Efficiency gains in least squares estimation: A new approach
提出一种新的最小二乘估计方法，通过考虑误差项变异和异方差性来构造目标函数，得到比普通最小二乘更有效的估计量，并推广到工具变量估计。
In pursuit of efficiency, we propose a new way to construct least squares estimators, as the minimizers of an augmented objective function that takes explicitly into account the variability of the error term and the resulting uncertainty, as well as the possible existence of heteroskedasticity. We initially derive an infeasible estimator which we then approximate using Ordinary Least Squares (OLS) residuals from a first-step regression to obtain the feasible “HOLS” estimator. This estimator has negligible bias, is consistent and outperforms OLS in terms of finite-sample Mean Squared Error, but also in terms of asymptotic efficiency, under all skedastic scenarios, including homoskedasticity. Analogous efficiency gains are obtained for the case of Instrumental Variables estimation. Theoretical results are accompanied by simulations that support them.