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A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models

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Author Info
Patrick Bajari (University of Minnesota and NBER)
Jeremy T. Fox (University of Chicago)
Kyoo il Kim (University of Minnesota)
Stephen Ryan (MIT and NBER)

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Abstract

We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coefficients. The estimator is linear regression subject to linear inequality constraints and is robust, simple to program and quick to compute compared to alternative estimators for mixture models. We discuss three methods for proving identi?fication of the distribution of heterogeneity for any given economic model. We prove the identi?fication of the logit mixtures model, which, surprisingly given the wide use of this model over the last 30 years, is a new result. We also derive our estimator?s non-standard asymptotic distribution and demonstrate its excellent small sample properties in a Monte Carlo. The estimator we propose can be extended to allow for endogenous prices. The estimator can also be used to reduce the computational burden of nested ?fixed point methods for complex models like dynamic programming discrete choice.

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File URL: http://www.concorrencia.pt/download/WP36_Paper_Bajarietal.pdf
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File Function: First version, 2007
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Publisher Info
Paper provided by Portuguese Competition Authority in its series Working Papers with number 36.

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Length: 51 pages
Date of creation: Dec 2007
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Handle: RePEc:pca:wpaper:36

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Daniel A. Ackerberg, 2001. "A New Use of Importance Sampling to Reduce Computational Burden in Simulation Estimation," NBER Technical Working Papers 0273, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Review of Economic Studies, Blackwell Publishing, vol. 71, pages 613-654, 07. [Downloadable!] (restricted)
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  3. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Patrick Bajari & Jeremy Fox & Stephen Ryan, 2008. "Evaluating wireless carrier consolidation using semiparametric demand estimation," Quantitative Marketing and Economics, Springer, vol. 6(4), pages 299-338, December. [Downloadable!] (restricted)
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