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

2026-07-23

AI Summary

This study addresses the vulnerability of conventional difference-in-differences (DID) estimators to bias under post-treatment shocks, which arises from their reliance on the parallel trends assumption. To overcome this limitation, the authors propose a novel inference approach that dispenses with this assumption by constructing a DID-specific predictor based on pre-treatment outcome dynamics and embedding it within a conformal inference framework. This method explicitly models potential post-treatment shocks and leverages pre-treatment information to impose identification constraints, thereby enabling robust causal inference even when parallel trends fail to hold. The proposed procedure substantially enhances the reliability and applicability of DID estimates in settings characterized by non-parallel trends.

Abstract

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.

Problem

• Difference-in-Differences
• pre-trends
• inference
• parallel trends
• conformal inference

Innovation

• Difference-in-Differences
• pre-trends
• conformal inference
• parallel trends
• inference