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Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity

Ferman, Bruno and Pinto, Cristine (2015): Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity.

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Abstract

We show that existing inference methods used in Differences-in-Differences might not perform well with few treated groups and heteroskedastic errors. This is restrictive because variation in the number of observations per group inherently leads to heteroskedasticity in the group x time aggregate model. We provide theoretical justification and empirical evidence from placebo simulations with real datasets showing that this problem may remain relevant even in datasets with a large number of observations per group. We then derive an alternative inference method that works when there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Combined with feasible generalized least squares estimation, our test is uniformly most powerful under normality and a consistent estimator for the variance-covariance matrix, while it can still provide a test with correct size if the serial correlation is misspecified or errors are not normally distributed.

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