Non-parametric identifiability and sensitivity analysis of synthetic control models

TL;DR

This paper establishes non-parametric identifiability of synthetic control models without assuming assumptions hold for all time periods, introduces a causal framework, and develops a sensitivity analysis method validated on real and simulated data.

Contribution

It proves identifiability from invariant causal mechanisms, formulates synthetic control models within Pearl's causal framework, and introduces a sensitivity analysis approach for assumption violations.

Findings

Identifiability can be achieved without assuming all-time validity of model assumptions.

The proposed sensitivity analysis quantifies robustness to assumption violations.

Empirical results demonstrate the effectiveness of the sensitivity framework on real and simulated data.

Abstract

Quantifying cause and effect relationships is an important problem in many domains. The gold standard solution 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 in the widely-used linear synthetic control framework.