On inflation and inflation uncertainty in the G7 countries

Transcription

1 ELS EV IER Journal of International Money and Finance 17 (1998) Journal of International Money and Finance On inflation and inflation uncertainty in the G7 countries Kevin B. Griera, Mark J. Perryb?* adivisi6n de Economia, CIDE, Carretera M&ico Toluca, Col. Lomas de Sta. Fe, M&ico D.F , Mexico bdepadment of Economics, University of Michigan-Flint, Flint, MI , USA Abstract The relationship between inflation and inflation uncertainty is investigated in the G7 countries from 1948 to GARCH models are used to generate a measure of inflation uncertainty and then Granger methods are employed to test for causality between average inflation and inflation uncertainty. In all G7 countries, inflation significantly raises inflation uncertainty as predicted by Friedman and Ball. Weaker evidence is found that inflation uncertainty Granger-causes inflation. In three countries (US, UK and Germany) increased inflation uncertainty lowers inflation while in two countries (Japan and France) increased inflation uncertainty raises inflation Elsevier Science Ltd. All rights reserved. Keywords: Inflation; Inflation uncertainty; GARCH models; Monetary policy; Central banking 1. Introduction The cost of inflation is a subject that has long troubled macroeconomists. While surprise inflation redistributes wealth, it is difficult to show significant welfare losses from moderate, predictable inflations.' Yet inflation is extremely unpopular *Corresponding author. Tel.: ; fax: ; mjperry@umich.edu 'For example Cooley and Hansen (1991) find the welfare cost of moderate inflation so small when compared to the costs of other taxes that Benabou (1991) characterizes their paper as examining 'The welfare costs of ending moderate inflations' /98/$ Elsevier Science Ltd. All rights reserved. PII: S (9 8 ) OOO 2 3-0

2 672 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) with the public. One answer to this dilemma is that average inflation has indirect real costs through its effect on nominal uncertainty. Milton Friedman s Nobel lecture (Friedman, 1977) stresses the potential of increased inflation to create nominal uncertainty that lowers welfare and possibly even output growth? The innovative model by Ball (1992) formalizes Friedman s insight. Other recent work changes the direction of causation in the inflation-inflation uncertainty relationship to a world where greater uncertainty causes higher average inflation. Cukierman and Meltzer (1986) and Cukierman (1992) developed a game-theoretic model of Fed behavior that predicts that higher inflation uncertainty will raise the average inflation rate. In this paper we investigate the relationship between inflation and inflation uncertainty. We first use a GARCH model to generate a time-varying conditional variance of surprise inflation. With this conditional variance as a measure of inflation uncertainty, we then employ Granger methods to test the direction of causality between average inflation and uncertainty. We conduct these tests using monthly data from 1948 through 1993 first for the US and then for the other G7 countries. In all seven countries, lagged inflation is significantly and positively correlated with inflation uncertainty. We also find weaker evidence that inflation uncertainty Granger-causes inflation for some countries in our sample. In two countries (the US and Germany) increased uncertainty lowers inflation while in two countries (Japan and France) increased uncertainty raises inflation, as the Cukierman- Meltzer model predicts3 Thus increased uncertainty significantly affects future inflation in more than half the countries in the sample, but not all in the same manner. In the US and Germany, the inflation rate falls in response to increased inflation uncertainty. In Japan and France, the inflation rate rises. This response is consistent with opportunistic central bank behavior as in Cukierman and Meltzer. Interestingly, these differential responses to inflation uncertainty are correlated with measures of central bank independence. Using Cukierman s (1992) ratings, the US and Germany s central banks average on an independence scale that goes from zero to one (maximum independence) while Japan and France average only Beyond their macroeconomic implications, our results are notable in that we use a GARCH-generated conditional variance as our measure of uncertainty and find a significant positive relationship between it and past inflation. Engle (1983) and Bollerslev (1986) estimate ARCH or GARCH models of US inflation and then informally compare their estimated conditional variance series with average inflation. They both conclude that average inflation is not obviously related to uncertainty as the Friedman-Ball hypothesis predicts. However, neither Engle nor Bollerslev conduct any statistical test of the hypothesis. We construct and conduct This theme can also be found in the work of Okun (1971). 31n Canada, uncertainty does not Granger-cause inflation at any lag length, while in Italy the sign of the effect depends on the lag length.

