Is the relationship between ination and its uncertainty linear?

We use parametric power ARCH models of the conditional variance of inflation and monthly data in Germany, the Netherlands and Sweden for the period 1962-2004 to examine the relationship between inflation and inflation uncertainty. In two out of the three countries inflation significantly raises inflation uncertainty as predicted by Friedman. Increased nominal uncertainty affects inflation in all countries but not in the same manner. The results for Germany and the Netherlands support the Cukierman-Meltzer hypothesis. In Sweden uncertainty about the future inflation appears to have a negative impact on inflation