Using Pre-Trends for Inference in Difference-in-Differences

Difference-in-differences (DID) are sometimes estimated with many pre-treatment periods.

In such settings, the observed pre-treatment outcome evolutions provide direct information about the magnitude of shocks that could also occur after treatment.

This paper proposes a simple inference procedure that uses those pre-trends as the reference distribution for the post-treatment DID.

The procedure is closely related to existing conformal inference procedures, but its DID-specific predictor leads to a distinct identifying restriction.

Existing procedures assume parallel trends, while this paper's procedure does not require parallel trends.