Eli Ben-Michael, Avi Feller, Jesse Rothstein
arXiv 6 Dec 2019 · Statistics — Methodology · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2021) · 23 citations (OpenAlex)
arXiv:1912.03290 · PDF · DOI · OpenAlex · Extracted main text
Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units that closely balances the treated unit's pre-treatment outcomes. In this paper, we generalize SCM, originally designed to study a single treated unit, to the staggered adoption setting. We first bound the error for the average effect and show that it depends on both the imbalance for each treated unit separately and the imbalance for the average of the treated units. We then propose "partially pooled" SCM weights to minimize a weighted combination of these measures; approaches that focus only on balancing one of the two components can lead to bias. We extend this approach to incorporate unit-level intercept shifts and auxiliary covariates. We assess the performance of the proposed method via extensive simulations and apply our results to the question of whether teacher collective bargaining leads to higher school spending, finding minimal impacts. We implement the proposed method in the augsynth R package.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Paglayan, A. S (2019) Public-sector unions and the size of government | 1.000 | 9 | 4 | 100% |
| 2 | Abadie, A., A. Diamond, and J. Hainmueller (2015) Comparative Politics and the Synthetic Control Method | 1.000 | 6 | 3 | 100% |
| 3 | Abadie, A. and J. L'Hour (2018) A penalized synthetic control estimator for disaggregated data | 1.000 | 5 | 5 | 100% |
| 4 | Abadie, A., A. Diamond, and J. Hainmueller (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program | 0.961 | 9 | 5 | 89% |
| 5 | Ben-Michael, E., A. Feller, and J. Rothstein (2019) The Augmented Synthetic Control Method self | 0.950 | 7 | 4 | 86% |
| 6 | Callaway, B. and P. H. C. Sant'Anna (2020) Difference-in-Differences With Multiple Time Periods | 0.928 | 5 | 4 | 80% |
| 7 | Arkhangelsky, D., S. Athey, D. A. Hirshberg, G. W. Imbens, and S. Wa… (2019) Synthetic Difference In Differences | 0.928 | 4 | 3 | 100% |
| 8 | Doudchenko, N. and G. W. Imbens (2017) Difference-In-Differences and Synthetic Control Methods: A Synthesis | 0.928 | 4 | 3 | 100% |
| 9 | Hoxby, C. M (1996) How teachers' unions affect education production | 0.874 | 5 | 2 | 100% |
| 10 | Abadie, A (2019) Using synthetic controls: Feasibility, data requirements, and methodological aspects | 0.843 | 3 | 3 | 100% |
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