On Zipf’s law and the bias of Zipf regressions

Christian Schluter

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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.

Keywords: regular variation; city size distributions; Zipf's law; rank size regression; extreme value index; heavy tails (search for similar items in EconPapers)
Date: 2021-08
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Published in Empirical Economics, 2021, 61 (2), pp.529-548. ⟨10.1007/s00181-020-01879-3⟩

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Journal Article: On Zipf’s law and the bias of Zipf regressions (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02880544

DOI: 10.1007/s00181-020-01879-3

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