Advanced Search
MyIDEAS: Login

Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments

Contents:

Author Info

Registered author(s):

    Abstract

    This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are iden­tified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important ap­plications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1650.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1650.

    as in new window
    Length: 60 pages
    Date of creation: Apr 2008
    Date of revision: Oct 2008
    Handle: RePEc:cwl:cwldpp:1650

    Contact details of provider:
    Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
    Phone: (203) 432-3702
    Fax: (203) 432-6167
    Web page: http://cowles.econ.yale.edu/
    More information through EDIRC

    Order Information:
    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

    Related research

    Keywords: Nonsmooth residuals; Nonlinear ill-posed inverse; Penalized sieve minimum distance; Modulus of continuity; Average derivative of a nonparametric nonlinear IV regression; Non-parametric additive quantile IV regression;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. 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.
    2. 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.
    3. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    4. Xiaohong Chen & Demian Pouzo, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Cowles Foundation Discussion Papers 1640R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
    5. Thomas A. Severini & Gautam Tripathi, 2005. "Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors," Working papers 2005-12, University of Connecticut, Department of Economics.
    6. Matzkin, Rosa L., 2007. "Nonparametric identification," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 73 Elsevier.
    7. 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.
    8. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    9. Xiaohong Chen & Demian Pouzo, 2008. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP09/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, 07.
    11. 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.
    12. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
    13. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    14. Victor Chernozhukov & Patrick Gagliardini & Olivier Scaillet, 2006. "Nonparametric Instrumental Variable Estimators of Structural Quantile Effects," Swiss Finance Institute Research Paper Series 08-03, Swiss Finance Institute, revised Aug 2009.
    15. Cohen, Albert & Hoffmann, Marc & Reiß, Markus, 2002. "Adaptive wavelet Galerkin methods for linear inverse problems," SFB 373 Discussion Papers 2002,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Chen, Xiaohong & Pouzo, Demian, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Working Papers 38, Yale University, Department of Economics.
    17. Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
    19. Xiaohong Chen & Sydney C. Ludvigson, 2004. "Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Behavior," NBER Working Papers 10503, National Bureau of Economic Research, Inc.
    20. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
    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 in new window

    Cited by:
    1. Xiaohong Chen & Demian Pouzo, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP20/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Ivana Komunjer & Andres Santos, 2010. "Semi-parametric estimation of non-separable models: a minimum distance from independence approach," Econometrics Journal, Royal Economic Society, vol. 13(3), pages S28-S55, October.
    3. Joel Horowitz & Sokbae 'Simon' Lee, 2009. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," CeMMAP working papers CWP18/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Xiaohong Chen & Demian Pouzo, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Cowles Foundation Discussion Papers 1640R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
    5. Horowitz, Joel L., 2012. "Specification testing in nonparametric instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 167(2), pages 383-396.
    6. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions," Cowles Foundation Discussion Papers 1731, Cowles Foundation for Research in Economics, Yale University.
    7. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    8. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    9. Horowitz, Joel L. & Lee, Sokbae, 2009. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," Journal of Econometrics, Elsevier, vol. 152(2), pages 141-152, October.
    10. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1650. 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: (Glena Ames).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.