IDEAS home Printed from https://ideas.repec.org/p/fip/fedpwp/101774.html

(Visualizing) Plausible Treatment Effect Paths

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.philadelphiafed.org/-/media/FRBP/Assets/working-papers/2025/wp25-27.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.21799/frbp.wp.2025.27?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    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.
    2. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    3. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    4. 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 Jan 2026.
    5. Freyberger, Joachim & Rai, Yoshiyasu, 2018. "Uniform confidence bands: Characterization and optimality," Journal of Econometrics, Elsevier, vol. 204(1), pages 119-130.
    6. Mikkel Plagborg-Møller, 2016. "Essays in Macroeconometrics," Working Paper 441671, Harvard University OpenScholar.
    7. Òscar Jordà, 2023. "Local Projections for Applied Economics," Working Paper Series 2023-16, Federal Reserve Bank of San Francisco.
    8. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    9. José Luis Montiel Olea & Mikkel Plagborg-Møller & Eric Qian & Christian K. Wolf, 2024. "Double Robustness of Local Projections and Some Unpleasant VARithmetic," NBER Working Papers 32495, National Bureau of Economic Research, Inc.
    10. Dake Li & Mikkel Plagborg-Møller & Christian K. Wolf, 2021. "Local Projections vs. VARs: Lessons From Thousands of DGPs," Working Papers 2021-55, Princeton University. Economics Department..
    11. Regis Barnichon & Christian Brownlees, 2019. "Impulse Response Estimation by Smooth Local Projections," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 522-530, July.
    12. Shiller, Robert J, 1973. "A Distributed Lag Estimator Derived from Smoothness Priors," Econometrica, Econometric Society, vol. 41(4), pages 775-788, July.
    13. Pirmin Fessler & Maximilian Kasy, 2019. "How to Use Economic Theory to Improve Estimators: Shrinking Toward Theoretical Restrictions," The Review of Economics and Statistics, MIT Press, vol. 101(4), pages 681-698, October.
    14. Levi Boxell & Matthew Gentzkow & Jesse M. Shapiro, 2024. "Cross-Country Trends in Affective Polarization," The Review of Economics and Statistics, MIT Press, vol. 106(2), pages 557-565, March.
    15. Òscar Jordà, 2023. "Local Projections for Applied Economics," Annual Review of Economics, Annual Reviews, vol. 15(1), pages 607-631, September.
    16. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    17. Li, Dake & Plagborg-Møller, Mikkel & Wolf, Christian K., 2024. "Local projections vs. VARs: Lessons from thousands of DGPs," Journal of Econometrics, Elsevier, vol. 244(2).
    18. Emi Nakamura & Jón Steinsson, 2018. "Identification in Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 59-86, Summer.
    19. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2019. "Simultaneous confidence bands: Theory, implementation, and an application to SVARs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 1-17, January.
    20. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    2. Milov{s} Ciganovi'c & Elena Scola Gagliardi & Massimiliano Tancioni, 2025. "Disentangling the Distributional Effects of Financial Shocks in the Euro Area," Papers 2510.11289, arXiv.org.
    3. Philipp Roderweis & Jamel Saadaoui & Francisco Serranito, 2023. "The Unintended Consequences of ECB’s Asset Purchases. How Excess Reserves Shape Bank Lending," Working Papers of BETA 2023-34, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    4. Oriol González-Casasús & Frank Schorfheide, 2025. "Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs," NBER Working Papers 33474, National Bureau of Economic Research, Inc.
    5. Nabil Daher, 2025. "Is growth at risk from natural disasters ? Evidence from quantile local projections," EconomiX Working Papers 2025-9, University of Paris Nanterre, EconomiX.
    6. Atsushi Inoue & `Oscar Jord`a & Guido M. Kuersteiner, 2023. "Inference for Local Projections," Papers 2306.03073, arXiv.org, revised Aug 2024.
    7. Lucas Ordóñez, 2025. "The Transmission of Supply Shocks to Inflation: the Case of Argentina (2004-2022)," Working Papers 351, Red Nacional de Investigadores en Economía (RedNIE).
    8. Herbst, Edward P. & Johannsen, Benjamin K., 2024. "Bias in local projections," Journal of Econometrics, Elsevier, vol. 240(1).
    9. Shah, Syed Sadaqat Ali & Wu, Kai, 2025. "How effective are green spending multipliers? Eco-friendly vs non-eco-friendly spending in OECD economies," Energy Policy, Elsevier, vol. 204(C).
    10. Philipp Roderweis & Jamel Saadaoui & Francisco Serranito, 2023. "Is Quantitative Easing Productive? The Role of Bank Lending in the Monetary Transmission Process," Working Papers hal-04159825, HAL.
    11. Li, Dake & Plagborg-Møller, Mikkel & Wolf, Christian K., 2024. "Local projections vs. VARs: Lessons from thousands of DGPs," Journal of Econometrics, Elsevier, vol. 244(2).
    12. Montiel Olea, José Luis & Nesbit, James, 2021. "(Machine) learning parameter regions," Journal of Econometrics, Elsevier, vol. 222(1), pages 716-744.
    13. Sheng, Xin & Kim, Won Joong & Gupta, Rangan & Ji, Qiang, 2023. "The impacts of oil price volatility on financial stress: Is the COVID-19 period different?," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 520-532.
    14. De Graeve, Ferre & Westermark, Andreas, 2025. "Long-lag VARs," Journal of Monetary Economics, Elsevier, vol. 156(C).
    15. Masahiro Tanaka, 2025. "Quasi-Bayesian Local Projections: Simultaneous Inference and Extension to the Instrumental Variable Method," Papers 2503.20249, arXiv.org, revised Dec 2025.
    16. repec:osf:socarx:v75aw_v1 is not listed on IDEAS
    17. Ordoñez Lucas Sebastián, 2024. "The transmission of Supply Shocks to inflation: The case of Argentina (2004-2023)," Asociación Argentina de Economía Política: Working Papers 4750, Asociación Argentina de Economía Política.
    18. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    19. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "Bayesian local projections," Working Papers hal-03373574, HAL.
    20. Jesús Fernández-Villaverde & Yiliang Li & Le Xu & Francesco Zanetti, 2025. "Charting the Uncharted: The (Un)Intended Consequences of Oil Sanctions and Dark Shipping," CESifo Working Paper Series 11684, CESifo.
    21. Mar'ia Dolores Gadea & `Oscar Jord`a, 2025. "Local Projections Bootstrap Inference," Papers 2509.17949, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedpwp:101774. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Beth Paul (email available below). General contact details of provider: https://edirc.repec.org/data/frbphus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.