measuring human capital returns

Measuring Human Capital ReturnsAuthor(s): C. M. LindsaySource: Journal of Political Economy, Vol. 79, No. 6 (Nov. - Dec., 1971), pp. 1195-1215Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1830097 .

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Measuring Human Capital Returns

C. M. Lindsay University of California, Los Angeles

The correct measure of the return on human capital investment is the wealth effect of the wage increase which the investment makes possible. A geometric model of this investment decision is examined. The currently pervasive "income difference" measure is shown to contain an upward bias positively related to the size of the investment. Alternative tests for "shortage' and "surplus" conditions are developed which correct for this bias. It is shown that labor supply schedules may bend backward only when the relevant wage changes are incorrectly anticipated. It also is shown that among individuals who differ only in wealth, those with less wealth will elect to invest in human capital at lower wage levels in the relevant employments.

The application of investment theory to the study of occupational choice is yielding generous positive returns. The similarity of career decisions to investment portfolio decisions has nevertheless obscured a fundamental difference in the two choices which is of some importance. This difference, and the resulting confusion it has generated, concerns the appropriate definition of returns to human capital investment-what it is that potential investors consider in weighing the profitability of training for a career. This paper will attempt some clarification here by constructing a

model of human capital investment decision and tracing its implications for past and future manpower research.

I

From this vantage point, an economic shortage in a particular labor

market may be said to exist when investment in training for a career in

I wish to acknowledge the advice of Armen Alchian, James Buchanan, Jack Hirshleifer, and Robert Michael regarding earlier drafts of this paper. Regrettably, only I may be held accountable for errors introduced since their generous criticisms.

I s95



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that sort of work is more attractive to potential entrants than alternative work/investment combinations available to the chooser. Received investment theory informs us that the strictly pecuniary attractiveness (profitability) of investments is a matter of the present value of the return stream through time discounted at the opportunity rate facing the potential investor.' Virtual consensus seems to exist among human capitalists on the appropriate measure of this return stream as the difference in wage earnings flows with and without the investment.2 This measure will be shown to be incorrect, introducing a bias into empirical calculations em- ploying such returns.

The return on any investment may be identified only in terms of the choice facing the investor. An investor will select a particular investment only if he considers that it will make him better off. Normally, investments produce returns in the form of assets (for example, income or service streams). These assets for which title is obtained via the investment may be retraded at a profit providing a surplus from which the investor may draw to add to his consumption bundle. As none of the prices of the items in that bundle are disturbed by investment transactions, those producing positive net yields may be described as unambiguously welfare-increasing. On this basis, external observers may (within limits) select the "best" investment for wealth-holders,3 and in a similar fashion deduce when a "capital shortage" exists in a particular area.

In the case of training investment, however, the return comes-not in the form of assets-but as a price change. The investor purchases with his investment-not an income or service stream in the future but the option of selling his holding of one item (that is, his labor services) at a higher price. There is no conveniently observable value comparable to the yield on asset-producing investments upon which external observers may rely in identifying human capital values. The correct measure of this return is the wealth effect of this price change. The "difference between net earnings" of trained and untrained individuals describes merely the increase in the investor's command over a subset of the items in his consumption bundle. It ignores the fact that one of the most important items in that bundle, leisure,4 has become costlier in the process. Considered as

1 W. Lee Hansen (1967) has expressed an opposing view. Hansen apparently does not recognize that choosing a career is typically a mutually exclusive choice. Hence, the internal rate of return technique of weighing the profitability of investments (which he favors) may yield erroneous results. See Alchian (1955) and Hirshleifer (1958) for a fuller discussion of this point.

2 See, for example, Becker (1962, p. 3) and Hansen (1964, p. 85). Schultz (1968) has recognized that measured income differences may contain a bias as an indicator of pecuniary returns. Although clearly aware of the problem, the model he developed contained several errors which will be discussed below.

3 For a careful and provocative discussion of these limits, see Buchanan (1969). 4 The average man devotes approximately three-fourths of his time (128 of a

possible 168 hours per week) to the acquisition and enjoyment of leisure, compared



HUMAN CAPITAL RETURNS II97

an estimate of the wealth effect of the price change, it will be shown that this income-difference measure systematically overstates the value of this return. Substitute estimates will be offered which contain less bias.

An interesting offshoot of this analysis is that, if long-run equilibrium is approached in every employment to the extent that relative wages reflect the required investments in each, cross-sectional studies of wages and workweeks always should find the two variables positively related. Back- ward-bending supply schedules for labor may be identified only in the "short run." Full equilibrium "long-run" adjustment of wage changes in each employment always must find higher wages associated with greater output.

