Before revision: In this note we prove Pearl's conjecture , showing that the exclusion restriction of an instrument  cannot be tested without structural assumptions in general instrumental variable models with a continuously distributed endogenous variable .
After revision: Instrumental variables have informed the research on causal inference in economics over the last century. Despite their ubiquity and decided usefulness, the current consensus in the literature is that the validity of an instrument cannot be tested, particularly when the treatment is continuous. This note addresses this issue in two ways. As a first contribution, it presents a proof confirming the conjecture in Pearl (1995) , showing that the exclusion restriction of an instrument cannot be tested without structural assumptions in general instrumental variable models with a continuously distributed endogenous variable .