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Published July 8, 2022 | Submitted
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Approximating Choice Data by Discrete Choice Models


We obtain a necessary and sufficient condition under which parametric random-coefficient discrete choice models can approximate the choice behavior generated by nonparametric random utility models. The condition turns out to be very simple and tractable. For the case under which the condition is not satisfied (and hence, where some stochastic choice data are generated by a random utility model that cannot be approximated), we provide algorithms to measure the approximation errors. After applying our theoretical results and the algorithm to real data, we found that the approximation errors can be large in practice.

Additional Information

A part of this paper was first presented at the University of Tokyo on July 29, 2017. This paper subsumes parts of "Axiomatizations of the Mixed Logit Model" by Saito (The paper is available at http://www.hss.caltech.edu/content/axiomatizations-mixed-logit-model). We would like to thank Hiroki Saruya and Haruki Kono for their help as RAs. We appreciate the valuable discussions we had with Brendan Beare, Victor Aguirregabiria, Doignon Jean-Paul , John Rust, Giovanni Compiani, Steven Berry, Yi Xin, Alfred Galichon, Jay Lu, Ariel Pakes, Whitney K. Newey, and Matt Shum. Jay Lu also read an earlier version of the manuscript and offered helpful comments. We appreciate the insightful comments made by Victor Aguirregabiria at the ASSA meetings in January 2022. Saito acknowledges the financial support of the NSF through grants SES-1919263 and SES-1558757.

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