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

Author

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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.

Suggested Citation

  • Jean-Pierre H. Dubé & Jeremy T. Fox & Che-Lin Su, 2009. "Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation," NBER Working Papers 14991, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:14991
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    Citations

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    Cited by:

    1. 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.
    2. German Zenetti & Thomas Otter, 2014. "Bayesian estimation of the random coefficients logit from aggregate count data," Quantitative Marketing and Economics (QME), Springer, vol. 12(1), pages 43-84, March.
    3. Pesendorfer, Martin & Schiraldi, Pasquale & Silva-Junior, Daniel, 2023. "Omitted budget constraint bias in discrete-choice demand models," International Journal of Industrial Organization, Elsevier, vol. 86(C).
    4. Lai, Yufeng & Yue, Chengyan, 2020. "Consumer Willingness to pay for Organic and Animal Welfare Product Attributes: Do Experimental Results Align with Market Data?," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304328, Agricultural and Applied Economics Association.
    5. Christopher R. Knittel & Konstantinos Metaxoglou, 2011. "Challenges in Merger Simulation Analysis," American Economic Review, American Economic Association, vol. 101(3), pages 56-59, May.
    6. Laura Grigolon & Frank Verboven, 2014. "Nested Logit or Random Coefficients Logit? A Comparison of Alternative Discrete Choice Models of Product Differentiation," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 916-935, December.
    7. Michael Cohen & Adam Rabinowitz, 2012. "An Empirical Analysis of Equilibrium Pricing and Advertising in the Ready-To-Eat Cereal Market," Working Papers 15, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    8. 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.
    9. Yu Zheng & Juan Pantano, 2012. "Using Subjective Expectations Data to Allow for Unobserved Heterogeneity in Hotz-Miller Estimation Strategies," 2012 Meeting Papers 940, Society for Economic Dynamics.
    10. Peter Davis & Pasquale Schiraldi, 2014. "The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products," RAND Journal of Economics, RAND Corporation, vol. 45(1), pages 32-63, March.
    11. Steven Berry & Panle Jia, 2010. "Tracing the Woes: An Empirical Analysis of the Airline Industry," American Economic Journal: Microeconomics, American Economic Association, vol. 2(3), pages 1-43, August.
    12. Panle Jia Barwick & Parag A. Pathak, 2015. "The costs of free entry: an empirical study of real estate agents in Greater Boston," RAND Journal of Economics, RAND Corporation, vol. 46(1), pages 103-145, March.
    13. 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, School of Economics, La Trobe University.
    14. Joachim Freyberger, 2012. "Asymptotic theory for differentiated products demand models with many markets," CeMMAP working papers 19/12, Institute for Fiscal Studies.
    15. Jessie Handbury, 2019. "Are Poor Cities Cheap for Everyone? Non-Homotheticity and the Cost of Living Across U.S. Cities," NBER Working Papers 26574, National Bureau of Economic Research, Inc.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L0 - Industrial Organization - - General

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