Random Coefficient Logit Model for Large Datasets

49 Pages Posted: 7 Jun 2010

See all articles by Carlos H. Mireles

Carlos H. Mireles

University of Texas at Austin

D. Fok

Econometric Institute - Erasmus University Rotterdam; Erasmus Research Institute of Management (ERIM); Tinbergen Institute Rotterdam

Date Written: 31 2010 5,

Abstract

We present an approach for analyzing market shares and products price elasticities based on large datasets containing aggregate sales data for many products, several markets and for relatively long time periods. We consider the recently proposed Bayesian approach of Jiang et al [Jiang, Renna, Machanda, Puneet and Peter Rossi, 2009. Journal of Econometrics 149 (2) 136-148] and we extend their method in four directions. First, we reduce the dimensionality of the covariance matrix of the random effects by using a factor structure. The dimension reduction can be substantial depending on the number of common factors and the number of products. Second, we parametrize the covariance matrix in terms of correlations and standard deviations, like Barnard et al. [Barnard, John, McCulloch, Robert and Xiao-Li Meng, 2000. Statistica Sinica 10 1281-1311] and we present a Metropolis sampling scheme based on this specification. Third, we allow for long term trends in preferences using time-varying common factors. Inference on these factors is obtained using a simulation smoother for state space time series. Finally, we consider an attractive combination of priors applied to each market and globally to all markets to speed up computation time. The main advantage of this prior specification is that it let us estimate the random coefficients based on all data available. We study both simulated data and a real dataset containing several markets each consisting of 30 to 60 products and our method proves to be promising with immediate practical applicability.

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

JEL Classification: C44, M31, M, M31

Suggested Citation

H. Mireles, Carlos and Fok, Dennis, Random Coefficient Logit Model for Large Datasets (31 2010 5,). ERIM Report Series Reference No. ERS-2010-021-MKT. Available at SSRN: https://ssrn.com/abstract=1620715

Carlos H. Mireles (Contact Author)

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

Dennis Fok

Econometric Institute - Erasmus University Rotterdam ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1333 (Phone)
+31 10 408 9162 (Fax)

Tinbergen Institute Rotterdam ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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