IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2012-12.html
   My bibliography  Save this paper

Late again, whithout Monotonicity

Author

Listed:
  • Clément de Chaisemartin

Abstract

Monotonicity is not necessary for the Wald ratio to identify a Local Average Treatment Effect. Under random assignment and exclusion restriction, if for every value of potential outcomes there are more compliers than defiers, the Wald ratio identifies the average treatment effect within a subpopulation of compliers. I use a simple Roy selection model to show that this "less defiers than compliers" condition is substantially weaker than monotonicity. It has two implications which are testable from the data, and it is closely related to those testable implications. Similarly, the local monotonicity condition in Huber & Mellace (2012) is not necessary for their identification results to hold and can also be replaced by a substantially weaker condition

Suggested Citation

  • Clément de Chaisemartin, 2012. "Late again, whithout Monotonicity," Working Papers 2012-12, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2012-12
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2012-12.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Huber, Martin, 2012. "Statistical verification of a natural "natural experiment": Tests and sensitivity checks for the sibling sex ratio instrument," Economics Working Paper Series 1219, University of St. Gallen, School of Economics and Political Science.
    2. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
    3. Luc Behaghel & Bruno Crépon & Marc Gurgand & Thomas Le Barbanchon, 2015. "Please Call Again: Correcting Nonresponse Bias in Treatment Effect Models," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1070-1080, December.
    4. DiNardo, John & Lee, David S., 2011. "Program Evaluation and Research Designs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 5, pages 463-536, Elsevier.
    5. 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.
    6. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    7. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1071-1102.
    8. Clément de Chaisemartin, 2017. "Tolerating defiance? Local average treatment effects without monotonicity," Quantitative Economics, Econometric Society, vol. 8(2), pages 367-396, July.
    9. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
    10. Jeffrey R. Kling, 2006. "Incarceration Length, Employment, and Earnings," American Economic Review, American Economic Association, vol. 96(3), pages 863-876, June.
    11. Clément de Chaisemartin & Xavier d'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.
    12. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    13. Kelly Bedard & Elizabeth Dhuey, 2006. "The Persistence of Early Childhood Maturity: International Evidence of Long-Run Age Effects," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1437-1472.
    14. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    15. Rashmi Barua & Kevin Lang, 2009. "School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE," NBER Working Papers 15236, National Bureau of Economic Research, Inc.
    16. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
    17. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    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. 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.
    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. Committee, Nobel Prize, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    4. Schmieder, Julia, 2021. "Fertility as a driver of maternal employment," Labour Economics, Elsevier, vol. 72(C).
    5. Chaisemartin, Clément de, 2014. "Tolerating defiance? Local average treatment effects without monotonicity," CAGE Online Working Paper Series 197, Competitive Advantage in the Global Economy (CAGE).
    6. Julia Schmieder, 2020. "Fertility as a Driver of Maternal Employment," Discussion Papers of DIW Berlin 1882, DIW Berlin, German Institute for Economic Research.
    7. Clément de Chaisemartin & Xavier d'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.
    8. Kaspar Wüthrich, 2020. "A Comparison of Two Quantile Models With Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 443-456, April.
    9. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    10. Westphal, Matthias & Kamhöfer, Daniel A. & Schmitz, Hendrik, 2020. "Marginal college wage premiums under selection into employment," DICE Discussion Papers 341, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    11. Fiorini, Mario & Katrien Stevens, 2014. "Assessing the Monotonicity Assumption in IV and fuzzy RD designs," Working Papers 2014-13, University of Sydney, School of Economics.
    12. 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.
    13. Claudia Noack, 2021. "Sensitivity of LATE Estimates to Violations of the Monotonicity Assumption," Papers 2106.06421, arXiv.org.
    14. Yu-Chin Hsu & Ta-Cheng Huang & Haiqing Xu, 2018. "Testing for Unobserved Heterogeneous Treatment Effects with Observational Data," Papers 1803.07514, arXiv.org, revised Aug 2021.
    15. David Card & David S. Lee & Zhuan Pei & Andrea Weber, 2015. "Inference on Causal Effects in a Generalized Regression Kink Design," Econometrica, Econometric Society, vol. 83, pages 2453-2483, November.
    16. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    17. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," Review of Economic Studies, Oxford University Press, vol. 85(2), pages 999-1028.
    18. Michael R.M. Abrigo & Timothy J. Halliday & Teresa Molina, 2022. "Expanding health insurance for the elderly of the Philippines," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 500-520, April.
    19. Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    20. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.

    More about this item

    Keywords

    local average treatment effect; instrumental variable; monotonicity; local monotonicity; defiers;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

    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:crs:wpaper:2012-12. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.