Modeling Multiple Regimes in the Business Cycle

The interest in business-cycle asymmetry has been steadily increasing over the past 15 years. Most research has focused on the different behavior of macroeconomic variables during expansions and contractions, which by now is well documented. Recent evidence suggests that such a two-phase characterization of the business cycle might be too restrictive. In particular, it might be worthwhile to decompose the recovery phase in a high-growth phase (immediately following the trough of a cycle) and a subsequent moderate-growth phase. The issue of multiple regimes in the business cycle is addressed using smooth-transition autoregressive (STAR) models. A possible limitation of STAR models as they currently are used is that essentially they deal with only two regimes. We propose a generalization of the STAR model such that more than two regimes can be accommodated. It is demonstrated that the class of multiple-regime STAR (MRSTAR) models can be obtained from the two-regime model in a simple way. The main properties of the MRSTAR model and several issues that are relevant for empirical specification are discussed in detail. In particular, a Lagrange multiplier-type test is derived that can be used to determine the appropriate number of regimes. A limited simulation study indicates its practical usefulness. Application of the new model class to U.S. real GNP provides evidence in favor of the existence of multiple business-cycle phases.