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.

翻译：颗粒工具变量（GIV）方法利用具有因子误差结构的面板数据构建工具变量，以估计即使控制潜在因子后仍存在内生性的结构性时间序列模型。我们从多个维度扩展了GIV方法。首先，我们将识别过程扩展到大规模N和大规模T的框架，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。其次，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。第三，我们证明了高维精度矩阵中的抽样误差在我们的估计算法中可忽略不计。第四，我们通过额外构建的工具变量对结构参数进行过度识别，从而提高了效率。蒙特卡洛证据支持了我们的渐近理论，对全球原油市场的应用也产生了新的结果。