Instrument-based estimation with binarised treatments: issues and tests for the exclusion restriction

When estimating local average and marginal treatment effects using instrumental variables (IVs), multivalued endogenous treatments are frequently converted to binary measures, supposedly to improve interpretability or policy relevance. Such binarisation introduces a violation of the IV exclusion if (a) the IV affects the multivalued treatment within support areas below and/or above the threshold and (b) such IV-induced changes in the multivalued treatment affect the outcome. We discuss assumptions that satisfy the IV exclusion restriction with a binarised treatment and permit identifying the average effect of (a) the binarised treatment and (b) unit-level increases in the original multivalued treatment among specific compliers. We derive testable implications of these assumptions and propose tests which we apply to the estimation of the returns to college graduation instrumented by college proximity.