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The role of parallel trends in event study settings: An application to environmental economics

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  • Michelle Marcus
  • Pedro H. C. Sant'Anna

Abstract

Difference-in-Differences (DID) research designs usually rely on variation of treatment timing such that, after making an appropriate parallel trends assumption, one can identify, estimate, and make inference about causal effects. In practice, however, different DID procedures rely on different parallel trends assumptions (PTA), and recover different causal parameters. In this paper, we focus on staggered DID (also referred as event-studies) and discuss the role played by the PTA in terms of identification and estimation of causal parameters. We document a ``robustness'' vs. ``efficiency'' trade-off in terms of the strength of the underlying PTA, and argue that practitioners should be explicit about these trade-offs whenever using DID procedures. We propose new DID estimators that reflect these trade-offs and derived their large sample properties. We illustrate the practical relevance of these results by assessing whether the transition from federal to state management of the Clean Water Act affects compliance rates.

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  • Michelle Marcus & Pedro H. C. Sant'Anna, 2020. "The role of parallel trends in event study settings: An application to environmental economics," Papers 2009.01963, arXiv.org.
  • Handle: RePEc:arx:papers:2009.01963
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    File URL: http://arxiv.org/pdf/2009.01963
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    References listed on IDEAS

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    1. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2019. "Synthetic Difference in Differences," Working Papers wp2019_1907, CEMFI.
    2. Athey, Susan & Imbens, Guido W., 2018. "Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption," Research Papers 3712, Stanford University, Graduate School of Business.
    3. Laporte, Audrey & Windmeijer, Frank, 2005. "Estimation of panel data models with binary indicators when treatment effects are not constant over time," Economics Letters, Elsevier, vol. 88(3), pages 389-396, September.
    4. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods," Papers 1803.09015, arXiv.org, revised Dec 2020.
    5. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
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