Working Paper: NBER ID: w14991
Authors: Jean-Pierre H. Dub; Jeremy T. Fox; Chelin 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.
Keywords: Discrete Choice Models; Demand Estimation; Numerical Methods; Random Coefficients
JEL Codes: C01; C61; L0
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| NFP algorithm (C45) | significant numerical inaccuracies (C60) |
| loose tolerance in inner loop (C69) | propagation of errors into outer loop (C59) |
| propagation of errors into outer loop (C59) | convergence to non-local minima (C62) |
| MPEC approach (E17) | avoids numerical issues associated with NFP (G59) |
| MPEC (E17) | faster and more reliable than NFP (C45) |
| MPEC (E17) | consistently converges to local minima (C62) |
| NFP (F53) | does not consistently converge to local minima (C62) |