A control function approach to estimate panel data binary response model

We propose a new control function (CF) method to estimate a binary response model in a triangular system with multiple unobserved heterogeneities The CFs are the expected values of the heterogeneity terms in the reduced form equations conditional on the histories of the endogenous and the exogenous variables. The method requires weaker restrictions compared to CF methods with similar imposed structures. If the support of endogenous regressors is large, average partial effects are point-identified even when instruments are discrete. Bounds are provided when the support assumption is violated. An application and Monte Carlo experiments compare several alternative methods with ours.