressions of (log) earnings on years of schooling inthe empirical overtaking as presented in Table 3.3, column 5,must, therefore, overstate the true residual variation.

9. Information on, direct costs and earnings of students can be incorporated intothe calculation of investment ratios k during school years, instead of assuming thateach k= 1.

10. National Science Foundation data for 1966 from the Nationat Register ofScientific and Technical Personnel indicate standard deviations of 2 to 3 years forages at which B.A. and higher degrees were obtained (Weiss, 1971).


TABLE 3.3REGRESSIONS IN OVERTAKING SETS

Years ofExpe-rience

(1)

Number ofObser-vations

(2)

Regression Equation(3)

R2

(4)o-2(u)

(5) (6)Y) o-(r)

(7)

8 790 (1) In Y=6.36+.162s(16.4)

.306 .333 .48 .046

12.1

02(s) = 7.4(2) In Y= 2.14+ .115s+ 1.27 In

(15.1) (21.0)W .575 .204 .036

6—10 3,689 (1) In 'Y= 6.75 + .133s(36.1)

.261 .422 .56 .052

s= 12.2cr2(s) 7.9

(2) In Y=2.07+ .104s+ 1.31 In(34.0) (43.4)

W .511 .279 .042

7—9 2,124 (1) In Y= 6.30 + .165s(26.5)

.328 .353 .52 .048

= 12.2o2(s) = 7.7

(2) In Y= 1.89 + .121s + 1.29 In(24.6) (30.6)

W .596 .218 .037

(3) In Y= 4.78 + .424s — .01 Os2(10.0) (—6.1)

.347

(4) In Y= 1.60 + .183s — .002s2(5.3) (—1.7)

.602 .215

+ 1.270 In W(29.7)

NOTE: Figures in parentheses are t ratios; Y= earnings in 1959 of white nonfarm men;s = years of schooling; ff2(s) = variance of years of schooling; W= weeks worked in 1959;A2 = coefficient of determination; o2(u) = residual variance; a2(In Y) aggregate variance;0(r) = standard deviation of rates of return.

SOURCE: 1/1,000 sample of U.S. Census, 1960.

Regressions were run in several alternative subsets of thesample, representing approximations to the overtaking stage of ex-perience. Experiments were carried out with subgroups of differentsizes, running from 790 in a single experience year (1 = 8) to 3,689individuals in an aggregated (6-10) year-group. The coefficients ofdetermination (R2) and the regression slopes differ somewhat de-pending on which interval of experience is chosen. The R2 in theseregressions run from 0.26 to 0.33, while the slopes of the schooling


variable, which are estimates of the (average) rate of return to school-ing, vary between 0.13 and 0.16.

Table 3.3 contains results for three subgroups varying in level ofaggregation, but centering around 1=8. The regression slopes inTable 3.3 are estimates of rates of return to schooling. The size of theslope is affected by the number of weeks worked during the year.When the regression is expanded to include the number of weeks(in logs) worked during 1959 as a second variable, the partialcoefficients of schooling (at s) are several percentage points lowerthan were the simple coefficients. This is because (logs of) W arepositively correlated with schooling: on the average, longer-schooledindividuals work more weeks during the year. The coefficients for Ware above unity, implying a positive correlation between weeklyearnings and weeks worked during the year even for workers with thesame schooling attainment.

If the positive correlation between weeks worked and schoolingand between weeks worked and weekly earnings reflected primarilya positively sloped labor supply curve, then the coefficient at s basedon weekly earnings would be the more appropriate estimate of ratesof return to schooling. These correlations may be, however, a conse-quence of a greater incidence of turnover, unemployment, seasonal-ity, and illness at lower levels of schooling and earnings. In that casecoefficients at s based on annual earnings would be the more appro-priate estimates, if the reduction of such incidence is an effect ofSchool i n g ."

Estimates of rates of return directly calculated from age profilesof earnings (such as those of Becker, Hansen, and Hanoch) areusually higher at lower levels of schooling. A statistical test of thisinverse relation between r and s is performed in regressions (3) and(4) in Table 3.3. A quadratic term in s is added to the regression toallow for a systematic change in r with changing levels of s. A signifi-cant negative coefficient at & means that rates of return are lower athigher levels of schooling. This is, indeed, the case in regression (3).However, the same test performed in regression (4), where weeksworked are included, yields a negative sign but a small and statis-tically insignificant coefficient at the quadratic term. It appears,therefore, that differences in the amount of time worked during the

11. For further discussion of the working-time variable, see Chapter 7, below.


year almost fully account for the higher rates of return at the towerlevels of schooling.

A comparison of regressions (2) and (3) suggests that about halfof the rate of return to elementary school graduates can be at-tributed to their greater amount of employment during the year com-pared to people with less schooling. The employment factor accountsfor about a third of the rate of return at the high school level, and is oflittle importance at the college level: From quadratic regression (3)estimates of marginal r8 are:

d(ln Y)= .424 — .021s.

ds

Fors=s=12, r8= .172s=16, .088

The explanatory power of schooling investments in the distribu-tion of earnings at overtaking is underestimated by the regressionsof Table 3.3. Variations in quality of schooling and in ages of school-leaving are left in the residual. The latter may account 12 for 0.01 to0.04 in o2(u), but the former is likely to be more important. Accordingto figures quoted by Becker (1964, p. 108) the coefficient of variationin expenditures on a college education in New York State alone wasno less than the coefficient of variation in the national distribution ofyears of schooling. Solmon and Wachtel (1972) adjusted years ofschooling for "quality" by expressing expenditures per student as aratio to estimated student opportunity costs and adding these time-equivalents to each student's reported years of schooling. •Forstudents with at least a college education in the NBER-Thorndikesample,'3 the variance in the "quality-adjusted" years of schoolingwas three times the size of the variance of unadjusted years ofschooling. According to the same data the dispersion in high schoolquality was smaller, but still quite considerable. At any rate, a con-servative guess would be that the "quality-adjusted" variance ofschooling at all levels exceeds the unadjusted variance by a third.If so, R2 corrected for schooling quality could increase from the ob-

12. If the standard deviation of ages at school-leaving is ito 2 years within school-ing groups (judging by data of Weiss, 1971).

13. For a description of NBER-TH, see Juster (1972).


served 33 per cent to over 40 per cent in the regressions which do notinclude the weeks-worked variable, and from the observed 60 percent to perhaps 70 per cent in those that do include it.

Variation in rates of return, which cannot be observed, is prob-ably the main component of residual variation in these regressions.The correlation between these rates and the quantity of schoolinginvestment across individuals is evidently weak, as experiments withthe inclusion of S2 in the regressions (Table 3.3) suggested. It so, theassumption of independence between and s, across individuals canbe used and provides a way of estimating upper limits for the disper-sion of individual rates of return o-2(r). In this case the schoolingmodel, equation (1.3), in variance form is:

o2(ln = Po-2(s) + + o-2(s)o-2(r) + o-2(v), (3.1)

where v is a residual due to other unmeasured factors. The residualvariance in the regressions of Table 3.3 is: -

o2(U) = ± o-2(s)o-2(r) ± o2(v), (3.2)

with o-2(v) larger in regressions (1) than (2), since the effects of weeksworked are in the residuals of (1). Therefore,

a.2(r) (3.3)

The values of the upper limit for o(r) are shown in column 7 of Table3.3. They range from 4 per cent in the regressions which are stand-ardized for weeks worked to 5 per cent in those that are not. Thecoefficient of variation in individual average rates of return is there-fore at most a third in each of the regressions.

It is difficult to judge whether the estimated (upper limit) coeffi-cient of variation is "small" or "large." It is apparently much smallerthan the coefficient of variation in corporate rates of return, observedby Stigler (1963) in annual data It should be noted thatthe dispersion of rates of return to schooling is not a good measure ofrisk to the extent that abilities and opportunities underlying this dis-persion are known to the individual.

14. Note also that year-to-year instability is far greater in business incomes thanin earnings of male adults: The interyear correlations in corporate earnings decayrapidly over time (Stigler, p. 71) in contrast to the slow decline in panel correlationsof induyidual earnings shown in Table 7.1,. below.


TABLE 3.4CORRELATION OF LOG EARNINGS WITH SCHOOLING

WITHIN EXPERIENCE OR AGE GROUPS

Coeff. of Det. (r2)Coeff.of Oct.Year-

Years of Afl a round Years of (r2)Experience (1) (2) Age (3)

1—3 .31 .25 .

4—6 .30 .27 20—24 .027—9 .33 .30 25—29 .04

10—12 .26 .30 30—34 .11

13—15 .20 .25 35—39 .1416—18 .17 .20 40—44 .1619—21 .16 .18 45—49 .1222—24 .13 .17 50—54 .1225—27 .13 .15 55—60 .0928—30 .12 .14 60—64 .0831—33 .07 .1434—36 .05 .0737—39 .07 .09

Aggregate .07 .08 Aggregate .07

SOURCE: 1/1,000 sample of the U.S. Census, 1960.a. All workers, including both year-round and those whose work was

part time, seasonal, or otherwise intermittent.

Without standardization for weeks worked and without adjust-ment for quality, the schooling model explains a third of the in-equality of earnings in the overtaking subset of the earnings distri-bution. This is a great deal more than the 7 per cent found in thesimple regression of log earnings on schooling in the aggregatedistribution. The greater applicability of the schooling model to theovertaking period than to subsequent stages of experience is shownclearly in Table 3.4.

As measured by simple coefficients of determination, the effectsof schooling on earnings decay continuously in successive three-year experience groups after the first decade of experience. This isshown in columns 1 and 2 of Table 3.4.

The decay of the coefficient of determination (A2) reflects the


growing importance of accumulated experience in the determina-tion of earnings. R2 is the ratio of "explained" to total variance oflog earnings. In the overtaking set

= r2cr2(s) + cr2(U)(3.4)

The content of the residual variance o-2(u) was already discussed. Atlater stages when j> assuming little or no correlation betweentime-equivalents of schooling and post-school investments:

R2— j—i ( )

declines because the denominator grows with experience, sincethe right-hand term in it must grow. The decline in may bestrengthened for additional reasons: The coefficient of schooling (r)may decline over time—a possibility suggested by a "vintage" hy-pothesis of schooling effectiveness.'5 A random shock structure in theresidual u would give rise to a growing thereby increasing therate of decay in R2.

The systematic effects of accumulated experience are obscuredwhen the schooling model is applied to age groups (Table 3.4,column 3): The coefficient of determination at its highest is half thesize of that found in the overtaking group.'6 Its peak is reached inthe 40—44 age group, and it is quite small before age 30. The weakerfit of the schooling model in age groups compared to experiencegroups is due to the negative correlation between schooling andpost-school investments at given ages. This is most pronounced atthe early post-school ages, when investment in experience is heav-iest. The later decay is due to the accumulation of post-school in-vestments, as already discussed.

During the first decade of experience, the coefficients of deter-mination are relatively high but somewhat less than at overtaking. Itis plausible though not necessary that the denominator in the expres-

15. Welch (1972) observes declines in regression coefficients of schooling overexperience in both 1960 Census data and 1967 data of the U.S. Department of LaborSurvey of Economic Opportunity, and interprets them as "vintage" effects.

16. The contrast is somewhat overstated, as the age intervals are wider.


sion for A2 decline during the first decade, as suggested in the dis-cussion in Chapter 2.

In a longitudinal study of over 1,500 men who were 30—39 yearsold in 1968, BIum (1971) also found that the correlation betweenschooling and earnings was higher after ten years of work experience(A2 = .24) than in the initial year (R2 = .16). Differential post-schoolinvestments of individuals can account for the difference.17

3.2 SOME QUALITATIVE IMPLICATIONS

When applied to the proper data, the schooling model can be a use-ful tool for quantitative analysis. More generally, though less rigor-ously, the model also yields several important qualitative implica-tions about distributions of earnings.

1. A tendency toward positive skewness of earnings is producedby the transformation of absolute differences in years of schoolinginto relative differentials in earnings. Clearly, by equation (1.3) asymmetric distribution of years of schooling implies a positivelyskewed distribution of earnings. Unless the skew in the distributionof schooling is highly negative, a positive skew will be imparted tothe distribution of earnings. Because of the finite lower limit (zero,or a legal minimum) empirical schooling distributions are more likelyto be positively skewed when the average level of schooling is low.Skewness may change from positive to negative as the average levelof schooling reaches high levels. Thus the U.S. distribution of school-ing has become negatively skewed in the cohorts below age 40, asshown in Table 3.5. Even so, negative skewness in schooling is notsufficient to create negative skewness in earnings. It will be recalled(Chapter 2, note 1) that, according to the schooling model, positiveskewness in earnings obtains so long as 1 — (d2/d1) < rd1, where d1is the schooling interval (in years) between the median and a lower(say tenth) percentile and d2 is the interval between the median and acorresponding upper (ninetieth) percentile. Given rates of return r inexcess of 10 per cent, the above condition is empirically satisfied inTable 3.5 in all age groups. A fortiori (Cf. section 2.4), the aggregate

17. The notion that schooling has a positive effect on earnings merely as a"credential" is difficult to reconcile with the pattern of correlations observed inTable 3.4 and in the longitudinal study.


TABLE 3.5DIsTRIBuTION OF YEARS OF SCHOOLING (s), BY AGE GROUPS, 1959

(U.S. white, nonfarm males)

AgeP10

(1)Md(2)

P90

(3) (4) (5)— d1

(6)

14—19 6.0 9.8 11.8 10.5 2.2 —1.8

20—24 8.1 11.9 15.2 12.1 2.8 —0.525—29 6.8 12.0 16.0 12.2 3.2 —1.2

30—34 6.4 11.8 16.0 11.7 3.4 —1.2

35—39 6.3 11.7 15.9 11.7 3.4 —1.2

40—44 5.7 11.3 15.6 11.2 3.4 —1.3

45—49 5.3 10.5 15.4 10.5 3.6 —0.350—54 5.1 9.5 15.0 10.1 3.6 +1.155—59 4.7 8.5 14.2 9.4 3.7 +1.960—64 4.4 7.8 13.9 8.8 3.7 +2.765 or older 3.5 7.4 13.2 8.5 4.0 +1.9

All 6.2 10.5 15.7 10.9 3.5 ±0.9

P10 = 10th percentile. = arithmetic mean schooling.Md = median. = standard deviation.P90 = 90th percentile. = P90 — Md; d1 = Md — P10.SOURCE: 1/1,000 sample of U.S. Census, 1960.

distribution of earnings is likely to be positively skewed. As the U.S.level of schooling is the highest in the world, its distribution is morenegatively (less positively) skewed than that of any other country.Hence positive skewness in earnings is likely to be universal.

2. The schooling model implies that relative dispersion of earn-ings is larger the larger the absolute dispersion in the distribution ofschooling and the higher the rate of return. In terms of the schoolingregression, where the variance in r is suppressed:

o-2(ln Y8) = r2o-2(s) + o2(u). (3.6)

Chiswick's (1967) regional comparisons of income inequality do in-deed show that inequality and skewness of income are larger thelarger the variance in the distribution of schooling and the higherthe rate of return as measured by the size of the regression slope in(1.3). According to Chiswick, these factors jointly explain over a third


of the differences in inequality among regions,18 with the rate of re-turn apparently the more important factor.

Rapid upward trends in years of schooling attainment in theUnited States are reflected in Table 3.5 in the systematically differentdistributions of years of schooling in the separate age groups of em-ployed men in 1959. The typical (median) 25-year-old was a highschool graduate in 1959, while the typical 60-year-old was an ele-mentary school graduate. Dispersion in the distribution of schooling,as measured by a percentile range or a standard deviation, narrowedsomewhat from the older to the younger cohorts, while skewnesschanged from positive to negative as the level

The systematically larger dispersion and skewness of the school-ing distribution with increasing age is paralleled by increases inrelative dispersion and skewness in earnings in the age groups, asshown in Tables 3.6 and 6.3. However, the consistency of this phe-nomenon with predictions of the schooling model is only qualitative:The actual rate of increase of earnings inequality with age is far toostrong to be attributable in the main to the mild increase in the dis-persion of schooling. The schooling model in variance form (equation3.6) predicts a smaller percentage increase in o-2(ln Y) than in o-2(S),if r2 and o-2(u) do not increase. The variance of schooling is only about20 per cent larger in the 55—59 age group than in the 30—34 age group(Table 3.5, column 5), yet the variance of relative (log) earnings is 70per cent greater in the older compared to the younger group2°(Table 6.3, column 1). The variance of schooling is about 25 per centlarger in the 55—64 age group than in the 25—34 age group in Table3.5, but the variance of income doubles in this range in every annual

18. In his current work, Chiswick greatly increases the explanatory power of theearnings function by expanding it to include post-school investments. Lydall (1968),who did not employ the rate of return as an explicit variable, found the dispersion inthe distribution of schooling to be a significant factor in explaining differences in theinequality of earnings among a set of countries.

19. In their survey of trends in educational attainment of the U.S. population,Folger and Nam (1967) found that "educational attainment is more evenly distributedin the population than it used to be." The data in their Chapter 5 show mild trends indispersion, as well as a pronounced change from positive to negative skewness in thedistribution of schooling.

20. As shown in Table 6.3, the relative variance of earnings has a U-shaped agepattern with low values in the 30—34 age group. The age and experience patterns ofdispersion are more fully analyzed in Chapter 6.


TABLE 3.6COHORT AND CROSS-SECTIONAL CHANGES IN INCOME INEQUALITY,

ALL U.S. MEN, 1947—70(variance of logs of income)

Year

Age CrossSection

(col. 3 lesscol. 1) Cohort a

25—34 35—44 45—54

(1) (2) (3)

194719571967

.352 .494 .541

.420 .518 .697

.387

.189

.277

.159 .194

194819581968

.585.445 .727.389 .454

.230

.282

.178 .212

194919591969

.680.442 .692.418 .469

.301

.250

.154 .193

195019601970

.642.428 .554 .719.458 .486 .585

.254

.291

.097 .207

Average .225 .204

SOURCE: Schultz (1971, Table 2).a. In each twenty-year span, column 3 of the last year of the span minus

column 1 of the first year.

cross section (1947 to 1970) in Table 3.6. The observed age gradientin earnings inequality cannot be ascribed to cohort differences in thedistribution of schooling. Rather, it is a phenomenon connected withaging of the same cohort whose distribution of schooling is, ofcourse, fixed.

The within-cohort changes can be observed directly in the re-peated cross sections of Table 3.6: Individuals who were 35—44 yearsold in 1959 were in the 25—34 age group in 1949, and in the 45—54 agegroup in 1969. Income variances can be compared in thethree surveyyears to detect changes within fixed cohorts. This procedure was ap-plied to variances of logs of income of men in decade age intervals,


which were calculated by T. P. Schultz (1971) from Current Popula-tion Surveys for the years 1947—70. The results shown in Table 3.6indicate that the cross-sectional age differences in income inequalitywere mainly a consequence of changes within the same cohorts.2'The cross-sectional changes are shown in the rows, the within-cohortchanges along the diagonals. As the last two columns show, thecross-sectional increase in inequality is only slightly greater than thewithin-cohort increase. At the same time there are no clear trends ininequality within fixed age groups.22 Apparently, the cross-sectionalincreases in inequality with age are produced, in the main, by factorsother than the secular change in the distribution of schooling. Thetheoretical analysis suggested that an explanation for much of theage difference in parameters of earnings distribution would be foundin the distribution of post-school investments. We now proceed to anempirical exploration of the age and experience differences in earn-ings.

21. Very similar results are produced by comparing Gini coefficients, calculatedfrom the same data by H. P. Miller (1963, Table 12). Though the data underlyingTable 3.6 are incomes of all men, rather than earnings of nonfarm white men, it isnot likely that the conclusions are affected by this inaccuracy. Age patterns of logvariances are not very different under the two definitions, though levels of incomeexceed levels of earnings by 20—30 per cent in each age group.

22. For an analysis of these trends see Chiswick and Mincer (1972).

4

Age and Experience Profilesof Earnings

The experiments reported in the previous section were meant toprovide evidence on the extent to which the schooling model is ap-plicable to the analysis of earnings. They indicate the need for cautionin extending the schooling model beyond the 'overtaking" subset ofearnings distributions, even for qualitative analyses. Confidence inthe validity of the schooling model as a component of human capitalanalysis is strengthened, but it is necessary to turn to the post-schoolphase of investment behavior in order to extend the analysis to thewhole earnings distribution.

If productivity-augmenting investments in human capital con-tinue after the completion of schooling, the time distribution of theseinvestments over the working life creates age variation in earnings,referred to as the age profile. In proceeding to the empirical analysisof earnings profiles in the light of the investment model, no claim ismade, of course, that the observed age profile of an individual re-

1. My analysis does not cover the "post-retirement" stage of the life cycle. At thatstage, special emphasis must be placed on depreciation of human capital and on thebehavior of the labor supply, subjects which are beyond the scope of the present study.

