Conditions Sufficient to Infer Causal Relationships Using Instrumental Variables and Observational Data

Econometritions frequently believe that standard instrumental variables (IV) methods can prove causal relationships. We review the relevant formal causal inference literature, and we demonstrate that this belief is not justified. Couching the problem in terms of falsification, we describe the more stringent conditions that are sufficient to reject a null hypothesis concerning observed, but not deliberately manipulated, variables of the form $$H_{0}$$ H 0 : $$A\not \rightarrow B$$ A ↛ B in favor of an alternative hypothesis $$H_{A}$$ H A : $$A\rightarrow B$$ A → B , even given the possibility of causally related unobserved variables. Rejection of such an $$H_{0}$$ H 0 can rely on the availability of two observed and appropriately related instruments. We also characterize, using Monte Carlo simulations, the confidence that can be placed on such judgments for linearly-related, jointly normal random variables. While the researcher will have limited control over the confidence level of such tests, type I errors occur with a probability of less than 0.15 (often substantially less) across a wide range of circumstances. The power of the test is limited if there are but few observations available and the strength of correspondence among the variables is weak. We demonstrate the method by testing a hypothesis with critically important policy implications relating to a possible cause of childhood malnourishment.