A Joint Test of Unconfoundedness and Common Trends

ABSTRACT We introduce an overidentification test of two alternative assumptions to identify the average treatment effect on the treated in a two‐period panel data setting: unconfoundedness and common trends. Under unconfoundedness, treatment assignment and post‐treatment outcomes are independent, conditional on control variables and pre‐treatment outcomes, which motivates including the pre‐treatment outcomes in the set of controls. Under common trends, the trend and the treatment assignment are independent, conditional on control variables, motivating a Difference‐in‐Differences (DiD) approach. Given the non‐nested nature of these assumptions and their often ambiguous plausibility in empirical settings, we propose a joint test using a doubly robust statistic that can be combined with machine learning to control for observed confounders in a data‐driven manner. We discuss causal models satisfying either common trends, unconfoundedness, or both assumptions. Applying the proposed method to publicly available datasets, we find that the test rejects the null hypothesis in two out of four cases.