The Industrial Curvature Index A Geometric Framework for Regional Recession Resilience and Adjustment Speed: Evidence from 3,115 U.S. Counties, 2001–2024

Villines, Gregory (2026): The Industrial Curvature Index A Geometric Framework for Regional Recession Resilience and Adjustment Speed: Evidence from 3,115 U.S. Counties, 2001–2024.

Abstract

I introduce the Industrial Curvature Index (ICI), a geometric measure of how distinctive a county’s industrial composition is from that of its geographic neighbors. ICI is constructed by representing each county-quarter as a point on the simplex of NAICS supersector employment shares, equipping the simplex with the Fisher–Rao information metric, and computing time-averaged Ollivier–Ricci curvature on the Census-defined county adjacency graph. High ICI corresponds to counties embedded in tightly coupled regional clusters; low ICI to counties whose industrial composition is structurally distinctive from their neighbors’. The principal empirical finding is that ICI is a strong and robust predictor of cross-county heterogeneity in recession-trough employment loss. Across 3,115 retained U.S. counties from 2001 through 2024, a one-standard-deviation increase in ICI corresponds to a 4.86 percentage-point deeper 2008–2009 employment trough (β = −4.86, HC3 p < 0.001, R² = 0.145, Tier A pooled), and a 3.91 percentage-point deeper 2020 trough (β = −3.91, HC3 p < 0.001, R² = 0.129, replication). With full controls for the Herfindahl–Hirschman index of industrial concentration, Shannon entropy of supersector shares, top-three-sector concentration, share Gini, and log-employment, the standardized ICI coefficient remains highly significant (R08 Spec 3: β = −1.91, p < 0.001, R² = 0.392; R20 Spec 3: β = −1.77, p < 0.001, R² = 0.305). The finding survives a comprehensive battery of robustness checks. State fixed effects, eliminating between-state variation entirely, yield β = −1.39 for R08 and β = −0.98 for R20 (both p < 0.001). Out-of-sample temporal identification, in which ICI is constructed using only QCEW data preceding each recession, yields effectively identical magnitudes (β = −4.75 for R08 and β = −3.88 for R20, both p < 0.001), addressing reverse-causality concerns. The relationship is approximately nine times stronger in counties below the median in mean total employment (R² = 0.156) than in those above (R² = 0.017), suggesting that small-county industrial geometry is a substantively important resilience determinant. A secondary and weaker finding is that ICI also predicts unemployment-rate adjustment speed (Tier A pooled β = −0.20, p < 0.001, R² = 0.005), with a sub-period decomposition demonstrating that an apparent anomalous Texas effect dissolves into null sub-period coefficients—a methodological caution against full-sample regressions when underlying dynamics are heterogeneous. Substantively, the paper provides evidence that geometric distinctiveness functions as a portfolio-diversification mechanism at the regional scale: counties whose industrial composition does not co-vary with their neighbors’ are partially insulated from shocks that hit the regional and national average composition. The framework offers a measurement contribution distinct from existing scalar diversification measures—Herfindahl–Hirschman, entropy, top-share concentration, and Gini—which exhibit pairwise correlations exceeding 0.85 among themselves but only 0.33 to 0.39 with ICI.

• Item Type: MPRA Paper
• Language: English
• Keywords: regional resilience, information geometry, Ollivier–Ricci curvature, Fisher–Rao metric, Quarterly Census of Employment and Wages, Local Area Unemployment Statistics, regional adjustment dynamics, employment recessions
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; J - Labor and Demographic Economics > J6 - Mobility, Unemployment, Vacancies, and Immigrant Workers > J64 - Unemployment: Models, Duration, Incidence, and Job Search; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R11 - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

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