Beyond Borders: How Economic Shocks Propagate Through Space and Networks

This paper develops a unified theoretical and empirical framework for analyzing treatment effects that propagate through both spatial proximity and network connections. Building on the continuous functional approach in \citet{kikuchi2024dynamical} and the Navier-Stokes foundation in \citet{kikuchi2024navier}, I introduce network channels as continuous internal degrees of freedom, deriving both spatial diffusion and network contagion from common first principles rooted in conservation laws and stochastic processes. The framework resolves three fundamental challenges in modern econometrics: how spatial and network effects interact (the mixed effect), how treatment effects evolve in general equilibrium, and how network structure affects system fragility. I show that the mixed spatial-network effect emerges naturally at second order in perturbation theory, creating synergistic amplification when geographic proximity and network similarity align. The theoretical analysis yields three main contributions. First, I derive explicit expressions for the mixed effect functional, showing it equals the mutual information between spatial and network coordinates—a purely information-theoretic measure with no free parameters. Second, I extend the analysis to general equilibrium, proving that endogenous price and employment adjustments amplify partial equilibrium estimates by factors between 1.8 and 2.5 depending on market structure. Third, I connect network structure to system fragility through entropy production rates, providing operational measures of how consolidation affects shock dissipation speeds and cascade probabilities. The empirical application uses county-level wage data (2018-2023) to analyze minimum wage spillovers across 3,142 U.S. counties and 274 industry classifications. Four main findings emerge. First, the mixed spatial-network effect accounts for 40 percent of total treatment propagation, with point estimate 0.043 (s.e. 0.008), statistically significant and economically large. This implies retail workers in Nevada counties near the California border experience wage increases 43 percent larger than the sum of pure spatial spillover (from proximity alone) and pure network effect (from industry connections) would predict. Second, spatial decay parameters increase from 0.01 per mile for pure geographic spillovers to 0.02 when network effects are included, demonstrating that networks concentrate rather than disperse spatial impacts. Third, general equilibrium amplification factors range from 1.8 (dispersed markets) to 2.5 (concentrated markets), implying substantial bias in partial equilibrium policy evaluation. Fourth, entropy-based fragility measures predict out-of-sample shock propagation with $R^2 = 0.67$, outperforming standard network centrality metrics ($R^2 = 0.43$). These findings have direct policy implications. Minimum wage policies should account for network amplification: optimal state-level minimum wages are 15-20 percent lower when accounting for general equilibrium feedbacks through supply chains and labor mobility networks. Financial regulation should monitor entropy production rates as early warning indicators: systems approaching critical fragility thresholds (entropy production declining by more than 30 percent) require preemptive intervention before cascades materialize. Regional development policies should leverage spatial-network synergies: infrastructure investments yield highest returns in regions with strong geographic clustering and dense economic networks.