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June 12, 1979

    
LOS ANGELES -- Education is the largest single industry in the United States. It is highly suhsidized by the government.  Estimating the economic value of an education required the application of benefit-cost techniques to transform so-called intangiblebenefits into policy parameters.
     It is, therefore, highly appropriate to devote in this study considerable space for the treatment of public-expenditure analysis in education.
    The general case for government intervention in the economy appears to be relatively important. Although education is not a pure public good, it is generally regarded as a quasi-public good.
     For example, a lecture that is given to five students may be given, without substantial loss to one hundred students, provided that a large enough lecture hall is available.
     Some loss to the five original students may be sustained due to the reduced personal contact with the lectul c but it is clear that some element of joint consumption exists. Of course, excludability is possible. And for that reason an educational system could and does operate through the free market system.
     Perhaps the most important reason for government's involvement in education is the alleged existence of external effects. It is commonly felt that, for example, elementary education for Mr. Jones' children is not entirely Mr. Jones' business.
    If Mr. Jones fails to provide such education to his children, society as a whole may suffer. This may be reflected in the fear that an uneducated child may be so unproductive that he is likely to become a public charge.
     Further, it many parents, like Mr. Jones, fail to provide "adequate" education to their children, society will suffer in the form of a less educated electorate - considered to be less able to make "rational" electoral selections - reduced demwid for and usefulness of such items as checking accounts, books and magazines, alld so on.
     Moreover, education is expected to affect one's associates, employers, acid 83 children; studies have documented that the more educated parents are likely to provide more education to their children (what is termed the intergenerational effect).
     So, the belief that external effects of education are quite important is probably the single most important reason for government involvement in education. Other reasons, such as risk and time preference, are also relevant.
     Even more important is the desire to effect income redistribution through educational expenditures. It has long been asserted that government subsidization of education permits a greater degree of equality of educational opportunity, which, in turn, leads to greater equality of income and wealth.
     Whether each or both parts of this assertion are true is subject to at least some controversy.' Despite the lack of consensus in this regard, it appears that public funds have frequently been channeled into education on the basis of income distribution goals rather than allocative ones.
     Of paramount importance to a rational analysis of public investment in education is the ability to provide comprehensive measures of costs and benefits.
     Clearly, the measurement of educational benefits is far from simple. Furthermore, measurement of educational costs is not quite as simple as one might expect. The reason for this is that direct costs (operating costs, interest on debt, and capital costs) are only a part of total costs.
     An important cost element that must be estimated is earnings foregone, i.e., the opportunity cost of employment to persons who choose to engage in an educational endeavor.
     Educational costs may be thought of in three ways, separate direct and indirect costs. As a general principle, all economic costs are opportunity costs, i.e., the opportunities foregone because an educational investment is undertaken. The direct costs are more readily measurable because educational institutions systematically provide expenditure data. Indirect costs must be imputed.
     In addition, educational cost data usually reflect the total cost, or average cost, of educational services provided over a wide range of educational programs.
     For policy purposes it is frequently necessary to estimate marginal costs associated with a given program or range of programs. In what follows we will give consideration to both the general scheme by which cost categories might be estimated and the analytical framework that might be utilized to estimate average and/or marginal costs.
     Estimates of direct costs of education have been obtained for a wide range of educational activities over the present century. Various studies endeavored to measure the costs of specific educational programs (such as costs of compensatory education, dropout programs, vocational programs, etc.).
     The data base for most of the studies has been expenditures on school operations, debt service, and capital outlay. The expenditure data provided by school reports are highly useful for some purposes and only marginally useful for others.
     For example, if it is desired to obtain estimates of aggregate resources entering elementary and secondary public education, data reported by the U.S. Office of Education or the National Education Association are highly useful, even if not complete.'
     On the other hand, if one wishes to consider the costs of specific programs within the general framework of public elementary and secondary schools, the availability of desired data is often limited. One problem with expenditure data is that they are not necessarily identical to costs.
     If a set of expenditure data is based on an academic year whereas comparable benefit data are available only for a fiscal or calendar year, some adjustment in the data must be made. Further, if expenditure data are based on methods other than accrual, some difference between expenditure and costs is likely to exist.
    Capital outlays are not generally identical to capital costs. Capital costs should be estimated on the basis of capital consumption (depreciation) and implicit rent, while capital outlays and interest reflect payment for new and old structures, respectively.
