Evans-

Discovering the Link Between Inflation Rates and Inflation Uncertainty Author(s): Martin Evans Source: Journal of Money, Credit and Banking, Vol. 23, No. 2 (May, 1991), pp. 169-184 Published by: Ohio State University Press Stable URL: http://www.jstor.org/stable/1992775 Accessed: 10-09-2017 07:15 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Ohio State University Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of Money, Credit and Banking This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms MARTIN EVANS Discovering the Link between Inflation Rates and Inflation Uncertainty IT IS WIDELY BELIEVED THAT moderated rates of inflation impose significant economic costs on society through increased inflation uncertainty. In fact many policymalcers and economists argue that moderate rates of inflation merit tough anti-inflationary policies precisely because the benefits from reduced uncertainty outweigh the costs associated with the accompanying recession. In this paper I try to assess the case for such policies by presenting some new statistical evidence on the link between inflation uncertainty and the level of inflation in the United States. I find that uncertainty about the long rather than short-term prospects for inflation has moved strongly with the rate of inflation since the early 1970s. Although economists have long suspected that inflation rates and inflation uncertainty are tightly linked, the statistical evidence is surprisingly ambiguous. While high rates of inflation are often observed to be variable [see Okun (1971), Logue and Willett (1976), Logue and Sweeney (1981), and Taylor (1981) for cross-country evidence], increased variability need not imply greater uncertainty. In fact the ARCH studies by Engle (1983), Holland (1984), Cosimano and Jansen (1988), and Jansen (1989) provide counterexamples.l Engle, for example, finds little evidence of a link between the relatively high rates of inflation experienced by the United States in the 1970s and uncertainty measured by the conditional variance of inflaThe author thanks James Lothian, Paul Wachtel, and two anonymous referees for their comments on an earlier draft. lAs an alternative to the ARCH methodology, several studies have constructed proxies for inflation uncertainty from the time series data. Katsimbris (1985), for example, uses eight-quarter, nonoverlapping moving averages. Aside from the issues of measurement, this approach has not been any more successful in identifying a statistically significant link between the rate of inflation and inflation uncertainty in the United States. MARTIN EVANS is assistant professor of economics, Stern School of Business, New York University. Journal of Money, Credit, and Banking, Vol. 23, No. 2 (May 1991) Copynght @ 1991 by The Ohio State University Press This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 170 : MONEY, CREDIT, AND BANKING tion. By contrast, the results from cross-sectional survey studies of inflationary expectations appear to support a link. Wachtel (1977), Carlson (1977), and Cukierman and Wachtel (1979) all Elnd a positive correlation between the rate of inflation and the dispersion of inflation forecasts gathered from the Michigan and Livingston surveys that proxy for inflation uncertainty. The methodology used in this paper differs from previous studies in two impor- tant respects. First, it is recognized that there are many aspects to inflation uncertainty. For example, uncertainty about the short-term prospects for inflation may be very different from the long-term prospects for the reasons discussed in Klein (1977). In contrast with earlier time series studies, I therefore consider several statistical measures that focus on different aspects of inflation uncertainty. The paper also differs from recent time series studies of inflation uncertainty in the modeling of inflation. Although ARCH models for inflation have become popular, I shall use a more complicated specification that allows for time-varying parameters and an ARCH speciElcation for inflation shocks. This model, developed in Evans and Wachtel (1989), offers both theoretical and practical advantages over ARCH specifications. The plan of the paper is as follows: Section 1 describes the time series model for inflation and discusses its merits. Section 2 begins by discussing the data before presenting the model estimates. The link between inflation rates and inflation uncer- tainty is examined in Section 3 using three statistical measures derived from the time series model. As in Engle's study, uncertainty about the short-term prospects for inflation-measured by the conditional variance of monthly inflation turns out to be almost completely unrelated to the level of inflation. Uncertainty about long-term inflation, however, has a strong positive association with the rate of inflation. Thus, the survey results cited above may indeed be consistent with the time series evidence provided the dispersion of inflationary forecasts reflects this type of uncertainty. The paper ends with a summary of the main results and a discussion of their policy implications. 