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A nonparametric test of exogeneity

  • Richard Blundell

    ()

    (Institute for Fiscal Studies and University College London)

  • Joel Horowitz

    ()

    (Institute for Fiscal Studies and Northwestern University)

This paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables. The function is nonparametric. It satisfies mild regularity conditions but is otherwise unknown. The paper presents test of the hypothesis that g is the mean of a random variable Y conditional on a covariate X . The need to test this hypothesis arises frequently in economics. The test does not require nonparametric instrumental-variables (IV) estimation of g and is not subject to the ill-posed inverse problem that nonparametric IV estimation entails. The test is consistent whenever g differs from the conditional mean function of Y on a set of non-zero probability. Moreover, the power of the test is arbitrarily close to 1 uniformly over a set of functions g whose distance from the conditional mean function is O(n-1/2), where is the sample size.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0415.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP15/04.

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Date of creation: Dec 2004
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Handle: RePEc:ifs:cemmap:15/04
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  1. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  2. 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.
  3. 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.
  4. 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.
  5. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  6. 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.
  7. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  8. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  9. 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.
  10. 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.
  11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  12. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-99, September.
  13. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
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