Weak identification with many instruments
综述了单个内生回归元下多工具变量的估计与推断方法，讨论了弱识别稳健检验，并提出了新的刀切拉格朗日乘子检验，适用于异方差和多个外生回归元的情形。
Summary Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ‘technical’ instruments and more recently from the empirical strategy of ‘judge design’. This paper surveys and summarises ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak identification robust inference under heteroskedasticity. We establish new results for a jack-knifed version of the Lagrange Multiplier test statistic. Furthermore, we extend the weak identification robust tests to settings with both many exogenous regressors and many instruments. We propose a test that properly partials out many exogenous regressors while preserving the re-centring property of the jack-knife. The proposed tests have correct size and good power properties.