1. MODELING THE INFLATION PROCESS Theoretical Issues Recent time series studies of inflation uncertainty have focussed on one aspect of uncertainty, namely the (conditional) variance of period to period inflation. However, it seems unlikely that any single statistical measure completely captures all the economically relevant aspects of inflation uncertainty. An increase in the condi- tional variance of next period's inflation rate may, for example, be unrelated to the precision with which the long-term rate of inflation can be forecast. The time series model used in this paper will therefore allow several different aspects of inflation uncertainty to be examined. The advantages of this approach are easily recognized when we consider how uncertainty about inflation is likely to affect economic decision making. There are This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms MARTIN EVANS : 171 two types of decisions to consider, temporal and intertemporal. Temporal decisions are most likely to be affected by the conditional variance of period-to-period movements in inflation. In the well-known Lucas model (Lucas 1973) changes in the variance of inflation next period affect the inferences drawn from aggregate price movements about shifts in the current set of individual relative prices. These inferences, in turn, determine current production decisions. Individuals face a similar problem in Deaton's (1977) analysis of how inflation affects consumption. By contrast, variations in this short-term conditional variance may have little impact on intertemporal decisions that cannot be easily or costlessly reversed. For example, the decision to buy a Certificate of Deposit should depend more upon the degree of precision with which inflation can be forecast over the next year than over the next month. This suggests that intertemporal decision making including the negotiation of long-term contracts is more likely to be affected by variations in the conditional variance of annual or long-term inflation. With these differences in mind, I shall use the time series model in subsequent sections to examine not only the short-term variance of inflation that affects temporal decisions, but also the variance of inflation forecasts far out into the future that are important in intertemporal decision making. Practical Issues Uncertainty is not the same as variability. If individuals have very little information, they may view the future with a large amount of uncertainty even though the econometrician observes little volatility in actual inflation ex post. Conversely, there may be very little uncertainty accompanying a large change in actual inflation observed by an econometrician because individuals have a good deal of advanced information about a change in (say) monetary policy. Thus, estimates of inflation uncertainty based on the variability or simple variance of actual inflation over some subsample of the data may be unreliable and even misleading. Many recent studies have sought to avoid this problem by modeling inflation as an ARCH process. Here greater variability in ex post inflation is only equated with increased uncertainty when the time-varying estimates of the conditional variance rises. To motivate my model, I shall begin by discussing this approach to identifying inflation uncertainty. Let AP.+l denote the rate of inflation between t and t + 1. A generic ARCH specification for the inflation rate can be represented by APr+1 = m r, = r + i=O x, + e,+l e,+l N(O,r,) (1) oyir,_i (2) n 2. Xie,2_i + 2 i=l where x, is a vector of explanatory variables known at time t, ,8 is a vector of parameters and e,+ 1 is the shock to inflation that cannot be forecast with informa- This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 172 : MONEY, CREDIT, AND BANKING tion at t. e,+ 1 is usually assumed to be normally distributed with a time-varying conditional variance rt, specified as a linear function of current and past squared forecast errors (simple ARCH) and sometimes past variances (GARCH). When x, and fi are known at time t, the conditional variance of inflation at t is simply the variance of e,+l. Thus changes in uncertainty about future inflation lvP.