The local level model with stochastic volatility, recently proposed for U.S. Inflation by Stock and Watson (Why Has U.S. Inflation Become Harder to Forecast?, Journal of Money, Credit and Banking, Supplement to Vol. 39, No. 1, February 2007), provides a simple yet sufficiently rich framework for characterizing the evolution of the main stylized facts concerning the U.S. inflation. The model decomposes inflation into a permanent component, evolving as a random walk, and a transitory component. The volatility of the disturbances driving both components is allowed to vary over time. The paper provides a full Bayesian analysis of this model and readdresses some of the main issues that were raised by the literature concerning the evolution of persistence and predictability and the extent and timing of the great moderation. The assessment of various nested models of inflation volatility and systematic model selection provide strong evidence in favor of a model with heteroscedastic disturbances in the permanent component, whereas the transitory component has time invariant size. The main evidence is that the great moderation is over, and that volatility, persistence and predictability of inflation underwent a turning point around 1995. During the last decade, volatility and persistence have been increasing and predictability has been going down.
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