Non-parametric identifiability and sensitivity analysis of synthetic control models
This work provides a more robust foundation for causal inference in synthetic control models, benefiting researchers and practitioners in fields relying on observational data, though it is incremental by refining existing assumptions.
The paper addresses the challenge of causal identifiability in synthetic control models by proving that identifiability can be achieved without assuming underlying assumptions hold for all time periods, using the principle of invariant causal mechanisms, and it introduces a sensitivity analysis framework for violations of these assumptions, demonstrated on simulated and real data.
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.