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

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

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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14991.

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Date of creation: May 2009
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Handle: RePEc:nbr:nberwo:14991

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Find related papers by JEL classification:
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
L0 - Industrial Organization - - General

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September. [Downloadable!] (restricted)
  2. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470. [Downloadable!]
  3. Nair, Harikesh, S., 2006. "Intertemporal Price Discrimination with Forward-Looking Consumers: Application to the US Market for Console Video-Games," Research Papers 1947, Stanford University, Graduate School of Business. [Downloadable!]
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  1. Steven Berry & Panle Jia, 2008. "Tracing the Woes: An Empirical Analysis of the Airline Industry," NBER Working Papers 14503, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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