    The need to obtain separate estimates of capital costs has recently been recognized by several economists. A more fundamental problem with expenditure data is that they do not necessarily reflect the absolute minimum costs necessary to sustain a given educational activity.
     The fact that Edison High School spends $2.5 million on its secondary education curricula cannot be taken to imply that the same educational services could not be obtained for less than that sum.
     Studies have shown that schools that are too small (and perhaps too large) are likely to spend more per pupil for the same educational output (variously measured by achievement scores and/or an index of "key" educational in puts).4
     Since economic cost implies the absolute minimum cost necessary to sustain a given activity, utilization of school expenditure data is likely to overestimate the true potential social costs.
     Indirect cost expenditure data, even if the above mentioned difficulties are assumed away, do not provide a sufficiently broad basis for determining educational costs.
     The most important omission is earnings foregone. It should be noted at the outset that the relevance of earnings foregone has been a source of controversy in recent years. Yet most authors - this author included - hold the view that foregone earnings should be considered explicitly.
     The rationale for this is quite simple: suppose a given group of individuals who are presently in Edison would have decided against going to school. Presumably, they would have been engaged in some activity, most likely they would have gone to work.
     The earnings that they could have earned if they did not go to school should be considered an integral part of the cost of going to school. The argument that some schooling is in any event compulsory or that child labor laws restrict the work activities of young persons does not really hold water.
     Here is why. These individuals would still have been capable of performing some or any productive activities. Therefore, estimates should be made to provide as accurate an estimate of earnings foregone as is practicable.
     Another objection to earnings foregone has been the argument that when educational costs of a large number of students are considered - as distinct from a consideration of a few students only - the measurement of earnings foregone is impossible since an injection of a large number of individuals into the labor force would likely upset wages and the occupational structure of the labor force.
     That such an "aggregation problem" is likely to exist cannot be dismissed. The dilemma facing the decision maker is whether he should ignore earnings foregone altogether, or provide estimates based on current labor market conditions. It seems to this author that ignoring earnings foregone is clearly indefensible.
     In the absence of a method by which the aggregation problem could be solved, it is convenient to assume that the existence of an aggregation problem would not materially affect estimates of earnings foregone. Capital Costs.
     Since capital outlays and interest cannot be used as measures of capital costs (in any given year), and since depreciation must also be imputed, one might consider the estimation of capital costs under the "indirect cost" category.
     To estimate depreciation of buildings and equipment one should obtain, ideally, a schedule of actual wear and tear as well as obsolescence of the assets. Such schedules can rarely be obtained, however.
     Consequently, some other methods must be used. The simplest procedure would be to use one of the acceptable depreciation methods used by accountants ( allowed by the Internal Revenue Service), such as the straight-line depreciation schedule which is merely a function of expected life of the asset and its salvage value.'
     If a given 'Depreciation in a given year = (original cost of asset less salvage value) =(number of years of economic life of asset). If an asset was purchased at a sum of $X, has an expected economic life of n years, and has an expected salvage value of $S, the straight-line method would imply an annual depreciation of $(X - S)/n.
     There are other methods.
     One could obtain the market value of assets and compute depreciation for each class of assets on the basis of past experience. Market value may be estimated on the basis of insurance valuations (unless undepreciated original cost is the basis for insurance) or independent appraisals.
     One other method that has been used in several studies is the capital recovery factor (CRF), which provides for annual ammortization of original cost and interest payments.'
     In addition to the depreciation estimates, one should consider the rental value of school properties. If the buildings and equipment were rented to private schools or to other enterprises, some rental value would be forthcoming.
     Clearly, there is no uniform rental value on school properties. In areas where such facilities do not have alternative uses, at least in the short run, rental values would be negligible. In other, more populated areas, rental values may be rather large.
     Cost of Tax Exemption. Several other types of costs must be considered. One of these is the cost of tax exemption. The fact that educational institutions are exempted from payments of various federal, state, and local taxes, reduces the prices at which schools are able to buy goods and services.
     If market prices are the correct guide for efficient resource allocation, the lower effective prices paid by schools should be adjusted to reflect going market prices. Here, again, there is an element of aggregation involved, since property taxes, for instance, in a given locality are by-andlarge levied for the purpose of running the schools.
     Had the schools been eliminated, most of the property tax would be superfluous. It follows that a full adjustment for lower effective prices is not required.
