Treatment Effects with Correlated Spillovers: Bridging Discrete and Continuous Methods

TL;DR

This paper introduces a continuous framework for analyzing treatment effects with correlated spillovers, unifying discrete and continuous methods, and providing robust inference tools that outperform conventional estimators in the presence of spillovers.

Contribution

It develops a fundamental, economically grounded continuous model that bridges existing discrete methods and introduces a bias-resistant estimator for spillover effects.

Findings

Conventional estimators are biased by 25-38% with spillovers.

The proposed estimator maintains correct inference regardless of spillover presence.

The framework links treatment effects to economic linkages via a stochastic path representation.

Abstract

This paper develops a continuous functional framework for treatment effects propagating through geographic space and economic networks. We derive a master equation from three independent economic foundations -- heterogeneous agent aggregation, market equilibrium, and cost minimization -- establishing that the framework rests on fundamental principles rather than ad hoc specifications. The framework nests conventional econometric models -- autoregressive specifications, spatial autoregressive models, and network treatment effect models -- as special cases, providing a bridge between discrete and continuous methods. A key theoretical result shows that the spatial-network interaction coefficient equals the mutual information between geographic and network coordinates, providing a parameter-free measure of channel complementarity. The Feynman-Kac representation characterizes treatment effects as accumulated policy exposure along stochastic paths representing economic linkages, connecting the continuous framework to event study methodology. The no-spillover case emerges as a testable restriction, creating a one-sided risk profile where correct inference is maintained regardless of whether spillovers exist. Monte Carlo simulations confirm that conventional estimators exhibit 25-38% bias when spillovers are present, while our estimator maintains correct inference across all configurations including the no-spillover case.