Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption

TL;DR

This paper analyzes the properties of Difference-In-Differences estimators in staggered adoption settings, highlighting conditions for unbiasedness and the conservativeness of variance estimates from a design-based perspective.

Contribution

It provides a novel design-based analysis of DiD estimators under staggered adoption, clarifying their unbiasedness and variance properties.

Findings

Standard DiD estimator is unbiased under random adoption timing.

Variance estimator tends to be conservative.

Characterizes the weighted average causal effect estimated by DiD.

Abstract

In this paper we study estimation of and inference for average treatment effects in a setting with panel data. We focus on the setting where units, e.g., individuals, firms, or states, adopt the policy or treatment of interest at a particular point in time, and then remain exposed to this treatment at all times afterwards. We take a design perspective where we investigate the properties of estimators and procedures given assumptions on the assignment process. We show that under random assignment of the adoption date the standard Difference-In-Differences estimator is is an unbiased estimator of a particular weighted average causal effect. We characterize the proeperties of this estimand, and show that the standard variance estimator is conservative.