Statistical Dynamics of Regional Populations and Economies

TL;DR

This paper models the statistical dynamics of regional populations and GDPs in China, revealing their distributional shifts over time and predicting a future Gaussian distribution for GDPs.

Contribution

It introduces a generalized Langevin equation for population variation and links population and GDP distributions through theoretical modeling.

Findings

Population distribution shifts from Gaussian to shifted power law

GDP distribution transitions from shifted power law to Gaussian

Identifies a critical point in population distribution transformation

Abstract

A practical statistical analysis on the regional populations and GDPs of China is conducted. The result shows that the distribution of the populations and that of the GDPs obeys the shifted power law, respectively. To understand these characteristics, a generalized Langevin equation describing variation of population is proposed based on the correlation between population and GDP as well as the random fluctuations of the related factors. The equation is transformed into the Fokker-Plank equation, and the solution demonstrates a transform of population distribution from the normal Gaussian distribution to a shifted power law. It also suggests a critical point of time at which the transform occurs. The shifted power law distribution in the supercritical situation is qualitatively in accordance with the practical result. The distribution of the GDPs is derived based on the Cobb-Douglas production function, and presents a change from a shifted power law to the Gaussian distribution. This result indicates that the regional GDP distribution of our society will be the Gaussian distribution in the future. The analysis on the growth trend of economy suggests it will become a reality. These theoretical attempts may draw a historical picture of our world in the aspects of population and economy.