Instrument Validity Tests with Causal Trees: With an Application to the Same-sex Instrument

The use of instrumental variables (IVs) to identify causal effects is widespread in empirical economics, but it is fundamentally impossible to proof their validity. However, assumptions sufficient for the identification of local average treatment effects (LATEs) jointly generate necessary conditions in the observed data that allow to refute an IV's validity. Suitable tests exist, but they may not be able to detect even severe violations of IV validity in practice. In this paper, we employ recently developed machine learning tools as data-driven improvements for these tests. Specifically, we use the causal tree (CT) algorithm from Athey and Imbens (2016) to directly search the covariate space for violations of the LATE assumptions. The new approach is applied to the sibling sex composition instrument in census data from China and the United States. We expect that, because of son preferences, the siblings sex instrument is invalid in the Chinese context. However, existing IV validity tests are unable to detect violations, while our CT based procedure does.