Closed Form Estimators for a Class of Semiparametric Multinomial Choice Models

We consider a semiparametric multinomial choice model that allows for an arbitrary joint distribution of choice specific unobservables that are independent of explanatory variables. This model permits relatively flexible substitution patterns between choices. To minimize computational difficulties, we restrict attention on estimators of the model that can be expressed in closed form. We combine and extend various results from the existing literature to enforce economic restrictions implied by the model and to attain “as efficient estimators as we can” - given the closed form requirement. Some aspects of our estimators achieve the semiparametric efficiency bound, while others do not. In Monte-Carlo experiments, we study how various strategies increase efficiency, and compare the efficiency of our best estimators to computationally more challenging, non-closed form, estimators that are efficient.