3 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) such a test and find strong support for the Friedman-Ball hypothesis in the US and all the other G7 co~ntries.~ The paper proceeds as follows. In Section 2, we consider hypotheses about the causality between inflation and inflation uncertainty in more detail. Section 3 discusses previous empirical testing in this area, introduces GARCH models, and explains the use of conditional residual variances as measures of uncertainty. Section 4 presents our empirical results for the US. In Section 5, we extend our tests to the other G7 countries. In Section 6 we compare our results to other recent work on this issue. Section 7 is a summary and conclusion. 2. On the direction of causality between inflation and uncertainty In his Nobel address, Friedman claims that there is a positive correlation between inflation and nominal uncertainty. He argues that the causation runs from inflation to uncertainty about future inflation. Ball (1992) uses a game of asymmetric information, where the public knows that one type of policy-maker is willing to bear the economic costs of reducing inflation while the other type is not. When inflation is low, both types of policy-makers will keep it so. When inflation is high only the tough type will disinflate. Since Ball s policy-makers stochastically alternate in office, an increase in inflation now raises uncertainty about the path of future inflation because it is not known how long it will be before a tough type comes into power and disinflates. Thus, Ball s work provides a formal justification of Friedman s well-known insight. Cukierman and Meltzer (1986) and Cukierman (1992) start with the familiar Barro-Gordon model of Fed beha~ior.~ Here the Fed dislikes inflation but also seeks to stimulate the economy with surprise inflation. The lack of a commitment mechanism produces an inflationary bias in equilibrium. Cukierman and Meltzer model both the policy-maker s objective function and the money supply process as random variables. Therefore the public has an inference problem when observing higher inflation. Has the Fed s weight on increased employment gone up or is the higher inflation due to a random money supply disturbance? Cukierman and Meltzer show that, in their model, increases in inflation uncertainty raise the optimal average inflation rate by increasing the incentive for the policy-maker to create inflation surprises. In contrast to the Friedman-Ball view that high inflation 4Baillie et al. (1996) do find a significant positive relationship between inflation and uncertainity in Argentia, Brazil and Israel. Holland (19951, using Granger-causality testing, finds a positive relationship between inflation and a survey based measure of forecaster uncertaintiy in the US. We discuss these works in greater detail in Section 6. Barro and Gordon (1983) assume that the Fed dislikes inflation but values the higher employment that results from surprise inflation. They show that if the public has rational expectations and policy is discretionary that there is an inflationary bias to monetary policy that has no effect on employment.

4 614 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) creates uncertainty, the causation in Cukierman and Meltzer is from increased uncertainty to higher average inflatior6 However, this opportunistic response by the central bank is not the only possible outcome. While the contribution of our paper is primarily empirical, we do want to make the point that if inflation does cause uncertainty there may also be a negative partial correlation between inflation uncertainty and inflation, due to stabilization motives. If lower inflation lowers the nominal uncertainty that is generating real welfare costs, then policy-makers will have increased incentives to lower the inflation rate to reduce uncertainty and its concomitant real costs.7 Holland (1995) refers to this incentive as the stabilization motive. 3. Measuring inflation uncertainty Testing any of the above theories requires the construction of a specific measure for inflation uncertainty. The empirical literature began with a series of papers that assume the differences in the standard deviation of inflation across countries is a valid measure of the differences in inflation uncertainty across countries. As the literature turned to time-series tests, the two uncertainty measures typically used are the cross-sectional dispersion of individual forecasts from surveys or a moving standard deviation of the variable under consideration.* Neither of these techniques obviously capture the type of uncertainty modeled in the work of Ball or Cukierman and Meltzer where uncertainty is the variance of the stochastic, or unpredictable, component of a variable. As is well known, there can be a very large difference between variability and uncertainty, depending on whether the variability is predictable in the model under consideration. Predictable fluctuations in a variable will show up in standard deviation measures although they create no true economic uncertainty. Survey based measures summarize the range of disagreement among individual forecasters at a point in time. However, they do not give information about each 6Deveraux (1989) also starts with the Barro-Gordon model and adds a stochastic element to money growth. He then allows workers to endogenously choose the level of wage indexation that will exist in the economy. Deveraux shows that an exogenous increase in the variability of real shocks lowers the optimal amount of wage indexation. From the perspective of the policy-maker, less indexing makes surprise inflation more effective, thus increasing the incentive to create surprises. In equilibrium, the increased incentive to inflate translates into a higher average inflation rate. Even though there will be a gross correlation between average inflation and inflation uncertainty, Deveraux argues that this link is not causal, but derives from the public s response to increased real uncertainty (less indexation) and the Fed s response to declines in private indexation (more surprise inflation). The unique prediction of Deveraw s work is that output growth uncertainty increases average inflation. 7Given that inflation raises uncertainty and that Grier and Perry (1996a,b) show that increased inflation uncertainty raises the dispersion of relative prices and lowers real output growth, this reduction in inflation may be welfare-enhancing. 8Holland (1993) and Golob (1993) both contain tables that summarize many of these papers, including the measure of uncertainty employed in each. Brunner and Hess (1993) is an important exception to the critique of the literature offered in this section.

