Micro Economices essay

American Economic Association

Education and the Distribution of Earnings Author(s): Gary S. Becker and Barry R. Chiswick Source: The American Economic Review, Vol. 56, No. 1/2 (Mar. 1, 1966), pp. 358-369 Published by: American Economic Association Stable URL: https://www.jstor.org/stable/1821299 Accessed: 28-12-2018 07:08 UTC

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide

range of content in a trusted digital archive. We use information technology and tools to increase productivity and

facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at

https://about.jstor.org/terms

American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION

EDUCATION AND THE DISTRIBUTION OF EARNINGS

By GARY S. BECKER and BARRY R. CHIswIcK

Colutmbia University and National Bureau of Economic Research

I. Introduction

The history of interest among economists in the distributioil of income is as long as the history of modern economics itself. Smith, Mill, Mar- shall, and others recognized that many areas of considerable economic importance were affected by it. Although poverty, for example, was partly defined in absolute terms, they recognized that each generation's "poor" are mainly those significantly below the average income level. In addition to poverty, the degree of opportunity, aggregate savings and investment, the distribution of family size, and the concentration of private economic power were thought to be affected.

How does one explain then that in spite of the rapid accumulation of empirical information and the persisting and even increasing interest in some of these question, such as poverty, economists have somewhat neglected personal income distribution during the last generation?' In our judgment the fundamental reason is the absence, notwithstanding some ingenious and valiant efforts, of a theory of income distribution that both articulates well with general economic theory and is useful in explaining differences among regions, countries and time periods. Some earlier work2 by one of us led to the belief that an analysis of investment in human capital provides a theory of income distribution that satisfies both desiderata.

This is a report on a National Bureau of Economic Research study in progress3 that is developing such a theory and applying it to a variety of evidence. Not only is the report preliminary, but brevity of space re- quires that many details and proofs be skipped and the discussion con- centrated on a few highlights. We expect to publish the full study before too long, which would permit our methods and conclusions to be ex- amined more closely.

1 As one test of this statement, try to find many textbooks on economic principles that pay it much attention.

2 See G. S. Becker, Human Capital (Columbia Univ. Press for N.B.E.R., 1964), especially pp. 61-66. w- Financed by the Carnegie Corp. of New York. We are greatly indebted to Linda Kee for valuable research assistance, and to members of the Labor Workshop at Columbia University for useful comments.

358

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION 359

II. Theory

The total earnings of any person after he has finished investing in human capital can be said to equal the sum of the returns on his invest- ments and the earnings from his "original" human capital. If returns could be treated as constants for essentially an indefinitely long period, this relation could be expressed as

m

(1) E, = Xi + E rijCii, jl1

where Cij is the amount spent by the ith person on the jth investment, rij is his rate of return on this investment, and Xi are the effects of the original capital.4 Note that our analysis directly applies to earnings alone, which is just a part, although the dominant one, of total income. While the framework developed here could also be usefully applied to property income, we have not done any empirical work on such income and ignore it in the rest of the paper.

The point of departure for our approach, which integrates it with economic analysis in other fields, is an assumption that the amount in- vested in human capital results from optimizing behavior: each person is supposed in effect to invest an amount that maximizes his economic welfare. This assumption permits the investment decision to be ana- lyzed in terms of the following familiar figure. The curve D shows a person's marginal rate of return on an additional dollar of investment, while S shows his marginal "interest" cost. Equilibrium is assumed to occur at p, where the total amount invested would be OC, and the (gross) income on this investment would be ODpC, represented in dis- crete form by the term Erij Cij in equation (1). In this framework, there- fore, the distribution of earnings is simply determined by the shape and distribution of the supply and demand functions,6 and we now dwell a while on these determinants.

Legal and other obstacles to financing investments in human capital have been a significant "institution" in Western societies. As a result, these investments have been financed either by gifts from parents and others, reduced consumption during the investment period, or various kinds of loans. Since financing usually becomes more difficult as the amount invested increases because gifts become less available, reduced consumption more onerous, and risks to lenders greater, the effective supply curve of funds, say S in the figure, would be positively inclined, its elasticity measuring the rate of increase of these difficulties.

