Real Analytic Discrete Choice Models of Demand: Theory and Implications

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.