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On Zipf’s law and the bias of Zipf regressions

Author

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  • Christian Schluter

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

City size distributions are not strictly Pareto, but upper tails are rather Pareto like (i.e. tails are regularly varying). We examine the properties of the tail exponent estimator obtained from ordinary least squares (OLS) rank size regressions (Zipf regressions for short), the most popular empirical strategy among urban economists. The estimator is then biased towards Zipf's law in the leading class of distributions. The Pareto quantile–quantile plot is shown to offer a simple diagnostic device to detect such distortions and should be used in conjunction with the regression residuals to select the anchor point of the OLS regression in a data-dependent manner. Applying these updated methods to some well-known data sets for the largest cities, Zipf's law is now rejected in several cases.

Suggested Citation

  • Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Post-Print hal-02880544, HAL.
    • Handle: RePEc:hal:journl:hal-02880544
    DOI: 10.1007/s00181-020-01879-3
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02880544
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    Cited by:

    1. Rocco Rante & Federico Trionfetti & Priyam Verma, 2025. "Geography and City Size: From Remains of Bukhara to the Modern US," Working Papers 2025.13, International Network for Economic Research - INFER.
    2. Rocco Rante & Federico Trionfetti & Priyam Verma, 2024. "The Size Distribution of Cities: Evidence from the Lab," Working Papers hal-04556678, HAL.

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    Keywords

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    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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