Instrumental Variable Estimation with Many Instruments Using Elastic-Net IV

Instrumental variables (IV) are commonly applied for identification of treatment effects and subsequent policy evaluation. The use of many informative instruments improves the estimation accuracy. However, dealing with high-dimensional sets of instrumental variables of unknown strength may be complicated and requires model selection or regularization of the first stage regression. Currently, lasso is established as one of the most popular regularization techniques relying on the assumption of approximate sparsity. I investigate the relative performance of the lasso and elastic-net estimators for fitting the first-stage as part of IV estimation. As elastic-net includes a ridge-type penalty in addition to a lasso-type penalty, it generally improves upon lasso in finite samples when correlations among the instrumental variables are not negligible. I show that IV estimators based on the lasso and elastic-net firststage estimates can be asymptotically equivalent. Via a Monte Carlo study I demonstrate the robustness of the sample-split elastic-net IV estimator to deviations from approximate sparsity, and to correlation among possibly high-dimensional instruments. Finally, I provide an empirical example that demonstrates potential improvement in estimation accuracy gained by the use of IV estimators based on elastic-net.