AGE AND EXPERIENCE PROFILES OF EARNINGS 65

flects only investment behavior. Elements of chance, of changingmarket opportunities, and of biopsychological development are im-portant. Nonetheless, there is evidence that work experience is muchmore important than age in affecting productivity and earnings. I

interpret productivity-augmenting work experience as an investmentphenomenon. The assumption of costless opportunities for aug-menting productivity, which is sometimes implied in the notion of"learning by doing," cannot be descriptive of labor markets wherelabor mobility is the norm rather than the exception.2 At any rate, theinvestment interpretation lends itself to empirical analysis. Theproper question is how well the investment model handles the data,and whether alternative models can do better.

Given individual differences in investment behavior, earningsprofiles differ both among and within schooling groups. I study firstthe typical shapes of earnings profiles of individua's at a given levelof schooling. I then inquire into differences among such averageearnings profiles of different schooling groups. Later I consider theconsequences of individual differences in earnings profiles amongpersons who have the same amount of schooling.

The earnings data shown in Chart 4.1 are mean earnings in thesample of men, by years of schooling and by two-year age intervalsup to age 40, and five-year age intervals thereafter.3 Experience pro-files are shown in Chart 4.2. Profiles of annual and weekly earnings inlog scales are shown in Charts 4.3 and 4.4. The basic features of theage profiles are easily summarized: except for the initial years ofgainful activity, earnings are higher at higher levels of schooling, andincrease with age through much of the working life. The absolute and,more consistently, relative rate of increase in annual earnings

2. The argument is spelled out by Becker (1964, pp. 45—47): Greater opportunitiesfor learning will attract larger supplies of labor. Consequently, the steeper earningsprofiles will shift downward to intersect the flatter ones, giving rise to opportunitycosts of learning.

3. Earnings data by single-year intervals were also calculated from the 1/1,000sample. These showed apparently erratic sawtooth patterns in the profiles, particu-larly at older ages. This, however, should not be interpreted to mean that typicalindividual profiles fluctuate erratically over the life cycle. Sample sizes for singleyears of age and schooling are often quite small. They decrease with age, particularlyin higher schooling groups. The pronounced instability of the year-by-year sampleaverages of earnings can be accounted for by sampling fluctuations as well as earn-ings variances that are large and increase with age.


CHART 4.1AGE PROFILES OF EARNINGS OF WHITE, NONFARM MEN, 1959

(annual earnings classified by years of age, for indicated schooling groups)

1q000

6,000

5,000

4,000

3,000

2,000

1,000

NOTE: Figures on curves indicate years of schooling completed.SOURCE: 1/1,000 sample of U.S. Census, 1960.

70

Annual earnings (dollars)

11,000

9,000

8,000

7,000

15 20 30 40 50 60Age


CHART 4.2EXPERIENCE PROFILES OF EARNINGS OF WHITE, NONFARM MEN, 1959

(annual earnings classified by years of experience, for indicated schooling

0

III

I1II

IIIIIIIIIII

groups)

NOTE: Figures on curves indicate years of schooling completed.SOURCE: 1/1,000 sample of U.S. Census, 1960.

Annual earnings (dollars)12,000

I.—III

/

I 13-15

11,000—

10,000 —

9,000 —

8,000 —

7,000 —

6,000 —

5,000

4,000

3,000

2,000 —

1,000

0

— .

.

.

.

9—11.

. ...• ••.

..

0-4

..

_1 I I I I i I i I i i I i i i i I i Ii i i i

30Years of experience

40 50 60

CH

AR

T 4

.3

17+

S —

——

—S

—

/

III11

1111

1111

1111

1111

111

iiilii

t iii

1111

1111

1111

111

I itli

iii

3040

5060

Yea

rs o

f exp

erie

nce

NO

TE

: Fig

ures

on

curv

es in

dica

te y

ears

of s

choo

ling

com

plet

ed.

SO

UR

CE

: 1/1

,000

sam

ple

of U

.S. C

ensu

s, 1

960.

Ann

ual e

arni

ngs

AG

E A

ND

EX

PE

RIE

NC

E P

RO

FIL

ES

Age

Pro

files

OF

RE

LAT

IVE

AN

NU

AL

EA

RN

ING

S

Ann

ual e

arni

ngs

(dof

lars

)15

,000

OF

WH

ITE

, NO

NF

AR

M M

EN

, 195

9

Exp

erie

nce

Pro

f Ues

0)

10,0

00 —

— -5,

000

—

4,00

0 —

3,00

0 —

2,00

0 -

1,00

0 -

800. 0

Age

1020

Rat

io s

cale

0) (0

CH

AR

T 4

.4A

GE

AN

D E

XP

ER

IEN

CE

PR

OF

ILE

S O

F R

ELA

TIV

E W

EE

KLY

EA

RN

ING

S O

F W

HIT

E, N

ON

FA

RM

ME

N, 1

959

Age

Pro

files

Wee

kly

earn

ings

(do

llars

)30

0

Exp

erie

nce

Pro

files

Age

NO

TE

: Fig

ures

on

curv

es in

dica

te y

ears

of s

choo

ling

com

plet

ed.

SO

UR

CE

: 1/1

,000

sam

ple

of U

.S. C

ensu

s, 1

960.

010

2030

Yea

rs o

f exp

erie

nce

Wee

kly

earn

ings

(do

llars

)

200

—

17+

13-1

5

p.—

.__

12

1520

3040

5060

65

Rat

io s

cale

30 li

ii lii

II 1

1111

III I

iiI

IIi

iiIi

iiiiii

iIii

4045


diminishes with age, becoming negative, if it changes at all, duringthe last decade of working life. There is no visible decline at theselater ages in weekly earnings. Apparently, declines in weeks workedper year are the main factor in the decline of annual earnings duringthe preretirement years (cf. Table 7.2, column 3).

The differences among schooling groups are systematic: atgiven ages the absolute and relative rate of growth of earnings in-creases with schooling. Earnings level off at earlier ages in the lowerschooling groups. Since earnings reach a plateau at later ages in themost highly educated groups, both dollar and relative annual earn-ings differentials among schooling groups grow with age until age45—50, and later still for weekly earnings.

The picture changes drastically when earnings profiles are com-pared by years of work experience rather than age.4 Chart 4.3 showsthat the experience profiles of log earnings tend to converge withgrowing years of experience, in contrast to age profiles, which di-verge with growing years of age.

Logarithmic experience profiles of weekly and hourly earnings,shown in Charts 4.4 and 4.5, are more nearly parallel, suggesting thatrelative "skill" (measured by schooling attainment) differentials inwage rates do not change perceptibly with years of experience.6Dollar differentials do increase with experience in annual earnings,and in weekly and hourly rates as well, though not nearly as much asthey do with age. In view of the parallelism or convergence of

4. Years of experiende start at ages indicated in column 3 of Table 3.1.5. The degree of convergence of experience profiles of annual earnings is partly

affected by the state of the labor market, since in a recession unemployment ratesincrease more among the young and unskilled than in other groups.

6. 'Skill" differentials in wages are commonly measured by the percentage dif-ference between adult male wage rates in sets of pairs of narrowly defined occupa-tions, one skilled, the other unskilled. The choice of pairs, the definition of wages,and the changing skill contents make the interpretation of such comparisons and oftrends in them as trends in relative factor prices rather uncertain. The often steep riseof earnings with age suggests that differing age distributions in the occupations beingcompared are another source of ambiguity in these measures. For example, an accele-ration of upward trends in schooling raises the average age in the lower schooling andskill groups and lowers it in the upper groups. This produces an apparent narrowingof relative wage differentials, which may be misinterpreted as a relative price effect ofthe change in relative supplies of skills. Standardization for age is not sufficient, how-ever. As we have seen, relative wages increase with age. But my finding of near-parallelism of the experience profiles suggests that standardization for experienceis the more appropriate procedure.

AGE AND EXPERIENCE PROFILES OF EARNINGS

CHART 4.5

71

5—

3

2

I

Ratio scale

.,•

/

/ 13-15

5-8

itt iii I 111111 It iiiliiiil III thu i hiuiil tiii0 5 10 15 20 25 30 35 40 45

Years of experience

NOTE: Figures on curves indicate years of schooling completed.SouRcE: Fuchs (1967, Table A-i).

EXPERIENCE PROFILES OF AVERAGE HOURLY EARNINGS OF WHITE NONFARMMEN, 1959

Hourly earnings (dollars)6

4- ////

...//

12•

•

9—11 ••S•••I•.e•e••••••• •••••

I.... — — — — — — —•

-F——I•

••

i' •••• // 0-4•• // •• /•

/•••I

•I

1.111

1


logarithmic experience profiles, the strong increase in relative earn-ings differentials by age must be attributed entirely to the faster rateof growth of earnings at earlier compared to later years of experience.Let the earnings profiles be interpreted as being a consequence ofpost-school investments. Then the life-cycle or profile rate of growthg1 of log earnings at time t is derived from the log-earnings function(1.15) in its continuous form:

(4.1)

Assume rates of return to post-school investment to be fixed,and think of the ratio (ks) of investment to gross earnings as a "time-equivalent" amount of investment incurred in period t. Let thesecond term on the right of (4.1) be either negligible or unrelated tolevels of schooling. Then the empirical findings suggest that, atgiven ages, the amount of "time" people invest in human capitalincreases with the years of their schooling. The longer-schooled,however, do not spend more "time" than the less-schooled atcomparable years of experience. Indeed, the convergence oflogarithmic experience profiles means that, over the working life,the more educated workers spend less "time" in post-school invest-ment activities. Profiles of annual earnings converge, but profilesof weekly earnings are parallel, and it is not clear which is moreappropriate for gauging the comparative "time" measures.7

Another interpretation of convergence is that rates of return topost-school investment, rather than volumes, differ among schoolinggroups. By(4.1)thesteepergrowth in earningsinthelowerschoolinggroups may reflect a higher rate of return to post-school investments(rg) rather than a larger time-equivalent (ks). An attempt was made toascertain this by deflating the observed rates of growth of earnings,at comparable stages of experience, by the available estimates of

7. The parallelism of weekly earnings indicates that convergence of annual earn-ings, or the margin by which less schooled persons spend more "time" in post-school investment, arises from their lower employment levels when they are young.To the extent that the greater discontinuity of employment of poorly educated youngmen represents labor mobility—people in search of better jobs—the periods of unem-ployment can be properly reckoned as "time" spent in investment, If, however, thedifferences in employment experience between them and the more educated repre-sent differences in length of involuntary unemployment or in leisure preferences,"time" spent in post-school investments is overstated for the former.


TABLE 4.1ESTIMATES OF POST-SCHOOL INVESTMENTS IN DOLLARS

AND TIME-EQUIVALENTS PER PERSON

Years ofSchooling

DollarsC(10—15)

(1)

Yearsk(1 0—1 5)

(2)

DollarsC1,8

(3)

Years

(4)

0—4 $3,470 1.23 $10,120 3.785—7 4,430 1.26 13,350 4.27

8 4,310 1.10 13,570 3.569—11 6,000 1.26 14,220 3.1012 5,920 1.05 15,420 2.68

13—15 7,550 1.09 17,270 2.4616 8,300 1.09 30,500 3.25

NOTE: = earnings at peak; V8 = earnings at overtaking; r= rate of re-turn.

Col. 1: C(1O—15)= (Y15— Y10)/r= dollar investments between the tenthand fifteenth year of experience.

Col. 2: k(10—15); (In Y15— In Y10)/r= year-equivalents of investment be-tween the tenth and fifteenth year of experience.

Col. 3: = — Y8)/r= total dollar post-school investments.Col. 4: = (In Y,. — In Yj/r= total year-equivalents of post-school in-

vestments.SOURCE: Earnings data from Charts 4.1—4.3; rfrom Table 3.1, column 9.

overall rates of return, assuming that they are similar to rates of returnon post-school investments. The results, shown in column 2 of Table4.1, indicate that the deflated slopes decline as schooling level in-creases, but increase mildly above the high school level.8

Table 4.1 also contains estimates of total amounts of net post-school investment incurred by workers in each schooling group overtheir working life, in dollars and 'year-equivalents" (columns 3 and4). It can be seen that total dollar values rise with schooling, but thetime-equivalents are only weakly related to schooling. Total year-equivalents of post-school investment calculated from estimatedwage rate data (Chart 4.5) are very similar in all schooling groupsand amount to three to four years.

8. The observed convergence may also be due to "vintage" or obsolescenceeffects. Obsolescence diminishes total investment and its rate of decline over time(Becker, Koeune). This is reflected in flatter and less concave earnings profiles, pre-sumably at higher levels of skill (schooling).


TABLE 4.2ALTERNATIVE ESTIMATES OF POST-SCHOOL INVESTMENT COSTS

PER PERSON, 1939, 1949, 1958

YearEst i -

mates

Years of Schooling

8 12 16

C3C3

1958

1949

1939

OldNewOldNewOldNew

2.2

1.8

1.3

4.99.24.48.23.97.0

3.9

3.8

4.6

2.8

6.4

5.2

7.611.7

9.715.4

8.514.1

2.9

4.2

4.9

24.1

18.0

14.7

28.822.927.430.915.217.8

3.3

4.4

3.6

C3 = investment in schooling in constant dollars (thousands).= post-school investment in constant dollars (thousands).= post-school investment in year-equivalents.

SOURCE: Mincer (1962, Table 1 and appendix data).

In a previous study, dollar estimates of post-school investmentwere calculated in a stepwise fashion by estimating instalments ofsuch investments (Mincer, 1962). The totals in dollars and time-equivalents are here re-estimated from the same data, and a compari-son of the old and new estimates is shown in Table 4.2.

The old estimates are very similar to the new at the college level,but about half the size at lower levels, primarily because the 0—4schooling group age profile was used as the "zero investment" baseline in the disaggregated procedure. It is difficult to believe thatindividuals in the lowest schooling group incur no post-school invest-ments, but it may also be argued that the "no-investment" profile isnot horizontal but concave, for biotogical reasons. It is perhaps best,therefore, to consider the alternative estimates in Table 4.2 asbracketing the true values. This would mean, in turn, that the time-equivalents in the table are also overstated somewhat, particularlyat the lower levels of schooling. If the time values are midway be-tween the two estimates, the dollar volumes of post-school invest-ment are overstated 20—25 per cent on average when a horizontalshape is assumed for the zero investment profile.

The investment behavior inferred from the earnings profiles,


though in some respects unclear, is quite plausible in the light ofhuman capital theory. The logarithmic concavity of the earnings pro-files is actually strongly implied by the analysis of optimal distribu-tion of human capital investments over the life cycle.9

The differences among schooling groups are plausible: thosewho invest more (dollars) in schooling also spend more in post-school investments. Greater ability and better access to financingopportunities are common factors in both forms of investment. Thesefactors evidently dominate whatever incentives and opportunitiesexist for substitution between the two kinds of investment. As fortime-equivalent measures of investment, the cross-sectional figuresin Tables 4.1 and 4.2 indicate a negative or zero correlation betweentime spent in schooling and in post-school investments. Over time,total schooling and post-school investments grew in dollar terms.However, schooling expenditures grew more rapidly than expendi-tures on post-school investments (compare C8 with in Table 4.2).The growth of public subsidies to education may have been an im-portant incentive for substituting schooling for job training. In timeunits, this substitution accelerated the upward trend in years ofschooling and reduced somewhat the time spent in job training.

The empirical findings about levels and shapes of the averageearnings profiles in the different schooling groups imply the follow-ing intergroup differentials in earnings:

1. Dollar differentials among schooling groups increase with ex-perience. Because the earnings profiles are concave, the increase ismuch more pronounced with age.

2. Relative intergroup differentials in annual earnings grow withage, but diminish with experience. Weekly and hourly relative wagedifferentials among schooling groups do not perceptibly change withexperience. Given a sufficiently small decline in differentials by ex-perience, the increase by age is due to a strong logarithmic concavityof the earnings profiles. As already explained, concavity of earningsreflects diminishing investments over the working life.

The intergroup differentials account for only a part of the totalinequality (variance) among individuals within age or experiencegroups intragroup dispersion—ditterentiats in earnings among mdi-

9. See Becker (1967, Part I, Chap. 1), and Ben-Porath (1968).


viduals of the same schooling and age—is the other component ofthe variance. Because both components of inequality are large, wecannot explain variances in age or schooling subgroups without aprior analysis of ungrouped, individual data.'°

Before we proceed to an econometric analysis of earnings pro-files, it will be useful to consider somewhat more closely two im-portant qualifications to the investment interpretation of earningsprofiles: (1) The allocation of investment over the life cycle cannotbe simply "read into" the cross-sectional profiles, which representearnings differences among distinct individuals who differ by age.Though they had the same years of schooling, the different cohortsmay have had different patterns of post-school experience.1' (2) Thelife-cycle earnings profile partly reflects biopsychological develop-ment: of maturation at young ages and decline at older ages. Thisdevelopment is systematic and largely independent of (exogenous to)the individual's will. To the extent that this development creates aconcave earnings profile, the investment interpretation must bemodified.

Granted the validity of these qualifications in principle, theirweight remains to be settled on empirical grounds: (1) How differentare cohort earnings profiles from cross-sectional profiles in the sameschooling groups, abstracting from economywide fluctuations andsecular trends? (2) How important are the "inherent" age effects inthe observed earnings profiles? Empirical evidence is needed to indi-cate whether we are dealing with major objections or minor qualifica-tions. Scanty though it is, some evidence on the matter is available,and it bears consideration:

1. In a study based on annual income data of the Current Popu-lation Survey, H. P. Miller calculated average annual age-incomeprofiles of U.S. men in each of the several schooling groups for

10. In my analysis of 1950 data (Mincer, 1957, 1958), variances in age and school-ing groups were explained only in terms of intergroup differentials observed in typicalearnings profiles. No contradiction arises in dollar variances, but the structure of rela-tive variances is more intricate, as will be shown.

11. It should be clear, however, that even if major problems were to be posed bythe differences between cohorts and cross sections and between 'autonomous" andinvestment-induced components of earnings profiles, they do not represent argu-ments against a human capital analysis. When better understood, these phenomenacan and will be incorporated into the human capital models.


1956—66. Cohort changes in income can be calculated from thesedata by comparing pairs of cross sections. Individuals in a givenschooling group who were 25 years in 1956 were 35 in 1966. InChart 4.6, the percentage rate of growth of their income in thisperiod is the ordinate of the upper (solid) line corresponding to age25 on the horizontal scale, while the ordinate of the lower (broken)line at this point shows the growth rate from age 25 to 35 in the 1956cross section.12

The upper and lower lines are similar in shape, i.e., cohort pro-files are similar in shape to the cross sections. They are displaced up-ward by some 20—30 per cent per decade in most schooling groupsand ages, that is, actual growth of income was that much greater ineach cohort than in the cross section —a common effect of economy-wide secular growth.

Table 4.3 shows the vertical displacement of the cohort from thecross-sectional profiles at selected ages in the several schoolinggroups. The variation in these numbers may reflect "non-neutrality"in income growth, in favor of more educated and younger males, orit may represent a relative understatement in the cross sectionof the cohort post-school investments of these groups. Whicheverthe correct interpretation may be, the concavity of logarithmic pro-files is evident in cohorts. Indeed, the suggested non-neutralitywould result in more pronounced concavity in the cohort than in thecross section and a greater divergence of profiles with advancingage.

2. Studies of 1964 and 1966 earnings of economists and a com-panion study of 1966 earnings of all full-time employed persons re-ported to the National Register of Scientific and Technical Per-sonnel 13 included data on years of professional work experience inaddition to six other characteristics: age, years of schooling, pro-fession, type of employer, work activity, and sex.

Economists of the same years of schooling and age had a con-siderable dispersion of years of work experience: About 20 per cent

12. The years 1956 and 1966 were chosen because of their similar cyclical posi-tions. The use of income rather than earnings is a minor drawback.

13. The 1964 study is reported in Tolles et al. (1965). The studies are based on over10,000 reports from economists, and over 200,000 reports from all personnel in theRegister. The very informative multivariate statistical analysis of the data was de-signed and carried out by E. Melichar of the Federal Reserve Board.

78

C,

0

a,

C0

.gC.,

4-Ca,UI-

EMPIRICAL ANALYSIS

CHART 4.6AGE PROFILES OF DECADAL PERCENTAGE CHANGES

SCHOOLING COHORTS, 1956—66, AND IN CROSS SECTION, 1956IN MALE INCOMES, BY

10

5

0

18 20 25 30 35 40 45 50 54Age

NOTE: Figures on curves indicate years of schooling completed.SOURCE: U.S. Bureau of the Census (August 1968, Table 11).


TABLE 4.3ANNUAL GROWTH RATE OF INCOME OF MEN IN SELECTED AGE

AND SCHOOLING GROUPS, 1956—66(income in 1966 dollars)

Age in

Years of Schooling

Under 16 or1956 8 8 9—11 12 13—15 More

25 3.2% 2.2% 2.4% 2.7% 3.5% 4.0%30 2.3 2.1 2.4 2.4 3.0 3.1

35 2.2 2.1 2.6 2.3 3.1 2.240 2.2 2.1 2.7 2.3 2.4 1.745 1.8 1.8 2.8 2.0 1.9 2.1

50 1.4 1.8 2.8 1.6 1.7 2.5

SouRcE: U.S. Census (1968, Table 11).

of persons in the same five-year age interval differed by more than 10years of work experience (Tolles et al., 1965, Table 7, p. 40). Thisvariability and the large sample sizes permitted a statistically signifi-cant separation of the effects of age and of experience on earnings.Correlation of log earnings of economists with years of experienceyielded an A2 of .41; correlation with years of age yielded A2 = .23.For all scientists, the simple coefficient of determination of earningswith experience was .34; with age, it was .24. In the multiple regres-sions on the seven characteristics, length of professional experienceand schooling (measured by highest degree) were the two mostpowerful, and age was the least important, variable (Tolles andMelichar, 1968, Table 11-2, p. 60; and Tolles et al., 1965, p. 64).

