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

Time: Dec. 22 (Wed.), 11:30 am – 13:00 pm

About the Speaker:

Xiaoxia Shi is a Lowell and Leila Robinson Professor at the Economics Department of the University of Wisconsin at Madison. Her research interests include inference for moment inequality models, identification and inference in discrete choice models, and model selection tests. She has published papers in Econometrica, Journal of Political Economy, Journal of Econometrics, Econometric Theory, Quantitative Economics, etc. She is on the editorial board of Review of Economics and Statistics, and is an associate editor at Quantitative Economics and Econometric Theory.

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.