Juan Carlos Escanciano
Published: 2007
Total Pages: 47
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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 misspecification. 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 amp;χ 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.