Granular Instrumental Variables in Large Panels: Identification and Inference Across Strong, Nearly Weak, and Weak GIV

I develop asymptotic theory for Granular Instrumental Variables (GIV) in large panels with both $N$ and $T$ growing. The granular instrument is constructed from individual shocks that must be estimated from the panel. I show that this estimation has a first-order effect on the asymptotic variance of the GIV estimator. Existing methods do not account for this effect, leading to incorrect standard errors and invalid inference. I derive corrected standard errors that deliver valid inference. I also characterize how instrument strength changes as $N$ grows. This yields strong, nearly-weak, and weak regimes for GIV. In particular, I identify a previously uncharacterised nearly-weak regime in which the instrument vanishes asymptotically, but GIV remains valid. If $T$ grows sufficiently fast relative to $N$, the estimator remains consistent and asymptotically normal at a rate slower than $\sqrt{T}$. When $N$ and $T$ grow proportionally, the estimator instead exhibits standard weak-instrument behavior. I apply the theory to estimate short-run demand and supply elasticities for copper, natural gas, and crude oil. Across the six elasticities, accounting for instrument estimation changes standard errors by up to a fifth.