Identification of consumer preference from market-level data in a multinomial logit model with random coefficients

Abstract

We present a proof of identification for a multinomial logit model with random coefficients. Assuming a family of distributions for the consumer preferences governed by two parameters we will show these can be obtained by observing the market shares of all products in the market. The proof is entirely elementary and requires only that the choice probabilities for the products with the highest and lowest values of the observed attributes be convex as functions of each other. We apply the identification result and the techniques used in the proof to study the convexity of the identified set for two simple under-identified models.