4 See Becker, op. cit., Chap. III. 6 For the moment we ignore the distribution of XI; it is incorporated into the analysis in

section III.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

360 AMERICAN ECONOMIC ASSOCIATION

Supply and Demand for Investment in Human Capital

Marginal rate of return

O ~~~~~~C

A mount i nvested

FIGuE 1

One factor decreasing the marginal rate of return, at least eventu- ally, with increases in the amount invested is a presumed diminishing marginal product from adding more capital to a fixed human body. Moreover, increased investment usually requires a longer investment period, and with a finite lifetime the marginal rate of return would tend

to be inversely related to the length of this period.6 The rates of return to any person depend, however, not only on his investments but also on those by others and on the derived demand for persons with different kinds of human capital. For example, a college education might yield a very high payoff if few persons manage to get one and if those who do are in great demand. Consequently, depending on general supply and

derived demand conditions, the marginal rate of return might well

6 See Becker, op. cit., pp. 49-52.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION 361

increase over different investment intervals. Although, therefore, the curve D might not always decline,7 our analysis requires only a decline relative to S, especially around the point of intersection p, and that seems plausible enough.

Let us turn to the distribution of these curves and thus to the distribu- tion of earnings. Since the income and wealth of parents, the willingness to forego consumption, and the availability of scholarships and loans vary from person to person, the supply of funds would also vary, as

illustrated by the curves Si, S and Si in the figure. If the demand curve D was the same for everyone, the equilibrium positions would lie along D at the points of intersection, given in the figure by pi, p, and pj. Knowledge of the various equilibrium positions would permit an "identification" of the demand for funds curve D."

The distribution of earnings would be determined by the distribution of the areas under D, which in turn would be determined by the distribu- tion of supply curves, their shape and the shape of D. For example, if the marginal rate of return was constant so that D was horizontal, earnings would have the same inequality and skewness as the amount invested. If, however, marginal rates decreased, the inequality and positive skewness in earnings would be less than that in investments because large investors would receive lower rates of return; conversely if mar- ginal rates increased.9

More usually the demand for funds would also vary, probably sig- nificantly, because of differences in "ability," attitudes toward risk, and other personal characteristics. The figure shows three demand curves

Dk, D, and D,, with D,, reflecting the most "ability," and Dk the least. If the supply curve S was the same for everyone, the equilibrium posi- tions would lie along S at the points of intersection, given in the figure

by pi, p, and pk, and knowledge of the various positions would permit an "identification" of S. If S was positively inclined as in the figure, the inequality and positive skewness in earnings would exceed that in in- vestments because large investors would receive higher rates of return.10

7 Since the marginal rate of return to any person would depend not only on his investments but also on those by others, the demand curve D would be defined only for given amounts invested by others.

8 This kind of technique has been used by G. Hanoch in his "Personal Earnings and In- vestment in Schooling" (unpublished Ph.D. dissertation, Univ. of Chicago, 1965), Chap. II.

I If D was a straight line, the average as well as marginal rate of return would be linearly related to the amount invested, and earnings from human capital would be

FCC = (a + bC)C = aC +bC2,

where C is the total amount invested, *, its average rate of return, and a and b are constants. If b=O, earnings simply equals aC; if b9#, the term bC2 either increases or reduces the in- equality and positive skewness in earnings as b>O.

10 If S was linear as well as positively inclined, the average rate of return would be linearly and positively related to the total amount invested, and earnings from human capital would be

w,>C = (e + C) C = eC + fC2, wheref>O.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

362 AMERICAN ECONOMIC ASSOCIATION

In the usual case where supply and demand curves both vary, the

different equilibrium positions could still be found at the intersections of the relevant curves, but knowledge of these positions would no longer be sufficient to "identify" either set of curves. In addition to the factors already discussed, the distribution of earnings would now also depend on the correlation between supply and demand conditions. These condi- tions might well be positively correlated, say because of a positive cor- relation between ability or the psychic earnings received from human capital with either parental wealth or scholarships; in the figure the de-

mand curve Di could be associated with the supply curve Sj, Dk with Si, and D with S. The resulting equilibrium positions plj, p, and pki indicate sizable dispersions in rates of return and amounts invested, and a strong

positive relation between them. If Si was associated with DI and Sj with Dk, supply and demand conditions would now be negatively correlated,

and the resulting equilibrium positions would be pli, p, and pk. The inequality and skewness in earnings would be reduced because the negative correlation between these conditions would reduce the invest- ment and earnings of persons with favorable demand conditions, say

Di, and increase that of persons with unfavorable conditions, say Dk. Before passing on to a quantitative implementation of this model, we

might dwell a little on one interesting implication. The often discussed but seldom defined concept of "equality of opportunity" can be rigor- ously defined in our framework as a situation in which low parental wealth and other supply disadvantages were sufficiently offset so that the effective supply curve of funds was the same to everyone."1 One way to achieve this would be to make investment in human capital a free good through subsidies from public or private agencies; all supply curves, in effect, would then lie along the horizontal axis.12 Our definition of equality of opportunity would imply not equal investment but equal opportunity to invest, the actual amount depending on ability and other

personal characteristics (see the points pk, p, and pi in the figure). The elimination of unequal supply conditions would reduce the inequality in investments unless supply and demand conditions had been sufficiently negatively related. On the other hand, it would increase the positive correlation between the amount invested and its rate of return unless supply and demand conditions had been sufficiently positively related.

