Reproducing business cycle features: are nonlinear dynamics a proxy for multivariate information?

We consider the extent to which different time-series models can generate simulated data with the same business cycle features that are evident in US real GDP. We focus our analysis on whether multivariate linear models can improve on the previously documented failure of univariate linear models to replicate certain key business cycle features. We find that a particular nonlinear Markov-switching specification with an explicit “bounceback” effect continues to outperform linear models, even when the models incorporate variables such as the unemployment rate, inflation, interest rates, and the components of GDP. These results are robust to simulated data generated either using Normal disturbances or bootstrapped disturbances, as well as to allowing for a one-time structural break in the variance of shocks to real GDP growth.