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We compare different approaches to accounting for parameter instability in the context of macroeconomic forecasting models that assume either small, frequent changes versus models whose parameters exhibit large, rare changes. An empirical out-of-sample forecasting exercise for U.S. gross domestic product (GDP) growth and inflation suggests that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models although they fail to produce better point forecasts. Model combinations deliver similar gains in predictive performance although they fail to improve on the predictive accuracy of the single best model, which is a specification that allows for time-varying parameters and stochastic volatility. Supplementary materials for this article are available online.