Identification and Estimation of Discrete-Continuous Choice Models with Vertical Product Differentiation

Research over the past several years has led to development of models characterizing equilibrium in a system of local jurisdictions. More recently, there have been a number of studies which have tried to estimate these models. The evidence suggests that simple parametric models can explain the observed sorting of individuals by income among local jurisdictions reasonably well. One drawback of the approach adopted in most empirical studies is that identification of important parameters of the model may be primarily due to functional form assumptions which are hard to evaluate. In this paper, we provide a discussion of identification and estimation of hierarchical equilibrium models in a semi-parametric framework. We show that a broad class of models is identified without imposing strong parametric restriction on the distribution of unobserved tastes for local public goods. We then extend the framework and consider a broad class of non-hierarchical model. Our results suggest that identification of non-hierarchical model may ultimately have to rely on stronger assumptions on the distribution of unobserved tastes for public goods than those used in hierarchical models.