完整子集平均与众多工具变量
Complete Subset Averaging with Many Instruments
AI总结：
本文提出一种基于完整子集平均的两阶段最小二乘法估计量，通过优化子集大小提升估计精度，实验证明在工具变量相关时具有更优性能。
摘要：
我们提出了一种两阶段最小二乘法(2SLS)估计量，其第一阶段是对可用工具变量中k个完整子集进行等权平均，我们称之为完整子集平均( CSA) 2SLS。通过Nagar(1959)展开推导出近似均方误差(MSE)作为子集大小k的函数。子集大小通过最小化样本近似MSE的样本对应量来选择。我们证明该方法在不同子集大小的估计量中达到渐近最优。为处理平均过多个增长的无关工具变量，我们将近似MSE推广发现最优k大于其他情况。广泛的模拟实验显示，当工具变量相关时，CSA-2SLS估计量优于其他估计量。作为实证说明，我们估计Berry, Levinsohn, and Pakes(1995)中的逻辑需求函数，并发现CSA-2SLS估计量比其他估计量更受经济理论支持。
英文摘要：
We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with $k$ instruments among $K$ available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size $k$ by the Nagar (1959) expansion. The subset size is chosen by minimizing the sample counterpart of the approximate MSE. We show that this method achieves the asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalize the approximate MSE to find that the optimal $k$ is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry, Levinsohn, and Pakes (1995) and find the CSA-2SLS estimate is better supported by economic theory than the alternative estimates.
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