11 One might also want to offset some of the forces, such as discrimination or nepotism, making for differences in demand curves.

12 Free public schools are not a perfect example, since foregone earnings, often an important cost of schooling, are not subsidized. The GI Bill, on the other hand, does cover at least some foregone earnings by providing living allowances as well as tuition. Legislation making school- ing compulsory is still another and quite different example, for some persons may be forced to continue in school longer than they would like (or even than is good for them). Incidentally, because of space limitations our discussion in this paper must abstract from forces, such as compulsory school legislation or the rationing of school places, that make the actual amount invested( differ from the desired amount.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

TIIE ECONOMICS OF EDUCATION 363

III. A Statistical Formulation

The contribution of human capital to the distribution of earnings could be easily calculated empirically if the rates of return and invest- ments in equation (1) were known. Although information on investment in human capital has grown significantly during the last few years, it is still limited to aggregate relations for a small number of countries. Much more is known about one component of these investments; namely, the period of time spent investing, as given, for example, by years of school- ing.

To utilize this information we have reformulated the analysis to bring out explicitly the relation between earnings and the investmenet period. The principal device used is to write the cost of the jth "year" of in- vestment to the ith person as the fraction ki5 of the earnings that would be received if no investment was made during that year. If for conven- ience rij in equation (1) is replaced by fj+r*ij, where ri is the average rate of return on the jth investment and r*ij is the (positive or negative) permium to the ith person resulting from his (superior or inferior) per- sonal characteristics, then it can be shown that equation (1) could be rewritten as

(2) Ei = Xj1 + ka,(f, + r*ii)][1 + ki2(f2 + r*2) ] * * [1 + ki,i(ni + r1,)] where n2 is the total investment period of the ith person." If the effect of luck and other such factors on earnings is now incorporated within a multiplicative term eui, the log transform of equation (2) is

(3) log Ei = log Xi + E log [1 + kij(f, + r*j)] + us. j=1

By defining Xi=X (1+ai), where ao measures the "unskilled" personal characteristics of the ith person, and kij= kj+tij, where kj is the average fraction for the jth investment, and by using the relation

(4) log [1 + k1j(ij + r*)] = k,j(fj + ri*), equation (3) could be written as

ni

(5) log Ei a + F r + vi, j=1

where a = log X, f'j = kj,j, and

(6) vi = log (1 + ai) + kijr* + tijrj + ui- j i

13 We cannot take space to give a proof here; the interested reader can find a proof for a somewhat special case in Becker, op. cit., p. 64.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

364 AMERICAN ECONOMIC ASSOCIATION

The term vi largely shows the combined effect on earnings of luck and ability. If the f'j was the same for each period of investment, the equa- tion for earnings is simply

(7) log Ei a + ?'ni + vi

If r', the average rate of return adjusted for the average fraction of

earnings foregone, and the investment period ni were known, equation (7) could be used to compute their contribution to the distribution of earnings. For example, they would jointly "explain" the fraction

(2(n)

(8) R2 = (WY) 2(n) 0'2(looa E)

of the total inequality in earnings, where or2 (n) is the variance of invest- ment periods, and U2 (log E) is the variance of the log of earnings, the measure of inequality in earnings.'4 Ability and luck together would "explain" the fraction 02 (V)/U2 (log E), and the (perhaps negative) remainder of the inequality in earnings would be "explained" by the covariance between ability, luck and the investment period.

Even equations (5) and (7), simplified versions of (2), make excessive demands on the available data. For one thing, although the period of formal schooling is now known with tolerable accuracy for the popula- tions of many countries, only bits and pieces are known about the periods of formal and informal on-the-job training, and still less about other kinds of human capital. Unfortunately, the only recourse at pres- ent is to simplify further: by separating formal schooling from other human capital, equation (5) becomes

qi

(9) log Ei = a + E rSi + v', j=1

where f'1 is the adjusted average rate of return on each of the first Si years of formal schooling, f'2 is a similar rate on each of the succeeding

S2 years of formal schooling, etc.;

qi

Si = E Sj is then the total formal schooling years of the ith person, and 1

(10) V- = vi + E rkTk

includes the effect of other human capital.

