We use Granger causality tests within a conditional Gaussian Markov switching vector autoregressive (MS-VAR) model using monthly data for G-7 countries covering the period 1959:122008:10 to examine the relationship between inflation and inflation-uncertainty. The MS-VAR model allows us to model parameter time-variation so as to reflect changes in Granger causality, assuming that these changes are stochastic and governed by an unobservable Markov chain. Inflation uncertainty is measured as the conditional variance generated by a Fractionally Integrated Smooth Transition Autoregressive Moving Average-Asymmetric Power ARCH (FISTARMA-APARCH) model. The distinguishing feature of our approach from the previous studies is the determination of the sign of the Granger causality relationship between inflation and its uncertainty over time. First, using a rolling VAR model, we show that the relationship between inflation and inflation uncertainty is time varying with frequent breaks. Second, using the MS-VAR model, we obtain strong evidence in favour of the Holland's stabilizing Fed hypothesis for Canada, France, Germany, Japan, United Kingdom, and the United States. We also find evidence in favour of the Friedman hypothesis for Canada and the United States.