Using Time Structure to Estimate Causal Effects

2025-04-15

AI Summary

This paper addresses the identification of causal effects in time-series data under latent confounding, without relying on instrumental variables or negative controls. We propose the first linear identification framework grounded in structural vector autoregression (SVAR) and the full-time graph. Leveraging Wright’s path tracing rules and covariance algebra, we derive sufficient conditions—comprising graphical structure constraints and lag-order criteria—for the identifiability of both direct and total causal effects, assuming only knowledge of the temporal structure. We formally prove that, under these conditions, the causal parameters are uniquely identifiable. Numerical experiments demonstrate the method’s accuracy, robustness to model misspecification, and substantial improvement in feasibility for settings where no auxiliary variables are available.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Estimating causal effects in time series without auxiliary variables
• Using SVAR process to solve linear equations for direct effects
• Providing graphical and lag-based criteria for identifiability

Innovation

• Estimates causal effects without auxiliary variables
• Uses Structural Vector Autoregressive process
• Solves linear equations from covariances