Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation
Jean-Pierre H. Dube
University of Chicago - Booth School of Business
Jeremy T. Fox
University of Michigan
University of Chicago Booth School of Business
October 1, 2011
Chicago Booth School of Business Research Paper No. 11-41
The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP's estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward-looking demand models where the Bellman equation must also be solved repeatedly. Several Monte Carlo and real-data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization. For static BLP, the constrained optimization algorithm can be as much as ten to forty times faster.
Number of Pages in PDF File: 34
Keywords: demand estimation, logit, random coefficients, dynamic, nested-fixed-point, constrained optimization
JEL Classification: C1, C5, C6, L00, M3
Date posted: February 5, 2009 ; Last revised: December 31, 2011
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