Exponential or power distance-decay for commuting? An alternative specification

In this paper we investigate the form of the distance-decay function for commuting, on the basis of an analysis of home-to-work relationships between municipalities in Denmark. The equation for the number of commuters is taken from Alonso's Theory of Movements, in which the Spatial Interaction Models of Wilson's Family are nested. Our estimation method separates the decay function F from the balancing factors, and includes a weighting procedure that takes specification error and heteroscedasticity into account. It appears that neither an exponential nor a power distance-decay function fits the data well. The specification of log F as a (downwards) logistic function of log cost results in a better fit. We find that the cost elasticity reaches a value of –4 for distances around 24 km, while it is close to for both very short and very long distances. Finally, we demonstrate that the choice of functional form for distance-decay can make an important difference for predictions concerning the effect of infrastructure improvements on commuting flows.