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Abstract

This paper examines how to implement difference-in-differences techniques when there are time-varying covariates. Two-way fixed effects (TWFE) models are popular in the current literature but have been shown to have biased results when solving models with time-varying covariates. This paper presents conditions under which researchers can still recover the average treatment effect of the treated (ATT) of some treatment when there are time-varying covariates and provides doubly robust estimators that work with these assumptions. In addition, the paper offers an example for how to use imputation techniques to estimate difference-in-differences models, using a data set on stand-your-ground laws from Cheng and Hoekstra, 2013. Imputation involves using untreated data to make predictions on the untreated potential outcomes of treated units. The paper also provides a proof for the asymptotic normality of imputation techniques in both the two-period case and the multiple-period case.

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