Exponential or Power Distance-Decay for Commuting? An Alternative Specification

Abstract

IntroductionCommuting has been the subject of increasing public attention and intensive research in recent decades (see Nijkamp and Rouwendal, 2004;Rouwendal and Nijkamp, 2004). The increasing role of commuting has far-reaching consequences for public policy concerning traffic, infrastructure, and spatial planning. Commuting flows connect labor and housing markets. Knowledge of the intensity and spatial range of this interaction is required to determine the accessibility of a location to centers of population and employment. Theoretical and applied research on commuting issues can help to clarify the relevant effects.The analysis of the sizes of commuting flows between cities or regions, and their effects on housing and labor markets, is part of the much wider area of spatial interaction modeling (Batten and Boyce, 1986;Fotheringham and O'Kelly, 1989;Nijkamp and Reggiani, 1992). Spatial interaction models are applied not only to commuting but also to migration, international trade, shopping behavior, and other topics related to origin^destination flows. An essential element of these models is that interaction decreases with distance or travel cost. This is described by a distance-decay function. However, distance is not the only factor affecting the intensity of the interaction. Also important are the sizes (however measured) of origin and destination. And it is increasingly recognized that additionally the positions of origin and destination in the spatial system are relevant. The research in this paper is an application of spatial interaction modeling, and the methodological issues are not limited to commuting.An important issue in spatial interaction modeling is the choice of the functional form of distance or travel cost. In the literature, the distance-decay function is usually assumed to be an exponential or a power function:`I n practice, the debate over the form of the cost function in spatial interaction models has evolved to a reasonably widespread consensus that the exponential function is more appropriate for analysing short distance interactions such as those that take place within an urban area. The power function, conversely, is generally held to be more appropriate for analysing longer distance interactions such as migration flows '' (Fotheringham and O'Kelly, 1989, pages 12^13 Abstract. 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 À4 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 (downwar...

Do More Hospital Beds Lead to Higher Hospitalization Rates? A Spatial Examination of Roemer’s Law

“…These data were employed to create a model that provided weight values for the E2SFCA. The empirical cumulative probability ( C ) and travel time ( d ) data were used to estimate the parameters of the downward log-logistic decay function [55]: …”

Field theory for recurrent mobility

“…Their main difference lies in the way in which the geographical distance affects the flows. While in the gravity model the flows decay with a certain deterrence function (usually, with an exponential or power law-like forms [26][27][28][29]), the intervening opportunity models depend on the "opportunities" or jobs enclosed within a given area. Since the opportunity distribution can be highly heterogeneous in space, the distance plays an indirect role on the final assignment of the trip destinations and, in turn, on the decay of the total flows [14,30].…”

A New Method of Adaptive Zoning for Spatial Interaction Models

“…These results show no substantial difference between the two models. The discrepancy between the models and the recorded commuting pattern is reasonable given the simplistic nature of the model and its known limitations (De Vries, Nijkamp, and Rietveld ).…”