Non-parametric identifiability and sensitivity analysis of synthetic control models

Jakob Zeitler, Athanasios Vlontzos, Ciarán Mark Gilligan-Lee
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:850-865, 2023.

Abstract

Quantifying cause and effect relationships is an important problem in many domains, from medicine to economics. The gold standard solution to this problem is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such trials, many methods have been devised to quantify the causal impact of an intervention from observational data given certain assumptions. One widely used method are synthetic control models. While identifiability of the causal estimand in such models has been obtained from a range of assumptions, it is widely and implicitly assumed that the underlying assumptions are satisfied for all time periods both pre- and post-intervention. This is a strong assumption, as synthetic control models can only be learned in pre-intervention period. In this paper we address this challenge, and prove identifiability can be obtained without the need for this assumption, by showing it follows from the principle of invariant causal mechanisms. Moreover, for the first time, we formulate and study synthetic control models in Pearl’s structural causal model framework. Importantly, we provide a general framework for sensitivity analysis of synthetic control causal inference to violations of the assumptions underlying non-parametric identifiability. We end by providing an empirical demonstration of our sensitivity analysis framework on simulated and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-zeitler23a, title = {Non-parametric identifiability and sensitivity analysis of synthetic control models}, author = {Zeitler, Jakob and Vlontzos, Athanasios and Gilligan-Lee, Ciar\'an Mark}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {850--865}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/zeitler23a/zeitler23a.pdf}, url = {https://proceedings.mlr.press/v213/zeitler23a.html}, abstract = {Quantifying cause and effect relationships is an important problem in many domains, from medicine to economics. The gold standard solution to this problem is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such trials, many methods have been devised to quantify the causal impact of an intervention from observational data given certain assumptions. One widely used method are synthetic control models. While identifiability of the causal estimand in such models has been obtained from a range of assumptions, it is widely and implicitly assumed that the underlying assumptions are satisfied for all time periods both pre- and post-intervention. This is a strong assumption, as synthetic control models can only be learned in pre-intervention period. In this paper we address this challenge, and prove identifiability can be obtained without the need for this assumption, by showing it follows from the principle of invariant causal mechanisms. Moreover, for the first time, we formulate and study synthetic control models in Pearl’s structural causal model framework. Importantly, we provide a general framework for sensitivity analysis of synthetic control causal inference to violations of the assumptions underlying non-parametric identifiability. We end by providing an empirical demonstration of our sensitivity analysis framework on simulated and real data.} }
Endnote
%0 Conference Paper %T Non-parametric identifiability and sensitivity analysis of synthetic control models %A Jakob Zeitler %A Athanasios Vlontzos %A Ciarán Mark Gilligan-Lee %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-zeitler23a %I PMLR %P 850--865 %U https://proceedings.mlr.press/v213/zeitler23a.html %V 213 %X Quantifying cause and effect relationships is an important problem in many domains, from medicine to economics. The gold standard solution to this problem is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such trials, many methods have been devised to quantify the causal impact of an intervention from observational data given certain assumptions. One widely used method are synthetic control models. While identifiability of the causal estimand in such models has been obtained from a range of assumptions, it is widely and implicitly assumed that the underlying assumptions are satisfied for all time periods both pre- and post-intervention. This is a strong assumption, as synthetic control models can only be learned in pre-intervention period. In this paper we address this challenge, and prove identifiability can be obtained without the need for this assumption, by showing it follows from the principle of invariant causal mechanisms. Moreover, for the first time, we formulate and study synthetic control models in Pearl’s structural causal model framework. Importantly, we provide a general framework for sensitivity analysis of synthetic control causal inference to violations of the assumptions underlying non-parametric identifiability. We end by providing an empirical demonstration of our sensitivity analysis framework on simulated and real data.
APA
Zeitler, J., Vlontzos, A. & Gilligan-Lee, C.M.. (2023). Non-parametric identifiability and sensitivity analysis of synthetic control models. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:850-865 Available from https://proceedings.mlr.press/v213/zeitler23a.html.

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