Outlier robust inference in the instrumental variable model with applications to causal effects

The Anderson-Rubin (AR) test is an important method that allows for reliable inference in the instrumental variable model when the instruments are weak. Yet, the robustness properties of this test have not been formally studied. As it turns out that the AR test is not robust to outliers, we show how to construct an outlier robust alternative—the robust AR test. We investigate the robustness properties of the robust AR test and show that the robust AR statistic asymptotically follows a chi-square distribution. The theoretical results are illustrated by a simulation study. Finally, we apply the robust AR test to three different case studies that are affected by different types of outliers.