Bounding program benefits when participation is misreported

Instrumental variables (IV) are commonly used to estimate treatment effects in case of noncompliance. However, program participation is often misreported in survey data and standard techniques are not sufficient to point identify and consistently estimate the effects of interest. In this paper, we show that the identifiable IV estimand that ignores treatment misclassification is a weighted average of local average treatment effects with weights that can also be negative. This is troublesome because it may fail to deliver a correct causal interpretation, and this is true even if all the weights are non-negative. Therefore, we provide three IV strategies to bound the program benefits when both noncompliance and misreporting are present. We demonstrate the gain of identification power achieved by leveraging multiple exogenous variations when discrete or multiple-discrete IVs are available. At last, we use our new Stata command, ivbounds, to study the benefits of participating in the 401(k) pension plan on savings.