Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variables

We propose a procedure that 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.