Urban non-residential density functions: Testing for the appropriateness of the exponential function using a generalized box-cox transformation function

Abstract

A predominant view among urban economists is that the exponential function is an accurate representation of the spatial distribution of population densities in urban areas but an inadequate representation of the spatial distribution of non-residential activities. In this paper we suggest that such a view is not warranted either on theoretical or empirical grounds. Discreditation of the exponential function for non-residential density is not based on valid statistical tests, which refute the function, but on scholars' impression of how good the function fits the data. It is suggested in this paper that proper tests of the functional form can be conducted using the generalized Box-Cox transformation function, which permits estimation and testing of many functional forms. Such testing is conducted using 1996 data on densities of total floor-space and industry floor-space for manufacturing, commerce and services from Tel Aviv-Yafo. The results obtained are illuminating in showing that, contrary to the popular view in the literature, the exponential function is an appropriate form for representing the spatial distribution of total non-residential densities in Tel Aviv-Yafo which cannot be dismissed on formal statistical grounds. As far as the individual industries are concerned we cannot reject the exponential form, at the 1% significance level, for services and commerce and it is rejected for manufacturing.