The notion that high inflation breeds high uncertainty about future inflation is widely accepted.' This acceptance is based largely on a positive correlation between the mean and variability of inflation across countries.2 This positive relationship is taken as evidence that high inflation creates high uncertainty.3 Recently though, Driffill, Mizon, and Ulph [10] have questioned the relevance of this cross-country evidence for making inferences about welfare issues within countries. They argue that it is the relationship between the time-series mean and variance within a country that is important when considering the potential costs of inflation. In this paper we examine the within country time-series link between the level and uncertainty of inflation for ten countries that experienced a period of very high inflation. We use data generated from regression based forecasts of inflation, and historical data on actual forecasts. Our sample does not provide evidence of a general positive link within these countries. The ten countries we study are: Argentina, Bolivia, Brazil, Chile, Colombia, Israel, Mexico, Peru, Turkey, and Uruguay. In these countries the average annualized rate of inflation from the quarterly data in our sample was about 54% per year, and the average sample standard deviation,