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

Jean-Pierre H. Dubé, Jeremy T. Fox, Che-Lin Su

NBER Working Paper No. 14991
Issued in May 2009
NBER Program(s):The Industrial Organization Program

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.

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Document Object Identifier (DOI): 10.3386/w14991

Published: Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation Jean-Pierre Dubé1, Jeremy T. Fox2, Che-Lin Su3,† Article first published online: 25 SEP 2012 DOI: 10.3982/ECTA8585 © 2012 The Econometric Society Issue Econometrica Econometrica Volume 80, Issue 5, pages 2231–2267, September 2012

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