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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

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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Bibliographic Info

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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Publication status: published as 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
Handle: RePEc:nbr:nberwo:14991

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  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.
  2. Aviv Nevo, 2000. "Mergers with Differentiated Products: The Case of the Ready-to-Eat Cereal Industry," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 395-421, Autumn.
  3. 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.
  4. Christopher R. Knittel & Konstantinos Metaxoglou, 2008. "Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings," NBER Working Papers 14080, National Bureau of Economic Research, Inc.
  5. Harikesh Nair, 2007. "Intertemporal price discrimination with forward-looking consumers: Application to the US market for console video-games," Quantitative Marketing and Economics, Springer, vol. 5(3), pages 239-292, September.
  6. repec:cdl:compol:217 is not listed on IDEAS
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Cited by:
  1. Dae-Yong Ahn & Jason A. Duan & Carl F. Mela, 2011. "An Equilibrium Model of User Generated Content," Working Papers 11-13, NET Institute, revised Dec 2011.
  2. Vivienne Pham & David Prentice, 2010. "An empirical Analysis of the Counter-factual: A Merger and Divestiture in the Australian Cigarette Industry," Working Papers 2010.08 EDIRC Provider-In, School of Economics, La Trobe University.
  3. Reynaert, Mathias & Verboven, Frank, 2014. "Improving the performance of random coefficients demand models: The role of optimal instruments," Journal of Econometrics, Elsevier, vol. 179(1), pages 83-98.
  4. Christopher R. Knittel & Konstantinos Metaxoglou, 2011. "Challenges in Merger Simulation Analysis," American Economic Review, American Economic Association, vol. 101(3), pages 56-59, May.
  5. Panle Jia Barwick & Parag A. Pathak, 2011. "The Costs of Free Entry: An Empirical Study of Real Estate Agents in Greater Boston," NBER Working Papers 17227, National Bureau of Economic Research, Inc.
  6. German Zenetti & Thomas Otter, 2014. "Bayesian estimation of the random coefficients logit from aggregate count data," Quantitative Marketing and Economics, Springer, vol. 12(1), pages 43-84, March.
  7. Grigolon, Laura & Verboven, Frank, 2011. "Nested logit or random coefficients logit? A comparison of alternative discrete choice models of product differentiation," CEPR Discussion Papers 8584, C.E.P.R. Discussion Papers.
  8. 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.

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