This paper uses Monte Carlo techniques to assess the loss in terms of forecast accuracy which is incurred when the true data generation process (DGP) exhibits parameter instability which is either overlooked or incorrectly modelled. We find that the loss is considerable when a fixed coefficient models (FCM) is estimated instead of the true time varying parameter model (TVCM), this loss being an increasing function of the degree of persistence and of the variance of the process driving the slope coefficient. A loss is also incurred when a TVCM different from the correct one is specified, the resulting forecasts being even less accurate than those of a FCM. However, the loss can be minimised by selecting a TVCM which, although incorrect, nests the true one, more specifically an AR(1) model with a constant. Finally, there is hardly any loss resulting from using a TVCM when the underlying DGP is characterised by fixed coefficients.