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

Juan Carlos Escanciano and Kyungchul Song ()
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Kyungchul Song: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, 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.

Keywords: Average Partial Effects; Omnibus tests; Optimal tests; Semi- parametric Efficiency; Efficient Score (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2007-01-29
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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