DSGE model meets data gently : the importance of trend modelling

DSGE models are often specified so that the long-run variation of variables is driven by one or two common trends, which rarely holds in the data. We find that when this discrepancy exists, high-frequency components (measurement errors) capture variable-specific time variation in trends. When high-frequency components are restricted to be small or ignored, the discrepancy is captured by the model component, which distorts shock decompositions. We show that incorporating variable-specific trend components directly into the measurement equations yields a decomposition in which the high-frequency, model, and trend components each capture what they are intended to. We also find trend modelling useful in forecasting.