[Paper Review] Difference-in-Differences Estimation with Spatial Spillovers

Kyle Butts|arXiv (Cornell University)|May 8, 2021

Advanced Causal Inference Techniques30 references47 citations

TL;DR

The paper develops a potential outcomes framework to address spatial spillovers in Difference-in-Differences analyses, identifying total and switching effects, and proposing nonparametric identification and practical estimation strategies including event-study extensions.

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.

Motivation & Objective

• Motivate and formalize how geographic spillovers bias standard Difference-in-Differences estimates.
• Introduce a potential outcomes framework that accounts for own treatment status and spillovers from nearby treated units.
• Define and distinguish total effects, switching effects, and spillover effects under local spillovers.
• Provide identification results that remove bias from standard DiD when spillovers are local or controlled with spillover indicators.
• Offer practical estimation strategies, including distance-based exposure rings and event-study extensions, for staggered treatment timing.

Proposed method

• Define exposure mappings h_i(D) to capture spillovers and extend potential outcomes Y_it(D_i, h_i(D)).
• Reformulate parallel trends to a modified assumption (Parallel Counterfactual Trends) that allows spillovers.
• Derive decomposition of the DiD estimand into total effect minus spillover on controls.
• Propose identification strategies: (i) local spillovers with controls distant from treatment; (ii) use of spillover indicators S_i and distance rings to estimate ring-specific effects.
• Extend DiD estimation to estimate total effects and spillover effects under the local spillover and parallel trends framework.
• Discuss event-study extension for staggered treatment timing and spillovers.

Experimental results

Research questions

• RQ1 What are the policy-relevant treatment effects when spillovers occur across space in a DiD setting?
• RQ2 Under local spillovers, can we identify the total effect and the switching/spillover effects without fully specifying the exposure mapping?
• RQ3 How does incorporating spillover indicators or distance-based rings affect identification and estimation of treatment effects?
• RQ4 How should researchers implement DiD with staggered treatment timing in the presence of spatial spillovers?
• RQ5 What are the implications for empirical applications of place-based policies when spillovers are present?

Key findings

• The standard DiD estimator is biased for the total effect in the presence of spillovers on control units.
• The proposed local-spillover identification strategy can identify the total effect by conditioning on units farther than a maximum spillover distance.
• Using a simple spillover indicator can bias estimates, but using a set of distance rings interacted with the treatment can recover ring-specific spillover effects.
• Parallel trends modifications allow estimating the total effect without specifying the exact spillover mechanism, as long as exposure is correctly classified.
• The method is illustrated with place-based policy contexts, such as the Tennessee Valley Authority, highlighting potential magnitude changes in traditional DiD results.
• An event-study extension is provided to accommodate staggered treatment timing while accounting for spillovers.