Stochastic origin of scaling laws in productivity and employment dispersion

Labor and productivity play central roles in the aging population problem in all developed countries. The understanding of labor allocation among different productivity levels is required for policy issues, specifically, the dynamics of how workers are allocated and reallocated among sectors. We uncover an empirical fact that firm-level dispersions of output and employment satisfy certain scaling laws in their joint probability distributions, which closely relate to the dispersion of productivity. The empirical finding is widely observed in large databases including small and medium-sized firms in both Japan and European countries. We argue that a stochastic process generates a steady-state allocation of labor across firms of differing output and productivity, which results in the observed distributions of workers,productivity, and output.