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.
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