A Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data

Journal of Marketing Research, Forthcoming

Johnson School Research Paper Series No. 08-08

38 Pages Posted: 16 May 2008

See all articles by Sungho Park

Sungho Park

Arizona State University (ASU) - W.P. Carey School of Business

Sachin Gupta

Cornell University - Samuel Curtis Johnson Graduate School of Management

Abstract

We propose a Simulated Maximum Likelihood estimation method for the random coefficient logit model using aggregate data, accounting for heterogeneity and endogeneity. Our method allows for two sources of randomness in observed market shares - unobserved product characteristics and sampling error. Because of the latter, our method is suitable when sample sizes underlying the shares are finite. By contrast, the commonly used approach of Berry, Levinsohn and Pakes (1995) assumes that observed shares have no sampling error. Our method can be viewed as a generalization of Villas-Boas and Winer (1999) and is closely related to the "control function" approach of Petrin and Train (2004). We show that the proposed method provides unbiased and efficient estimates of demand parameters. We also obtain endogeneity test statistics as a by-product, including the direction of endogeneity bias. The model can be extended to incorporate Markov regime-switching dynamics in parameters and is open to other extensions based on Maximum Likelihood. The benefits of the proposed approach are achieved by assuming normality of the unobserved demand attributes, an assumption that imposes constraints on the types of pricing behaviors that are accommodated. However, we find in simulations that demand estimates are fairly robust to violations of these assumptions.

Keywords: Random Coefficients, Logit Model, Endogeneity, Heterogeneity, Simulated Maximum Likelihood, Aggregate data, Brand Choice, Scanner Data

Suggested Citation

Park, Sungho and Gupta, Sachin, A Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data. Journal of Marketing Research, Forthcoming; Johnson School Research Paper Series No. 08-08. Available at SSRN: https://ssrn.com/abstract=1133557

Sungho Park (Contact Author)

Arizona State University (ASU) - W.P. Carey School of Business ( email )

Marketing Department
PO Box 874106
Tempe, AZ 85287-4106
United States

Sachin Gupta

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

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