IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2017-007.html

Testing missing at random using instrumental variables

Author

Listed:
  • Breunig, Christoph

Abstract

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic's asymptotic distribution under the MAR hypothesis is derived. In particular, our results can be applied to testing missing completely at random (MCAR). A Monte Carlo study examines finite sample performance of our test statistic. An empirical illustration analyzes the nonresponse mechanism in labor income questions.

Suggested Citation

  • Breunig, Christoph, 2017. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2017-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2017-007
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/162508/1/882060872.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    2. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, July.
    3. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    4. Kani Chen, 2001. "Parametric models for response‐biased sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 775-789.
    5. repec:hum:wpaper:sfb649dp2015-050 is not listed on IDEAS
    6. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    7. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    8. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    9. Joel L. Horowitz, 2006. "Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables," Econometrica, Econometric Society, vol. 74(2), pages 521-538, March.
    10. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    11. Breunig, Christoph, 2015. "Goodness-of-fit tests based on series estimators in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 184(2), pages 328-346.
    12. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 343-364.
    13. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    14. 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.
    15. Breunig, Christoph & Huck, Steffen & Schmidt, Tobias & Weizsäcker, Georg, 2021. "The Standard Portfolio Choice Problem in Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 131(638), pages 2413-2446.
    16. Annie Qu, 2002. "Testing ignorable missingness in estimating equation approaches for longitudinal data," Biometrika, Biometrika Trust, vol. 89(4), pages 841-850, December.
    17. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    18. 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.
    19. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1035-1058.
    20. Keisuke Hirano & Guido W. Imbens & Geert Ridder & Donald B. Rubin, 2001. "Combining Panel Data Sets with Attrition and Refreshment Samples," Econometrica, Econometric Society, vol. 69(6), pages 1645-1659, November.
    21. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    22. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
    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. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    2. repec:hum:wpaper:sfb649dp2017-007 is not listed on IDEAS
    3. Breunig, Christoph, 2015. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2015-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. repec:hum:wpaper:sfb649dp2015-016 is not listed on IDEAS
    5. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    6. Breunig, Christoph & Haan, Peter, 2021. "Nonparametric regression with selectively missing covariates," Journal of Econometrics, Elsevier, vol. 223(1), pages 28-52.
    7. Christoph Breunig & Peter Haan, 2018. "Nonparametric Regression with Selectively Missing Covariates," Papers 1810.00411, arXiv.org, revised Oct 2020.
    8. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
    9. repec:hum:wpaper:sfb649dp2015-050 is not listed on IDEAS
    10. Laurent Davezies & Xavier d'Haultfoeuille, 2013. "Endogenous Attrition in Panels," Working Papers 2013-17, Center for Research in Economics and Statistics.
    11. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    12. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    13. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    14. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Leibniz Centre for European Economic Research.
    15. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202004, University of Kansas, Department of Economics, revised Feb 2020.
    16. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
    17. Egshiglen Batbayar & Christoph Breunig & Peter Haan & Boryana Ilieva, 2025. "Quantile Selection in the Gender Pay Gap," Papers 2511.16187, arXiv.org, revised Jan 2026.
    18. Lukáš Lafférs & Bernhard Schmidpeter, 2021. "Early child development and parents' labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 190-208, March.
    19. Kim, Kyoo il & Petrin, Amil & Song, Suyong, 2016. "Estimating production functions with control functions when capital is measured with error," Journal of Econometrics, Elsevier, vol. 190(2), pages 267-279.
    20. Kenichi Nagasawa, 2018. "Treatment Effect Estimation with Noisy Conditioning Variables," Papers 1811.00667, arXiv.org, revised Sep 2022.
    21. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    22. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    23. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:zbw:sfb649:sfb649dp2017-007. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.