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We provide theory and evidence that relative price shocks can cause aggregate inflation and act as aggregate supply shocks. Empirically, we show that exogenous positive energy price shocks have a positive impact not only on headline but also on U.S. core inflation while depressing U.S. real activity. In a two-sector monetary model with upstream and downstream sectors and heterogeneous price stickiness, we analytically characterize how upstream shocks propagate to prices. Using panel IV local projections, we show that the responsiveness of sectoral PCE prices to energy price shocks is in line with model predictions. Motivated by post-COVID inflation in the U.S., a model experiment shows that a one-time relative price shock generates persistent movements in headline and core inflation similar to those observed in the data, even in the absence of aggregate slack. The model also emphasizes that monetary policy stance plays an important role in propagation of such shocks