Using Time Structure to Estimate Causal Effects
This work addresses a specific challenge in causal inference for time series data, offering a novel approach that could benefit researchers in fields like economics or epidemiology, though it appears incremental as it builds on existing SVAR frameworks.
The paper tackles the problem of estimating direct causal effects in time series with latent confounding without relying on auxiliary variables, by proposing a method based on Structural Vector Autoregressive processes and linear equations, with numerical experiments confirming its correctness and applicability.
There exist several approaches for estimating causal effects in time series when latent confounding is present. Many of these approaches rely on additional auxiliary observed variables or time series such as instruments, negative controls or time series that satisfy the front- or backdoor criterion in certain graphs. In this paper, we present a novel approach for estimating direct (and via Wright's path rule total) causal effects in a time series setup which does not rely on additional auxiliary observed variables or time series. This approach assumes that the underlying time series is a Structural Vector Autoregressive (SVAR) process and estimates direct causal effects by solving certain linear equation systems made up of different covariances and model parameters. We state sufficient graphical criteria in terms of the so-called full time graph under which these linear equations systems are uniquely solvable and under which their solutions contain the to-be-identified direct causal effects as components. We also state sufficient lag-based criteria under which the previously mentioned graphical conditions are satisfied and, thus, under which direct causal effects are identifiable. Several numerical experiments underline the correctness and applicability of our results.