+ 1 can be identified from the estimated sequence of conditional variances r,. The specification for r, also fonnalizes the idea that uncertainty increases when past forecasts of inflation badly missed the mark. There is, however, one potentially serious drawback to modeling the inflation process in this manner. Over time it is highly likely that changes in private sector behavior, economic policy, andXor institutions have induced significant variations in the structure of the inflation process.2 Although variations in the structure of inflation could be incorporated into (1) by allowing the vector of parameters , to vary over time as ,S,, this extension to the model may make r, a poor estimate of inflation uncertainty. To illustrate, suppose at time t the Federal Reserve (credibly) announces that it will change policy at t + 1. If the implications for the stmcture of inflation (that is, the link between Ap,+ 1 and x,) are well understood, the expected rate of inflation can be identified by E,lNp,+ l = x,",+ l and the variance of inflation by r,. On the other hand, the implications of the policy change may be very poorly understood so that individuals have to "estimate" its impact on the inflation process. Under these circumstances, expected inflation is more appropriately identified as E,2\p,+ l = x,E,fi,+ 1, where E,p},+ l is the estimate of S,+ l under the new policy. Moreover, r, will misrepresent the true degree of uncertainty about inflation because it ignores the perceived uncertainty surrounding the true value °f ,S,+ 1 The model used in this paper explicitly allows the variations in the structure of inflation to contribute to inflation uncertainty. This is done by replacing equation (1 ) with Ap,+ I = x,S,+ I + e,+ l e,+ l N(0,r,), (3) and x, -[1, i\p,, * - * i\P.-k] 1}r+ 1 = 1S, + V,+ l V,+ 1 N(0,Q), (4) where V,+, is a vector of normally distributed shocks to the parameter vector ",+, with a (homoskedastic) covariance matrix Q. Equations (2), (3), and (4) describe a time-varying kth-order autoregressive process with an ARCH specification for the shocks to inflation. 2For example, the dynamics of inflation implied by Taylor's (1980) staggered contract model depend upon the nature of wage contracts and form of the monetary policy rule. Kaufman and Woglom (1983) show that relatively small policy changes have substantial effects on the dynamics of nominal wages in this model, and hence inflation. They also point out that there have been significant variations in both the cost-of-living adjustments found in wage contracts and their duration. These changes should also affect the dynamics of inflation. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms MARTIN EVANS : 173 The effects of variations in the structure of inflation on uncertainty are readily analyzed with the aid of the Kalman Filter [see Chow (1984) for details]. For this model the filtering equations are APt+1 Ht = = XtEtfit+1 xtQt+ l,txt + Nt+19 + rt s (5) (6) Et+ lfit+2 = Ett+ 1 + [Qt+ lxtxtHt 1] Nt+ 1 (7) and [2t+2xt+ 1 = [I-Qt+ lxtxt'Ht- lxt]Qt+ l/t + Q * (8) Uncertainty about the structure of the inflation process is represented by Qt+ l/t which is the conditional covariance matrix °f pt+ 1 given information available at t. Since the innovations in Apt+ 1 [identified as Nt+ 1 in (5)] may originate from both inflation shocks et+ l and unanticipated changes in the structure of inflation Vt+ l, the conditional variance of inflation Ht depends upon both rt and the conditional variance of xt,S,+ 1 which is x,Qt+ l,tx't. When there is no uncertainty about fit+ 1 (that is, Qt+ l/t iS equal to the null matrix), the dynamics of rt completely govern the conditional variance of inflation so that the model encompasses the simple ARCH specification in (1) and (2) as a special case. Under other circumstances, rt will tend to understate the true conditional variance Ht because XtQt+ lxtxtt > 0.3 Equations (7) and (8) show how the conditional distribution Of fit+ 1 iS updated over time in response to new information about actual inflation. Equation (7), in particular, indicates how innovations in inflation are used to update the