Extensions for Inference in Difference-in-Differences with Few Treated Clusters

TL;DR

This paper develops new inference methods for Difference-in-Differences designs with few treated units, accommodating treatment timing variation and heterogeneous effects, and enabling uniform confidence bands.

Contribution

It introduces novel inference techniques for DID with few treated units that handle treatment timing variation and heterogeneity, and support uniform confidence bands.

Findings

Methods are valid with few treated units and treatment timing variation.

Enables construction of uniform confidence bands for event-study plots.

Addresses limitations of existing DID inference in small-sample, complex settings.

Abstract

In settings with few treated units, Difference-in-Differences (DID) estimators are not consistent, and are not generally asymptotically normal. This poses relevant challenges for inference. While there are inference methods that are valid in these settings, some of these alternatives are not readily available when there is variation in treatment timing and heterogeneous treatment effects; or for deriving uniform confidence bands for event-study plots. We present alternatives in settings with few treated units that are valid with variation in treatment timing and/or that allow for uniform confidence bands.