Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: Conventional critical values based on asymptotics often lead to severe size distortions; and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to over-rejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.
翻译:基于非临界值的测试是计量经济学实践中的一个重要技术。但是,选择正确的关键值并不简单:基于无症状的常规关键值往往会导致严重的体积扭曲;现有的调整,包括靴子装置,也是如此。为了避免这些问题,我们建议使用最小大小控制关键值,我们在本篇文章中为常用的测试统计所证明的这些关键值的一般存在情况。此外,为这些关键值的存在提供了易于核实的足够而且往往也是必要的条件。考虑到这些关键值的存在,这些关键值是明理的选择:较大的关键值导致不必要的功率损失,而较小的关键值导致无效假设下的过度反射,使虚假发现的可能性更大,因而是无效的。我们建议采用算法,以数字方式确定拟议的关键值,并在随附的软件中提供实施。最后,我们用数字方式研究拟议测试程序的行为,包括其功率特性。