Equations of Motion for an Economy: Capital Deepening, Technology, and Firm Survival

Battle Count: 67

The paper is primarily a macroeconomic growth theory contribution with a statistical mechanics flavor. It does not directly address asset pricing, trading signals, or portfolio construction. However, the sector-level growth decomposition (capital deepening vs. productivity) and the finding that ϕ=0 across all postwar sectors could inform long-horizon sector allocation and macro-regime identification. The firm survival/exit-rate model could be relevant for credit risk or distressed-asset strategies. The falsifiable prediction about AI productivity (ϕ>0) could be a macro signal for technology-sector positioning, but the timescale (decades) is far beyond typical trading horizons.

The core ODE system (4 equations, 4 parameters per sector) is mathematically tractable and can be implemented with standard numerical ODE solvers. The main complexity lies in: (1) constructing the BEA data pipeline with proper deflation, sector mapping, and interpolation of w(t), τ(t), f_p(t); (2) implementing the Nelder-Mead calibration in log-parameter space with the sandwich constraint as an invariant; (3) the firm survival convolution with Zipf distribution via Laplace transforms. The Kalman filter moment closure and Fokker-Planck extensions (in companion/supplemental papers) add significant complexity. No ML frameworks are needed; standard scientific Python (scipy, numpy) suffices for the core model.

All input data (BEA GDP-by-Industry, Fixed Assets, BDS establishment-age, CBP firm-size) are publicly available U.S. government datasets. Calibration procedure (Nelder-Mead in log-parameter space) is described. Companion paper [3] and Supplemental Material [1] provide full derivations, data pipelines, and sector-by-sector figures. No proprietary data or code is required. However, the full derivation details are in the supplemental material, and the ODE system requires careful implementation of the sandwich constraint invariant.