Difference-in-Differences with a Misclassified Treatment

This paper studies identification and estimation of the average treatment effect of a latent treated subpopulation in difference-in-difference designs when the observed treatment is differentially (or endogenously) mismeasured for the truth. Common examples include misreporting and mistargeting. We propose a twostep estimator which corrects for the empirically common phenomenon of onesided misclassification in the treatment status. The solution uses a single exclusion restriction embedded in a partial observability probit to point-identify the latent parameter. We demonstrate the method by revisiting two large-scale national programs in India; one where pension benefits are under-reported and second where the program is mistargeted.