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This study demonstrates the existence of a testable condition for theidentification of the causal effect of a treatment on an outcome inobservational data, which relies on two sets of variables: observed covariatesto be controlled for and a suspected instrument. Under a causal structurecommonly found in empirical applications, the testable conditional independenceof the suspected instrument and the outcome given the treatment and thecovariates has two implications. First, the instrument is valid, i.e. it doesnot directly affect the outcome (other than through the treatment) and isunconfounded conditional on the covariates. Second, the treatment isunconfounded conditional on the covariates such that the treatment effect isidentified. We suggest tests of this conditional independence based on machinelearning methods that account for covariates in a data-driven way andinvestigate their asymptotic behavior and finite sample performance in asimulation study. We also apply our testing approach to evaluating the impactof fertility on female labor supply when using the sibling sex ratio of thefirst two children as supposed instrument, which by and large points to aviolation of our testable implication for the moderate set of socio-economiccovariates considered.

Testing the identification of causal effects in observational data