estimates of fit + 1 on which the forecast of future inflation is made. One important implication of this procedure is that, unlike traditional ARCH models, the forecasts of inflation generated by the model (that is, EtApt+ 1 = xtEtfit+ l) only use historically available data. At this point it is worth considering the motivation for the chosen specification in a little more detail. In particular, one might ask why the parameter vector fit should follow a random walk rather than some other process. Unfortunately, it is impossible to provide a theoretical rationale for the dynamics in (4) without a very detailed model of the inflation process because movements in fit represent the effects of changes in policy and/or private sector behavior. Here the choice of a random walk is justified solely on empirical grounds.4 In the next section I show that there is no 3The specification also encompasses the inflation model used by Ball and Cecchetti (1990) to look at the differences between short- and long-term uncertainty. They take xr to be a constant and set r, = r. However, these simplifications severely limit variations in the conditional variance of inflation and the measures of long-term uncertainty defined below. 4It is possible to justify the random walk theoretically. Suppose, for example, that all the structural variations in inflation reflect changes in monetary policy which in turn are due to changing views about the structure of the economy. Since it would be very hard to predict any future change in policy and hence movements in ", under these conditions, E,fi,+ X = E,fi, as implied by a random walk for ",. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 174 : MONEY, CREDIT, AND BANKING statistical evidence to favor alternative specifications. This is due, in pa that monthly inflation contains a unit root. The random walk specif for this feature because shocks to the first element in the ,S, vector h effects on the rate of inflation.5 One also might ask why it is necessary to allow for both time-varyin and ARCH within a single model. For, as equations (5)-(8) demonstrate in the parameter vector ,S, would be sufficient to generate condition skedasticity in the inflation process. To answer this we must enquire into the possible theoretical sources of heteroskedasticity in the inflation shocks e,+ 1 . In principle, inflation shocks represent combinations of structural disturbances such as productivity, money supply, and price shocks. Over time it is unlikely that the actual or perceived frequency with which these structural disturbances occur remains constant. For example, the variance of monetary shocks is likely to be higher during periods of greater uncertainty about the future course of monetary policy. Similarly, the variance of price shocks probably rises around OPEC meetings. This suggests one reason why r, is likely to vary over time. The Lucas critique provides another reason. Since the inflation process represents the result of a large number of price-setting decisions, shocks to the aggregate price level must in part depend upon how individual price setters respond to structural disturbances. For example, the pricing strategies of individual firms will determine the aggregate effects of a given nominal demand shock. Such pricing rules are subject to change. In particular, the analysis in Ball, Mankiw, and Romer (1988), Evans (1989), and others suggests that the frequency of individual price changes should rise as the economy moves toward regimes of higher inflation so that the aggregate price level will respond more quickly to nominal shocks. Under these circumstances, a prolonged increase in the rate of inflation will induce a rise in the conditional variance of inflation independently of the perceived frequency of nominal shocks. These arguments suggest that the time-varying parameter and ARCH specification provides a general and flexible framework with which to study a complicated process like inflation. In fact, both behavioral and policy changes seem likely to induce both ARCH effects and time variation in the structure of inflation. In the following sections we shall see that both effects have important implications for our study of the different aspects of inflation uncertainty. 