IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.12720.html
   My bibliography  Save this paper

Generalized Lee Bounds

Author

Listed:
  • Vira Semenova

Abstract

Lee (2009) is a common approach to bound the average causal effect in the presence of selection bias, assuming the treatment effect on selection has the same sign for all subjects. This paper generalizes Lee bounds to allow the sign of this effect to be identified by pretreatment covariates, relaxing the standard (unconditional) monotonicity to its conditional analog. Asymptotic theory for generalized Lee bounds is proposed in low-dimensional smooth and high-dimensional sparse designs. The paper also generalizes Lee bounds to accommodate multiple outcomes. It characterizes the sharp identified set for the causal parameter and proposes uniform Gaussian inference on the support function. The estimated bounds achieve nearly point-identification in JobCorps job training program (Lee (2009)), where unconditional monotonicity is unlikely to hold.

Suggested Citation

  • Vira Semenova, 2020. "Generalized Lee Bounds," Papers 2008.12720, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2008.12720
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.12720
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    2. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    3. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    4. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    5. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    6. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    7. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2016. "Post-Selection Inference for Generalized Linear Models With Many Controls," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 606-619, October.
    8. Sendhil Mullainathan & Jann Spiess, 2017. "Machine Learning: An Applied Econometric Approach," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 87-106, Spring.
    9. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Aureo de Paula, 2019. "Inference on Causal and Structural Parameters using Many Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1867-1900.
    10. Victor Chernozhukov & Mert Demirer & Esther Duflo & Ivan Fernandez-Val, 2017. "Generic machine learning inference on heterogenous treatment effects in randomized experiments," CeMMAP working papers CWP61/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    12. Joshua Angrist & Eric Bettinger & Erik Bloom & Elizabeth King & Michael Kremer, 2002. "Vouchers for Private Schooling in Colombia: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1535-1558, December.
    13. Ashenfelter, Orley C, 1978. "Estimating the Effect of Training Programs on Earnings," The Review of Economics and Statistics, MIT Press, vol. 60(1), pages 47-57, February.
    14. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    15. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers 43/12, Institute for Fiscal Studies.
    16. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    17. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    18. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    19. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    20. Amy Finkelstein & Sarah Taubman & Bill Wright & Mira Bernstein & Jonathan Gruber & Joseph P. Newhouse & Heidi Allen & Katherine Baicker, 2012. "The Oregon Health Insurance Experiment: Evidence from the First Year," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1057-1106.
    21. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    22. Peter Z. Schochet & John Burghardt & Sheena McConnell, 2008. "Does Job Corps Work? Impact Findings from the National Job Corps Study," American Economic Review, American Economic Association, vol. 98(5), pages 1864-1886, December.
    23. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    24. repec:mpr:mprres:6097 is not listed on IDEAS
    25. 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.
    26. Harold D. Chiang, 2018. "Many Average Partial Effects: with An Application to Text Regression," Papers 1812.09397, arXiv.org, revised Jan 2022.
    27. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    28. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    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. Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.

    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. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    2. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    4. Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org.
    5. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute of Labor Economics (IZA).
    6. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    7. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Victor Chernozhukov & Carlos Cinelli & Whitney Newey & Amit Sharma & Vasilis Syrgkanis, 2021. "Long Story Short: Omitted Variable Bias in Causal Machine Learning," Papers 2112.13398, arXiv.org, revised Nov 2023.
    10. Simon Calmar Andersen & Louise Beuchert & Phillip Heiler & Helena Skyt Nielsen, 2023. "A Guide to Impact Evaluation under Sample Selection and Missing Data: Teacher's Aides and Adolescent Mental Health," Papers 2308.04963, arXiv.org.
    11. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    12. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    13. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    14. Jonathan Fuhr & Philipp Berens & Dominik Papies, 2024. "Estimating Causal Effects with Double Machine Learning -- A Method Evaluation," Papers 2403.14385, arXiv.org.
    15. German Blanco & Xuan Chen & Carlos A. Flores & Alfonso Flores-Lagunes, 2020. "Bounds on Average and Quantile Treatment Effects on Duration Outcomes Under Censoring, Selection, and Noncompliance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 901-920, October.
    16. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.
    17. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    19. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.

    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:2008.12720. 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.