TY  - JOUR
AU  - Dubé,Jean-Pierre H.
AU  - Fox,Jeremy T.
AU  - Su,Che-Lin
TI  - Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 14991
PY  - 2009
Y2  - May 2009
UR  - http://www.nber.org/papers/w14991
L1  - http://www.nber.org/papers/w14991.pdf
N1  - Author contact info:
Jean-Pierre H. Dube
University of Chicago
Booth School of Business
5807 South Woodlawn Avenue
Chicago, IL 60637
Tel: 773/834-5377
Fax: 773/702-0458
E-Mail: jdube@chicagobooth.edu

Jeremy T. Fox
Economics Department
University of Michigan
238 Lorch Hall
611 Tappan Ave
Ann Arbor, MI 48104
Tel: 734-330-2854
Fax: 734-274-2331
E-Mail: jeremyfox@gmail.com

Che-Lin Su
University of Chicago
E-Mail: che-lin.su@ChicagoBooth.edu
AB  - 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.
ER  -