First we will address the problem of identifying the bias in income difference estimates of returns. The actual dimensions of this bias in returns calculations and the interaction of the human capital investment decision with the choice of hours worked are illustrated in figure 1. It embodies the following simplifying assumptions:

1. The model is timeless in the sense that lifetime earnings are considered earned in the current period. The point to be illustrated is not related to or affected by discounting considerations, and such a procedure enables us to view the choice in a simpler diagramatic setting.

2. All persons have identical preferences for work and leisure, have identical innate abilities and employment acceptability, and are indifferent regarding the type of employment they pursue.

3. The productivity of time in leisure is unaffected by training for work. In other words, individual regard for leisure and income is not affected by the type of work being done.

4. Job opportunities for all are assumed to be limited to one profession where admittance to practice requires a fixed program of investment in training and an alternative "unskilled" employment where productivity is unaffected by training.

5. Current work/leisure decisions are made on the basis of permanent income and are unaffected by wage changes considered to be transitory. The implications of relaxing some of these assumptions will be discussed in Section IV.

Figure 1 is a conventional indifference map representing the preferences of each of the (identical) prospective professionals regarding labor (a bad) on the abscissa and wealth (a good) on the ordinate. Consider that each person is endowed originally with OC wealth and may add to that wealth only by doing work. If the equilibrium wage for raw untrained labor is given by the slope of CIV, all persons would elect to perform OG units, for which they would receive income CE.

with the proportion of time spent working to produce income with which to procure all other items. Valued at its price at the margin, in other words, three-fourths of his budget (from human resources) is devoted to the purchase of leisure.



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12 w

w F L

M?K

Li C/

A ~I I

0 G H MANHOURS OF LABOR

FIG. 1

Suppose now that in order to do skilled work, persons must undergo training at cost AC. Were this the typical type of investment paying an asset return, the necessary return would have to have a money value slightly greater than AC in order for it to increase the wealth of investors. As we have noted, however, human capital returns are earned in the form of price changes. The question then becomes what change in the price of their labor will just compensate our investors for their outlay of wealth AC. It is clear from the figure that individuals must earn a wage equal to the slope of A W' before they will agree to pay for the training. If the slope of the skilled wage line were any less, the potential trainees would perceive that no amount of work-after having paid the training cost- would make them as well off as they could be by doing unskilled labor and retaining their wealth.5

If workers were paid the skilled-labor wage which would just induce them to enter this market, each would perform OH units of work for which he would receive earnings of AF. The bias in conventional measures of human capital returns is now obvious. These measures identify as returns the whole of the difference between AF and CE (that is, AC + EF). Clearly, this is an overstatement. External observers comparing this mea-

5 Nothing is changed by alternatively assuming that all must borrow to pay for their training. That possibility may be treated by simply permitting point A to drop below the horizontal axis.



HUMAN CAPITAL RETURNS II99

sure of the return with the outlay AC would be led to conclude that excess returns in amount EF are being earned, when it is clear that such a wage difference in fact leaves the investor indifferent about investing in training. We really wish to measure the wealth effect of the existing wage difference (once the investment is made), since the investor compares this value with the outlay in assessing the profitability of such an investment.

The equivalent income variation measure of the wealth effect is adopted here. That is the lump-sum subsidy which would lift these individuals to the same level of indifference that would be reached through the wage increase offered by the trained employment.6 The return measured in this way for the wage increase depicted in figure 1 is AC, just the value of the invested outlay, the expected result at equilibrium. The excess of the income-difference measure of the return (AC + EF) over this amount is EF, the compensation received at the higher wage for the additional hours worked in the trained employment.

It can be shown that this bias in returns as measured by simple income differences should be positively related to the level of investment. In figure 2, the equilibrium wages are shown for two training investments of different amounts. The value of the bias for investment AC is EF, as in figure 1. The income difference, as noted, includes this amount which is not return but rather compensation for working additional hours. If, however, the amount of investment required for a particular trade or profession is HC, the wage necessary to persuade individuals to make this investment is the slope of HW". This wage would induce these skilled workers to work even longer increasing the amount of pure compensation for extra work to EG. Thus, as the level of required investment in training is increased, the significance of this bias in the returns data must increase as well.

The immediate question raised by these results is whether it is possible to observe and measure the real return on investment in human capital. May we, in other words, separate income differences which exist into their return-to-training investment and hours-premium components? It would appear that without knowledge of individual utility functions we cannot.

The customary approach of economists when forced to make welfare predictions where price changes are present is to construct an index.

6 The equivalent variation measure is preferred for this purpose, since it reflects the opportunity cost of failing to invest in training in terms of the original prices-the appropriate frame of reference for this decision. That is, if the value of the return in terms of wealth is to be compared with the outlay, then this comparison must be made under conditions of constant prices. The compensating variation measure would be inappropriate, since the value of the return so measured would be meaningful only in the context of the new higher relative price of leisure. A packet of currency is equivalent to another of the same nominal value only coincidentally unless all prices remain constant.



