Towards Reverse Causal Inference on Panel Data: Precise Formulation and Challenges

Seeking causal explanations in panel (or longitudinal/multivariate time-series) data is a difficult problem of both academic and industrial importance. Although there exists huge literature on forward causal inference where the treatment/outcome/covariates are well-defined, it is unclear how to answer the reverse question: which covariates have effects on the outcome? In this paper, we set forth our expedition on this reverse question from the first principles. We formulate the precise problem definition in terms of causal patterns and causal paths, propose a linear-time greedy algorithm that makes use of forward causal inference estimators, and identify a set of optimality conditions under which the proposed algorithm is able to find the best causal path. To substantiate our meta algorithm, we propose a generalized version of the synthetic control estimator by fitting both synthetic treatments and controls by conditioning on the partial causal paths. We perform simulation studies on synthetic datasets and demonstrate the potential of our method.