Multivariate Star Analysis Of Money–Output Relationship

This paper investigates the potential for nonlinear Granger causality from money to output. Using a standard four-variable linear (subset) vector error-correction model (VECM), we first show that the null hypothesis of linearity can be rejected against the alternative of smooth-transition autoregressive nonlinearity. An interesting result from this stage of the analysis is that the yearly growth rate of money is identified as one of the variables that may govern the switching between regimes. Smooth-transition VECM's (STVECM's) are then used to examine whether there is nonlinear Granger causality in the money–output relationship in the sense that lagged values of money enter the model's output equation as regressors. We evaluate this type of nonlinear Granger causality with both in-sample and out-of-sample analyses. For the in-sample analysis, we compare alternative models using the Akaike information criteria, which can be interpreted as a predictive accuracy test. The results show that allowing for both nonlinearity and for money–output causality leads to considerable improvement in model's in-sample performance. By contrast, the out-of-sample forecasting results do not suggest that money is nonlinearly Granger causal for output. They also show that, according to several criteria, the linear VECM's dominate the STVECM's. However, these forecast improvements seldomly are statistically significant at conventional levels.