Abstract

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.

摘要

为了追求效率，我们提出了一种构建最小二乘估计量的新方法，作为增强目标函数的最小化器，它明确考虑了误差项的可变性和由此产生的不确定性，以及可能存在的异方差。我们最初推导出一个不可行的估计量，然后我们使用来自第一步回归的普通最小二乘 (OLS) 残差进行近似，以获得可行的“HOLS”估计量。这个估计量的偏差可以忽略不计，在有限样本均方误差方面是一致的，并且在渐近效率方面优于 OLS，在包括同方差在内的所有怀疑情景下。在工具变量估计的情况下获得了类似的效率增益。理论结果伴随着支持它们的模拟。