IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v83y2015i3p1013-1079.html
   My bibliography  Save this article

Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models

Author

Listed:
  • Xiaohong Chen
  • Demian Pouzo

Abstract

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

Suggested Citation

  • 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.
  • Handle: RePEc:wly:emetrp:v:83:y:2015:i:3:p:1013-1079
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    2. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression," Cowles Foundation Discussion Papers 1923, Cowles Foundation for Research in Economics, Yale University.
    3. Otsu, Taisuke, 2011. "Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions," Econometric Theory, Cambridge University Press, vol. 27(01), pages 8-46, February.
    4. repec:oup:restud:v:84:y:2017:i:3:p:1238-1263. is not listed on IDEAS
    5. Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August.
    6. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    7. Antonio Merlo & Áureo de Paula, 2017. "Identification and Estimation of Preference Distributions When Voters Are Ideological," Review of Economic Studies, Oxford University Press, vol. 84(3), pages 1238-1263.
    8. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    9. Xiaohong Chen & Jack Favilukis & Sydney C. Ludvigson, 2013. "An estimation of economic models with recursive preferences," Quantitative Economics, Econometric Society, vol. 4(1), pages 39-83, March.
    10. 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.
    11. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, June.
    12. 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.
    13. 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.
    14. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    15. 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.
    16. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    17. Bryan S. Graham & James L. Powell, 2012. "Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models," Econometrica, Econometric Society, vol. 80(5), pages 2105-2152, September.
    18. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    19. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    20. 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.
    21. Patrick Gagliardini & Olivier Scaillet, 2012. "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects," Econometrica, Econometric Society, vol. 80(4), pages 1533-1562, July.
    22. 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.
    23. Antonio Merlo & Aureo de Paula, 2010. "Identification and Estimation of Preference Distributions When Voters Are Ideological, Second Version," PIER Working Paper Archive 13-055, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 13 Oct 2013.
    24. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    25. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    26. Xiaohong Chen & Sydney C. Ludvigson, 2009. "Land of addicts? an empirical investigation of habit‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1057-1093, November.
    27. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    28. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
    29. 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.
    30. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    31. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, January.
    32. 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.
    33. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    34. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    35. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    36. Gary Chamberlain, 2010. "Binary Response Models for Panel Data: Identification and Information," Econometrica, Econometric Society, vol. 78(1), pages 159-168, January.
    37. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    38. 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.
    39. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Davezies, Laurent & Le Barbanchon, Thomas, 2017. "Regression discontinuity design with continuous measurement error in the running variable," Journal of Econometrics, Elsevier, vol. 200(2), pages 260-281.
    2. Vladimir Spokoiny & Mayya Zhilova, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers SFB649DP2014-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. repec:eee:econom:v:202:y:2018:i:2:p:268-285 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. Babii, Andrii, 2017. "Honest confidence sets in nonparametric IV regression and other ill-posed models," TSE Working Papers 17-803, Toulouse School of Economics (TSE).
    7. Ben Deaner, 2018. "Nonparametric Estimation and Identification in Non-Separable Models Using Panel Data," Papers 1810.00283, arXiv.org.
    8. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org.
    9. 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.
    10. Bruno Merlevede & Angelos Theodorakopoulos, 2016. "Productivity effects from inter-industry offshoring and inshoring: Firm-level evidence from Belgium," FIW Working Paper series 165, FIW.
    11. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jun 2019.
    12. Xiaohong Chen & Demian Pouzo & James L. Powell, 2019. "Penalized Sieve GEL for Weighted Average Derivatives of Nonparametric Quantile IV Regressions," Papers 1902.10100, arXiv.org.
    13. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Demian Pouzo, 2014. "Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension," Papers 1411.2701, arXiv.org, revised Aug 2015.
    15. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-Norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression," Cowles Foundation Discussion Papers 1923R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2017.
    16. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.

    More about this item

    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:wly:emetrp:v:83:y:2015:i:3:p:1013-1079. 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: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/essssea.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.