Targeting inflation

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A Note on Inflation TargetingChing-Chong Lai & Juin-Jen Chang

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To cite this article: Ching-Chong Lai & Juin-Jen Chang (2001): A Note on Inflation Targeting,

The Journal of Economic Education, 32:4, 369-380

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A Note on Inflation TargetingChing-chongLaiand J uin-jen ChangAbsrracr: The authors present a pedagogical graphical exposition to illustrate thestabilizing effect of price target zones. Based on a textbook AD-AS apparatus,they find that authorities commitment to defend a price target zonewill affectthe publics inflation expectations and, in turn, reduce actual inflation. They alsofind that, when the economy experiences supply shocks, the announcement thatthe monetary authorities intend to defend a price target zonewill reduce the vari-ability of domestic prices but raise the variability of domestic output relative toa free-price regime. However, when the economy experiences demand shocks, aprice target zone tends to lower the variability of both domestic prices and out-put relative to a free-price regime.Key words:AD-AS apparatus, inflation expectations, inflation targetingJ EL code: E52

The monetary authorities of some industrialized countries, including Australia,Canada, Finland, Israel, New Zealand, Spain, Sweden, and the United Kingdom,recently have taken a more active role in the management of consumer prices.Typically, they announce a specific band within which consumer prices areallowed to adjust freely fora given time horizon. Once consumer prices reach theboundsof the target zone, the monetary authorities intervenein the money mar-ket to adjust the money supply. The motivation for such announcements is thatthe authorities commitment will affect the publics inflation expectations and, in

Ching-chongh is u reseurch fellow of econonrics ar Sun Yut-Sen nstitutefo r Sociul Sciences undPhilosophy, Acudenriu Sinicu (e-nlail: ccbi @ssp. si ni cu. edu. hU) . und J uin-jen Chang is an assistantprofessor of econonrics ut Fu-J en Cutholic University, Tuiwun. The uuthors are indebted to HirschelKasper and three anonymous refereesfor their constructive suggestions and insightful conrnwnts. Wewish to thunk Yi-ring Chenfor helpful discussions.Fall 2001 369

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turn, reduce actual inflation.*Sofar, inflation-targeting countries generally havehad a good performancein fulfilling the target they set. Observing this fact, Lei-derman and Svensson(1995, 15) recognize that over time there seems to be atrend of more countries attempting to achieve and maintain low inflation with thehelpof explicit inflation targets for monetary policy. In his popular money andbanking textbook, Mishkin (1998,500)points out that inflation targets mightbecome the wave of the future for central bank strategy.Our purposein this article is to present a pedagogical graphical exposition toillustrate two related issues concerning inflation targets. It is widely known thatthe publics inflation expectations are crucial for inflation-targeting countries tokeep the prices at a moderate level. Therefore, the first issues we address are whythe authorities announcement affects the publics inflation expectations, andhow the public reacts to this announcement. In addition, the experience of infla-tion-targeting countries, for example, Canada and New Zealand, would lead toachieving reductionsin price fluctuation at the cost of increasesin output fluctu-ation. The next issue deals with whether this price control policy has stabilizingeffects on the relevant macro variables. We will also address whether the stabi-lizing effects of inflation targeting are related to the type of random shocks andthe credibility of policymakers.

INFLAT ION TARGET ZONESThe theoretical model is made as simple as possible. The economy can be rep-resented by the aggregate supply and aggregate demand functions:y=cy, +& ; a>O, ( 1 )y =p(m - p) +F +p; (2)>0,y>0.The variables are defined as follows:y equals real output, measured in natur-al logarithms;p equals price level, measured in natural logarithms; m equalsnominal money supply, measuredin natural logarithms;IF equals expected infla-tion rate; E equals random disturbance terms of aggregate supply; and p equalsrandom disturbance terms of aggregate demand.Equation( I ) is the aggregate supply function in which aggregate production is

specified tobepositively related to prices (01 >0).The rationalefor this settingcan be justified by the fact that workers have imperfect information about pricechanges or their wages are set with contracts.3 Equation (2) is the aggregatedemand function. It is a straightforward extension of the standard IS-LM model.In the goods market, the consumption expenditure is an increasing function ofreal outputy, and investment is a decreasing function of the real interest rateR -xe, where R is the nominal interest rate.4 In the money market, real moneydemand is positively related toy, but is negatively related to R . On the supplyside of the money market, we assume for simplicity that the money stock is con-trolled unilaterally by the central bank. Putting both markets together and elimi-nating the nominal interest rate between them, we can represent the aggregatedemand function for the economy most conveniently by the linear relationship370 JOURNAL OF ECONOMIC EDUCATION



