Empirical nonextensive laws for the county distribution of total personal income and gross domestic product

TL;DR

This paper demonstrates that nonextensive statistical mechanics effectively models the distribution of income and GDP across various regions and countries, capturing the entire spectrum from low to high values over several decades.

Contribution

It introduces a phenomenological approach using generalized exponential distributions to describe economic and geographical distributions, revealing potential links to nonextensive statistical mechanics.

Findings

Distributions are well described by nonextensive models across the entire spectrum.

Parameters show regular patterns over time, indicating underlying dynamic connections.

The approach applies to income, GDP, land areas, and land prices.

Abstract

We analyze the cumulative distribution of total personal income of USA counties, and gross domestic product of Brazilian, German and United Kingdom counties, and also of world countries. We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectrum of the distributions (within acceptable errors), ranging from the low region to the middle region, and, in some cases, up to the power-law tail. The analysis over about 30 years (for USA and Brazil) shows a regular pattern of the parameters appearing in the present phenomenological approach, suggesting a possible connection between the underlying dynamics of (at least some aspects of) the economy of a country (or of the whole world) and nonextensive statistical mechanics. We also introduce two additional examples related to geographical distributions: land areas of counties and land prices, and the same kind of equations adjust the data in the whole range of the spectrum.