A statistical mechanic view of macro-dynamics in economics

In this study, based on a statistical mechanic perspective, some technical insights for macroeconomic analysis are presented with regard to (1) "modeling the behaviour of a many-interacting-heterogeneous agents system through the analysis of fractions' stochastic dynamics over a state space" (Delli Gatti and Gallegati, Eterogeneita degli agenti economici ed interazione sociale: teorie e verifiche empiriche, 2005) and (2) suggesting a new microfoundation method based on jump Markov processes to mimic fluctuation dynamics of macro variables (Aoki, New approaches to macroeconomic modeling, 1996; Aoki, Modeling aggregate behaviour and fluctuations in economics, 2002; Aoki and Yoshikawa, Reconstructuring macroeconomics. A perspective from statistical physics and combinatorial stochastic processes, 2006). The main aim is to review and to describe how the statistical mechanic methodology provides systematic methods to solve master equation problems to be applied in macroscopic dynamics analysis in economics. The results are achieved in terms of a mean field system of equations to model average and volatility of a macroscopic quantity. By means of a macroscopic ordinary differential equation, the drift component is detached and, by means of a Fokker-Planck equation, the spread component around such a deterministic path is derived.