Spillover Gridlock: Revisiting Interference in Difference-in-differences

I decompose the canonical Difference-in-differences (DiD) estimator in presence of spillovers into a weighted average of 2×2 estimators that compare treated and untreated units across different levels of exposure to treatment. Identifying the ATT requires strong homogeneity conditions: that spillover magnitudes and exposure probabilities are both identical across treatment status, conditions unlikely to hold in observational studies. While a common response is to control for researcher-proposed interference structures, such estimators induce a selection bias if misspecified, a serious concern given the complex and unknown nature of interference. I propose instead spill-imputation, which identifies individual treatment and spillover effects under a unit-level parallel trends assumption —weaker than correct specification of the interference structure— and recovers spillover heterogeneity ex-post, in a data-driven way. Monte Carlo simulations show deviations of up to 31.2% for the parametric DiD against at most 0.25% for spill-imputation, with standard errors 42% smaller, reflecting greater estimation efficiency. An application to road paving in Mexico finds positive spillover effects of 19.5% on nearby unpaved plots’ property values, and no heterogeneous effects along the distance to the paved street.