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IFE

A /

H

? MANHOURS OF LABOR

FIG. 2

Schultz (1968) has suggested such an index using income differences standardized at the unskilled work level as an estimate of these returns. Unfortunately, his work contains serious analytical errors,7 but his basic approach has merit. As long as each individual receives strictly an equilibrium return, such a measure understates the real return. This may be seen in figure 1. First note that AB is equal to CE, the income of the unskilled workers. Then, AD represents the income of the skilled worker "standardized" at the unskilled work level OG. On the other hand, BE must equal the real return AC. The estimate of the return as work level- standardized income difference BD always must be less than BE as long as '2 is strictly convex. It is also obvious from figure 1 that the understate- ment using this approach may actually exceed in absolute value the bias in the unstandardized estimate EF which the standardization was introduced to correct.

By a similar process, it may be shown that standardizing at the skilled work level will overstate the real return at equilibrium. Measured return

7 Schultz (1968) makes several errors in his attempt to identify the return. He appreciates that the return is the income effect of the wage differential, but errs in his attempt to isolate this effect. First, he disregards the net wealth effect of the required outlay on training. Second, he confuses the real income effect of a price change with the observed difference in pay before and after a compensating payment has been made. These errors lead him to err in attempting to predict the direction of the bias in hours-standardized estimates (pp. 15-18).



HUMAN CAPITAL RETURNS I20I

JL will always exceed JK ( -AC). In this case, however, the overstatement KL must always be less than EF, the bias contained in the unadjusted income difference. The difference in overstatement via these two measures will always reflect the difference in unskilled income and the imputed unskilled income at the skilled work level; that is EM in figure 1. As a single measure of these returns, income differences standardized at the skilled level always will be a more accurate estimate than unadjusted income differences by this amount.

Summarizing our findings here, we see that an analyst examining markets in equilibrium by standardizing income differences at the unskilled work level would conclude that a surplus exists (that is, costs exceed measured returns). His result when income differences were standardized at the skilled level would indicate a shortage (measured returns exceed costs). Unstandardized income differences would indicate a shortage of even greater magnitude than the latter measure.

As none of these estimates is likely to give us an unbiased measure of these returns, we may legitimately ask whether, as a second-best alternative, we may produce something equivalent to the certainty cases associated with the Lespeyre and Paasche indexes. That is, using either standardized estimate, may we at least identify shortage and surplus market conditions with confidence? This question is affirmatively answered with reference to figure 3.

w4

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vE

uLJ

B

A

0 G H

MANHOURS OF LABOR

FIG. 3



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Figure 3 is identical to figure 1, except that here a number of dis- equilibrium wages together with their respective equivalent variations have been introduced. The untrained hours choice is represented by the tangency of I2 with wage constraint W.. The work level for the unskilled is therefore OG. Amount AC is again the required investment in training. Wage rate W1 is clearly inadequate to repay this investment. The equivalent variation measure of the value of this wage difference is only AB. By the same token, wages We and W4 more than return investment AC, since they have values of AD and AE, respectively.

Let us first look to the matter of surpluses. It will be noted that, whatever market conditions prevail, income differences standardized at the skilled level overstate the value of the return, just as was the case at equilibrium. For example, at the surplus condition wage W1 the skilled work level is OH. Following the procedure established in figure 1, we see that the income difference standardized at this work level would be SU, which must be greater than equivalent variation ST (-AB). Similarly, with respect to shortage wage W4, standardized income difference JR must exceed the value of this wage difference JQ. The convexity of indifference curves insures that returns will always be overstated using this estimate. As in figure 1, unadjusted income differences overstate the return at every wage by an even larger margin.

We therefore may conclude that surpluses identified using the skilled labor work level estimate are genuine. If even an overstated return is less than that required to make the investment attractive to prospective entrants, then we may be certain that the real return is inadequate. This does not imply that all surpluses may be identified in this way any more than Lespeyre price indexes identify all favorable price level changes. Obviously, an overstated return will begin to register excess returns before that investment truly becomes attractive. Nevertheless, those surplus identifications which are made in this way may be treated with confidence.

The case of shortages is somewhat more complex. If standardization of the income difference at the unskilled work level conveniently understated all returns as it must at equilibrium, we might make a similar argument with respect to shortages. Unfortunately, as is apparent in figure 3, standardization at the unskilled work level OG may overstate the real return for certain shortage wages. XWage W4 by this estimate is evaluated at JR, while the equivalent variation measure of the value of this wage improvement over W() is only JQ.

It therefore may appear that some apparent shortages identified by standardizing income differences at the unskilled level may perhaps be overstated surpluses instead. The confidence associated with our measure of surpluses may seem to be lacking here. Fortunately, this is not the case;



HUMAN CAPITAL RETURNS I203

surpluses may not be misidentified as shortages using this measure under what seem to be realistic restrictions.

