Difference-in-Differences with Interference: A Finite Population Perspective

Abstract

In many scenarios, such as the evaluation of place-based policies, potential outcomes are not only dependent upon the unit's own treatment but also its neighbors' treatment. Despite this, "difference-in-differences" (DID) type estimators typically ignore such interference among neighbors. I show in this paper that the canonical DID estimators generally do not identify interesting causal effects in the presence of neighborhood interference. To incorporate interference structure into DID estimation, I propose doubly robust estimators for the direct average treatment effect on the treated as well as the average spillover effects under a modified parallel trends assumption. When spillover effects are of interest, we often sample the entire population. Thus, I adopt a finite population perspective in the sense that the estimands are defined as population averages and inference is conditional on the attributes of all population units. The general and unified approach in this paper relaxes common restrictions in the literature, such as partial interference and correctly specified spillover functions. Moreover, robust inference is discussed based on the asymptotic distribution of the proposed estimators