The Consolidation Paradox in Labor Markets: Network Fragility and Spatial Wage Spillovers

Spatial econometrics lacks principled methods for measuring minimum wage spillovers. Existing approaches assume arbitrary functional forms without theoretical justification, preventing researchers from answering basic questions: How far do effects reach? Through which channels? At what speed? This paper derives spatial treatment effects from first principles using Navier-Stokes equations. Three theoretical predictions emerge and are validated empirically. First, treatment boundaries exhibit self-similar scaling, growing proportional to the square root of elapsed time as predicted by diffusion theory (estimated exponent: 0.500, standard error: 0.001). Second, spatial weights follow Modified Bessel K-zero functions, the exact Green's function solution to the two-dimensional Helmholtz equation. This theoretically-derived specification fits observed spillover patterns substantially better than exponential, Gaussian, or power-law alternatives commonly assumed in applied work (R-squared: 0.99 versus 0.35). Third, network consolidation paradoxically increases rather than dampens wage volatility during stress periods, with consolidation-volatility correlation rising from near-zero to positive 0.0067 following COVID-19. Using 64,421 county-quarter observations from 2018 to 2023, I estimate characteristic spillover distance of 100 miles with cumulative effects reaching 0.44 log points over four quarters. Economic network linkages dominate geographic proximity by factor of eight, demonstrating that institutional connections matter more than physical distance. Spatial decay parameters increased 27 percent during COVID-19 (from 0.0155 to 0.0196), shrinking effective spillover radius from 65 to 51 miles and confirming time-varying dynamics predicted by perturbation theory. The framework provides concrete policy guidance. Regional minimum wage coordination should encompass 100-mile radius under normal conditions, contracting to 65 miles during crises. For Japan's minimum wage reform targeting 1,500 yen per hour by 2030, spillovers from Tokyo will substantially affect surrounding prefectures within 160 kilometers. Self-similar scaling implies effects reach half of final magnitude within one year but continue expanding indefinitely, requiring multi-year coordination frameworks.