Revisiting non-linearities in business cycles around the world

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to (re)assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. We find evidence supporting the presence of significant non-linearities in 2/3 of the cases only. Hence, it does not provide full support to some descriptions. Linear models cannot be simply dismissed as they are sometimes useful and in many cases they do not seem to leave a substantial fraction of variation to be explained by nonlinear rivals. Nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. Therefore, our evidence broadly agrees with the one that has recently emerged from the ``features approach''. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this marginal to our study, based on indirect methods only and can hardly be invoked to support nonlinearity in classical business cycles. However, it is relevant from the output gap perspective