Econom~s o/Educnnon Rerrew. Vol. 3. No. 2. pp. 97-1l)j. 1984. Printed m Great Britain

OT-77v51 s3 M) + 0.00 Q 1~81 P&mm Press Ltd.

An Econometric Estimate of the Demand for MBA Enrollment

ELMORE R. ALEXANDER. III* and DONALD E. FREY?

* Tennessee Emplovment and Trainin, o Institute, Center for Llanpower Studies,

Memphis State University. Memphis. TN 38153. U.S.A.

and

: Department of Economics. Wake Forest University, Winston-Salem, NC. U.S.A

Abstract - A demand equation for MBA enrollment was estimated to test the theory of human capital as an explanation of enrollment decisions in higher education. Three of four variables associated with a human capital interpretation were found to be significant. The functional form of the demand equation

(log-reciprocal) was of importance in establishing these results. Although the failure of the interest rate to be significant might suggest imperfections in access to capital for potential students, we could not find support for the alternative view that students relied on subsidization by family. Several elasticities

proved to be large enough to imply that feasible changes in the rates of change of underlying economic variables could produce noticeable changes in MBA enrollment.

INTRODUCTION

THE THEORY of human capital provides a coherent interpretation of the decision to enroll in degree programs in higher education. Yet empirical support for this interpretation is less than overwhelming. Studies of the demand for undergraduate enroll- ment, in particular, have produced results that seem most consistent with demographic or consumption theories of enrollment demand. Demographic deter- minants of enrollment include such things as the stock and flow of high-school graduates eligible to enroll in college or institutional factors such as the size of the armed forces, which may reduce the availability of young people for enrollment (e.g. Galper and Dunn, 1969). Typically, enrollment projections for higher education by the National Center for Education Statistics (NCES) depend on the extrapolation of demographic trends. Theories that interpret enrollment as a consumption decision are supported by findings that tuition (price) and

family incomes are important determinants of en- rollment (e.g. Campbell and Siegel, 1967; Frey and Alexander, 1976). While the tuition variable may be consistent with both the consumption and the human capital models of the enrollment decision. the family income variable cannot be squared readily with the human-capital model. Finally, some models have been hybrids, combining elements of consumption, demographic and human capital models (e.g. Lehr and Newton, 1978; Tannen. 1978).

All this is not to say that the human-capital hypo- thesis is wholly without support. The Tannen study, despite the introduction of consumption motives, provides evidence favorable to the human capital perspective with regard to undergraduate education. A forecasting model of demand for enrollment at a particular university (Hoenack and Weiler, 1979) tested the significance of several variables usually associated with human-capital theory and reported mixed results.

[Manuscript received 7 May 1982; revision accepted for publication 30 July 1982.1

97

98 Economics of Education Review

Evidence for the human capital approach might be found more readily by examining enrollment demand for professional degree programs, where the relation of education to enhance earnings is much clearer than with undergraduate education. Freeman (1971) has found that engineering enroll- ment is significantly related to the relative salaries of engineers; this clearly supports a human-capital interpretation of the enrollment decision. However, Freeman did not report that engineering enrollment was determined by the other variables that one would associate with the human-capital view. Fur- thermore, his study also supports a demographic interpretation. A study by White et al. (1978) of MBA enrollment found that enrollment was deter- mined, in part, by the relative salaries of MBA holders but, like Freeman, the study depended heavily on demographic determinants of enrollment and failed to support other hypotheses generated by human-capital theory. A study (Sloan, 1971) on application demand to medical schools used an investment model which included proxies for direct and opportunity costs and for expected return, but it failed to find that all the coefficients were consist- ently significant although the direct-cost variable (tuition) generally performed well.

The purpose of the present paper is to report results on the demand for ,MBA enrollment that tend to support the human-capital interpretation. In the next section we present a short discussion of the hypotheses to be tested; included is a discussion of the proper specification of the equations to be tested. In the third section we discuss data sources, an area of constant vexation for researchers in the economics of education. The fourth section presents the empirical results.

