identifying program benefits when participation is misreported (replication data)

In cases of non-compliance with an assigned treatment, estimates of causal effects typically rely on instrumental variables (IV). However, when participation is also misreported, the IV estimand may become a non-convex combination of local average treatment effects that fails to satisfy even a minimal condition for being causal. The aim of our paper is to generalize the MR-LATE approach (Calvi, Lewbel and Tommasi, 2022). This is an alternative IV estimand that is more robust in cases of non-compliance and non-differential misclassification of the treatment variable. Our generalization is threefold: first, we incorporate discrete and multiple-discrete instrument(s); second, we consider the use of instrument(s) under a weaker, partial monotonicity condition; third, we provide a general inferential procedure. Under relatively stringent assumptions, MR-LATE is either identical to the IV estimand or less biased than the na\"ive IV estimand. Under less stringent assumptions, the MR-LATE estimand can identify the sign of the IV estimand. We conclude with the use of a dedicated Stata command, ivreg2m, to assess the return on education in the U.K.