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Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

Matias D. Cattaneo, Yingjie Feng, Filippo Palomba, Rocio Titiunik

arXiv 10 Oct 2022 · Econometrics · publishedThe Review of Economics and Statistics (2025) · 8 citations (OpenAlex)

arXiv:2210.05026 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly different points in time. From a theoretical perspective, our uncertainty quantification methods improve on prior literature by (i) covering a large class of causal predictands in staggered adoption settings, (ii) allowing for synthetic control methods with possibly nonlinear constraints, (iii) proposing scalable robust conic optimization methods and principled data-driven tuning parameter selection, and (iv) offering valid uniform inference across post-treatment periods. We illustrate our methodology with an empirical application studying the effects of economic liberalization on real GDP per capita for Sub-Saharan African countries. Companion software packages are provided in Python, R, and Stata.

Citation extraction

12
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Cattaneo, M. D., Feng, Y., and Titiunik, R (2021) Prediction Intervals for Synthetic Control Methods self0.87462100%
2Cattaneo, M. D., Feng, Y., Palomba, F., and Titiunik, R (2025) scpi: Uncertainty Quantification for Synthetic Control Methods self0.64422100%
3Boyd, S., and Vandenberghe, L (2004) Convex Optimization0.51121100%
4Raic, M (2019) A Multivariate Berry–Esseen Theorem with Explicit Constants0.51121100%
5Billmeier, A., and Nannicini, T (2013) Assessing Economic Liberalization Episodes: A Synthetic Control Approach0.40511100%
6Bratton, M., and Van de Walle, N (1997) Democratic Experiments in Africa: Regime Transitions in Comparative Perspective0.40511100%
7Chang, Y., Park, J. Y., and Song, K (2006) Bootstrapping Cointegrating Regressions0.40511100%
8Ferman, B., and Pinto, C (2021) Synthetic Controls with Imperfect Pre-Treatment Fit0.40511100%
9Hoerl, A. E., Kannard, R. W., and Baldwin, K. F (1975) Ridge Regression: Some Simulations0.40511100%
10Ravishanker, N., Hochberg, Y., and Melnick, E. L (1987) Approximate Simultaneous Prediction Intervals for Multiple Forecasts0.40511100%

Showing the top 10 of 12 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Debiasing and $t$-tests for synthetic control inference on average causal effects1.00073
2scpi: Uncertainty Quantification for Synthetic Control Methods1.00074
3Large-Sample Properties of the Synthetic Control Method under Selection on Unobservables0.64422
4Inference for Synthetic Controls via Refined Placebo Tests0.64422
5On the relationship between prediction intervals, tests of sharp nulls and inference on realized treatment effects in settings with few treated units0.64422
6Inference with few treated units0.51121
7Synthetic Control Inference for Staggered Adoption0.40511
8Synthetic Blips: Generalizing Synthetic Controls for Dynamic Treatment Effects0.40511
9Estimating Variances for Causal Panel Data Estimators0.40511
10Distributionally Robust Synthetic Control: Ensuring Robustness Against Highly Correlated Controls and Weight Shifts0.40511