Regularization based Anderson Rubin tests for many instruments

This paper studies the asymptotic validity of the regularized Anderson Rubin (AR) tests in linear models with large number of instruments. The regularized AR tests use informationreduction methods to provide robust inference in instrumental variable (IV) estimation for data rich environments. We derive the asymptotic properties of the tests. Their asymptotic distribution depend on unknown nuisance parameters. A bootstrap method is used to obtain more reliable inference. The regularized tests are robust to many moment conditions in the sense that they are valid for both few and many instruments, and even for more instruments than the sample size. Our simulations show that the proposed AR tests work well and have better performance than competing AR tests when the number of instruments is very large. The usefulness of the regularized tests is shown by proposing confidence intervals for the Elasticity of Intertemporal Substitution (EIS).