2. ESTIMATING THE INFLATION PROCESS Although the United States has experienced relatively large swings in over the past twenty-five years, the periods of high inflation have been r sWhen the shocks to ", are viewed as permanent shocks to the inflation process, the Kalm (5)-(8) indicates how uncertainty about the persistence of inflation shocks contributes uncertainty. Of course, this type of confusion can have even more widespread effects Brunner, Cukierman, and Meltzer (1980). This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms MARTIN EVANS : 175 TABLE 1 ESTIMATES OF THE INFLATION MODEL: 1960:1-1988:6 AP+1 = 1 t+l + 2t+1^Pt + e+l rt = 5.271 + 0.181 e2 (9.757) (2.417) lst+l 2,t+1 Residual = = lst 2,t P1 + + P2 Vlst+l V2,t+1 1 2 = = Residual Diagnostics P3 P4 Ps 0.404 (4.082) 0.025 P6 (1.867) x2(6) X2(l2) etirt 0.064 0.015 -0.113 -0.073 -0.018 0.009 11.41 16.28 e,21r, 0.022 -0.025 -0.001 -0.019 0.107 0.171 7.44 14.52 NOTES: Asymptotic t-statistics are reported in parenthesis. The x2 statistics report on two conditional moment tests for sixth- and twelfthorder serial colTelation in each set of standardized residuals. The S percent cntical values are 12.59 for X2(6) and 21.02 for X2(l2). short-lived. For this reason, monthly data was used to provide a reasonable number of observations during the episodes of high inflation. The inflation series is calculated as the monthly difference in the natural log of the Consumer Price index for all urban consumers (CPI-U). Since 1983 the index utilizes a rental equivalence calculation for the owner-occupied housing component that eliminates the undue weighting of mortgage interest costs. Prior to 1983, I use the CPI based on the rental equivalence measure calculated by the BLS. This series is called the CPIX. The inflation data were also corrected for the influence of the Nixon price controls. This was done by regressing the raw inflation rate on a dummy variable multiplied by the change in the proportion of the CPI covered by price controls from one month to the next. These proportions were estimated by Blinder (1979, p. 125) and were nonzero for thirty-three months from 1971 to 1974. The time varying ARCH model uses the residuals from this regression. Before the model was estimated, I conducted some unit root tests. An AR(1) model was estimated using the residuals from the dummy variable regression and the t-test on the autoregressive parameter calculated. After allowing for various degrees of serial correlation in the error term using the method in Phillips (1987), the test statistics indicate that the presence of a unit root cannot be rejected at the 5 percent level.6 This evidence offers some support for the choice of the random walk specification (4). The preferred specification for the inflation processes together with the maximum likelihood estimates are shown in Table 1.7 Generally speaking, the parameter 6The test statistics are-2.52 and-2.13 when adjusted for a sixth- and twelfth-order MA process. 7Estimates of Q and the ARCH parameters in r, are obtained by maximizing the likelihood ,T= X -log(2X) + log|H,|- I/2(N,'H,- 1N,) where , and H, are derived from (5)-(8). The estimates of the past forecast errors used in the ARCH process for r, are obtained from e, = lvp,-x,_ 1E,fi, = [ 1-x,_ l Q,/,_ lx,' _ lH,- l l ],. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 176 : MONEY, CREDIT, AND BANKING estimates support the idea that both time-varying parameter and ARCH effects are present in the inflation process.8 Furthermore, once time variation in the parameters has been accounted for, an AR(1) specification appears to capture the serial correlation in inflation. This can be seen by examining the autocorrelations for the estimated innovations reported in the lower portion of the table. The second set of statistics reports the autocorrelations of the standardized squared innovations. If the dynamics of the covariance matrix H, implied by the ARCH specification truly capture the dynamics of inflation, then all these correlations should be zero. The two sets of Conditional Moment tests (Newey 1985) reported in the lower-righthand corner of the table formally indicate that there is no statistically significant evidence of mispecification. Since the variations in inflation uncertainty are heavily influenced by the dynamics of ,, it is also important to check for mispecification in the random walk model. To do this I conducted a Lagrange multiplier test against an alternative model for pt t+ 1 = fi + M[t-] + Vt+ 1 V,+ l N(0,Q) (9) where M is a 2 x 2 matrix and , is the long-run level of S,. The model in Table 1 restricts M to be equal to the identity matrix so that shocks to ,S, have permanent effects. If some shocks