Refining the Notion of No Anticipation in Difference-in-Differences Studies

TL;DR

This paper clarifies the ambiguous no-anticipation assumption in difference-in-differences studies, proposing new definitions and identification results to improve the interpretation and application of this widely used empirical method.

Contribution

It introduces refined definitions of the no-anticipation assumption and provides new identification results to address existing ambiguities in difference-in-differences analysis.

Findings

New formal definitions of no-anticipation assumption

Identification results that clarify when effects can be attributed correctly

Resolution of ambiguity in intervention interpretation

Abstract

We address an ambiguity in identification strategies using difference-in-differences, which are widely applied in empirical research, particularly in economics. The assumption commonly referred to as the "no-anticipation assumption" states that treatment has no effect on outcomes before its implementation. However, because standard causal models rely on a temporal structure in which causes precede effects, such an assumption seems to be inherently satisfied. This raises the question of whether the assumption is repeatedly stated out of redundancy or because the formal statements fail to capture the intended subject-matter interpretation. We argue that confusion surrounding the no-anticipation assumption arises from ambiguity in the intervention considered and that current formulations of the assumption are ambiguous. Therefore, new definitions and identification results are proposed.