In this paper we propose Granger (non-)causality tests based on a VAR model allowing for time-varying coefficients. The functional form of the time-varying coefficients is a Logistic Smooth Transition Autoregressive (LSTAR) model using time as the transition variable. The model allows for testing Granger non-causality when the VAR is subject to a smooth break in the coefficients of the Granger causal variables. The proposed test then is applied to the money-output relationship using quarterly US data for the period 1952:2-2002:4. We find that causality from money to output becomes stronger after 1978:4 and the model is shown to have a good out of sample forecasting performance for output relative to a linear VAR model.