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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)

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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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Publisher 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;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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    Other versions:
  8. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
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    Other versions:
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  16. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July. [Downloadable!] (restricted)
  17. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-223, September. [Downloadable!] (restricted)
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    Other versions:
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