5 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) individual's uncertainty regarding their own forecast. It is possible for each forecaster to be extremely uncertain about future events but for them to submit very similar point estimates. Then, the survey measure would fail to capture the amount of existing uncertainty.' In contrast to the above measures, GARCH techniques specifically estimate a model of the variance of unpredictable innovations in a variable, rather than simply calculating a variability measure from past outcomes (moving standard deviation) or conflicting individual forecasts. That is, a GARCH model estimates a time-varying residual variance that corresponds well to the notion of uncertainty in Ball and Cukierman and Me1tzer.l' In the empirical work reported below, we estimate GARCH models for inflation and then use the time-varying residual variance as a measure of inflation uncertainty. A general autoregressive - GARCH(1,l) model for inflation is presented in Eqs. (1),(2) below. Eq. (1) is simply an autoregressive representation of the conditional mean of inflation. Eq. (2) is a GARCH(1,l) representation of the conditional variance. The model assumes the conditional variance of inflation follows an ARMA(1,I) process." 4. US results This section examines the relationship between inflation and inflation uncertainty in the US using monthly CPI data from 1948 through We begin with the GARCH(1,l) model described above to generate our measure of inflation uncertainty and then test it against two alternative conditional variance models. We then go on to report a series of Granger-causality tests to provide some statistical evidence nature of the relationship between inflation and inflation uncertainty. 'See Zamowitz and Lambros (1987) for a discussion of using survey dispersion to measure uncertainty. 10 Furthermore, because it is a parametric model, GARCH estimation gives an explicit test of whether the movement in the conditional variance of a variable over time is statistically significant. That is, we can construct a test of the null hypothesis that uncertainty is constant over the sample period. At a minimum, one should be able to reject this null hypothesis before doing a time series test of the effect of uncertainty on macroeconomic performance. While survey or variability based measures of uncertainty do fluctuate over time, there are no tests for whether those fluctuations are statistically significant. l1 There is another strand of this literature that attempts to disentangle long-run vs. short-run inflation uncertainty stemming from the work of Klein (1975) [see for example Ball and Cecchetti (1990) and Evans and Wachtel (1993)l.

6 616 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) A GARCH time series model for US inflation We need to establish that the inflation data series is stationary, that the residuals of the chosen time-series model of inflation are white noise, and that the residual variance of inflation is significantly time-varying." We use both the Phillips-Perron (PP) and augmented Dickey-Fuller (ADF) tests of the null hypothesis that inflation has a unit root. The last spike in the partial autocorrelation function for inflation is at the 12th lag, so we use 11 lagged difference terms in the ADF test. Both tests reject the null hypothesis of a unit root in US inflation at the 0.01 level.13 Over this sample at least, the US inflation rate is clearly stationary. Panel A of Table 1 shows the results of a 12th order autoregressive model for the inflation rate. The R2 is 0.45 and the Q-tests on the residuals show no sign of autocorrelation out to 18 lags. However, the squared residuals are extremely correlated. The Q2 statistic testing the hypothesis of no pattern in the squared residuals is 118 at six lags (critical value = 12.6) and 167 at 18 lags (critical value = 28.9). The AR(12) regression model captures any pattern in the mean of inflation, but does not account for this strong pattern in the conditional variance. Panel B of Table 1 adds a GARCH(1,l) model of the conditional variance to the AR(12) model of the conditional mean. We estimate this model using the quasimaximum-likelihood technique of Bollerslev and Wooldridge (1991). Q-statistics for the residuals of the GARCH model are shown in panel B and reveal no pattern in the residuals or squared residuals. The AR(12)-GARCH(1,1) model seems to fit both the mean and variance of inflation well4 However, before we accept GARCH(1,l) as an adequate time series model of inflation uncertainty for use in the Granger tests and VAR results reported below, it is important to consider some alternatives Is GARCH(1,l) an adequate specifcation of the conditional variance of inflation? The GARCH(1,l) conditional variance model is widely used and approximates any arbitrary ARCH model. However, there are viable alternative models of the conditional variance. Here we consider two, the asymmetric GJR model (Glosten et al., 1993) and the Engle-Lee component GARCH model (1993). In the standard GARCH model, positive and negative residuals have a symmetric impact on the conditional variance. The GJR model allows for negative '*Cosimano and Jansen (1988) make the point that any pattern in the residuals will bias tests for gtterns in the squared residuals in favor of falsely finding ARCH effects. Our results are not sensitive to the number of lagged difference terms. The ADF test rejects a unit root in this series at least the 0.05 level using anywhere from one to 24 lagged difference terms. We use a lag truncation parameter of five in estimating the PP (Phillips-Perron) test for a unit root. The PP test is not sensitive to the choice of lag truncation parameter either. 14 The estimated coefficients in the variance equation are highly significant as can be seen by their individual t-statistics as well as by noting that the log of the likelihood function increases from to from panel A to panel B. The estimated conditional variance is stable as the two slope coefficients in the GARCH equation sum to which is less than 1.0.

