The Chained Difference-in-Differences

TL;DR

This paper introduces the chained difference-in-differences estimator for analyzing long-term treatment effects in unbalanced panel data, accommodating various complexities like missing data, heterogeneity, and multiple treatment timings.

Contribution

It develops a novel estimator that leverages overlapping short-term effects to identify long-term impacts in unbalanced panels, improving upon existing methods.

Findings

Estimator performs well in simulations.

Application reveals policy effects in France.

Asymptotic properties established.

Abstract

This paper studies the identification, estimation, and inference of long-term (binary) treatment effect parameters when balanced panel data is not available, or consists of only a subset of the available data. We develop a new estimator: the chained difference-in-differences, which leverages the overlapping structure of many unbalanced panel data sets. This approach consists in aggregating a collection of short-term treatment effects estimated on multiple incomplete panels. Our estimator accommodates (1) multiple time periods, (2) variation in treatment timing, (3) treatment effect heterogeneity, (4) general missing data patterns, and (5) sample selection on observables. We establish the asymptotic properties of the proposed estimator and discuss identification and efficiency gains in comparison to existing methods. Finally, we illustrate its relevance through (i) numerical simulations, and (ii) an application about the effects of an innovation policy in France.