American Economic Association

Optimal Inflation Targets, "Conservative" Central Banks, and Linear Inflation Contracts Author(s): Lars E. O. Svensson Source: The American Economic Review, Vol. 87, No. 1 (Mar., 1997), pp. 98-114 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2950856 Accessed: 03/05/2010 22:58 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. 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 [email protected].

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OptimalInflationTargets, "Conservative"CentralBanks, and LinearInflationContracts By LARS E. 0. SVENSSON * Inflation-targetingregimes (like those of New Zealand, Canada, the United Kingdom, and Sweden) are interpretedas having explicit inflation targets and implicit employment targets. Without employment persistence, an "inflation-targetconservative" central bank eliminates the inflation bias, mimics an optimal inflation contract, and dominates a Rogoff "weight-conservative" central bank. Withemploymentpersistence, a state-contingent inflation bias and a stabilization bias also arise. A constant inflation target and a constant inflation contract are still equivalent. A state-contingent inflation target combined with a weightconservative central bank can achieve the equilibrium corresponding to an optimal rule under commitment.(JEL E42, E52, E58)

Recently, a number of countries-New Zealand,Canada,the United Kingdom,Sweden, Finland,Australia,and Spain-have introduced explicit inflation-targetingmonetary policy regimes.' This paper representsan attemptto un* Institute for InternationalEconomic Studies, Stockholm University, S-106 91 Stockholm, Sweden. I have benefited from comments by Robert Barro, Claes Berg, Alan Blinder, Alex Cukierman,Jon Faust, Stanley Fischer, Stefan Gerlach, John Green, Dale Henderson, Berthold Herrendorf,Lars Horngren, Peter Isard, GunnarJonsson, Mervyn King, Leo Leiderman, Paul Levine, Christian Nilsson, Torsten Persson, Andrew Rose, Paul Soderlind, Guido Tabellini, Carl Walsh, Janet Yellen, anonymous referees, and participantsin seminars at the Bank of England, the Centre for Economic Policy Research Summer Symposium, the Federal Reserve Board, the Federal Reserve Bank of San Francisco, the Institutefor International Economic Studies, the International Monetary Fund, Sveriges Riksbank,the Universityof Californiaat Berkeley, and the University of California at Santa Cruz. Remaining errors and obscurities are my own. I thank Christina Lonnblad for secretarial and editorial assistance and Stefan Palmqvist for research assistance. ' See the papers in Leonardo Leiderman and Svensson (1995) and those in Andrew G. Haldane (1995), as well as John Ammer and Richard T. Freeman (1995) and Bennett McCallum (1995a). Some of the operational and monitoring aspects of inflation-targetingare discussed in Svensson ( 1997). Inflation-targeting,allowing base drift in the price level, results in price levels that are random walks or more generally integrated of order one. Pricelevel-targeting, which results in (trend-) stationary price levels, is discussed and compared to inflation-targeting in, for instance, Pierre Duguay ( 1994) and Svensson ( 1996b). 98

derstandinflation-targetingand its propertiesin relationto the literatureon commitmentand discretion in monetary policy initiated by Finn Kydland and Edward Prescott (1977) and Robert Barro and David Gordon (1983). That literature starts from the realistic assumption that distortions create a short-run benefit from surprise inflation (for instance, taxes or unemployment benefits make the natural rate of unemployment inefficiently high). The first-best equilibrium can be achieved by removing the distortions. If that is infeasible, a second-best equilibrium can be achieved by a commitment to a monetary policy rule. If the commitment mechanism is infeasible, monetary policy will be discretionary. The secondbest equilibrium can still be achieved if the naturalrate is accepted as the employment target. If that is infeasible, for political or other reasons, discretionarypolicy leads to a fourthbest equilibrium with an inflation bias relative to the second-best equilibrium. Possible improvements to the discretionary fourth-best equilibrium have been discussed extensively in the literature.Barro and Gordon (1983 pp. 589-610 [footnote 19]) noted that their model could be interpreted as a principal-agent problem, where the discretionary equilibrium can be improved by modifying central-bank preferences (for instance, by regarding the natural unemployment rate as optimal) or where the inflation bias can be eliminated by

