IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/31686.html
   My bibliography  Save this paper

Distribution of residuals in the nonparametric IV model with application to separability testing

Author

Listed:
  • Babii, Andrii
  • Florens, Jean-Pierre

Abstract

We develop a uniform asymptotic expansion for the empirical distribution function of residuals in the nonparametric IV regression. Such expansion opens a door for construction of a broad range of residual-based specification tests in nonparametric IV models. Building on obtained result, we develop a test for the separability of unobservables in econometric models with endogeneity. The test is based on verifying the independence condition between residuals of the NPIV estimator and the instrument and can distinguish between the non-separable and the separable specification under endogeneity.

Suggested Citation

  • Babii, Andrii & Florens, Jean-Pierre, 2017. "Distribution of residuals in the nonparametric IV model with application to separability testing," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:31686
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2017/wp_tse_802.pdf
    File Function: Full text
    Download Restriction: no

    References listed on IDEAS

    as
    1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    2. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers CWP32/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1035-1058.
    4. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
    5. 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.
    6. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    7. Michael G. Akritas, 2001. "Non-parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567.
    8. repec:eee:econom:v:199:y:2017:i:1:p:35-48 is not listed on IDEAS
    9. 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.
    10. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    11. 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.
    12. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    13. Horowitz, Joel L., 2012. "Specification testing in nonparametric instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 167(2), pages 383-396.
    14. 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.
    15. 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.
    16. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    17. 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.
    18. 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.
    19. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    separability test; distribution of residuals; nonparametric instrumental regression; Sobolev scales;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:tse:wpaper:31686. 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: http://edirc.repec.org/data/tsetofr.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 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.

    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.