On the Assumptions of Synthetic Control Methods
Claudia Shi, Dhanya Sridhar, Vishal Misra, David Blei
Abstract
Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit’s counterfactual outcomes using a weighted combination of some other units’ observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of analysis from “large units" (e.g., states) to “small units" (e.g., individuals in states). Under the re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We show that, in some settings, existing linear SC estimators are valid even when the data generating process is non-linear. We highlight two implications of the reformulation: 1) it clarifies where “linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model; 2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual.
BibTeX
@InProceedings{pmlr-v151-shi22b,
title = { On the Assumptions of Synthetic Control Methods },
author = {Shi, Claudia and Sridhar, Dhanya and Misra, Vishal and Blei, David},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {7163--7175},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/shi22b/shi22b.pdf},
url = {https://proceedings.mlr.press/v151/shi22b.html},
abstract = { Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit’s counterfactual outcomes using a weighted combination of some other units’ observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of analysis from “large units" (e.g., states) to “small units" (e.g., individuals in states). Under the re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We show that, in some settings, existing linear SC estimators are valid even when the data generating process is non-linear. We highlight two implications of the reformulation: 1) it clarifies where “linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model; 2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual. }
}