On the size distortion of tests after an overidentifying restrictions pretest
在线性工具变量模型中，研究了先进行过度识别约束检验再进行第二阶段假设检验的两阶段检验的规模扭曲问题，推导了渐近规模的下界，发现该下界可能高达1减去预检验名义规模。
SUMMARY In the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two‐stage hypothesis test that uses a test of overidentifying restrictions (OR) in the first stage. We derive a lower bound for the asymptotic size of the two‐stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 − ε P , where ε P is the pretest nominal size, for a parameter space that allows for local non‐exogeneity of the instruments but rules out weak instruments. Copyright © 2011 John Wiley & Sons, Ltd.