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Artificial increasing returns to scale and the problem of sampling from lognormals

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posted on 2023-06-07, 07:07 authored by Andrés Gómez-Liévano, Vladislav VysotskiyVladislav Vysotskiy, José Lobo
We show how increasing returns to scale in urban scaling can artificially emerge, systematically and predictably, without any sorting or positive externalities. We employ a model where individual productivities are independent and identically distributed lognormal random variables across all cities. We use extreme value theory to demonstrate analytically the paradoxical emergence of increasing returns to scale when the variance of log-productivity is larger than twice the log-size of the population size of the smallest city in a cross-sectional regression. Our contributions are to derive an analytical prediction for the artificial scaling exponent arising from this mechanism and to develop a simple statistical test to try to tell whether a given estimate is real or an artifact. Our analytical results are validated analyzing simulations and real microdata of wages across municipalities in Colombia. We show how an artificial scaling exponent emerges in the Colombian data when the sizes of random samples of workers per municipality are 1% or less of their total size.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Environment and Planning B: Urban Analytics and City Science

ISSN

2399-8083

Publisher

SAGE Publishing

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-05-28

First Open Access (FOA) Date

2020-05-28

First Compliant Deposit (FCD) Date

2020-05-28

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