IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2016-032.html
   My bibliography  Save this paper

Specification testing in nonparametric instrumental quantile regression

Author

Listed:
  • Breunig, Christoph

Abstract

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This paper develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly speci ed. Our test statistic is asymptotically normally distributed under correct speci cation and consistent against any alternative model. In addition, test statistics to justify model simpli cation are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration.

Suggested Citation

  • Breunig, Christoph, 2016. "Specification testing in nonparametric instrumental quantile regression," SFB 649 Discussion Papers 2016-032, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-032
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/148868/1/867097876.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    2. 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.
    3. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    4. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    5. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation," Cowles Foundation Discussion Papers 1923R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
    6. Patrick GAGLIARDINI & Olivier SCAILLET, 2017. "A Specification Test for Nonparametric Instrumental Variable Regression," Annals of Economics and Statistics, GENES, issue 128, pages 151-202.
    7. 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.
    8. 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.
    9. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    11. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    12. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    13. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers 32/15, Institute for Fiscal Studies.
    14. 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.
    15. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    16. repec:hal:journl:peer-00732534 is not listed on IDEAS
    17. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    18. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    19. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    20. Patrick Gagliardini & Olivier Scaillet, 2012. "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects," Econometrica, Econometric Society, vol. 80(4), pages 1533-1562, July.
    21. Lewbel, Arthur & Lu, Xun & Su, Liangjun, 2015. "Specification testing for transformation models with an application to generalized accelerated failure-time models," Journal of Econometrics, Elsevier, vol. 184(1), pages 81-96.
    22. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    23. 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.
    24. 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.
    25. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    26. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    27. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
    28. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
    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. repec:hum:wpaper:sfb649dp2016-032 is not listed on IDEAS
    2. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    3. 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.
    4. 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.
    5. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    6. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
    7. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers 38/14, Institute for Fiscal Studies.
    8. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    9. Jia-Young Michael Fu & Joel L. Horowitz & Matthias Parey, 2015. "Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions," CeMMAP working papers 68/15, Institute for Fiscal Studies.
    10. Fabian Dunker, 2015. "Adaptive estimation for some nonparametric instrumental variable models," Papers 1511.03977, arXiv.org, revised Aug 2021.
    11. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    12. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    13. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of nonparametric conditional moment models with possibly nonsmooth moments," CeMMAP working papers CWP12/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    15. Krief, Jerome M., 2017. "Direct instrumental nonparametric estimation of inverse regression functions," Journal of Econometrics, Elsevier, vol. 201(1), pages 95-107.
    16. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    17. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    18. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    19. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    20. 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.
    21. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.

    More about this item

    Keywords

    Nonparametric quantile regression; instrumental variable; specification test; local alternative; nonlinear inverse problem;
    All these keywords.

    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:zbw:sfb649:sfb649dp2016-032. 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.