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Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors

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  • Severini, Thomas A.
  • Tripathi, Gautam

Abstract

Let Y=μ∗(X)+ε, where μ∗ is unknown and E[ε|X]≠0 with positive probability but there exist instrumental variables W such that E[ε|W]=0 w.p.1. It is well known that such nonparametric regression models are generally “ill-posed” in the sense that the map from the data to μ∗ is not continuous. In this paper, we derive the efficiency bounds for estimating certain linear functionals of μ∗ without assuming μ∗ itself to be identified.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 170 (2012)
Issue (Month): 2 ()
Pages: 491-498

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Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:491-498

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1349-82, November.
  2. Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(02), pages 258-278, April.
  3. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, Econometric Society, vol. 60(3), pages 567-96, May.
  4. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 453-464, March.
  5. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
  6. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, Econometric Society, vol. 71(6), pages 1795-1843, November.
  7. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, Elsevier, vol. 141(1), pages 5-43, November.
  8. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  9. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  10. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, Elsevier, vol. 102(1), pages 23-66, May.
  11. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP28/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, Econometric Society, vol. 75(6), pages 1613-1669, November.
  13. 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.
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Cited by:
  1. Laurent Davezies & Xavier d'Haultfoeuille, 2013. "Endogenous Attrition in Panels," Working Papers 2013-17, Centre de Recherche en Economie et Statistique.
  2. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP48/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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