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REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS
Published online by Cambridge University Press: 20 May 2024
Abstract
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.
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- 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.
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- © 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.”