IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2009.00553.html
   My bibliography  Save this paper

A Vector Monotonicity Assumption for Multiple Instruments

Author

Listed:
  • Leonard Goff

Abstract

When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call vector monotonicity, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal parameters that are point identified under vector monotonicity, when the instruments are binary. This class includes, for example, the average treatment effect among units that are in any way responsive to the collection of instruments, or those that are responsive to a given subset of them. The identification results are constructive and yield a simple estimator for the identified treatment effect parameters. An empirical application revisits the labor market returns to college.

Suggested Citation

  • Leonard Goff, 2020. "A Vector Monotonicity Assumption for Multiple Instruments," Papers 2009.00553, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2009.00553
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2009.00553
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    2. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    3. Lewbel, Arthur & Yang, Thomas Tao, 2016. "Identifying the average treatment effect in ordered treatment models without unconfoundedness," Journal of Econometrics, Elsevier, vol. 195(1), pages 1-22.
    4. 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.
    5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    6. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 499-527.
    7. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    8. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    9. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    10. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
    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. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Dec 2024.
    2. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).

    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. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2024. "Endogeneity in weakly separable models without monotonicity," Journal of Econometrics, Elsevier, vol. 238(1).
    2. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    3. Songnian Chen & Shakeeb Khan & Xun Tang, 2022. "Endogeneity in Weakly Separable Models without Monotonicity," Papers 2208.05047, arXiv.org.
    4. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    5. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    6. Leonard Goff, 2024. "When does IV identification not restrict outcomes?," Papers 2406.02835, arXiv.org, revised Sep 2024.
    7. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    8. Robert A. Moffitt & Matthew V. Zahn, 2019. "The Marginal Labor Supply Disincentives of Welfare: Evidence from Administrative Barriers to Participation," NBER Working Papers 26028, National Bureau of Economic Research, Inc.
    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. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    11. Ma, Jun & Marmer, Vadim & Yu, Zhengfei, 2023. "Inference on individual treatment effects in nonseparable triangular models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2096-2124.
    12. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    13. Roland A. Amann & Tobias J. Klein, 2012. "Returns to type or tenure?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(1), pages 153-166, January.
    14. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    15. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    16. Hsu, Yu-Chin & Huang, Ta-Cheng & Xu, Haiqing, 2023. "Testing For Unobserved Heterogeneous Treatment Effects With Observational Data," Econometric Theory, Cambridge University Press, vol. 39(3), pages 582-622, June.
    17. 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).
    18. Heckman, James J., 2010. "The Assumptions Underlying Evaluation Estimators," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(2), December.
    19. Amann, R. & Klein, T.J., 2011. "Returns to Type or Tenure?," Other publications TiSEM 2bbdd8bc-f35b-49fa-a430-c, Tilburg University, School of Economics and Management.
    20. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.

    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:2009.00553. 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.