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This paper provides new insights into the asymptotic properties of the synthetic control method (SCM). We show that the synthetic control (SC) weight converges to a limiting weight that minimizes the mean squared prediction risk of the…

Econometrics · Economics 2022-11-23 Xiaomeng Zhang , Wendun Wang , Xinyu Zhang

The method of synthetic controls is widely used for evaluating causal effects of policy changes in settings with observational data. Often, researchers aim to estimate the causal impact of policy interventions on a treated unit at an…

Econometrics · Economics 2025-01-17 Florian Gunsilius , David Van Dijcke

This article extends the widely-used synthetic controls estimator for evaluating causal effects of policy changes to quantile functions. The proposed method provides a geometrically faithful estimate of the entire counterfactual quantile…

Econometrics · Economics 2022-01-03 Florian Gunsilius

The synthetic control method estimates the causal effect by comparing the treated unit's outcomes to a weighted average of control units that closely match its pre-treatment outcomes, assuming the relationship between treated and control…

Methodology · Statistics 2026-01-07 Taehyeon Koo , Zijian Guo

We consider the asymptotic properties of the Synthetic Control (SC) estimator when both the number of pre-treatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which…

Econometrics · Economics 2020-05-27 Bruno Ferman

Synthetic Control methods have recently gained considerable attention in applications with only one treated unit. Their popularity is partly based on the key insight that we can predict good synthetic counterfactuals for our treated unit.…

Econometrics · Economics 2025-07-15 Tzvetan Moev

The synthetic control method is a an econometric tool to evaluate causal effects when only one unit is treated. While initially aimed at evaluating the effect of large-scale macroeconomic changes with very few available control units, it…

To estimate the causal effect of an intervention, researchers need to identify a control group that represents what might have happened to the treatment group in the absence of that intervention. This is challenging without a randomized…

Methodology · Statistics 2026-03-20 Robert Pickett , Jennifer Hill , Sarah Cowan

Estimating weights in the synthetic control method, typically resulting in sparse weights where only a few control units have non-zero weights, involves an optimization procedure that selects and combines control units to closely match the…

Econometrics · Economics 2026-02-03 Rong J. B. Zhu

Synthetic Control Methods (SCMs) have become a fundamental tool for comparative case studies. The core idea behind SCMs is to estimate treatment effects by predicting counterfactual outcomes for a treated unit using a weighted combination…

Econometrics · Economics 2025-11-10 Masahiro Kato , Akari Ohda

We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A…

This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse…

Methodology · Statistics 2025-10-31 Le Wang , Xin Xing , Youhui Ye

Synthetic control (SC) methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. An SC is a weighted average of control units built to match the treated unit, with weights typically…

Methodology · Statistics 2023-02-21 Xu Shi , Kendrick Li , Wang Miao , Mengtong Hu , Eric Tchetgen Tchetgen

Since their introduction in Abadie and Gardeazabal (2003), Synthetic Control (SC) methods have quickly become one of the leading methods for estimating causal effects in observational studies in settings with panel data. Formal discussions…

Econometrics · Economics 2023-07-20 Lea Bottmer , Guido Imbens , Jann Spiess , Merrill Warnick

In causal inference with observational studies, synthetic control (SC) has emerged as a prominent tool. SC has traditionally been applied to aggregate-level datasets, but more recent work has extended its use to individual-level data. As…

Machine Learning · Computer Science 2025-03-28 Saeyoung Rho , Andrew Tang , Noah Bergam , Rachel Cummings , Vishal Misra

Mixed-frequency data, where variables are observed at different temporal resolutions, commonly occur in economic and financial studies. Classical synthetic control methods (SCM) are ill-suited for such data, often necessitating aggregation…

Methodology · Statistics 2026-05-13 Lu Zhang , Shijin Gong , Xinyu Zhang

We analyze the properties of the Synthetic Control (SC) and related estimators when the pre-treatment fit is imperfect. In this framework, we show that these estimators are generally biased if treatment assignment is correlated with…

Econometrics · Economics 2021-01-13 Bruno Ferman , Cristine Pinto

In a seminal paper Abadie, Diamond, and Hainmueller [2010] (ADH), see also Abadie and Gardeazabal [2003], Abadie et al. [2014], develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single…

Applications · Statistics 2017-09-21 Nikolay Doudchenko , Guido W. Imbens

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…

Methodology · Statistics 2021-01-19 Eli Ben-Michael , Avi Feller , Jesse Rothstein

The synthetic control method (SCM) estimates causal effects in panel data with a single-treated unit by constructing a counterfactual outcome as a weighted combination of untreated control units that matches the pre-treatment trajectory. In…

Machine Learning · Statistics 2026-05-13 Yuxin Wang , Dennis Frauen , Emil Javurek , Konstantin Hess , Yuchen Ma , Stefan Feuerriegel
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