In order to see this, we need only establish that all surpluses are understated -using this measure. If all surplus returns are understated, then clearly none may be mistaken for a shortage (above cost) return. What is not a surplus return must be either an equilibrium return or a shortage return. As we already have established that equilibrium returns when measured in this way are understated, it must be the case that shortages so identified can be nothing but shortages.

All surpluses must be understated by this technique as long as leisure is a normal good. Observe surplus wage W1. The standardized income difference at the unskilled work level is JK. This estimate will understate the real return JL as long as the unskilled work level OG is less than the level at which schedules AW1 and BLT intersect. At points to the right of this intersection, the value of the estimate (the vertical distance between AW1 and AJS) will be greater than the real return, while at points to the left, it must be less. Clearly, if leisure is normal, point N (identifying the unskilled work level) must lie to the left of point V or its equivalent for any surplus wage, hence to the left of the relevant intersection. As long as leisure is normal, returns estimates using this measure which indicate surpluses must indeed represent surpluses.

In summary, we may conclude that there is no externally observable measure of the real return to investment in human capital, even when the entire return manifests itself in the increased earning ability of investors. Income differences standardized at the skilled work level will overstate this return. Income differences standardized at the unskilled work level will inevitably understate surplus returns, but may overstate shortage returns. We may nevertheless identify some shortages and surpluses with confidence. Inadequate returns, when measured as the present value of expected income differences standardized at skilled work levels, will always reflect a surplus in the relevant market. Excess returns, on the other hand, when measured as the present value of expected income differences standardized at the unskilled work level, inevitably will reflect genuine shortages.

II

Thus far we have identified a bias in current measures of returns to human capital investment. We have noted that the significance of the bias increases with the cost of training. And finally, we have suggested alternative techniques for estimating these returns which, although biased them- selves, will permit us to identify shortages and surpluses with confidence. Before addressing the implications of these results for the existing human capital literature, the model developed will be applied to a somewhat older




area of concern-namely, the price elasticity of the supply of labor. It will be shown that current theoretical treatment of wage changes and their effects on labor output a la Hicks and Slutsky is inadequate to explain the wage/output choices observed empirically. This inadequacy of the models referred to arises from their failure to differentiate between two concep- tually distinct types of wage differences. These will be designated "anticipated" and "unanticipated" wage differences for exactness, but little loss of clarity would result from considering them in the more familiar context of short-run and long-run differences.

Discussion of the slope of the supply function of labor must begin at the individual's choice of the quantity of labor which he will offer at different wages. Yet rarely considered in this context is the crucial issue of why wages differ. If we assume a competitive labor market, fully anticipated wage differences may exist among the employment alternatives in our model only if the level of training investment differs. Short-run wage differences among employments requiring the same training investment may result, on the other hand, from shifts in demand or productivity, as long as such shifts are not fully anticipated.

This difference is important for discussions of price elasticity of leisure, because individuals' labor/leisure choices will differ according to the type of wage differences they confront. Theorizing regarding the positive or negative price elasticity of labor supply functions is carried on almost exclusively in terms of unanticipated differences, while observed wage differences must certainly reflect large elements of anticipated differences. While it is possible for higher wages to be associated with offers of less labor in the traditional theory which treats only unanticipated differences, only positively sloped individual supply schedules will result where all wage differences are fully anticipated

The reason for this is quite simple. In traditional wage theory, the income effect of a wage difference makes possible a negatively sloped supply schedule. Substitution effects always influence output to change in the same direction as the wage. With respect to unanticipated differences, nonhuman wealth remains intact; hence the income effect of the price difference is fully realized as an increment to wealth. But at equilibrium, as has been noted in Section I, no such wealth effect results from anticipated wage differences. The wealth effect of the price differences is "used up" in repaying the required investment in training. If a surplus is anticipated, entry will eliminate it, driving down the wage until the difference which remains merely compensates for the invested outlay. Individuals earning only equilibrium returns even those who might otherwise have backward-bending supply curves-will always work longer hours in their higher-paying skilled occupations than they would in lower-paying unskilled work.

This is illustrated in figure 4. Indifference curves have been con-




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MANHOURS OF LABOR FIG. 4

structed here such that wage increases where nonhuman wealth is held constant result in less labor being offered. Consider an individual who has an initial endowment of OC nonhuman wealth. If he elects to pursue the untrained career, and wages rise unexpectedly from CW to CW', he will reduce his work level from OH to OR. Alternatively, if he elects to invest DC in training for the skilled career and wages fall unexpectedly from DW' to DW, he will increase his work level from OK to O.

