Difference-in-Differences with a Misclassified Treatment

Abstract: This paper studies identification and estimation of the average treatment effect on the treated (ATT) in difference-in-difference (DID) designs when the variable that classifies individuals into treatment and control groups (treatment status, D) is endogenously misclassified. We show that misclassification in D hampers consistent estimation of ATT because 1) it restricts us from identifying the truly treated from those misclassified as being treated and 2) differential misclassification in counterfactual trends may result in parallel trends being violated with D even when they hold with the true but unobserved D*. We propose a solution to correct for endogenous one-sided misclassification in the context of a parametric DID regression which allows for considerable heterogeneity in treatment effects and establish its asymptotic properties in panel and repeated cross section settings. Furthermore, we illustrate the method by using it to estimate the insurance impact of a large-scale in-kind food transfer program in India which is known to suffer from large targeting errors.