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Register a new userA common trajectory recapitulated by urban economies
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Is there a general economic pathway recapitulated by individual cities over and over? Identifying such evolution structure, if any, would inform models for the assessment, maintenance, and forecasting of urban sustainability and economic success as a quantitative baseline. This premise seems to contradict the existing body of empirical evidences for path-dependent growth shaping the unique history of individual cities. And yet, recent empirical evidences and theoretical models have amounted to the universal patterns, mostly size-dependent, thereby expressing many of urban quantities as a set of simple scaling laws. Here, we provide a mathematical framework to integrate repeated cross-sectional data, each of which freezes in time dimension, into a frame of reference for longitudinal evolution of individual cities in time. Using data of over 100 millions employment in thousand business categories between 1998 and 2013, we decompose each citys evolution into a pre-factor and relative changes to eliminate national and global effects. In this way, we show the longitudinal dynamics of individual cities recapitulate the observed cross-sectional regularity. Larger cities are not only scaled-
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Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community - income inequality. We propose a new method to study the scaling of income distributions by analyzing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyze the shapes of income distributions. First, we find that mean, variance, skewness, and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a citys income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.
Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent alpha are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent alpha = 1.4 is related to built-in human social and biological constraints.
We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth & death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrats law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being entrenched incumbents and tokens as an explosive immature ecosystem, largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.
In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear power-scaling with total population, while measures of resource use show sub-linear power-law scaling. Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms, including logarithmic growth, and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates). The remaining dependence of productivity on city size is explained by concentration of specialist service industries, with high value-added per worker, in larger cities, in accordance with the long-standing economic notion of the hierarchy of central places.
Using the mechanics of creep in material sciences as a metaphor, we present a general framework to understand the evolution of financial, economic and social systems and to construct scenarios for the future. In a nutshell, highly non-linear out-of-equilibrium systems subjected to exogenous perturbations tend to exhibit a long phase of slow apparent stable evolution, which are nothing but slow maturations towards instabilities, failures and changes of regimes. With examples from history where a small event had a cataclysmic consequence, we propose a novel view of the current state of the world via the logical scenarios that derive, avoiding the traps of an illusionary stability and simple linear extrapolation. The endogenous scenarios are muddling along, managing through and blood red abyss. The exogenous scenarios are painful adjustment and golden east.
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