7 KB. Grier, M.J. Perry /Journal of International Money and Finance I7 (1998) Table 1 Time series models of the US inflation rate 12) Least squares results II, = n,-, II IIt_3 + 0.O18IIt rI-, t-, + (3.06) (4.00) (2.53) (1.25) (0.33) (1.44) (0.19) 0.111II II,-, rI II II nt-12 + ~t (1.94) (2.16) (2.16) (1.37) (0.73) (2.54) Log-likelihood = , R2 = 0.45 Q(6) = 1.50, Q(12) = 4.90, Q(18) = Q2(6> = 118, Q2(12) = 154, Q2(18> = 167 (B) GARCH(1,l) results IIt = II II II, II II n,-, + (2.39) (5.46) (4.07) (1.19) (0.52) (1.80) (1.41) t rI-s II n,-,, II-1, nt-1, + ~t (0.84) (1.71) (3.00) (1.02) (0.01) (1.84) u2st = ~~~ ~~~,-~ (2.26) (2.22) (10.7) Log-likelihood = Q(6) = 1.44, Q(12) = 2.79, Q(18) = Q2(6> = 8.42, Q2(12) = 13.42, Q2(18) = Note: Numbers below the coefficients are t-statistics. Sample is monthly from February 1948 through December The critical values of the Q-statistics at 6, 12 and 18 lags are 12.6, 21 and residuals to have a different impact on the conditional variance than do positive re~idua1s.l~ The GJR model for the conditional variance is given by Eq. (3) below. g: = a. + al~f-l + a2~f-~d,-, 2 + a3getpl Where dt-l = 1 if E ~ < - 0 ~ and = 0 otherwise. Here the coefficient a2 # 0 implies asymmetry in the conditional variance. In a stationary GARCH model, the conditional variance displays long run mean reversion to a constant level given by a. in Eq. (2) or Eq. (3) above. By contrast, the Engle and Lee (1993) Component-GARCH model allows the mean reversion level of the conditional variance to itself be time-varying. The model, given by Eqs. (4),(5) below, divides the conditional variance into permanent and transitory components. (3) 2 2 g: = 4, + al(ct-l - qt-j + " 2bE,_, t = a0 + P4t-1 + 'y3(&t-1 - gt-1) (4) (5) "The GJR model comes from finance applications where it is often found that bad news has a greater impact on uncertainty than good news. For a GARCH-GJR comparison using stock returns see Engle and Ng (1993).

8 618 KB. Grier, M.J. Perry /Journal of International Money and Finance I7 (1998) Table 2 Alternative conditional variance models for US inflation 64) GJR asymmetric model 2 cr = ~~,-~ ~~,-~d,-~ ~~,,-~ Ef (2.09) (2.61) (0.67) (10.6) Log-likelihood = [do not reject GARCH(1,l)I (B) Longer memory model 1. Likelihood ratio test Garch(1,l) vs. Garch (2,2) = [Reject GARCH(1,l) at the 0.01 level] 2. Component GARCH model qf = q, (~~,-1 - ~ ' ~ ~ - 1 ) (6.27) (155) (0.41) Log-likelihood = Note: For each variance equation reported the mean equation contained 12 lags of inflation. The sample period is February 1948-December Numbers in parentheses are t-statistics robust to non-normality. If p in Eq. (5) is equal to 1.0 then the conditional variance contains a unit root. If p < 1.0 and p > a1 + a2, then qt is the longer memory component of the conditional variance.16 It is not obvious that the Component GARCH model is a superset of the GARCH(1,l) model, but Engle and Lee show that it is equivalent to a GARCH(2,2) model with appropriate restrictions on the coefficients. We can thus crudely test between the GARCH(1,l) and Component GARCH models by using a likelihood ratio test between a GARCH(1,l) and GARCH(2,2) model. Table 2 reports the results of testing for asymmetry and longer memory in the conditional variance of US inflation. The coefficients for the 12 lags of inflation are not reported in order to save space. The results show no evidence of any asymmetry in the conditional variance since the coefficient for ag in the GJR model [Eq. (311 is insignificant. However, a GARCH(2,2) model does fit the data significantly better than the GARCH(1,l) model, leading us to prefer the Component GARCH model for US inflation. However, the GARCH(1,l) and Component 16 The Component GARCH model simplifies to the Garch(1,l) model if p = 0 or if a1 + a2 = 0. Engle and Lee also show that the Component GARCH model can be written as a GARCH(2,2) model with appropriate restrictions on the coefficients.

9 KB. Grier, M.J. Peny /Journal of International Money and Finance 17 (1998) GARCH(1,I) Model Component GARCH I o~,, Fig. 1. GARCH(1,l) and Component GARCH estimates of the conditional standard deviation of US inflation GARCH conditional variances are highly correlated (correlation coefficient of 0.87) and none of the results reported below depend on which uncertainty measure is used. Fig. 1 displays the GARCH(1,l) and Component GARCH estimates of the conditional standard deviation of the US inflation rate Granger-causality tests With these preliminaries established, consider now the Granger-causality tests for inflation and inflation uncertainty in Table 3. Panel A uses the GARCH(1,l)

