To develop a way to analyze the dynamic relationship between the economic growth and the level of inflation in Japan, we propose a Bayesian regression method to estimate the dynamic dependence of the stationary component of GDP on a stationary component of the CPI. First, we extract stationary components from original GDP and CPI time series using a set of state space models. Then, we construct a set of Bayesian regression models with a time-varying coefficient. We also analyze the dynamic relationship between the stationary components of GDP and the CPI using Japanese economic statistics from 1980 to 2005.