Estimating the Link Function in Multinomial Response Models under Endogeneity

Abstract

This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are included as arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. The large sample properties of the estimators are also developed in the context of a quasi-likelihood modeling framework.