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Zipf's Law for Cities: On a New Testing Procedure

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  • Sebastien TERRA

Abstract

In this paper, we provide a new framework to assess the validity of Zipf 's Law for cities. Zipf 's Law states that, within a country, the distribution of city sizes follows a Pareto distribution with a Pareto index equal to 1. We adopt a two-step approach where we formally test if the distribution of city sizes is a Pareto distribution and then we estimate the Pareto index. Through Monte Carlo experiments, we investigate the nite sample performances of this testing procedure and we compare the small-sample properties of a new estimator (the minimum variance unbiased estimator) to those of commonly used estimators. The minimum variance unbiased estimator turns out to be more efficient and unbiased. We use this two-step approach to examine empirically the validity of Zipf 's Law on a sample of 115 countries. Zipf 's Law is not rejected in most countries (62 out of 115, or 53.9%).

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  • Sebastien TERRA, 2009. "Zipf's Law for Cities: On a New Testing Procedure," Working Papers 200920, CERDI.
    • Handle: RePEc:cdi:wpaper:1102
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    Cited by:

    1. P. Nijkamp & A. Reggiani, 2012. "Did Zipf Anticipate Socio-Economic Spatial Networks?," Working Papers wp816, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Aura Reggiani & Peter Nijkamp, 2015. "Did Zipf Anticipate Spatial Connectivity Structures?," Environment and Planning B, , vol. 42(3), pages 468-489, June.

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    Keywords

    Zipf 's Law; Pareto distribution; Monte Carlo study; Minimum variance unbiased estimator; Developing countries;
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