We propose a novel empirical structural inflation model that captures non-linear shock transmission using a Bayesian machine learning framework that combines VARs with non-linear structural factor models. Unlike traditional linear models, our approach allows for non-linear effects at all impulse response horizons. Identification is achieved via sign, zero, and magnitude restrictions within the factor model. Applying our method to euro area energy shocks, we find that inflation reacts disproportionately to large shocks, while small shocks trigger no significant response. These non-linearities are present along the pricing chain, more pronounced upstream and gradually attenuating downstream.
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