Bounds with Imperfect Instruments: Leveraging the Implicit Assumption of Intransitivity in Correlations

Instrumental variables (IV) is an indispensable tool for establishing causal relationships between variables. Recent work has focused on improving bounds for cases when an ideal instrument does not exist. We leverage a principle, "Intransitivity in Correlations," related to an under-utilized property from the statistics literature. From this principle, it is straightforward to obtain new bounds. We argue that these new theoretical bounds become increasingly useful as instruments become increasingly weak or invalid.