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 purpose, we find that the MSE and SMSE are at least sqrt(n)-consistent. Comparing this rate to the parametric MLE’s convergence rate, we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000)’s parametric MLE converges at a rate of n^(3/4) and its limiting distribution is a mixed normal. Finally, we show briefy how to apply our estimation method to a nonstationary single index model.