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

34 Pages Posted: 5 Feb 2009 Last revised: 11 Jul 2016

Jean-Pierre Dubé

University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER)

Jeremy T. Fox

University of Michigan

Che-Lin Su

University of Chicago - Booth School of Business

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Date Written: October 1, 2011

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 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.

Keywords: demand estimation, logit, random coefficients, dynamic, nested-fixed-point, constrained optimization

JEL Classification: C1, C5, C6, L00, M3

Suggested Citation

Dubé, Jean-Pierre and Fox, Jeremy T. and Su, Che-Lin, Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation (October 1, 2011). Chicago Booth School of Business Research Paper No. 11-41. Available at SSRN: https://ssrn.com/abstract=1338152 or http://dx.doi.org/10.2139/ssrn.1338152

Jean-Pierre H. Dube (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 South Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://gsb.uchicago.edu/fac/jean-pierre.dube

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Jeremy T. Fox

University of Michigan ( email )

611 Tappan St.
Ann Arbor, MI 48104
United States
734 330-2854 (Phone)

Che-Lin Su

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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