arXiv 19 May 2026 · Econometrics
arXiv:2605.20359 · PDF · DOI · OpenAlex · Extracted main text
Synthetic control methods can produce misleading counterfactual predictions when outcome series contain unit-specific stochastic trends, a common feature of nonstationary macroeconomic data. Existing remedies, such as pre-filtering or differencing, reduce spurious matching but may discard shared nonstationary variation that helps estimate donor weights. We propose Harmonic Synthetic Control (HSC), which replaces this binary choice with a soft allocation mechanism. HSC jointly estimates donor weights and a treated-unit-specific smooth residual component, then extrapolates this component into post-treatment periods using a time-series forecaster. A tuning parameter, selected by rolling-origin cross-validation, governs the division between donor matching and forecasting. As it varies, HSC continuously interpolates between synthetic control applied to differenced outcomes and synthetic control applied to raw outcomes with an intercept or trend. We provide a spectral interpretation showing how HSC downweights low-frequency residual components in donor matching and assigns them to the forecasting branch. A prediction-error decomposition separates weight-estimation distortion from residual-forecasting error. Monte Carlo exercises show that HSC adapts across regimes, performing well when stochastic trends are predominantly common or idiosyncratic, while estimators fixed to one regime can fail in the other.
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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 | Doudchenko, Nikolay and Imbens, Guido W (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis | 1.000 | 5 | 4 | 100% |
| 2 | Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… (2021) Synthetic difference-in-differences | 0.969 | 11 | 6 | 91% |
| 3 | Shi, Zhentao and Xi, Jin and Xie, Haitian (2025) A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data | 0.953 | 15 | 5 | 87% |
| 4 | Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program | 0.928 | 4 | 3 | 100% |
| 5 | Ben-Michael, Eli and Feller, Avi and Rothstein, Jesse (2021) The augmented synthetic control method | 0.928 | 4 | 3 | 100% |
| 6 | Hsiao, Cheng and Ching, H Steve and Wan, Shui Ki (2012) A panel data approach for program evaluation: measuring the benefits of political and economic integration of Hong Kong with mai… | 0.843 | 10 | 3 | 60% |
| 7 | Abadie, Alberto (2021) Using synthetic controls: Feasibility, data requirements, and methodological aspects | 0.811 | 4 | 2 | 100% |
| 8 | Ferman, Bruno and Pinto, Cristine (2021) Synthetic controls with imperfect pretreatment fit | 0.811 | 4 | 2 | 100% |
| 9 | Masini, Ricardo and Medeiros, Marcelo C (2022) Counterfactual analysis and inference with nonstationary data | 0.811 | 4 | 2 | 100% |
| 10 | Masini, Ricardo and Medeiros, Marcelo C (2021) Counterfactual analysis with artificial controls: Inference, high dimensions, and nonstationarity | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 21 scored citations.