Semiparametric maximum likelihood estimation of polychotomous and sequential choice models

Abstract

This article considers semiparametric estimation of discrete choice models. The estimation method is a semiparametric maximum likelihood method which generalizes Klein and Spady (1993) to the estimation of polychotomous choice and sequential choice models. Special emphasis is on the estimation of models with indices of which the density function is not bounded away from zero, issues on trimming indices, the correction of asymptotic bias, and issues of negative kernel density estimation. A semiparametric efficiency bound is derived for the polychotomous choice model with index restrictions. Our estimator is shown to be √ n-consistent, asymptotically normal, and almost asymptotically efficient. Monte Carlo experiments are provided to evaluate the finite-sample performance of the estimator.