Selection and parallel trends

Dalia Ghanem, Pedro Sant'Anna () and Kaspar W\"uthrich

Papers from arXiv.org

Abstract: 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. We also provide templates for justifying DiD in applications with and without covariates. Reanalyses of the causal effect of NSW training programs and the effect of the Medicaid expansion demonstrate the usefulness of our selection-based approach to benchmarking the bias of DiD.

Date: 2022-03, Revised 2026-02
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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Working Paper: Selection and Parallel Trends (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2203.09001

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