Discrete choice models with capacity constraints: An empirical analysis of the housing market of the greater Paris region

Discrete choice models are based on the idea that each user can choose both freely and independently from other users in a given set of alternatives. But this is not the case in several situations. In particular, limitations and interactions can occur when the number of available products of one type is smaller than the total demand for this type. As a consequence, some individuals can be denied their preferred choice. We develop a methodology to address those constraints and we apply it to residential location choice, where our empirical data suggest that availability constraints may bias actual choices. The analysis provides some theoretical developments and elaborates an iterative procedure for estimating demand in the presence of capacity constraints. The empirical application relies on the location choice model developed and estimated in [A. de Palma, K. Motamedi, N. Picard, P. Waddell, A model of residential location choice with endogenous housing prices and traffic for the Paris region, European Transport, 2006] for Ile-de-France (Paris region) and generalizes it to integrate capacity constraints.