Testing for time variation in an unobserved components model for the U.S. economy

This paper analyzes the amount of time variation in the parameters of a reduced-form empirical macroeconomic model for the U.S. economy. We decompose output, inflation and unemployment in their stochastic trend and business cycle gap components, with the latter linked through the Phillips curve and Okun׳s law. A novel Bayesian model selection procedure is used to test which parameters vary over time and which components exhibit stochastic volatility. Using data from 1959Q2 to 2014Q3 we find substantial time variation in Okun׳s law, while the Phillips curve slope appears to be stable. Stochastic volatility is found to be important for cyclical shocks to the economy, while the volatility of permanent shocks remains stable.