  We propose a procedure which combines hierarchical clustering with a test of
overidentifying restrictions for selecting valid instrumental variables (IV)
from a large set of IVs. Some of these IVs may be invalid in that they fail the
exclusion restriction. We show that if the largest group of IVs is valid, our
method achieves oracle properties. Unlike existing techniques, our work deals
with multiple endogenous regressors. Simulation results suggest an advantageous
performance of the method in various settings. The method is applied to
estimating the effect of immigration on wages.
