A smoothed maximum score estimator for the binary choice panel data model with an application to labour force participation

In a binary choice panel data model with individual effects and two time periods, Manski proposed the maximum score estimator based on a discontinuous objective function and proved its consistency under weak distributional assumptions. The rate of convergence is low ( N ^1/3) and its limit distribution cannot easily be used for statistical inference. In this paper we apply the idea of Horowitz to smooth Manski's objective function. The resulting smoothed maximum score estimator is consistent and asymptotically normal with a rate of convergence that can be made arbitrarily close to N ^1/2, depending on the strength of the smoothness assumptions imposed. The estimator can be applied to panels with more than two time periods and to unbalanced panels. We apply the estimator to analyze labour force participation of married Dutch females.