THEORY

The essential premise of human-capital theory is that the decision to enroll in a program like that for the MBA degree is an investment decision. As such, enrollment occurs only when the discounted present value of future returns created by the investment is equal to, or exceeds, the cost of the investment (which in some cases must also be discounted). In the simplest form, future returns are viewed as the excess of earnings with the MBA over earnings under the next best alternative without the degree. Returns must be discounted by a factor that should account for the return that may be had in alternative

investments and for risk. (Presumably the risk of investments in human beings is substantially higher than in high-quality corporations or the govern- ment.) The costs of the investment are convention- ally divided into direct costs (i.e. tuition and fees) and opportunity costs (i.e. foregone earnings). The results of the model should be the same whether the analysis is conducted with constant prices or in- flation assumed; if some rate of inflation is antici- pated, the nominal dollar returns on the investment would be adjusted upward, but this would be offset by an increase in the discount factor since it is conventionally assumed that anticipated inflation will raise the interest rate.

Even this short synopsis of the theory suggests several hypotheses. We expect MBA enrollment demand to be positively related to some proxy for the return on the investment and negatively related to proxies for direct and indirect costs and the discount factors. Tuition in MBA programs is a straightforward proxy for the direct costs of enroll- ment, and the interest rate for bonds with maturities approximately as long as the expected working lifetime of graduates with MBAs is presumably a good proxy for a major component of the discount factor. Although the interest rate on bonds may not capture the risk-premium portion of the discount factor, we would not expect riskiness to be highly variable over time, so that little is lost by using this proxy. As a proxy for the opportunity cost of enrolling in the MBA program, the unemployment rate should serve well. The unemployment rate is more highly variable over time than some of the other proxies that might be used for opportunity cost. In addition, for aggregate enrollment studies the unemployment rate should roughly represent the experience of large numbers of potential en- rollees.

The greatest problem is associated with finding a proxy for future returns to the investment. Before it is possible to address the issue of an operational proxy for returns, one must first consider how potential enrollees form expectations of fufure returns. While it is hardly an original hypothesis, there is some merit in the view that recent past experience is the empirical basis upon which expec- tations would be based. Only if this simple view were rejected should one resort to more exotic views of expectations of formation. The simplest proxy for returns, therefore, would be the ratio of earnings of MBA recipients to holders of undergraduate de-

An Econometric Estimate of the Demand for MBA Enrollment 99

srees in comparable fields. Following Freeman, we will specify further that the relevant earnings are

starting salaries; although there may be no strong theoretical reason to argue that expectations of future earnings are informed more by starting salaries than, say, average salaries. it seems likely that potential MBA enrollees are more aware of the starting salaries offered to contemporaries than of mean or median salaries in the business world.

If the decision to enroll in an MBA program is a pure human-capital investment decision and if capital markets operate perfectly so that students can compete effectively for education loans (at a high enough interest rate), then income should not be a determinant of the demand for enrollment in MBA school. One should be able to finance the education by borrowing and repay from the higher earnings stream. On the other hand, if capital markets are closed to potential students, enrollment may depend on self-financing, or gifts from family or the schools (scholarships). In this event, the ability to finance oneself or for families or schools to contribute would seem to be correlated with the real standard of living of the economy. If this were the case, we would expect to find income to be a determinant of enrollment. Although income would be a determinant of enrollment if the MBA were a ‘consumption’ program, as perhaps the undergradu- ate degree is, we do not consider this to be very likely. Therefore we will test income as a determin- ant of MBA enrollment primarily to test the hypothesis that capital markets are imperfect in their provision of funds to potential MBA students.