     What portion of tax advantage should be considered as reflecting effective lower prices depends on the extent to which the cost of educational services determines the tax rate. Also, it is necessary to obtain the assessed valuation of tax-exempt properties.
     Other Costs. Finally, transportation costs, costs of supplies and books, and other costs sustained by parents and children (not accounted for in operating expenditures) must be estimated and included in the calculations. Lack of data has forced researchers to employ arbitrary rules of thumb to estimate such costs.
     Ideally, data should be gathered from students, their families, or sellers of school supplies, for the approximate costs of such activities.
     The benefits of education are atone and the same time obvious but difficult to measure. It is common knowledge that education is a means by which persons could climb up both the social and economic ladders in society.
     But the exact magnitudes of such benefits are extremely difficult to estimate. Still, consider able progress has been made in recent years in this area.
     For descriptive purposes, it would be useful to distinguish between direct and indirect benefits and between consumption and investment benefits. Direct `' benefits are those that may be directly attributable to a given educational endeavor.
    Several classes of indirect benefits will also be discussed. In addition, estimation of benefits has largely been confined to what has been termed the investment component, as distinct from the consumption element. The investment component includes the benefits of education that are manifested in increased productivity of individuals.
     Consumption benefits are largely confined to the satisfaction people get while undertaking an educational endeavor; it should be noted, however, that insofar as education increases one's capacity to enjoy literature, art, etc., consumption benefits extend to future periods (following completion of the educational program) as well. Direct Benefits.
     Most econoicsts who have attempted to tackle the job of measuring educational benefits have employed the "human capital" approach. This approach is based on the presumption that educational investment is much like other investments which individuals could undertake - an investment which has an expected return over cost - the only difference being that education is an investment in persons, not physical assets.
     The most common procedure to measure such returns has been the additional lifetime earnings method. This method is used to calculate the extra income an individual is likely to earn over a lifetime as a consequence of a given educational investment.
    Consider additional lifetime earnings and benefits to an individual with 8 years of schooling of completing high school (12 years of schooling). Census data cross-classified by age and education have been available for three consecutive decades (1950, 1960, and 1970).
     Take the 1970 Census, for example, and calculate mean incomes for all individuals who completed 12 years of schooling for each age. Do the same for lifetime incomes of individuals who completed only 8 years of schooling.
     Then calculate, for each age, the difference between mean income at age x with 12 years of schooling and mean income at this age with only 8 years. When these differences are summed over one's expected productive lifetime, say up to age 65, we obtain the extra lifetime income due to secondary education.
     Symbolically, let mean income at age x for an individual with schooling level s be denoted by YXs. Mean income at age x for persons undertakings - 1 Table 7-3 Benefits of Higher Horizons Progam Elementary School Junior High School 1.
     Discounted additional lifetime income associated with one extra year of schooling $2,410 $2,838 2. Average percent of equivalent year of schooling gained due to the program 3% 3.3% 3. Benefits per student (line 1 X line 2) $ 72 $ 94 Source: Adapted from Ribich (1968), Table 5, p. 71. ferentials, and then the simpler method (outlined above) could be employed to calculate the adjusted lifetime income streams.
     Value of Incremental Achievement. An interesting method for studying the potential of special programs for increasing the achievement of "disadvantaged" students (known generally as compensatory education programs) was suggested by Ribich. This method assumes that the major educational output is achievement in basic skills.
     Ideally, a production function approach should be used to estimate the extra achievement in basic skills due to a given extra educational effort.'9
     Since achievement scores are given in terms of equivalent years of education, the method permits an evaluation of how many equivalent years of education (or fraction thereof) the average student acquired as a result of a specific program.
     The additional educational output is then transformed into additional lifetime earnings, utilizing the cross-sectional additional lifetime-income approach.
     This method is illustrated in Table 7-3 for the Higher Horizons program in New York City. These benefits are based on 1959 data, on the assumption that a discount rate of 5 percent is appropriate.   When the Ribich method is properly utilized, it has far-reaching implications.
     However, Ribich himself did not consider explicitly an educational production function in determining educational benefits. The education production function would isolate the benefits of a given program when other factors are considered simultaneously.
     In general, let output (achievement scores in the Ribich case) be denoted by Y. Consider, further, a vector of n schooling-related factors, X1 , X2, . . . , Xn, and 18Ribich (1968), Chapters IV-V. 19 The educational production function is described below.
