In predictive regressions with variables of unknown persistence, the use of extended IV (IVX) instruments leads to asymptotically valid inference. Under highly persistent regressors, the standard normal or chi-squared limiting distributions for the usual t and Wald statistics may, however, differ markedly from the actual finite-sample distributions which exhibit in particular noncentrality. Convergence to the limiting distributions is shown to occur at a rate depending on the choice of the IVX tuning parameters and can be very slow in practice. A characterization of the leading higher-order terms of the t statistic is provided for the simple regression case, which motivates finite-sample corrections. Monte Carlo simulations confirm the usefulness of the proposed methods.

中文翻译：

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预测回归中基于 IVX 的测试的有限样本大小控制

在具有未知持久性变量的预测回归中，使用扩展 IV (IVX) 工具会导致渐近有效的推理。在高度持久的回归变量下，通常的标准正态或卡方限制分布吨然而，Wald 和 Wald 统计可能与实际的有限样本分布明显不同，后者尤其表现出非中心性。显示收敛到极限分布的速度取决于 IVX 调整参数的选择，并且在实践中可能非常缓慢。的主要高阶项的表征吨为简单回归情况提供了统计数据，这激发了有限样本校正。蒙特卡罗模拟证实了所提出方法的有用性。