Identifying Program Benefits When Participation Is Misreported

In cases of non-compliance with a prescribed treatment, estimates of causal effects typically rely on instrumental variables. However, when participation is also misreported, this approach can be severely biased. We provide an instrumental variable method that researchers can use to identify the true heterogeneous treatment effects in data that include both non-compliance and misclassification of treatment status. Our method can be used regardless of whether the treatment is misclassified because it is missing at random, missing not at random, or was generally mismeasured. We conclude with the use of a dedicated Stata command, ivreg2m, to assess the return on education in the United Kingdom.