Misclassification in Difference-in-differences Models

TL;DR

This paper examines how misclassification of treatment variables affects the identification and bias of difference-in-differences estimates, providing bounds and sensitivity analysis methods.

Contribution

It characterizes the bias introduced by treatment misclassification in DID models and offers practical bounds and empirical tools for sensitivity analysis.

Findings

DID estimand is biased and reflects a weighted average of two subpopulations.

Misclassification can lead to incorrect sign and attenuation of estimates.

Bounds on treatment effects can be derived when misclassification extent is known.

Abstract

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.