A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments
针对弱工具变量问题，提出在控制函数表示中使用L2范数正则化来改进两阶段最小二乘估计，通过正则化参数得到高阶近似并减少有限样本偏差，蒙特卡洛模拟显示其与Fuller有限信息最大似然估计等方法的比较。
Abstract The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O ( n ) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O ( n ), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.