Semi-Nonparametric Estimation of Random Coefficient Logit Model for Aggregate Demand

Abstract

In this paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficient logit demand model. In the first step, exploiting the structure of logit choice probabilities, we transform the full demand system into a partial linear model and estimate the fixed (non-random) coefficients using standard linear sieve generalized method of moment (GMM). In the second step, we construct a sieve minimum distance (MD) estimator to uncover the distribution of random coefficients nonparametrically. We establish the asymptotic properties of the estimator and show the semi-nonparametric identification of the model in a large market environment. Monte Carlo simulations and empirical illustrations support the theoretical results and demonstrate the usefulness of our estimator in practice.