VOL. 87 NO. I

99

SVENSSON: OPTIMALINFLATIONTARGETS

reducing the weight on unemployment stabilization to zero. Kenneth Rogoff (1985) suggested delegation of monetary policy to an independent, appropriatelyconservative centralbank, where "conservative"means weightconservative, having less (but still positive) weight on employment stabilization than society. This reduces the inflation bias but brings higher employment variability than is optimal, a "stabilization bias," and hence leads to a third-best equilibrium rather than the second best. Escape clauses with simple (outcome) rules, like constant low inflation for small supply shocks and discretionary behavior for large shocks, were examined by Robert F. Flood and Peter Isard (1989), and escape clauses with weight-conservativecentral banks were studied by Susanne Lohmann (1992). These also lead to third-bestequilibria. An optimal central-bank contract proposed by Carl Walsh (1995) and extended upon by Torsten Persson and Guido Tabellini (1993) can achieve the second-best equilibrium,however. The contract, the "linear inflation contract," consists of adding a linear cost of inflation to the central bank's loss function. The study of commitment and discretion in monetarypolicy has been extended beyond the standard static framework to the realistic situation with persistence in output and employment. Such persistence introduces lagged effects of monetary policy, requires monetary policy to be conducted with a view to the future, and substantially affects the equilibria. Results in Ben Lockwood and Apostolis Philippopoulos (1994), Gunnar Jonsson (1995), and Lockwood et al. (1995) imply that discretionthen leads to a state-contingentinflation bias relative to the second-best equilibrium. The average inflation bias is then larger than it would be without persistence. Also, under discretionthereis a stabilizationbias, in that inflation variabilitybecomes too high, and employment variabilitytoo low, relativeto the second best. David Currie et al. (1995) and Lockwood et al. (1995) have examined thirdbest Rogoff delegation of monetarypolicy to a central bank that puts more weight on inflation stability than society does; the latter paper has also shown that a state-contingentlinear inflation contractcan achieve the second-best equilibrium when there is persistence.

The present paper examines the performance of inflation-targeting regimes relative to these previous results, with and without persistence in employment. This then requires a theoretical representation of a stylized regime. An inflation-targeting inflation-targeting regime is interpretedhere as a principal-agent arrangement,where society, the principal, delegates monetarypolicy to the central bank, the agent. It is taken for granted that commitment to a complicated state-contingent rule for the central bank's instrument is infeasible (commitment to a simple instrument rule might at best be feasible, but suboptimal). Society, however, can commit to targets for the central bank, for example, in the form of a loss function over macroeconomic outcomes. More precisely, the delegation of monetary policy has three components: (i) society assigns a loss function to the central bank (e.g., with a legislated price-stability goal); (ii) the central bank is given independence to minimize the assigned loss function without interference from the government or other interests; and (iii) the central bank is held accountable for minimizing the assigned loss function. Note that with such delegation, the central bank is given operational independence (instrument independence) rather than goal independence (Guy Debelle and Stanely Fischer, 1994).2 In the real world, the New Zealand regime is closest to this kind of delegation. In the other countries with inflation targets, the commitment to the target appears to be weaker, and there is less accountability and independence of the central banks. These differences are discussed furtherin Svensson ( 1996a). For concreteness, I will follow the literature and assume that society has preferences over inflation and employment that correspond to a quadratic social loss function over inflation, wr,,and employment (rate), E,, in period t, (1)

L(ir,, ,; ir*,C*, X) = 2[(-irt

*)2 + X(t,

-

*)'I

2 McCallum ( 1995b) has criticized the commitmentdiscretion framework.The critique is discussed in a longer version of this paper, Svensson ( 1996a).

100

THE AMERICANECONOMICREVIEW

The loss function is characterizedby three parameters: lr* is the socially desirable inflation rate, t * is the socially desirable employment rate, and A > 0 is the social weight on employment stabilization relative to inflation stabilization. An inflation-targetingregime is then interpreted as the delegation of monetary policy to the central bank as above, with an assigned loss function L(-r,, ,; irb, fb, Ab) with the three parameters:irb, an explicit announcedinflation target; fb, an implicit but known employment target; and Xb > 0, an implicit but known relative weight on employment stabilization. These parameters may differ from the corresponding parameters of the social loss function. The interpretationof inflationtargeting regimes as having a loss function involving both inflation and employment targets is supported by several circumstances (see the contributions in Leiderman and Svensson [1995 ] ). (i) Actual inflation-targetingregimes (with the exception of Finland and Australia) have explicit tolerance bands aroundthe target level, indicating that some variability of inflation around the target is acceptable. (ii) No central bank with an explicit inflation target seems to behave as if it wishes to achieve the target at all cost, regardless of the employment consequences. (iii) A prominent central banker, Mervyn King (1995), has interpreted inflation-targeting regimes precisely in this way. Thus, an inflation-targetingregime is not interpretedas corresponding to Xb = 0, what King (1995) calls the case of an "inflation nutter." An inflation-targeting regime need not have explicit escape clauses for supply shocks in orderto incorporatesome preference for employment stabilization, counter to the interpretationin Fischer ( 1995).' In the inflation-targetingregimes to be discussed below, in the standardcase it will be assumed that the central bank has the same employment target as society, and the same

- Jon W. Faust and Svensson (1997) examine the situation when implicit employment targets, in contrast to explicit inflation targets, are stochastic and unobserved and have to be estimated by the public from observations of the macroeconomic outcome and the central bank's instrument.

