Statistical Mechanics of Household Income and Wealth: Derivation from Firm Dynamics via Maximum Entropy and Mixture Aggregation

Battle Count: 50

The paper is primarily a theoretical econophysics contribution focused on deriving income and wealth distributions from firm-level microeconomics. It does not propose trading strategies, portfolio optimization methods, or market prediction models. However, the understanding of wealth distribution dynamics (Pareto tail volatility linked to capital markets, firm survival rates, capital return scaling) could inform macro-level risk models or understanding of wealth concentration effects on market structure. The firm exit rate prediction and firm-value scaling exponent could be tangentially relevant to equity factor models or sector rotation strategies. Overall relevance to quantitative trading is minimal.

The analytical derivations involve Fokker-Planck equations, Itô-Stratonovich calculus, maximum entropy optimization, mixture aggregation integrals, and first-passage time calculations. Numerical implementation requires finite-difference integration of coupled Fokker-Planck equations and Monte Carlo agent simulations (detailed in Supplemental Material). The parameter-free predictions (α_w from θ, firm exit exponent) are straightforward to validate. However, the full mechanistic chain from Gibrat's law through Zipf to BG/Pareto distributions requires careful handling of boundary conditions (reflecting vs absorbing), Itô corrections, and Laplace transform convolutions. Moderate complexity for a physics-trained researcher; higher for an ML practitioner unfamiliar with stochastic calculus.

The paper provides detailed analytical derivations, references public data sources (US Census BDS, Compustat 1990-2023 with n>300,000 firm-years, BEA accounts, Federal Reserve Survey of Consumer Finances), and includes Supplemental Material [13] with complete derivations, equilibrium/stability analysis, finite-difference Fokker-Planck integration, and Monte Carlo agent simulation. However, no explicit code repository is linked. The derivation chain is fully specified with equations, and all empirical parameters are sourced from published literature. The parameter-free nature of key predictions (α_w from θ, firm exit exponent) enhances reproducibility.