Mixed Logit and Pure Characteristics Models

Abstract

Mixed logit or random coefficients logit models are used extensively in empirical work while pure characteristic models feature in much of theoretical work. We provide a theoretical analysis of the relationship between the two classes of models. First, we show an approximation theorem that precisely characterizes the extent and limitations of mixed logit approximations of pure characteristic models. Second, we present two conditions that highlight novel behavioral differences. The first is a substitutability condition that is satisfied by many pure characteristic models (including models of horizontal differentiation such as Hotelling) but is violated by almost all mixed logit models. The second is a continuity condition that is satisfied by all pure characteristic models but is violated by all mixed logit models. Both conditions pertain to choice patterns when product characteristics change or new products are introduced and illustrate the limitations of using mixed logit models for counterfactual analysis.