Tatsuru Kikuchi
arXiv 13 Oct 2025 · Econometrics
arXiv:2510.11013 · PDF · Extracted main text
This paper develops a unified framework for identifying spatial and temporal boundaries of treatment effects in difference-in-differences designs. Starting from fundamental fluid dynamics equations (Navier-Stokes), we derive conditions under which treatment effects decay exponentially in space and time, enabling researchers to calculate explicit boundaries beyond which effects become undetectable. The framework encompasses both linear (pure diffusion) and nonlinear (advection-diffusion with chemical reactions) regimes, with testable scope conditions based on dimensionless numbers from physics (P\'eclet and Reynolds numbers). We demonstrate the framework's diagnostic capability using air pollution from coal-fired power plants. Analyzing 791 ground-based PM$_{2.5}$ monitors and 189,564 satellite-based NO$_2$ grid cells in the Western United States over 2019-2021, we find striking regional heterogeneity: within 100 km of coal plants, both pollutants show positive spatial decay (PM$_{2.5}$: $\kappa_s = 0.00200$, $d^* = 1,153$ km; NO$_2$: $\kappa_s = 0.00112$, $d^* = 2,062$ km), validating the framework. Beyond 100 km, negative decay parameters correctly signal that urban sources dominate and diffusion assumptions fail. Ground-level PM$_{2.5}$ decays approximately twice as fast as satellite column NO$_2$, consistent with atmospheric transport physics. The framework successfully diagnoses its own validity in four of eight analyzed regions, providing researchers with physics-based tools to assess whether their spatial difference-in-differences setting satisfies diffusion assumptions before applying the estimator. Our results demonstrate that rigorous boundary detection requires both theoretical derivation from first principles and empirical validation of underlying physical assumptions.
appendix boundary found by appendix_command · 73% of the source is main text. Read the extracted text to check this.
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 | Kikuchi, T (2024) Stochastic boundaries in spatial general equilibrium: A diffusion-based approach to causal inference with spillover effects self | 0.928 | 4 | 4 | 100% |
| 2 | Kikuchi, T (2024) A unified framework for spatial and temporal treatment effect boundaries: Theory and identification self | 0.928 | 4 | 3 | 100% |
| 3 | Butts, K. and Gardner, J (2023) Difference-in-differences with spatial spillovers | 0.811 | 4 | 2 | 100% |
| 4 | Byun, D. W. and Schere, K. L (1999) Review of the governing equations, computational algorithms, and other components of the Models-3 Community Multiscale Air Quali… | 0.644 | 2 | 2 | 100% |
| 5 | Cimorelli, A. J., Perry, S. G., Venkatram, A., et al (2005) AERMOD: A dispersion model for industrial source applications | 0.644 | 2 | 2 | 100% |
| 6 | Colella, F., Lalive, R., Sakalli, S. O., and Thoenig, M (2019) Inference with arbitrary clustering | 0.511 | 2 | 1 | 100% |
| 7 | Deryugina, T., Heutel, G., Miller, N. H., Molitor, D., and Reif, J (2019) The mortality and medical costs of air pollution: Evidence from changes in wind direction | 0.511 | 2 | 1 | 100% |
| 8 | Fowlie, M., Holland, S. P., and Mansur, E. T (2012) What do emissions markets deliver and to whom? Evidence from Southern California's NO$_x$ trading program | 0.511 | 2 | 1 | 100% |
| 9 | Knittel, C. R., Miller, D. L., and Sanders, N. J (2016) Caution, drivers! Children present: Traffic, pollution, and infant health | 0.511 | 2 | 1 | 100% |
| 10 | Allcott, H (2015) Site selection bias in program evaluation | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 37 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.