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REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS

Published online by Cambridge University Press:  20 May 2024

Alessandro IariaOpen the ORCID record for Alessandro Iaria[Opens in a new window] and
Ao WangOpen the ORCID record for Ao Wang[Opens in a new window]
Alessandro Iaria
Affiliation:
University of Bristol and CEPR
Ao Wang*
Affiliation:
University of Warwick and CAGE Research Centre
*
Address correspondence to Ao Wang, Department of Economics, University of Warwick and CAGE Research Centre, Coventry, United Kingdom, e-mail: ao.wang@warwick.ac.uk
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Abstract

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We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 41 , Issue 5 , October 2025, pp. 1080 - 1128
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We are grateful to the Editor (Peter C. B. Phillips), the Co-Editor (Simon Lee), and two anonymous referees for comments and suggestions which greatly improved the article. An early version of this paper circulated under the title “The Mixed Logit and Mixed Probit are Real Analytic.”

References

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