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

98 Pages Posted: 17 Dec 2019 Last revised: 7 Oct 2022

See all articles by Zhentong Lu

Zhentong Lu

Government of Canada - Bank of Canada

Xiaoxia Shi

University of Wisconsin - Madison; Yale University

Jing Tao

University of Washington, College of Arts and Sciences, Department of Economics, Students

Date Written: February 6, 2021

Abstract

In this paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficients logit demand model. The approach applies to the same setup as Berry, Levinsohn, and Pakes (1995, BLP)-type of models with many products, but has the advantage of not requiring computing demand inversion. In particular, the first step of our approach estimates the fixed coefficients via a computationally very easy linear sieve generalized method of moments (GMM).
The second step uncovers the distribution of the random coefficient via a sieve minimum distance or GMM procedure. We show identification and derive the asymptotic properties of the estimator in a large market environment. Monte Carlo simulations and empirical illustrations support the theoretical results and demonstrate the usefulness of our estimator in practice.

Suggested Citation

Lu, Zhentong and Shi, Xiaoxia and Tao, Jing, Semi-Nonparametric Estimation of Random Coefficient Logit Model for Aggregate Demand (February 6, 2021). Journal of Econometrics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3503560 or http://dx.doi.org/10.2139/ssrn.3503560

Zhentong Lu

Government of Canada - Bank of Canada ( email )

234 Wellington Street
Ontario, Ottawa K1A 0G9
Canada

Xiaoxia Shi

University of Wisconsin - Madison ( email )

1180 Observatory Drive
Madison, WI 53706
United States

Yale University

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Jing Tao (Contact Author)

University of Washington, College of Arts and Sciences, Department of Economics, Students ( email )

Box 353330
Seattle, WA 98195-3330
United States

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