Testing the rank size rule hypothesis with an efficient estimator

Article Abstract:

The relation of distributions of population sizes of urban areas within city systems is governed by a complex structure of economic and social rules that exhibit regularities across different countries. The rank size rule holds that the product of a city's size and its rank is a constant of the city system. The rank size rule holds that the the distribution of population sizes of city systems are in accordance with the Pareto distribution with parameter alpha = 1. Research using a maximum likelihood approach in a statistical model was conducted to to test the validity of the rank size rule by analyzing the population size distribution in several counties. Research results reveal that population sizes of urban areas are distributed in accordance to Pareto's law, and that if the sample of observed cities is reduced, then the ML estimator for the Pareto distribution parameters is gamma-distributed.

Population research

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Truncated error structure in the estimation of generalized urban density functions

Article Abstract:

Urban economic analysis relies on the estimation of spatial patterns of population densities; population density is assumed to decline exponentially with distance from the central business district. Box-Cox estimation procedures for calculating urban density, due to the transformation of the dependent variable, necessitate an accounting for of the implied truncation in the error distribution through a restructured generalized gradient specification. Using the framework provided by Poirier and Poirier and Melino, researchers derived a likelihood specification to yield consistent parameter estimates for the density functions of 38 US cities. The research model incorporated the function form parameter based directly on the magnitude and response of the expected value of population density in relation to urban location variations.

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Mean city - a consistent approximation of bid rent equilibria

Article Abstract:

Residential location in a monocentric city is modeled using a bid rent approach. The proposed model assumes a continuum of consumers and that transportation costs shrink towards the center as the number of consumers grows. The former assumption is made for mathematical convenience, while the latter implies a constant per capita endowment for land of the same quality. Consistent approximation is difficult if the total area on which the population is located is taken as the aggregate land supply. However, analysis shows that from the perspective of mean demand and mean supply, the normalized equilibrium equations converge in the bid rent solution, wherein the limiting 'mean city' area reflects the average land parcel mean supply and mean demand.

Economic aspects, Housing development, Urban land use

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