  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.
