Incorporating structural uncertainty in causal decision making

TL;DR

This paper investigates when accounting for structural uncertainty in causal models improves decision-making, proposing Bayesian model averaging as a solution under specific conditions, supported by theoretical and simulation results.

Contribution

It introduces a framework for incorporating structural uncertainty into causal decision making, with conditions when model averaging is advantageous and proofs of optimality.

Findings

Model averaging benefits when structural uncertainty is high and effects differ substantially.

Simulations show modern causal discovery methods can quantify structural uncertainty.

The proposed approach complements existing robust causal inference methods.

Abstract

Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal structures). Focusing on bivariate relationships ($X \rightarrow Y$ vs. $X \leftarrow Y$), we establish that model averaging is beneficial when: (1) structural uncertainty is moderate to high, (2) causal effects differ substantially between structures, and (3) loss functions are sufficiently sensitive to the size of the causal effect. We prove optimality results of our suggested methodological solution under regularity conditions and demonstrate through simulations that modern causal discovery methods can provide, within limits, the necessary quantification. Our framework complements existing robust causal inference approaches by addressing a distinct source of uncertainty typically overlooked in practice.