Improving the Numerical Performance of Blp Static and Dynamic Discrete Choice Random Coefficients Demand Estimation
Jean-Pierre H. Dube
University of Chicago - Booth School of Business
Jeremy T. Fox
University of Michigan
University of Chicago Booth School of Business
NBER Working Paper No. w14991
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.
Number of Pages in PDF File: 52working papers series
Date posted: May 26, 2009
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