Analysis of Discrete Choice Models: A Welfare-Based Framework

Abstract

Based on the observation that many existing discrete choice models admit a welfare function of utilities whose gradient gives the choice probability vector, we propose a new perspective to view choice models by treating the welfare function as the primitive. We call the resulting choice model the welfare-based choice model. The welfare-based choice model is meaningful on its own by providing an alternative way of constructing choice models. Moreover, it provides great analysis convenience for establishing connections among existing choice models. We prove by using convex analysis theory, that the welfare-based choice model is equivalent to the representative agent choice model and the semi-parametric choice model, establishing the equivalence of the latter two. We show that these three models are all strictly more general than the random utility model, while when there are only two alternatives, those four models are equivalent. Moreover, the welfare-based choice model subsumes the nested logit model with positive dissimilarity parameters. We then define a new concept in choice models: substitutability/complementarity between alternatives. We show that the random utility model only allows substitutability between different alternatives; while the welfare-based choice model allows more flexible substitutability/complementarity patterns. We argue that such flexibility could be desirable in capturing certain practical choice patterns, such as the halo effects. We also present ways of constructing new choice models using our approach.