Is the relationship between inflation and its uncertainty linear?

We use parametric power ARCH models of the conditional variance of inflation to model the relationship between inflation and its uncertainty using monthly data for Germany, the Netherlands and Sweden over a period ranging from 1962 to 2004. For all three countries inflation significantly raises inflation uncertainty as predicted by Friedman. Increased uncertainty affects inflation in all countries but not in the same manner. For Sweden we find a negative impact in accordance with the Holland hypothesis, whereas for Germany and the Netherlands we find the opposite in support of the Cukierman-Meltzer hypothesis. In a sensitivity analysis we show that an arbitrary choice of the heteroskedasticity parameter influences this relationship significantly.