Misclassified Treatment Status and Treatment Effects: An Application to Returns to Education in the U.K.

In this paper we study the impact of misreported treatment status on the estimation of causal treatment effects. We characterise the bias introduced by misclassification on the average treatment effect on the treated under the assumption of selection on observables. Although the bias of matching-type estimators computed from misclassified data cannot in general be signed, we show that the bias is most likely to be downward if misclassification does not depend on variables entering the selection-on-observables assumption, or only depends on such variables via the propensity score index. We extend the framework to multiple treatments. We provide results to bound the returns to a number of educational qualifications in the UK semi-parametrically, and by using the unique nature of our data we assess the plausibility for the two biases from measurement error and from omitted variables to cancel out.