Granular Instrumental Variables in Large Panels: Identification and Inference Across Strong, Nearly Weak, and Weak GIV
Granular Instrumental Variables (GIV), introduced by Gabaix and Koijen (2024), use idiosyncratic shocks to large units as instruments for aggregate endogenous variables. I develop asymptotic theory for GIV in large panels where both the cross section and time series grow (\(N,T\to\infty\)). I make two main contributions. First, I show that estimating the individual shocks used to construct the granular instrument 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. I derive corrected inference. Second, I characterize how instrument strength changes as \(N\) grows, yielding strong, nearly-weak, and weak regimes. In the newly characterized nearly-weak regime, the instrument vanishes asymptotically but the estimator remains consistent and asymptotically normal, at a slower rate, when \(T\) grows sufficiently fast relative to \(N\). I apply the theory to estimate short-run supply and demand elasticities for crude oil, copper, and natural gas.