Various researchers have tried different func- tional forms for the enrollment-demand equation. While others have used linear (Hopkins, 1974; White et al., 1978), log-linear (Campbell and Siegel, 1967) and differences of lagged variables (Galper and Dunn, 1969). we believe that a log-reciprocal form is best justified (see below; also, Frey and Alexander, 1976). This would result in the following specification of the demand equa- non:

R = ec+LtB,X, (1)

where R is the per-capita demand for an MBA (the ratio of individuals enrolled for an MBA to the total population of potential enrollees), c is a negative constant, f3; are coefficients and Xj are variables. Specifically, where the Xj are hypothesized to have a

positive effect on the enrollment ratio the inverse of the variable is what would be included in the

equation. Equation (1) can be justitied for several reasons.

First, with regard to the use of the enrollment ratio as opposed to the absolute enrollment figures, most previous research into the demand for higher edu- cation has preferred the use of a ratio. Since enrollments as well as potential enrollees have been steadily increasing in numbers. the use of the ratio helps to counter the potential problem of serial correlation of error terms. Second, since R must vary between zero and one no matter what values are taken by the X,. a formulation such as (1) which places upper and lower asymptotic limits on R’s value is preferable. Furthermore. the specification is such that for the variables vvhich we expect to have a positive effect (therefore to be entered in reciprocal form) R will approach an upper asymptote from below and a lower one from above. This is precisely the behavior we would expect of R; further, if the asymptotes are estimated to have plausible values. this would provide a check on the estimated demand function beyond those criteria usually applied to regression equations. The equation ultimately to be estimated is the logarithmic form:

IogR = C + B,X, + B&z + SPYI + BJ, + B&j,

(?I

where C is constant, X, is tuition (B, should be negative), X2 is the appropriate interest rate (Bz should be negative). X3 is the reciprocal of the ratio of MBA salaries to undergraduate-degree salaries (B, should be negative - because of the reciprocal specification), X, is the reciprocal of the unemploy- ment rate (B., should be negative - again, because of the reciprocal specification) and Xj is the reci- procal of an income variable (B5 should be nega- tive - for the same reason). We note that negative coefficients associated with variables in reciprocal form imply a positive relationship between the variable and the enrollment ratio, R; derivatives and elasticities are positive for these variables. We note also that the income variable, Xj, would be ex- pected to have a significant impact on R only if access by potential students to capital markets were imperfect; the human capital model, as such, does not imply that income is a determinant of MBA enrollment.

SOURCES OF DAT.4 this is a characteristic of most time-series work on the demand for higher education.

To calculate the hlBA enrollment ratio, an appropriate denominator had to be determined. EhIPIRICAL RESULTS Certainly, it is questionable as to what the exact pool of potential MBA enrollees is. We chose to Table 1 reports the final estimated enrollment follow the lead of White et al. (1975) and to assume regressions.’ Preliminarv regressions revealed that that those under 34 years of age with bachelor’s neither the interest rate variable nor the income degrees were the most likely MBA students. There- variable were statistically significant determinants of fore for each year we summed the preceding 12 the demand for MBA enrollment. Thus these two years’ bachelor’s degrees. From this figure we variables are omitted from the final regressions. The subtracted the summation of the preceding 10 years failure of the interest rate to prove significant in the of MBA degrees. After getting one MBA, an regressions need not imply that the discount factor is individual is unlikely to want another: and since the unimportant. Variations in the interest rate due to XIBA is typically a two-year degree, it is appropriate inflation would be offset by revised estimates of to subtract the summation of the preceding 10 years. future returns: yet the ‘real’ component of the The resulting figure became the denominator for the interest rate may be too stable on an annual basis to enrollment ratio, with MBA enrollment being the have much effect. On the other hand, if the interest numerator.’ The number of undergraduate degrees rate is not significant because of imperfect access by as well as the number of graduate business degrees potential students to capital markets, one might was obtained from various editions of Projections of expect enrollment to be sensitive to family income, Education Statistics (NCES, 1976). which is pub- since students would have to rely on the subsidies of lished by NCES. MBA enrollment was also ob- parents, spouses, etc. for their education. The tained from an NCES publication, Students Enrolled failure of the income variable to prove significant for Advanced Degrees (NCES, 1976). provides no evidence for this hypothesis. Thus while