10 680 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) measure of inflation uncertainty and shows that the null hypothesis that inflation does not Granger-cause inflation uncertainty is rejected at the 0.01 level using four, eight or 12 lags. The null hypothesis that uncertainty does not Granger-cause inflation is rejected at the 0.05 level using eight or 12 lags. This latter result should not be interpreted as showing support for the Cukierman and Meltzer model because the sum of the coefficients on lagged uncertainty in the inflation equation is negative. In the US, increased inflation uncertainty lowers future inflation. Panel B repeats the experiment using the Component GARCH measure of inflation uncertainty. The results are virtually identical. The only real difference is that the significance level of uncertainty in the inflation equation at eight lags falls from 0.05 to The results suggest that the 'stabilizing Fed' notion discussed in Section 2 above is plausible. Increased inflation first raises uncertainty, which creates real welfare losses and then leads to monetary tightening to lower inflation and thus also inflation uncertainty On the size of the inflation-inflation uncertainty relationship Our results show that taking the conditional variance as given, there is a significant correlation between it and average inflation. Here we provide some evidence on the quantitative size of the relationship. To do so, we use the regressions behind the twelve lag Granger-causality tests reported in panel A of Table 3. First we simulate the effect of a sustained rise in inflation from its sample mean of 3.96% to one standard deviation (1 S.D.) above its mean (i.e. to 8.31%). The results are shown in Fig. 2. Uncertainty rises quickly from its mean of up to almost 17 within 11 months and then falls steadily. At the peak of the effect, the 1-S.D. increase in inflation is associated with approximately a 0.7-S.D. increase in inflation uncertainty. Fig. 3 shows the effect of increased inflation uncertainty on the average inflation rate. A 1-S.D. increase in uncertainty from its average level of to produces an irregular and smaller decline in average inflation from its mean of "As one of our referees pointed out, one could conceive of doing these tests simultaneously in a single model by putting lagged inflation in the conditional variance equation and the conditional variance in the inflation equation. Baillie et al. (1996) do this for the US using a fractionally integrated GARCH-M model and do not find any significant relationships. However, we do not want to restrict the effects we are studying here to occur within a month. If increased inflation raises uncertainty which produces real costs, and the Fed subsequently decides to stabilize, it is extremely unlikely that the lower inflation will appear in the same month that the uncertainty increases. Furthermore, as we discuss elsewhere, putting lagged inflation in the variance equation can cause problems with the non-negativity of the variance. For these reasons, we have chosen the two-step strategy used in the paper. We have estimated a component GARCH-M with lagged inflation in the variance equation for the US. The coefficient on lagged inflation in the conditional variance equation is positive and significant, which is contrary to the insignificant coefficient found by Baillie, Chung and Tieslau (BCT) and the coefficient on the conditional variance in the inflation equation is negative, but insignificant. This is consistent with our two-step approach where we generally find uncertainty affects average inflation only with a lag of several months. The Appendix contains the model summarized here.

11 KB. Grier, M.J. Peny /Journal of International Money and Finance 17 (1998) Table 3 Granger causality tests for inflation and inflation uncertainty in the US H,: Inflation does not Granger-cause inflation uncertainty H,: Inflation uncertainty does not Granger-cause inflation 64) Using GARCH(1,l) measure of uncertain8 (January 1948-December 1993) Four lags 9.32*** (+) 1.26 Eight lags 3.91*** (+) 2.21** (-1 Twelve lags 3.72*** (+> 2.45* * ( - ) (B) Using Component GARCH measure of uncertain8 (January 1948-December 1993) Four Lags 5.54*** (+I 1.71 Eight Lags 4.06*** (+) 1.88* (-) Twelve Lags 3.99*** (+) 2.20* * (- Note: ***, ** and * indicate significance at the 0.01, 0.05 and 0.10 levels, respectively. In column 1, a (+> indicates the sum of the coefficients on lagged inflation are positive and significant. In column 2, a (-1 indicates that the sum of the coefficients on lagged uncertainty are negative and significant. 3.96%. At the peak of the effect, the 1-S.D. increase in inflation uncertainty is associated with approximately a 0.25-S.D. decrease in average inflation. The effect of inflation on uncertainty is the quantitatively dominant effect. Since these results are not from a fully specified model of the inflation process, they are intended only to be suggestive of the relative quantitative importance of the two effects. 5. Extension to the other 67 countries In this section we apply the same empirical method used above to the other countries in the G7 (Germany, Japan, the UK, Canada, Italy and France). We use monthly data from DRI on the consumer price index for each country from January 1948 to December 1993.l' Table 4 presents ADF and PP tests of the unit root hypothesis for each country. Only the ADF test for Canada fails to reject the null hypothesis of a unit root at the 0.10 level. We will treat these inflation series as stationary in our analysis. We use an AR(12) plus 11 seasonal dummy variables model for the mean inflation rate and begin with a GARCH(1,l) model for the conditional variance of the inflation rate in each country.'' In each case the GARCH coefficients are highly significant and neither the standardized residuals nor their squares show any pattern. We then perform the same specification tests for the adequacy of the GARCH(1,l) model as we did for the US above. "The only exception is Germany whose series begins in July "There is significant seasonality in these six countries' inflation series while there was none in the US inflation data.

12 682 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) Months since increase in average inflation Fig. 2. The effect of a 1-S.D. increase in average inflation on the level of inflation uncertainity. In none of the six countries do we find any evidence of asymmetry in the conditional variance. The GARCH(1,l) model is never rejected in favor of the GJR model. However, in four of the countries, Germany, France, Japan and Italy, a GARCH(2,2) model fits the data significantly better than the GARCH(1,l) model (Table 5). As in the case of the US, we take this as evidence in favor of the Component GARCH model. For Canada and the UK, the GARCH(1,l) model fits the data best.20 In the Granger tests below, we report results using both GARCH(1,l) and Component GARCH measures of uncertainty for the four countries where a longer memory model improves the fit of the equation and only GARCH(1,l) results for Canada and the UK. Months since the Increase in Uncertainty Fig. 3. The effect of a 1-S.D. increase in inflation uncertainty on the average rate of inflation.

