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What drives the recent inflation surge? To answer this question, one must
decompose inflation fluctuations into the contribution of structural shocks. We document
how whimsical an historical shock decomposition can be in standard vector
autoregressive (VAR) models. We show that the deterministic component of the VAR
is imprecisely estimated, making the shock contributions poorly identified under general
conditions. Our preferred approach to solve the problem—the single-unit-root
prior—massively shrinks the uncertainty around the estimated deterministic component.
Once this uncertainty is taken care of, demand shocks are the main drivers
of the inflation surge in the United States, the euro area, and in four small open
economies.