  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.
