Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters

TL;DR

This paper develops wild bootstrap inference methods for instrumental variable regressions with few large clusters, ensuring valid size control and power under various identification conditions, supported by simulations and an empirical application.

Contribution

It introduces new wild bootstrap tests for IV regressions with limited clusters, handling weak and partial identification scenarios effectively.

Findings

Wild bootstrap Wald test controls size with strong identification.

Number of clusters needed for power against local alternatives.

Wild bootstrap Anderson-Rubin test controls size under weak identification.

Abstract

We study the wild bootstrap inference for instrumental variable regressions in the framework of a small number of large clusters in which the number of clusters is viewed as fixed and the number of observations for each cluster diverges to infinity. We first show that the wild bootstrap Wald test, with or without using the cluster-robust covariance estimator, controls size asymptotically up to a small error as long as the parameters of endogenous variables are strongly identified in at least one of the clusters. Then, we establish the required number of strong clusters for the test to have power against local alternatives. We further develop a wild bootstrap Anderson-Rubin test for the full-vector inference and show that it controls size asymptotically up to a small error even under weak or partial identification in all clusters. We illustrate the good finite sample performance of the new inference methods using simulations and provide an empirical application to a well-known dataset about US local labor markets.