Micro-Macro Relation of Production - The Double Scaling Law for Statistical Physics of Economy -

TL;DR

This paper demonstrates a double scaling law in economic systems, linking micro-level agent behaviors to macroeconomic distributions through empirical and theoretical analysis of sales and labor data.

Contribution

It introduces a novel double scaling law framework that characterizes economic equilibrium distributions using a small set of scaling indices, bridging micro- and macro-economics.

Findings

Empirical evidence of double scaling law in Japanese firms' sales and labor.

Lognormal joint distributions of sales and labor confirmed.

Scaling law for labor productivity validated empirically.

Abstract

We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the labor of one million Japanese firms. Theoretical study of the scaling laws suggests lognormal joint distributions of sales and labor and a scaling law for labor productivity, both of which are confirmed empirically. This framework offers characterization of the equilibrium distribution with a small number of scaling indices, which determine macroscopic quantities, thus setting the stage for an equivalence with statistical physics, bridging micro- and macro-economics.