Regularized LIML for many instruments
针对工具变量过多导致有限样本偏差的问题，提出三种正则化LIML估计量，在异方差下一致且渐近正态，同方差下达到半参数效率界，蒙特卡洛模拟和实证应用验证了其有效性。
The use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators. However, in finite samples, the inclusion of an excessive number of moments increases the bias. To solve this problem, we propose regularized versions of the limited information maximum likelihood (LIML) based on three different regularizations: Tikhonov, Landweber–Fridman, and principal components. Our estimators are consistent and asymptotically normal under heteroskedastic error. Moreover, they reach the semiparametric efficiency bound assuming homoskedastic error. We show that the regularized LIML estimators possess finite moments when the sample size is large enough. The higher order expansion of the mean square error (MSE) shows the dominance of regularized LIML over regularized two-staged least squares estimators. We devise a data driven selection of the regularization parameter based on the approximate MSE. A Monte Carlo study and two empirical applications illustrate the relevance of our estimators.