On the testability of common trends in panel data without placebo periods

We demonstrate and discuss the testability of the common trend assumption imposed in Difference-in-Differences (DiD) estimation in panel data when not relying on multiple pre-treatment periods for running placebo tests. Our testing approach involves two steps: (i) constructing a control group of non-treated units whose pre-treatment outcome distribution matches that of treated units, and (ii) verifying if this control group and the original non-treated group share the same time trend in average outcomes. Testing is motivated by the fact that in several (but not all) panel data models, a common trend violation across treatment groups implies and is implied by a common trend violation across pre-treatment outcomes. For this reason, the test verifies a sufficient, but (depending on the model) not necessary condition for DiD-based identification. We investigate the finite sample performance of a testing procedure that is based on double machine learning, which permits controlling for covariates in a data-driven manner, in a simulation study and also apply it to labor market data from the National Supported Work Demonstration.