The studies showed that for economists under the age of 35, fiveadditional years of age provided a $300—$400 advantage, given thesame length of experience, while an additional five years of expe-rience were associated with a gain of $1,500—$2,000, given the sameage (Tolles et al., 1965, p. 42). If so, the net age effect is about 20 percent of the combined effect of age and experience on earnings at theyounger ages. The net incremental value (partial regression coeffi-cient) of years of experience declined as length of service increased,but the increments remained positive throughout the observed work-ing lives (Tolles et al., 1965, pp. 43, 49, 50).


The partial regression coefficient of age showed a deceleratingprogression of salary with age which continued to about age 50, andthen became negative, that is, a net decline was associated with ad-vancing age (Tolles et al., 1965, p. 70). Compared to the gross effect,the net effect of age was quite small, but the net effect of experiencewas almost as large as the gross effect (Tolles et al., 1965, Figure 1,pp. 66—67).

The findings for all scientific professions are similar to those foreconomists. The observed experience profiles of earnings differ agreat deal among specialities, type of employer, and type of workactivity. These differences can be attributed to the differentialeffects of experience.

If we interpret the contribution of years of experience as invest-ment-induced effects on earnings, and the contribution of age as the"inherent" effects of biopsychological individual development, thequantitative evidence of the AEA studies strongly supports the inter-pretation of observed earnings profiles in terms of investment inhuman capital.

It is important to note, however, that the "age effect," smallthough it is, contributes to the concavity of the observed earningsprofiles. If ignored, as it is perforce in the current study, investmentis overstated somewhat (20 per cent was suggested above) at agesbelow 35, though understated later.14

Even if experience is shown to be a much more powerful deter-minant of earnings than age, nevertheless an objection to the invest-ment interpretation of the earnings profile could be made on theground that the growth of earnings with experience may reflect theprevalence of institutional arrangements such as seniority provisionsin employment practices. Such practices, however, do not contradictthe productivity-augmenting investment hypothesis, unless it can beshown that growth of earnings under seniority provisions is largelyindependent of productivity growth.'5

A recent BLS study, Seniority in Promotion and Transfer Pro vi-sions, makes clear that this is not the case. The study is based onan examination of virtually all major collective bargaining agree-ments (1,851 in all), each covering 1,000 workers or more (exclusive

14. This is comparable to the conclusions reached on the basis of Table 4.2.15. In this study, productivity growth is not assumed to be costless.


of railroads, airlines, and government). The majority of the agree-ments, covering over 70 per cent of workers subject to the agree-ments, contain specific provisions for promotions. The absence ofsuch provisions is typical of industries with one or more of the follow-ing characteristics: (1) Sharply differentiated skills and upwardmovement to journeyman status through apprenticeship; (2) laboragreements where no promotion is possible within the bargainingunit; and (3) relatively high enterprise mortality, emplàyeeturn-over, or sporadic or seasonal employment (Seniority, p. 3). Promotionbased only on seniority occurred in agreements covering less than 2per cent of workers (Seniority, p. 5). In all other cases seniority wasconsidered jointly with merit, skill, aptitude, and other factors.Seniority was cited as a principal factor in agreements covering 20per cent of the workers. However, in agreements covering 50 per centof the workers, seniority applied only if other qualifying factors werethe same among the employees being considered for promotion. Atypical clause is:

When a vacancy occurs in one of the higher rate crafts, employees withseniority shall be given full consideration before an appointment is made;however, seniority shall not be the governing factor and shall not preventthe transfer or appointment of an employee with less seniority, whoseability and qualifications are greater than those of the senior employeeunder consideration for the work on the higher paid job (Seniority, p. 6).

Seniority is more important as a factor in promotion of blue-collar than of white-collar workers. It is least important in the profes-sional, technical, sales, and supervisory categories of jobs. Skill andability are the principal nonseniority factors in agreements coveringabout 75 per cent of the workers. Education is mentioned in onlyabout 7 per cent of the agreements as a factor in promotion.

In most of the agreements the employer is required to makeselections for promotion from the group of employees who had ex-pressed an interest in the vacancy. In some agreements promotion isrestricted to specific employees in a line of progression, but such"automatic" promotions are largely confined to smaller or narrowerjob units—usually with a narrow occupational classification. A fewagreements call for tests to be administered to workers applying forpromotion. Many call for a (1—2 months) trial and training period onthe new job. Such a period allows the company to determine whether


the employee can perform the job satisfactorily and gives the em-ployee time to decide whether the job suits him. The bid for promo-tion can be costly: disqualification during the probationary period isconsidered in most of the agreements, and while in most of themthe disqualified worker is allowed to return to his previous job, insome penalties are attached, such as some loss of seniority rights,and even downward job transfers (Seniority, p. 31).

Long training periods following the promotion were in most in-stances unnecessary, since employees covered by the provisions (un-like those in formal training or apprenticeship programs) ordinarilyhad acquired the necessary skills in lower-rated jobs, or were ad-vanced through a series of semiskilled tasks requiring relatively littletraining at each step. This situation is a vivid demonstration of theprocesses of accumulation of human capital on the job.

In sum, it appears that productivity is a major criterion for promo-tion in rules developed in collective bargaining. Moreover, the con-finement of "automatic" promotion to narrow job classifications isan indication that productivity growth looms larger the bigger thejob advancement.

The negligible role of school education in promotion is consis-tent with the view that post-school productivity growth is causally re-lated not to schooling but to post-school investments. This view wassupported by evidence (Table 3.4, above) of a declining correlationbetween schooling and earnings as work experience accumulates.

5

The Human CapitalEarnings Function

5.1 EMPIRICAL SPECIFICATION

The interpretation of age and experience profiles of earnings asconsequences of investment behavior makes it possible to expandthe schooling model to include post-school investments in an econ-ometric analysis of the distribution of earnings.

The importance of the life-cycle distribution of post-schoolinvestments in creating earnings inequality is empirically quite ob-vious: As Charts 4.1—4.3 show, annual earnings nearly double aftertwo to three decades of experience in each schooling group, a dif-ferential almost as great as that between the earnings of males with8 and 16 years of schooling. It is, of course, known from previous work,not tied to human capital analysis, that the inclusion of age in addi-tion to schooling in a multivariate regression analysis of earnings in-creases the explanatory power of the analysis. It is also known thatsince age interacts with schooling in affecting earnings (in dollarsand in logs), a linear additive form of regression without interactionterms is not adequate. Now, we have not only obtained a behavioralinterpretation of this interaction but also noticed that there is less of


an interaction, if any, between experience and schooling than be-tween age and schooling: experience profiles of log earnings aremuch more nearly parallel than age profiles. If so, in an earnings func-tion in which earnings are logarithmic, years of work experienceshould be entered additively 1 and in arithmetical form. The ex-perience term is, of course, not linear, but concave. For example (seeformulation 5.2a, below) the earnings function might be parabolic inthe experience term:

In

where t is years of experience and E8 is earning capacity after com-pletion of schooling. Since

In E0+rs;

In E==ln E0+rs+f31t—/32t2.

If work experience is continuous and starts immediately after com-pletion of schooling, then work experience is equal to current ageminus age at completion of schooling; t = (A — s b), where A iscurrent age and b is age at the beginning of schooling. Thus, the useof age alone instead of experience in the earningsfunction results inthe omission of some variables, as can be seen if the expression for t,above, is substituted in the function:

In E0+rs+/31(A—s—b)+/32(A—s—b)2.

The quadratic term leaves out an age-schooling interaction variable(As). What is more, the partial omission of s leads to a change in itscoefficient which can no longer be interpreted as a rate of returnto schooling.2

1. The possibility of interaction between experience and schooling is explored inthe regression analysis in the next section.

2. The coefficient is biased downward. A simplified example is (cf. Griliches andMason, 1972):

In Ya0+a,s+a24.Neglecting the quadratic term also in the alternative specification

In

and substituting t = (A — s — b), yields

In

Thus a1 is an underestimate of r.

THE HUMAN CAPITAL EARNINGS FUNCTION 85

The proper form of the experience function depends on the formof the life-cycle investment function. The economic theory of optimiz-ing behavior implies that investment in human capital declines overthe life cycle, at least beyond an early stage. Apart from this,economic theory provides no guidance to the specific form of the in-vestment function. Accordingly, a few simple specifications ofinvestment profiles are introduced here. From these, earnings func-tions are derived which are applied, in the next section, to the indi-vidual data in an analysis of the entire cross section of male earningsin 1959.

Mathematical simplicity and statistical tractability call for a con-sideration of linear and log-linear experience functions (profiles) ofnet dollar investments (Ci) and "time-equivalent" investment ratios(k1). Four simple specifications are considered:

(5.1) C0 — t (5.3) C1 =

(5.2) k1 k0 — t (5.4) k1 =

k0 and investment ratiosduring the initial period of experience, t = 0. T is the total period ofpositive net investment; e, the base of natural logs; and /3, a param-eter indicating the rate of decline of investment.

It is convenient, at this point, to treat the investment and earningsfunctions as continuous functions of time. The "gross" dollar earn-ings function is:

E1 = E8 + r1J

C3dj, (a)i=O

where denotes earnings obtainable after s years of schooling withno further investments, and r1 is the rate of return to post-school in-vestment, which is assumed to be equal in all periods t.

The logarithmic version is:

IflE1lflE8+r1j k3dj. (b)3=0

3. T need not be specified a priori. It is implicit in the statistically estimated param-eters.


By substitution of specifications (5.1) and (5.3) into the arith-metical earnings function (a), and (5.2) and (5.4) into the logarithmicfunction (b), the earnings functions are transformed from functionscontaining investment variables or that cannot be observedinto functions of years of experience,4 which can be observed andcan therefore be used in empirical analysis. Since observed earningsare more akin to "net" earnings (Vt) than to "gross" earnings,must first be transformed into V1 by letting = E1 — and In Y1 =In E1+ln(1 —k1).

I now derive the empirically observable earnings functions cor-responding to the four specifications of investment profiles:

1. The assumption of a linear decline in dollar net investmentsyields the gross earnings function:

t2; (5.la)

and the net earnings function:

Y= (E8— C0) + c0 t— t2. (5.lb)

Here both the dollar earnings profiles are parabolic in years of ex-perience (t). Note also that the time derivative of E1 and that is,the dollar increment of earnings, is a linearly declining function oftime.

2. If the investment ratio is assumed to decline linearly, the grosslog-earnings function becomes parabolic:

In E1=In (5.2a)

and the net earnings function becomes:

In Y1=ln t2+ln (1—k1). (5.2b)

In this case, the logarithmic increment in earnings is only approxi-mately a linear declining function of time.

4. Years of experience were directly observed in the AEA study of economists'earnings. Direct information is, unfortunately, not available in the Census data. In thecurrent study, therefore, the "observable" is only an imperfect estimate. Its construc-tion was shown in columns 1 and 3 of Table 3.1.


3. If dollar investments decline exponentially with increased ex-perience, then the earnings functions are:

(5.3a)

and

= E8 +rC0 — (r + f3)C0

(5.3b)

Here, both dollar earnings and dollar increments of earnings are ex-ponential in t. The logarithm of the increment islinear, since

= (r + (5.3c)

In discrete form:

—= (r + /3)C0

—

Let = y and E8 + (rC0/f3) = (peak earnings). Then

— = (1 — — Y1)

and

= (1 — + )'Yt. (5.3d)

According to (5.3d), dollar earnings follow a first-order linear auto-regression.

4. Finally, if the investment ratio declines exponentially, then theearnings functions are:

In (5.4a)

and

In (1 (5.4b)

The gross earnings function (5.4a) is the familiar modified Gom-pertz curve. The percentage increments d(ln are exponential,while d(ln are approximately so.


Here also:

In E=(1 —y)(ln Er—In (5.4c)

and

In —y)ln In (5.4d)

The Gompertz earnings function (5.4c) is equivalent to a Koyckadjustment equation in logs (5.4c) and follows a log-linear first-order autoregression (5.4d).. The net earnings function (5.4b) is

approximately Gompertz, and has the corresponding approximateproperties.

For regression analysis, the logarithmic forms (5.2b) and (5.4b)are preferable, because the schooling investment data used in thisstudy are in years. This requires the use of In E8(= In E0 + r8s) ratherthan in the earnings function. Also, as was abQve, thelogarithmic form minimizes the need for interactiOn terms, per-mitting an application of the same estimating equation to the wholecross section.

The parameter estimates in the earnings function can also beinterpreted in terms of gross rather than net investment, if a fixeddepreciation rate is assumed. As was shown in Part I, equation(1.21), the general earnings function in those terms is:

Ct

In E=InJ

where k* is the gross investment ratio. For example, the parabolicearnings function becomes:

In t2, (5.2e)

where T* is the gross investment period; and the correspondingGompertz function is:

In (5.4e)

Some empiricaj analyses of earnings relate dollar earnings toyears of schooling. This is a misspecification from the point of viewof the human capital model. In the NSF study, described in the pre-ceding chapter, it was reported that logarithms of earnings yielded


stronger statistical fits than dollar earnings when related to years ofschooling and experience.5

Another form of earnings function, which is not derived from ahuman capital model, was used in a recent study by Thurow (1970).He used the log of schooling, instead of years of schooling, in theregression with earnings in logs:

In t.

Goodness of fit cannot be compared because the function wasfitted by Thurow to averages of groups, not to microdata. However,Heckman and Polachek fitted it at the microlevel and found the fitinferior to specification (5.2b), above. Apparently, also, the rate ofreturn to schooling is underestimated in the Thurow equation, andthe returns to experience are substantially overstated.6

5.2 REGRESSION ANALYSIS OF INDIVIDUAL EARNINGS

We are now ready to apply the human capital earnings function tothe cross-sectional distribution of individual earnings. The specifica-tion of that function relates the distribution of logs of earnings tothe distribution of cumulated ratios of investment to gross earnings.If the post-school investment profile can be summarized by a pair ofparameters, k0 and /3, as in equation (5.4), then the earnings func-tion will involve the variables s and t and the parameters k0,

and /3, where and rg are rates of return to schooling and to poStschool investments, k0 is the initial post-school investment ratio, and/3 is its rate of decline:

In = In E0, + + + (5.5)

5. Multiple R2 was .55 for log earnings compared to .41 for dollar values (Tolleset al., p. 65). The goodness of, fit could not be directly compared. However, statisticaltests devised by Box and Cox (1964) confirm the superiority of the logarithmic de-pendent variable in the earnings regressions based on the Census 1/1,000 sample,reported in the next section. See Heckman and Polachek (1972).

6. Since r3 = a In V/as, and b = a In V/a In s, r, = = .72/11 = .06 in the 9-to-i 2-year schooling group. This is half the size of my estimates. At the same timea In Y/at= Ct= .65 over the 6-to-is-year experience range. Since k cumulated overthis range is not likely to exceed 2—it is less than 2 in the first decade of experienceaccording to Table 4.1, above—the implicit estimate of the rate of return to post-school experience, is very high.


If information were available on all variables and parameters for eachindividual i, the equation would represent a complete accounting(short of the random factor of the human capital characteristicsentering into the formation of earnings.

Of course, the availability of such information is not even con-ceivable. A more modest research objective is to abstract from indi-vidual variation in initial earning capacity (In E01) and in rates ofreturn on investments, and consider only the effects of the volume ofinvestment on earnings. Average parameters in E0, r8, and wouidthen appear in the statistically estimated coefficients of equation (5.6):

In = In F0 + + f(t/k01, + Ui. (5.6)

Individual variation in and In E0, would be impounded inUnfortunately, while information on schooling attainment s, is

available for each individual, this is not true for post-school invest-ment. Differences in quantities of post-school investment amongindividuals are given by differences in and in addition to dif-ferences in years of experience. It is therefore necessary to suppressthe index i inside the experience function f, and use as the earningsfunction:

In = In E0 + r8s, + f(t/k0, f3, r1) + (5.7)

The data selected from the 1/1,000 sample which were usable forthe regression analysis were 31,093 observations of annual earningsin 1959 of white, nonfarm, nonstudent men up to age 65. Parabolicand Gompertz functions [equations (5.2b) and (5.4b) of the precedingsection] were fitted to this set, as well as to a somewhat smaller set(28,678 observations) consisting of earnings in each of 4o years aftercompletion of schooling. Here, the oldest age was 55 for men with 8years of schooling and 64 for those with 16 years of schooling. Thevariance of log earnings in the (40 years of) experience set was 0.668,compared to 0.694 in the age (under 65) set.

The parabolic and Gompertz estimating equations were specifiedto a quadratic approximation in a Taylor expansion. Formulated interms of net investments the parabolic earnings function,

In In E0± t2±In (1— t), (5.2b)


is estimated by

(P)

where

a=ln E0_k0(1 +k0);

b — [r1k0 (k0)23__L2T+2T2

The Gompertz earnings function,

In (1 (5.4b)

is estimated by:

(G)

where

= —b2—

a=lnE0+b3 — 2

When earnings are expressed as a function of gross investment,replaces k0, r replaces T, and is an additional term in the coeffi-cients b1 and b2.

Table 5.1 contains the estimated parabolic (P) and Gompertz (G)regression equations and multiple coefficients of determination ofthe earnings distribution for forty years of experience.7

All the estimated coefficients shown in Table 5.1 are highlysignificant in a sampling sense: the coefficients are many timeslarger than their standard errors. This is due to the very large samplesize, though size alone is not a sufficient condition for statisticalsignificance.

The coefficient of determination A2 is of special interest as an

7. The regression results of the under-65 age distribution are not presented. Theregression coefficients in the age cross section were very close to those in the ex-perience cross section, but the multiple coefficients of determination were .02—.03points lower in the age set in both the parabolic and Gompertz formulations.


TABLE 5.1REGRESSIONS OF INDIVIDUAL EARNINGS ON SCHOOLING (s),

EXPERIENCE (x), AND WEEKS WORKED (W)(1959 annual earnings of white, nonfarm men)

Equation Forms R2

S(1) In Y= 7.58 + .070s .067(43.8)

P(1) In Y=6.20+.107s+.081t—.0012t2 .285(72.3) (75.5) (—55.8)

P(2) In Y=4.87+ .255s— .0029s2— .0043ts+ .148t— .0018t2 .309(23.4) (—7.1) (—31.8) (63.7) (—66.2)

P(3) In Y= f(D3) + .068t— .0009t2 + 1.207 In W .525(13.1) (10.5) (119.7)

G(la) In Y=7.43+.110S1.651Xat .313(77.6) (—102.3)

G(lb) In Y=7.52+.113s— .307(74.3) (—101.4)

G(2a) In Y= 7.43+ .108s— 1.183 In W .546(65.4) (—16.8) (—10.2) (105.4)

G(2b) In V = 7.50 + .111 s — 1.291 — .1 + 1.174 In W .551(65.0) (—3.5) (—16.0) (107.3)

0(3) In Y= + 1.142 In W .557(108.1)

G(4) In V= 7.53 + .109s —1 — — .012t+ 1.155 In W .556(—2.4)

NOTE: Figures in parentheses are t ratios. A2 = coefficient of determina-tion; S = linear form; P = parabolic form; G = Gompertz form; = dum-mies for schooling and experience; Xat = = embot; W= weeksworked during 1959.

estimate of the fraction of earnings inequality that is associated withthe distribution of human capital investments. The regression coeffi-cients are not the primary concern in this study. They do, however,represent an important check on the consistency of the interpreta-tion of the regression equations as human capital earnings functions.

5.3 MAJOR FINDINGS OF THE REGRESSION ANALYSIS

1. Equations (P1), (Gi), and (G2) specify the same shape of logarith-mic experience functions for each individual, permitting only dif-


ferences in levels. They also specify the same rate of return to school-ing for all. Despite these strong restrictions, the two variables s and talone explain about 30 per cent—28.5 per cent in (P), 32 per cent in(G)—of aggregate earnings inequality.

2. Relaxation of these restrictions is achieved in a parametricfashion in (P2): Here the s2 term is added to allow for systematicallydifferent rates of return to schooling at different levels of schooling.The results are statistically significant and already familiar: the coeffi-cient at s2 is negative, indicating a lower rate of return to schooling athigher levels of schooling.

A similar nonparametric relaxation is obtained in (G3) by use ofdummy variables. These yield separate intercepts for each schoolinglevel. They are not shown in the table, as their features are the sameas those already seen in (P2).

3. The partial coefficient of schooling is an estimate of theaverage rate of return to schooling. The marginal rates are approxi-mated in nonlinear formulations, such as (P2), which permit the esti-mation of different rates at different levels of schooling. In (P2), themarginal rates:

Inds

when estimated at t= 8 (roughly at overtaking), are 17.4 per cent at8 years of schooling, 15.1 per cent at 12 years, and 12.8 per cent at16 years.

