Benefit-cost analysis of public programs for education and training

Socio-Eeon. Plan. Sci. Vol. 4, pp. 283-289 (1970). Pergamon Press. Printed in Great Britain

BENEFIT-COST ANALYSIS OF PUBLIC PROGRAMS

FOR EDUCATION AND TRAINING

PAUL FELDMAN* and NEIL M. SINGER?

(Received 13 Ocroher 1969)

Government training programs such as the Job Corps are usually evaluated as investments in human capital which are desirable if the net present value of trainees’ incremental future earnings is positive. In a properly-functioning market economy, however, subsidies for self-investment are never efficient and must actually reduce real national income.

If the assumption of perfect markets is dropped, subsidies may still be inefficient. Differences in the psychic cost of training, or barriers to entry, or a mal-distribution of income may be the basis for “too low” a level of educational investment. Subsidies are not necessarily the appropriate public policy in any of these cases.

Subsidies may be efficient if the external benefits from training exceed the amount of the subsidy. Accordingly, the efficient amount of public expenditures on Job Corps and other training programs is the amount of external benefit conferred upon society. The trainee should be asked to invest the difference between the total cost of the program and the efficient subsidy. Equity considerations may then determine the government’s willingness to lend or grant additional funds to the trainee.

GWERNMENT training programs such as the Job Corps, Neighborhood Youth Corps, or those aimed at dropout prevention are usually evaluated on the basis of their efficiency as investments in human capita1.S The criterion applied in benefit-cost studies of such programs is, “Does the program increase the present value of the earnings of trainees by more than the cost of the program ?” The usual conclusion of these benefit-cost studies is that the net present value is positive (although close to zero), and that the programs are made more desirable by their external effects. It is not our purpose to criticize the con- clusions reached in these studies. Rather, we suggest that the usual comparison of private benefits with public expenditures is irrelevant in determining the efficient level of Govern- ment funding of training and education.

To make the argument clear, it is helpful to consider the opportunity for Government increases in social welfare when markets function perfectly, and then to consider the opportunities as the assumptions of perfection are relaxed. In a perfectly competitive economy in which all workers possessed identical physical and mental endowments and had equal wealth, the distribution of money income might nonetheless show extensive

* Program Analysis Division, Institute for Defence Analysis, 400 Army-Navy Drive, Arlington, Virginia 22202.

t Department of Economics, College of Business and Public Administration, University of Maryland, College Park, Maryland 20742.

: For example, Cain [3] p. 3, says, “The impact of Job Corps on increasing the earnings of the Corpsmen above what their earnings would have been in the absence of the program is the sole measure of benefits used.” Page [6] p. 260, says, “ . . . benefits to be derived from retraining in terms of our efficiency objective may be measured as the change in individual income streams.” A number of other studies follow the same general approach. See, for example, [ 1,2 4,5,7-91.

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284 PAUL FFLDMAN and NEIL M. SINGER

inequality. Among the possible sources of income inequality are: (I ) different preferences among workers for jobs of varying degrees of odium, (2) differences in the “psychic cost” of education to workers, (3) different demands for income, and (4) different attitudes toward risk. In such an economy, all individuals would not invest equally in education (or anything else) even if all had equal access to capital and, therefore, all would not receive the same monetary rate of return on investment. For each worker, the optimum amount of self-investment would equate at the margin the monetary rate of return and the money equivalent of his disutility for self-investment.

These equilibria are shown in Fig. I. Since all workers are identically endowed, they all face the same marginal efficiency of investment (MET) curve showing the monetary rates of return to different amounts of training. The market rate of interest is assumed to be Y,. Workers need not be indifferent to the act of self-investing through training. Those who experience disutility from training will incur a psychic cost in addition to the market interest rate, and hence will “supply” themselves for training along an upward-sloping curve such as Wz. At equilibrium, they will obtain T, units of training having a monetary rate of return of rs. The difference I’? --I’, is, of course, the psychic cost of the marginal unit of training. Conversely, those workers who derive utility from training will receive a non- monetary return that will lead them to undertake training to the level T,, where the net monetary cost (r, mPr,l) is equal to the marginal utility of training. Only workers who are indifferent to training will “supply” themselves along W, and invest at T,, the level at which the monetary rate of return equals the market interest rate.

