  The difference-in-differences (DID) design is one of the most popular methods
used in empirical economics research. However, there is almost no work
examining what the DID method identifies in the presence of a misclassified
treatment variable. This paper studies the identification of treatment effects
in DID designs when the treatment is misclassified. Misclassification arises in
various ways, including when the timing of a policy intervention is ambiguous
or when researchers need to infer treatment from auxiliary data. We show that
the DID estimand is biased and recovers a weighted average of the average
treatment effects on the treated (ATT) in two subpopulations -- the correctly
classified and misclassified groups. In some cases, the DID estimand may yield
the wrong sign and is otherwise attenuated. We provide bounds on the ATT when
the researcher has access to information on the extent of misclassification in
the data. We demonstrate our theoretical results using simulations and provide
two empirical applications to guide researchers in performing sensitivity
analysis using our proposed methods.
