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.

本文提出了一种新的方案，通过不需要强假设的方法，利用原因不变性原则来检验干预的因果效应，并给出了敏感性分析框架以克服这些方法中的违反非参数识别的假设的问题，从而使基于线性合成控制模型的因果推断更加精确可靠。

合成控制模型的非参数识别性和敏感性分析