How to Eliminate Certain Defects of the Potential Formula

Abstract

The potential formula, defined as a sum of regional ‘masses’ weighted by a decreasing function of distance, is a conventional indicator of accessibility in spatial econometrics. If applied to a system of discrete points in space, however, the standard potential formula with an exponential distance-friction does not convey the desired information in the case of sufficiently large distance-friction parameters. The reason for this defect is that the so-called eigenpotential is inappropriately defined by the standard formula. After reviewing the theoretical foundations of the potential index and advocating its derivation from stochastic choice theory, this paper proposes a modification of the potential formula. The basic idea is to handle the region to which the potential refers as a continuous space with equally distributed density of mass. This leads to an index with desirable limiting properties with respect to the distance-friction parameter.