On Zipf’s law and the bias of Zipf regressions
On Zipf’s law and the bias of Zipf regressions
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.
City size distributions, Extreme value index, Heavy tails, Rank size regression, Regular variation, Zipf’s law
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
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.
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More information
Accepted/In Press date: 30 April 2020
e-pub ahead of print date: 6 June 2020
Additional Information:
Funding Information:
I thank the referees for their constructive comments that have helped to improve the paper. Financial support from ANR-DFG (Grant ANR-15-FRAL- 0007-01) and ANR-17-EURE-0020 is also gratefully acknowledged.
Publisher Copyright:
© 2020, The Author(s).
Keywords:
City size distributions, Extreme value index, Heavy tails, Rank size regression, Regular variation, Zipf’s law
Identifiers
Local EPrints ID: 441630
URI: http://eprints.soton.ac.uk/id/eprint/441630
ISSN: 0377-7332
PURE UUID: c0eaff06-9177-4b51-9950-b8aa62a949d7
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Date deposited: 23 Jun 2020 16:30
Last modified: 16 Mar 2024 08:13
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