Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters

We study the wild bootstrap inference for instrumental variable regressions with a small number of large clusters. We first show that the wild bootstrap Wald test 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. Second, we establish the conditions for the bootstrap tests 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 even under weak identification in all clusters. We illustrate their good performance using simulations and provide an empirical application to a well-known dataset about US local labor markets.
This version only contains results for linear IV regressions. The results for IVQR in the previous versions will be put in a separate paper