Sample selection bias with multiple selection rules: An application to student aid grants

Abstract

This paper extends the sample selection bias correction procedure, developed by James J. Heckman, to the case of multiple selection rules. Estimators are presented for independent selection rules and a consistent estimator for the variance-covariance matrix is derived. The methodology is applied to the problem of estimating the financial aid available to U.S. highschool students for college education. In order to be observed in receipt of financial aid, a student has to be both enrolled in college and to have had an expected value of aid in excess of the costs of applying. Both of these sources of selection bias were found to be important.