# UNDERGRADUATE FINANCIAL AID AND SUBSEQUENT GIVING BEHAVIOR

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1 Discussion Paper No. 57 Williams Project on the Economics of Higher Education Denison Gatehouse Williams College Williamstown, MA UNDERGRADUATE FINANCIAL AID AND SUBSEQUENT GIVING BEHAVIOR Kelly Dugan, Charles H. Mullin and John J. Siegfried Vanderbilt University November, 2000 DP (Kelly Dugan, Charles Mullin, and John Siegfried) This paper is intended for private circulation and should not be quoted or referred to without the permission of the authors.

2 Abstract Data on 2,822 Vanderbilt University graduates are used to investigate alumni giving behavior during the eight years after graduation. A two stage model accounting for incidental truncation is used to first estimate the likelihood of making a contribution and second estimate the average gift size conditional on contributing. The type of financial aid received as an undergraduate appears to have a greater influence on subsequent alumni generosity than the amount received. Adding some scholarship to a loanonly package or eliminating all loans from a mixed loan-grant package increases the likelihood of a subsequent contribution. Increasing the total size of the package or altering the proportions of an already mixed package appears to be inconsequential for future donations. Students who receive small merit scholarships contribute more as alumni than students who receive either no merit scholarship or a large merit scholarship. 1

6 where a donation is given whenever d is greater than zero. We assume that the error term is normally distributed and estimate the implied probit model. Second, the magnitude of the donation is modeled as a linear function of observables, i.e. y * = Zγ + ε where Z may contain, but is not restricted to, the variables in X. Furthermore, there are no cross equation restrictions between β and γ, even for coefficients on the same explanatory variable. For example, the effect of receipt of financial aid on the likelihood of giving is allowed to differ from its effect on the expected magnitude of the gift. Finally, we do not observe y * for all respondents. Instead we observe y = y y = 0 * if d > 0 if d 0 i.e. we observe the gift size for the sub-population of individuals who desire to make a positive donation, but observe a gift size of zero for all others. In general, the selection imposed by the first stage is correlated with the error term in the second stage, resulting in an omitted variables problem if OLS estimates are computed ignoring the selection. In particular, if ε has a normal distribution, then m r m r b g ε * E y d > 0 = Zγ + E ε d > 0 = Zγ + ρσ λ Xβ where ρ is the correlation between ε and µ, σ ε is the standard deviation of ε, and λ b Xβg is the inverse Mills ratio. Therefore, we compute the inverse Mills ratio based on the estimates in the first stage and include this estimate of the inverse Mills ratio as an additional regressor in the second stage. This procedure was introduced in Heckman (1979) and has been shown to produce consistent estimates. Finally, standard errors are corrected both for the heteroscedasticity induced by selection and the fact that the inverse Mills ratio is an estimated regressor. 3. Data The data consist of 2,822 full-time students who entered Vanderbilt University as freshmen between August 1984 and August 1986 and graduated between May 1988 and May No transfer students (either into or out of Vanderbilt) are in the sample. Contributions from each graduate in our 3 Data are unavailable for earlier cohorts. 5

20 Section of the American Statistical Association (Alexandria, VA: American Statistical Association 1991): Okunade, Albert Ade, Phanindra V. Wannava and Raymond Walsh, Jr. Charitable Giving of Alumni: Micro-data Evidence from a Large Public University, American Journal of Economics and Sociology Volume 53 (January, 1994): Stuttler, Doug and Dave Calvario, In Alumni Support, Satisfaction Matters, Fund Raising 27 (November, 1996):

### UNDERGRADUATE FINANCIAL AID AND SUBSEQUENT GIVING BEHAVIOR

Discussion Paper No. 57 Williams Project on the Economics of Higher Education Denison Gatehouse Williams College Williamstown, MA 01267 http://www.williams.edu/wpehe UNDERGRADUATE FINANCIAL AID AND SUBSEQUENT

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