Zipf's Law for Cities: On a New Testing Procedure
AbstractIn 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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Bibliographic InfoPaper provided by CERDI in its series Working Papers with number 200920.
Date of creation: 2009
Date of revision:
Zipf 's Law; Pareto distribution; Monte Carlo study; Minimum variance unbiased estimator; developing countries;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-05 (All new papers)
- NEP-ECM-2009-12-05 (Econometrics)
- NEP-GEO-2009-12-05 (Economic Geography)
- NEP-URE-2009-12-05 (Urban & Real Estate Economics)
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- P. Nijkamp & A. Reggiani, 2012. "Did Zipf Anticipate Socio-Economic Spatial Networks?," Working Papers wp816, Dipartimento Scienze Economiche, Universita' di Bologna.
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