CONDITIONAL LIKELIHOOD RATIO TEST WITH MANY WEAK INSTRUMENTS
将Moreira(2003)的条件似然比检验扩展到误差方差未知且存在多弱工具变量的工具变量回归模型，提出修正的临界值函数，证明其渐近有效性，并通过模拟展示良好有限样本性质。
This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003, Econometrica 71(4), 1027-–1048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that our modified test achieves asymptotic validity under many weak instruments asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003, Econometrica 71(4), 1027-–1048). A simulation study illustrates the desirable finite sample properties of our test.