We thank Daniel Ackerberg, Steven Berry, John Birge, Amit Gandhi, Philip Haile, Lars Hansen, Panle Jia, Kyoo il Kim, Samuel Kortum, Kenneth Judd, Sven Leyffer, Denis Nekipelov, Aviv Nevo, Jorge Nocedal, Ariel Pakes, John Rust, Hugo Salgado, Azeem Shaikh, and Richard Waltz for helpful discussions and comments. We also thank workshop participants at CREST-INSEE/ENSAE, EARIE, the ESRC Econometrics Study Group Conference, the Econometric Society, the Federal Trade Commission, INFORMS, the International Industrial Organization Conference, the 2009 NBER winter IO meetings, Northwestern University, the Portuguese Competition Commission, Santa Clara, the Stanford Institute for Theoretical Economics, the UK Competition Commission, the University of Chicago, and the University of Rochester. Dubé is grateful to the Kilts Center for Marketing and the Neubauer Faculty Fund for research support. Fox thanks the NSF, Grant 0721036, the Olin Foundation, and the Stigler Center for financial support. Su is grateful for the research support from the NSF (award no. SES-0631622) and the IBM Corporation Faculty Research Fund at the University of Chicago Booth School of Business.
Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation
Version of Record online: 25 SEP 2012
© 2012 The Econometric Society
Volume 80, Issue 5, pages 2231–2267, September 2012
How to Cite
Dubé, J.-P., Fox, J. T. and Su, C.-L. (2012), Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation. Econometrica, 80: 2231–2267. doi: 10.3982/ECTA8585
- Issue online: 25 SEP 2012
- Version of Record online: 25 SEP 2012
- Manuscript received May, 2009; final revision received October, 2011.
- Random coefficients logit demand;
- constrained optimization;
- numerical methods;
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.