A study of a semiparametric binary choice model with integrated covariates

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purposes, we find that the maximum score estimator and smoothed maximum score estimator are at least √n-consistent. Comparing this rate to the convergence rate of the parametric maximum likelihood estimator (MLE), we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000, Econometrica 68, 1249-1280) parametric MLE converges at a rate of n^3/4 and its limiting distribution is a mixed normal. Finally, we show briefly how to apply our estimation method to a nonstationary single-index model.