# Doubly Robust Difference-in-Differences Estimators

## TL;DR

This paper introduces doubly robust estimators for the ATT in DID designs, which are consistent if either the propensity score or outcome model is correct, and attain efficiency bounds under correct specification.

## Contribution

It develops novel doubly robust estimators for DID that improve robustness and efficiency, with theoretical derivations and practical implementation tools.

## Key findings

- Estimators are consistent if either model is correct.
- They attain the semiparametric efficiency bound when models are correct.
- Simulation and empirical results show good finite-sample performance.

## Abstract

This article proposes doubly robust estimators for the average treatment effect on the treated (ATT) in difference-in-differences (DID) research designs. In contrast to alternative DID estimators, the proposed estimators are consistent if either (but not necessarily both) a propensity score or outcome regression working models are correctly specified. We also derive the semiparametric efficiency bound for the ATT in DID designs when either panel or repeated cross-section data are available, and show that our proposed estimators attain the semiparametric efficiency bound when the working models are correctly specified. Furthermore, we quantify the potential efficiency gains of having access to panel data instead of repeated cross-section data. Finally, by paying articular attention to the estimation method used to estimate the nuisance parameters, we show that one can sometimes construct doubly robust DID estimators for the ATT that are also doubly robust for inference. Simulation studies and an empirical application illustrate the desirable finite-sample performance of the proposed estimators. Open-source software for implementing the proposed policy evaluation tools is available.