On the other hand, in a static society where wage differences are fully anticipated and in full equilibrium, we should expect a cross-sectional survey to reveal a positive relationship between wages and work level. If we observe the behavior of an individual before and after investing in training (or alternatively, if we observe two similar individuals at equilibrium, only one of whom has invested in training), we should observe higher wages associated with longer workweeks. An individual with OC wealth, for example, would work only OH hours for wage CW. If required to invest DC in training, he would work OK hours at the higher wage DW'.

Observed wage differences are, of course, of both types. Certain "struc- tural" differences exist and are generally acknowledged to reflect the investment required for higher-paying skilled employment. At the same



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time, unanticipated changes in demand, productivity, and level of required training investment are constantly changing relative wages. As such changes may be largely unanticipated by current members of the affected trades or professions, the wage changes may provide windfall gains or losses which may offset the substitution effects of these changes.8

Therefore, within an employment having experienced a recent increase in such training costs, we might expect to find older members (for whom the resulting wage increase represents a windfall gain) working less, while new entrants (who must repay the new higher training costs) work relatively long hours. On the other hand, in areas where investment in training is substantial but has been stable for some time, we might expect workweeks to be longer than in unskilled work, even though wages are considerably higher.

Before leaving the topic of the slope of labor supply schedules, some comments are in order concerning an ambiguity in a recent paper by Feldstein (1970, p. 130). Drawing upon traditional sources, he notes, that where labor supply schedules are backward-bending, wage ceilings may induce increased output. From this he concludes, with regard to the "shortage" of physicians, that a ceiling on doctors' fees may be a viable means of overcoming this problem in that such ceilings would lead to increased output of physician services.

The folly of such a prescription is evident from the foregoing. Rapid increases in medical training costs, in conjunction with recent demand shifts resulting from Medicare and the growth of insurance, may have provided previously trained practitioners with windfall fee increases which produced a short-run negative supply elasticity in his empirical tests. Fee ceilings may indeed elicit greater output from those already practicing. The long-run effects of such a policy may nevertheless be disastrous. If higher fees are required to make investment in medical training attractive to prospective entrants, and fees are restrained from reaching this level, such a policy must exacerbate the shortage in the long run. More services may be provided currently, but at the cost of a shrinking and aging physician force. Halting the flow of young men into medicine-those incidently who are likely to work relatively longer hours anyway as we have seen-seems a curious way to attempt to correct a shortage of physicians.

8 Rottenberg (1962) has shown that changes in the level of required investment for licensed practice are less likely to be unanticipated by existing practitioners than changes in training investment for unlicensed work. Specifically, he shows that members of licensed guilds and professions have an incentive to raise the level of investment required for entry into their career fields. This will provide windfalls to already licensed practitioners as long as time limitations or direct restriction prevents numbers of individuals from "loading up" in the field in anticipation of the hike in required investment.




III

The model employed here has made sweeping assumptions with regard to both investor motivations and investor alternatives in the human capital market. Let us examine the implications of relaxing only one of these assumptions-namely, that all investors are initially endowed with equal amounts of nonhuman capital.

As noted above, figure 4 is constructed so as to reflect negatively sloped individual supply schedules for labor where nonhuman wealth remained constant over the price changes. For our purposes here, let us assume this to be the case over the entire range of relevant wage differences and associated levels of wealth endowments. If we assume further that individuals differ only with respect to initial holdings of nonhuman wealth, we can show that those with less of this wealth will tend to invest in training for higher-paying trades and professions, while those with greater wealth will choose the lower-paying occupations.

Consider two sets of individuals, one set with only OC wealth and another with OB wealth. The required investment in training is DC which is shown equal to CB (the wealth difference). Let us assume that at wages given by the slopes of CW and CW' (equal to the slopes of BW and DW', respectively), no excess demand exists for either skilled or unskilled labor. By this we mean that this relative price maintains the flow of new workers into each employment at such a rate that relative wages are undisturbed. At the higher skilled wage, the set with OC wealth will receive only the equilibrium return equivalent to investment DC. Under our assumptions of negative supply elasticity, it is impossible for the individual with greater wealth OB to favor making this investment.

First, by our negative supply elasticity assumptions, an indifference curve must be tangent to CW' to the left of output OH. Negative supply elasticity requires that leisure be a normal good. An indifference curve must therefore be tangent to BW at some work level lower than OH. Finally, since BW is parallel to CW, and CW' is parallel to DW', CW' may not intersect BW at a lower work level than OH. Hence point G must be preferred to point F. The wealthier individual will decline to make the investment in training, preferring the unskilled employment. Furthermore, it may be verified by additional manipulation of geometry embodying the same assumptions that everyone with less than OC wealth will prefer to invest in training, while those with greater than OB wealth will view it with increasing disdain.

