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.

翻译：暂无翻译