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stated in equation (2). Because a rise in the expected inflation rate leads to a fallin the real interest rate, hence boosting the investment activities, equation (2)specifies that aggregate demand is an increasing function of x e (y>0).Moreover,an increasein real money supply lowers the nominal interest rate (hence the realinterest rate). This, in turn, increases investment, raising aggregate demand. As aconsequence, equation (2) specifies that aggregate demand is an increasing func-tion of real money supply I n -p (p >0). In addition, the economy experiencesboth the supply shockE and the demand shockp.To focus on the essentials, we assume that the changeof the supply shock Efollows a discrete-state random walk. To be specific, in each step the supplyshock E moves either up or down by the same step-lengthwith the same proba-bility, 1/2. As exhibited n Figure1,at step1, the supply shock begins at a knownlevel E,, and may move either up toE, ordown to E, with the same distance [i.e.,E, - c0= (E , -Eo)], each with probability 1/2. In addition,it is assumed thattheprobability that E moves up or down in each step is independent of what hap-pened in the previous steps. Analogously, at step2, E, will moveup to E,) withprobability 1/2, and will move downtoE~with probability 1/2. It is clear in Fig-ure 1 that at any step the mean of the supply shockE is its initial level.5For exam-ple, at step 1, the mean of E at Eo isE&= &,/2+E2/2); at step 2, the mean of E at

FIGURE 1Random Walk Representation

Step 1 Step2 Step3 Step4

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E, is&,(=6 2 +c3/2).Accordingly, the expected change of E at any step is zero.For example, at step 1, the expected change of E at e0 is

A t step2 the expected change of E at isEo 9& I + ,-I =0.

L L

The same characteristics of distribution apply to the aggregate demand shockp.We now use a textbook graphical presentation to address the stabilizing effectof inflation target zones. In Figure2, theAS curve represents the pairs of outputand prices that satisfy the aggregate supply function. TheA D curve traces thelociof output and prices that satisfy the aggregate demand function. Assume that themonetary authorities announce that they stand ready to adjust the money supplywhen the level of prices exceeds the upper bound or falls short of the lowerbounde.6Although the price is in the interior of the band0,he monetaryFIGURE 2TheStabilizingEffectof Inflation Targeting:A SupplyShock

P

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authorities do not alter the money stock.' In addition, we assume that the author-ities' commitment to defend the target band is perfectly credible (the imperfect-ly credible case will bediscussed later).Wefirst deal withthesupply shock and assume that there are no shocksin theaggregate demand (i.e.,p =0).For analytical simplicity, assume that initially thesupply shock isE~and the public's inflation expectations arenil (i.e.,ne=0).Theinitial equilibrium is at point Qo, which is the intersection of the curves AS(&,,)and AD(n' =0).The initial output and prices areyoandPo,respectively. To makethe analysis meaningful in Figure2, we depictpo inside the band. In response toa fall in the supply shock fromE,, toE,, the AS(&,,)curve shifts leftward toAS(&,).If the public does not change expectations (i.e., II' =0), intersects AD(x'=0)at point Q l,withy andp beingy, andp,, respectively.A question naturally arises in the foregoing discussion:Is the naive view thatthere is no change in the public's expectations valid? As indicated in Figure 1,two states may occur at the level of E,. First,with probability 1/2, E, will increaseto E,. Second, with probability 1/2, E, will decrease to E ~ . t step2 in Figure2,if E, rises to E,,, the prices will then fall frompI topo. If E, falls toE ~ ,he priceswill increase fromp, to the upper edge of the bandF , rather thanp3,because themonetary authorities will act to defend the target band. This implies that, whenthe shock isE,, the public's inflation expectations under a price target zone(7Z)are given by

Given-(po - P I ) > j - P I , I T&0 is true. The changein expectations fromxe=0to I ' C ~


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The fact that aggregate supply shocks present a thornier problem for inflationtargeting countries owing to larger output fluctuations is stressed by Friedmanand Kuttner(1996). Fortunately, in practice, inflation-targeting central banks usea varietyof techniques to cope with this problem. By defining well the long-runand short-run inflation goals, Bernanke et al. (1999, 291) claim that,a numberof countries, including Canada and Sweden, set their initial inflationtar-gets to take effect onlywith substantial delay,soasnot to impose unnecessary short-run costs in termof lostoutputor employment. . . .By adjusting the speed of con-vergencewith the long-mn goa (or, nearly equivalently, the target horizon), thepolicy-makers can moderate thereal costsof reducing inflation, and also reduce out-put fluctuations.. I i

