Population density gradients and urbanisation measurement

Summary. The exponential density function has been used widely to describe and compare the patterning of urban population. In this article it is argued that the exponent within the function can be biassed by the misidentification of the CBD and of the centroids of census tracts. Using a least-squares method it is shown that such misspecification (of the location of the CBD) leads to an underestimation of the gradient, and shows that the magnitude of the bias is itself related to the extent of the distance error by which the CBD is misidentified. Understanding the factors and processes which stand behind and shape the spatial distribution of population in urban areas is a long and continuing preoccupation of urban economists. Urban population den-sity functions, particularly exponential forms, have persistently been employed in the literature as simple measures for des-cribing and comparing the patterning of population in different urban areas and through time. This occupation is well documented in two surveys undertaken by Edmonston (1975), which reviews studies published before 1975, and by McDonald (1989), which reviews studies conducted thereafter. The method used for this pur-pose utilises the estimate of the exponent of the exponential density function, desig-nated also as the gradient, as the main vehicle for measuring differences in sub-urbanisation in various urban areas (Mills and Hamilton, 1989). The relevance of this method for analysing the tendency for urbanisation is supported both by theoreti-cal and empirical justifications. Accepting the theoretical framework developed and 132