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A Non-Parametric Test of Exogeneity

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Author Info

  • Richard Blundell
  • Joel L. Horowitz

Abstract

This paper presents a test for exogeneity of explanatory variables that minimizes the need for auxiliary assumptions that are not required by the definition of exogeneity. It concerns inference about a non-parametric function g that is identified by a conditional moment restriction involving instrumental variables (IV). A test of the hypothesis that g is the mean of a random variable Y conditional on a covariate X is developed that is not subject to the ill-posed inverse problem of non-parametric IV estimation. The test is consistent whenever g differs from E (Y ∣ X) on a set of non-zero probability. The usefulness of this new exogeneity test is displayed through Monte Carlo experiments and an application to estimation of non-parametric consumer expansion paths. Copyright 2007, Wiley-Blackwell.

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File URL: http://hdl.handle.net/10.1111/j.1467-937X.2007.00458.x
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Bibliographic Info

Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 74 (2007)
Issue (Month): 4 ()
Pages: 1035-1058

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Handle: RePEc:oup:restud:v:74:y:2007:i:4:p:1035-1058

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References

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  1. 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.
  2. Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
  3. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-99, September.
  4. 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.
  5. Peter Hall & Joel L. Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  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. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  8. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  9. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  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. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1139-1171, October.
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Citations

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Cited by:
  1. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
  2. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, 06.
  3. Paulo Parente & Richard Smith, 2012. "Exogeneity in semiparametric moment condition models," CeMMAP working papers CWP30/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Massacci, Daniele, 2013. "A variable addition test for exogeneity in structural threshold models," Economics Letters, Elsevier, vol. 120(1), pages 5-9.
  5. Joel Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers CWP37/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009. "Identification and Estimation by Penalization in Nonparametric Instrumental Regression," TSE Working Papers 09-076, Toulouse School of Economics (TSE).
  7. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
  8. Jinhyun Lee, . "A Consistent Nonparametric Bootstrap Test of Exogeneity," Discussion Paper Series, Department of Economics 201316, Department of Economics, University of St. Andrews.
  9. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.
  10. Joel Horowitz, 2007. "Comments on: Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(3), pages 459-461, December.
  11. Joel Horowitz, 2013. "Adaptive nonparametric instrumental variables estimation: empirical choice of the regularisation parameter," CeMMAP working papers CWP30/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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