A New Method for Uniform Subset Inference of Linear Instrumental Variables Models

Abstract

We propose a procedure for testing simple hypotheses on a subset of the structural parameters in linear instrumental variables models. Our test is valid uniformly over a large class of distributions allowing for identification failure and heteroskedasticity. The large-sample distribution of our test statistic is shown to depend on a key quantity that cannot be consistently estimated. Under our proposed procedure, we construct a confidence set for this key quantity and then maximize, over this confidence set, the appropriate quantile of the large-sample distribution of the test statistic. This maximum is used as the critical value and Bonferroni correction is used to control the overall size of the test. Monte Carlo simulations demonstrate the advantage of our test over the projection method in finite samples.