OF RETURN

Benefit-Cost Analysis of Public Programs for Education and Training 285

Typically, each worker will have a unique W curve expressing his marginal utility for training. To simplify the analysis, we assume the existence of only two groups of workers,

Group 1 indifferent to training and Group 2 deriving constant marginal disutility from it. Although Group 1 and Group 2 workers are identically endowed, the “net” ME1 for Group 2 will lie below the ME1 for Group 1 by the monetary equivalent of the (constant) marginal disutility of training. This situation is shown in Fig. 2, in which the vertical

distance between (linear) MEl, and MEI, is constant. Group 1 workers invest up to T, and Group 2 workers to T,, where the monetary rate of return r2 exceeds the market interest rate rl.

RATE OF RETURN

FIG. 2.

Monetarily efficient self-investment can be increased only by subsidizing Group 2 workers, who could earn a monetary rate of return equal to rl by increasing their investment to r,. The size of the necessary subsidy is shown by the shaded area in the graph. The subsidy would in effect, shift MEI, to MEI,. But in no case in which markets operate perfectly will subsidies improve the efficiency of resource allocation. The point is that when net returns to self-investment are calculated inclusive of psychic costs and returns, the efficient amount of investment is realized by the independent actions of individuals who will invest to the point at which the marginal utility of the return to self-investment equals the marginal disutility of the act of self-investment.

A typical benefit-cost analysis of the subsidies, however, would certainly indicate that they should be provided if the income increase of the trainee exceeded the total opportunity cost of the training. Benefits/unit of training would be measured in all cases by the monetary rate of return to subsidized workers, a rate by definition greater than the market interest

286 PAUL FELDMAN and NEIL M. SINGER

rate. The benefit-cost criterion, therefore, would indicate incorrectly that subsidies were justified on an efficiency basis. In fact, subsidies would merely leave the real incomes of subsidized workers unchanged, since these workers must be compensated by the subsidy for the net disutility of investjng to earn additional income. The reaf incomes of unsubsidized workers, on the other hand, would fall, due either to a tax or to higher market interest rates and co]~sequentIy reduced self-illvestment. * In a general equ~I~br~um context, the eventual increase in total income would exceed the investment cost, but it could not guarantee compensation of the unsubsidized workers. There are thus two arguments against the usual benefit-cost approach: subsidies are “efficient” only if the non-monetary component of subsidized workers’ incomes is ignored,t and they produce a net monetary benefit only if the distributional effect is ignored.

The real world does not, of course, correspond to the perfectly competitive model, particularly in the assumption that individual workers’ endowments are identical. Argu- ments for income redistribution may rest upon differences in individuals’ abilities to earn income and the resulting presence of some families at “lower than acceptable” income levels. Arguments for Government interference in individual choice concerning investments in education may also arise from market jmperfectior~. If all ind~vjduals do not have equal access to capital, for example, rational investment behavior by individuals will be socially ine~~cient. Simil~~r~y, if some workers are barred from certain occupatioIls, the amount of investment will not be efhcient.

Nonetheless, subsidies to self-investment cannot be justified on the basis of efhciency even in a less-than-perfectly competitive economy. Redistributive subsidies will benefit (in a monetary sense) those workers with high disutility for earning income through self- investment, but that group of workers has not been shown to be identical to the group of workers with low incomes. “Efficient” loans to train individuals who are unable to borrow privately will increase total investment in human capital, but need not be subsidized. Barriers against workers’ freedom to enter particular occupations cannot easily be over- come by training, since barriers typically are noneconomic; in any case, investment subsidies will discriminate against barred workers in occupations where the training require- ments are low.

The only basis on which subsidies to self-investment may be efficient is that subsidized self-investment confers external benefits on other individua1s.S It is frequently asserted that externalities of this type do exist, although the efficiency argument for Government subsidies never is rested upon them. Weisbrods suggests that among these “real” externalities are the reduction in losses due to crime and delinquency, increased participation in social cultural and political activities, and intergenerational effects. Other externalities arise from reduced costs of administering welfare transfers, to the extent that the need for such transfers is eliminated by investment in training and education. In addition, there

* These statements are true because we have assumed linear ME1 and constant disutility of training for Group 2. If these assumptions were relaxed, the statements would hold only at the margin.

