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This note investigates the numerical performance of an existing asymptotic test for the null hypothesis of equality between the average treatment effect (ATE) and the group fixed-effect (FE) estimands based on the standardized difference between ATE and FE estimators. It shows that this test has a size distortion. This distortion has implications to empirical economic research. It can lead to erroneously confirm the relevance of heterogeneous responses to policy interventions.

On the Size Distortion of a Test for Equality between the ATE and FE Estimands