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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

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

Synthetic control methods (SCMs) are a canonical approach used to estimate treatment effects from panel data in the internet economy. We shed light on a frequently overlooked but ubiquitous assumption made in SCMs of "overlap": a treated…

Econometrics · Economics 2026-02-26 Daniel Ngo , Keegan Harris , Anish Agarwal , Vasilis Syrgkanis , Zhiwei Steven Wu

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

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

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

The synthetic control method (SCM) has become a popular tool for estimating causal effects in policy evaluation, where a single treated unit is observed, and a heterogeneous set of untreated units with pre- and post-policy change data are…

Methodology · Statistics 2023-08-21 Jizhou Liu , Eric J. Tchetgen Tchetgen , Carlos Varjão

To infer the treatment effect for a single treated unit using panel data, synthetic control methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear…

Methodology · Statistics 2024-05-07 Hongxiang Qiu , Xu Shi , Wang Miao , Edgar Dobriban , Eric Tchetgen Tchetgen

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 has pioneered a class of powerful data-driven techniques to estimate the counterfactual reality of a unit from donor units. At its core, the technique involves a linear model fitted on the pre-intervention…

Artificial Intelligence · Computer Science 2022-11-28 Bhishma Dedhia , Roshini Balasubramanian , Niraj K. Jha

This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating…

Econometrics · Economics 2025-05-29 Zhentao Shi , Jin Xi , Haitian Xie

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

We analyze the synthetic control (SC) method in panel data settings with many units. We assume the treatment assignment is based on unobserved heterogeneity and pre-treatment information, allowing for both strictly and sequentially…

Econometrics · Economics 2023-12-27 Dmitry Arkhangelsky , David Hirshberg

In this article we propose a set of simple principles to guide empirical practice in synthetic control studies. The proposed principles follow from formal properties of synthetic control estimators, and pertain to the nature, implications,…

Methodology · Statistics 2022-03-15 Alberto Abadie , Jaume Vives-i-Bastida

The purpose of this work is to transport the information from multiple randomized controlled trials to the target population where we only have the control group data. Previous works rely critically on the mean exchangeability assumption.…

Machine Learning · Statistics 2023-09-29 Yuhang Zhang , Yue Liu , Zhihua Zhang

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…

Econometrics · Economics 2025-02-04 Matias D. Cattaneo , Yingjie Feng , Filippo Palomba , Rocio Titiunik

This paper studies inference on treatment effects in panel data settings with unobserved confounding. We model outcome variables through a factor model with random factors and loadings. Such factors and loadings may act as unobserved…

Econometrics · Economics 2023-12-05 Guido W. Imbens , Davide Viviano

The synthetic control method offers a way to quantify the effect of an intervention using weighted averages of untreated units to approximate the counterfactual outcome that the treated unit(s) would have experienced in the absence of the…

Methodology · Statistics 2022-10-12 Matias D. Cattaneo , Yingjie Feng , Filippo Palomba , Rocio Titiunik

The synthetic controls (SC) methodology is a prominent tool for policy evaluation in panel data applications. Researchers commonly justify the SC framework with a low-rank matrix factor model that assumes the potential outcomes are…

Econometrics · Economics 2024-08-27 Anish Agarwal , Devavrat Shah , Dennis Shen

The synthetic control method (SCM) allows estimating the causal effect of an intervention in settings where panel data on a small number of treated and control units are available. We show that the existing SCM, as well as its extensions,…

Applications · Statistics 2022-05-20 Giovanni Mellace , Alessandra Pasquini