Keywords: panel data, casual inference, synthetic control, time-series
TL;DR: We formulate the reverse causal inference problem on panel data and propose a greedy algorithm to solve it with a generalized synthetic control estimator.
Abstract: Seeking causal explanations in panel (or longitudinal/multivariate time-series) data is a difficult problem of both academic and industrial importance. Although there exists a large amount of literature on forward causal inference, where the treatment/outcome/covariates variables 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, and propose a linear-time greedy meta algorithm that makes use of forward causal inference estimators. We further identify a set of optimality conditions under which the proposed algorithm is able to find the optimal causal path. To substantiate our greedy 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. Promising results on on synthetic datasets demonstrate the potential of our method.