A multivariate STAR analysis of the relationship between money and output

Using a standard 4-variable linear vector error correction model (VECM), we first show that the null hypothesis of linearity can be strongly rejected against the alternative of smooth transition autoregressive nonlinearity. An important result from this stage of the analysis is that the quarterly growth rate of money is identified as the transition variable, the variable which governs the smooth switching between regimes. This implies there is a nonlinear causal relationship between money and output. A smooth transition VECM (STVECM) is then used to examine whether money nonlinearly Granger causes output 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 analysis. For the in-sample analysis we compare alternative models using predictive accuracy tests. These results vary strongly across use of the AIC and SIC. Our use of an out-of-sample forecasting exercise to study money-income Granger causality, both linear and nonlinear, we believe is new to the literature. The forecasting results do not suggest that money is nonlinearly Granger causal for output. In fact, they show that by allowing money to nonlinearly Granger cause output, the forecasting performance of the STVECM is significantly worsened.