Causal mechanism and mediation analysis for macroeconomics dynamics: a bridge of Granger and Sims causality

This paper introduces a novel concept of impulse response decomposition to disentangle the dynamic contributions of the mediator variables in the transmission of structural shocks. We justify our decomposition by drawing on causal mediation analysis and demonstrating its equivalence to the average mediation effect. Our result establishes a formal link between Sims and Granger causality. Sims causality captures the total effect, while Granger causality corresponds to the mediation effect. We construct a dynamic mediation index that quantifies the evolving role of mediator variables in shock propagation. Applying our framework to studies of the transmission channels of US monetary policy, we find that investor sentiment explains approximately 60% of the peak aggregate output response in three months following a policy shock, while expected default risk contributes negligibly across all horizons.