Supplement to “ Stepping stone and option value in a model of postsecondary education ”

Several studies claimed that there is underinvestment in education. Judd (2000) combines Capital Asset Pricing Model (CAPM) techniques with the indivisibility of human capital to compare the return to four-year college graduation with assets of similar risk to find an excess of return to the college investment option. Heckman, Lochner, and Todd (2008) evaluate the internal rate of return of the four-year college investment option relative to work to find that since 1960, internal rates of return have been around 10 percent or higher, depending on the cohort and different specifications of labor markets and taxes. Cunha, Heckman, and Navarro (2005), using data from NLSY/1979, extend the analysis to evaluate the internal rate of return for the marginal student, the agent with the lowest observable measures of ability who enrolls in four-year college, to find an unexplained wedge in returns.1 Cunha, Heckman, and Navarro (2005) concluded that this wedge is explained by nonpecuniary costs of education, namely, tastes for school, risk aversion, and other. The evidence presented in this paper points in a different direction: the wedge in returns is explained by the existence of academic two-year colleges (in fact, it is actually more general because vocational schools explain the wedge in returns for students who enroll in academic two-year colleges), as high school graduates sort across the different enrollment alternatives. In particular, high school graduates who enroll in fouryear colleges have measures of observables that lie above those who enroll in academic two-year colleges. It follows that the high school graduate with the lowest measures of observables who enrolls in a four-year college is indifferent to enrollment at academic two-year colleges as opposed to being indifferent to joining the labor force. Using the parameterized version of the model, it is possible to quantify the return for this marginal student and how much of average returns for the population that enrolls in four-year colleges is explained by the return of the marginal student. The return for the student