This study investigates the dynamics of quarterly real GDP per capita growth rates across four countries, the US, UK, Canada and France. I obtain estimates for ARIMA(p,q) processes for first differences of log quarterly real GDP per capita using Reversible Jump Markov Chain Monte Carlo, allowing me to account for model uncertainty when comparing the implied impulse responses across countries. The results are checked for robustness with respect to the detrending device. The estimated impulse response functions are different in shape. The persistence estimates for the US, France, Canada and Italy are clustered together, while the UK and Japan are clear outliers. Significant posterior uncertainty remains regarding the persistence estimates and the appropriate ARMA models. The results for the UK is sensitive to the time period. An analysis of the components of GDP for the US suggests that the dynamics are mainly driven by consumption.