Optimal Linear Instrumental Variables Approximations
Optimal Linear Instrumental Variables Approximations
复制标题
最优线性工具变量近似
DOI：
10.1016/j.jeconom.2020.05.002
复制
发表时间：
2018
影响因子：
6.3
通讯作者：
Wei Li
中科院分区：
文献类型：
--
作者：
J. Escanciano;Wei Li
本文研究了结构回归函数的最佳线性逼近的辨识和估计问题。线性近似中的参数称为最优线性工具变量近似(Oliva)。本文证明了在线性模型中，Oliva上标准推断的必要条件也是IV估计存在的充分条件。第四次估计中的工具未知，也可能无法确定。提出了一种基于Tikhonov正则化的两步IV(TSIV)估计器，该估计器可以用标准回归程序实现。我们建立了TSIV估计量的渐近正态分布，假设工具既不是完备性，也不是可识别性。作为我们分析的一个重要应用，我们针对线性结构模型的错误说明，证明了经典的Hausman检验的外生性。我们还讨论了加权最小二乘准则的推广。蒙特卡罗模拟表明，所提出的推论具有很好的有限样本性能。最后，在一个使用美国数据估计跨期替代弹性(EIS)的实证应用中，我们得到的TSIV估计比标准IV估计的要大得多，我们的稳健Hausman检验未能拒绝实际利率外部性的零假设。
This paper studies the identification and estimation of the optimal linear approximation of a structural regression function. The parameter in the linear approximation is called the Optimal Linear Instrumental Variables Approximation (OLIVA). This paper shows that a necessary condition for standard inference on the OLIVA is also sufficient for the existence of an IV estimand in a linear model. The instrument in the IV estimand is unknown and may not be identified. A Two-Step IV (TSIV) estimator based on Tikhonov regularization is proposed, which can be implemented by standard regression routines. We establish the asymptotic normality of the TSIV estimator assuming neither completeness nor identification of the instrument. As an important application of our analysis, we robustify the classical Hausman test for exogeneity against misspecification of the linear structural model. We also discuss extensions to weighted least squares criteria. Monte Carlo simulations suggest an excellent finite sample performance for the proposed inferences. Finally, in an empirical application estimating the elasticity of intertemporal substitution (EIS) with US data, we obtain TSIV estimates that are much larger than their standard IV counterparts, with our robust Hausman test failing to reject the null hypothesis of exogeneity of real interest rates.