Gokul Gopalan Ramachandran

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 → ∞). 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.

We study efficiency and inference for granular instrumental variable estimators with a fixed number of cross-sectional units. We show that the efficient instrument equals the share-weighted granular instrument of Gabaix and Koijen plus an additional term, which leads to efficiency gains. When factor loadings are unknown, we provide conditions under which the loadings and the idiosyncratic error covariance matrix are identified while allowing for cross-sectional heteroscedasticity. We then propose GMM estimators whose inference accounts for the estimation of the factor structure. In an application to the global crude oil market, we provide estimates of oil demand and supply elasticities, which are robust to heteroscedasticity.

We study interactive fixed effects panel models with common time-series regressors whose slope coefficients vary across units. Such heterogeneity is common in applications. Existing estimators either impose common slopes or require additional structure to accommodate slope heterogeneity. We propose a computationally tractable semiparametric estimator based on kernel methods to separate the heterogeneous slopes from the factor structure. In this work in progress, we aim to derive the estimator's asymptotic distribution as both the cross section (N) and the time dimension (T) grow, and characterize how estimation error in the factor structure interacts with bandwidth choice.