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## Does Inflation Uncertainty Really Increase With Inflation?## Peijie Wang## Manchester School of Management, UMIST, PO Box 88, Manchester M60 1QD, UK## AbstractThis paper proposes a two-factor model for analysing inflation uncertainty. Inflation pressure is relatively more persistent than policy intervention, which characterises the pattern of inflation uncertainty. Inflation uncertainty is found to increase with inflation in the medium to high range of inflation. Beyond that range, inflation uncertainty does not increase with inflation.
## 1. IntroductionIt is claimed that uncertainty about future inflation is higher the
higher the inflation rate. This may be true in a certain range of
inflation but In this paper, we first propose an economic analytical framework in section 2, illustrating why inflation uncertainty would be time-varying and related to the level of inflation; then we translate this analytical framework into a testable econometric specification. Section 3 presents an empirical case to support our propositions. Finally, section 4 is a brief summary. ## 2. Modelling Inflation Uncertainty## 2.1. The economic model and analytical frameworkThere are several conceivable descriptions about a possible link between the level of inflation and inflation uncertainty. In general, when inflation is regarded as high, the possibility of policy intervention, differing from the prevailing policies, becomes larger. However, the intervention is only a possibility and takes place with a probability which may increase with the level of or the shock in inflation. Therefore, future inflation may be more uncertain when the current inflation is above or around a certain level to possibly trigger a policy intervention and, consequently change the future evolutionary path in inflation. The other source of uncertainty is inflation "pressure" which is naturally inherited in the economic system, in its production and distribution processes. Unlike policy intervention, inflation pressure remains in the same state when inflation is very high as well as very low. Total uncertainty is the combined effect of these two sets of variables. Let p (1) Where dz The model can be called the two-factor model. The expected level of inflation would be: (2) the variance (assuming these two variables are orthogonal for
simplicity) in p (3) and the variance of dz It is reasonable to assume that p To analyse the pattern of inflation uncertainty, we take the different
characteristics of policy intervention and inflation pressure into
consideration. Pg
The two-factor model is well posed to explain the mixed results in
empirical studies. As Friedman (1977) puts, "A burst of inflation
produces strong pressure to counter it. Policy goes from one direction to
the other, encouraging wide variation in the actual and anticipated rate
of inflation". Obviously, inflation uncertainty will be higher if
inflation is higher and, if the behaviour and effect of policy
intervention alone is considered. However, the ## 2.2. Econometric specificationsWe use an autoregression for the mean process, similar to the mean equations in Stockton and Glassman (1987) and Golob (1994). But, the assumptions underlined by equation (1) are different. The mean process in our model is stochastic in state transitions. Hamilton (1989) shows that such a process would appear as an autoregression, but unlike the conventional autoregression, it would have different variances in different states. Let us have two alternative hypotheses, H ),
it does not increase when p_{H}-1>
p_{t} or
p_{H}-1<
p_{t}.
Expressing them in testable statistical forms: _{L}(4) and (5) where w
and zero otherwise, w_{L}_{2} is the dummy taking value of unity when
p p_{L£
}-1<
p_{t}.
and zero otherwise, w_{H}_{3} is the dummy taking value of unity when
p-1³
p_{t}
and zero otherwise. The coefficients b_{H}_{1},
b_{2}
and b_{3
}represent three slopes in the three ranges of inflation. It
is obvious that the specification of equation (5) encompasses that of
equation (4). There are two advantages in applying equation (5). First, it
is able to detect a more general inflation-inflation uncertainty pattern
and the turning point. Second, if b_{1},
b_{2}
and b_{3}
have different values, b in equation
(4) is likely to be less statistically significant or statistically
indifferent from zero, incorrectly ruling out a time-varying variance and
any links between inflation uncertainty and inflation levels. In the
following section, the two hypotheses will be empirically tested.## 3. Results and findingsThe US consumer price index (CPI) is used in this study. The data set runs from January 1960 to March 1995. The index is of monthly frequency but inflation rate is calculated on the year-on-year basis as reported in the press. This would result in serial correlation of up to 12 lags and is carefully taken into consideration in the mean equation. The results are reported in table 1.
Panel A is for hypothesis H The residual in all three specifications displays no serial correlation
by the criterion of the Q statistic, though H
## 4. SummaryThis paper proposes a two-factor model for analysing inflation uncertainty. The model states that there are two influential factors underlying and inducing inflation uncertainty and the two factors have rather different property. Inflation pressure is relatively more persistent than policy intervention, which characterises the pattern of inflation uncertainty. To empirically verify the model, the econometric specification of differential slopes in different ranges of inflation is applied. There is one major finding in our study. Inflation uncertainty is found to increase with inflation in the medium to high range of inflation. Beyond that range, inflation uncertainty does not increase with inflation. In addition, our results have two implications. ## ReferencesBall, L. (1992), Why does high inflation raise inflation uncertainty, Journal of Monetary Economics, 29, 371-388. Brunner, A.D. and Hess, G.D. (1993), Are higher levels of inflation less predictable? a state-dependent conditional heteroscedasticity approach, Journal of Business and Economic Statistics, 11, 187-197. Engle, R.F. (1982), Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica, 50, 286-301. Fischer, S. (1986), Indexing, Inflation, and Economic Policy, The MIT Press, Cambridge, Massachusetts. Friedman, M. (1977), Inflation and unemployment, Journal of Political Economy, 85, 451-472 Golob, J.E. (1993), Inflation, inflation uncertainty, and relative price variability: A survey, Federal Reserve Bank of Kansas City Research Working Paper 93-15. Golob, J.E. (1994), Does inflation uncertainty increase with inflation? Federal Reserve Bank of Kansas City Economic Review, 3rd Quarter, 27-38. Hamilton, J.D. (1989), A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357-384. Stockton, D.J. and Glassman, J.E. (1987), An evaluation of the forecast performance of alternative models of inflation, The Review of Economics and Statistics, 69, 108-117. ## Footnotes
with 0.005 increment, to maximise the log likelihood function value. _{H}
_{1}p-1+
b_{t}_{2}(p-1)_{t}^{2}+
b_{3}(p-1)_{t}^{3}.
With this specification, not only the variance is the continuous function
of inflation, but also it first derivative. The local minimum and maximum
are obtained by letting the first derivative equal zero, and the former
(0.0036) with a positive second derivative value (0.00749) and the latter
(0.117) with a negative second derivative value (-0.00749). |

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