Clearly, what is occurring here is economically obvious in view of the foregoing discussion. Earning a return on investment in training entails working longer hours. Since we have assumed that leisure is a normal good, these longer hours are relatively more costly to the wealthy man than to




the poor man. The poorer person views leisure as relatively less valuable, hence requires less compensation for his lost time, pricing his wealthier neighbor out of the market.

The point made here is applicable only where all individual labor supply schedules are backward-bending in the traditional sense, and individuals of equal wealth offer roughly similar work levels for equal wages. The results where these conditions are not satisfied are unpredict- able. Whether these requirements can be supported empirically is a question beyond the scope of this paper. The hypothesis is certainly interesting, however, and deserves further investigation. The suggestion that today's poor will provide tomorrow's educated managerial and professional classes, while the rich filter into less-skilled, lower-paying jobs is a much different interpretation of the cycle of poverty from that currently received.9

IV

Relaxing the other assumptions of our basic model does not alter these or our previous results. For example, in reality individuals choose among a host of professional and nonprofessional careers, rather than between only two as depicted here. The expansion of alternatives has no effect on the predictions of our model. Choices among professional careers may be viewed as mutually exclusive investment opportunities. Some comments on the nature of this choice have already been given. The point remains that at some stage the chooser must test the "best" such opportunity against the alternative of making no investment. This choice will be made along the lines outlined in our model.

The "world of identical" assumptions may be similarly dropped. Once it is admitted that individuals' preferences for work and leisure vary, the picture depicted here reduces to that of conditions which will exist at equilibrium for the marginal individual. All those with a lower regard for leisure in both occupations will receive suppliers' surplus in the form of

9 We might expect this tendency to be offset to a certain degree by the acknowledged superior access of the wealthy to financing for education. This problem is referred to with annoying frequency as somehow arising out of "imperfections" in the capital market. Clearly, however, it results because capital markets function with some sensitivity. Information differences exist between borrowers and lenders with respect to expected earnings and the degree of risk associated with each training investment. These information differences are reflected in the discount rates offered by lenders, which in most cases contain a higher risk component than that dictated by the "real" degree of risk. Individuals with transferrable wealth may overcome this information difference by pledging "collateral," thus converting the unsecured loan to a "riskless". one. As the reduction in the lending charges will exceed the cost of securing the loan (the value of the loan discounted by the real probability of default), the wealthy may in this way reduce their borrowing costs. The poor, who lack such assignable wealth, are prevented from taking advantage of such a possible savings. This must raise the relative cost of the same career preparation for this group. The fact that the wealthy may finance internally has the same effect.




quasi rents reflecting their greater willingness to work. The price at the margin must reflect supply conditions at the margin, however, and the equilibrium return must be earned there.

Relaxing the assumption that individuals are indifferent among types of employment is a good deal more complex. Again, the preferences of the marginal individual are relevant. The fact that some in any employment have a pronounced preference for that employment is irrelevant. What is relevant is the case where some individuals who choose one employment would, were all other things equal, choose another. That is the case, in other words, where the number of those who have a pronounced preference for an employment exceeds the number demanded at the income net of training costs which could be obtained in a less-favored job. In this case, clearly the pecuniary income in the favored employment must fall until the differential in real income just compensates the individual at the margin for his acceptance of the less-favored employment.10 Doubtless some such cases exist. It may be that, if all things were equal, many individuals would prefer to be in an employment requiring investment in training than the one they currently pursue. In that case, we should expect some under- statement of returns from this source, if measured using the standardized income-difference techniques developed in Section I. On the other hand, if untrained employments are preferred, some overstatement may be present. In the former case, this effect would offset to some extent the bias in conventional estimates identified here, while in the latter case it would reinforce it. Whatever the direction of occupational preference, it is clear that this hours bias remains operative. Were it possible to isolate the occupational preference characteristic in measuring returns, the hours bias would still affect results.

At this point we may note how this bias was overlooked by one study which did address itself directly to the question of the length of work week. The Friedman-Kuznets (1945) study was explicit in this regard. Their treatment of the longer hours worked in the professional employment (medicine) was to include it among the list of nonpecuniary advantages and disadvantages which act to form in the minds of the choosers net occupational preferences of the type just considered (Friedman and Kuznets 1945, p. 130). As such a disadvantage, it was seen as being

10 It is interesting to note that a bias similar to that noted above can enter estimates of the value of this preference. If one identifies the value of this preference as the present value of the difference in money earnings of two occupations which require the same investment in training, the result again will be biased upward. The fixed element, the compensation, being returned through an increase in the earning rate will influence individuals to work longer hours. The resulting income differential will thus consist of two elements: compensation for accepting the less-preferred occupation and compensation for working more hours.

11 See also Hunt 1963, p. 327.



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offset by such compensating factors as the high prestige of the profession and the opportunity to render service which medicine offered.