MARCH 1997

relative weight on employment stabilization, although I will also reportresults for different employment targets and different relative weights. Society's employment target is above the natural rate of employment because, for instance, distortions in the labor market make the naturalrate of unemployment inefficiently high. The role of this employment target in the analysis is to introduce a benefit from a surprise inflation. As noted in the literature,such benefits can also arise for other reasons: for instance, if a surprise real depreciation of the nominal public debt is less distortionary than explicit taxation. Thus, in the standardcase the central bank will have an "overambitious" employment target which, under discretion, results in an inflationbias. A more rationaldelegation of monetary policy would assign an employment target corresponding to the natural rate. Such a rationaldelegation is assumed to be infeasible in the standard case, for instance, because of political difficulties (e.g., a powerful labor movement prevents an employment target less than full employment) or difficulties in verifying the delegation of a natural employment rate, or lack of unanimity of estimates of the naturalemployment rate. The assumption reflects the general temptation in monetary policy to err on the lax side, if only because raising interest rates is (politically) unpopular and lowering interest rates is popular.4 As will be seen, however, even if the employment target were to be fixed at the long-run natural-rate level, if there is persistence only the average inflation bias is eliminated. The state-contingent inflation bias and the stabilization bias remain. Section I presents the model and derives the commitment and discretion equilibria. Section II discusses the various suggestions to improvements of the discretion equilibrium. Section III summarizes the results,

'In the words of Charles A. E. Goodhart ( 1994 pp. 1426-27), "Even without political subservience, there will usually be a case for deferring interest rate increases, until more information on currentdevelopments becomes available. Politicians do not generally see themselves as springing surpriseinflation on the electorate. Instead, they suggest that an electorally inconvenient interest rate increase should be deferred, or a cut 'safely' accelerated. But it amounts to the same thing in the end."

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considers empirical predictions, and concludes. The appendices report technical details. I. Commitmentand Discretion The model has three agents: the private sector, the government, and the central bank. The private-sector behavior is characterized by an expectations - augmented Phillips curve with rational expectations and employment persistence (2)

Et = pt,-

+ a}(,7 - 7r,) + st,

with 0 - p < 1, where E,is employment (rate) (the log of the share of actual employment in full employment) in period t, a is a positive constant, 1rtis the (log of the gross) inflation rate, wr' denotes inflation expectations in pe-

riod t - 1 of the inflation rate in period t, and s, is an independently

and identically

distributed supply shock with mean 0 and variance a 2. The private sector has rational expectations, (3)

7re=

101

the infinite-horizon case. The optimal rule under commitment and the decision rule under discretion are compared in Jonsson ( 1995 ) for the two-period case and in Lockwood et al. (1995 ) for the infinite-horizon case.5 The (long-run) naturalrate of employment, which I identify with the unconditional mean of employment, E [t], is for convenience normalized to zero. The government is assumed to have the same preferences as society. They are represented by the social loss function - 00-

(4)

V=Eo [ x

-ILL(T,i?;7rr*,*,x)

1

with the "period" loss function (1) and the discount factor 3, 0 < / < 1. The (log of the) socially desirable employment rate, t *, is assumed to exceed the natural rate of employment and, hence, fulfills ( * > 0. The central bank is, for simplicity, assumed to have perfect control over the inflation rate 7r,. It sets the inflation rate in each period after having observed the currentsupply shock st.6

Et_ 17r,

A. Commitmentto an Optimal Rule where Et1 l denotes expectations conditional upon the realization of all variables up to and including period t - 1, as well as the constant parametersof the model. The autoregressive term in the Phillips curve can arise in a number of different ways: for instance, in wage-setting models where trade unions set nominal wages one period in advance, disregardnonunion workers' preferences, and only take into account union members' preferences for real wages and employment, and where union membership depends on previous employment. Although a natural extension of the standard Phillips curve, employment persistence has only recently been incorporated into the commitment-discretion literature. Employment persistence will introduce lagged employment as a state variable, which will be important for the relations between the optimal rule under commitment, linear inflation contracts, and inflation targets. The equilibrium under discretion has been studied by Lockwood and Philippopoulos (1994) for

Consider first the situation when the central bank is directly controlled by the government, so that the governmentcan choose the inflation rate in each period, conditional upon the supply shock in the period. Assume temporarily that the government can commit to a statecontingent rule for the inflation rate.

' Barro and Gordon (1983) included the case of an exogenous persistentnatural(un)employment rate. The only change in the equilibrium then is that the inflation bias is exogenous and persistent. This is very different from the case of an endogenous persistent employment rate, where there are substantial changes in the equilibrium, as demonstrated in what follows. 6 The results are not affected in any essential way if an errorterm is added on inflation, indicating imperfect control of inflation. Neither are the results affected if: (1) output is considered the control variable; or (2) if an aggregate demand equation is also added, where aggregate demand depends on the real interest rate and the nominal interest rate is the instrument of monetary policy; or (3) if a money-demandequation is also added and money supply is the instrument(e.g., see Rogoff, 1985).

