Panel Data Binary Response Model in a Triangular System

We propose a new control function (CF) method for binary response outcomes in a triangular system with unobserved heterogeneity of multiple dimensions. The identified CFs are the expected values of the heterogeneity terms in the reduced form equations conditional on the endogenous, Xi ≡ (xi1, . . . ,xiT ), and the exogenous, Zi ≡ (zi1, . . . , ziT ), variables. The method requires weaker restrictions compared to traditional CF methods for triangular systems with imposed structures similar to ours, and point-identifies average partial effects with discrete instruments. We discuss semiparametric identification of structural measures using the proposed CFs. An application and Monte Carlo experiments compare several alternative methods with ours