Technical Note-On the Relation Between Several Discrete Choice Models

Abstract

In this paper, we study the relationship between several well known classes of discrete choice models, i.e., the random utility model (RUM), the representative agent model (RAM), and the semiparametric choice model (SCM). Using a welfare-based model as an intermediate, we show that the RAM and the SCM are equivalent. Furthermore, we show that both models as well as the welfare-based model strictly subsume the RUM when there are three or more alternatives, while the four are equivalent when there are only two alternatives. Thus, this paper presents a complete picture of the relationship between these choice models.