102

THE AMERICANECONOMICREVIEW

As in Lockwood et al. (1995), the optimal rule under commitment can conveniently be derived from the Bellman equation, (5)

V*(t,_ ) =

min E,1 {[(7t U(*w)2_

MARCH 1997

That is, the expected inflation rate equals the socially desirable inflation rate and is independent of the employment level. Since the problem is linear - quadratic, V *( ', I1) must be quadratic.Then I can write (8)

V*(f')

+

y* + Y'f

=

I

*'2

7rt,7r t

+

where the coefficients yo*, y1 , and y * need to be determined. (I will only be interested in y and 2*.) Substitutionof (2), (3), (7), and (8) into (6) results in a decision rule:

(,-*)2

+ f3V*(.C,)} subject to (2) and (3). Thus, the government chooses ir,, which may depend on _- l and ?,, and inflation expectations irr, which may only depend on E, I, subject to the condition that inflation expectations are rational. Put differently, the government internalizes the effects of its decision rule on expectations. This problem differs from the standard commitment problem in that lagged employment enters as a state variable. The first-orderconditions with respect to 7rt and 7r'result in (6)

(9)

7r, = qr* -b*?,

with (10)

b* = 1

1

(X+/3y2)

2(X + 63*)~

Employment will then fulfill (11)

', = Pt,-I + (1 - ab*)t,.

In orderto find b *, y 2* has to be determined. Substitution of (8)- (11) into (5) and iden-

(7rt--7r)

tificationof the coefficientsof ', - and tC1+ Xa(,

-

t*) + QaV *(Et)

- Et_ l [1a(ft - E*) +aV

*(t,)]

results in (12)

y*

where the Lagrange multiplier of (3) has been eliminated. The first term is the marginal current loss from increasing inflation, the second is the marginal currentloss from the resulting increase in employment (normally negative since employment is normally below t *), the third is the discounted expected marginal future loss of the resulting increase in employment (normally negative since higher employment in the future is normally beneficial), and the fourth is the marginal loss of the resulting increase in expected inflation (normally positive since increased inflation expectations reduce employment). Taking expectations at t - 1 of (6) gives Et- rt=rr*.

____

0, * Y2

(7)

= _

72_= 1

Xp2

pP

-

Using this in (10) results in (13)

b* =

a 1 + Xa2

-

O

Setting p = 0 results in the standard static commitment equilibrium. Examining (13), one sees that the optimal inflation response to employment shocks is largerunderpersistence than without. Since the employment shock has future as well as current effects on employment, it becomes more important to stabilize employment; hence, inflation is allowed to fluctuate more.

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SVENSSON: OPTIMALINFLATIONTARGETS

B. Discretion Assume now that the government retains direct control of the central bank, but that the government cannot commit to a statecontingent rule. Instead it acts under discretion. Then the decision problem of the government/central bank can be written as (14)

V(C,_, ) =

2

Et - 1 min{2[ (r, -r*

decision rule also will be a function of past employment. Taking expectations of (15) gives (16)

Et_ 17r,= 7r*+ (At *-

+ (8V(e,)

},

tion [this is incorporatedin V(i,), which in turn incorporates future behavior of the government/central bank]. The first-ordercondition will be -r,

- 7r*+ Xa(Ct- E*) + 6aVf(f,) = F,-

7r*

- 1.

Combining (15) and (16), using (2) and (3), gives a decision rule (a, b, c) of the form rt = a - bs, - cft- I

with

where the minimization in period t is subject to (2) but is done for given inflation expectations ir' (since the minimization is done for each t after observing the supply shock, min1, can be moved inside the expectations operator). The government/central bank thus no longer internalizes the effect of its decisions on inflation expectations, although it takes into account that changes in current employment will affect currentexpectations of future infla-

(15)

y,)a

- (X + /3y2)apt,

(17) + \(,-t*)2]

103

(18)

a =Tr* + a(Xe*-,6yi) a(X + PY2) 1 + a 2(X + /PY2) c = ap(X +

Employment will then fulfill (19)

,=pet-I+(I-ab)st.

In order to determine a, b, and c, y I and Y2 have to be determined. This can be done by substituting (17)- (19) into (14) and identifyingthecoefficientsfor, -t and 2_l. In Appendix A it is shown that this results in (20) ( 20)

a

xae*

ir*

+1 a-=w*+Sa

-

+ (X + PY2)aft b =

(XA* - 6y1)a = 0,

where I exploit the fact that V(f) must be quadraticas in (8) and let the discretion case have coefficients yo, -y1, and 72 (without asterisks). The marginal loss of increased inflation expectations has vanished from the first-order condition. Note that the decision rule can be written as a feedback rule for inflation on current employment. I prefer to express the decision rule as a function of the supply shock, though. Since past employment is a state variable in the problem, the

/Y2).

pa +

1 + Xa2

-

-

/3p

/3ac

2aC2

6 p2 +

6a2C21

where c is given by (21)

c=

I 2a/3p

-

[1 - _3p2

V(1 _ 6p2)2

-

4Xa2/p2]

