Tommasi, D. and Zhang, L. (2024). Identifying program benefits when participation is misreported Journal of Applied Econometrics, 39(6):1123--1148.

In cases of noncompliance 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 nonconvex 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. This is an alternative IV estimand that is more robust in cases of noncompliance and nondifferential 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 naïve 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 United Kingdom.