Transmission channels, dynamic mediation, and higher-order impulse responses

Jean-Marie Dufour and Endong Wang

Papers from arXiv.org

Abstract: Impulse responses measure the total effect of causal changes (or shocks) but do not show how that effect is divided among mediator variables. We use the recursion between Sims and higher-order impulse responses (Dufour and Renault, 1998) to decompose an impulse response into the contributions of mediator variables at every propagation stage. A mediator's contribution is the product of an exposure margin, which measures how the shock moves the mediator, and a propagation margin, the multi-horizon projection coefficients that carry these movements over to the outcome. We show that multi-horizon Granger noncausality from a mediator to the outcome implies a zero propagation margin and that a mediator's contribution equals a controlled mediator-path effect. We provide inference for the contributions and a test of the propagation margin. Applying the decomposition to U.S. oil supply news shocks, we find that consumer-price movements in the first six months make a large contribution to the subsequent decline in industrial production, whereas the contribution of the federal funds rate is small throughout.

Date: 2025-09, Revised 2026-10
New Economics Papers: this item is included in nep-cba
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