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 set up an unobserved components model to decompose output, inflation and unemployment in their stochastic trend and business cycle gap components. The latter are related through the Phillips curve and Okun's Law. Key parameters such as the potential output growth rate, the slope of the Phillips curve and the strength of Okun's Law, are allowed to change over time in order to account for potential structural changes in the U.S. economy. Moreover, stochastic volatility is added to all components to account for shifts in macroeconomic volatility. A Bayesian stochastic model specification search is employed to test which parameters are time-varying and which unobserved components exhibit stochastic volatility. Using quarterly data from 1959Q2 to 2014Q3 we find substantial time variation in Okun's Law, while the Phillips curve slope appears to be stable. The potential output growth rate exhibits a drastic and persistent decline. Stochastic volatility is found to be important for cyclical shocks to the economy, while the volatility of permanent shocks remains stable.