REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS
证明一大类离散选择需求模型可用实解析函数逼近，结合混合Logit和混合Probit的实解析性质与有限混合的逼近性质，为非参数识别、反事实推断和数值实现提供便利。
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.