have less than permanent effects in reality, the roots of M should be less than unity. The Lagrange multiplier test of the restriction that M is equal to the identity matrix gives the remarkably low statistic of 0.015 which is far from significant.9 Thus, there seems little evidence that the inflation model using the random walk is at odds with the data. The path of expected monthly inflation implied by the maximum likelihood estimates is depicted in Figure la.l° Here we see that expected inflation climbs through the mid-1960s to a peak over 13 percent in 1974 before falling off sharply in 1976. The second peak in expected inflation occurred around the time of the second oil price rise in 1979. From 1981 to 1983 expected inflation fell rapidly; it averaged under 2 percent in 1986 before increasing to a 4 percent average in 1987. Figures lb and lc present the estimates °f "1 t and "2 t' the trend and autocorrelation component of inflation. The trend in inflation differs sharply from the path of expected inflation because the latter includes the effects of the Nixon price controls. Once the effects of these controls are accounted for, the trend rate of inflation fell sharply during the early 1970s. The trend inflation rate peaked at over 6 percent in the early 1980s and has now leveled off at about 3 percent. Figure lc shows how the 8It should be noted that a formal test for parameter stability cannot be based on the asymptotic tstatistics associated with the estimated parameter variances. The reason is that the x2 distribution is only an approximation to the true asymptotic distribution of the Wald statistic when O is on the boundary of the parameter space for the variances. 9It should be acknowledged that little is known about the asymptotic theory associated with this particular LM test because the model contains unit roots under the null hypothesis. Nevertheless, the result seems to be fairly unambiguous. l°The effects of the Nixon price controls are included in this figure by adding the predicted values from the dummy variable regression to those from the time varying ARCH model. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms wwwswwwwwwswww MARTIN EVANS : 177 'v c c FIG. la. The Expected Rate of Monthly Inflation 1 960 1 964 1 968 1972 1 97e; 1 sea 1 984 n 988 FIG. lb. Trend Variation in Inflation ,BI, ,4 J r . 1 9 60 . 1 . 964 . 1 . . 9fi8 . 1972 vf . . . . 1 97e; 1 98O . . 1 . 984 . n 988 FIG. lc. Autocorrelation Coefficient in Inflation Process 2 t persistence of inflation measured by p2 t rose from near zero in the early 1960s to a peak of approximately 0.5 in 1979 before falling off in the 1980s. These changes in the persistence of inflation are more readily interpreted by writing the estimated inflation equation in first differences. After some straightforward simplifications we find that ^2p,+ 1 = 2,t+ 1^2Pt + V2,t+ 1^P.- 1 + vl,,+ 1 + e,+ 1-e, This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 178 : MONEY, CREDIT, AND BANKING where ^2p,-Ap,-Ap.- 1- Thus, the increase in 2, shown in Figure lc represents an increase in the persistence of inflation changes. As a result, current change in the inflation rate become a useful predictor of future month-to-month changes in inflation into the future. This finding turns out to be useful in interpreting the result presented below. 3. INFLATION UNCERTAINTY AND INFLATION RATES We can now consider how different aspects of inflation uncertainty are r the rate of inflation. I shall study three statistical measures of inflation un (i) H,, the conditional variance of inflation given information at t ident (6), (ii)a,2(E,Ap,+l)-x,Q,+l,,x',,theconditionalvarianceofexpectedinflation E,Ap,+l, and (iii) a,2(^p,*), the conditional variance of steady-state inflation. Recall that temporal decisions, such as those found in the Lucas model, are likely to be affected by the short-term conditional variance of inflation, H temporal decisions will be influenced by either at2(EAp+ l) or C,2(^p*) depen upon the horizon. Measures (i) and (ii) are readily available from the Kalman filtering equations employing the maximum-likelihood parameter estimates reported in Table 1. The steady-state rate of inflation Ap,*, is implicitly defined by the restriction that Ap, = AP.- 1 for all t. This is the rate of inflation that would eventually prevail in the economy if there were no future inflation shocks e,, or parameter shocks Vt. It varies from period to period as permanent inflation shocks hit the economy. In the inflation model this implies Apr*= The l,[l - 2,]-1 conditional . (10) variance a,2(^p,* )--V(E,fi,+ 1 )Q,+ 1x,V(E,",+ 1 ) ( 1 1 ) where V(E,fi,+ l)- [ [1-E,1s2 ,+l]-1, E,"1 .