13 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) Table 4 Tests for the stationarity of inflation rates Country ADF t- statistic Germany Japan UK Canada Italy France 4.85*** 6.95*** * 5.12*** Phillips-Perron t-statistic 17.73* ** 22.19*** 20.03*** 19.29*** 21.95*** 15.82*** Note: The tests in the first column are augmented Dickey-Fuller tests with 11 lagged difference terms. The tests in the second column are Phillips-Perron tests with the lag truncation set at five. Results of this test are not sensitive to the choice of truncation parameter. In each case, the t-statistic tests the null hypothesis that inflation in the relevant country has a unit root. *** **, and * indicate rejection of the null at the 0.01, 0.05 and 0.10 levels, respectively. We use a monthly sample from Inflation rates are calculated from the CPI for each country. Table 6 presents the relevant Granger-causality tests. In each country at each lag length the null hypothesis that inflation does not Granger-cause uncertainty is rejected at the 0.05 level except for Japan at a lag length of four. In each country except Canada, for at least one lag length, the null hypothesis that uncertainty does not Granger-cause inflation is rejected at the 0.05 level. While these results on the effect of inflation on uncertainty conform closely to the US results in that higher inflation raises inflation uncertainty, the effect of uncertainty on the inflation rate varies. Germany shows a highly significant negative effect of uncertainty on inflation as is the case in the US. The UK shows a much weaker, but still overall negative effect. These three countries (Germany, US and UK) show the response to uncertainty that we label as the stabilizing Fed where inflation shocks raise uncertainty, which causes welfare losses and the central bank then stabilizes by reducing inflation. In contrast, both Japan and France show a highly significant positive effect of uncertainty on inflation. The results for these two counties support the Cukierman-Meltzer hypothesis we label as the opportunistic Fed. Inflation uncertainty does not Granger-cause inflation in Canada, and the sign of the effect varies with the lag length for Italy. Interestingly, this division of countries by how their inflation rate responds to inflation uncertainty is closely related to Cukierman s ranking of central bank independence on a scale from 0 (minimal independence) to 1. Germany and the US are rated as highly independent with scores of 0.66 and On the low side of This is not surprising because the component model is a longer memory model, and inflation uncertainty is less persistent in Canada and the UK than in the other five G7 countries. The coefficient on the lagged conditional variance in the GARCH(1,l) is a rough measure of the persistence of inflation uncertainty, and the coefficient is for the UK and for Canada. In the other five countries, the autoregressive coefficient in the GARCH(1,l) model is above 0.80.

14 684 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) the independence spectrum, France s rating is 0.28 and Japan s is only 0.16F1 A lack of independence as measured by Cukierman corresponds to opportunistic behavior where the central bank can use an increase in uncertainty to raise average inflation in an attempt to increase output. The most independent central banks are in countries where inflation falls in response to increased uncertainty. 6. Comparison with other work Engle (1983) and Bollerslev (1986) estimate ARCH and GARCH models, respectively for the US inflation rate. They then compare a graph of the conditional variance of inflation to the average inflation rate. Inflation uncertainty is highest in the late 1940s and early 1950s when inflation is not particularly high and inflation uncertainty is lower in the late 1970s and early 1980s when inflation is quite high. Given this, both authors conclude that high inflation levels are not correlated with unpredictable inflation. Such a conclusion is unsatisfactory in that it is not based on any kind of statistical test.22 Our conditional variance measure for the US is also highest at the beginning of the sample and lower when inflation is highest, yet lagged inflation has a significant and sizeable effect on inflation uncertainty as we have shown. Baillie et al. (1996) estimate a fractionally integrated GARCH model of the inflation rate and then test the hypotheses that lagged inflation is a significant regressor in the conditional variance equation and that the conditional variance is a significant regressor in the inflation equation. For the US they do not find any relationship between inflation and uncertainty. Our work differs from theirs in that we do not consider fractional differencing and we use more than one lag of monthly inflation and uncertainty to look for a link between the two. Baillie et al. do find significant links between inflation and its conditional variance for the UK, Argentina, Brazil and Israel, but not for the US or the remaining five G7 countries.23 Holland (1995) uses a semi-annual, survey based, measure of inflation uncertainty and conducts Granger-causality tests on uncertainty and average inflation for the US over a sample. He too finds that inflation Granger-causes uncertainty and that uncertainty has a weaker but negative effect on average 21 The rankings are from Cukierman (1992, Table 19.3) where he ranks 68 countries central banks on overall legal independence. Germany was ranked second, the US sixth, France 44th and Japan 64th. 221n fairness to both authors, it should be pointed out that the main point of each paper was to show the utility of time-varying conditional variance models for economic time series and not to test any hypotheses about the effect of average inflation on uncertainty. 23Baillie et al. put lagged inflation into their GARCH variance equation as an exogenous regressor. Since the inflation rate can be negative, that specification could produce a negative conditional variance. To avoid the possibility of a negative variance one must use the square or absolute value of inflation. Brunner and Hess (1993) point out that such symmetric measures, where high inflation and high deflation enter the data with the same value are not consistent with a test of Friedman s hypothesis.

