Efficient Estimation with Many Weak Instruments Using Regularization Techniques
针对弱工具变量问题，提出通过增加工具变量数量并采用正则化技术来提升估计效率，证明正则化两阶段最小二乘和有限信息最大似然估计量的一致性和渐近正态性，模拟显示在弱工具变量下仍接近中位数无偏。
The problem of weak instruments is due to a very small concentration parameter. To boost the concentration parameter, we propose to increase the number of instruments to a large number or even up to a continuum. However, in finite samples, the inclusion of an excessive number of moments may be harmful. To address this issue, we use regularization techniques as in Carrasco (2012) and Carrasco and Tchuente (2014). We show that normalized regularized two-stage least squares (2SLS) and limited maximum likelihood (LIML) are consistent and asymptotically normally distributed. Moreover, our estimators are asymptotically more efficient than most competing estimators. Our simulations show that the leading regularized estimators (LF and T of LIML) work very well (are nearly median unbiased) even in the case of relatively weak instruments. An application to the effect of institutions on output growth completes the article.