A test of the relationship between the Pareto exponent and sample size

Rafael González-Val and Fernando Sanz-Gracia
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Fernando Sanz-Gracia: Universidad de Zaragoza

INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, 2026, vol. 64, issue 64, 5-16

Abstract: This paper uses un-truncated city population data from three countries—the United States, Spain and Italy—to empirically test Proposition 1 put forth by Eeckhout (2004 American Economic Review, 94: 1429–1451). Eeckhout’s hypothesis was that the estimate of the Pareto exponent in a standard Zipf regression decreases with sample size, if the underlying city size distribution is lognormal. Using rolling sample regressions, we find that this proposition is only valid once we enter the lognormal body of the distribution; for the Pareto-distributed upper-tail, the estimated exponent does not vary with sample size.

Keywords: City size distribution; Zipf’s law; Pareto exponent; Pareto distribution; lognormal distribution; rolling sample regressions (search for similar items in EconPapers)
JEL-codes: C12 R11 R12 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:ris:invreg:022190

DOI: 10.38191/iirr-jorr.24.064

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