15 KB. Grier, M.J. Perry /Journal of International Money and Finance I7 (1998) Table 5 Conditional variance models for the rest of the G7 countries Canada, GARCH(1,l) a*,, = E*~-, a*ct- (3.14) (3.08) (4.38) &Test for GJR model asymmetry = 0.88 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = 1.82 Do not reject GARCH(1,l) at the 0.05 level France, GARCH(1,I) Log likelihood = a,, = E*, a*,,- Log likelihood = (2.27) (3.02) (20.9) t-test for GJR model asymmetry = 0.91 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = 8.32 Reject GARCH(1,l) at the 0.05 level France, Component GARCH a2,t = qt (~~,-, - qt-l) (0~,,-~ - qt-l) Loglikelihood = (4.30) (0.70) Germany, GARCH(1,I) a,, = E,-, a,,- Log likelihood = (3.89) (0.75) (87.1) t-test for GJR model asymmetry = 1.56 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = Reject GARCH(1,l) at the 0.01 level Germany, Component GARCH a*,, = qf (~*,-~ - qf-l) (1~*~,-, - qf-l) Log likelihood = (4.30) (0.70) qt = O.979qt (~*,-1 - (15.5) (588) (1.86) Italy, GARCH(1,I) a*,, = ~~~ a*,f- Log likelihood = (1.05) (3.24) (22.7) t-test for GJR model asymmetry = 1.80 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = 6.20 Reject GARCH(1,l) at the 0.05 level Italy, Component GARCH = q, (~,-~ - qt-l) (a2,,-, - qt-l) Log likelihood = (2.02) (1.09)

16 686 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) Table 5 (Continued) Japan, GARCH(1,I) crzsf = ~~,-~ a2,,-, Log likelihood = (1.60) (2.91) (38.2) t-test for GJR model asymmetry = 0.56 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = Reject GARCH(1,l) at the 0.01 level Japan, Component GARCH cr2,, = q, ~~,-, - qt-l) (u2,,-, - qt-l) Loglikelihood = (2.89) (1.76) U& GARCH(1,l) 2 cr Ef = ~~,-, ~~,,-~ Log likelihood = (5.51) (3.61) (2.85) t-test for GJR model asymmetry = 0.47 Likelihood ratio test, GARCH(1,l) vs. GARCH(2,2) = 4.83 Do not reject GARCH(1,l) at the 0.05 level Note: For each variance equation reported the mean equation contained 12 lags of inflation and 11 monthly dummies. The sample period is February 1949-December 1993 except for Germany (August 1949-December 1993). Numbers in parentheses are t-statistics robust to non-normality. The Q-statistics for the standardized residuals and squared residuals show no patterns in any country with the exceptions of a significant spike at the 12th lagged squared residual in the French data and a significant spike at the 15th lagged squared residual in the UK data. inflation. However, we use a different uncertainty measure and sample period, test for the effects of asymmetry, allow for inflation uncertainty to have permanent and transitory effects and extend the analysis to the rest of the G7 countries. 7. Conclusion In this paper we use GARCH models to construct measures of monthly inflation uncertainty in the G7 countries from We then examine the relationship between inflation and inflation uncertainty in the G7 countries using Grangercausality tests. We find overwhelming evidence that increased inflation raises inflation uncertainty even over a very short horizon, confirming the theoretical predictions made by Friedman and Ball. There is mixed evidence on the effect of inflation uncertainty on average inflation. Japan and France show the relationship predicted by Cukierman and Meltzer where increased uncertainty is associated with higher inflation. The US and Germany (and the UK, though less strongly) reveal the opposite pattern; increased inflation uncertainty leads to lower average inflation.

17 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) Table 6 Granger causality tests for inflation and inflation uncertainty H,: Inflation does not Granger-cause H,: Inflation uncertainty does not Granger-cause inflation uncertainty inflation GARCH(1,l) Component GARCH(1,l) Component (A) Germany Four lags Eight lags Twelve lags 4.6*** (+) 6.4*** (+> 4.5*** (+> 2.3 ** (+> 3.9 *** (+> 4.5 *** (+) 6.1*** (-1 2.9*** ( *** (-) 2.2** (-1 2.2** (-1 (B) Japan Four lags Eight lags Twelve lags *** (+) 6.9*** (+) *** (+) 6.1*** (+) 2.6** (+> 3.6*** (+) 2.1** (+) 6.2*** (+) 4.3*** (+> 2.3** (+) (C) UK Four lags Eight lags Twelve lags 23.5*** (+) 11.4*** (+> 8.8*** (+) ** (-1 (D) Canada Four lags Eight lags Twelve lags 13.2*** (+) 7.1*** (+) 5.5*** (+) (E) Italy Four lags Eight lags Twelve lags 2.4** (+) 12.4*** (+) 13.1*** (+) 2.5** (+) 13.4*** (+) 13.7*** (+) 3.7 *** (-) 2.7 *** (+) *** (-1 2.6*** (+) 1.4 (F) France Four lags Eight lags Twelve lags 12.6*** (+) 12.5*** (+) 6.9*** (+) 12.8*** (+) 8.7*** (+) 7.0*** (+) 4.5*** (+I 5.2*** (+) 4.7*** (+) 2.7** (+) 2.2** (+I 5.5*** (+) Note: *** and ** indicate significance at the 0.01 and 0.05 levels. A (+) indicates the sum of the coefficients are positive and significant. A (-1 indicates that the sum of the coefficients are negative and significant. The US and German cases suggest behavior by the central bank that we and Holland call stabilizing. Increased inflation has real costs through its impact on costly uncertainty. When uncertainty is high, the central bank reduces those real costs at the margin by reducing inflation. When we look for institutional reasons why the inflation response to increased uncertainty varies across countries, we note that the two countries associated with an opportunistic response have much lower central bank independence ratings that the two countries associated with a stabilizing response.