+ 1 [1 -E,1s2 ,+1] 2 ] The standard deviations associated with each of the conditional variances are shown in Figure 2. The early 1970s clearly stand out as a period of greater inflation uncertainty whichever way we care to identify uncertainty. Although the largest changes are in the standard deviation of month-to-month inflation ,, the standard deviations of expected inflation and steady-state inflation, A/a,2(E,AP,+ 1) and VtS,2(^p,>, also rose. It is also interesting to note that S,2(^p,: displays a good This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms o inflation rate; A/at2(EtApt+ ,) is the conditional standard deviation of next month's expec l l l l l l l l l LL; 1 Zt '2 . 1 . 962 FIG. . 1 2. , 966 k 1 970 . . 1974 Different . . 1978 Measures the conditional standard deviation of steady state inflation. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms . . 1982 of In 180 : MONEY, CREDll*, AND BANKING deal more persistence than either of the other statistics. In fact, it never returns to its pre-1972 level. The differences between the three measures are even more pronounced during the early 1980s. While both Xand A/(7t2(EtApr+ l) remained fairly constant, the standard deviation of steady-state inflation rose to a distinct peak in 1980. When compared with the path of expected inflation shown in Figure la, the evidence in Figure 2 suggests that the conditional variance of steady-state inflation is more closely related to expected inflation than the other two statistics. This can be seen more clearly in Figure 3. After 1972 there is a strong positive correlation between the two variables. The sample correlation for the period 1960: 1 to 1988:6 is 0.720. l l It is also clear that the link between the two variables is quite unstable. For example, the initial rise in the variance begins almost a year before the sharp increase in expected inflation in 1973. There also appears to be a good deal more persistence in the variance than in the level. Nevertheless, the general impression from Figure 3 is that high rates of expected inflation have been associated with greater uncertainty about the long-term prospects for inflation since the early 1970s. A more formal evaluation of the link between the different measures of inflation uncertainty can be made with the aid of Table 2. This shows the results of regressing the month-to-month changes in the three conditional variances against the changes in inflation and the change squared. 12 The results for the variance of steady-state inflation at2(Apt: contrast sharply with the other statistics. The upper panel of the table indicates that over the whole sample changes in both the conditional variance of actual and expected inflation [lllt and (rt2(EtApt l)] have been negatively associated with changes in inflation. This surprising result appears to reflect the undue influence of the first inflationary episode during the early 1970s; there is much less evidence of a negative link when the regressions are reestimated over a subsample that begins in 1976. The link between the variance of steady-state inflation a2(;Apt: and the rate of inflation appears to be far more robust. In all three samples there is a significant positive link.l3 There also appears to be some evidence that greater month-to-month changes in the inflation rate appear to have less than a proportional effect on the variance. These findings seem to reconcile the conflicting results of previous research on inflation uncertainty cited in the introduction. For if the dispersion of inflation forecasts gathered from the Michigan and Livingston surveys are good indicators of uncertainty about steady-state inflation, the results presented in Table 2 support the conclusions of Wachtel (1977), Carlson (1977), and Cukierman and Wachtel (1979). On the other hand, the absence of any link between the short-term variance of inflation and the rate of inflation also conElrms the findings of previous ARCH 1 lThe sample correlations between H, and a,2(EtApt + 1) and expected inflation are respectively 0.202 and 0.293. 12The regressions use the month-to-month changes in the variances and inflation because inflation has a unit root and all three variances are complicated functions of past inflation. 