Simple Estimators for Semiparametric Multinomial Choice Models

This paper considers estimation of the coe¢ cients in a semiparametric multinomial choice model with linear indirect utility functions (with common coe¢ cients but di¤ering regressors) and errors that are assumed to be independent of the regressors. This implies that the conditional mean of the vector of dependent indicator variables is a smooth and invertible function of a corresponding vector of linear indices. The estimation method is an extension of an approach proposed by Ahn, Ichimura, and Powell (2004) for monotone single-index regression models to a multi-index setting, estimating the unknown index coe¢ cients (up to scale) by an eigenvector of a matrix de…ned in terms of a …rststep nonparametric estimator of the conditional choice probabilities. Under suitable conditions, the proposed estimator is root-n-consistent and asymptotically normal. JEL Classi…cation: C24, C14, C13.