Choosing the Number of Instruments
推导了最小化均方误差的准则，用于选择工具变量集，适用于2SLS、LIML和偏差调整的2SLS估计量，蒙特卡洛实验和实际应用表明该方法能改善估计性能。
Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross-section applications. In this paper we address this problem by deriving simple mean-square error criteria that can be minimized to choose the instrument set. We develop these criteria for two-stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean-square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.