IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp17805.html
   My bibliography  Save this paper

Quantifying the Internal Validity of Weighted Estimands

Author

Listed:
  • Poirier, Alexandre

    (Georgetown University)

  • Sloczynski, Tymon

    (Brandeis University)

Abstract

In this paper we study a class of weighted estimands, which we define as parameters that can be expressed as weighted averages of the underlying heterogeneous treatment effects. The popular ordinary least squares (OLS), two-stage least squares (2SLS), and two-way fixed effects (TWFE) estimands are all special cases within our framework. Our focus is on answering two questions concerning weighted estimands. First, under what conditions can they be interpreted as the average treatment effect for some (possibly latent) subpopulation? Second, when these conditions are satisfied, what is the upper bound on the size of that subpopulation, either in absolute terms or relative to a target population of interest? We argue that this upper bound provides a valuable diagnostic for empirical research. When a given weighted estimand corresponds to the average treatment effect for a small subset of the population of interest, we say its internal validity is low. Our paper develops practical tools to quantify the internal validity of weighted estimands.

Suggested Citation

  • Poirier, Alexandre & Sloczynski, Tymon, 2025. "Quantifying the Internal Validity of Weighted Estimands," IZA Discussion Papers 17805, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp17805
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp17805.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Isaiah Andrews & Jonathan Roth & Ariel Pakes, 2023. "Inference for Linear Conditional Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 2763-2791.
    2. Gregory Cox & Xiaoxia Shi, 2023. "Simple Adaptive Size-Exact Testing for Full-Vector and Subvector Inference in Moment Inequality Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(1), pages 201-228.
    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. Betsey Stevenson & Justin Wolfers, 2006. "Bargaining in the Shadow of the Law: Divorce Laws and Family Distress," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(1), pages 267-288.
    5. JoonHwan Cho & Thomas M. Russell, 2024. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 563-578, April.
    6. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2024. "Revisiting Event-Study Designs: Robust and Efficient Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3253-3285.
    7. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2022. "Contamination Bias in Linear Regressions," Working Papers 2022-15, Princeton University. Economics Department..
    8. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    9. Joshua D. Angrist, 1998. "Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants," Econometrica, Econometric Society, vol. 66(2), pages 249-288, March.
    10. Douglas L. Miller & Na’ama Shenhav & Michel Grosz, 2023. "Selection into Identification in Fixed Effects Models, with Application to Head Start," Journal of Human Resources, University of Wisconsin Press, vol. 58(5), pages 1523-1566.
    11. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    12. Peter M. Aronow & Cyrus Samii, 2016. "Does Regression Produce Representative Estimates of Causal Effects?," American Journal of Political Science, John Wiley & Sons, vol. 60(1), pages 250-267, January.
    13. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrew Baker & Brantly Callaway & Scott Cunningham & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2025. "Difference-in-Differences Designs: A Practitioner's Guide," Papers 2503.13323, arXiv.org.

    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. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    2. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    3. Andrew Baker & Brantly Callaway & Scott Cunningham & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2025. "Difference-in-Differences Designs: A Practitioner's Guide," Papers 2503.13323, arXiv.org.
    4. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2025. "Design-based identification with formula instruments: a review," The Econometrics Journal, Royal Economic Society, vol. 28(1), pages 83-108.
    5. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    6. Bernardus F Nazar Van Doornik & Armando Gomes & David Schoenherr & Janis Skrastins, 2023. "Financial access and labor market outcomes: evidence from credit lotteries," BIS Working Papers 1071, Bank for International Settlements.
    7. Federico A. Bugni & Ivan A. Canay & Steve McBride, 2023. "Decomposition and Interpretation of Treatment Effects in Settings with Delayed Outcomes," Papers 2302.11505, arXiv.org, revised Sep 2024.
    8. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    9. Nibbering, Didier & Oosterveen, Matthijs & Silva, Pedro Luís, 2022. "Clustered Local Average Treatment Effects: Fields of Study and Academic Student Progress," IZA Discussion Papers 15159, Institute of Labor Economics (IZA).
    10. Michael C. Knaus, 2024. "Treatment Effect Estimators as Weighted Outcomes," Papers 2411.11559, arXiv.org, revised Dec 2024.
    11. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    12. Alvarez, Luis A.F. & Toneto, Rodrigo, 2024. "The interpretation of 2SLS with a continuous instrument: A weighted LATE representation," Economics Letters, Elsevier, vol. 237(C).
    13. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2024. "Revisiting Event-Study Designs: Robust and Efficient Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3253-3285.
    14. David Card & Fabrizio Colella & Rafael Lalive, 2021. "Gender Preferences in Job Vacancies and Workplace Gender Diversity," NBER Working Papers 29350, National Bureau of Economic Research, Inc.
    15. Jeffrey Smith & Arthur Sweetman, 2016. "Viewpoint: Estimating the causal effects of policies and programs," Canadian Journal of Economics, Canadian Economics Association, vol. 49(3), pages 871-905, August.
    16. Matthias Breuer & Ed Dehaan, 2024. "Using and Interpreting Fixed Effects Models," Journal of Accounting Research, Wiley Blackwell, vol. 62(4), pages 1183-1226, September.
    17. Bhalotra, Sonia R. & Britto, Diogo & Pinotti, Paolo & Sampaio, Breno, 2021. "Job Displacement, Unemployment Benefits and Domestic Violence," IZA Discussion Papers 14543, Institute of Labor Economics (IZA).
    18. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    19. Francesco Ruggieri, 2023. "Dynamic Regression Discontinuity: An Event-Study Approach," Papers 2307.14203, arXiv.org, revised Mar 2025.
    20. Tymon Słoczyński, 2022. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 501-509, May.

    More about this item

    Keywords

    weakly causal estimands; two-way fixed effects; two-stage least squares; treatment effects; representativeness; ordinary least squares; internal validity; weighted estimands;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

    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:iza:izadps:dp17805. 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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.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.