2

0

and an existence condition, detailed in Appendix A must hold. For p = 0 (without

104

THE AMERICANECONOMICREVIEW

persistence), c = 71 = 72 0, and the standard discretion equilibrium occurs. Comparing the decision rules under commitment, (9), and discretion, (17), one sees that under discretion there is an inflation bias, a-ce,t I -r*. The inflation bias can be decomposed into a constant average inflation bias, a - lr*, and a state-contingent inflation bias, - ce, - . With employment persistence, the average inflationbias is largerthan without employment persistence. The reason is that with persistence an increase in current employment also increases future employment. Hence, it is more tempting to increase current employment, which will increase the average inflation bias. With employment persistence, there is also a state-contingent inflation bias, whereas the inflation bias is constant without persistence. The reason is that with employment persistence the gap between the employment target, t *, and the short-runnaturalrate of employment, pt - I, is state-contingent. Comparing (20) and (13), one sees that with persistence there is also a stabilization bias under discretion, in that the inflation response to employment shocks is larger than under commitment, b > b *. Since under discretion the future inflation bias depends on current employment, it becomes even more importantto stabilize employment, which requires a larger inflation response. Hence, employment will be too stable, whereas inflation will be too variable, relative to the commitment case. Thus, discretion results in a fourth-best equilibrium with too high inflation. With persistence, inflation is also too variable, and employment too stable, relative to the commitment equilibrium. If the equilibrium employment rate deviates from the socially optimal employment rate because of distortions, removing the distortions would presumably result in a first-best equilibrium. If the distortions cannot be removed, a commitment to an optimal state-contingentrule would lead to a second-best equilibrium. Since such a commitment does not appear to be feasible, other improvements have to be found, which at most will result in a second-best equilibrium. I will now consider how such improvements can be achieved by delegating policy to an instrument-independentcentral bank with different assigned objectives.

MARCH 1997

II. Improvements of the Discretion Equilibrium A. Delegation to a Weight-Conservative

Central Bank For the case without persistence, Rogoff (1985) has shown that the discretionaryequilibrium can be improved if monetary policy is delegated to a weight-conservative central bank. In the literature, this mostly has been interpreted as meaning that the government delegates monetary policy to a central bank with both goal and instrument independence, and that the government can observe the preferences of a potential central-bankgovernor or board and can select a governor or board with the desired preferences. Alternatively, it can be interpretedas meaning that the government delegates monetary policy to an instrumentindependent central bank that is assigned a particular loss function. This is the interpretation utilized here. Thus, the central bank is given the period loss function L(1r,,

,; -r*, f*,

Xb), where Xb

differs from Xin the social period loss function (1). Rogoff 's result is that there exists a Xb, O< Xb < X, that achieves a lower value of (1) than under discretion. For the case without persistence, the central bank's decision rule (17) has a = lr* + Xbae*, b = Xba/(l + Xba'2), and c = 0. Compared to the optimal

rule (9), there is still an inflation bias, Xbat *, but the inflation bias is lower. Without persistence there is no initial stabilization bias, however. Since the inflation response to the supply shock is decreasing in X, the weightconservative central bank will let the inflation response be lower, and the employment response be larger, than under commitment; hence, a stabilization bias is introduced.Thus, the lower inflation bias comes at the cost of increased employment variability. The second-best equilibrium cannot be achieved. With persistence, the consequences of a weight-conservative central bank are more complex, as shown by Lockwood et al. (1995). Since there is an initial stabilization bias toward too high inflation variability and too low employment variability, a lower weight on employment stabilization reduces both the average and the state-contingent inflation bias and the stabilization bias (since both b and c

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SVENSSON: OPTIMALINFLATIONTARGETS

are increasing in X) and, as a result, it brings three benefits. Nevertheless, it is clear that a weight-conservativecentralbankcannotachieve the second-bestequilibrium.Eliminatingthe average and state-contingentinflationbias requires Xb to be zero, but then there is no inflationresponse at all. The initial stabilizationbias then has been reversed to a strong stabilizationbias towardtoo low inflationvariabilityand too high employmentvariability. Thus, with or without persistence, a weightconservative central bank can at best achieve a third-bestequilibrium. B. A Constant Linear In;flationContract For the case without persistence, Walsh (1995 ) has shown that a simple linear inflation contract for the central bank can achieve the second-best equilibrium. The contract adds a linear cost to inflation to the social period loss function. Let the central bank be assigned the period loss function L(r-, et; -r*, t*, X) + f(-rt - 1-*). Using the Bellman equation as above, the first-ordercondition will be 7r -

r* +

f

+ (A + /Y2)aft

(X\E*

-

63y,)a

=

0.

This differs from the first-ordercondition ( 15) only in that lr* is replaced by lr* -f. It follows that the only change in the equilibrium is that the decision rule (17) will have

105

equilibrium. With persistence, it can only achieve a third-best equilibrium. A linear inflation contract is a very elegant way to remove the average inflation bias. However, it has been noted in the literature that it faces both practical and political difficulties. One practical difficulty is that the linear cost is presumably a monetary cost, whereas the rest of the loss function is in utility units. Thus, the constant f must translatemonetary costs into utility and, hence, incorporate the governor's or board's marginal utility of money. A political difficulty is that the contract stipulates higher monetary rewardsto the governor or boardwhen inflation is low, which may be provocative to the public if correlated with higher unemployment (Goodhart and Jose Viiials, 1994 p. 153). C. A Constant Inflation Target Consider now assigning an explicit inflation target 1rb to the central bank. The target may differ from the socially desirable inflation rate. Furthermore,let this assignment be with the understandingthat the employment target and the weight on employment stabilization are the same as in the social loss function. The central bank is then assigned the period loss function L( 1rt, f,; -xb, t *, X) ratherthan ( 1 ). The first-order condition under discretion will now differ from (15) only in that lr* is replaced by 1rb. It is immediately obvious that only average inflation, a, is affected in the decision rule (17), according to

xat * 1 - /p - facr-

a =irp )+

act * 1

/3p

-

-

f3rc-

Hence, by choosing (22)

f

-

1

Therefore, by selecting an inflation target that fulfills

a

1-p

- fac

(23) the average inflation bias can be eliminated, and the decision rule will be (ir*, b, c). A constant linear inflation contract can eliminate the average inflation bias. It does not affect the stabilization bias or the statecontingent inflation bias. It follows that, without persistence, it achieves the second-best

