Modeling nonlinearity of business cycles: Choosing between the CDR and STAR models

Nonlinear modeling has become popular in applied macroeconomics. Successful attempts include Beaudry and Koop's CDR (current depth of the recession) model of real GNP, and various STAR (smooth transition autoregression) models of industrial production. However, these models have not been directly compared. We compare CDR and STAR models of U. S. real GNP and industrial production. We find (i) within sample, the CDR model fits slightly better than the STAR model; (ii) out of sample, the CDR model forecasts better than the STAR model; and (iii) the CDR model generates very different dynamics than the STAR model.