A Smoothed Maximum Score Estimator for Multinomial Discrete Choice Models

We propose a semiparametric estimator for multinomial discrete choice models. The term “semiparametric” refers to the fact that we do not specify a particular functional form for the error term in the random utility function and we allow for heteroskedasticity and serial correlation. Despite being semiparametric, the rate of convergence of the smoothed maximum score estimator is not affected by the number of alternative choices and does not suffer from the “curse of dimensionality”. We show the strong consistency and asymptotic normality of the smoothed maximum score estimator for multinomial discrete choice models. The smoothed maximum score estimator is obtained by maximizing a smoothed version of Manski’s score function using a pairwise scoring rule initially proposed by Manski (1975) and later developed by Fox (2007). The rate of convergence of the smoothed maximum estimator for multinomial discrete choice models can be made arbitrarily close to √ N , which is the same as the rate of convergence of Horowitz’s (1992) smoothed maximum score estimator for the binary response model. Monte Carlo experiments provide the evidence that the proposed estimator has smaller mean squared error than the conditional logit estimator and the maximum score estimator.