DE ECONOMIST 140, NR. 3, 1992 AN EMPIRICAL ANALYSIS OF UNIVERSITY CHOICE AND EARNINGS BY HESSEL OOSTERBEEK*, WIM GROOT** AND JOOP HARTOG* 1 INTRODUCTION By introducing the concept of 'human capital,' economists express a view of education as an investment of current time and money in return for future pay (cf. Freeman (1986), p. 367). According to this human capital theory, there are two interdependent relationships between the amount of education an in- dividual obtains and his or her future earnings. In the first, the level of earnings depends on the amount of education and other human capital variables such as experience and experience squared. This relationship has become extremely popular in empirical research due to work by Mincer (1974). Estimation of the Mincerian earnings equation per se, however, ignores the fact that the ex- planatory variable 'education' is not exogenous. On the contrary, the very no- tion of education as an investment implies a second relationship: namely, that individuals choose their optimal amount of education on the basis of their ex- pectations with regard to future earnings (cf. Rosen (1977), Willis (1986)). As a result, the Mincerian earnings equation is only compatible with optimizing in- dividual behaviour under restrictive assumptions. Since Rosen's detection of this inconsistency in Mincer's schooling model, a number of contributions in the literature have focussed on this so-called self- selection problem in the context of educational choices. I Willis and Rosen (1979) analyze the choice of whether or not to attend college in the United States, and find that the expected earnings differential between college and high school has a significantly positive effect on the probability of choosing to do so. Similar results are reported by Micklewright (1989) for Great Britain and * University of Amsterdam, Microeconomics Section, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. ** University of Leiden, Department of Law. 1 In modern labour economics the problem of self-selection has been widely recognized; well- known examples include the choices of whether to join a union (Lee (1978)), and whether to work in the private or the public sector of the economy (Van der Gaag and Vijverberg (1987)). 294 H. OOSTERBEEK, W. GROOT AND J. HARTOG by Oosterbeek (1990) for The Netherlands. 2 All these studies employ datasets containing observations from a cross-section of working individuals. Conse- quently, the information with respect to earnings does not really reflect ex- pected earnings, but realized earnings predicted by the model. These models therefore operate on the strong assumption of expost lack of bias in expecta- tions, which is more stringent than the usual rational-expectations assumption of lack of bias apriori (cf. Manski and Wise (1983), p. 108). The idea of education as an investment is not necessarily restricted to the choice of the level of education, but might also apply to an individual's deci- sion to attend a particular university. In this paper we carry out an analysis of this particular decision. The questions addressed are therefore: (i) whether dif- ferent earnings prospects are associated with attending different universities and, if so, (ii) whether the decision to choose a particular university is governed by these differing earnings prospects. Both questions have an inherent policy interest. An assessment of earnings differentials among graduates from different universities might indicate quali- ty differences between the various establishments. Earnings as an index of labour market performance are then viewed as a measure of post-academic per- formance. Information about the quality of the courses that universities offer is important from the point of view of university funding. At present, many western countries use input-financing schemes for the allocation of available public funds to their various universities. Discussions among public ad- ministrators, however, point to a shift towards output-financing schemes (cf. Commissie Financieringsstructuur (1985)). A necessary precondition for the implementation of such schemes is, however, the availability of information with respect to the quality of output. The issue of whether decisions to attend a particular university are influenc- ed by earnings prospects is also of interest from the point of view of a possible differentiation in tuition fees. To date, the level of tuition fees in The Netherlands has been decided by central government, and has been equal for all students (irrespective of field or phase of study). Recently, however policy- makers have proposed giving establishments a measure of autonomy in this respect. Universities might then increase their tuition fees and use the extra revenues to improve the quality of their courses and thereby (presumably) the future