IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v235y2023i2p1257-1279.html
   My bibliography  Save this article

Nonparametric identification and estimation with discrete instruments and regressors

Author

Listed:
  • Loh, Isaac

Abstract

In a nonparametric instrumental regression model in which the regressor and instrument are discretely distributed, we strengthen the conventional moment independence assumption between instrument and residual to include higher order moments. We give conditions under which a function of interest is partially identified when the regressor has more mass points than the instrument. We also show that the function is point identified as long as certain latent parameters corresponding to conditional moments of the residual lie outside of a set of measure zero. We give an asymptotically normal estimator for the structural function when it is point identified. We also provide a straightforward method for inference under partial identification. These perform well in Monte-Carlo simulations and in two empirical applications.

Suggested Citation

  • Loh, Isaac, 2023. "Nonparametric identification and estimation with discrete instruments and regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1257-1279.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1257-1279
    DOI: 10.1016/j.jeconom.2022.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407622001907
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2022.10.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    3. Fabian Dunker, 2015. "Adaptive estimation for some nonparametric instrumental variable models," Papers 1511.03977, arXiv.org, revised Aug 2021.
    4. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    5. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    6. Dunker, Fabian & Florens, Jean-Pierre & Hohage, Thorsten & Johannes, Jan & Mammen, Enno, 2014. "Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 178(P3), pages 444-455.
    7. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    8. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    9. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, January.
    10. Lance Lochner & Enrico Moretti, 2015. "Estimating and Testing Models with Many Treatment Levels and Limited Instruments," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 387-397, May.
    11. 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.
    12. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    13. Hong, Shengjie, 2017. "Inference in semiparametric conditional moment models with partial identification," Journal of Econometrics, Elsevier, vol. 196(1), pages 156-179.
    14. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    15. 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)

    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. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    2. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    3. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    4. Hong, Shengjie, 2017. "Inference in semiparametric conditional moment models with partial identification," Journal of Econometrics, Elsevier, vol. 196(1), pages 156-179.
    5. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    6. Escanciano, Juan Carlos & Li, Wei, 2021. "Optimal Linear Instrumental Variables Approximations," Journal of Econometrics, Elsevier, vol. 221(1), pages 223-246.
    7. Krikamol Muandet & Arash Mehrjou & Si Kai Lee & Anant Raj, 2019. "Dual Instrumental Variable Regression," Papers 1910.12358, arXiv.org, revised Oct 2020.
    8. Chen, Qihui, 2021. "Robust and optimal estimation for partially linear instrumental variables models with partial identification," Journal of Econometrics, Elsevier, vol. 221(2), pages 368-380.
    9. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    10. Krief, Jerome M., 2017. "Direct instrumental nonparametric estimation of inverse regression functions," Journal of Econometrics, Elsevier, vol. 201(1), pages 95-107.
    11. Fan, Yanqin & Shi, Xuetao & Tao, Jing, 2023. "Partial identification and inference in moment models with incomplete data," Journal of Econometrics, Elsevier, vol. 235(2), pages 418-443.
    12. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    13. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    14. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    15. Andrii Babii & Jean-Pierre Florens, 2017. "Are Unobservables Separable?," Papers 1705.01654, arXiv.org, revised Mar 2021.
    16. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    17. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    18. Jad Beyhum & Elia Lapenta & Pascal Lavergne, 2023. "One-step smoothing splines instrumental regression," Papers 2307.14867, arXiv.org, revised Apr 2024.
    19. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    20. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.

    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:eee:econom:v:235:y:2023:i:2:p:1257-1279. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.