Does Inflation Uncertainty Vary with the Level of Inflation?

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The purpose of this study is to test the hypothesis that inflation uncertainty increases at higher levels of inflation. Our analysis is based on the generalized autoregressive conditional heteroscedasticity (GARCH) class of models, which allow the conditional variance of the error term to be time-varying. Since this variance is a proxy for inflation uncertainty, a positive relationship between the conditional variance and inflation would be interpreted as evidence that inflation uncertainty increases with the level of inflation.

We apply GARCH techniques to two models of the inflation process in Canada: a simple autoregressive model and a reduced-form Phillips-curve model. Our findings concerning the link between inflation and its uncertainty are somewhat model-dependent. In the autoregressive case, there is a significant positive relationship between inflation and inflation uncertainty. The estimated relationship is weaker in the reduced-form model, and is not significant at the standard 5 per cent level of significance.

The difference in the strength of the relationship in the autoregressive and reduced-form models makes it difficult to draw firm conclusions about the relationship between inflation and inflation uncertainty. However, given the extreme information assumptions underlying each model, the true relationship may lie somewhere between the two sets of results. By excluding all explanatory variables other than past inflation, the simple autoregressive approach undoubtedly ignores some information that agents would have used to forecast inflation. Accordingly, the autoregressive model will tend to overstate the actual uncertainty faced by agents. Conversely, the reduced-form model may understate the uncertainty that existed, since it implicitly assumes that agents had more information on the structure of the economy than was actually available at each point in time. Future research, covering more low-inflation years and based on alternative models of inflation that explicitly incorporate policy-regime uncertainty, might clarify whether inflation uncertainty increases with the level of inflation.