Their error lay in treating the long hours of medicine as a characteristic peculiar to medical practice itself. There is little about the practice of medicine per se which requires that physicians work extraordinary hours per week. On the contrary, medical practice offers physicians unusual freedom in determining the number of hours they do work. Many a harried clerk or assembly-line technician must envy the physician's power to vary his workload by accepting or rejecting new patients. Indeed, it would seem that it is not the long hours of medicine but the freedom to establish his own work/leisure proportions which would affect an individual's net occupational preference in this case. And the effect would appear more likely to be a favorable than unfavorable influence.

In Section II, we noted that in careers having for some time required substantial training investment we should expect longer work hours associated with high incomes. Medicine is just such a career, and the grueling hours long associated with this profession simply confirm our hypothesis. The individual choosing this career selects medicine, realizing that in so doing he is choosing an occupation at which he will work more diligently. But he associates the longer hours, not with the profession he is considering, but with the higher wages found there. If private training costs sud- denly fell to zero in medicine (for example, through income maintenance grants for all medical students), the resulting flood of entrants would cause physicians' fees to fall until they equaled wage rates in untrained work. Under such conditions we would expect the long hours characteristic of medical practice to disappear.

V

Several new hypotheses have been suggested by the foregoing. Systematic testing of these propositions is beyond the scope of the present paper. Nevertheless, limited confirmation of two of these hypotheses may be found in already reported data.

First, in Section I, it was postulated that the amount of bias in unadjusted income difference return estimates should vary positively with the level of investment. This would imply that, if wages in every employment approximate equilibrium, the properly discounted present values12 of earnings differences should be positively related to the level of investment. We therefore should expect to observe professions and trades which require

12 The rate chosen must, of course, reflect the true opportunity cost rate at the time the investment is contemplated. The internal rate of return on human capital (occa- sionally employed for this purpose) is clearly not the appropriate rate. See below.



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higher investment in training consistently appearing to offer higher apparent returns when they are measured in this way.'3

A second hypothesis derived from this model is that, regardless of the elasticity-of-work effort with respect to wages among existing members of any occupational groups, a positive relationship should exist between investment in training and work level across occupational groupings. If short-run schedules do have a negative slope, we should in fact expect to observe the seemingly paradoxical case of negative local responsiveness of hours to wages among existing members of both unskilled and professional groups, where hours actually worked by the latter exceed the former.

While few man-hour studies have been made which isolate the effect of training, those which exist tend to lend support to the hypothesis that greater investment in training leads to longer workweeks. Bureau of Labor Statistics studies by Henle (1966) and Wetzel (1965) in the mid-1960s reported that individuals in professional occupations worked much longer than the average workweek, in spite of the fact that this is one of the few groups which lacks premium pay incentives toward working overtime. Several fairly recent cross-sectional studies also note this tendency (Wilen- sky 1961; Morgan et al. 1962; Morgan 1965; Barlow, Brazer, and Morgan 1966).

Finegan's (1962) results are most interesting in this regard. Using a number of various data sources, he attempted to explain work levels in the United States on the basis of wages, education, and a number of other variables. Finegan noted that when wages alone were regressed on work levels, little if any backward-bending supply response was identified (a positive relationship was identified in some cases). When the effect of education on work levels was accounted for in a multiple regression, however, the negative response of work to wages became highly significant.

13 Observers seeking to calculate the return to some initial formal training or school- ing by measuring income differences may find that their results contain an additional bias. Investment in human capital is likely to be a continuing process over much of any worker's productive life-that is, beyond the period of formal training which is being evaluated. At least some of this continuing investment will take the form of foregone earnings as working time is diverted to investment. If the time path of this subsequent investment is altered by the decision to make this initial investment, then (ignoring leisure considerations) income differences will isolate, not only increased earning ability, but these resulting differences in investment programs. Increased subsequent investment would, for example, inflate these returns. Ben-Porath (1967, pp. 361-62) shows that the direction of change in subsequent investment resulting from such a change in the capital stock may be of either sign, depending upon the induced change in the productivity of time in earning as opposed to capital-formation activities. There would seem to be no reason for the direction of this change in relative productivities to be systematically related to the size of the initial investment, however. That is, it seems unlikely that a large initial investment in training would be more likely to increase the relative productivity of time in earning, say, than a smaller one. We therefore have no reason to expect this bias to affect the results predicted here.



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A simple regression of education on work level was also significantly positive. Finegan was totally unsuccessful in explaining his findings,14 although they are quite consistent with the model presented here. Both negative supply elasticity with respect to wages where investment in training is held constant and positive elasticity with respect to training itself are exactly what we should expect.

