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Register a new userStability of Pareto-Zipf Law in Non-Stationary Economies
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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.
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Using an exhaustive list of Japanese bankruptcy in 1997, we discover a Zipf law for the distribution of total liabilities of bankrupted firms in high debt range. The life-time of these bankrupted firms has exponential distribution in correlation with entry rate of new firms. We also show that the debt and size are highly correlated, so the Zipf law holds consistently with that for size distribution. In attempt to understand ``physics of bankruptcy, we show that a model of debtor-creditor dynamics of firms and a bank, recently proposed by economists, can reproduce these phenomenological findings.
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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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