Difference-in-Differences With a Misclassified Treatment

Abstract

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 two-step estimator that corrects for the empirically common phenomenon of one-sided 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 underreported and second where the program is mistargeted.