Some Methods for Assessing the Need for Non-linear Models in Business Cycle Analysis and Forecasting

There is a long tradition in business cycle analysis of arguing that non-linear models are needed to explain the business cycle. In recent years many non-linear models have been fitted to data on GDP for many countries, but particularly for the U.S. In this paper we set our criteria to evaluate the success of non-linear models in explaining the cycle and then evaluate three recent models in the light of these criteria. We find that the models are capable of explaining the "shape" of expansions, something linear models cannot do, but do so at the cost of making expansions longer than they should be and in producing transition probabilities to recessions that are too low.