Milton Friedman proposed that there is a positive relationship between inflation and uncertainty about the future path of inflation. In contrast to previous studies of this hypothesis, we find strong statistical evidence that higher levels of inflation are less predictable, although innovations in inflation are somewhat better predictors of future volatility than the actual level of inflation. We argue that previous failures to find an inflation-uncertainty relationship are due to two factors. First, none of the previous work directly tested Friedman's hypothesis by including the level of inflation in the model of the conditional variance. Second, these studies also used symmetric models, which appears inconsistent with Friedman's hypothesis. Our results are robust to different sample periods and to assumptions about the presence of a unit root in inflation. To test the inflation-uncertainty hypothesis, we use state-dependent models (SDM's) of conditional moments to estimate the time-varying conditional variance of inflation. SDM's have three distinct advantages for this application: (1) They include the inflation rate in the model of the conditional variance, (2) they allow for asymmetric relationships, and (3) they nest several alternative, but symmetric, models such as ARCH, GARCH, and Rx models of conditional heteroscedasticity. For completeness, we compare our estimates of conditional variance to estimates using EGARCH models, an alternative to SDM models that also allows for asymmetric relationships but that does not nest ARCH, GARCH, and Rx models.
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