Identifying program benefits when participation is misreported

In cases of noncompliance with an assigned treatment, estimates of causaleffects typically rely on instrumental variables (IV). However, when participa-tion is also misreported, the IV estimand may become a nonconvex combinationof local average treatment effects that fails to satisfy even a minimal condition forbeing causal. The aim of our paper is to generalize the MR-LATE approach. Thisis an alternative IV estimand that is more robust in cases of noncompliance andnondifferential misclassification of the treatment variable. Our generalizationis threefold: First, we incorporate discrete and multiple-discrete instrument(s);second, we consider the use of instrument(s) under a weaker, partial mono-tonicity condition; third, we provide a general inferential procedure. Underrelatively stringent assumptions, MR-LATE is either identical to the IV estimandor less biased than the naïve IV estimand. Under less stringent assumptions,the MR-LATE estimand can identify the sign of the IV estimand. We concludewith the use of a dedicated Stata command, ivreg2m, to assess the return oneducation in the United Kingdom.