Does inflation uncertainty increase with the level of inflation?

This paper presents evidence that if agents forecast inflation rationally, using an estimate of the reduced form equation which generated the data, then the size of their forecast errors is positively correlated with the level of inflation. Forecast errors are measured first as the residuals from a full sample OLS regression, and secondly from one period ahead, outside sample, forecasts using a regression estimated from only data available at the time of the forecast. Thus, agents who form rational expectations about the variance, as well as the mean, of inflation should form conditional variances dependent on the level of inflation, at the date of the forecast.