The negative coefficient of the interaction term (st) describes theapparent convergence of experience profiles. Both the nonlinearityof s and the interaction St become insignificant when weeks workedis included in the regressions, such as (P2) and (G2). The same be-havior of s2 was observed in the overtaking set (Cf. Table 3.3); and theparallelism of weekly earnings (no interaction st), in Chart 4.4.

4. The experience variable = in the Gompertz equationswas iterated for /3, the rate of decline of time-equivalent investments,between 0.30 and 0.05 in 0.05 intervals. The highest R2 and mostplausible coefficient values were found in the 0.10—0.15 range. WhileR2 changes little in a wider interval, the partial regression coefficientsare sensitive to the specification of /3. The coefficient at the quadraticterm is particularly unstable when different values of /3 are tried.

At any rate, k0 and can be calculated from the b2 and b3 co-


efficients of the Gompertz equations, since b3 = and b2 =+ 1]. When /3 = 0.15 in (G2a), k0 = 0.81, and = 6.7 per

cent, while for /3 = 0.10 in (G2b), k0 = 0.56, and = 13.1 per cent.The post-school investment parameters cannot be identified in

the parabolic equations unless values of T, the period of positive netinvestment, can be specified. Since Tcorresponds to the number ofyears of experience until earnings reach a plateau, T= 20 is used forannual earnings (P1) and T= 30 for weekly earnings (P3). In (P1)k0 = 0.58 and r1 = 6.3 per cent, while in (P3), k0 = 0.42 and = 11.9per cent.

In order to interpret the parameters of the earnings function interms of gross investment and depreciation the Gompertz functionis expanded to include a linear term in experience (equation 5.4g).This is shown in (G4). The coefficient of the linear term is an esti-mate of the depreciation rate (= 1.2 per cent). The estimate of initialgross investments is 0.54, and the rate of return to post-schoolinvestment is estimated to be 12.1 per cent.

The high values of k0 and low values of r,, in (Gb) make the as-sumed rate of decline of investment, /3 = 15 per cent, somewhat lessplausible than the alternative assumption of /3 = 10 per cent in (Ga).8

The parabolic gross investment formulation precludes the identi-fication of the parameters: two need to be assumed to identify theremaining three.

5. Adding variation in weeks worked by (In W) to the equationraises the explanatory power of the regressions to 52.5 per cent inthe parabolic, and to 55.7 per cent in the Gompertz, equations. Inboth cases the coefficient at In W is significantly larger than unity,suggesting a positive correlation between weeks worked and weeklyearnings within schooling and experience levels.

Even without W, adding an (imperfect) experience term in the hu-man capital earnings function raises its explanatory power from 7 percent in the schooling regression to over 30 per cent in the Gompertzfunction while the bias in the estimated rate of return to schooling islargely eliminated. How well the regression coefficients of the ex-

8. All the estimates of k0 seem rather high. The overstatement maybe due to someconfounding of investment with maturation effects, or with higher rates of return topost-school investment than to schooling.


perience variables estimate the post-school investment parameters isdifficult to tell.

Firmer estimates will require more evidence. The rates of returnto schooling are somewhat lower than they were in the overtaking set(Table 3.3). Possibly, these rates decline with experience in thecross section, as older cohorts have older vintages of schooling. TheA2 measures do not seem to be very sensitive to alternative specifica-tions, and the R2 are of major interest here.

While the expansion of the schooling model to a function whichincludes post-school experience greatly increases the power of thehuman capital analysis of earnings, our regressions still understatethat power. Because there is no direct information on individual post-school investments, these were assumed to be the same for all per-sons within a schooling group. In effect, estimates were made of thecontribution of individual investments in schooling measured inyears, and of average post-school investments in each schoolinggroup to total earnings inequality. This contribution amounts toabout one-third of total inequality in annual earnings. The remaindercontains effects of individual differences in post-school investments,in quality of schooling, in time supplied to the market or spent in un-employment, in individual rates of return, and in "transitory" factors.Because the first two are components of the volume of human capitalinvestment, the regressions understate the potential explanatorypower of the distribution of human capital investments.

How much larger would R2 be if information were available onpost-school investments for each individual? This question can beanswered in an indirect fashion. Assume that the desired equation(5.6) which includes individual information on post-school invest-ments is homoscedastic. Then o-2(uj is the same for all sets of valuesof the independent variables in equation (5.6):

In Y=lnE0+rs,+f1(t)+u1,

where f1(t) is the contribution of post-school investments to earnings.To estimate hence A2 = 1 — Y)], it is sufficient toestimate the residual variance in one instance only. This has alreadybeen done in the case where 0, i.e., in the overtaking set. Theresidual variance in the regression of log earnings on schooling inthat set serves, therefore, as an estimate of the residual variance in


the unobservable regression form (5.6). Based on the regressions inthe overtaking set, previously shown in Table 3.3, cr2(u) = 0.333.Hence ñ2 = 1 — (0.333/0.668) = 0.50.

In a similar fashion, the residual variance from the multiple re-gression of log earnings on schooling and log weeks worked in theovertaking set can be compared to the aggregate variance of logearnings net of the contribution of log weeks. The resulting1 — (0.20/0.53) = 0.62.

If most of the variation in weeks worked were considered transi-tory, the 62 per cent figure would be an estimate of the contributionof human capital investment to a longer-run earnings inequality. Ifall of it were permanent and related to human capital investments,then A2 = 1 — (0.200/0.668) 0.70.

In analyzing the regressions in the overtaking set I suggested thatquality of schooling might account for at least 0.06 of the residualvariance. If so, the indirect estimates A2 of the explanatory power ofthe distribution of human capital for the inequality of earnings in-creases to 0.55, 0.69, and 0.78, respectively.

It appears that, whatever the fraction of transitory variation inweeks worked, schooling and post-school investment accounted forclose to two-thirds of the inequality of earnings of adult, white, urbanmen in the United States in 1959.

9. The residual variance in equation (2) in the top panel of Table 3.3 is 0.204;0.53 — (1.142)2o-2(In W), where 1.142 is the coefficient in (G4) in Table 4.4.

6

Analysis of Residuals:Distributions of EarningsWithin Schooling and Age Groups

6.1 VARIANCES

It was possible to make indirect estimates of the contribution ofhuman capital investments to total earnings inequality by assumingthat the latent residuals (ui) in the earnings function (equation 5.6)were homoscedastic. Is this assumption consistent with the empiricaldata? This question is an invitation to explore the structure of earn-ings distributions within groups defined by years of schooling andyears of age (experience). Since the variation in earn-ings is quite large, such an exploration is of interest in its own right,and not merely as a test of particular assumptions.

The estimated values of the regression equations, which wereshown in Table 5.1, are estimates of means in the schooling-ex-perience groups. The within-group distributions are, therefore,distributions of residuals 1 (vi) (equation 5.7). Since v, = u, + (v, — ui),

cr2(v1g) = o-2(u2) + o-2(v, — u1) + 2po(ujo(v1 — uj.

1. Apart from the sampling errors of the means in each cell.


The observed residual variance in a schooling group changesover the life cycle (t) only if o-2(v, — u2) changes, assuming is

homoscedastic and fixed.By definition of equations (5.6) and (5.7) of Chapter 5, — uj con-

tains unobserved individual differences in returns to post-schoolinvestment. The human capital model (Chapter 2) predicts that theresidual variance in a schooling group, cr2(vj, will change system-atically with age and experience.

6.1.1 EXPERIENCE PROFILES OF DOLLAR AND

LOG VARIANCES OF EARNINGS

To analyze the experience profiles of both dollar variances andlog variances = o-2(ln consider three in the workinglife: the initial stage t = 0, the overtaking stage t = I, and the peakearnings stage t = The arbitrariness and difficulty of deriving func-tional forms of profiles of variances is avoided by using this proce-dure, while making it possible to determine whether the profiles aremonoton ic.

First the expressions for dollar variances at the three points arederived:

= — C01; .. cr2(Y3) = cr2(E81) + o.2(Co) — 2pC0E8cr(E5)r(CO). (6.1)

'4 = = ff2(E3). (6.2)

+ rCT; = o-2(E3) + + 2rpCT,ESo-(ES)o-(Cr). (6.3)

In each equation, C0 is initial-period post-school investment; CT, thesum of positive post-school net investments; E8, initial post-schoolearning capacity; peak earnings; p, correlation coefficient; and r,the rate of return to post-school investments.

In general, o2(Y) must vary over the life cycle. The pattern ofvariation depends on the dispersion in post-school investments andon the correlation between the dollar volumes of post-school invest-ment and earning capacity If, as appears from intergroup analysis(Chapter 2), the correlation between (dollar) schooling and post-school investment is positive, p is positive and dollar variances mustrise from overtaking to peak earnings. In addition, dollar varianceswill rise throughout if o-2(Y0) <o2(Yj), which must be true if

ANALYSIS OF RESIDUALS 99

p(Co, >

Chart 6.1 and Table 6.1 show that dollar variances indeed in-crease monotonically and sharply throughout working life. Thestandard deviations more than double between the eighth andthirtieth year of experience in the middle and upper schoolinggroups, but increase at a slower rate in the lower ones. The same dataalso show that the profiles of variances of the more

at all stages of experience. A sufficient condi-tion for this phenomenon can be found by comparing the variances atovertaking: Here cr2(Y;) = + o2(u), when the variation in E0andr8 is impounded in the residual. o-2(C3) evidently increases with levelof schooling. This is quite plausible: over time, total costs of school-ing cumulate with level of schooling, and so do individual differencesin total costs.

The rate of growth of variances from ito is obtained by dividing(6.2) into (6.3):

o-2(Y)2

o(CT)— 1 = r

ff2(E3)+ 2rp

o'(E3)(6.4)

The weaker growth of variances at lower levels of schooling suggestseither a weaker correlation (p) between earnings capacity (E3) andpost-school investments (Cr), or a smaller ratio Definethe regression slope of on which is equal to p{o-(CT)/o-(ESfl asthe "marginal propensity to invest" (MPI). Evidently, MPI tends to besmaller at lower levels of schooling.2

The important conclusion resulting from the analysis of dollarvariances is that the usually observed increases of variances withexperience and age are strongly influenced by the staggering ofpost-school investments over individual working lives. A largeenough dispersion of post-school investments and a positive correla-tion between dollar schooling and post-school investments can ex-plain the sharp age gradients. The increases of dollar variances witheducation are likely to reflect the almost necessarily larger residualdollar dispersion of total schooling costs at higher levels of schooling.

2. Cf. the findings of Salmon (1972) that the marginal propensity to save is alsosmaller at lower levels of schooling.


CHART 6.1

5—

EXPERIENCE PROFILES OF VARIANCESWHITE, NONFARM

OF ANNUAL EARNINGS OFMEN, 1959

220 25 30 35 40 45

Years of experience

NOTE: Figures On curves indicate years of schooling completed.SOURCE: 1/1,000 sample of U.S. Census, 1960.

Ratio scale

(million dollars)

100908070

60—

50—

16//40—

30—

20—

//////// 12/

r/

10—98

7—

6— 0////

4

3—

0 10 15L5


TABLE 6.1AGE PROFILES OF DISPERSION IN EARNINGS, 1959

(white, nonfarm men)

Years of Schooling

5—8 12 16 5—8 12 16

Age Standard Deviation Variance of Logs

20—24 $2,200

Annual Earnings

$1,730 ($ 2,360) .562 .454 —

25—29 2,280 1,970 3,270 .457 .258 .36030—34 2,110 2,590 4,530 .336 .231 .251

35—39 2,570 3,650 6,040 .358 .240 .31740—44 2,200 3,680 7,340 .371 .272 .42145—49 2,730 4,070 8,590 .360 .339 .55550—54 2,620 4,710 10,550 .392 .403 .62655—59 2,820 5,390 8,920 .424 .451 .61260—64 3,360 6,340 9,700 .525 .460 .933

20—24 $53.3

Weekly Earnings

$ 46.3 $ 46.1 .489 .363 —

25—29 47.1 39.0 70.6 .320 .205 .23530—34 44.7 46.0 75.1 .263 .183 .21235—39 43.3 65.0 102.2 .266 .203 .27740—44 46.0 69.0 121.7 .275 .226 .33645—49 56.2 77.1 144.4 .310 .270 .42450—54 53.2 82.3 176.6 .292 .312 .43655—59 55.1 93.0 153.3 .328 .317 .55260—64 63.3 107.8 162.8 .409 .369 .748


A positive correlation between means and variances of economicvariables is a frequently encountered empirical phenomenon. Itmight be taken for granted as an arithmetical necessity, which it isnot. The structure of means and variances of earnings in theseschooling-age cells is an example of it. In this case, however, thehuman capital model provides an explanation: higher levels of earn-ings represent returns cumulated by additional investment. Thus ifH1 is a lower stock of human capital and H2 = H1 + is a higher one,earnings E1 = rH1 and E2 = r(H1 + Then E2 > E1 and u2(E2) >


o2(E1) so long as the correlation between H1 and is not exces-sively negative. Indeed, a positive correlation is expected, since thedeterminants of investment in current and past periods are likely topersist for a given individual.

6.1.2 ANALYSIS OF MARGINAL VARIANCES OF EARNINGS

Dollar standard deviations of earnings in marginal distributions, thatis, in distributions of all earnings in a given row or column of the two-way classification of the population by schooling and experience (orage), are shown in Table 6.3, column 2, below. The total variance insuch a group (say an age group) is, by (2.12):

18

n is the number of observations in the age group; the num-ber of observations in the ith schooling cell; the within-cellvariance; and d2 = — Xa), the differential between the mean in thecell and the overall mean of the age group.

Clearly, marginal variances (therefore, standard deviations)must increase with experience and with age, because within-cellvariances increase, and because differentials among profiles ofmeans, also increase, as we learned in Chapter 4. The increase of

is sharper in age groups than in experience groups, because theintergroup differential d, grows more rapidly in the former: age pro-files of mean earnings diverge more strongly than experience pro-files.

Similarly, variances in the marginal distributions by schoolingmust increase with schooling, again because cell variances andmean age differentials d, increase with schooling.

These statements are based on the assumption that the relativefrequencies n1/N are the same in each marginal row or column, thatis, the age distributions are the same in all schooling groups, andthe schooling distribution is the same in all age groups. This wouldbe the case in a cohort which is followed over its working life, or inthe cross section if there were no secular trends in schooling. Theeffect of such secular trends is, of course, that the weights ne/Ndiffer systematically in the cross section: they are bigger in older age


cells at lower levels of schooling, and in higher schooling cells atyounger ages. For this reason the age increases in marginal variancesare likely to be less in the cross sections than in cohorts. In the cross-sectional age comparisons, there is, however, an offsetting effect dueto secular trends in the dispersion of schooling. Whatever the dif-ference from cohorts, the cross-sectional gradients are quite strong,as shown in Table 6.3, below.

6.1.3 ANALYSIS OF LOG VARIANCES OF EARNINGS

We now turn to a similar analysis of relative variances, cr2(ln ingroupings of the earnings distribution. The observations are shownin Table 6.1 and in Charts 6.2—6.4. Again, consider three points in theworking life:

In (1—k01); (6.6)

.. o-2(In Y3) = a2(In E8) + if2 In (1 — k0) + 2p1o-(ln Eào- In (1 — k0).

In Y11 = In if2(ln Y) = cr2(ln E8). (6.7)

In = In E31 + rKTl; o-2(ln

= o-2(ln E8) + + 2p2rcr(ln E3)cr(Kr). (6.8)

Now, the change in log variances over the working life dependson the size of the dispersion in cumulated post-school investmentsratios and on the correlation between In E(= In E0 + rs) and KT. Apositive correlation between time-equivalent post-school invest-ment and initial post-school earning capacity In E3 implies anegative correlation between In E3 and In (1 — k0). If the correla-tions are weak, P2 Pi = 0 and the profile of log variances is U-shaped, with the bottom at overtaking. The U-shape is preserved ifthe correlations are within a specified interval bracketing zero.3 Amore pronounced negative value of P2 implies a monotonic declinein log variances over the working life, while a stronger positive P2implies a monotonic growth in log variances.

A zero correlation between the investment ratio and initial post-

1 a[In (1—k0)] 1 r(!<)3. The intervals are <

E8)and

<2 cr(In


CHART 6.2EXPERIENCE PROFILES OF LOG VARIANCES

OF WHITE, NONFARM MEN,Variance of logs1.5 —

1.4

1.3

1.2

1.1

1.0-

0.9—

0,8—

0.7—

0.6—

0.5—

0.4—

0.3—

0.2-

0.1

05 8 11 14 17 20 23 26 29

Years of experience

OF ANNUAL EARNINGS1959

32 35 38 41 44 47 50

NOTE: Figures on curvesSOURCE: 1/1,000 sample

indicate years ofof U.S. Census, 1

schooling960

completed.

school earning capacity may be due to a unitary elasticity of dollarpost-school investment with respect to initial earning capacity.Positive correlations may be caused by elasticities above 1; negativecorrelations, by elasticities below 1. Charts 6.2 and 6.3 indicate thatexperience profiles of log variances are largely U-shaped in the cen-tral (12 years) schooling groups, suggesting a weak correlationbetween post-school investment ratios and earning capacity withinthis schooling level; tend to be positively inclined (show pronouncedgrowth) in the upper schooling groups, suggesting a positive correla-tion; and are negatively inclined (decline, by and large) at lower

6

/,12///

8

/-p

02I I I I I I I I I I I I I I I


EXPERIENCE

1.4

1.3

1.2

1,1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

PROFILES OFNONFARM

CHART 6.3LOG VARIANCES OF ANNUAL EARNINGS OF WHITE,MEN WORKING YEAR-ROUND, 1959

NOTE: Figures on curvesSOURCE: 1/1,000 sample

indicate years of schooling completed.of U.S. Census, 1960.

suggesting a negative correlation.4 Apparently, the within-elasticity of post-school investment is a positive function ofing. This finding is formally consistent with the other findings:

4. The stronger growth of both dollar and relative variances at higher than at lowerlevels of skill (occupation or education) was noted in different data by several analysts.Cf. Adams (1958), Hill (1959), LydaIl (1968), Mincer (1957), and Morgan et al. (1962).

VarLonce of logs1.5

0 2 5 8 11 14 17 20 23 26 29 32 35 38 41 44Years of experLence

levels,groupschool


CHART 6.4PROFILES OF RELATIVE SKEWNESS OF ANNUAL EARNINGS OF WHITE, NONFARM

MEN, 1959

NOTE: Figures on curves indicate years of schoolingSOURCE: 1/1,000 sample of U.S. Census, 1960.

completed.

The ratio is an "average propensity to invest." According tothe analysis of log-experience profiles of mean earnings in Table4.1, it tends to decline from lower to higher schooling groups. At thesame time, the profiles of dollar variances suggest that the "marginalpropensity to invest" increases with the level of schooling. Elastici-ties, therefore, increase correspondingly and more strongly.

Another explanation of the difference in log-variance profiles

CoeffLcient of skewness

0- 5 10 15 20 25 30 35 40 45Years of experience


among schooling groups may be found in the serial correlations ofinvestments (the correlation between and E3 is an example of it).Less stability in investment (and in employment) behavior over thelife cycle results in weaker growth of variances at lower levels ofschooling. It is also possible, as we noted before, that the meanearnings profile overstates the size of post-school investments inthe lower schooling groups. If so, the dispersion of post-school in-vestments is likely to be a less important component in explainingpatterns of earnings inequality at lower than at middle and higherlevels of schooling.5

While dollar variances were larger at higher schooling levels atovertaking, with the plausible interpretation that cr2(C3) increaseswith schooling, no comparable statement can be made a priori aboutcr2(s), unless the ranking of the variation in schooling quality wereknown. The observed log variances (Chart 6.3) indeed differ verylittle among schooling groups below college at that stage in the dis-tribution of full-time earnings. Relative (time equivalent) variation incollege quality evidently exceeds that at lower levels of schooling. Inall earnings (Chart 6.2), variances of the schooling groups below highschool are inflated, an effect of large variation of weeks worked dur-ing the year (cf. Chapter 7). Because the differently inclined profilesof variances intersect in the second decade of experience, there is areversal of ranking in inequality by level of schooling: inverse at firstand direct in the later parts of the working life. This pattern is notchanged much by shifting from the experience comparisons to com-parisons based on age.

It is easy to see that these configurations, together with the struc-ture of mean log-earnings profiles, produce U-shaped patterns ofmarginal relative variances by age. These are shown in Table 6.3,column 1. The strong growth of mean differentials with age con-tributes to the stronger age gradient of inequality and to the earlierreversal of it by age than by experience. In published empirical re-search, this reversal was noted as a persistent feature of relativeearnings structures.6

The distinction between cross-sectional and cohort patterns of

5. Some evidence on the particu'ar importance of the variation in weeks worked atlower levels of schooling is seen in the comparison of Charts 6.2 and 6.3 and in Table7.2, below.

6. Cf. Morgan (1962).


marginal relative variances can be analyzed by means of equation6.5, above, as were the dollar variances. The implications are similar,except that because of differences in the numbers included in theold and young age groupings within schooling groups, the cross-sectional relation of inequality to schooling has a more negative tiltthan that in the cohort, though still somewhat U-shaped, as Table 6.3,column 1, indicates.

