Bayesian Analysis of Random Coefficient Logit Models Using Aggregate Data

43 Pages Posted: 16 Jun 2007 Last revised: 9 Sep 2008

See all articles by Renna Jiang

Renna Jiang

University of California, Davis - Graduate School of Management

Puneet Manchanda

University of Michigan, Stephen M. Ross School of Business

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management

Date Written: August 1, 2008

Abstract

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry, Levinsohn and Pakes (1995) which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a re-parameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who willing to trade off one additional distributional assumption for increased efficiency in estimation.

Keywords: random coefficient logit, aggregate share models, Bayesian analysis

JEL Classification: C11, M3

Suggested Citation

Jiang, Renna and Manchanda, Puneet and Rossi, Peter E., Bayesian Analysis of Random Coefficient Logit Models Using Aggregate Data (August 1, 2008). Available at SSRN: https://ssrn.com/abstract=994311 or http://dx.doi.org/10.2139/ssrn.994311

Renna Jiang

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

Puneet Manchanda

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-936-2445 (Phone)
734-936-8716 (Fax)

Peter E. Rossi (Contact Author)

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States
773-294-8616 (Phone)

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