Estimation and exclusion restrictions in clustered linear models

TL;DR

This paper introduces a new estimator for clustered linear models with high-dimensional controls and complex exclusion restrictions, enabling robust inference and accommodating within-cluster dependence, demonstrated through a large-scale fiscal intervention case.

Contribution

It develops a correctly centered internal instrument estimator that handles broad exclusion restrictions and dependence, extending dynamic panel methods to general clustered data.

Findings

Estimator is computationally tractable and has a simple leave-out interpretation.

Derived a central limit theorem for the quadratic form used in inference.

Proposed robust variance estimation and identification-robust inference procedures.

Abstract

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.