Year: 2016
Type: article
Abstract: One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼x (β) ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)-(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed.
Source: Royal Society Open Science
DOI: 10.1098/rsos.150649
Authors: J. C. Leitão, J. M. Miotto, M. Gerlach, E. G. Altmann
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $1,471
OpenAlex ID: W2341046739