A second difficulty is that although an almost bewildering array of

H Note that this measure, one of the most commonly used measures of income inequal- ity, is not just arbitrarily introduced but is derived from the theory itself,

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION 365

rates of return have been estimated in recent years, our empirical analy- sis requires many more. Additional estimates could be developed by making equation (9) do double duty: first it could be used to estimate the adjusted rates and only then to show the contribution of schooling, including these rates, to the distribution of earnings. If the Sj and v' were uncorrelated, an ordinary least squares regression of log E on the Sy would give unbiased estimates of these rates, and, therefore, of the

contribution of schooling. If, however, the Sj and v' were positively or negatively correlated, the estimated rates would be biased upward or downward, and so would the estimated direct contribution of schooling

Some components of v' are probably positively and others are nega- tively correlated with years of schooling, and the net bias, therefore, is not clear a priori. It is not unreasonable to assume that ao and ui in equation (6) are only slightly correlated with the S. The rij* term in (6), on the other hand, would be positively correlated with the Sj'5 since the theory developed earlier suggests that persons of superior ability and other personal characteristics would invest more in themselves. Some empiri- cal evidence indicates a positive correlation between years of schooling and the amount invested in other human capital.16 The term v' depends, however, on the correlation between years of schooling and years in- vested in other human capital, a correlation which might well be nega- tive. Certainly persons leaving school early begin their on-the-job learning early, and possibly continue for a relatively long time period (see fn. 17). Finally, one should note that random errors in measuring the period of schooling would produce a negative correlation between the measured period and v'. Although the correlations betweeen the S5 and these components of v' go in both directions and thus to some extent must offset each other, a sizable error probably remains in estimating the adjusted rates and the contribution of schooling to the distribution of earnings.

IV. Empirical Analysis

The sharpest regional difference in the United States in opportunities and other characteristics is between the South and non-South, and the following table presents some results of regressing the log of earnings on years of schooling separately in each region for white males at least age 25. Adjusted average rates of return have been estimated by these re- gressions separately for low, medium, and high education levels. As columns 1, 2, 6, 7 and 8 indicate, the adjusted rates at each of these school levels and the variances in the log of earnings and in years of schooling are all a fair amount larger in the South. Moreover, these

16 That is, unless a negative correlation between kij and rij* was sufficiently strong. 16 See Becker, op. cit., p. 89.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

366 AMERICAN ECONOMIC ASSOCIATION

RESULTS OF REGRESSING NATURAL L,OG OF EARNINGS ON EDUCATION FOR 1959 EARNINGS OF WHITE MALES AGED 25-64 IN THE SoUTrn

AND NON-SOUTHr

Adjusted Rates of Return* Adjusted

] Variance v l l l l ,idjusted Rates of Retur * | Coefficient Residual Variance nce Average - _____-of Determi- Variance of Variance tra Average Inter- nation in

Natu, I Log of Education cepts? Low Medium Hgh (R2) Natural Log of EducationEangs (4) (5) Education Education Education Log of Earnings (2) E ig (6) (7) (8) Unadjusted Earnings 1) l l l (st andard error s)t R; (10) 1.09 .05 .06 .08 o07 .39

Non-South .. .42 11.28 1.66 10.78

(.67) (.09) (.06) (.06) .11

.66 .07 .09 .09 .16 .46

South ........... .55 15.23 1.43 9.96

(.50) (.08) (.07) (.06) .20

* "Low" education is defined as 0-8 years of school completed, "medium" as 8-12 years, and "high" as more than 12 years.

t In calculating the standard errors and the the adjusted coefficients of determination, the number of degrees of freedom was assumed to equal the

number of cells minus the number of parameters estimated. The true number is clearly somewhat greater than this.

? Earnings measured in thousands of dollars.

SOURCE: United States Cenisus of Population: 1960, Subject Reports-Occupation by Earnings and Education (Bureau of the Census, Washington,

1963), Tables 2 and 3.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION 367

differences in schooling and rates exceed the difference in earnings, for as column 9 shows, the coefficient of determination, or the fraction of the variance in the log of earnings "explained" by schooling, is con- siderably higher in the South. The regional difference in earnings does not entirely result from schooling, however, for column 10 shows that

the "residual" inequality in earnings is also larger in the South. These results can be given an interesting interpretation within the

framework of the theory presented in section II. The greater inequality in the distribution of schooling in the South is presumably a consequence of the less equal opportunity even for whites there and would only be

strengthened by considering the differences in schooling between whites and nonwhites. The higher adjusted rates of return in the South17 are probably related to the lower education levels there, shown in

column 4, which in turn might be the result of fewer educational oppor- tunities.