13It is worth stressing that the link between the vanance of steady-state inflation and the level of inflation is not imposed by the structure of the time series model. Using ( 12) it is easy to show that there could be no relation if there was no movement in 2 t. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms c9 - - u Et^Pt+l a2(Apt) cs ' ' l ' , ' ' ' ' ' , ' 1 1 960 1 964 1 968 1 S372 1 976 1 980 1 . FIG. 3. Expected Inflation and the Condition variance of steady state inflation; EtApt+, is th This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms 182 : MONEY, CREDIT, AND BANKING TABLE 2 REGRESSION EVIDENCE ON THE LINK BETWEEN INFLATION UNCERTAINTY AND INFLATION Independent Variables Dependent Valiable Measure ^2p, (A2p,)2 Std. EU. D^W Sample 1960:1 to 1988:2 (i) AH, -0.179 O.036 (3.808) (6.798) 2.820 2.70 (ii) AC2(E,APt+ 1) -0.032 0.005 0.396 2.56 (iii) Aa2(AP*) Sample 1960: 1 to 1975: 12 (i) AH, (4.799) (6.554) 0.039 -0.002 (6.610) (3.232) -0.245 0.N4 (3.808) (6.798) 0.350 3.272 1.86 2.60 (ii) ACr2(E,I\P,+ I ) -0.W1 0.006 0.450 2.55 (iii) AC2(AP*) ' (3.497) Sample 1976:1 to 1988:2 (i) AH, (4.479) (6.313) 0.027 -0.001 0.387 1.70 (1.469) -0.059 -0.001 (1.172) (0.062) 1.741 2.42 (ii) A(J2(E,/\P,+I) -0.018 0.001 0.262 2.43 (4.799) (6.554) (iii) /\(r2(Ap*) 0.048 -0.001 0.235 1.86 (7.104) (5.388) NOTES: ^2p, is e monthly change in the rate of inflation, AH, is t change in the variance of expected inflation, and 5ff,2(5p,*) iS the chang parenthesis. studies unduly influenced by his choice of sample period. This study does not include periods like the Korean War that witnessed the "extraordinary" combination of low inflation and high variance. Of course, my model uses a different measure of shortterm inflation uncertainty H,, rather than the ARCH variance rt. However, both measures appear to have very similar dynamics. Between 1960:1 and 1988:2 the ratio r,lH, has a sample mean of 0.82 and a standard deviation of 0.02. Thus, the absence of a link between short-term uncertainty and the level of inflation reported in Table 2 does not appear to be a product of the modeling strategy. To summarize, the results in this section are both simple and striking. It is clear that no one statistical measure captures all the economically relevant aspects of inflation uncertainty. Furthermore, the measures used here seem to have quite differ- ent dynamics. Variations in short-term uncertainty as represented by measures (i) and (ii), are largely independent of the level of inflation except in the mid-1970s. Long-term uncertainty, by contrast, appears to have moved strongly with the level of inflation from the early 1970s onward. 4. CONCLUSIONS AND POLICY IMPLICATIONS Economists have long suspected that inflation rates and inflation uncertain tightly linked. The results presented in this paper support this position. Us measure that can be unambiguously interpreted within the paradigm of rat This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 07:15:37 UTC All use subject to http://about.jstor.org/terms MARTIN EVANS : 183 expectations, uncertainty about the long-term prospects for inflatio strongly linked to the actual rate of inflation. The policy implications of this result largely depend upon the sou inflation uncertainty. In section 2 we saw that the late 1970s an witnessed a nse and fall in the persistence of inflationary changes. inflation is largely determined by monetary growth in the long ru monetary policy were probably a contnbuting factor to the variation persistence. Since changes in the structure of the inflation process c conditional variance of steady-state inflation, it seems likely th changes in policy may be responsible for much of the uncertainty ab inflation documented in section 3. If true, this conclusion suggests t tary authonties may be able to eliminate much of the costs associat inflation by following well-understood policy rules. However, faili may be a good case for tough anti-inflationary policies since low lev growth would imply less uncertainty about inflation. Of course, the idea that uncertainty surrounding future policy bec the rate of inflation nses is not new. Various forms of this hypoth Logue and Willet (1976), Fleming (19763, Fnedman (1977), Fischer an (1978), Cukierman and Meltzer (1986), and Ball (1990). This is, howe study that provides compelling statistical evidence linking long-term tainty to inflation rates in a way that seems consistent with the hy LITERATURE CITED Ball, Laurence. 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