Since the purpose of this study was to relate the structure and in-equality in the distribution of earnings to the distribution of amountsinvested in human capital, individual variation in rates of return wasignored. However, in studying the patterns of residuals variation inrates of return cannot be entirely ignored. But a hypothesis that theobserved residual variances contain mainly variation in rates of returnrather than variation in post-school investment can be rejected. It wasshown, in Part I, that the assumptions o-2(r) > 0, while = 0,leads to a monotonic increase in the residual dollar variances overworking life, provided 0. However, = 0 means that thesame dollar amount is invested by each individual, so the invest-ment ratio, is perfectly negatively correlated with earnings But thatwould produce sharp monotonic decreases in log variances over thelife cycle. The empirical evidence contradicts such a hypothesis.

The hypothesis that cr2(r) > 0 and = 0, while > 0, meansthat there is a perfect positive correlation between and E8. How-ever, the strong decay of the correlation between schooling and earn-ings shown in Table 3.4 (Chapter 3) contradicts this hypothesis.

I conclude that post-school investment varies among personswith the same schooling both in dollars and in time-equivalents. Thevariation in rates of return has no effect on the profiles of residualvariances, unless there is post-school investment and it has a non-zero variance. Indeed, the latter is a sufficient explanation of the pro-files of residual variance shown in Charts 6.1—6.3. This, of course,does not deny the existence of dispersion in rates of return.7

The negative ranking of inequality with respect to schoolingseen in the profiles of relative variance in the earlier stages of work-ing life and the reverse ranking later are in no obvious way related to

7. Indeed, as I argued in Chapterl, post-school investment has no effect on thedistribution of earnings in the overtaking set. Hence the residual variance in that dis-tribution, after correction for schooling quality and weeks worked, can be inter-preted as resulting from individual variation in rates of return.


secular trends in human capital, such as the upward trend in school-ing. The presence of these trends does affect our understanding ofthe cross section, as we noticed, only when we aggregate the two-way groupings (age and schooling) into marginal, that is, one-waygroups (age or schooling). Because of these trends, higher schoolinggroups are more prevalent at younger ages, and conversely. In aggre-gating cross sections, therefore, parameters of the more educatedgroups receive greater weight in the younger age groups, and thoseof the less educated receive greater weight in the older ones. Giventhe reversal of profiles of inequality, therefore, the stronger the up-ward trend in schooling, the greater the attenuation of aggregate in-equality, as larger weights are attached to the smaller relativevariances. Or, to put it differently, if there were no trends in schooling,and the distribution of schooling in each age group were the same asthe currently observed distribution among all earners, regardless ofage, aggregate inequality would be larger than currently observed.The hypothetical distribution would, in effect, be a distribution overthe working life of a fixed cohort. A simulation experiment utilizing13 x 9 experience parameters and frequencies of schooling groupsshows that, under these assumptions, the aggregate log variance inthe cohort, that is, in the trendless cross section, would be 0.805compared to 0.668. Thus the growth of schooling reduces the aggre-gate inequality observed in the cross section by about 17 per cent,and this effect is obtained not by narrowing the distribution ofschooling but by diminishing the importance of groups whose post-school behavior generates a great deal of dispersion in earnings.

The same experiment which keeps the distribution of schoolingin each experience group the same as at overtaking (j = 7—9 years)yields an aggregate variance of logs of 0.721. This is an estimate ofthe inequality in the cohort which was at overtaking in 1959. Thefraction of aggregate inequality attributable to human capital invest-ment based on this figure is an estimate which abstracts from seculartrends in schooling. It is a few percentage points higher than the esti-mates based on the observed cross section.

6.2 SHAPES OF RESIDUAL DISTRIBUTIONS

Shapes of the within-group earnings distributions are portrayed inChart 6.4, which shows experience profiles of asymmetry (relative


TABLE 6.2AGE PROFILES OF SKEWNESS IN EARNINGS, 1959


Years of Schooling

5—8 12 16 5—8 12 16

Age Bowley's Coefficient Ratio: Mean to Median

20—24 .107 .039 .232 1.100 1.015 1.17825—29 —.009 —.025 .119 1.046 1.002 1.10130—34 .077 .154 .281 1.043 1.045 1.16735—39 —.028 .211 .256 1.028 1.095 1.12140—44 —.078 .180 .362 1.022 1.100 1.20045—49 .057 .222 .463 1.035 1.131 1.18250—54 .017 .200 .527 1.023 1.132 1.27155—59 .074 .252 .328 1.049 1.173 1.22060—64 —.005 .295 .584 1.051 1.238 1.410


skewness) of earnings in each of the schooling groups. The measureof skewness is Bowley's coefficient:

(P90 — Md) — (Md — P10)RSk==

where P denotes percentile and Md median of the distribution. Quitesimilar results are obtained when the ratio of mean to median is usedas a measure of skewness (Table 6.2).

Skewness grows montonically in the upper schooling groups, itsprofile is U-shaped in the high-school group, and it first rapidly de-clines and then levels off in the lowest group. Its ranking is directlyrelated to schooling level, except during the first decade of ex-perience, when the ranking is inverse. The pattern resembles the pro-files of log variances and can be interpreted in much the samefashion: A strong positive correlation between investment ratiosand earning capacities within higher levels of schooling, a weakcorrelation in the middle, and a negative correlation at the lowerlevels of schooling.

The similarity of the behavior of skewness measured by themean-to-median ratio and of the log variances is theoretically as-


sured when the distributions are log-normal.8 More generally, con-sider the experience profile of gross earnings: = + rk).

By a theorem of C. C. Craig (1936), the distribution is morepositively (less negatively) skewed than the distribution of if thecorrelation between and is zero or positive. During the firstperiod of observed earnings, = E3(1 — k0). If the correlation ofwith is strongly positive, so is that of k0 with In that case, skew-ness of initial earnings is likely to be smaller than at overtaking(E8). The U-shaped result of a near-zero correlation, and a decliningprofile of skewness due to a negative correlation are deduced in thesame way.

The association between schooling and skewness, at givenstages of experience, appears positive more often than the associa-tion between schooling and inequality (log variance), since the re-versal of ranks takes place earlier in the working life (Chart 6.4). Thisis partly because the greater incidence of employment instability re-duces positive skewness at lower levels of schooling.9 In conse-quence, in the marginal distributions skewness generally increaseswith age and with schooling (see Table 6.3). This is not only becausewithin-group skewness is larger at higher schooling levels and olderages. As noted before, in the aggregation process, the positive cor-relation between group variances and group means augments skew-ness and sharpens the gradient.

Positive skewness is a persistent feature of aggregate incomedistributions. Its presence has drawn a great deal of attention, start-ing with Pareto. Many of the theories of income distribution,'0 par-ticularly the stochastic models, which will be discussed in the nextsection, were concentrated almost exclusively on this feature of thedistribution. As we have seen, in human capital models, skewness isanalyzed and explained at several levels. In the schooling model,skewness is made conditional on the shape of the distribution ofschooling, and is not predicted as an inherent and persistent feature:the shape of the schooling distribution is exogenous to the modeland does change secularly. Already the schooling distributions ofthe younger cohorts in the United States are negatively skewed. Whythen does positive skewness persist?

8. See Aitchison and Brown (1957, pp. 22—23).9. See discussion section 7.2.

10. Cf. Mincer (1970).


TABLE 6.3INEQUALITY AND SKEWNESS IN MARGINAL DISTRIBUTIONS

OF EARNINGS, 1959(white, nonfarm men)

. LogDollar

StandardSkewness

Variance Deviation Logs a Dollars a RM b

(1) (2) (3) (4) (5)

Age25—29

30—34.433.343

2,61013,0605

—.206[—.020

1.. .1401.0151.068

35—39

40—44.388.426

4,05014,3805

—.1311.1571.167

1.1071.119

45—4950—54

.498

.5064,88015,1805

—.1511.172 1.163

1.17455—59

60—64.590.671

4,62015,4905

—.193(.1761.185

1.1621.188

Schooling(years)

Under 8 .740 2,120 .018 1.0708 .682 3,020 —.350 .066 1.0579—11 .542 3,280 .128 1.07212 .397 3,740 —.242 .178 1.11113—15 .503 5,160 .349 1.21116 or more .534 6,810 +.046 .440 1.314

a. Bowley's measure of skewness.b. Ratio of mean to median.

The answer lies in the positive correlation between dollar meansand variances in the age-schooling groups of the earnings structure.As was pointed out before, this correlation reflects persistence inhuman capital accumulation: individuals who accumulate more capi-tal over a lifetime invest larger amounts in most of the successivetime periods.

Some of the stochastic or mathematical theories of income dis-tribution generate Pareto or log-normal "equilibrium" distributions.Both forms are positively skewed. The Pareto distribution is alsopositively skewed in logs, while the log-normal one is symmetric inlogs. Observed distributions, however, are typically positively skewedin dOllars and negatively skewed in logs (Table 6.3, column 3).h1

11. See also the findings of T. P. Hill (1959).


In the 1959 earnings data, the dollar distribution of earnings atovertaking was practically symmetric. It was, therefore, negativelyskewed in logs, as was the distribution of schooling in years. Sincedollar skewness grows with experience and age, logarithmic negativeskewness diminishes correspondingly, as is shown in Table 6.3,column 3.

It also appears from the analysis of profiles of relative variances(Charts 6.2 and 6.3) that the sign of the overall correlation betweengroup means and variances in logs is neither clearly positive nornegative: Group variances are positively related to means at upperlevels of schooling and experience, negatively at lower levels. Thereis, therefore, little reason for the aggregation process to producepositive skewness or symmetry in logs in the overall distribution,when this is not true of the components. There is an implication,however, that aggregation within upper schooling-experiencegroups, hence upper earnings groups, tends to impart positivelogarithmic skewness, while aggregation within lower earningsgroups does the opposite. This may well explain the leptokurtic shapeof the overall distribution, which has been observed in a number ofstudies (Rutherford, 1955; Bjerke, 1969; Lydall, 1968). When drawnon log-normal probability paper, the graph of the cumulative distri-bution is S-shaped, strongly concave at lower levels of earnings, andconvex at upper levels. This reflects strong negative skewness (inlogs) at lower levels and some positive skewness at upper levels ofearnings. When drawn on normal probability paper, the lower levelof the graph is linear (zero dollar skewness), the upper sharply con-vex (strong positive skewness in dollars). Chart 6.5 shows that thegraph of a component distribution at a lower age-schooling groupshows a relatively good fit to the normal distribution, while the graphof a higher age-schooling group shows a closer fit to the log-normal.

Summing up: If earnings distributions are to be classified on ascale of skewness somewhere between normal distributions (zerodollar skewness), log-normal (zero log skewness), and Pareto (posi-tive log skewness), they fit between the normal and log-normal. Asindicated by the curves in Chart 6.5, shapes of component distribu-tions when ranked by average level of human capital systematicallyrange from symmetry in dollars to symmetry in logarithms. This isentirely consistent with the theoretical conjecture in Chapter 2.

CHART 6.5Fii OF ANNUAL EARNINGS DISTRIBUTIONS TO NORMAL AND LOG-NORMAL

Dollars

CURVES, 1959(white, nonfarm men)

CumulatWe probabUity

NOTE: Figures on each curve show age (inschooling completed.

parentheses) and years of


114

Logarithms

2 5 10 15 20 30 40 50 60 70 8085 90 95 98 99Cumulative probobilLty

2 5 10 15 20 30 40 50 60 70 8085 90 95 98 99

7

Random Shock, EmploymentVariation, and Aggregation

7.1 HUMAN CAPITAL VERSUS RANDOM SHOCK MODELS

According to the foregoing analysis, the "residual," that is, within-group variation in earnings can be attributed to individual variation inreturns to post-school investment, in rates of return, in quality ofschooling, and to a variety of other factors which may be lumped to-gether as the "unexplained" or, rather, "unmeasured" component

(equation 5.5).In stochastic theones of income distribution is interpreted as

year-to-year individual fluctuation in earnings and the whole struc-ture of earnings is explained by a stochastic process that is attributedto this "random shock" These models specify that:

where the are homoscedastic and mutually independent. This leadsto a monotonically increasing log variance as a function of t (age orexperience), and a positively skewed aggregate distribution (log-normal or Pareto, depending on differences in assumptions). But, as


we have seen, the prediction that logarithmic variances of incomegrow monotonically and equally in all skill (schooling) groups islargely incorrect.

The greater and richer explanatory power of the human capitalmodel need not preclude some validity in the random shock äp-proach. Moreover, some of the predictions are similar: log variancesof earnings do grow in some schooling groups and over certainphases of the working life. Even so, the same empirical phenomenaare differently interpreted in the two models. In the stochastic modelstemporal variation in income is interpreted as chance variation. Incontrast, in human capital models, much of the temporal variation inearnings is viewed as a systematic and persistent consequence ofcumulative investment behavior. Discrimination between the two

be sought in so-called panel correlations of earnings ofthe same cohort in two different time. periods.

If we follow the earnings experience of a cohort m years afterthe initial year t, the random shock model implies that: (1) logvariances will increase by the same amount each year, so that:

cT2(lfl Yt+m) = + (7.1)

and (2) panel correlations, that is, correlations between In andIn Yt+m, will decay continuously as the interval m is widened:

R2(ln In Yg+m) = v (7.2)'t+m)

and

1 r a2(€) 1+mYe)]

(7.3)

According to the random shock model, both variances and thereciprocals of the coefficients of determination should increaselinearly with the time interval m. We have already seen (Charts 6.2and 6.3) a contradiction in that the profiles of variances are notlinear. If it could be assumed that the profiles are linear, the steeperslope at the higher schooling level (Charts 6.2 and 6.3) implies agreater importance of random shock there, that is, a larger o.2(€),hence a more rapid decay of panel correlations in the higher school-ing groups (since a'2(€)/o-2(ln would be larger at higher schoolinglevels). Again, this implication is not substantiated in Table 7.1,

TA

BLE

7.1

NO

TE

: Ear

ning

s at

t ye

ars

of e

xper

ienc

e ar

e co

rrel

ated

with

ear

ning

s at

t +

m y

ears

of e

xper

ienc

e; t

+ m

is in

195

9 fo

rea

ch o

f the

coho

rts;

m =

2, 7

, or

11, a

s in

dica

ted

in th

e co

lum

n he

adin

gs.

PA

NE

L C

OR

RE

LAT

ION

S O

F M

ALE

EA

RN

ING

S, B

AS

ED

ON

CO

NS

UM

ER

S U

NIO

N P

AN

EL,

1959

SU

RV

EY

—4

Yea

rs o

f Sch

oolin

g

All

Initial

Year(t)

l2orLess

13-15

16

l7orMore

22

711

711

27

11

27

11

27

11

Coefficients of Determination

(R2)

4.989

.227

.312

.911

.444

.518

.854

.302

.376

.803

.441

.316

.822

.388

.430

7.951

.220

.268

.852

.324

.265

.691

.383

.381

.760

.430

.388

.752

.426

.348

9.711

.491

.279

.800

.396

.483

.712

.598

.527

.800

.461

.381

.785

.503

.453

12.8

37.6

54.4

98.9

07.6

48.6

16.8

89.5

81.5

52.8

97.5

28.6

79.8

78.5

78.5

86

15.8

46.5

20.4

12.8

16.6

84.5

07.9

32.5

38.6

15.8

73.5

55.6

08.8

24.6

30.6

08

18.8

18.5

88.3

99.8

98.6

04.5

91.9

18.6

52.6

62.8

87.6

52.7

39.8

98.6

81.7

14

21.8

99.4

83.4

98.8

39.6

99.6

43.8

74.7

71.7

55.9

25.7

71.5

96.8

71.7

16.6

58

24.

.828

.419

.403

.931

.764

.688

.966

.768

.715

.908

.868

.637

.930

,.7

88.6

48

27.9

02.6

82.7

44.9

35.8

01.8

60.9

55.7

65.7

57.9

82.7

94.4

19.9

52.7

93.7

81

Ave

rage

.864

.476

..4

23.8

76.5

96.5

74.8

65.5

95,

.593

.870

.611

.529

.856

.611

.580

Rec

ipro

cals

of R

2

Ave

rage

of

t=4,

71.

031

4.47

53.

468

1.13

52.

669

2.85

21.

308

2.96

02.

641

1.28

02.

301

2.87

21.

272

2.46

22.

598

AU

1.16

52.

451

2.58

81.

143

1.83

41.

914

1.17

01.

845

1.89

61.

155

1.74

42.

051

1.17

21.

735

1.83

3

t= 1

21.

170

1.84

52.

129

1.12

91.

440

1.57

61.

085

1.50

31.

498

1.09

71.

505

1.68

31.

128

1.45

11.

515


which is based on a 1959. survey of the Consumers Union Panel,1 andcontains panel correlations (A2) and their inverses (1/R2). Data onpast earnings from which the correlations were calculated are basedon recall of respondents. Recall data probably contain a great deal oferror, which may affect the level and pattern of the coefficients ofdetermination. In an attempt to minimize this error, correlations ofearnings at t and t+ m years of experience were observed only inthose cohorts whose experience did not exceed t + m. Thus, onlyrows in Table 7.1 pertain to given cohorts. Years of experience wereprovided by respondents as time elapsed since they first enteredfull-time employment.

Despite the unpredictable effects of errors in such data, thereare two features in the table that are noteworthy: (1) As the interval mis widened from two to seven years, the correlation declines sharplywhen the panel base t is in the first decade of experience. The de-cline is much milder thereafter. (2) When the interval m is widenedfurther, from seven to eleven years, the decline in correlation, if any,is negligible. The growth in hR2 is not linear, particularly over theearlier decades of experience. These findings are clearly inconsistentwith the random shock model. They do seem reasonable in the light ofthe human capital model: panel correlations bracketing the overtak-ing stage would be expected to be relatively weak, but strongerthereafter.2 The sharp deceleration or even halt in the decline of cor-relations beyond a seven-year span is not implausible: beyond over-taking, the ranking of individual earnings acquires a long-run sta-bility, though disturbed by short-run, "transitory" fluctuations.

The panel correlations are consistent with a human capital model

1. There were 4,191 usable responses in the recall data. Over half of the re-spondents were college graduates. For a detailed description of the data, see Juster(1964).

2. When the interval brackets the overtaking point, we are correlating

In

witht+m—1

In E8 + (rk, — ki+m).1=1

By definition, the post-school investment component of earnings is negative beforeovertaking and positive thereafter. The bracketing, therefore, introduces a negativecorrelation between the investment components of earnings, which weakens the panelcorrelation. Indeed, if E8) were zero, this correlation would be negative.

RANDOM SHOCK, EMPLOYMENT VARIATION, AND AGGREGATION 119

in which post-school investments and their ratios to earnings varyamong individuals > 0]. In a model in which this variation is de-emphasized but the variation in rates of return is stressed instead[o2(r) > 0], the implicit panel correlations would be high and inde-pendent of either the span of the panel interval m or the stage in theworking life. Since the current-investment component is, in that case,constant for all individuals, panel correlations of net earnings wouldbe the same as panel correlations of gross earnings. It is preciselythe difference between net and gross earnings that creates some ofthe indicated features of the observed panel correlations.

7.2 VARIATION IN EMPLOYMENT AS A FACTORIN EARNINGS INEQUALITY

The finding that systematic investment components account for alarge part of the temporal and individual variation in earnings doesnot preclude the existence of a random component panei correla-tions are certainly less than unity. But even a modest random com-ponent need not have the stochastic properties specified in the ran-dom shock models. Instead of being independent of the previouslevel of income, thereby creating an explosive variance, the random"transitory" component may be unrelated to a latent "permanent"level of income, so that the variance does not change much overtime, if at all. Under this formulation, introduced by Friedman (1957),the contribution of the "transitory" component to total income in-equality was estimated from income and consumption data to beabout 20—30 per cent. This fraction is probably somewhat smaller inearnings than in total income,a and roughly compares in size to myestimates of the separate contributions of age variation and em ploy-ment variation to total earnings inequality. The size of the log vari-ance of earnings at the overtaking stage of the life cycle is about 25per cent smaller than the aggregate variance, which may be viewed asa rough estimate of the contribution of age variation to total in-equality. The contribution of employment variation, according to theregressions in Table 5.1, was also nearly one-fourth of total inequal-ity.

3. "Transitory" variation in property and self-employment income is likely to bemore pronounced than in earnings.


Which of the two factors should be considered transitory? Theirjoint contribution greatly exceeds the contribution of "transitories"as estimated from consumption data. The answer is that not all of theage variation can be considered transitory in the sense used in con-sumption studies: the consumption "horizon" is short relative to thefull length of the earnings profile. Similarly, not all of the employmentvariation, such as in weeks worked during the year, is transitory:some persons usually work less than others, some regularly exper-ience greater turnover and unemployment than others.

Some of the "permanent" variation in weeks worked is an effectof human capital investments: larger investments by workers and em-ployers tend to reduce worker turnover and unemployment (Becker,1964, p. 18 ff.). Moreover, increased wages resulting from humancapital investments may affect the labor supply. In either case, to theextent that employment during the year is an effect of human capitalinvestments, and not an independent factor, the contribution of em-ployment variation to earnings inequality should be credited to thedistribution of human capital.

