Inference in Difference-in-Differences with Few Treated Units and Spatial Correlation

Abstract

We consider the problem of inference in Difference-in-Differences (DID) when there are few treated units and errors are spatially correlated. We first show that, when there is a single treated unit, some existing inference methods designed for settings with few treated and many control units remain asymptotically valid when errors are weakly dependent. However, these methods may be invalid with more than one treated unit. We propose a menu of alternatives that are asymptotically valid in this setting, even when the relevant distance metric across units is unavailable. These alternatives vary in terms of the length of the resulting confidence intervals and the strength of the required assumptions. Our methods are also valid for comparison-of-means estimators and for construction of prediction intervals for counterfactual imputation methods.