A smoothed maximum score estimator for the binary choice panel data model with individual fixed effects and applications 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. However, the rate of convergence of this estimator is low (N) and its limit distribution cannot be used for making inference. This paper overcomes this problem by applying the idea of Horowitz to smooth Manski's objective function. The paper extends the resulting smoothed maximum score estimator to the case of more than two time periods and to unbalanced panels (assuming away selectivity effects). Under weak assumptions the estimator is consistent and asymptotically normal with a rate of convergence that is at least N 2/5 and can be made arbitrarily close to N1/2, depending on the strength of the smoothness assumptions imposed. Statistical inferences can be made. The estimator is applied to an equation for labour force participation of married Dutch.