7rb

a Ae*

-

1

-

/3p - facrc

the decision rule will be (ir*, b, c), and the average inflation bias has been eliminated. The state-contingent inflation bias and the stabilization bias remain. Hence, a constant linear inflation contract and a constant inflation target are equivalent.

106

THE AMERICANECONOMICREVIEW

It is easy to see that an optimal inflation target (23) is equivalent to an optimal linear inflation contract (22), since L(irt,

E;qTb t*,

F + (ir*

b)(1

)= -

Taking expectations, one sees that Et_

17r,=

(,,

7r*+ (*

ir*) + 2(1r*

-

D. A State-ContingentLinear Inflation Contract Consider next more complex arrangements: first, a state-contingent linear inflation contract, where the added cost of inflation has a marginal cost of inflation that depends on lagged employment. The loss function will be Et; lr*, t*, X) + (fo +fit-

)(rt

-*)

-

63y ) a-

fo

[(X + 63Y2)ap+fi]i-.

-

Therefore, the inflation-target loss function L(-r,, ,; 1rb , X)differs from the social loss function L(-r,, E; -r*, t*, X) by a term that is linear in -r, and a constant. When 1rb fulfills (23), that linear term is the same as for an inflation contract with (22). Without persistence, an optimal constant inflation target results in the second-best equilibrium. Then, delegating monetary policy to an "inflation-target-conservative" central bank with an explicit inflation target according to (23), but with an unchanged weight on employment stabilization and an unchanged employment target, is clearly better than delegating monetary policy to a Rogoff weightconservative central bank with relatively less weight on employment stabilization.7

L(7rt,

MARCH 1997

= Hence, by selectingfo 63y,) and a((E*f, = -cr p(A + 63^Y2), one can eliminate both the average and the state-contingent inflation bias, E, 1r, = 1-* and c = 0. Substitution of this into the Bellman equation and identification of -y' and Y2 will produce the results in ( 12) as in the optimal rule. Combining ( 12) with the values offo andf, above, one sees that

* = I

(25) f=

Xcp

-

Aap 1

-

results in the optimal decision rule under commitment (-x*, b*, 0). Thus, the average and the state-contingent inflation bias and the stabilization bias vanish. A state-contingentlinear inflation contractcan achieve the second-best equilibrium under persistence, as has been shown by Lockwood et al. (1995). E. A State-ContingentInflation Target Next, consider a state-contingent inflation target, with the loss function L(-rx, (,; irx ,) * A), where

where fo and f' are constant. With the corresponding Bellman equation, the first-order condition will be

(26)

(24)

and go and g1 are constant. The first-order condition for the Bellman equation will be

, - 1r* -

(X*

+ fo + f,Et -/3yi)a

+ (X + 6Y2)aft =

irt = go + get- I

0.

7 After the first version of this paper was completed, I , received a copy of V. Anton Muscatelli (1995), which observes that a low inflation target can remove the inflation bias for the situation without persistence and then discusses the consequences of uncertain preferences of goal-independent central banks.

(27)

irt

-

g0

-

(At*

-

gt

I

-

+ (X + /y2)aet

6y,)a

=

0.

Taking expectations of (27) and using (8) gives E,t_ 1rt= go + a(X* + [gi

-

6y,)

ap(X + /372)eI t-I

SVENSSON: OPTIMALINFLATIONTARGETS

VOL. 87 NO. I

- 63y,) Hence, by selecting g0 = -r*-a(AE and g, = cap(X + /6Y2), one can eliminate the average and state-contingent inflation bias, E, -,Ir, = -r*. It is shown in Appendix B that this implies that y, and 72 are the same as under discretion, ratherthan as under commitment. This in turn implies that g0 and g1 fulfill (28)

xAe*

go

I

6p - 6ac

where c is given by (21), and thatthe resulting decision rule will be (-r*, b, 0) with b given by (20) rather than by (10). Hence, the average and state-contingentinflation bias can be eliminated, but the inflation response to the supply shock will be the same as with a constant inflation target and, therefore, the stabilization bias remains. Why cannot a state-contingent inflation target induce the optimal rule when a statecontingent linear inflation contract can? Compare the first-order condition for the linear inflation contract, (24), and for the inflation target, (27). It appears that by selecting (29) (29)

71rb

= 1*rit -fo

-f]

it should be possible to induce the second-best equilibrium. This appearance is misleading, though. One can understandthis by comparing the loss functions in the two cases, assuming (29). With a linear inflation contract, one has

(30)

L(7r, ,t; 7*, t *, A) + (fo +fi(t-)(rt-

*)

while with an inflation target,

(31)

L(7r,,; =

b t*A

L(7r,, t; lr*, (*, X) + (fo +flft-)(rt+ I(fo +fit,)2.