     Similar frameworks have been employed by Hunt and Rogers to study the returns to college education, Cross-Sectional and Cohort Methods.
     Another difficulty with the additional-lifetime-income approach as discussed here is the use of cross-section data. That is, income expected at age x was based upon mean income of those who were x years old at the time the census was taken.
     Consequently, the method assumes no change in the earnings structure as well as no increase in earnings differentials due to economic growth. (If economic growth were to increase all wages in the economy by the same absolute amount, no change in earnings differentials would be expected; however, if economic growth increase all wages by the same percent, income differentials would increase.)
     There are two alternatives that may be employed to account for economic growth. The simplest approach, used by Becker, Klinov-Malul, and Danielsen, is to assume that earnings differentials are likely to increase at, say, one or two percent, and then recalculate expected earnings differentials accordingly.
     In Becker's calculations, an adjustment in earnings differentials for an assumed growth rate of 2 percent is shown to increase the internal rate of return to college education by over two percentage points. The other, more complex alternative, is to employ the so-called cohort method." In principle, the idea is simple.
     One needs to follow the earnings experience of a given cohort over a period of time and then use such age-earning information to project current expected income of individuals in a given educational level.
     For example, we may observe the earnings of secondary school graduates, all of whom were 18 in 1925, from 1921 to 1972 (when they reache the assumed retirement age of 65). The stream of,earnings over that period would reflect changes in the structure of the labor market as well as economic growth. If the same procedure were employed to measure earnings of another cohort, who were 18 in 1925 but who completed only 8 years of schooling, it would be possible to study the earnings differentials due to secondary schooling (with adjustment made to control for nonschooling effects).
     Although the cohort method should work rather well in studying educational returns in retrospect, it is doubtful that the method is very useful for predicting future earnings.
     For it would be necessary to employ data dating bac as many as 50 years if we are to get a complete earnings stream based on the cohort method. Nevertheless, it has been shown by Miller that the cohort method can be used to suggest the expected effect of economic growth on earning difference. [Hunt (1963) and Rogers (1969].
     Another method for studying the potential of special programs for increasing the achievement of "disadvantaged" students (known generally as compensatory education programs) assumes that the major educational output is achievement in basic skills.
     Ideally, a production-function approach should be used to estimate the extra achievement in basic skills due to a given extra educational effort.
     Since achievement scores are given in terms of equivalent years of education, the method permits an evaluation of how many equivalent years of education the average student acquired as a result of a specific program.
     The additional educational output is then transformed into additional lifetime earnings, utilizing the cross-sectional additionallifetime-income approach. This method is based on the assumption that a discount rate of 5 percent is appropriate.
     When the method is properly utilized, it has far-reaching implications. However, the education production function isolates the benefits of a given program when other factors are considered simultaneously.
     In general, the meaning of the equation derived is, simply, that schooling and nonschooling factors simultaneously determine the level of output. Among the schooling factors we may consider such variables as teacher attributes, building and equipment resources, library books, administrative and clerical help, and so on.
     Among nonschooling attributes one might include socioeconomic conditions, intelligence, student motivation, race, sex, and other "environmental" factors.
     In the compensatory education case discussed above, we would add another variable to distinguish between those who did and those who did not enroll in the particular program. If that variable had the form: 1 = participated in program, 0 = otherwise, the coefficient of this variable (determined through the employment of a regression equation) would indicate the extra output Y associated with enrollment in the program, other things remaining equal.
     Although the production-function approach is theoretically valid, its empirical counterpart has so far been generally far less than staisfactory. One problem is that we do not as yet have a firm learning theory that would enable us to hypothesize a priori the shape of the production function given by equation (7.8).
     For example, we do not know whether it should be linear or nonlinear (and if so of what exact form) with respect to each of the variables. So, the analysis is limited to one output only - even if it is such an important factor as achievement in basic skills - we are bound to distort the facts since it is obvious that the educational system does more than just train people to read, write, and do some arithmetic.
     What is clearly needed is a model with a system of equations, each of which pertains to a single output, to be solved by means of one of the simultaneous-equation methods.
     In addition to the direct benefits (in form of expected increased lifetime earnings), it has long been asserted that educational investments bring forth benefits to society that go beyond the mere increase in productivity. Consumption benefits have already been mentioned.
