When Is Parallel Trends Sensitive to Functional Form?

This paper assesses when the validity of difference‐in‐differences depends on functional form. We provide a novel characterization: parallel trends assumption holds under all strictly monotonic transformations outcome if and only stronger “parallel trends”‐type condition for cumulative distribution function untreated potential outcomes. to be insensitive form is satisfied essentially population can partitioned into subgroup which treatment effectively randomly assigned remaining outcomes stable over time. These conditions have testable implications, we introduce falsification tests null that