Nonparametric Identification and Estimation of Spatial Treatment Effect Boundaries: Evidence from 42 Million Pollution Observations

Abstract

This paper develops a nonparametric framework for identifying and estimating spatial boundaries of treatment effects in settings with geographic spillovers. While atmospheric dispersion theory predicts exponential decay of pollution under idealized assumptions, these assumptions -- steady winds, homogeneous atmospheres, flat terrain -- are systematically violated in practice. I establish nonparametric identification of spatial boundaries under weak smoothness and monotonicity conditions, propose a kernel-based estimator with data-driven bandwidth selection, and derive asymptotic theory for inference. Using 42 million satellite observations of NO$_2$ concentrations near coal plants (2019-2021), I find that nonparametric kernel regression reduces prediction errors by 1.0 percentage point on average compared to parametric exponential decay assumptions, with largest improvements at policy-relevant distances: 2.8 percentage points at 10 km (near-source impacts) and 3.7 percentage points at 100 km (long-range transport). Parametric methods systematically underestimate near-source concentrations while overestimating long-range decay. The COVID-19 pandemic provides a natural experiment validating the framework's temporal sensitivity: NO$_2$ concentrations dropped 4.6\% in 2020, then recovered 5.7\% in 2021. These results demonstrate that flexible, data-driven spatial methods substantially outperform restrictive parametric assumptions in environmental policy applications.