Quantile regression with sample selection: Estimating women’s return to education in the U.S.

Abstract

This study uses quantile regression techniques to analyze changes in the returns to education for women. The data used is the March Current Population Survey for the years 1968, 1973, 1979, 1986 and 1990. The first step in estimating the single (linear) index selection equation uses Ichimura’s (1993) semiparametric procedure. To correct for an unknown form of a sample selection bias in the quantile regression, the second step incorporates a nonparametric method, using an idea similar to one developed by Heckman (1980) and Newey (1991) for mean regression, and Buchinsky (1998) for quantile regression.

The results show that: (a) the returns to education increased enormously for the younger cohorts, but very little for the older cohorts; (b) in general the returns are higher at the lower quantiles in the beginning of the sample period and higher at the higher quantiles by the end of the sample period; (c) there is a significant sample selection bias for all age groups at almost all quantiles; (d) toward the end of the sample period there is a significant convergence of the returns at the various quantiles, especially for the younger cohorts and age groups; and (e) the semiparametric estimates of the selection equation are considerably different from those obtained for a parametric probit model.

This paper was presented at the conference on “Economic Applications of Quantile Regression” held in Konstanz, Germany, June 2000. I wish to thank Don Andrews, Josh Angrist, Claudia Goldin, Jenny Hunt, Larry Katz, Jacob Mincer, Ariel Pakes, Jean-Marc Rubin, John Rust, Steve Stern, Joe Tracy, and Joel Waldfogel, as well as seminar participants in Columbia University, Yale University, University of Montreal, University of Virginia, and the Hebrew University of Jerusalem for comments and discussions. I have benefited greatly from insightful comments on earlier drafts by Gary Chamberlain, Jim Powell, James Heckman, Roger Koenker, Bernd Fitzenberger, and an anonymous referee. I am, nonetheless, fully responsible for any remaining errors in this paper.