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(Visualizing) Plausible Treatment Effect Paths

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  • Simon Freyaldenhoven
  • Christian Hansen

Abstract

We consider estimation and inference for treatment effect paths. Examples include dynamic treatment effects, impulse response functions, and event study paths. We present two sets of plausible bounds to help visualize uncertainty associated with these paths. Both plausible bounds are often tighter than traditional confidence intervals, and can provide insights even when traditional (uniform) confidence bands appear uninformative. Our first set of bounds covers the average (or overall) effect rather than the entire path. Our second set of bounds imposes data-driven smoothness restrictions on the treatment path, using post-selection inference (Berk et al. [2013]) to provide formal coverage guarantees.

Suggested Citation

  • Simon Freyaldenhoven & Christian Hansen, 2025. "(Visualizing) Plausible Treatment Effect Paths," Working Papers 25-27, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:101774
    DOI: 10.21799/frbp.wp.2025.27
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    References listed on IDEAS

    as
    1. Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
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    13. Shiller, Robert J, 1973. "A Distributed Lag Estimator Derived from Smoothness Priors," Econometrica, Econometric Society, vol. 41(4), pages 775-788, July.
    14. Jos'e Luis Montiel Olea & Mikkel Plagborg-M{o}ller & Eric Qian & Christian K. Wolf, 2024. "Double Robustness of Local Projections and Some Unpleasant VARithmetic," Papers 2405.09509, arXiv.org, revised Nov 2025.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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