The Interpretation of Urban Scaling Analysis in Time

16 Pages Posted: 26 Sep 2019

See all articles by Luis Bettencourt

Luis Bettencourt

University of Chicago - Mansueto Institute for Urban Innovation

Vicky Chuqiao Yang

Santa Fe Institute

José Lobo

Arizona State University (ASU)

Chris Kempes

Santa Fe Institute

Diego Rybski

City College of New York

Marcus Hamilton

The University of Texas at San Antonio

Date Written: September 25, 2019

Abstract

Scaling is a general analytical framework used by many disciplines — from physics to biology and the social sciences — to characterize how population–averaged properties of a collective vary with its size. The observation of scale invariance over some range identifies general system types, be they ideal gases, ecosystems, or cities. The use of scaling in the analysis of cities quantifies many of their arguably fundamental general characteristics, especially their capacity to create interrelated economies of scale in infrastructure and increasing returns to scale in socioeconomic activities. However, the measurement of these effects, and the relationship of observable parameters to theory, hinge on how scaling analysis is used empirically. Here we show how two equivalent approaches to urban scaling — cross-sectional and temporal — lead to the measurement of different mixtures of the same fundamental parameters describing pure scale and pure temporal phenomena. Specifically, temporal exponents are sensitive to the intensive growth of urban quantities and to circumstances when population growth vanishes, leading to instabilities and infinite divergences. These spurious effects are avoided in cross-sectional scaling, which is more common and closer to theory in terms of quantitative testable expectations for its parameters.

Keywords: Urban scaling, Growth, Statistics, Regression, Cities, Congestion

Suggested Citation

Bettencourt, Luis and Yang, Vicky Chuqiao and Lobo, Jose and Kempes, Chris and Rybski, Diego and Hamilton, Marcus, The Interpretation of Urban Scaling Analysis in Time (September 25, 2019). Mansueto Institute for Urban Innovation Research Paper. Available at SSRN: https://ssrn.com/abstract=3459540 or http://dx.doi.org/10.2139/ssrn.3459540

Luis Bettencourt (Contact Author)

University of Chicago - Mansueto Institute for Urban Innovation ( email )

5735 S Ellis Avenue
Chicago, IL 60637
United States

Vicky Chuqiao Yang

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Jose Lobo

Arizona State University (ASU) ( email )

Farmer Building 440G PO Box 872011
Tempe, AZ 85287
United States

Chris Kempes

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Diego Rybski

City College of New York ( email )

Convert Avenue at 138th Street
New York, NY 10031
United States

Marcus Hamilton

The University of Texas at San Antonio ( email )

ONE UTSA Circle
San Antonio, TX 78249
United States

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