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.

翻译：本文针对可能具有高度持久性的多个预测变量，提出了一种稳健的假设检验程序。我们的方法改进了广泛使用的扩展工具变量（IVX）检验方法（Phillips and Lee, 2013; Kostakis et al., 2015），除了解决Hosseinkouchack和Demetrescu（2021）中发现的两个偏差效应外，还发现并处理了方差扩大效应。研究表明，两类高阶项会在检验统计量中引发这些扭曲效应，导致单侧检验和多项预测回归检验出现显著的过度拒绝。改进后的基于IVX的检验包含三个步骤，以解决上述所有关于有限样本偏差项和方差项的问题。因此，该检验统计量在尺寸控制方面表现良好，而其势性能与原IVX方法相当。通过蒙特卡洛模拟和关于债券风险溢价可预测性的实证研究，证明了新提出方法的有效性。