Bootstrap Methods for Inference with Cluster Sample IV Models

Microeconomic data often have within-cluster dependence. This dependence affects standard error estimation and inference in regression models, including the instrumental variables model. Standard corrections assume that the number of clusters is large, but when this is not the case, Wald and weak-instrument-robust tests can be severely over-sized. We examine the use of bootstrap methods to construct appropriate critical values for these tests when the number of clusters is small. We find that variants of the wild bootstrap perform well and reduce absolute size bias significantly, independent of instrument strength or cluster size. We also provide guidance in the choice among possible weak-instrument-robust tests when data have cluster dependence. These results are applicable to fixed-effects panel data models.