A survey of preference estimation with unobserved choice set heterogeneity

Abstract

We provide an introduction to the estimation of discrete choice models when choice sets are heterogeneous and unobserved to the econometrician. We survey the two most popular approaches: “integrating over” and “differencing out” unobserved choice sets. Inspired by Chamberlain (1980)’s original idea of constructing sufficient statistics from observed choices, we introduce the term “sufficient set” to refer to any combination of observed choices that lies within the true but unobserved choice set. The concept of sufficient set helps to unify notation and organize our thinking, to map econometric assumptions onto economic models, and to implement both methods in practice.