IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2601.16749.html

Finite Population Inference for Factorial Designs and Panel Experiments with Imperfect Compliance

Author

Listed:
  • Pedro Picchetti

Abstract

This paper develops a finite population framework for analyzing causal effects in settings with imperfect compliance where multiple treatments affect the outcome of interest. Two prominent examples are factorial designs and panel experiments with imperfect compliance. I define finite population causal effects that capture the relative effectiveness of alternative treatment sequences. I provide nonparametric estimators for a rich class of factorial and dynamic causal effects and derive their finite population distributions as the sample size increases. Monte Carlo simulations illustrate the desirable properties of the estimators. Finally, I use the estimator for causal effects in factorial designs to revisit a famous voter mobilization experiment that analyzes the effects of voting encouragement through phone calls on turnout.

Suggested Citation

  • Pedro Picchetti, 2026. "Finite Population Inference for Factorial Designs and Panel Experiments with Imperfect Compliance," Papers 2601.16749, arXiv.org.
    • Handle: RePEc:arx:papers:2601.16749
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2601.16749
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David W. Nickerson, 2007. "Quality Is Job One: Professional and Volunteer Voter Mobilization Calls," American Journal of Political Science, John Wiley & Sons, vol. 51(2), pages 269-282, April.
    2. Matthew Blackwell, 2017. "Instrumental Variable Methods for Conditional Effects and Causal Interaction in Voter Mobilization Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 590-599, April.
    3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    4. Iavor Bojinov & Neil Shephard, 2019. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1665-1682, October.
    5. Hyunseung Kang & Laura Peck & Luke Keele, 2018. "Inference for instrumental variables: a randomization inference approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1231-1254, October.
    6. Jing Cheng & Dylan S. Small, 2006. "Bounds on causal effects in three‐arm trials with non‐compliance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 815-836, November.
    7. Peter Z. Schochet, 2020. "The Complier Average Causal Effect Parameter for Multiarmed RCTs," Evaluation Review, , vol. 44(5-6), pages 410-436, October.
    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. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Jun 2025.
    2. Máté Kormos & Robert P. Lieli & Martin Huber, 2025. "Interacting Treatments With Endogenous Takeup," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(4), pages 424-437, June.
    3. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    4. Hui Nie & Jing Cheng & Dylan S. Small, 2011. "Inference for the Effect of Treatment on Survival Probability in Randomized Trials with Noncompliance and Administrative Censoring," Biometrics, The International Biometric Society, vol. 67(4), pages 1397-1405, December.
    5. Didier Nibbering & Matthijs Oosterveen, 2023. "Instrument-based estimation of full treatment effects with movers," Papers 2306.07018, arXiv.org.
    6. Yuehao Bai & Shunzhuang Huang & Sarah Moon & Azeem Shaikh & Edward J. Vytlacil, 2024. "On the Identifying Power of Generalized Monotonicity for Average Treatment Effects," NBER Working Papers 32983, National Bureau of Economic Research, Inc.
    7. Jing Cheng, 2009. "Estimation and Inference for the Causal Effect of Receiving Treatment on a Multinomial Outcome," Biometrics, The International Biometric Society, vol. 65(1), pages 96-103, March.
    8. Yuehao Bai & Shunzhuang Huang & Sarah Moon & Andres Santos & Azeem M. Shaikh & Edward J. Vytlacil, 2024. "Inference for Treatment Effects Conditional on Generalized Principal Strata using Instrumental Variables," Papers 2411.05220, arXiv.org, revised Nov 2025.
    9. Toru Kitagawa & Weining Wang & Mengshan Xu, 2025. "Nonlinearity in Dynamic Causal Effects: Making the Bad into the Good, and the Good into the Great?," Papers 2504.01140, arXiv.org, revised Jun 2025.
    10. Santiago Acerenza & Julian Martinez-Iriarte & Alejandro S'anchez-Becerra & Pietro Emilio Spini, 2025. "Bounds for within-household encouragement designs with interference," Papers 2503.14314, arXiv.org.
    11. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
    12. Ashesh Rambachan & Neil Shephard, 2019. "When do common time series estimands have nonparametric causal meaning?," Papers 1903.01637, arXiv.org, revised Jan 2025.
    13. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    14. Peter Z. Schochet, 2020. "The Complier Average Causal Effect Parameter for Multiarmed RCTs," Evaluation Review, , vol. 44(5-6), pages 410-436, October.
    15. Geoffrey Henderson & Matto Mildenberger & Leah C. Stokes, 2025. "The effect of environmental voter mobilization on voter turnout and environmental attitudes: evidence from a field experiment in British Columbia, Canada," Climatic Change, Springer, vol. 178(6), pages 1-13, June.
    16. S Anukriti & Catalina Herrera‐Almanza & Praveen K. Pathak & Mahesh Karra, 2020. "Curse of the Mummy‐ji: The Influence of Mothers‐in‐Law on Women in India†," American Journal of Agricultural Economics, John Wiley & Sons, vol. 102(5), pages 1328-1351, October.
    17. González-Uribe, Juanita & Reyes, Santiago, 2021. "Identifying and boosting “Gazelles”: Evidence from business accelerators," Journal of Financial Economics, Elsevier, vol. 139(1), pages 260-287.
    18. Roxana Elena Manea, 2021. "School Feeding Programmes, Education and Food Security in Rural Malawi," CIES Research Paper series 63-2020, Centre for International Environmental Studies, The Graduate Institute.
    19. Clément de Chaisemartin & Luc Behaghel, 2020. "Estimating the Effect of Treatments Allocated by Randomized Waiting Lists," Econometrica, Econometric Society, vol. 88(4), pages 1453-1477, July.
    20. David Card, 2022. "Design-Based Research in Empirical Microeconomics," American Economic Review, American Economic Association, vol. 112(6), pages 1773-1781, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2601.16749. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.