Tatsuru Kikuchi
arXiv 16 Oct 2025 · Econometrics
arXiv:2510.14409 · PDF · Extracted main text
I develop a comprehensive theoretical framework for dynamic spatial treatment effect boundaries using continuous functional definitions grounded in Navier-Stokes partial differential equations. Rather than discrete treatment effect estimators, the framework characterizes treatment intensity as a continuous function $τ(\mathbf{x}, t)$ over space-time, enabling rigorous analysis of propagation dynamics, boundary evolution, and cumulative exposure patterns. Building on exact self-similar solutions expressible through Kummer confluent hypergeometric and modified Bessel functions, I establish that treatment effects follow scaling laws $τ(d, t) = t^{-α} f(d/t^β)$ where exponents characterize diffusion mechanisms. Empirical validation using 42 million TROPOMI satellite observations of NO$_2$ pollution from U.S. coal-fired power plants demonstrates strong exponential spatial decay ($κ_s = 0.004$ per km, $R^2 = 0.35$) with detectable boundaries at 572 km. Monte Carlo simulations confirm superior performance over discrete parametric methods in boundary detection and false positive avoidance (94% vs 27% correct rejection). Regional heterogeneity analysis validates diagnostic capability: positive decay parameters within 100 km confirm coal plant dominance; negative parameters beyond 100 km correctly signal when urban sources dominate. The continuous functional perspective unifies spatial econometrics with mathematical physics, providing theoretically grounded methods for boundary detection, exposure quantification, and policy evaluation across environmental economics, banking, and healthcare applications.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Müller, U. K., & Watson, M. W (2024) Spatial unit roots and spurious regression | 1.000 | 7 | 5 | 100% |
| 2 | Müller, U. K., & Watson, M. W (2022) Spatial correlation robust inference | 1.000 | 5 | 3 | 100% |
| 3 | Kikuchi, T (2024) A unified framework for spatial and temporal treatment effect boundaries: Theory and identification self | 0.644 | 2 | 2 | 100% |
| 4 | Abramowitz, M., & Stegun, I. A (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | 0.405 | 1 | 1 | 100% |
| 5 | Angrist, J. D., & Kolesár, M (2022) One instrument to rule them all: The bias and coverage of just-ID IV | 0.405 | 1 | 1 | 100% |
| 6 | Anselin, L (1988) Spatial Econometrics: Methods and Models | 0.405 | 1 | 1 | 100% |
| 7 | Athey, S., & Imbens, G. W (2017) The econometrics of randomized experiments | 0.405 | 1 | 1 | 100% |
| 8 | Butts, K., & Gardner, J (2023) Difference-in-differences with spatial spillovers | 0.405 | 1 | 1 | 100% |
| 9 | Conley, T. G (1999) GMM estimation with cross sectional dependence | 0.405 | 1 | 1 | 100% |
| 10 | Deaton, A (2010) Understanding the mechanisms of economic development | 0.405 | 1 | 1 | 100% |
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arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.