Discrete choice models for commuting interactions

An emerging quantitative spatial economics literature models commuting interactions by a gravity equation that is mathematically equivalent to a multinomial logit model. This model is widely viewed as restrictive because of the independence of irrelevant alternatives (IIA) property that links substitution behavior in response to changes in the attractiveness of choice alternatives to choice probabilities in a mechanistic way. This is relevant for counterfactual analysis. In this paper we examine the appropriateness of the commuting model from a theoretical as well as an empirical point of view. We show that conventional specification tests of the multinomial logit model are of limited use when alternative specific constants are used, as is common in the recent literature, and offer no information with respect to the validity of IIA. In particular, we show that maximum likelihood estimation of relevant nested logit model is impossible because the crucial parameters are not identified. We discuss cross-nested and mixed logit as alternatives. We argue that a comparison between predicted and actual changes in commuting flows in response to a change in the attractiveness of choice alternatives provides a more informative test for the validity of the multinomial logit model for commuting interaction and report the results of such a test – as well as others – for data referring to Copenhagen.