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.