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On the Completeness Condition in Nonparametric Instrumental Problems

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  • Xavier d'Haultfoeuille

    (Crest)

Abstract

The notion of completeness between two random variables has been consideredrecently to provide identification in nonparametric instrumental problems. This conditionis quite abstract, however, and characterizations have been obtained only inspecial cases. The aim of this paper is to provide general sufficient conditions toachieve completeness or bounded completeness. The difference between these twonotions is stressed, and implications for the nonparametric instrumental regressionare given.

Suggested Citation

  • Xavier d'Haultfoeuille, 2006. "On the Completeness Condition in Nonparametric Instrumental Problems," Working Papers 2006-32, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2006-32
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    1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    2. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    3. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    4. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    6. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    7. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    8. ZINDE-WALSH, Victoria, 2007. "Errors-in-Variables Models : A Generalized Functions Approach," Cahiers de recherche 14-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    10. Yingyao Hu & Susanne M. Schennach, 2006. "Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments," CeMMAP working papers CWP17/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    12. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    13. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    14. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    15. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    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. Jean-Pierre Florens & James Heckman & Costas Meghir & Edward Vytlacil, 2002. "Instrumental variables, local instrumental variables and control functions," CeMMAP working papers CWP15/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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    Cited by:

    1. 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.
    2. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(4), pages 839-873, August.
    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. Yingyao Hu & Ji‐Liang Shiu, 2018. "Identification and estimation of semi‐parametric censored dynamic panel data models of short time periods," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 55-85, February.
    5. Fève, Frédérique & Florens, Jean-Pierre, 2014. "Non parametric analysis of panel data models with endogenous variables," Journal of Econometrics, Elsevier, vol. 181(2), pages 151-164.
    6. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    7. Liu, Chu-An & Tao, Jing, 2016. "Model selection and model averaging in nonparametric instrumental variables models," MPRA Paper 69492, University Library of Munich, Germany.
    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. Manuel Arellano & Stéphane Bonhomme, 2017. "Nonlinear Panel Data Methods for Dynamic Heterogeneous Agent Models," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 471-496, September.
    10. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    11. 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.
    12. Hu, Yingyao & Huang, Guofang & Sasaki, Yuya, 2020. "Estimating production functions with robustness against errors in the proxy variables," Journal of Econometrics, Elsevier, vol. 215(2), pages 375-398.
    13. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    14. Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
    15. 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.
    16. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    17. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    18. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    19. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    20. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    21. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    22. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. 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.
    24. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    25. Takahiro Hoshino & Keisuke Takahata, 2018. "Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition," Keio-IES Discussion Paper Series 2018-005, Institute for Economics Studies, Keio University.

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