In the most detailed of these studies (Wilensky 1961), the predicted relationship also may be observed. Wilensky noted a positive correlation between workweek and general level of occupational strata (involving greater levels of education and training). Within the professional strata, this positive relationship between workweek and investment in training was more pronounced. Groups of lawyers, university professors, and engineers were asked to report their workweeks. The percentages of each of these groups working over fifty-five hours per week were then listed. The proportions of the lawyer and university professor groups in this long workweek category ranged from 29 to 38 percent, while those of the engineer groups ranged from 10 to 24 percent. Disaggregated data of this type is notoriously weak evidence of such relationships, since the influence of tastes and local technical constraints may dominate the influence of the variable of interest. Nevertheless, the failure of this and other studies cited to offer contrary evidence seems to suggest some probability of confirmation in a more thorough and rigorous test of this hypothesis.

The former hypothesis, that the apparent returns as calculated using the unadjusted income difference measure will be positively related to the size of the initial training investment requirement of the occupations, is consistent with studies reporting high returns to education (Hansen 1963; Becker 1964). More substantial support is found in studies which rank occupations by the present value of net returns. The familiar finding of Friedman and Kuznets (1945) that medicine (the more training- intensive profession) seemed to offer higher "returns" than dentistry supports our hypothesis, as does the more recent study of Carol and Parry (1968). In the latter study, sixty-seven occupational categories were ranked by the present value of their income streams net of training costs. While costs of training in individual categories was not reported, a cursory glance at their rankings is enough to establish some consistency with the above hypothesis. Of the twenty categories offering the lowest "returns," fifteen were among those for which absolutely minimal skills are required (for example, porters, janitors, laborers, etc.). On the other

14 Finegan (1962) noted the connection between investment in training and higher wages. Considering a portion of the wages of skilled workers to be human capital returns, he argued that work/leisure decisions of such workers would be affected by only the residual portion of the wage net of this return. Clearly, this is incorrect. Utility maximization requires that workers adjust to the work level at which their marginal rates of substitution equal the wage rate, regardless of previous investments.



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hand, ten of the sixteen categories offering the highest "return" required at least a college degree (for example, doctors, dentists, lawyers, chemists). With the exception of high school and elementary school teaching, no category requiring a college degree ranked below twenty-second. The re- mainder of the categories in the top twenty were for the most part skilled crafts (for example, toolmakers and designers) and various managerial categories where training investment was also obviously substantial.

Although such findings are consistent with the predictions of our model, we must treat them with considerable caution. These results may reflect positive selection according to ability in the more training-intensive occupations. More important is the sensitivity of such results to the discount rate employed. As Lewis (1963, pp. 118-24) has pointed out, the high relative returns to medicine identified by Friedman and Kuznets (1945) disappear if higher discount rates are used. Similarly, the apparent pecuniary attractiveness of training-intensive careers revealed by Carol and Parry (1968) simply may reflect that the higher incomes earned in later years were inadequately discounted.

The relevant discount rate must reflect the potential investors' opportunity costs of making such investments. Incomes of individuals investing in training should be below the levels of their permanent incomes. Hence we should expect them to be net borrowers as a group. Some question may be raised whether loans to finance training were available in the 1930s at 4 percent-the discount rate used by Friedman and Kuznets (1945)-or, in addition, whether similar loans could be had in the early 1960s at 5 percent, the rate used by Carol and Parry (1968). Future efforts to test this hypothesis more rigorously must therefore make every effort to ascertain with greater precision the cost of borrowing for this purpose.

VI

Although little has been established in this rather casual first pass through available evidence, the implications of the model itself seem of sufficient import to merit more careful testing than has been afforded them here. Confirmation of the model's predictive power would indicate that studies testing the "adequacy" of aggregate investment flowing into training and educational accounts (for example, Hansen 1963; Hunt 1963; Becker 1964) have overstated these returns. Future studies, cast along similar lines can be expected to contain the same bias.

Even more serious are the implications for those studies which attempt to use returns information to identify shortages of individuals with particular types of training. Identification of shortages by ranking such apparent returns to investment in training in each employment may lead to selection of the "wrong" occupations. As such rankings make no allowance for the additional hours worked in employments requiring greater investment in



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training, these opportunities appear superficially more attractive-at least to the analyst. The identification of such apparent shortages may lead such analysts to recommend that these professions be made more attractive through study grants, new schools, or enriched training programs. Adop- tion of such recommendations would have the effect of exacerbating real shortages in other employments. Alternative techniques for identifying some shortages and surpluses with greater precision have been offered.

That individuals are aware of the value of their leisure, as well as the incomes offered by various occupations, well may explain why such apparent shortages of trained personnel never seem to get satisfied. Chronic shortages of exotically trained individuals frequently bemoaned in govern- ment and manpower circles may not be shortages after all. Economists who suggest that restrictive practices are responsible for these shortages in critical professions such as medicine are therefore advised to take another look at the burdensome workweek which the average physician puts in.

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Lewis, H. G. Unionism and Relative Wages in the United States. Chicago: Univ. Chicago Press, 1963.

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