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

TL;DR

This paper addresses inference challenges in Difference-in-Differences models with few treated units and spatially correlated errors, proposing valid methods for multiple treated units even without a distance metric.

Contribution

It identifies limitations of existing methods with multiple treated units and introduces new asymptotically valid inference procedures for such settings.

Findings

Existing methods are valid with a single treated unit under weak dependence.

Methods may be invalid with multiple treated units.

Proposes alternative inference methods valid for multiple treated units.

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 alternatives that are asymptotically valid in this setting, even when the relevant distance metric across units is unavailable.