    Education may increase one's enjoyment of his job (or, alternatively, reduce his disutility of work), change one's attitudes and habits, and increase one's geographic and occupational mobility.
    Education enables individuals to perform various activities outside the market whose value is not commonly measured. An example is the filing of income tax returns.
     Other obvious "nonmarket" benefits are such common activities as driving and typewriting. Another type of benefit is the intergeneration effect, mentioned earlier. The additional education of one generation is likely to result in their offsprings receiving so much extra education that part or all of the older generation's educational investment is paid back in the form of intergenerational benefit. This suggests that educational investment not only increases the productivity of those undertaking the investment, but also enhances the probability that future generations will invest in educational endeavors that will increase society's productivity in the future.
     To all of these we may add another important item - external benefits. These are the benefits that an individual cannot himself capture but which are diffused into society. These include inventions and innovations for which the inventors or innovators cannot hope to be fully compensated. In many cases, indeed, an invention is recognized long after the inventor has already passed on.  

Other types of external benefits (for example, reduced juvenile crime) have not been measured. Considerable effort must be directed towards these issues before estimates may be used for policy purposes. Benefit-Cost Analysis To determine the social worth of a given educational program at Edison High School in Fresno, California, the benefits must be balanced against the costs.
     Since there is disagreement among educational economists on which benefit-cost framework is best (for a given decision problem), the literature supports broaderning the reasearch database to include studies in which the net-present-value criterion is employed, others in which the benefit/cost ratio rule was employed, others (perhaps the majority) in which the primary decision tool has been the internalrate-of return rule. Since the policy decision is sensitive to the choice of a decision rule, it would have been desirable if results were given in a manner flexible enough that each of the three rules can be utilized, if so desired.
     The manner by which the net-present-value rule may be deployed uses data produced by Hansen that discounted additional lifetime earnings for persons completing 12 years of schooling in comparison to only 8 years. From these discounted sums we deduct the present value of direct costs of schooling, estimated to be about $385 per student per year in 1949-1950. The difference is the net present value of secondary school education, based on 1949 data, for several rates of discount.
     Clearly, the data show that high school education was a worthwhile social investment in 1949. The data in Part II of Table 5-1 were derived in a similar manner - with annual direct college costs in 1949-1950 estimated by Hansen at 5943 per student per year.
     The results in the table suggest that positive net present values are obtained only when the rate of discount applied is somewhat less than 10 percent.
     Clearly, these results are based on a model in which virtually all of the costs were considered (earnings foregone are automatically deducted from the earnings stream) whereas only the direct (and measurable) benefits have been accounted for explicitly.
    The quantity and quality of research on the economic value of education has increased considerably in recent years. Yet, the study of the economic benefits to graduate education has lagged behind. Census data concerning earnings classified by age and educational attainment are now available but, only on individuals with at least some graduate work - and not for individuals with M.A. or Ph.D. degrees (or their equivalents).
     There are several puzzling issues related to the returns to graduate education.
     First: How, and to what extent, do (a) the private, and (b) the social returns to graduate education (measured by incremental current and/or lifetime income) vary by: number of years of study in a given degree program degree(s)earned field of study occupation ability and achievement quality of the institution or department granting the highest degree financial support while in school socioeconomic background location in one of several regions in the U.S. type of employer?
     Second: To what extent are the answers to the above question modified when estimates of the value of fringe benefits and nonpecuniary income are incorporated in the calculation of net earnings?
    Third: Are there significant external benefits due to graduate education?

    The importance of human capital in assessing the economic viability of a nation dates back to Adam Smith. Smith realized that the optimal attainment of efficiency in the division of labor would be impossible without education. He even dared compare man to a machine, insofar as individual skills are concerned.
     While other early writers recognized the concept of human capital, few considered human capital to be of central importance in the formulation of economic models.
    Recently published research has largely emanated from the pioneering works of Walter Becker, who recognized the need to adjust the gross relationship between education and earnings for ability difference (a function of superior intelligence and motivation, rather than schooling).Becker relies on past studies and then deducts a certain proportion of the earnings differentials from the gross estimate to reduce his estimates of earnings less than optimal.
    

    [Editor's Note: Dr. Howard Hobbs is a Ford Fellow emeritus and is completing post-doctoral economics reasearch at The University of Southern California on the Advanced Studies Program at Edison High School in Fresno, CA.]

Letter to Editor

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