Improving the Numerical Performance of Blp Static and Dynamic Discrete Choice Random Coefficients Demand Estimation

52 Pages Posted: 26 May 2009 Last revised: 19 Jun 2022

See all articles by Jean-Pierre Dubé

Jean-Pierre Dubé

University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER); Marketing Science Institute (MSI)

Jeremy T. Fox

University of Michigan

Che-Lin Su

University of Chicago - Booth School of Business

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Date Written: May 2009

Abstract

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 Bellman's 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.

Suggested Citation

Dube, Jean-Pierre H. and Fox, Jeremy T. and Su, Che-Lin, Improving the Numerical Performance of Blp Static and Dynamic Discrete Choice Random Coefficients Demand Estimation (May 2009). NBER Working Paper No. w14991, Available at SSRN: https://ssrn.com/abstract=1408911

Jean-Pierre H. Dube (Contact Author)

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Jeremy T. Fox

University of Michigan ( email )

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Che-Lin Su

University of Chicago - Booth School of Business ( email )

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United States