IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2203.08050.html
   My bibliography  Save this paper

Pairwise Valid Instruments

Author

Listed:
  • Zhenting Sun
  • Kaspar Wuthrich

Abstract

Finding valid instruments is difficult. We propose Validity Set Instrumental Variable (VSIV) estimation, a method for estimating local average treatment effects (LATEs) in heterogeneous causal effect models when the instruments are partially invalid. We consider settings with pairwise valid instruments, that is, instruments that are valid for a subset of instrument value pairs. VSIV estimation exploits testable implications of instrument validity to remove invalid pairs and provides estimates of the LATEs for all remaining pairs, which can be aggregated into a single parameter of interest using researcher-specified weights. We show that the proposed VSIV estimators are asymptotically normal under weak conditions and remove or reduce the asymptotic bias relative to standard LATE estimators (that is, LATE estimators that do not use testable implications to remove invalid variation). We evaluate the finite sample properties of VSIV estimation in application-based simulations and apply our method to estimate the returns to college education using parental education as an instrument.

Suggested Citation

  • Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2203.08050
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2203.08050
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    2. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    3. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    4. Rashmi Barua & Kevin Lang, 2016. "School Entry, Educational Attainment, and Quarter of Birth: A Cautionary Tale of a Local Average Treatment Effect," Journal of Human Capital, University of Chicago Press, vol. 10(3), pages 347-376.
    5. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    6. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    7. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    8. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 711-724, July.
    9. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    10. Désiré Kédagni & Ismael Mourifié, 2020. "Generalized instrumental inequalities: testing the instrumental variable independence assumption," Biometrika, Biometrika Trust, vol. 107(3), pages 661-675.
    11. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    12. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    13. Christian M Dahl & Martin Huber & Giovanni Mellace, 2023. "It is never too LATE: a new look at local average treatment effects with or without defiers," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 378-404.
    14. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    15. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    16. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    17. 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.
    18. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    19. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    20. Joshua D. Angrist & Jörn-Steffen Pischke, 2014. "Mastering ’Metrics: The Path from Cause to Effect," Economics Books, Princeton University Press, edition 1, number 10363.
    21. Thomas Carr & Toru Kitagawa, 2021. "Testing Instrument Validity with Covariates," Papers 2112.08092, arXiv.org, revised Sep 2023.
    22. Zhenting Sun & Brendan K. Beare, 2021. "Improved Nonparametric Bootstrap Tests of Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 189-199, January.
    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. Joshua D. Angrist, 2022. "Empirical Strategies in Economics: Illuminating the Path From Cause to Effect," Econometrica, Econometric Society, vol. 90(6), pages 2509-2539, November.

    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. Hongyi Jiang & Zhenting Sun, 2023. "Testing Partial Instrument Monotonicity," Papers 2308.08390, arXiv.org, revised Aug 2023.
    2. 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.
    3. Thomas Carr & Toru Kitagawa, 2021. "Testing Instrument Validity with Covariates," Papers 2112.08092, arXiv.org, revised Sep 2023.
    4. Blaise Melly und Kaspar W thrich, 2016. "Local quantile treatment effects," Diskussionsschriften dp1605, Universitaet Bern, Departement Volkswirtschaft.
    5. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    6. Black, Dan A. & Joo, Joonhwi & LaLonde, Robert & Smith, Jeffrey A. & Taylor, Evan J., 2022. "Simple Tests for Selection: Learning More from Instrumental Variables," Labour Economics, Elsevier, vol. 79(C).
    7. Christian M Dahl & Martin Huber & Giovanni Mellace, 2023. "It is never too LATE: a new look at local average treatment effects with or without defiers," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 378-404.
    8. 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.
    9. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    10. Mario Fiorini & Katrien Stevens, 2021. "Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1475-1526, December.
    11. Yinchu Zhu, 2021. "Phase transition of the monotonicity assumption in learning local average treatment effects," Papers 2103.13369, arXiv.org.
    12. Nadja van 't Hoff, 2023. "Identifying Causal Effects of Nonbinary, Ordered Treatments using Multiple Instrumental Variables," Papers 2311.17575, arXiv.org.
    13. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    14. Schmieder, Julia, 2021. "Fertility as a driver of maternal employment," Labour Economics, Elsevier, vol. 72(C).
    15. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    16. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    17. Toru Kitagawa, 2013. "A bootstrap test for instrument validity in heterogeneous treatment effect models," CeMMAP working papers CWP53/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Manu Navjeevan & Rodrigo Pinto & Andres Santos, 2023. "Identification and Estimation in a Class of Potential Outcomes Models," Papers 2310.05311, arXiv.org.
    19. Xintong Wang & Alfonso Flores-Lagunes, 2022. "Conscription and Military Service: Do They Result in Future Violent and Nonviolent Incarcerations and Recidivism?," Journal of Human Resources, University of Wisconsin Press, vol. 57(5), pages 1715-1757.
    20. Luis Antonio Fantozzi Alvarez & Rodrigo Toneto, 2024. "The interpretation of 2SLS with a continuous instrument: a weighted LATE representation," Working Papers, Department of Economics 2024_11, University of São Paulo (FEA-USP).

    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:2203.08050. 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.