This paper considers the extent to which fluctuations in Australian economic growth are affected by domestic and overseas economic performance. We investigate the performance of a range of non-linear models versus linear models, comparing the models using Bayes factors and posterior odds ratios. The posterior odds ratios favour non-linear specifications in which luctuations in economic activity in the US affect Australia's economic performance. Our results suggest that an exogenous negative shock will be more persistent, lead to greater output volatility, and have a greater impact on growth, than a positive shock of equal magnitude.