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We study the macroeconomic effects of a time-varying inflation target (IT), which stochastic volatility follows an autoregressive process. We show that the quantitative economic effects of IT uncertainty shocks depend crucially on the Taylor-rule type adopted by the monetary authority. Following this kind of disturbance, a less severe recession and deflation is observed under a more reactive interest rate rule, while an empirical plausible degree of interest rate smoothing leads output, unemployment, and inflation to react more strongly causing the recession to be more severe and deflationary.