Instrumentality Tests Revisited

An instrument is a random variable that is uncorrelated with certain (unobserved) error terms and, thus, allows the identification of structural parameters in linear models. In nonlinear models, instrumental variables are useful for deriving bounds on causal effects. Few years ago, Pearl introduced a necessary test for instruments which permits researchers to identify variables that could not serve as instruments. In this paper, we extend Pearl’s result in several directions. In particular, we answer in the affirmative an open conjecture about the non-testability of instruments in models with unrestricted variables, and we devise new tests for models with discrete and continuous variables.