arXiv 1 Oct 2025 · Econometrics
arXiv:2510.00754 · PDF · DOI · OpenAlex · Extracted main text
This paper develops a unified theoretical framework for detecting and estimating boundaries in treatment effects across both spatial and temporal dimensions. We formalize the concept of treatment effect boundaries as structural parameters characterizing regime transitions where causal effects cease to operate. Building on reaction-diffusion models of information propagation, we establish conditions under which spatial and temporal boundaries share common dynamics governed by diffusion parameters (delta, lambda), yielding the testable prediction d^*/tau^* = 3.32 lambda sqrt{delta} for standard detection thresholds. We derive formal identification results under staggered treatment adoption and develop a three-stage estimation procedure implementable with standard panel data. Monte Carlo simulations demonstrate excellent finite-sample performance, with boundary estimates achieving RMSE below 10% in realistic configurations. We apply the framework to two empirical settings: EU broadband diffusion (2006-2021) and US wildfire economic impacts (2017-2022). The broadband application reveals a scope limitation -- our framework assumes depreciation dynamics and fails when effects exhibit increasing returns through network externalities. The wildfire application provides strong validation: estimated boundaries satisfy d^* = 198 km and tau^* = 2.7 years, with the empirical ratio (72.5) exactly matching the theoretical prediction 3.32 lambda sqrt{delta} = 72.5. The framework provides practical tools for detecting when localized treatments become systemic and identifying critical thresholds for policy intervention.
appendix boundary found by none_found · 100% 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 | Anselin, L (1988) Spatial Econometrics: Methods and Models | 0.811 | 4 | 2 | 100% |
| 3 | Butts, K (2021) Difference-in-differences estimation with spatial spillovers | 0.644 | 2 | 2 | 100% |
| 4 | Callaway, B., & Sant'Anna, P. H (2021) Difference-in-differences with multiple time periods | 0.644 | 2 | 2 | 100% |
| 5 | Sun, L., & Abraham, S (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects | 0.644 | 2 | 2 | 100% |
| 6 | Acemoglu, D., Ozdaglar, A., & ParandehGheibi, A (2011) Spread of (mis) information in social networks | 0.405 | 1 | 1 | 100% |
| 7 | Acemoglu, D., Ozdaglar, A., & Tahbaz-Salehi, A (2015) Systemic risk and stability in financial networks | 0.405 | 1 | 1 | 100% |
| 8 | Achdou, Y., Han, J., Lasry, J. M., Lions, P. L., & Moll, B (2022) Income and wealth distribution in macroeconomics: A continuous-time approach | 0.405 | 1 | 1 | 100% |
| 9 | Akcigit, U., & Kerr, W. R (2021) Lack of selection and limits to delegation: Firm dynamics in developing countries | 0.405 | 1 | 1 | 100% |
| 10 | Allen, F., & Gale, D (2000) Financial contagion | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 63 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.