The theory of specific human capital (Becker, 1964) predicts aninverse relation between employment stability and the quantity ofinvestment.5 Assuming a positive correlation between specific andtotal post-school investments, as well as between schooling and jobtraining—all measured in dollar costs—the empirical prediction is ofa positive relation between schooling or age and the mean numberof weeks worked in a group, as well as a negative relation betweenschooling or age and the standard deviation of weeks worked in thegroup. Table 7.2 shows that these relations do hold.

The fact that weeks worked and their dispersion are inverselyassociated across schooling and age groups6 suggests that the em-ployment factor represents a force in the direction of negative skew-ness of earnings. The incidence of underemployment is strongest atthe lower levels of skill—a fact consistent with human capital theory.Yet for earnings distributions the employment implications of human

4. The planning horizon" of the consumer may be measured by the inverse ofthe consumer discount rate.

5. Human capital investment is specific to a firm to the extent that it increases themarginal productivity of workers in the firm more than in other firms.

6. This negative correlation of means with variances produces negative skewnessof the aggregate distribution of weeks worked.

w


TABLE 7.2WEEKS WORKED IN 1959, BY AGE AND SCHOOLING


Years of Schooling

5—8 12 16

o2(W) cr2(W)

Age W o(W) u2(ln Y) W ff(W) ff2(In Y) W a'(W) o'2(ln Y)

20—24 43.5 .288 .692 45.0 .209 .51825—29 44.2 .218 .485 48.4 .130 .333 46.9 .158 .36830—34 45.7 .179 .432 49.0 .105 .250 49.7 .074 .10435—39 45.9 .175 .397 49.0 .099 .200 40.6 .081 .11740—44 46.3 .175 .383 49.3 .125 .308 50.3 .074 .07845—49 46.0 .173 .353 48.7 .128 .250 49.8 .097 .07650—54 45.9 .168 .329 48.5 .133 .237 49.5 .093 .08655—59 45.6 .195 .413 48.5 .117 .165 49.0 .056 .02660—64 44.8 .232 .509 47.7 .129 .195 48.2 .143 .114

W= mean number of weeks.o(W) = standard deviation of (logs of) weeks.

cr2(W)/u2(ln Y) = ratio of variance of weeks to variance of earnings (inlogs).

capital theory are the exact opposite of the direct productivity impli-cations of the same theory. The latter produce a positive correlationbetween means and variances of subgroups, the former a negativecorrelation. Thus, the distribution of annual earnings shows moreinequality and less positive skewness than the distribution of weekly,hourly, or full-time earnings (Mincer,

7.3 FEMALE8 AND FAMILY DISTRIBUTIONS

The relative contribution of employment dispersion to earnings in-equality is fairly important in population groups with full and per-manent labor force attachment, but it is much more important in

7. For an analysis of the effects of cyclical changes in employment on the distribu-tion of earnings see Chiswick and Mincer (1972).

8. For a more intensive human capital analysis of earnings of women, see Mincerand Polachek (1974).


TABLE 7.3EARNINGS PROFILES OF WOMEN AND MEN, BY SCHOOLING, 1959

Age

Years of Schooling a

Elementary High School College All

Women Men Women Men Women Men Women Men

Hourly Wage Rates

25—34

45—54

All

1.37 2.181.43 2.541.41 2.40

1.78 2.57 2.55 3.301.83 3.16 3.01 5.331.74 2.78 2.77 4.31

1.821.851.76

2.623.182.87

CoefficIents of Variation of Annual Earnings

30—34

All workersYear-round

50—54


30—54


.62 .47

.41 .42

.65 .52

.47 .47

.69 .67

.49 .59

.60 .50 .56 .51

.38 .46 .41 .48

.62 .64 .56 .67

.48 .59 .50 .65

.70 .66 .62 .68

.48 .58 .50 .62

.69

.49

.68

.55

.77

.57

.57

.52

.73

.67

.74

.67

SOURCE: Hourly wage rates: Fuchs (1967, Table A-i); coefficients: 1/1,000 sampleof U.S. Census, 1960.

a. In upper panel, "elementary" refers to individuals with 5—8 years of schooling;"college," to those with 16 years or more. In lower panel, "elementary" refers to8 years of schooling; "college," to 16 years. High school" refers to 12 years ofschooling in both panels.

groups whose attachment is weak. Men and women exemplify thesedifferences in labor force behavior. The distribution of annual earn-ings of men is largely similar to the distribution of full-time maleearnings. However, the earnings distribution of all women workers isquite different from the full-time distribution. The inequality in an-nual earnings of all women workers is larger than the inequality in thecomparable male distribution, while the opposite is true of full-timeearnings (Table 7.3).

Some of the differences between earnings distributions of menand women can be explained by the effects of labor supply behavioron human capital investment decisions. Individuals who expect tospend only a part of their adult lives in the labor force have weakerincentives to invest in forms of human capital which primarily en-


hance market productivities than persons who expect to be per-manently attached to the labor force. Women are likely to invest lessthan men in vocational aspects of education, particularly in on-the-job training. This is reflected in the comparative (to males) structureof their full-time earnings by flatter age-earnings profiles (Table 7.3,upper panel), smaller variances within school and age classes, andless aggregate inequality of earnings (Table 7.3, lower panel).

The changes of relative inequality with age and schooling thatwe observed in the earnings structure of men are also less pronouncedin the full-time earnings of women, and completely obscured in an-nual earnings (Table 7.3, lower panel).

Mean annual earnings of women are substantially lower thanearnings of men. Sex differences in employment behavior and in hu-man capital investment behavior are important causes of differencesin means, as they are in affecting the variances and shapes of each ofthe distributions. An intensive analysis of these differences is outsidethe scope of the present study, as are comparisons of white, nonfarmmen with other groups of men.

Given the greater variance and lower mean of earnings of femaleworkers, a distribution of earnings of all workers, which includes bothsexes, must show a greater inequality than the earnings of menalone,9 as is clear from the aggregation formula (2.12):

dfl.

From many points of view, the "intensive" aggregation of maleand female earnings within family units is of greater interest than the"extensive" aggregation of persons. Certainly, analyses of consump-tion behavior and notions of economic welfare are more closely linkedto family than to personal distributions of income.

For simplicity, let us abstract from nonemployment income.Then, as a matter of arithmetic, dollar dispersion in family earnings isa positive function of the variances in earnings of family earners andof the correlation between these earnings:

= + + 2 Coy (YM, YF); (7.4)

where YM = LMWM; LFWF. Here T denotes family; M, husband; F,wife; L, hours of work; and W, wage rate. The sign of the covariance

9. This is confirmed by the data shown in Schultz (1971, Table 2).


depends partly on the correlation between the earning power (wagerates) of family members, and partly on their labor supply functions.The correlation between earning power, which is positive (classifiedby education for example), tends to impart a positive sign to the co-variance; however, the income effect in the labor supply relationstends to influence the covariance in the opposite direction.

It is perhaps easiest to explain these tendencies if we considerthe sign of Coy (In YM, In YF) which, on the assumption of mono-tonicity, is the same as the sign of Coy (YM,

Let the labor supply function be:

lnLF=a+/3InYM+ylnWF. (7.5)

By (7.5):

In Yp=a+f3 In YM+(1 +y)ln WF. (7.6)

If In YF is regressed on In the observed slope is:

+y)bwpyM, (7.7)

where bwpyM is the slope of the regression of wives' wage rates onhusbands' earnings, in logs.

>

____

1J

Empirical work on labor supply functions (cf. Mincer, 1962; Cain,1965; Bowen and Finegan, 1969) of married women suggests that J3'is close to zero; hence Coy (In YM, In is in the neighborhood ofzero. Since bwpyM is smaller when YM contains more of the transitorycomponents, the covariance tends to a smaller positive or larger neg-ative size in such groups.

When relative variances are considered, it is convenient to usethe expression:

VT = YM(1 + RF), (7.9)

where RF = The covariance In In (1 + RF) is of the samesign as

Coy (In YM, In RF) = Coy (In YM, In YF — In YM) (7.10)

= Coy (In YM, In YF) — cr2(ln YM).

Clearly if the first term on the right in equation (7.10) is close to zero,

as seems to be the case, the covariance on the left must be large and


negative. Again, it is stronger when YM contains transitory elementsthan otherwise.

The conclusion that the correlation of components of family in-come, Coy (YM, YF), is likely to be small, and even smaller when theearnings of heads of household contain transitory elements, impliesthat dollar variances of family earnings exceed those of husbands'earnings, and more so in families where husbands.work full time.

Similarly, the conclusion that Coy (In YM, In RF) is large and neg-ative suggests that relative variances of family income tend to besmaller than the inequality of the separate earnings of husbands orof wives, though this is less likely in distributions restricted to full-time working husbands.

These implications are empirically verified in Table 7.4 (page 126,below) based on the 1/1,000 sample of 1959 Census data, as theywere previously in the 1950 BLS Survey of Consumer Expenditures.1°Growth of the female labor force, while increasing the earnings in-equality among all persons, has actually been a factor in the mild re-duction of money income inequality among families.1'

7.4 AGGREGATION OF OMITTED GROUPS

The population group of white, nonfarm men, the major empiricalfocus of this study, represented about 70 per cent of all male earnersin 1959. Omitted are all nonwhite men, as well as white men who arestudents, men over 65, farm workers, and the self-employed. Theseomitted groups of male whites are characterized by highly dispersed,fluctuating, and often intermittent earnings. Analysis of their earn-ings distributions is outside the scope of this study. This is not to saythat human capital analysis is not applicable to these groups. It istrue, however, that employment variation, which is treated in alargely ad hoc manner in this study, must receive a great deal ofattention in the analysis of such groups.

As far as overall inequality (measured in variances of logs) isconcerned, the addition of a comparable nonwhite group to thewhite group (nonstudent, nonfarm, less than 65 years of age) in-

10. Cf. Mincer (1960, Table 4). Both tables show family incomes rather than earn-ings, a source of rather slight inaccuracy.

11. Cf. findings of D. Metcalf (1971) for the United States, and of H. LydalI (1959)for Britain.


TABLE 7.4HUSBANDS' EARNINGS (YH) AND FAMILY INCOME (Yr), 1959

VH VT o(YH) o(YT) cr(ln YH) o(ln YT)

All Families, Wife PresentAge

15—24 3,560 5,180 2,080 3,310 0.695 .61625—34 5,510 6,830 2,850 3,780 0.557 .511

35—44 6,610 8,454 4,210 5,520 0.586 .54745—54 6,520 9,100 5,100 6,520 0.656 .61255—64 5,970 8,620 5,200 6,790 0.754 .68365 and over 4,310 7,140 5,430 6,690 1.046 .750

Schooling5—8 4,690 6,610 3,040 4,230 0.697 .61012 6,060 7,960 3,790 5,070 0.678 .60016 9,000 11,210 6,950 8,450 0.678 .600All 5,890 7,530 4,330 5,580 0.692 .628

Husbands Working Year-roundAge

15—24 4,070 5,530 2,070 3,290 0.527 .51825—34 5,880 7,140 2,840 3,770 0.453 .45135—44 7,040 8,880 4,250 5,650 0.488 .49045—54 7,110 9,710 5,340 6,720 0.534 .53855—64 6,660 9,310 5,490 7,030 0.612 .61065 and over 6,140 8,980 6,390 7,740 0.782 .639

Schooling5—8 5,300 7,180 3,120 4,280 0.497 .50812 6,370 8,220 3,790 5,100 0.476 .48316 9,550 11,750 7,060 8,660 0.593 .575All 6,490 8,460 4,460 5,800 0.540 .536


creases inequality by no more than 2 percentage points. This is be-cause the nonwhite group is relatively small, and its relative varianceis not larger than that of the white group. The small effect is due al-most entirely to the differences in means of the two groups.

When all male wage and salary earners are compared with themore homogeneous subgroup we studied, the (log) variance of an-nual earnings rises to 0.78 from 0.67. Finally, inclusion of self-


employed and nonemployment income raises aggregate inequalityin male annual earnings to 0.92)2

It is worth noting, though without elaboration at this point, thatwhether we move toward a more inclusive ("extensive") aggregationof population groups, as described here, or an "intensive" aggrega-tion of income into a larger recipient unit, as described in the com-parison of husbands' and family income, the characteristic age-schooling structure of income which we observed in earnings ofwhite men remains very similar. Thus, the empirical "predictions" ofhuman capital analysis are not fatally obscured by differences in con-cepts of population, recipient unit, or even (to some extent) income)3

12. This is probably an understatement, as nonemployment income is underesti-mated in the Census.

13. This despite the different effects on inequality that are produced by "exten-sive" and "intensive" aggregation. My examples of each suggest that extensive aggre-gation tends to widen inequality (relative dispersion), while intensive aggregation tendsto narrow it. A more rigorous statement is that an extensive aggregation of com-ponents produces an aggregate relative dispersion which exceeds the weighted aver-age of component dispersions, while intensive aggregation produces a smaller thanaverage inequality. The tendency to widen inequality by extensive aggregation issimply due to the existence of differences among means of components > 0, inaggregation formula (6.5). The opposite tendency in intensive aggregation is bestviewed in terms of the coefficient of variation: given components of earnings, withmean S' and variance mean of total earnings = and r(Yr) =Only if the components are pairwise positively and perfectly correlated is the standarddeviation of a sum equal to the sum of standard deviations. Hence the aggregate co-efficient of variation

-

CVT< C

VT CYT

In the special case, where all are the same, aggregate inequality is neces-sarily less than the component inequality

8

Summary and Agenda

8.1 SUMMARY OF FINDINGS

The first task of the study was to derive and estimate the relation be-tween accumulated investments in human capital of workers andtheir earnings. This human capital earnings function was then appliedto answer two questions: (1) How much of the existing inequality inthe distribution of labor incomes can be attributed to individual dif-ferences in investments in human capital? (2) Can the intricate yetrather stable patterns of the earnings structure be understood interms of human capital investment behavior? The "earnings struc-ture" is the aggregate earnings distribution and its partition intoschooling and age subgroups. The "patterns" are the comparativesets of means, variances, and shapes of the component and aggre-gate distributions of earnings.

The summary which follows is by no means comprehensive, nordoes the exposition follow the sequence or methods of the analysis.The findings are described broadly and somewhat selectively interms of the three research objectives of the study:

SUMMARY AND AGENDA 129

8.1.1 THE EARNINGS FUNCTION

If completion of schooling meant completion of investment in humancapital, the earnings function would be approximately estimated by asimple regression of earnings (in logs) on years of schooling. As thepresent study indicates, the observed correlation using this 'school-ing model" is rather weak. Variation in earnings associated with ageis not captured by the schooling model, and this omission is, in part,responsible for the low correlation. Though age can be viewed as aninherent depreciation phenomenon in the human capital terminology,the growth of earnings with age can ultimately be interpreted in thehuman capital model as being a consequence of net self-ihvestmentactivities that are continued after the completion of schooling. Thetheory predicts that investments are concentrated at younger ages,but continue at a diminishing rate throughout much of the workinglife; because of increasing marginal costs, investments are not madeall at once in a short period, but are staggered over time, and declinecontinuously, both because benefits decline as the payoff periodshortens, and because opportunity costs are likely to rise with ex-perience. This is true of both gross and net investments.

Since earnings are a return on cumulated net investments, theyalso rise at a diminishing rate over the working life, and declinewhen net investment becomes negative, as in old age. The typical(logarithmic) working-life earnings profile is, therefore, concave frombelow, as illustrated in Chart 4.3. Its rate of growth is a positive func-tion of the amount invested and of the rate of return. Its degree ofconcavity depends on how rapidly investments decline over time. Ineffect, the earnings profile is directly proportional to the cumulatedinvestment profile. The magnitude of the cumulated investment can-not to be observed, but it is a concave function of experience. Hence,to expand the schooling model into a more complete earnings func-tion, the linear schooling term must be augmented by a nonlinear,concave, years-of-experience term. This function can be applied inmultiple regression analysis to earnings data of individuals who differin both schooling and age. While age is not the same as work ex-perience, the latter can be estimated as actual age minus estimatedage at completion of schooling, though direct information on ex-perience is preferable. Clearly, direct information on experience is


necessary for specifying earnings functions of individuals whose at-tachment to the labor force is not continuous.1

The human capital earnings function may be expressed either indollars or in logs. In part, the choice depends on whether absolute orrelative earnings inequalities are to be examined. If dollar values areused, the investment variables (schooling and experience) must alsobe expressed in dollars. If log earnings are used, then the investmentvariables can be expressed in units of time—years of schooling andyears of experience. The time measures of investment are far morereadily available than the dollar ones. For both reasons then—interest in relative comparisons and data availability—the logarithmicformulation is preferred.

The next choice concerns the specification of post-school in-vestment as a function of time. Here the only guidance provided bytheory is that annual instalments of post-school investment, and, afortiori, their time-equivalents, must decline over the working life.

The form of the investment profile determines the form of theearnings profile. To take the two simplest forms, a linear investmentdecline implies a parabolic experience function, while an exponentialdecline of investment ratios gives rise to a type of Gompertz function.The latter yields a somewhat better fit, though such discrimination israther weak. The Gompertz curve requires no decline of the earningsprofile, a condition that is largely satisfied if data are restricted tofour decades of working life and to weekly (or hourly) earnings. Theseconditions are fulfilled in the empirical analyses of annual earningswhen weeks worked during the year are used as a standardizing vari-able.

The two forms of the human capital earnings function used inthe analysis are the logarithmic parabola (P) and the Gompertzcurve (G):

In In E0 + t2; (P)

In E8,1 = In E0 + r3s + (1 — e'39 (G)

E8,1 is gross annual earnings of a worker with s years of school-ing and t years of work experience. "Gross" earnings are inclusive,

1. Analyses of female earnings demonstrate dramatically that it is experiencerather than age that matters (Mincer and Polachek, 1974).


"net" earnings exclusive, of investment expenditures. r8 and arerates of return on schooling and post-school investments, respec-tively. k0 is the ratio of investment to gross earnings at the start ofwork experience, and f3 is the annual decline of this ratio. T is thepositive net investment period.

In principle, the earnings function represents a unification ofanalyses of investment parameters and income distribution; it pro-vides an analytical expression for the earnings profile as an indi-vidual growth curve. Its coefficients combine estimates of rates ofreturn and volumes of investment. At the same time, the coefficientof determination of the multiple regression measures the fraction oftotal earnings inequality (variance of logs) that can be attributed tothe measured distribution of investments in human capital.

The standard procedure for estimating a rate of return to educa-tion involves discounting of differences in earnings between twogroups differing in education. However, the estimated rate is not arate of return to schooling but a weighted average of returns toschooling and to other investments in human capital in which thetwo groups differ.

In contrast, the earnings function regression procedure doesnot require pairwise comparisons and can be used to separate esti-mates of rates of return to schooling from the rates on other (post-school) investment activities. In the empirical work, the estimates ofrates of return to schooling are produced unambiguously, but thisis not quite true of the rate on post-school investments. Rough testsof the difference between these parameters are possible, however:at the present aggregative level of information, the null hypothesis ofno difference cannot be rejected. Whether rates of return differ atdifferent schooling levels can also be tested. The finding is that ratesdecline as schooling level rises for annual earnings, but not forhourly or weekly earnings.

Use of earnings functions also makes it possible to study the re-lation between schooling and post-school investments. In dollarvolumes the relation is found to be positive. This finding is consistentwith a notion of complementarity between the two investment forms,but does not constitute a proof. The positive correlation may simplymean that in comparing individual lifetime investment programs, thescale of investments varies more than their composition. On the basisof the comparative advantages enjoyed by different people and dif-


fering relative price structuresone form of investment for theand opportunity constraints inviduals tend to invest more oroutweigh substitution effects.

It should be noted that though more educated people invest moredollars after completion of schooling, they do not spend more timein post-school investments. The investment-earnings ratio wouldmeasure the amount of time (in years) spent in investment (training)

of time were involved. On the average,activity, if only expendituresthe correlation between "time-equivalents" (that is, investment-earnings ratios) of school and post-school investments appears to beweakly negative. The opportunity cost of an hour is, of course,greater at higher levels of schooling; hence, there is a positive cor-relation between dollar volumes of investment and schooling, eventhough "time" volumes are uncorrelated.