$ To be consistent in seeking efficiency in money terms, those who enjoy training and consequently over-invest should be taxed to reduce their investment to an “efficient” level. That following such a consistent policy would be clearly absurd should clarify the argument when the proposal is instead, a subsidy to increase investment.

5 Weisbrod [lo], p. 26, makes the same point: “If all benefits of education accrued to the student, then, assuming utility maximizing behavior and access to capital markets, there would be little reason for public concern for the adequacy of education expenditures . . .”

f See his comments in [ll], pp. 134-139: A more extensive list of externalities is presented in [IO].


may be effects on the productivity of other factors of production which are not recoverable by the worker who invests in himself.

The significance of these externalities is that they determine the extent to which society, as distinct from the subsidized worker, benefits from the self-investment of the latter.* Well known theorems of welfare economics state that, in the presence of a general externality, allocative efficiency can be attained only if the cost to the external beneficiaries is cqua1 to the external benefit received, at the margin. Government subsidies for individuals’ self- investment are efficient only to the extent that such investment yields benefits to society at large. The proper criterion to be applied in evaluating Government subsidies to self- invest?nent is the value of external benefits, such as those listed above. To the extent that the total cost of self-investing exceeds the external benefits, that excess should be borne by the individual. Subsidies greater than the external benefit will be inefficient even though the monetary rate of return to the individual is in excess of the market interest rate.

Despite the abstraction of the analysis, it may easily be applied to Goverilnlcnt programs of investment in human capital such as the Job Corps. At least one of the benefits of Job Corps training is that the productivity and income of the trainees are increased. Following the discussion above, there would be no efficiency basis for Government subsidy of Job Corps training if the trainee’s increased income and productivity were the only benefits derived.

If it is felt that Job Corps training yields substantial external benefits, two benefit-cost calculations must be made. First, the Government must calculate all benefits accruing to members of society orher rhnn the trainee. The extent to which external benefits are received presumably will vary with the location, the age and sex of the trainee and the level of training. On the basis of these factors, the Government should offer subsidies to individual trainees. The amount of subsidy, of course, may be greater than or less than the cost of training, but we may expect that the social demand curve will be downward-sloping since the external benefits listed above seem likely to diminish as training increases beyond some “threshold” level.

The second benefit-cost calculation must be made by the prospective trainee. His costs would be reduced by the amount of the subsidy offered by the Government; his benefits are the expected increase in his income and whatever other value he may place upon receiving training. In some (perhaps most) cases, the trainee would still incur some cost in entering a training program, although it is not di~cult to imagine that in some instances the value of external benefits might induce society in effect to bribe trainees to enter the program. It is, of course, economically efficient to charge the trainee the cost of training in excess of the subsidy. Only under such a set of subsidies and user charges can society obtain the e~cient amount of inves~ent in trainee capital.

Two points remain to be discussed. First, why is “increased income”, measured as the benefit in benefit-cost analyses of other Government investments, inapplicable here’? in general, the contribution to national income of a Government investment is appro- priateIy defined as the benefit when what is being produced is a “quasi-marketable” good.

* In a comment following Weisbrod [ll], Machlup restates this issue most clearly: “lf a program or measure is definitely to the benefit of a special group within society, then it is perfectly proper to ask whether the rest of society shall accept this program or measure though the entire benefit from it accrues only to that group, only to that particular part of society . . . It may be held that the rest of society should want at least to have some “cut” of the benefits-that, in other words, there should be truly external benefits accruing to the rest of society.” (pp. 151-l 52). This point is made, although not stressed, by Weisbrod Ill], p. 139. He there considers only external transfer effects, that is, reductions in the trainee’s welfare receipts and taxes paid by others.

288 PAUL FELDMAN and NEIL M. SINGER

By “quasi-marketable”, we mean a good for which it is possible to specify a dollar value, although for some reason the normal functioning of markets will not serve to set that value. The usual reason for the failure of markets is that an investment or its output is, to some extent, “public”: that it yields benefits to society which cannot be captured in the market by the producer. These conditions do not apply to the income generated by seff- investment, for the increase in earnings is completely private. The “public” elements of education and training, which should be the focus of the analysis, are usually excluded from consideration on the grounds that they cannot be quantified. Under the usual structuring of the problem, therefore, benefit-cost anaiysis does not provide valid grounds for determining Government subsidies.

