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Bayesian Synthetic Control with a Soft Simplex Constraint

Yihong Xu, Quan Zhou

arXiv 9 Mar 2025 · Statistics — Methodology

arXiv:2503.06454 · PDF · Extracted main text

Abstract

Whether the synthetic control method should be implemented with the simplex constraint and how to implement it in a high-dimensional setting have been widely discussed. To address both issues simultaneously, we propose a novel Bayesian synthetic control method that integrates a soft simplex constraint with spike-and-slab variable selection. Our model is featured by a hierarchical prior capturing how well the data aligns with the simplex assumption, which enables our method to efficiently adapt to the structure and information contained in the data by utilizing the constraint in a more flexible and data-driven manner. A unique computational challenge posed by our model is that conventional Markov chain Monte Carlo sampling algorithms for Bayesian variable selection are no longer applicable, since the soft simplex constraint results in an intractable marginal likelihood. To tackle this challenge, we propose to update the regression coefficients of two predictors simultaneously from their full conditional posterior distribution, which has an explicit but highly complicated characterization. This novel Gibbs updating scheme leads to an efficient Metropolis-within-Gibbs sampler that enables effective posterior sampling from our model and accurate estimation of the average treatment effect. Simulation studies demonstrate that our method performs well across a wide range of settings, in terms of both variable selection and treatment effect estimation, even when the true data-generating process does not adhere to the simplex constraint. Finally, application of our method to two empirical examples in the economic literature yields interesting insights into the impact of economic policies.

Citation extraction

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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
1Shi, Zhentao and Huang, Jingyi (2023) Forward-selected panel data approach for program evaluation1.00083100%
2Yang, Yun and Wainwright, Martin J and Jordan, Michael I (2016) On the computational complexity of high-dimensional Bayesian variable selection1.00063100%
3George, Edward I and McCulloch, Robert E (1997) Approaches for Bayesian variable selection0.92843100%
4Carvalho, Carlos and Masini, Ricardo and Medeiros, Marcelo C (2018) ArCo: An artificial counterfactual approach for high-dimensional panel time-series data0.87472100%
5Abadie, Alberto and Gardeazabal, Javier (2003) The economic costs of conflict: A case study of the Basque Country0.73732100%
6Hsiao, Cheng and Steve Ching, H and Ki Wan, Shui (2012) A panel data approach for program evaluation: measuring the benefits of political and economic integration of Hong Kong with mai…0.73732100%
7Li, Kathleen T (2020) Statistical inference for average treatment effects estimated by synthetic control methods0.73732100%
8Ignacio Martinez and Jaume Vives-i-Bastida (2022) Bayesian and Frequentist Inference for Synthetic Controls0.73732100%
9Guan, Yongtao and Stephens, Matthew (2011) Bayesian variable selection regression for genome-wide association studies and other large-scale problems0.64422100%
10Amemiya, Takeshi (1985) Advanced econometrics0.58531100%

Showing the top 10 of 40 scored citations.