Difference-in-Differences Estimation with Spatial Spillovers

TL;DR

This paper develops a framework for difference-in-differences estimation that accounts for spatial spillovers, addressing bias caused by treatment effects crossing geographic boundaries and proposing methods to identify and estimate spillover effects.

Contribution

Introduces a potential outcomes framework for modeling spatial spillovers in difference-in-differences, providing conditions for unbiased estimation and semi-parametric methods for spillover effects.

Findings

Bias in classical DID due to spillovers is decomposed into two parts.

Conditions for non-parametric identification of spillover effects are established.

Reanalysis of place-based interventions highlights the importance of accounting for spillovers.

Abstract

Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In this paper, I introduce a potential outcomes framework to model spillover effects and decompose the estimate's bias in two parts: (1) the control group no longer identifies the counterfactual trend because their outcomes are affected by treatment and (2) changes in treated units' outcomes reflect the effect of their own treatment status and the effect from the treatment status of 'close' units. I propose conditions for non-parametric identification that can remove both sources of bias and semi-parametrically estimate the spillover effects themselves including in settings with staggered treatment timing. To highlight the importance of spillover effects, I revisit analyses of three place-based interventions.