Statistics Seminar（2013-01）

Topic:A Smoothed Maximum Score Estimator for Multinomial Discrete Choice Models

Speaker:Jin Yan, University of Wisconsin-Madison

Time:Wednesday, 27 February, 10:30-12:00

Location:Room 217, Guanghua Building 2

Abstract：I propose a semiparametric estimator that allows for a flexible form of heteroskedasticity as well as a certain form of correlation across alternatives for multinomial discrete choice models. The estimator is semiparametric in that I do not specify a particular functional form for the error term in the random utility function. Despite being semiparametric, the rate of convergence of the smoothed maximum score (SMS) estimator is not affected by the number of alternative choices and does not suffer from the"curse of dimensionality". I show the strong consistency and asymptotic normality of the SMS estimator for multinomial discrete choice models. The SMS estimator for multinomial discrete choice models 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 SMS estimator for multinomial discrete choice models can be made arbitrarily close to N-1/2, which is the same as the rate of convergence of Horowitz’s (1992) SMS estimator for the binary response model. Monte Carlo experiments provide evidence that the proposed estimator has a smaller mean squared error than both the conditional logit estimator and the maximum score estimator when heteroskedasticity exists. Heteroskedasticity is relevant in empirical applications. Therefore, the SMS estimator is recommended for analyses that rely on estimates of parameters of the utility function.

I apply the SMS estimator to study the college decisions of high school graduates using a subset of Chilean data from 2011. The Hausman-McFadden test rejects the IIA assumption, and the estimation results of the SMS estimator differ significantly from the results of the conditional logit estimator. These findings suggest possible misspecification of parametric models and the usefulness of considering the SMS estimator as an alternative for estimating multinomial discrete choice models.