Stochastic Lotka-Volterra Dynamics in Macroeconomics: A Bounded Goodwin Wage-Employment Cycle

Abstract

This paper analyzes wage–employment dynamics using a bounded stochastic Goodwin model formulated within a Lotka–Volterra framework. Employment and wage share are mapped into latent positive coordinates, preserving natural bounds while allowing nonlinear interactions and stochastic shocks. Simulation results based on Python implementations of stochastic differential equations validate the estimation framework, and the model is then estimated on U.S. quarterly data from 1960–2025 using an approximate maximum likelihood approach. Phase-space analysis reveals a persistent wage–employment loop, with employment leading wage share by approximately seven quarters. Stochastic simulations reproduce key features of observed persistence, highlighting the role of nonlinear feedback in macroeconomic labor dynamics.