Second, what is the practical value of this discussion for policy formulation ? It is not easy to quantify external benefits such as “increased participation in social activities, etc.” and little or nothing is known about the rerationship between education and crime or about the costs of crime. Clearly, it is difficult to determine the optimum amount of pubiic investment in human capital, but this difficulty is characteristic of public sector allocation problems. Equally clearly, it is misleading or absolutely erroneous to substitute “the net increase in trainee income” for the proper investment criterion, “net external benefits”, because the substitute criterion will justify investment when investment is ine~~ient and, presumably, will discourage investment when external benefits are high but direct benefits low. Instead of relying on misleading studies, public officials would be better advised to make their current allocation decisions on the basis of intuitive judgments of the magnitude of external benefits. At the same time, to guide future allocation decisions, they shoufd support research on the measurement of externalities instead of studies which measure purely private benefits.

In this paper we have been concerned exclusively with allocative efficiency. If, however, there is a justification for training programs as a transfer activity, the justification is not simply that net income is positive. Failure on the part of trainees to undertake training when it has been demonstrated to be a profitable self-investment can be due only to (I) a high disutility for earning income, (2) lack of access to capital markets, or (3) ignorance (on the part of the trainee) of the direct benefits resulting from training. As argued above, (1) is not a justification for subsidies. The efficient policy in response to (2) is to make capital available to trainees, perhaps directly or through public insurance of private loans. (The Federal Government is no stranger to insurance of this sort.) The trainee may experience (3) for a variety of reasons, such as low expectations engendered by past unfavorable treatment, or high risk attached to earning future income, or the afore- mentioned barriers (perhaps associated with race). Whatever the basis for (3), its existence does not in itself represent an argument for a subsidy for training. A subsidy in the form of an advertising program to inform the potential trainee of the value to him of training would be much more appropriate.

If equity considerations militate for transfers to the trainee group, the question for policy makers is “What is the least-cost method of securing an increase of a given amount in the income of the target group?” An economist’s instinctive answer is, “The most efficient income transfer is a direct subsidy,” but secondary effects must be considered, such as social willingness to make direct transfers and the distinctive effects of such transfers. Nonetheless, it certainly is not obvious that training programs are efficient transfers refative lo other ways qf increasing fr~~nees’ incomes. Now that benefit-cost analysts have devoted such extensive efforts to measuring the relationship between training and income,


further efforts should be devoted to measuring the transfer magnitude of other expenditures, such as urban renewal. Only then may it be possible to justify public training programs on the basis of the increase in trainees’ incomes.

REFERENCES

1. W. BATEMAN, An Application of Cost-Benefit Analysis to the Work-Experience Program, AER (May 1967). (But see disagreeing comments of M. ANDERSON and H. ROWEN).

2. M. Bonus, The Economic Effectiveness of Retraining the Unempioyed, Research Report -35, Federal Reserve Bank of Boston (1966).

3. G. CAIN, Benefit/Cost Estimates for Job Corps, University of Wisconsin, Institute for Research on Poverty, Discussion Paper P-67.

4. G. CAIN and G. SOMERS, Retraining the Disadvantaged Worker, University of Wisconsin (Madison, 1966).

5. E. HARDIN and M. BORUS, An Economic Evaluation of the Retraining Program in Michigan. Pruceeding.s of the American Statisficai Association, Business and Economic Stafbtics Section ( 1966).

6. D. PAGE, Retraining Under the Manpower Development Act: A Cost-Benefit Analysis, Public Policy (1964).

7. T. RIBICH, Education and Poverty, Brookings Institution, Washington. In press. 8. D. &WELL, Training the Poor: Ration&e for a Ben&-Cost Ana1y.G qf MITCE,

Committee on Manpower and Economic Development, North Carolina Fund, Durham (I 967) mimeo.

9. G. SOMERS and E. STROMSDORFER, A Benefit-Cost Analysis of Manpower Retraining, Universitv of Wisconsin. Industrial Relations Reprint Series No. 64 (1964).

10. R. WEISB~OC), External ‘Benqtits of Public Educaiion: An Economic Analysis, Princeton Industrial Relations Section (1966).

I I. B, WEISBROD, Preventing High School Dropouts in R. DORFMAN, ed., M~~a.~~~rj~?~~ Beneath of ~overni~te~t lnuest~lents. Brookings Institution, Washington (1965).

Benefit-cost analysis of public programs for education and training

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