On the Assumptions of Synthetic Control Methods

Claudia Shi, Dhanya Sridhar, Vishal Misra, David Blei
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:7163-7175, 2022.

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.

Cite this Paper

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. } }
Endnote
%0 Conference Paper %T On the Assumptions of Synthetic Control Methods %A Claudia Shi %A Dhanya Sridhar %A Vishal Misra %A David Blei %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-shi22b %I PMLR %P 7163--7175 %U https://proceedings.mlr.press/v151/shi22b.html %V 151 %X 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.
APA
Shi, C., Sridhar, D., Misra, V. & Blei, D.. (2022). On the Assumptions of Synthetic Control Methods . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:7163-7175 Available from https://proceedings.mlr.press/v151/shi22b.html.

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