Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variables

We propose an instrumental variable (IV) selection procedure which combines the agglomerative hierarchical clustering method and the Hansen-Sargan overidentification test for selecting valid instruments for IV estimation from a large set of candidate instruments. Some of the instruments may be invalid in the sense that they may fail the exclusion restriction. We show that under the plurality rule, our method can achieve oracle selection and estimation results. Compared to the previous IV selection methods, our method has the advantages that it can deal with the weak instruments problem effectively, and can be easily extended to settings where there are multiple endogenous regressors and heterogenous treatment effects. We conduct Monte Carlo simulations to examine the performance of our method, and compare it with two existing methods, the Hard Thresholding method (HT) and the Confidence Interval method (CIM). The simulation results show that our method achieves oracle selection and estimation results in both single and multiple endogenous regressors settings in large samples when all the instruments are strong. Also, our method works well when some of the candidate instruments are weak, outperforming HT and CIM. We apply our method to the estimation of the effect of immigration on wages in the US.