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On The Completeness Condition In Nonparametric Instrumental Problems

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  • D’Haultfoeuille, Xavier

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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 03 (June)
Pages: 460-471

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Handle: RePEc:cup:etheor:v:27:y:2011:i:03:p:460-471_00

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  1. Guido W. Imbens & Whitney K. Newey, 2002. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," NBER Technical Working Papers 0285, National Bureau of Economic Research, Inc.
  2. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  3. 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.
  4. 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.
  5. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  7. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  8. Jean-Pierre Florens & James J. Heckman & Costas Meghir & Edward J. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," NBER Working Papers 14002, National Bureau of Economic Research, Inc.
  9. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  10. 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.
  11. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
  12. Yingyao Hu & Susanne 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.
  13. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  14. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
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Cited by:
  1. Pierre-Andre Chiappori & Ivana Komunjer & Dennis Kristensen, 2011. "Nonparametric Identification and Estimation of Transformation Models," CAM Working Papers 2011-01, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  2. Senay Sokullu, 2012. "Nonparametric Estimation of Semiparametric Transformation Models," Bristol Economics Discussion Papers 12/625, Department of Economics, University of Bristol, UK.
  3. Fève, Frédérique & Florens, Jean-Pierre, 2009. "The Practice of Non Parametric Estimation by Solving Inverse Problems: The Example of Transformation Models," IDEI Working Papers 615, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Florens, Jean-Pierre & Simon, Guillaume, 2010. "Endogeneity and Instrumental Variables in Dynamic Models," TSE Working Papers 10-178, Toulouse School of Economics (TSE).
  5. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, Department of Economics, University of Bristol, UK.
  6. Donald W.K. Andrews, 2011. "Examples of L^2-Complete and Boundedly-Complete Distributions," Cowles Foundation Discussion Papers 1801, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
  9. Florens, Jean-Pierre & Simon, Guillaume, 2010. "Endogeneity and Instrumental Variables in Dynamic Models," IDEI Working Papers 624, Institut d'Économie Industrielle (IDEI), Toulouse.
  10. Fève, Frédérique & Florens, Jean-Pierre, 2009. "The Practice of Non Parametric Estimation by Solving Inverse Problems: The Example of Transformation Models," TSE Working Papers 10-169, Toulouse School of Economics (TSE).
  11. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Cowles Foundation Discussion Papers 1650RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2011.
  12. Yingyao Hu & Ji-Liang Shiu, 2011. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Economics Working Paper Archive 581, The Johns Hopkins University,Department of Economics.

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