Misclassified Treatment Status and Treatment Effects: An Application to Returns to Education in the United Kingdom

We study the impact of misreported treatment status on the estimation of causal treatment effects, focusing on applications where no additional information or repeated measurements are available. We first characterize the bias introduced by misclassification on the average treatment effect on the treated (ATT) under a conditional independence assumption, in both a binary and a multiple-treatment setting. We find that the bias of matching-type estimators computed from misclassified data cannot in general be signed. We subsequently provide easily implementable methods to bound the ATT of interest semiparametrically, in particular allowing for very general forms of impact heterogeneity and of the no-treatment outcome equations, as well as for some dependence of the misreporting probabilities on individual characteristics. The empirical problem that motivates our paper is the estimation of the wage returns to a number of educational qualifications in the United Kingdom, allowing for misreporting in attainment. We investigate the sensitivity of the raw estimates to the presence of misclassification and explore the identification power of plausible restrictions on the nature and extent of misclassification. We show that the resulting bounds are sometimes wide but generally point to reasonable ranges of positive values for average returns to schooling among the schooled. For the range of educational qualifications considered, we further show that the claim sometimes made that measurement error bias roughly cancels out selection bias is not supported. More generally, our results show that under relatively mild restrictions, we can obtain strong conclusions regarding our questions of interest.