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Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects

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Author Info

  • Juan Carlos Escanciano

    ()
    (Department of Economics, Indiana University)

  • Kyungchul Song

    ()
    (Department of Economics, University of Pennsylvania)

Abstract

This paper proposes an asymptotically optimal specification test of single-index models against alternatives that lead to inconsistent estimates of a covariate’s average partial effect. The proposed tests are relevant when a researcher is concerned about a potential violation of the single-index restriction only to the extent that the estimated average partial effects suffer from a nontrivial bias due to the misspecifcation. Using a pseudo-norm of average partial effects deviation and drawing on the minimax approach, we find a nice characterization of the least favorable local alternatives associated with misspecified average partial effects as a single direction of Pitman local alternatives. Based on this characterization, we define an asymptotic optimal test to be a semiparametrically efficient test that tests the significance of the least favorable direction in an augmented regression formulation, and propose such a one that is asymptotically distribution-free, with asymptotic critical values available from the X 2/1 table. The testing procedure can be easily modified when one wants to consider average partial effects with respect to binary covariates or multivariate average partial effects.

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File URL: http://economics.sas.upenn.edu/system/files/working-papers/07-005.pdf
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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 07-005.

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Length: 47 pages
Date of creation: 29 Jan 2007
Date of revision:
Handle: RePEc:pen:papers:07-005

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Related research

Keywords: Average Partial Effects; Omnibus tests; Optimal tests; Semi- parametric Efficiency; Efficient Score;

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References

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  1. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
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  18. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
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  22. 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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Cited by:
  1. Kyungchul Song, 2007. "Testing Conditional Independence via Rosenblatt Transforms," PIER Working Paper Archive 07-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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