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

Author

Listed:
  • Rafael González-Val

    (Universidad de Zaragoza & Institut d'Economia de Barcelona (IEB))

  • Fernando Sanz-Gracia

    (Universidad de Zaragoza)

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.

Suggested Citation

  • Rafael González-Val & Fernando Sanz-Gracia, 2026. "A test of the relationship between the Pareto exponent and sample size," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, vol. 64(64), pages 5-16, February.
    • Handle: RePEc:ris:invreg:022190
    DOI: 10.38191/iirr-jorr.24.064
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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