高维粒度工具变量的推断理论
Inferential Theory for Granular Instrumental Variables in High Dimensions
AI总结：
本文在高维大N大T框架下扩展粒度工具变量方法，处理未知因子与载荷并构造额外工具变量实现过度识别，蒙特卡洛模拟和全球原油市场应用验证了理论有效性。
摘要：
粒度工具变量（GIV）方法利用具有因子误差结构的面板数据来构造工具变量，从而即使在控制潜在因子之后，也能估计存在内生性的结构时间序列模型。我们从多个维度扩展了GIV方法。第一，我们将识别程序扩展到大N和大T框架，该框架依赖于N个截面单元规模分布的渐近赫芬达尔指数。第二，我们将因子和载荷均视为未知，并证明在考虑结构参数的极限分布时，估计工具变量和因子中的抽样误差可以忽略不计。第三，我们证明在我们的估计算法中，高维精度矩阵中的抽样误差可以忽略不计。第四，我们利用额外构造的工具变量对结构参数进行过度识别，从而带来效率增益。本文给出了蒙特卡洛证据以支持我们的渐近理论，并将其应用于全球原油市场，得到了新的结果。
英文摘要：
The Granular Instrumental Variables (GIV) methodology exploits panels with factor error structures to construct instruments to estimate structural time series models with endogeneity even after controlling for latent factors. We extend the GIV methodology in several dimensions. First, we extend the identification procedure to a large $N$ and large $T$ framework, which depends on the asymptotic Herfindahl index of the size distribution of $N$ cross-sectional units. Second, we treat both the factors and loadings as unknown and show that the sampling error in the estimated instrument and factors is negligible when considering the limiting distribution of the structural parameters. Third, we show that the sampling error in the high-dimensional precision matrix is negligible in our estimation algorithm. Fourth, we overidentify the structural parameters with additional constructed instruments, which leads to efficiency gains. Monte Carlo evidence is presented to support our asymptotic theory and application to the global crude oil market leads to new results.
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