Selection and parallel trends

Understand

We study the role of selection into treatment in difference-in-differences (DiD) designs.

• We derive necessary and sufficient conditions for parallel trends assumptions under general classes of selection mechanisms.
• These conditions characterize the empirical content of parallel trends and clarify the trade-offs between assumptions about selection into treatment and restrictions on the time series properties of the potential outcomes required for DiD methods.
• We use the necessary and sufficient conditions to provide a selection-based decomposition of the bias of DiD and provide easy-to-implement strategies for benchmarking its components.