Economics of Education Review 20 2001 263–278 www.elsevier.comlocateeconedurev
A comparison of alternative specifications of the college attendance equation with an extension to two-stage
selectivity-correction models
Michael J. Hilmer
Visitor, Department of Economics, 130 FOB Brigham Young University, Provo, UT 84602-2363, USA Received 29 January 1999; accepted 21 October 1999
Abstract
This paper estimates a college attendance equation for a common set of students using three popular econometric specifications: the multinomial logit, the ordered probit, and the bivariate probit. The results suggest that while the
multinomial logit is rejected as an appropriate specification, the estimated marginal effects generally are not statistically different across the three specifications. Extending the analysis to two-stage corrections for selection bias suggests that
the biggest potential for cross-specification differences occur in the estimated significance of the second-stage coef- ficients and the predicted outcomes based on those estimates. This suggests that for such applications it is likely
important to carefully consider the choice of specification of the first-stage attendance equation.
2001 Elsevier Science
Ltd. All rights reserved.
JEL classification: I29
1. Introduction
A primary focus of the economics of higher education literature has been the college attendance decision.
Within the voluminous literature estimating the factors that affect the college attendance decision three promi-
nent econometric specifications have been used: the multinomial logit Ordovensky, 1995; Savoca, 1991, the
ordered probit Hilmer, 1998; Broomhall Johnson, 1994, and the bivariate probit Evans Schwab, 1995;
Ganderton, 1992. As it is entirely possible that estimates differ significantly across specifications, the choice of
specification may greatly influence the conclusions that can be drawn from the results. Moreover, most studies
appear to give little consideration to the alternative empirical models but rather make a seemingly ad-hoc
decision of which model to use. Consequently, it is important to develop some idea whether and by how
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much parameter estimates differ across the different specifications. Unfortunately, previous studies have esti-
mated the college attendance decision for different data sets and thus it is difficult to directly compare and con-
trast those results.
This study solves the comparison problem by estimat- ing a college attendance equation using each of the three
specification for a common subset of students from the High School and Beyond who reported as seniors in high
school that they expected to graduate from college. We then compare the estimated results from the three speci-
fications to assess potential cross-specification differ- ences. Simple specification tests reject the multinomial
logit but fail to reject the ordered and bivariate probits. At the same time, however, it is demonstrated that in
general the estimated marginal effects do not differ sig- nificantly across the specifications, suggesting that
choice of specification may not significantly affect the conclusions drawn from estimates of the college attend-
ance equation itself. Because the college attendance equ- ation has most recently been estimated as the first stage
264 M.J. Hilmer Economics of Education Review 20 2001 263–278
of Lee 1983 type two-stage corrections for self-selec- tion bias, we extend the analysis to consider such selec-
tivity correction models. The estimated results for the years of college completed by 2- and 4-year attendees
suggest that the choice of specification of the first-stage college attendance equation may have a significant
impact on the second-stage selectivity-corrected coef- ficient estimates. Namely, the effects of several key vari-
ables are estimated to be statistically significant under some specifications but not others. Prominent among
these are test scores, which are only estimated to have large and significant effects among 4-year attendees for
the ordered probit and a series of family background and high school performance measures, which are only esti-
mated to have large and significant effects among 2-year attendees for the multinomial logit. In addition to the
estimated coefficients differing across specifications, pre- dicted outcomes for students of different genders and
ethnicities possessing average sample characteristics appear to differ across specifications. Hence, the results
suggest the importance of considering specification issues before estimating the college attendance equation,
especially when being used as the first stage of selection correction models.
2. Econometric issues