In addition, inflation targets in some countries (e.g., New Zealand and Canada)are designed to exclude the short-run effects of certain supply shocks, such as arise in the price levels of volatile components (e.g., food, energy, and petrol) andthe increasein value-added taxes. Bernanke et al. (p. 291) specifically argue that,if the authorities adequately provide explanation to the public, inflation targetswith the escape clause can avoid destabilizing the economy in the short run,while still maintaining a strong commitment to the long-run price stability.'2In terms of the demand shock, we assume that there are no shocks to the aggre-gate supply (i.e., E =0). Figure 3 illustrates the consequence of a rise in thedemand shock. Similar to the previous case, assume initially thatp =p" andK'=0.The initial equilibrium, where theA S locus intersectsAD(p,,,n'=0) is estab-lished at point Q,,; he initial output and prices areyo and p,,, respectively. Giventhat the demand shock increases fromp,,topi.theAD(p,,,V=0) locus will shiftrightward to AD(p,,V =0).TheA S curve intersectsAD(pi,n'=0) at point Q,,withy andp beingy, andp,, respectively.Following the same inferencein Figure 2, given thatp, is closer to the top ofthe band, the public would expect a decline in prices in the future (i.e., r ~ &


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FIGURE 3The Stabilizing Effectof Inflation Targeting:A DemandShock

\Po I

AD(p0,ne=0)

ple, 2/3), and will move down to E~ with probability less than 112 (say, 1/3).Therefore, the mean of E at E , is 2~0/3 E J ~,which is greater than E,, and hencethe mean of E atE, has a tendency to converge to E~).n the other hand, at step2,E, will move up to E,, with probability less than 1/2 (say, 1/3), and will movedown to E,, with probability greater than 1/2 (say, 2/3). The mean of E at E, thusis &,I3+2&,/3, which is less than E,, and hence the mean of E at E* has a tenden-cy toconverge to E,.

Wenow use Figure5 to address what would happen if E is a mean-revertingshock. The initial state in Figure5 is the same as that in Figure 2: AS(&,) inter-sects AD(W=0)at point Q,. y andpbeingyoandpo, respectively. In response toa fall in the supply shock fromE" toE , , theAS(&,) curve shifts leftward toAS(&,).Based on the description in Figure4, E, will increase toE" with probability 2/3,and E , will decrease to E~ with probability 1/3.As expressed in Figure5 , underthe situation where the monetary authorities stand ready to defend the targetband, the prices will fall fromp, topo, f E, rises to E, and will increase fromp,to the upper edge of the band j (rather thanp3), if E , falls toE ~ .his implies that,when the shock is E , , under a price-target-zone regime, the public's inflationexpectations with a mean-reverting shock are given byFall 2001 375



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FIGURE 4The Random Walk Representationof M ean-RevertingProcess

Step3 ...tep 1 Step2

Given-(po- , )> -P I , n& -p, , we can infer n&


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FI GURE 5The Stabilizing Effectof Inflation Targeting:A Mean-RevertingSupplyShock

under a floating price(yy--y0). sa consequence, our conclusions of the discrete-state random walk in the previous section are valid when E is a mean-revertingshock.IMPERFECT CREDIBILITY

The problem of a central banks credibility has become a central concern ofthe scholarly literature on the effectiveness of policies. According to the Blinder(2000) report, among the 84 central bankers, there is an amazingly strong con-sensus on the importance of credibility to a central bank. However, until now wehave assumed that the authorities commitment to defend target zones is perfect-ly credible. It is of interest to address how the authorities credibility will governthe stabilizing performance of inflation target zones. We consider a situationwhere the public lacks full confidence in the willingness of the authorities todefend the band. Assume that the public anticipates that the policymakers willfollow their commitment with probabilityz (0


