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

In this paper we investigate the functional form of distance decay for commuting flows between municipalities in Denmark. Our inference is based on a single equation that includes variables to capture the effect of spatial structure. Special attention is given to a proper estimation method: we estimate the distance-decay parameters by nonlinear weighted least-squares with balancing factors. It appears that neither an exponential nor a power distance-decay function fits the data well. Using a spline regression we find a cost elasticity of -4 for distances around 20 km and a much smaller value for shorter and longer distances. It appears that the logarithm of distance decay can be described adequately as a (downward) logistic function of log cost.