Estimation and exclusion restrictions in clustered linear models

We study linear regression models with clustered data, high-dimensional controls, and intricate exclusion restrictions. We propose a correctly centered internal instrument IV estimator that accommodates a broad class of exclusion restrictions and allows within-cluster dependence. The estimator admits a simple leave-out interpretation and is computationally tractable. We derive a central limit theorem for the associated quadratic form and propose a robust variance estimator. We also develop identification-robust inference procedures. Our framework extends dynamic panel methods to general clustered settings. We illustrate the approach in a large-scale fiscal intervention in rural Kenya, where spatial interference generates the exclusion-restriction pattern.