The Gompertz curve is a familiar empirical representation of in-dustrial growth. Its fit as an individual growth curve of earningsis no mere coincidence, as the staggered investment interpretationis suitable in both cases. There is a widespread view that differswith this interpretation of individual earnings growth. According tothis view, the individual earnings curve is intrinsically an agephenomenon: it reflects productivity changes due to inherent bio-logical and psychological maturation, leveling off early and declin-ing much later because of declining physical and intellectual vigor.There is evidence, however, to indicate that aging affects earningsonly to a minor degree. In data where age and work experience canbe statistically separated, the position and shape of earnings curvesis found to be mainly a function of experience, not of age. Earningsprofiles differ by occupation, sex, and color in systematic ways thatcannot be attributed to aging phenomena. What is sometimesthought to be an alternative interpretation of the earnings profiles as"learning curves" is not at all inconsistent with the human capitalinvestment interpretation, provided it is agreed that learning in thelabor market is not costless: even if apparently costless differential"learning-by-doing" opportunities exist among jobs, competitiontends to equalize the net returns, thereby imposing opportunity costson such learning.

among them, individuals substituteother. Yet, because of similar abilityschooling and in job training, mdi-less in both. Evidently, scale effects


8.1.2 ACCOUNTING FOR INCOME INEQUALITY

As noted before, if only years of schooling are used in the earningsfunction, the correlation between years of schooling and (log) earn-ings of men of working age is less than 10 per cent. This does notmean, however, that schooling is unimportant. In part, the correla-tion is low because a mere counting of school years does not ade-quately measure direct costs of schooling and related quality aspectsof education. Moreover, when the effects of post-school investmentsare not explicitly specified, they obscure the effects of schooling onearnings. If post-school investments differ among individuals andare important, the distribution of earnings will be increasinglyaffected by returns to accumulating post-school investments asyears of experience increase. If post-school investments are notstrongly correlated with schooling, the correlation between school-ing and earnings will continuously decay with the passage of years ofexperience. The correlation between time-equivalents of school andpost-school investment is certainly weak. The correlation betweenearnings (in logs) and schooling (in years) is, indeed, initially strong,reaching a coefficient of determination of one-third before the firstdecade of experience is over, but it declines continuously thereafter.

Theoretically, the correlation would be highest at the outset ofwork experience if post-school investment costs were included aspart of income. Such initial "gross" earnings cannot be observed.However, the distribution of observed ("net") earnings 6—9 yearslater is likely to resemble the distribution of initial "gross" earnings,since net earnings are less than gross earnings, and both rise as post-school investments cumulate; after some years, net earnings begin toexceed the level of initial gross earnings. This "overtaking point" isreached after at most 1 /r years of experience, where r is the rate ofreturn to post-school investments. Hence this point is reached beforethe first decade of experience is over. In this period we observe thehighest correlation between earnings and schooling.

The coefficient of determination (.33) of schooling and earningswithin the overtaking subset of the earnings distribution representsan estimate of the fraction of earnings inequality that can be at-tributed to differences in years of schooling, since earnings are thenleast affected by post-school investments. The inequality of earnings


at overtaking is about 75 per cent of aggregate inequality, which sug-gests that the distribution of schooling accounts for 25 per cent ofthe total (.33 x .75). Together, 50 per cent of aggregate inequality,measured by the variance of logs of annual earnings, can be at-tributed to the distributions of schooling and post-school investments(Chapter 3). The 50 per cent figure is an understatement, however,since actual rather than time-equivalent years of schooling wereused. These fail to reflect quality differences among schools or thevariation in expenditures of time and money among students attend-ing schools of the same quality. An upward correction of the varianceof schooling investments to take account of such individual dif-ferences would raise the explanatory power of schooling to aboutone-third of the aggregate, and the joint effects of school and post-school investments to about 60 per cent. Transitory variation in weeksworked during the year accounts for another part of aggregate earn-ings inequality. If so, perhaps as much as two-thirds of the inequalityof "normal" (longer-run) earnings can be ascribed to the effects ofthe distribution of education and experience.

The estimates quoted above are largely indirect inferences, de-scribed in Chapter 3. If we restrict ourselves to direct (and incom-plete) regression estimates, we find that even with the use of only twovariables—years of schooling and of experience—the explanatorypower of the earnings function regressions compares favorably withresults of statistical studies of comparable microdata which employ alarge number of explanatory variables on a more or less ad hocbasis.2 It is far superior when weeks worked during the year is addedas an explanatory variable.

It appears that the substantive conclusions about the quantita-tive and qualitative importance of human capital investments in thedistribution of earnings are not much affected when the populationis extended from white urban men to all men in 1959, or changed from(male) persons to family units.

8.1.3 THE EARNINGS STRUCTURE

There are several prominent features of the "skill" (schooling and ex-perience) structure of earnings which appear rather stable in tern-

2. For a review of some of these studies, see Jencks et al. (1972).


poral and regional comparisons. Aggregate skewness and the growthof inequality with age are the best known. To these there may beadded patterns of dispersion (variances) cross-classified by school-ing and age. These are less familiar and perhaps also less stable.

The characteristic features of earnings distributions, such asaggregate skewness, and the relation of inequality to skill (or school-ing) and age (or experience) have puzzled observers since detailedstatistical data became available. Partial explanations, largely of the"random shock" variety, have been proposed.

In the human capital model, most features can be explained bythe correlation between the stock of human capital at any stage inthe life cycle and the volume of subsequent investment. That thiscorrelation is positive in dollar terms is understandable, if individualdifferences in ability and opportunity which affect investment be-havior tend to persist over much of the life cycle. The positive correla-tion between schooling and post-school investment is an example ofsuch persistence in behavior. (See Chapters 2 and 6.)

Several implications of the positive correlation between succes-sive instalments of investment in human capital in dollar terms canbe observed: Dollar profiles of earnings "fan out" with experienceand, a fortiori, with age, both across and within schooling groups.Dollar variances in these groups, therefore, increase with experienceand with age. Similarly, because the dispersion of dollar schoolingcosts increases with the level of schooling, variances of earnings in-crease with level of schooling. Since mean earnings increase withage and with schooling there is a positive correlation between meansand variances in age and schooling subgroups of the earnings distri-bution. This correlation contributes to the appearance of positiveskewness in the aggregate earnings distribution. This factor is inde-pendent of, and in a way more basic than, the shape of the distribu-tion of schooling, which in the past also contributed to the positiveskewness of earnings. The change in the distribution of schoolingduring the past two decades from positive to negative skewness im-plies that the distributicm of schooling is no longer an importantfactor in explaining the persistence of positive skewness in the dis-tribution of earnings, Indeed, the 1959 distribution of earnings at theovertaking stage of the life cycle is not skewed at all. The aggregatedistribution, however, remains positively skewed.

If we define relative skill differentials in wages by percentage dif-


ferentials in wage rates among schooling groups having comparableyears of experience, we find that these are almost invariant over theworking life. Since the logarithmic experience profiles of wages areconcave, this finding implies that relative wage differentials amongschooling groups increase with age. However, within schoolinggroups, relative wage dispersions, measured by variances of logs,show somewhat different profiles, depending on the level of school-ing. When plotted against age, all are U-shaped along at least someportion of the curve, and clearly so at the center of the schoolingdistribution, that is, for the high-school group (see Chart 6.2). Forthe post-high-school group, the profile is mainly increasing. Withinlower schooling groups, it first decreases and then levels off.

It was shown that both the wage differentials between schoolinglevels and the inequality patterns within the middle levels of school-ing reflect a negligible correlation between post-school earningcapacity and time-equivalent post-school investment. This samelack of correlation underlies the previously noted invariance betweenexperience and relative wage differentials among schooling groups.The phenomenon arises if experience profiles of post-school in-vestments, in time-equivalent units, are not systematically differentamong schooling groups. Put another way, it arises when the elastic-ity of post-school investments (in dollars) with respect to post-schoolearning capacity is, on average, unitary across schooling groups.Within schooling groups, however, the of investment withrespect to earning capacity appears to increase with schooling level:it is less than 1 at lower levels and greater than 1 at higher levels.

The size of the elasticities and the systematic positive relationbetween schooling level and elasticity of investment with respect toearning capacity raise questions for further research. In this con-nection, it is noteworthy and suggestive that very similar patternsare found in studying the consumption function: The "long-run"elasticity of saving with respect to income is not clearly differentfrom 1, and the "short-run" or cross-sectional elasticity increaseswith schooling level (Solmon, 1972).

The differential patterns of log variances by schooling level canalso be analyzed by age: the ranking of log variances of earnings isinverse to schooling level at young ages, positive at older ages. Also,the age-schooling profiles of absolute and relative wage distributionsaggregate to the well-known leptokurtic shape, with a skewness thatis positive in dollars and negative in logarithms. Together with some


observations on correlations of earnings of members of a Con-sumers Union panel, the distinctive profiles of relative variancesconstitute strong evidence for the human capital and against thepurely stochastic theories of income distribution: Systematic,rather than chance, variation dominates individual earnings his-tories and individual differences in earnings.

8.2 SOME QUESTIONS AND AN AGENDA FORFURTHER RESEARCH

8.2.1 ABILITY, OPPORTUNITY, AND INVESTMENT

The model of worker self-investment as the basic determinant ofearnings might be criticized as giving undue weight to the supply ofhuman capital while ignoring the demand side of the market. Cer-tainly, demand conditions in general, and employer investments inhuman capital of workers in particular, affect wage rates and timespent in employment, and thereby affect earnings. It should be clear,however, that the earnings function in this study is a 'reduced form"equation, in which both demand conditions and supply responsesdetermine the levels of investment in human capital, rates of return,and time worked. The present approach is an initial and simple one,and greater methodological sophistication is clearly desirable. Thereis a need to relate employers' behavior both as demanders of and di-rect investors in human capital to the observed distribution of earn-ings.3

The investment-earnings relation in this study is in reduced formalso in the sense of describing equilibrium loci in the (human)capital market as well as in the labor market in which human capitalis supplied as a factor of production. As Becker describes in hisanalysis, the cross-sectional earnings function results from twosimultaneous structural relations in the (human) capital market.These are demand functions (Di), which relate individual investmentsto marginal rates of return, and supply functions (S2), which relatethe volume of funds that can be obtained for human capital invest-ment to their marginal "interest" costs. Of course, worker demandfor self-investment (D1) is, in part, derived from employer demand forthe workers' human capital.

3. For an interesting attempt in an analysis of the earnings distribution in Japan,see Kuratani (1972).


The amount the individual invests, the magnitude of his marginaland average returns, and therefore the volume of his earnings aresimultaneously and optimally determined by the intersection of thedemand and supply curves. Overall labor and capital market condi-tions determine the group (or sectoral) levels of the D and S curves,individual levels of demand are determined by tastes and abilities,and differences in levels of supply curves represent differences ininvestment financing opportunities. Thus, it is equally correct to saythat the distribution of earnings is determined by the distribution ofaccumulated human capital and of rates of return to human capitalinvestment or that the distribution of earnings is determined by thedistribution of ability and opportunity. Or, putting it in a causalhierarchy, the distribution of accumulated human capital is a proxi-mate determinant of the distribution of earnings, and is treated thatway in this study. In turn, ability and opportunity determine the dis-tribution of human capital, and this is the focus of Becker's (1967)analysis.

A low correlation between investment in human capital and earn-ings would not constitute a rejection of the human capital hypothesis.Of course, if we had information on both volumes of investment andrates of return for each worker, the relations would be perfect andtautological. However, we are relating only volumes of (accumulated)investment to earnings, while the variation in rates of return and inunmeasured quantities of investment are left in the statistical resid-ual. Thus, aside from such measurement error, the correlation re-flects the structure of individual supply (opportunity) and demand(ability) conditions in the cross section: the wider the dispersion ofsupply and demand intersections (i.e., of rates of return at givenvolumes of investment), the weaker the correlation. The correlationwould be perfect if any of the following were true: perfect equality ofopportunity (i.e., a common supply curve for all); perfect equality ofability (i.e., a common demand curve); or perfect positive correlationbetween ability and opportunity. The greater the departure from theseconditions, the lower the correlation.

The fact that rates of return are negatively or not at all relatedto schooling level suggests that inequality of opportunity (disper-sion of supply curves) is at least as great as inequality of ability(dispersion of demand curves). At the same time, the positive asso-ciation of indexes of ability (l.Q. and other test scores) to invest-ments (schooling) suggests that ability and opportunity are positively


associated among individuals. Indeed, with sizable inequalities inability and opportunity from individual to individual, the correla-tion of human capital with earnings would be weak unlessthecorrela-tion between individual ability and opportunity were quite strong.

A single cross section, such as the 1959 one in this study, doesnot yield much insight into these aspects of the social structure, butcan provide a frame of reference for studying changes by means ofrepeated analyses of comparable periodic data, such as decennialcensuses.

To the extent that ability and opportunity affect rates of returnbut not volumes of investment, they create residual variation in earn-ings at given levels of human capital. The earnings function could beexpanded to incorporate ability or opportunity variables to accountfor some of the residual variation.4 However, the question in thisstudy is not what explains earnings, but what are the effects of humancapital investment on earnings. Moreover, the residual contains un-measured components of investment, such as quality of schoolingand within-group variation in post-school investment. Even in theresidual, therefore, ability and opportunity may be acting on earningsvia investment, rather than independently.

It is widely believed that the omission of ability from the earn-ings function creates a specification bias: leaving out a variablewhich is positively correlated with earnings and investment biasesthe coefficient of investment (average rate of return) upward.Whether this argument is correct depends on the concept of abilityand the causal structure of the model: if ability affects earnings onlybecause it affects investment in human capital, one of the variables isredundant when both are entered in the earnings function.5 When the

4. Note, incidentally, that at fixed levels of investment, ability and opportunity areperfectly negatively correlated. Both, therefore, could not be entered as explanatoryvariables in the same equation.

5. A similar redundancy occurs when parental education is entered in the earn-ings function. Parents' education is positively correlated with the education of theirchildren. Unless parents' education has an effect on children's earnings aside fromaffecting the investment in their human capital, its inclusion will obscure the esti-mated effects of human capital on earnings.

Another redundancy may result from the inclusion of occupation together witheducation in the earnings function. Occupational advancement is a medium by whichgrowth in human capital leads to higher earnings power. Entering both variables as co-ordinate leads to an apparent and misleading reduction in the coefficient (rate of re-turn) of education.


variables are not coordinate, but hierarchical, they should be treatedrecursively.

However, a specification problem does arise in my formulationof the earnings function. The function specifies accumulated (in-vested) human capital, while observed earnings are a return on thetotal human capital stock, including "original" or "initial" com-ponents and those not accumulated in the forms explicitly specifiedin the function, yet correlated with them. "Ability" may be viewed assuch an "initial" component, or E0 in my earnings function. Empiricalmeasures of ability, as imprecise as they are, have been found to bepositively associated with both schooling and earnings. Empiricalestimates of the bias in the rate of return (coefficient of the schoolingvariable) due to the omission of ability average less than two per-centage points, as against an uncorrected estimate of the rate of re-turn which exceeds 10 per cent.6 If these findings can be taken atface value, I have overstated the explanatory power of accumulatedhuman capital to some extent.

8.2.2 FAMILY INVESTMENT IN HUMAN CAPITAL OF CHILDREN

The process of investment in human capital is not restricted toschooling and job training. Much of it takes place in the home, parti-cularly during the preschool stage of the life cycle, as well as later.In empirical studies of intergenerational influences on educationalattainments it has been found that the education of parents is asignificant variable. This may be interpreted as evidence either ofthe transmission of parental tastes and motivations or of the greaterpropensity of more educated parents to invest in the education oftheir children, or both. One form of this investment is more andbetter schooling. Another is the time and other resources parentsspend on their children, which we may call "home" investments.These investments were not specified in my earnings function. Al-though time devoted to children may be viewed as a parental con-sumption activity, to the extent that measurable opportunity costs

6. This conclusion was reached in Becker's preliminary investigation (1964), andhas not been modified by a series of more intensive recent studies. See Griliches andMason (1972), Hause (1972), and a survey by Welch (1972). Somewhat greater bias wasfound in a sample studied by Taubman and Wales (1972).


are involved, an investment model can be developed for researchpurposes and can be used in the earnings function framework.

The visibi!ity of these opportunity costs emerges from researchon labor supply, viz., women reduce their market work to take care oftheir young (particularly preschool) children. The reduction inearnings which results from the reduction of time spent in thelabor market is a direct measure of the opportunity cost of theseinvestments. Estimates of these costs are feasible.7 Their analysisshould contribute to the explanation of phenomena such as the im-portance of family background in school performance of children;the effects of growing up in a broken home; the positive correlationbetween educational attainment of children and that of their parents,particularly that of the mother. Whether and how much these pre-school investments affect the children's earnings beyond affectingschool attainment of the child can only be answered by the properincorporation of the variable in the human capital earnings function.

The promise of this kind of research is its contribution not onlyto an understanding of the observed distribution of income at apoint in time, but also to the analysis of intergenerational social andincome mobility. Inferences about mobility depend on the strengthof the correlations between family income and education of parents,as well as on the structure of parental labor supply functions at dif-ferent levels of education and income. Depending on such param-eters, the same earnings function can produce different mixtures ofperpetuation and reshuffling of poverty and affluence.

8.2.3 THE DISTRIBUTION OF EMPLOYMENT AS A COMPONENTOF THE EARNINGS DISTRIBUTION

Annual earnings are a product of the wage rate and of time spent ingainful employment. Thus the distribution of employment is an im-portant component in the distribution of earnings, all the more so asthe correlation between wage rates and employment appears to bepositive, at least in the 1960 data: more skilled workers have higherannual earnings both because they are paid more per hour, and be-cause they work more during the year.

7. Research into these matters is currently being conducted by Arleen Leibowitzat NBER. See Leibowitz (1972). See also Mincer and Polachek (1974).


Much of the individual variation in weeks and hours of work israndom, particularly over short periods such as a year. Nevertheless,some of the employment variation may be attributed to differences inhuman capital, that is, to skill and experience differences amongworkers. The differences in employment, which consist of differencesin labor force participation and in unemployment, originate both onthe demand and supply side of the market. A number of hypothesesinvolving labor supply functions, health differentials, employer de-mand and investment in workers, household and market productionfunctions,8 and institutional factors, such as minimum wages andincome maintenance programs, can be brought to bear on the analy-ses of the employment distributions. Once the relation between em-ployment and wage rates is better understood, the employmentvariable, which is simply entered multiplicatively (additively in logs)in the earnings function, will be more appropriately specified. Theexpanded earnings function will appear as a product of two func-tions: the wage rate, or productivity, and the employment function,with independent variables in each. This is a schematic and opera-tional representation of how the labor market interacts with house-holds to produce the observed distribution of earnings.

8.2.4 FURTHER ELABORATION OF EARNINGS FUNCTIONS

The earnings function in this study represents an initial attempt at amore comprehensive formulation than the rudimentary schoolingmodel. The next development would be a more detailed specificationof various forms of human capital and of investment activities, be-yond the general categories of schooling and post-school invest-ment. Parental investments in children, particularly preschoolers,were already mentioned. Among other aspects of initial capacity,health levels should also be included. Both investments in health andthe life cycle of human capital depreciation, including the importantproblems of obsolescence, deserve special attention.9

The specification of schooling investments in this study leavesout direct cost components and students' earnings. As was mdi-

8. These are the subject of current research at NBER. See Mincer (1973).9. For a beginning on the subject of health in the context of human capital, see

Grossman (1972 and 1973). For attempts at analysis of depreciation plus obsolescence,see Koeune (1972) and Rosen (1974).


càted, such data, when available, can be entered in the earnings func-tion quite easily.'0

Perhaps the most important and urgent task is to refine thespecification of the post-school investment category. First, directinformation is needed on years of experience. In the present studyyears were estimated as age minus (estimated) year of graduation.For persons fully and continuously attached to the labor force thisproxy variable may serve well enough. (Still, even the analysis of maleearnings would be improved by direct information on experience, asthe National Science Foundation studies suggest.) For personswhose labor force attachment is partial and discontinuous such in-formation is indispensable.1' Of course, we need to remember that itis not the time spent in the labor market, but the volume of investmentactivity taking place during that time which determines earnings.Comprehensive data on this do not exist, but intensive even if f rag-mentary case studies might be feasible.

Even when work experience is measured in time units, the totalof it could be segmented into a sequence of jobs constituting thework history of the individual, if data were available. Whether inchronological or, preferably, in panel form, this is ultimately the wayin which the analysis of labor mobility should be incorporated intothe human capital framework.12 Search for and the acquisition of jobinformation are topics pertinent to the subject of labor mobility, buttheir inclusion in the earnings function would .depend on the avail-ability of data meeting rather exacting specifications.

8.2.5 TOWARD A FULLER ANALYSIS OF INCOME DISTRIBUTION

In sum, fuller analysis of the distribution of earnings would requireboth an expansion of the earnings function to include details (vari-ables) on a number of forms of investment in human capital, as wellas a system of equations that includes not only the investment-earnings relation but a formulation in which investment is the de-

10. Some work along these lines is currently being done by Solmon and Wachtel(1972) at NBER.

11. This point emerges forcefully from papers by Malkiel (1971) and Polachek(1973) and Mincer and Polachek (1974).

12. Longitudinal data recently collected in the National Longitudinal Samplesand by NBER (NBER-TH sample) make possible a start on such analyses.


pendent variable and another in which (time spent in) employment isthe dependent variable.

Coverage of the data used for the analyses should be expandedto include women, blacks, older people, and people who live in non-urban areas. Moreover, grouping of persons into households as wellas their behavior as members of households, needs to be studied inthe context of income distribution. For this, the merging of popula-tion, labor supply, and human capital theories is required.

Finally, to move toward the distribution of income as dis-tinguished from the distribution of earnings, nonemployment in-come must be brought into the analysis. This is not merely an ac-counting problem. Attention will have to be extended from humancapital to the interaction of human and nonhuman capital accumula-tion and use by households, and to the effects of transfer incomeson both.

