Yiqing Xu, Anqi Zhao, Peng Ding
arXiv 16 Jul 2024 · Statistics — Methodology · 4 citations (OpenAlex)
arXiv:2407.11937 · PDF · DOI · OpenAlex · Extracted main text
We formulate factorial difference-in-differences (FDID) as a research design that extends the canonical difference-in-differences (DID) to settings without clean controls. Such situations often arise when researchers exploit cross-sectional variation in a baseline factor and temporal variation in an event affecting all units. In these applications, the exact estimand is often unspecified and justification for using the DID estimator is unclear. We formalize FDID by characterizing its data structure, target parameters, and identifying assumptions. Framing FDID as a factorial design with two factors -- the baseline factor G and the exposure level Z, we define effect modification and causal moderation as the associative and causal effects of G on the effect of Z. Under standard DID assumptions, including no anticipation and parallel trends, the DID estimator identifies effect modification but not causal moderation. To identify the latter, we propose an additional factorial parallel trends assumption. We also show that the canonical DID is a special case of FDID under an exclusion restriction. We extend the framework to conditionally valid assumptions and clarify regression-based implementations. We then discuss extensions to repeated cross-sectional data and continuous G. We illustrate the approach with an empirical example on the role of social capital in famine relief in China.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cao, J., Y. Xu, and C. Zhang (2022, June) (2022) Clans and calamity: How social capital saved lives during China's Great Famine | 1.000 | 8 | 5 | 100% |
| 2 | Fouka, V (2019) How do immigrants respond to discrimination? The case of Germans in the US during World War I | 0.928 | 4 | 3 | 100% |
| 3 | VanderWeele, T. J (2009) On the distinction between interaction and effect modification | 0.874 | 5 | 2 | 100% |
| 4 | Bansak, K (2020) Estimating causal moderation effects with randomized treatments and non-randomized moderators | 0.811 | 4 | 2 | 100% |
| 5 | Angrist, J. D. and J.-S. Pischke (2009) Mostly harmless econometrics: An empiricist’s companion | 0.644 | 2 | 2 | 100% |
| 6 | Roth, J., P. H. Sant’Anna, A. Bilinski, and J. Poe (2023) What’s trending in difference-in-differences? a synthesis of the recent econometrics literature | 0.644 | 2 | 2 | 100% |
| 7 | Holland, P. W. and D. B. Rubin (1986) Research designs and causal inferences: On Lord’s paradox | 0.511 | 2 | 1 | 100% |
| 8 | Imbens, G. and D. B. Rubin (2015) Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction | 0.405 | 1 | 1 | 100% |
| 9 | Squicciarini, M. P (2020) Devotion and development: Religiosity, education, and economic progress in Nineteenth-Century France | 0.405 | 1 | 1 | 100% |
| 10 | Bertrand, M., E. Duflo, and S. Mullainathan (2004) How much should we trust differences-in-differences estimates? | 0.405 | 1 | 1 | 100% |
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|---|---|---|---|---|
| 1 | Triple Difference Designs with Heterogeneous Treatment Effects | 0.644 | 2 | 2 |
| 2 | Causal Panel Analysis under Parallel Trends: Lessons from a Large Reanalysis Study | 0.405 | 1 | 1 |
| 3 | Difference-in-Differences in the Presence of Unknown Interference | 0.405 | 1 | 1 |