Data for the ratio of MBA salaries to under- our research provides no positive evidence for graduate salaries was obtained from Corkhill (1980). discounting behavior on the part of potential MBA This variable, which we lagged 1 year, consisted of students, it also provides no support for the inter- the average monthly salary offers of MBAs with pretation that discounting is not observed because nontechnical undergraduate degrees divided by the capital markets are closed to potential students. It average monthly salary offers of general business, seems unlikely that the issue can be resolved with humanities and social science undergraduates. the data available to us.

Tuition data came from various editions of the In addition to the log-reciprocal form of the American Council on Education’s A Fact Book on regression, Table 1 also includes three alternative Higher Education (1976). Since graduate tuition forms for the sake of comparison - linear, log-

data were not available, undergraduate data were non-log (only dependent variable in log form, the used as a proxy; it is likely that over time the series rest linear) and log-log. The results appear to justify

would move in parallel. The average of public and our preference for the log-reciprocal form. While

private tuition was used since MBA enrollments the variables are of the correct sign and R’S and f have been split on an approximate 50-50 basis statistics are approximately equal in all equations, between public and private schools. Tuition aver- the coefficient for tuition is significant only in the ages were adjusted by the consumer price index. log-reciprocal equation. Additionally. the log-reci-

Data on both the unemployment rate and personal procal equation has a better Durbin-Watson stati-

income (CPI-adjusted)’ were taken from the Annual stic. For each of the other three equations the

Reports of the Council of Economic Advisors (1976). Durbin-Watson test for serial correlation of the Interest rates for corporate bonds of 30 years’ error terms is inconclusive. However, the Durbin- maturity were obtained from Standard and Poor’s Watson test concludes serial independence of error Statistical Services’ SecLtriry Price Index Record terms for the log-reciprocal equation.

(1980). Although the time series for which data Since the log-reciprocal equation approaches an

could be obtained was relatively short (13 years), upper asymptote, we can use our equation to define

100 Economics of Educarion Revieu

An Econometric Estimate of the Demand for MBA Enrollment 101

Table I. Regression analysis results

Regression Intercept Tuition Salary Durbin-Watson ratio Unemployment R’ F stattstic

I. Log-reciprocal+ - 1.93 -0.00062 -2.269 -0.699 0.95 -!S.-l3’ 7.217

(7.16)‘“’ (-l.j6)*’ (2.26)“’ [-0.6-t] [ l.j-!] [O. 131

2. Lineart -0.000s I -O.OOOOOjS 0.013 O.OOOJ-! 0.97 6j.S7* l.jj:t

(1.63) [-0.221

;u”:;2;* * ;;:3;;* -

3. Log-non-logt -j.42 -0.00032 0.94 0.026 0.96 j3.41’ 1.16:t

(1.19) [-0.331 I::&)**

;;;=ti)‘-*

4. Log-log: -1.72 -O.-!S/I L.44jj 0. I-lj] 0.96 jO.S9* 1.7jtt

(1.62) (4.08)** (2.19)“’

T statistics are provided in parentheses. Elasticities are provided in brackets. The other numbers are coefficients. Of course, the coefficients in the log-log equation are elasticities.

* P < 0.001; ** P < 0.01: *** P < 0.05. + Dependent variable is the natural log of the enrollment ratio. $ Dependent variable in the enrollment ratio. 8 The reciprocal of this variable was used for this equation. /! The natural log of this variable was used for this equation. 4 Durbin-Watson test concludes serial indeoendence of error terms.

