On the relevance of weaker instruments
研究了当存在比原始矩条件更弱的额外矩条件时，标准GMM估计量的渐近性质，发现这些弱条件能提高估计效率，且Hansen J检验能有效检测无效矩导致的虚假识别，其检验功效随额外条件变弱而增强。
We study the asymptotic properties of the standard GMM estimator when additional moment restrictions, weaker than the original ones, are available. We provide conditions under which these additional weaker restrictions improve the efficiency of the GMM estimator. To detect “spurious” identification that may come from invalid moments, we rely on the Hansen J-test that assesses the compatibility between existing restrictions and additional ones. Our simulations reveal that the J-test has good power properties and that its power increases with the weakness of the additional restrictions. Our theoretical characterization of the J-test provides some intuition for why that is.