Self-selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self-selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology which combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell, 1993). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that self-selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state-specific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state-to-state migration flows of college- versus high school-educated individuals respond strongly to differences in the return to education and amenities across states.

Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved hetero-geneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previous theoretical and empirical work and some new ones, and let the data decide among the competing specifications. Empirical results indicate that heterogeneity is present in re-turns to education. Furthermore, we find strong evidence that the heterogeneity follows a continuous rather than discrete distribution, and that bivariate Normality provides a very reasonable description of individual-level heterogeneity in intercepts and returns to schooling.

This research was supported by NSF 97-09-873, NSF-SES-0099195 and NICHD-40-4043-000-85-261. Carneiro benefited from support from Fundaçao Ciência e Tecnologia and Fundaçao Calouste Gulbenkian. We have benefitted from comments received at the Applied Price Theory Workshop, from comments received from Jaap Abbring, Flavio

ABSTRACT: Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved heterogeneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previous theoretical and empirical work and some new ones, and let the data decide among the competing specifications. Empirical results indicate that heterogeneity is present in returns to education. Furthermore, we find strong evidence that the heterogeneity follows a continuous rather than discrete distribution, and that bivariate Normality provides a very reasonable description of individual-level heterogeneity in intercepts and returns to schooling. 1

• This is to acknowledge my intellectual debt to Jacob Mincer as a student in his