*)

107

Note that the loss functions differ by the third term in (31). The fact that this employment-dependent term enters with an inflation target means that it will be more important to stabilize employment and, hence, to let inflation react more vigorously to supply shocks. Taking this into account, (29) with fo and f, given by (25) is not enough to eliminate the average and state-contingent inflation bias; instead, (26) with go and g, given by (28) is required.The coefficients y, and 72 are indeed different for the two cases. With a constant inflation contract and a constant inflation target,the thirdterm in (31 ) is constant, and the two loss functions result in the same equilibrium. F. A State-ContingentInflation Target and a Weight-ConservativeCentral Bank The second-best equilibrium can be achieved with a state-contingent inflation target, if combined with a Rogoff weightconservative central bank. By (20), b is decreasing in X [note that, by (21), c is decreasing in X]. Then there exists a ,b < X such that the correspondingb equals the optimal b * (note that b -+0 for ,b'-+ 0.) Thus, if the central bank is assigned a loss function with the appropriate relative weight Xb < X and the state-contingent inflation target (28) that corresponds to that relative weight, the optimal rule (ir*, b*, 0) will result. The intuition for this is that an appropriately weight-conservative central bank will eliminate the stabilization bias. Once the stabilization bias is removed, an appropriate state-contingent inflation target will eliminate the average and state-contingent inflation bias and, hence, restore the second-best equilibrium. Thus, inflation-targetingregimes should have not only low and possibly state-contingent inflation targets, but they should also put extra weight on inflation stabilization. Rogoff 's (1985) result about the desirability of a weight-conservative central bank is thus resurrected. But note that the reason for the weight-conservative central bank is different: it is to eliminate the stabilization

108

THE AMERICANECONOMICREVIEW

bias, rather than to reduce the inflation bias.8 G. A Rational EmploymentTarget The maintained hypothesis so far is that monetary policy inherits society's employment target. If feasible, it would be more rational for society to delegate a lower employment target to monetary policy and to reserve society's high employment target for other policies that may be able to deliver increased average employment (for instance, structuralmeasures that make the labor market work more efficiently). For completeness I will also report the results for two regimes with alternative employment targets, where the central bank has the period loss function L(7rt, Et; 7r*,,b, X). That is, the central bank has an inflation target equal to the socially desirable inflation rate 7r* and an employment target equal to #3> The results below follow easily from the analysis above. Suppose that the employment target is constant and equal to the natural rate, t' = 0 (this is the case analyzed by Lockwood and Philippopoulos [1994]). It follows directly from the analysis of the discretion equilibrium above that the decision rule (17) will be (-r*, b, c). The equilibrium is the same third-best equilibrium as for the constant linear inflation contract (22) and the constant inflation target (23). That is, the average inflation bias is eliminated, but there is a state-contingent inflation bias, and the stabilization bias remains. It is easily shown that the employment target has to equal the state-contingent "short-run" natural rate of employment, 3" = Et- # = P(t -I., in order to achieve the second-best equilibrium (1r*, b*, 0). III. Conclusions An inflation-targetingregime is interpreted here as the delegation of monetary policy to a central bank that is assigned an explicit infla-

8 Berthold Herrendorfand Lockwood ( 1996) consider a few other situations that result in a stochastic inflation bias and show that a weight-conservative central bank can improve the discretionaryequilibrium.

MARCH 1997

tion target, an implicit employment target, and an implicit relative weight on employment stabilization. Absent a commitment mechanism to an optimal rule, the central bank acts under discretion. If the implicit employment target exceeds the natural employment rate, there will be an average inflation bias, in that the average inflation rate will exceed the inflation target. With employment persistence, also if the employment target equals the long-run natural rate, in addition there will be a statecontingent inflation bias (in that inflation will depend on lagged employment) and a stabilization bias (in that inflation variability will be too high and employment variabilitytoo low). The equilibrium will be fourth best. The results of the paperimply several empirical predictions for inflation-targetingregimes. First, the inflationbias implies that realized inflation rates should, on average, exceed the inflation target. This prediction remains to be confirmed,since the periodof inflationtargetsis yet a bit shortto drawconclusionsaboutaverage inflation.None of the inflation-targeting regimes has yet been througha complete business cycle. Second, the inflationbias implies that an inflation targetnormallywill be imperfectlycredible, since inflationexpectationsnormallywill exceed the inflationtarget.This predictionis confirmed so far, since the inflationtargetsin the existing inflation-targetingregimes have indeedbeen imperfectlycredible(see Svensson, 1993;Haldane, 1995; Richard T. Freeman and Jonathan L. Willis, 1995; Leidermanand Svensson, 1995). Third, since lower inflation targets result in lower average inflation rates, without any effect on the variability of employment and output, lower inflation generally need not be associated with higher output variability. This is in contrast to the empirical implication of Rogoff (1985) that lower inflation should be associated with increased employment variability (if that lower inflation is the result of more weight-conservative central banks). The prediction in this paper is confirmed, since empirical studies have indeed found that lower inflation is not correlated with higher output variability (see Alberto Alesina and Lawrence H. Summers, 1993; Debelle and Fischer, 1994; Fischer, 1994; Eric Schaling, 1995). Among possible explanations of this finding, the literaturehas suggested that more-independent

