Replication Data for Post-Instrument Bias

When using instrumental variables, researchers often assume that causal effects are only identified conditional on covariates. We show that the role of these covariates is often unclear and that there exists confusion regarding their ability to mitigate violations of the exclusion restriction. We explain when and how existing adjustment strategies may lead to ``post-instrument'' bias. We then discuss assumptions that are sufficient to identify various treatment effects when adjustment for post-instrument variables is required. In general, these assumptions are highly restrictive, albeit they sometimes are testable. We also show that other existing tests are possibly misleading. Then, we introduce a sensitivity analysis that uses information on variables influenced by the instrument to gauge the effect of potential violations of the exclusion restriction. We illustrate it using a published study and summarize our results in easy-to-understand guidelines.