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FIGURE 6The Stabilizing Effectof Inflation Targeting and Imperfect Credibility

vY ; Y ; Y I Y o

fromE, to E,, theAS(&,) curve shifts leftward to AS(&,).TheAS(&,) locus inter-sectsA D ( f l =0)at point Ql , with y andp beingyI andpI , espectively.A s indi-cated in Figure6, the public expects that three states may happen. First, withprobability 112, the prices will fall fromp , top, when E, increases toE~ Second,with probability (112)~he prices will rise frompI to when E, decreases toE ~ .Third, with probability (1/2)(1 - T), the prices will rise fromp, to p3 whendecreases to E ~ . iven-@, -p,) =p3 P I , the publics inflation expectations are

wherene&(lC)denotes the publics expected inflation when the authorities tar-geting implementation is imperfectly credible. Recall that the publics expectedinflation with perfect credibility is

Then, substituting+-p,)=p3- , into this relation, we have378 JOURNAL OFECONOMIC EDUCATION



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With the relationship n&


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7. To simplify the graphical illustration, wespecify that the monetary authoritiesare not allowed toalter the money supply in the interior of the band, although some observers, for example, Bernankeet al. (1999.320). argue that the authorities often undertake intra-marginal interventions. Howev-er, our conclusionsare qualitatively valid in the presence of intra-marginal interventions.8. It should be noted thatAD(VFp=0)coincides withA D ( V = 0).9. Our conclusion is parallel to Krugmans (1991) insight on exchange-rate target zones: Anannouncement of exchange-rate target zones tends to lower the variability of the exchange rate.Krugmans(1991) result now is dubbed the honeymoon effect.10. The similar inference is applied to a rise in the supply shock.I I . For example, the central bankers may deal with the inflation resulting from supply shocks bysetting a short-term inflation goal so that, over time, the inflation is gradually eliminated, untilthe long-run inflation object is once again reached. In contrast to a purely discretionaryapproach, such an inflation-targeting framework gives the central bank a better chance to con-vince the public that the effects of a supply shock will be limited to a one-time rise in the pricelevel, rather than creating a permanent rise in the inflation rate. See Bernanke and Mishkin(1997) or Bernanke et al. (1999) for detailed illustrations.12. Weare grateful toan anonymous referee for bringing this point to our attention.13. Friedman and Kuttner(1996) claim that a price-stability target makesgood sense for monetarypolicy under some conditions but not others. A price-stability target may be optimal when theeconomy suffers from demand disturbances. Holding price stable, however, is not optimal in thepresence of supply shocks. The Friedman and Kuttner(1996) conclusions seem tobesimilar toour results. It should be noted that in our analysis the stabilizing performance of price targetzones stems from the fact that authorities commitment will affect the publics inflation expec-tations, and in turn govern actual inflation. n the interior of the band, the authorities do not alterthe money supply in practice. However, in the Friedman and Kuttner analysis, the authoritiesalways adjust the money supply to peg the target price. Obviously, the channel proposed in thisarticle is different from that addressed by Friedman and Kuttner.14. An anonymous referee. to whom we are grateful, raised this question.15. I n an international gold standard, the gold arbitragers stand ready to supply the foreign exchangeat a gold-export point and demand the foreign exchange at a gold-import point. A s a result, theexchange rate cannot move outside of the band bounded by the gold points. For a detailed expla-nation, see Chacholiades 1978, chapt. 7) .

REFERENCESBernanke, B. S.,T.Laubach, F.S.Mishkin, and A. S.Posen. 1999. Inf lut ion turgeting: Lessons ro mBernanke, B. S.,and F. S.Mishkin. 1997. Inflation targeting:A new framework for monetary policy?Blinder, A. S. 2000. Central-bank credibility: Why do wecare? How do we build it?Anrer icun Eco-Chacholiades,M. 1978. Intemutionul nroneturytheory and policy. New York: McGraw-Hill.Friedman, B., andK. Kuttner. 1996.A price target forU. S. monetary policy? Lessons from the expe-Krugman, P. 1991.Target zones and exchange rate dynamics. Quurterly J ournul of Economics 106Leiderman, L., and L.E.0.Svensson. 1995. Inf lut ion mrgets. London: CEPR.Miller,R. L., and D. VanHoose. 1998. Mocmecononiics: Theories. policies. un d i n t e m t i o n u l uppli-Mishkin, F. S. 1998. Th e econoniics of money, bunking u n d f i m n c i u l nrarkets. 5th ed. New York:

th e internut ionul experience. Princeton, N.J.: Princeton University Press.J o u m l ofEcononiic Perspectives 1 I (Spring):95-1 16.nomic Review 90 (December):1421-31.rience with money growth targets.Brookings f upe rs on Economic Act iviry 1:77-125.(August):669-82.cations. Cincinnati: South-Western.Addison-Wesley.

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