The residual v' is heavily influenced by the distributions of luck and ability, which usually do not vary much between large regions. There- fore, greater rates of return and inequality in the distribution of school- ing would go hand in hand not only with a greater absolute but also with a greater relative contribution of schooling to the inequality in earniings. The residual is also influenced, however, by investment in other human capital. Since the rates of return to and distribution of these investments would be influenced by the same forces influencing schooling, the absolute, but not relative, contribution of the residual to the inequality in earnings would tend to be greater when the absolute contribution of schooling was greater. Consequently, our theory can explain why both the coefficient of determination and the residual vari- ance in earnings are greater in the South.

In order to determine whether these relations hold not only for the most extreme regional difference in the United States but also for more moderate differences, similar regressions were calculated for all fifty states. To avoid going into details at this time let us simply report that the results strongly confirm those found at the extremes: there is a very sizable positive correlation across states between inequality in adult male incomes, adjusted rates of return, iinequality in schooling, coefli- cients of determination, and residual inequality in incomes, while they

17 Higher rates of return to whites in the South have been found when estimated by the "<present value" method from data giving earnings classified by age, education, and other variables (see Hanoch, op. cit., Chap. IV). Although estimates based on the present value method are also biased upward by a positive correlation between ability and schooling and downward by errors in measuring school years, they are less sensitive to the omission of other human capital (see Becker, op. cit., pp. 88-90). Consequently, the fact that Hanoch's es- timates are almost uniformly higher than ours (after adjustment for the k,) suggests, if any- thing, a negative correlation between school years and the years invested in other human capital. This could also explain why Hanoch's rates tend to decline with increases in years of schooling while ouirs tendl to rise.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

368 AMERICAN ECONOMIC ASSOCIATION

are all negatively related to the average level of schooling and income. Whereas only about 18 percent of the inequality in income within a state is explained, on the average, by schooling, the remaining 82 per- cent explained by the residual, about one-third of the differences in inequality between states is directly explained by schooling, one-third

directly by the residual and the remaining one-third by both together through the positive correlation between them.

Similar calculations have also been made for several countries having readily available data: United States, Canada, Mexico, Israel and Puerto Rico (treated as a country). Again there is a strong tendency for areas with greater income inequality to have higher rates of return,

greater schooling inequality, higher coefficients of determination, and greater residual inequality. While there is also a tendency for poorer countries to have lower average years of schooling, greater inequality in income, etc., there are a couple of notable exceptions. For example, Israel, for reasons rather clearly related to the immigration of educated Europeans during the 1920's and 1930's, had unusually high schooling levels and low inequality in earnings until the immigration of unedu- cated Africans and Asians after 1948 began to lower average education levels and raise the inequality in earnings.

V. Summary and Conclusions

This paper has developed and applied to several bodies of evidence a theory of the distribution of earnings. The principal attraction of the theory is that, unlike most other approaches to income distribution, it does not consist mainly of mechanical curve fitting or ad hoc probability mechanisms, but rather relies fundamentally on maximizing behavior, the basic assumption of general economic theory. Each person is assumed in effect to maximize his economic welfare by investing an appropriate amount in human capital, and the distribution of earnings is determined by the distribution of investments and their rates of re- turn. These determinants are in turn related to various "institutional" factors which also play an important part in our theory: inheritance of property income, equality of opportunity, distribution of abilities, sub- sidies to education, and other human capital, etc.

Limitations of the data available have reduced the scope of the empirical analysis to investment in formal education as measured by years of schooling. Evidence from states and regions within the United States and from several countries indicates that schooling usually ex- plains a not negligible part of the inequality in earnings within a geo- graphical area and a much larger part of differences in inequality be- tween areas. These and other findings are generally quite consistent with the implications of the theory.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms

THE ECONOMICS OF EDUCATION 369

The body of economic analysis desperately needs a reliable theory of the distribution of income. While this report is preliminary and more work is in progress, our approach seems to offer considerable promise of filling that need. In any case we hope to have demonstrated that a theory of income distribution need not be a patchwork of Pareto dis- tributions, ability vectors, and the toss of a coin, but can wear clothing as neat as that worn by the theory of households and firms.

This content downloaded from 125.253.35.209 on Fri, 28 Dec 2018 07:08:51 UTC All use subject to https://about.jstor.org/terms