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The Chained Difference-in-Differences

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  • Christophe Bell'ego
  • David Benatia
  • Vincent Dortet-Bernardet

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.

Suggested Citation

  • Christophe Bell'ego & David Benatia & Vincent Dortet-Bernardet, 2023. "The Chained Difference-in-Differences," Papers 2301.01085, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2301.01085
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    1. Gayani Rathnayake & Akanksha Negi & Otavio Bartalotti & Xueyan Zhao, 2024. "Difference-in-Differences with Sample Selection," Papers 2411.09221, arXiv.org, revised Dec 2024.

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