Equilibrium Distribution of Labor Productivity: A Theoretical Model

TL;DR

This paper develops a theoretical model for the equilibrium distribution of workers across sectors with varying productivity, successfully explaining observed empirical patterns including Boltzmann and power-law distributions.

Contribution

It introduces a novel theoretical formula for productivity distribution based on the Ehrenfest-Brillouin model and validates it with empirical data from Japan.

Findings

The model explains the observed Boltzmann distribution at low-to-medium productivity.

It accounts for a power-law decline at high productivity levels.

Empirical data supports the theoretical distribution across sectors.

Abstract

We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors on the basis of an exhaustive dataset in Japan. The theoretical formula succeeds in explaining the two distinctive observational facts in a unified way, that is, a Boltzmann distribution with negative temperature on low-to-medium productivity side and a decreasing part in a power-law form on high productivity side.