18 688 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) In future work we seek to extend the sample of countries and investigate whether the robust relation between inflation and uncertainty we find in the G7 holds throughout the world. We also want to discover whether the suggestive correlation we find between central bank independence and inflation policy we see in our data can be more formally tested in an expanded sample of countries. Acknowledgements We thank Richard Baillie, Robin Grier, Douglas Nelson, two anonymous referees and James Lothian for valuable comments and suggestions. Any remaining shortcomings are ours alone. Appendix A A Component GARCH-M model of inflation with lagged inflation in the conditional variance This appendix reports the estimation of the model discussed in the text. Here we simultaneously estimate a system of equations that allows only the current value of the conditional variance of inflation to affect average inflation and allows one lag of average inflation to influence the conditional variance. The model is given below. When estimated, the coefficient for the current conditional variance on average inflation ( p13) is with a t-statistic of The coefficient for the effect of lagged inflation on the conditional variance (a,) is 0.24 with a t-statistic of A likelihood ratio test rejects the plain component GARCH model reported in the text in favor of this model at the 0.05 level. We find a positive association between lagged inflation and uncertainty similar to that found with the two-step method used in the text. We do not find that uncertainty affects average inflation. However, as we emphasize in the text, any relationship where uncertainty influences average inflation takes time to show up and cannot be fairly tested in a model that restricts the effect to be contemporaneous. References Ball, L., Why does high inflation raise inflation uncertainty? J. Monet. Econ. 29, Ball, L., Cecchetti, S.G., Inflation and uncertainty at short and long horizons. Brook. Pap. Econ. Act. 1,

19 KB. Grier, M.J. Peny /Journal of International Money and Finance I7 (1998) Benabou, R., Comment on the welfare costs of moderate inflations. J. Mon. Cr. Bank. 23, Baillie, R., Chung, C.-F., Tieslau, M., Analysing inflation by the fractionally integrated ARFIMA-GARCH model. J. Appl. Econometr. 11, Barro, R., Gordon, D., A positive theory of monetary policy in a natural rate model. J. Polit. Econ. 91, Bollerslev, T., Generalized autoregressive conditional heteroskedasticity. J. Econometr. 31, Bollerslev, T., Wooldridge, J., Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances. Econ. Rev. 11, Brunner, A., Hess, G., Are higher levels of inflation less predictable? A state-dependent conditional heteroskedasticity approach. J. Bus. Econ. Stat. 11, Cooley, T., Hansen, G., The welfare costs of moderate inflations. J. Mon. Cr. Bank. 23, Cosimano, T., Jansen, D., Estimates of the variance of US inflation based upon the ARCH model. J. Mon. Cr. Bank. 20, Cukierman, A,, Meltzer, A,, A theory of ambiguity, credibility, and inflation under discretion and asymmetric information. Econometrica 54, Cukierman, A,, Central Bank Strategy, Credibility, and Independence. MIT Press, Cambridge. Deveraux, M., A positive theory of inflation and inflation variance. Econ. Inquiry 27, Engle, R., Estimates of the variance of U.S. inflation based on the ARCH model. J. Mon. Cr. Bank. 15, Engle, R., Lee, G., A permanent and transitory component model of stock return volatility. Discussion paper 92-44R3, University of San Diego. Engle, R., Ng, V., Measuring and testing the impact of news on volatility. J. Fin. 48, Evans, M., Wachtel, P., Inflation regimes and the sources of inflation uncertainty. J. Mon. Cr. Bank. 25, Friedman, M., Nobel lecture: Inflation and unemployment. J. Polit. Econ. 85, Glosten, L., Jagannathan, R., Runkle, D., On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Fin. 48, Golob, J., Inflation, inflation uncertainty and relative price variability: A survey. Working paper no , Federal Reserve Bank of Kansas City. Grier, K., Perry, M.J., 1996a. Inflation, inflation uncertainty and relative price dispersion: evidence from bivariate GARCH-M models. J. Monet. Econ. 38, Grier, K., Perry, M.J., 1996b. The effects of real and nominal uncertainty on inflation and output growth. Working paper, Tulane University. Holland, A.S., Comment on inflation regimes and the sources of inflation uncertainty. J. Mon. Cr. Bank. 25, Holland, A.S., Inflation and uncertainty: Tests for temporal ordering. J. Mon. Cr. Bank. 27, Klein, B., Our new monetary standard: The measurement and effects of price, Econ. Inq. 13, Okun, A., The mirage of steady inflation. Brook. Pap. Econ. Act. 2, Zarnowitz, V., Lambros, L., Consensus and uncertainty in economic prediction. J. Polit. &on. 95,