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 tests can either over-reject or under-reject and weak instrument robust tests can over-reject.
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 a variant of the wild bootstrap performs well and reduces absolute size bias significantly, even with a small number of clusters. We also provide guidance in the choice among possible weak instrument robust tests when data have cluster dependence. These results should extend to fixed effect panel data models.
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Contact :Gopalan Nair (08) 6488 3377; [email protected]