earnings of their graduates. Such a policy would, however, only pay off if future earnings did in fact play a role in the choice of a particular university. If that were not the case, students would be reluctant to pay the higher tuition fees. For the empirical investigation in this paper, we use a sample of economists who each graduated from one of the five economics departments in The Netherlands. This implies that the choice set of the respondents consists of five 2 Othercontributions include Kenny et al. (1979), Garen (1984) and Hartog, Pfann and Ridder (1989). AN EMPIRICAL ANALYSIS OF UNIVERSITY CHOICE 295 options. To model this, we employ the multinomial logit model. As far as we know, this study is the first application of the multinomial logit model (which determines the probability of attendance at each specific university) to the analysis of university choice. In the study by Manski and Wise (1983) concern- ing college choice in the United States, students did not choose between specific establishments, but between quality levels (universities are ranked according to the average SAT score of freshmen entering). The remainder of this paper is made up of four sections. In section 2 we describe the model, while in section 3 we offer a brief description of the data. In section 4 we present and discuss our empirical findings. Finally, section 5 summarizes our conclusions. 2 MODEL AND ESTIMATION METHOD For the model in this paper we adopt the random utility framework devised by McFadden (1974). Assume that individuals aim to maximize expected utility. Let V/ represent the utility for the individual of choosing option i. We distinguish five different options: studying economics at the: (1) University of Amsterdam (UvA), 3 (2) Free University of Amsterdam (VU); (3) University of Groningen (RUG); (4) Erasmus University of Rotterdam (EUR), and (5) Catholic University of Brabant (KUB). Furthermore, assume that the indirect utility function V/is linear in the log of the expected net present value of lifetime earnings (logNi) and in the individual's characteristics X. Vi = (logNi)y + Xfli + ui (1) where y and Pi are (vectors of) parameters and ui is a random term which reflects unobserved characteristics of the individual, unobserved taste varia- tion and genuine indeterminacy of individual behaviour (cf. Cramer (1991), p. 49). University i is chosen if, and only if, studying economics at this university provides the highest utility level: V~>maxVj i,j=1,2,3,4,5 andiCj (2) The net present value of lifetime earning is, of course, not measured. For each option we calculate this variable as Ni=~lw#h(l+r) -t i=1,2,3,4,5 (3) where t is a time index for years of working experience which ranges from 1 to 40, h is potential hours of work per year (= 2000), r is the discount rate which we set at 5 per cent, and wit is the wage rate associated with option i in the t-th 3 We use the Dutch abbrevations. 296 H. OOSTERBEEK, W. GROOT AND J. HARTOG year of experience. These university-specific expected wage rates are supposed to depend loglinearly upon a vector of individual characteristics Z, t and t2: logwit=l~i+aoit+Otlit2+ei, i = 1,2,3,4,5 (4) where/t i , a0i and O'li are (vectors of) parameters, and/~i is a disturbance term. Substituting (4) into (3) and the result into (1) gives the reduced form of the in- direct utility function 4 V i = WTt i q- Oi, i = 1,2, 3, 4, 5 (5) where W = [X, Z]. We further assume that the disturbances vi( = ci ~ + Ui) are independently and identically Gumbel distributed, where the distribution func- tion is denoted by F(. ). The probability that university i will be chosen, Pi, is then defined byS: Pi = { 2j exp(WTrj - Wrti) } - i (6) For each individual, Wg is only observed in one of the five possible wage regimes. Since individuals select themselves into one of the regimes by choosing their preferred university, the unobserved wages cannot be calculated by the OLS estimates of ~i, a0i and atg in equation (4) because of selection bias. Lee (1983) and Trost and Lee (1984) present a method for correcting for selection bias in wage equations in a model with more than two choices. We outline this method briefly in the paragraphs below. First define/~i ~ max Vj - vi (j = 1,2, 3, 4, 5; j :g i). Let (0 and ~ be the stan- dard normal density function and the distribution function respectively. And let J = q~- l(F(Wni)). Lee (1983) defines the selectivity bias correction term by: (o(J(W~i))/F(WTti). The selectivity-corrected wage rate equation of university i is then: log wi = Z#i - aiLoi(p(J(W~i) + 'Si (7) where the conditional expectation of e i is zero, ~r i is the standard deviation of eg, and ~i the correlation coefficient of e i and J(r/i). The estimation procedure of equation (7) involves two stages. In the first stage, we estimate the reduced form of the decision model (5).