’ it Durbin-Watson test inconclusive.

the upper limit on MBA enrollment. Assuming conditions most favorable to enrollment (i.e. tuition equal to zero, an unemployment rate of 100% and a salary ratio approaching infinity), the asymptote would be 0.14-l. Since our base contains all indi- viduals with bachelor’s degrees who are under 34 years of age (12 years’ worth of graduates) and assuming that the IMBA is a 2-year degree, the asymptote implies that 86% of the pool would enroll under ideal conditions. Certainly, we would not expect everyone to enroll, even under these con- ditions. Thus 86% seems quite reasonable.

An additional basis of comparison across equa- tions relates to elasticities. The elasticities are quite similar in the cases of unemployment and the salary ratio in all but the linear regression. The elasticities for the linear equation are substantially lower in both cases. For tuition, though. the log-reciprocal equation has a substantially higher elasticity. This should not be surprising since tuition was significant only in the log-reciprocal form.

The elasticities themselves deserve some atten- tion. Enrollment is very inelastic with respect to the

unemployment rate, our proxy for reduced oppor-

tunity cost, and moderately inelastic with respect to tuition. On the other hand, enrollment is relatively elastic with respect to the salary ratio. Since this is a ratio of starting salaries. which is but a proxy for an expected stream of returns, one might have ex- pected a less elastic response; presumably potential students in the MBA program would look at a number of things for form judgments about the future stream of returns so that swings in the current starting salary ratio would not alone precipitate large changes in estimated future returns. That the responsiveness to the salary ratio as defined is elastic suggests that potential students put a heavy weight on the recent experience of peers in forming expectations. The relatively large elasticity of this variable suggests that large swings in enrollment could be precipitated by changes in the salary ratio. However, since the salary ratio only varied from 1.3 to 1.6 during the period for which we have data, it is difficult to predict the impact of large changes.

Except for the non-significance of the interest rate as a determinant of enrollment demand, the results support a human capital interpretation of MBA enrollment. Of importance is the finding that the

Economics of Educarion Review

statistical significance of certain of the variables depended on the functional form of the enrollment regression. Our results suggest that the log-reci- procal form is recommended not only by a priori

considerations about the behavior of an enrollment ratio but by actual performance as well.

Three of four variables associated with a human- capital interpretation of demand for enrollment in MBA programs have been found to be significant in an aggregate time-series study. The functional form of the demand equation was of importance in

establishing these results; the direct-cost variable (tuition) was significant at high levels of confidence only in the preferred regression form. Further. only the log-reciprocal formulation permits the inference that error terms are serially independent. Although the failure of the interest rate to be significant might suggest imperfections in access to capital for poten- tial students, we could not find support for the alternative view that students relied on subsidization by family. as indicated by the failure of the income variable to be significant. Several of our estimated elasticities proved to be large enough to imply that feasible changes in the rates of change of underlying

economic variables could produce noticeable

changes in MBA enrollment.

NOTES

1. Actually the movement of various choices for the enrollment base is very similar. For example. we also calculated an enrollment base which was merely the summation of the preceding 5 years’ undergraduate degrees. The correlation between this base and the one we used was 0.97. When we used the 5-year base to calculate the regression equations the magnitude of the coefficients was changed but not the relatikr importance of variables or their signs.

2. Personal income figures were the aggregate personal income figures reported in the statistical tables accompanying the Annual Report of the Cottncil of Economic Advisors.

3. Our use of ordinary least squares to estimate the demand equation assumes that the supply of places in MBA programs is sufficient to provide an opportunity for all who want a degree to pursue one. While the validity of this assumption cannot be proven with certainty, the large number of state schools which admit all minimally qualified applicants would seem to suggest that ‘bottlenecks’ in the demand for MBA program positions are minimal.

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CAMPBELL. R. and SIEGEL, B. (1967) The demand for higher education in the United States, 1919-196-t. Am. econ. Rev. 57. 482-394.

CORKHILL, R. InfIation and the College Graduate (1980) Bethlehem, PA: College Placement Council. FREEMAN, R.B. (1971) The Market for College-trained Manpower. Cambridge, MA: Harvard

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An Econometric Estimate of the Demand for MBA Enrollment 103

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