Consider a parameter of interest, which can be consistently estimated under some conditions. Suppose also that we can at least partly test these conditions with specification tests. We consider the common practice of conducting inference on the parameter of interest conditional on not rejecting these tests. We show that if the tested conditions hold, conditional inference is valid but possibly conservative. This holds generally, without imposing any assumption on the asymptotic dependence between the estimator of the parameter of interest and the specification test.

翻译：考虑一个感兴趣的参数，该参数在某些条件下能够被一致估计。假设我们至少能够通过设定检验部分地检验这些条件。我们考察了在未拒绝这些检验的条件下对感兴趣参数进行推断的常见做法。我们证明，若被检验的条件成立，则条件推断是有效的，但可能趋于保守。这一结论具有普适性，无需对感兴趣参数的估计量与设定检验之间的渐近依赖性施加任何假设。