Econometrica: Sep 2012, Volume 80, Issue 5

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

https://doi.org/10.3982/ECTA8585
p. 2231-2267

Jean‐Pierre Dubé, Jeremy T. Fox, Che‐Lin Su

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 approach can be as much as ten to forty times faster for large‐dimensional problems with many markets.

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Supplemental Material

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

This appendix discusses the implementation details for MPEC and NFP applied to the BLP demand estimation problem, the KNITRO outputs for MPEC and NFP, how a researcher would adapt static MPEC to a likelihood-based estimation of random-coefficients-logit demand, varying the quality of the data, and dynamic BLP with one consumer type.

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Supplement to "Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation'

This zip file contains the replication files for the manuscript.

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