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

Patrick Bajari, Jeremy T. Fox, Kyoo il Kim, & Stephen Ryan

Abstract WP n.º 36:

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 identification of the distribution of heterogeneity for any given economic model. We prove the identification 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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After the Introduction, in Section 2 we discuss the variants of the estimator in detail. We discuss identification in Section 3 and provide asymptotic theory for our estimator in Sections 4 and 5. We demonstrate the small-sample performance of our estimator in a Monte Carlo in Section 6. Section 7 concludes.

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.pdf 'A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models'
Patrick Bajari, Jeremy T. Fox, Kyoo il Kim, & Stephen Ryan (WP n.º 36)
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