Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation
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.
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, 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 financial support from the NSF (award no. SES-0631622) and the University of Chicago Booth School of Business. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
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