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COVARIANCE-BASED ORTHOGONALITY TESTS FOR REGRESSORS WITH UNKNOWN PERSISTENCE

Published online by Cambridge University Press:  01 February 2009

Alex Maynard  and
Katsumi Shimotsu
Alex Maynard*
Affiliation:
University of Guelph
Katsumi Shimotsu*
Affiliation:
Queen's University
*
*Address correspondence to Alex Maynard, Department of Economics, McKinnan Building, University of Guelph, Guelph, ON N1G 2W1, Canada; e-mail: maynarda@uoguelph.ca.
†Katsumi Shimotsu, 229 Dunning Hall, Department of Economics, Queen's University, Kingston, ON K7L 3N6, Canada; e-mail: shimotsu@econ.queensu.ca.
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Abstract

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 63 - 116
Copyright
Copyright © Cambridge University Press 2009

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