Bibliography

Adams, F. G. "The Size of Individual Incomes: Socio-Economic Variables andChance Variation." Review of Economic Statistics, November 1958.

Aitchison, J., and Brown, J. A. C. The Lognormal Distribution. England: Cam-bridge University Press, 1957.

Bates, W. D. 'A Formula for Finding the Skewness of the Combination ofTwo or More Samples." Journal of the American Statistical Association,March 1935.

Becker, G. S. Human Capital. New York: NBER, 1964."Human Capital and the Personal Distribution of Income." W. S.

Woytinsky Lecture No. 1. Ann Arbor: University of Michigan, 1967.Becker, G. S., and Chiswick, B. R. "Education and the Distribution of Earn-

ings." American Economic Review, May 1966.Becker, G. S., and Ghez, G. "The Allocation of Time and Goods Over the Life

Cycle." Processed. New York: NBER, 1972.Ben-Porath, Y. "The Production of Human Capital and the Life-Cycle of

Earnings." Journal of Political Economy, August 1967."The Production of Human Capital OverTime." In Education, Income

and Human Capital. Studies in Income and Wealth 35. New York:NBER, 1970.

Birren, J. E. "Psychological Aspects of Aging." In International Encyclo-pedia of the Social Sciences, Vol. 1, 1968.

Bjerke, K. "Income and Wage Distributions." Processed. Copenhagen: May1969.

Blum, Z. D. "Income Changes During the First Ten Years of Occupational Ex-perience." Report No. 122, Center for Social Organization of Schools.Baltimore: Johns Hopkins University Press, 1972.

Bowen, W., and Finegan, T. The Economics of Labor Force Participation.Princeton, N.J.: Princeton University Press, 1969.

Box, G., and Cox, D. "An Analysis of Transformations." Journal of the RoyalStatistical Society, Series B, 1964.

Cain, G. G. Married Women in the Labor Force. Chicago: University of Chi-cago Press, 1966.

Chiswick, B. ft "Human Capital and Personal Income Distribution by Re-gion." Ph.D. dissertation. Columbia University, 1967.

146 BIBLIOGRAPHY

• "Income Inequality: Regional Analyses Within a Human CapitalFramework." Work in progress. New York: NBER, 1973.

Chiswick, B. R., and Mincer, J. "Time-Series Changes in Personal IncomeInequality." Journal of Political Economy, May 1972.

Craig, C. C. "On the Frequency Function of XY." Annals of MathematicalStatistics, March 1936

Folger, J. K., and Nam, C. B. Education of the American Population. CensusMonograph, 1967.

Friedman, M. A Theory of the Consumption Function. Princeton, N.J.: Prince-ton University Press, 1957.

Fuchs, V. A. Differentials in Hourly Earnings by Region and City Size. Oc-casional Paper 101. New York: NBER, 1967.

• "Differences in Hourly Earnings Between Men and Women." MonthlyLabor Review, May 1971.

Goodman, L. "On the Exact Variance of Products." Journal of the AmericanStatistical Association, December 1960.

Griliches, Z., and Mason, W. "Education, Income and Ability." Journal ofPolitical Economy, May 1972.

Grossman, M. The Demand for Health. Occasional Paper No. 119. New York:NBER, 1972.

Hanoch, G. "An Economic Analysis of Earnings and Schooling." Journal ofHuman Resources, Summer, 1967.

Hansen, W. L. "Total and Private Rates of Return to Investment in School-ing." Journal of Political Economy, April 1963.

Hause, J. C. "Earnings Profile: Ability and Schooling." Journal of PoliticalEconomy, May/June 1972, Part 2.

Heckman, J., and Polachek, S. "The Functional Form of the Income-School-ing Relationship." Processed. New York: NBER, 1972.

Hill, T. P. "An Analysis of the Distribution of Wages and Salaries in GreatBritain." Econometrica, 1959.

Jencks, C., et al. Inequality. New York: Basic Books, 1972.Johnson, T. "Returns from Investment in Schooling and On-the-Job Train-

ing." Ph.D. dissertation. North Carolina State University at Raleigh, 1969.Juster, F. T. Anticipations and Purchases. New York: NBER, 1964.Juster, F. T., ed. Education, Income, and Human Behavior. Carnegie Com-

mission on Higher Education. New York: McGraw-Hill, 1974.Koeune, J. C. "The Obsolescence of Human Capital." Ph.D. dissertation.

Columbia University, 1972.Kuratani, M. "Specific Training and Income Distribution in Japan." Ph.D.

dissertation. Columbia University, 1973.Leibowitz, A. "Education and Allocation of Women's Time." Processed. New

York: NBER, 1972.Lydall, H. "The Long Term Trend in the Size Distribution of Income." Journal

of The Royal Statistical Society, Series A, Part I, 1959.The Structure of Earnings. New York: Oxford University Press, 1968.

—

BIBLIOGRAPHY 147

Malkiel, J., and Malkiel, B. "Sex Differentials in Earnings." Processed.Princeton University, 1971.

Metcalf, D. "Income Distribution in the Business Cycle." American EconomicReview, Papers and Proceedings, May 1971.

Miller, H. P. Census Bureau Technical Paper No. 8, 1963.'Education and Lifetime Income." Current Population Survey, 1967.

Mincer, J. "A Study of Personal Income Distribution." Ph.D. dissertation.Columbia University, 1957.

"Investments in Human Capital and Personal Income Distribution."Journal of Political Economy, August 1958.

"Labor Supply, Family Income and Consumption." American Eco-nomic Review, May 1960.

"Labor Force Participation of Married Women." In Aspects of LaborEconomics. Universities—National Bureau Conference 14. Princeton,N.J.: Princeton for NBER, 1962 (1962a).

"On-the-Job Training: Costs, Returns and Some Implications."Journal of Political Economy, Supplement, October 1962 (1962b).

"The Distribution of Labor Incomes: A Survey." Journal of EconomicLiterature, March 1970.

"Education, Experience and the Distribution of Employment and In-come. In Juster, ed. (1973).

Mincer, J., and Polachek, S. "Family Investments in Human Capital: Earn-ings of Women." Journal of Political Economy, March 1974.

Morgan, J., et al. Income and Welfare in the United States. New York: Mc-Graw-Hill, 1962.

"The Anatomy of Income Distribution." Review of Economic Statis-tics, August 1962.

Polachek, S. "Post-School Investments and Sex Differentials in Earnings."Ph.D. dissertation. Columbia University, 1973.

Reder, M. "A Partial Survey of the Theory of Income Size Distribution." InSix Papers on the Size Distribution of Income and Wealth. Studies inIncome and Wealth 33. New York: NBER, 1969.

Rosen, S. "Measuring the Obsolescence of Knowledge." In Juster, ed. (1974).Rutherford, A. S. G. "Income Distributions: A New Model." Econometrica,

July 1955.Schultz, T. P., "Long Term Change in Personal Income Distributions," AEA

meetings, December 1971.Solmon, L. "Education and Saving." In progress. New York: NBER.

"The Relationship Between Schooling and Savings Behavior: An Ex-ample of the Indirect Effects of Education." Processed. New York:NBER, 1972.

Solmon, L., and Wachtel, P. "Effects of Schooling Quality on Earnings."Processed. New York: NBER, 1972.

Stigler, G. "Information in Labor Markets." Journal of Political Economy,October 1962:

148 BIBLIOGRAPHY

Capital and Rates of Return in Manufacturing Industries. New York:NBER, 1963.

Taubman, P., and Wales, 1. Mental Ability and Higher Educational Attain-ment in the Twentieth Century. New York: NBER, 1972.

Thurow, L. Poverty and Discrimination. Washington, D.C.: The BrookingsInstitution, 1969.

Tolles, N. A., et al. "The Structure of Economists' Employment and Salaries,1964." American Economic Review, Supplement, December 1965.

Tolles, N. A., and Melichar, E. "Studies of the Structure of Economists'Salaries and Income." American Economic Review, Supplement, De-cember 1968.

U.S. Bureau of the Census. Current Population Reports, Consumer Income,P-60, No. 56, August 1968.

U.S. Department of Labor, Bureau of Labor Statistics. Seniority in Promo-tions and Transfer Provisions. Bulletin 1425. March 1970.

U.S. Department of Labor, Bureau of Labor Statistics. Educational Attain-ment of Workers. Special Labor Force Report No. 83. March 1970.

Weiss, Y. "Investment in Graduate Education." American Economic Review,December 1971.

Welch, F. "Black-White Differences in Returns to Schooling." In "Researchinto Poverty Labor Markets." Processed. New York: NBER, 1972.

Index

Ability: and distribution of humancapital, 138—140; and earningsfunction, 140; measures of, 2—3,22n, 138—139, 140; and promotion,81; and schooling, 132

Adams, F. G., 105nAdaptation, 220Age: and biopsychological development,

76, 80; and depreciation of humancapital stock, 47, 129; and earningsprofiles, 28—30, 76—80, 84, 132; andgrowth of individual earnings, 129,132; and income inequality, 107—1 09;and weeks worked, 121. See also Ageprofiles

Age profiles: defined, 64; of earnings,30, 65—70, 101, 110; and income byschooling cohorts, 78; and investmentbehavior, 64—65

Aitchison, J., ilinApprenticeship, 20, 81, 82

Becker, G. S., 12—14, 19n, 23n, 27n, 43n,44, 50n, 54, 55, 65n, 73n, 75n, 120,137—138, 140n

Ben-Porath, Y., 14—16, 43n, 75nBiopsychological development, 76,

80, 132Birren, J. E., 22nBjerke, K., 113Blum, Z. D., 59Bowen, W., 124Box, G., 89nBrown, J. A. C., ilin

Cain, G. G., 124Chiswick, B. R., 19n, 43n, 44, 60—61,

63n, 121nCollective bargaining agreements, 80—82College graduates: earning capacity of,

103—1 09; earnings of, 110—113, 136;

and post-school investments, 74; ratesof return to, 53, 55

Competition, 132Consumer, "planning horizon" of, 120nConsumers Union Panel, 117—118, 136—

137Consumption, 120, 123—125, 136Cox, 0., 89nCraig, C. C., 111

Depreciation of human capital stock,20—22, 129, 142

Earning capacity: and hours of work,22—23; and increase in investment,28—29; initial, 12, 17, 33—34, 90,103—106; peak of, 20—22

Earning life. See Working lifeEarnings: age profiles of, 12—13, 30,

101, 110; analysis of log variances of,103—109; annual, 22—23, 48, 70n, 106,114, 123, 131; changes in, 8; as con-stant for individual, 8; cost of deferralof, 7, 9—11; determinants of dispersionof, 27, 35—36; distribution of, 36—37;of economists, 77—80; and experience,13, 45, 47, 65, 77—80, 132; family,123—125; formation of, 89—90; hourly,71, 131; and human capital invest-ment, 138—140; of husbands, 126;of individuals, 24—25, 89—92, 115—116;intergroup differentials in, 75;observed, 12n; of omitted groups,125—1 27; at overtaking age, 108—109,113, 118, 133; in overtaking sets,53—55; of post-school investors vs.noninvestors, 32—33; rate of growthof variances in, 98—1 02; and school-ing, 11, 44, 70, 88—89, 92; of scientists,77—80; skewness in marginal dis-tributions of, 112; "skill" structure of,

150 INDEX

Earnings (continued)134—135; of students, 7—8, 49n,52n, 125; value of lifetime, 10; weekly,65, 68—70, 131; and weeks worked,134; of women, 121—125. See alsoEarnings profiles; Gross earnings;Income inequality; Net earnings

Earnings inequality. See Incomeinequality

Earnings profiles: and age, 5—51,70—73, 76—80, 84; of cohorts, 76—80;and consumption, 120; defined, 11;and experience, 47, 70—73; humancapital analysis of, 12—20; ofindividuals, 2; instability in, 65n;intragroup dispersion in, 75—76; andinvestment model, 64—65; andinvestment profile, 17, 32—33, 74—76,129—130; non-neutrality in growth of,77; and schooling, 122; of women,122. See also Earnings; Incomeinequality

Economists, earnings of, 77—80Economy, secular trends in, 76—77Education: expenditures on, in New

York State, 55; growth of publicsubsidies to, 75; parental, 139n, 140;preschool, 140—141; and promotion,81—82; quality of, 133; rates of returnto, 50; and schooling, 1. See a/soSchooling

Elementary-school graduates: earningcapacity of, 103—1 09; earnings of,110—113, 136; and post-schoolinvestments, 74; rates of return to,53, 55

Employers, 136, 142Employment: distribution of, 121 —1 25,

141—142; seasonal, 54, 81; sexdifferences in, 123; stability of, 107,111, 119—121; turnover in, 54, 81,119—1 21

Experience: as chronological time, 28;continuous, 84; and earnings, 29—30,47, 67—69, 92, 100, 104, 105, 107—109,132; first decade of, 58—59; informa-tion on, 129—130; initial, 12, 98—99;measuring years of, 47; overtakingyear of, 49, 51, 98—99; and peakearnings Stage, 98—99; second decadeof, 107

32, 86, 87—88,

Hanoch, G., 8n, 44, 47, 48ri, 49n, 54Hansen, W. L., 44, 54Hause, J. C., 140nHealth: and distribution of employment,

142; and earnings, 54, 142; invest-ments in, 7, 22n, 142; and limitationsof work activities, 22n; and schooling,54

Heckman, J., 89High-school graduates: earning capacity

of, 103—109; earnings of, 110—113,136; and post-school investments,74; rates of return to, 53, 55

Hill, T. P., 105n, 112nHome environment, 2, 140—1 41Human capital: and ability measures,

2—3; accumulation of, 13—16, 82,112, 140; depreciation of, 22—23, 47,64n, 142; distribution of, 138;employer investments in, 137; grossinvestments in, 15—16; net investmentsin, 2; production of, 15; relevance ofanalysis of, 44—45; and schoolingmodel, 64; theories of, 3, 74—75, 120—121, 144; unmeasured quantities of,2. See also Human capital invest-ments; Human capital models

Human capital investments: andearnings, 138—1 40; and employmentstability, 120; and home environment,140—141; and hours worked, 23; andincome inequality, 43—44, 90, 91—92,97—98; information on, 2; and laborsupply, 120, 122—1 24; and marginalcost, 15—16; and marginal revenue,

Family, earnings of, 123—125Farm workers, 125—1 27Financing, access to, 75Finegan, T., 124Folger, J. K., 61nFriedman, M., 119Fuchs, V. R., 122n

Ghez, G., 23nGoodman, L., 27nGriliches, Z., 140nGross earnings, 16,

130—131, 133Gross investment, 20—22Grossman, M., 142n

INDEX 151

15—16; measured distribution of, 131;and productivity, 120n; rates ofreturn on, 7—9; restricted to schooling,24; sex differences in, 123; theory ofoptimal, 13—14, 85; total cost of, 7;and weeks worked, 120—1 21. Seealso Human capital; Human capitalmodels; Post-school investments;Schooling

Human capital models: and economicvariables, 101—102; expanded, 44—45;explanation of skewness in, 38;explanatory power of, 116—119; asqualitative analyses of incomedistributions, 43; as quantitativeanalyses of income distribution,43—45; and schooling, 1—3. See alsoHuman capital; Human capital invest-ments

Illness. See HealthIncome: annual growth rate of, 79;

family, 126; nonemployment, 123—125,126—127, 144; property, 119n; self-employment, 119. See also Earnings;Income distribution; Income inequality

Income distribution: analysis of, 2,143—144; of households, 144; andskewness, 37—38; stochastic theoriesof, 35, 111—112, 115—116; theories of,111—112. See also Earnings; Income;Income inequality

Income inequality: absolute, 130; andage, 107—109; accounting for, 133—134; cohort and cross-sectionalchanges in, 62; in cohorts, 32—34;contribution of "transitory" com-ponent to, 119—121; and employmentdispersion, 119—121, 122—125; andexperience, 107—109; amongfamilies, 125; and human capitalinvestments, 43—44, 90, 91—92,97—98; marginal distributions of,112; at overtaking age, 133—1 34; andpost-school investments, 83, 95—96;regional comparisons of, 60—61;relative, 130; reversal of profiles of,108—109; and schooling, 25—26,27—28, 95—96; and schooling model,44—45, 57—59; study of, 18

Income maintenance programs, 142

Individuals, as firms, 14—16Investment: and age profiles, 28—29; and

earnings profiles, 64—65, 129—130;income elasticity of, 31—32; propensityto, 99, 106—107; stability in behavior,107; time measures of, 130. See alsoHuman capital investments; Post-school investments; Schooling

Jencks, C., 134nJohnson, T., 22nJuster, F. T., 55n, 118n

Koeune, J. C., 22n, 73n, 142nKuratani, M., 137

Labor force: attachment to, 1129—130; growth of female,mobility of, 65

Labor supply, 120, 142"Learning by doing," 65, 132Learning capacity, 22n, 31Leibowitz, A., 141nLeisure, 72nLydàll, H., 43n, 50n, 61n, 105n, 113, 125n

Malkiel, J., 143nMason, W., 140nMelichar, E., 77n, 79Metcalf, D., 125nMigration, 7Miller, H. P., 63n, 76—77Mincer, J., 20n, 22n, 43n, 50n, 63n, 74,

76n, 105n, ilin, 121, 124, 125n, 141n,142n, 143n

Minimum wages, 142Mobility, 65, 141Morgan, J., 105n, 10Th

Nam, C. B., 61nNational Bureau of Economic Re-

search—Thorndike sample, 55Net concept, 8Net earnings, 16—18, 32—33, 86, 88,

130—131, 133

Obsolescence, 73n, 142On-the-job training, 7, 122—123, 132.

See also Post-school investmentsOpportunity, 138—140, 141

21—122,

125;

152 INDEX

Pareto, V., 111Polachek, S., 89, 121n, 141n, 143nPositive discount rate, 7—9Post-school investments: costs of, 18,

73, 74; differences among individ-uals, 29, 32—33, 108, 133; and earn-ings, 45—47; elasticity of, 103—106,136; and human capital models,44—45; identifying parameters of, 94;incentives for, 75; and incomeinequality, 52, 95—96; information onindividual, 95—96; and initial earningcapacity, 103—106; and level ofschooling, 16, 30—31, 72, 75, 131—132;measuring time units of, 18—20; andnet investments, 29; opportunities for,75; rates of return to, 18, 48, 72—73;staggering of, 98—1 02, 107, 129; intime equivalents, 73—75; total timedevoted to, 20. See also On-the-jobtraining

Productivity, 1, 65, 80, 82, 120n, 142Promotion, 80—82

Random shock models, 116—119Rates of return: individual differences

in, 2, 7—9, 34—36, 108; to schooling,48, 50. See also Human capitalinvestments; Post-school investments;Schooling

Retirement, 8—9, 30Rosen, S., 22n, 142nRutherford, R. S. G., 113

Schooling: costs of, 7—9, 10, 12—14,49n, 52n, 99, 133; as "credential,"59n; and earnings, 24—25,46, 48,57—59, 92; and education, 1, 55—56;high level of, 59; incentives for, 75;investments in, 8—9, 52; length of, 11,32—33, 54—56, 60, 61—63; low level of,59, 72n, 99; opportunities for, 75,132; and post-school investments, 72,75, 131 —132; and random shock,116—118; rates of return to, 10, 26—27,48, 50—51, 56, 93, 95, 131; seculartrends in, 37, 38, 45, 102—1 03, 108—109; symmetric distribution of, 25—26;

time-equivalent measures of invest-ment in, 73—75; United States levelof, 60—61; "vintage" hypothesis ofeffectiveness, 58; and weeks worked,121. See also College graduates;Education; Elementary-schoolgraduates; High-school graduates;Schooling model

Schooling model: and earnings, 24—28,59—63, 142; expansion of, 95—96,129—1 30; inadequacy of, 44—45, 129;and overtaking age, 57—58; andungrouped data, 51—59; use forquantitative analysis, 59; validity of,64; and variation in rates of return,56—59

Schultz, T. P., 62—63, 123nScientists, earnings of, 77—80Self-employed, 119n, 125—1 27Seniority, 81—82Skills: cost of increasing, 12; as factor

in promotion, 81; measuring, 70; andschooling, 31, 135—136

Solmon, L., 55, 99n, 136, 143nStigler, G., 32n, 33n, 56

Taubman, P., 140nThorndike, E. L., 22nThurow, L., 89Tolles, N. A., 77—80, 89nTraining programs, formal, 20Turnover. See Employment

Underemployment, 120Unemployment, 54, 72n, 120,United States Department of

Bureau of Labor Statistics,

Wachtel, P., 55, 143,,Wales, F., 140nWeiss, Y., 52n, 55nWelch, F., 58n, 140nWomen, 121—125Work experience. See ExperienceWorking life: cost of reduction of, 7;

decline of investments over, 14—16;length of, 8—9, 10—11; variation ofearnings over, 12—13

142Labor,80—82

"schooling, experience, and earnings" by jacob mincer

Documents

vice presidentresearchsherman

vice presidentresearchco

vice presidentresearchedward

vice presidentresearchrobert

vice chairmanjohn

vice presidentdirectors

wilson newman

york universityeugene