  We propose a robust hypothesis testing procedure for the predictability of
multiple predictors that could be highly persistent. Our method improves the
popular extended instrumental variable (IVX) testing (Phillips and Lee, 2013;
Kostakis et al., 2015) in that, besides addressing the two bias effects found
in Hosseinkouchack and Demetrescu (2021), we find and deal with the
variance-enlargement effect. We show that two types of higher-order terms
induce these distortion effects in the test statistic, leading to significant
over-rejection for one-sided tests and tests in multiple predictive
regressions. Our improved IVX-based test includes three steps to tackle all the
issues above regarding finite sample bias and variance terms. Thus, the test
statistics perform well in size control, while its power performance is
comparable with the original IVX. Monte Carlo simulations and an empirical
study on the predictability of bond risk premia are provided to demonstrate the
effectiveness of the newly proposed approach.
