Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data
Author: SUNGHO PARK AND SACHIN GUPTA
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A widely used tool for the analysis of market shares of competing brands is the random coefficient logit model. The authors propose a simulated maximum likelihood estimation method for this model. They show that their proposed method provides unbiased and efficient estimates of demand parameters. The method offers certain advantages relative to extant estimation approaches. First, it allows for two sources of randomness in observed market shares—unobserved product characteristics and sampling error. Because of the latter, the method is suitable when sample sizes underlying the shares are finite. In contrast, Berry, Levinsohn, and Pakes’s commonly used approach assumes that observed shares have no sampling error. Second, the authors obtain endogeneity test statistics as a by-product, including the direction of endogeneity bias. Third, 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, the authors find in simulations that demand estimates are fairly robust to violations of these assumptions. The proposed method can expand the set of econometric tools available for analyzing and understanding market competition.
Sungho Park is a doctoral student in the Johnson School of Management at Cornell University. He holds a BA in Linguistics from Seoul National University and an MS in Management Engineering from Korea Advanced Institute of Science & Technology. His research interests include dynamics in consumer choice and applications of structural econometric models to marketing.
Sachin Gupta is the Henrietta Johnson Louis Professor of Management and Professor of Marketing in the Johnson Graduate School of Management at Cornell University. He has published numerous articles in Journal of Marketing Research, Management Science, Marketing Science, and Cornell Hospitality Quarterly, and he is on the editorial boards of several major journals.Journal Marketing Research, Volume 46, Number 4, August 2009 View Table of Contents.