VOL. 87 NO. 1

SVENSSON: OPTIMALINFLATIONTARGETS

central banks are better at stabilization than less-independent banks; that fiscal policy is more disciplined in countries with more central-bankindependence; or that both inflation and employment performanceare primarily affected by shocks that differ from country to country. The most obvious, but nevertheless overlooked, explanation is that lower inflation is due to lower inflation targets rather than lower weights on employment stabilization! An important policy implication is that, even if an inflation-targeting regime would exceed its targets and be imperfectly credible, that is by itself not a reason for abolishing the regime. The resulting inflation still may be lower than it would have been without the inflation target. Even if the regime cannot be improved, it may be better to keep it. But the literature and the analysis in this paper also suggest several ways to improve the regime. The average inflation bias arises if the natural employment rate, due to some distortions, falls short of the socially desirable employment rate, the implicitly assigned employment target. As outlined in the beginning of the paper, this representsthe unfortunatebut realistic temptation to err on the lax side in monetary policy. A golden rule in economic policy is that distortions should be attacked directly at their source, if possible. This rule then implies taking structural measures to improve the working of labor markets, attempting to increase the natural employment rate to the socially desirable rate, and thereby reach a first-best equilibrium. When the temptation to err on the lax side has other roots, the golden rule, for instance, implies designing tax systems and pursuing a public debt policy that does not create benefits of surprise inflation (see Mats Persson et al., 1996). If it is infeasible to attackthe distortionsdirectly, the equilibrium can be improved instead by modifying the central bank's targets in several ways. Modifying the targets, indeed, acts as an indirect commitment mechanism-even if the central bank acts under discretion-if commitment to the new target is feasible. Modifying the target usually at best will lead to a second-best equilibrium. One way to improve the regime is to assign a more rational employment target to the cen-

109

tral bank. Creating mechanisms for rational assignment of employment targets generally should be a crucial aspect of monetaryreform. In this regard it is worth observing that only without employment persistence is it enough to assign the long-run natural rate as the employment target.Then the second-best equilibrium results. With persistence, assigning the long-run natural rate still leaves the statecontingent inflation bias and the stabilization bias in place. To remove these and get to the second-best equilibrium, the employment target should be state-contingentand equal to the short-runnatural rate. If, for various reasons, a more rational employment target is infeasible, several other remedies remain. Among these other remedies, the literature has suggested weight-conservative central banks, escape clauses with simple rules or weight-conservative central banks, and linear inflation contracts. The first two lead only to third-bestequilibria. Linear inflation contracts face both practical and political difficulties. This paper emphasizes the potential of lower inflationtargetsand comparesthis remedy with the alternatives.Without persistence, an inflation target equal to the socially desirable inflation rate less the inflation bias achieves the second-best equilibriumand is equivalentto an employment target equal to the naturalrate or to a linear inflation contract. Suppose, for instance, that the socially desirable inflation rate is 2 percentper year (perhapsbecause a quality bias in the consumer price index implies that a quality-adjustedinflation rate is zero). If the outcome with a 2-percent inflation target is 4percent inflation on average (i.e., the inflation bias is 2 percentage points), the socially desirable inflation rate can be achieved with a zero-inflation target. Thus, the optimal inflation target does not need to be negativesomething some may deem infeasible. Would an inflation targetbelow the socially desirable inflation rate be sustainable?It seems that a zero-inflation target that results in 2percent inflation would be no less sustainable than a 2-percent targetthat results in 4-percent inflation. If a zero-inflationtargetresults in actual inflation that is above zero but equal to the most socially desirable rate, a zero target may be more sustainable. It requires, though, that the central bank continues to suffer disutility,

110

THE AMERICANECONOMICREVIEW

depending on the deviation from zero, rather thanfromthe socially desirablelevel: thatis, that the target remains zero. This requires that the target'sdeviationfrom the socially desirableinflationrate clearly is motivatedand publicly understoodto be necessaryto counterthe inflation bias. This requirementdoes not appearto distinguish conservativeinflationtargetsfrom conservative weights on employment stabilization;it seems that a weight-conservativecentral bank also requiresmotivationand public understanding to be sustained. With employment persistence, a constant inflation target, a constant employment target equal to the naturalrate, and a constant linear inflation contract still are identical. They can eliminate the average inflation bias, but not the state-contingent inflation bias or the stabilization bias. To remove the state-contingent inflation bias, state-contingent targets are needed. I believe that such state-contingent targets may be too sophisticated to be feasible, especially if there are more state-variables than lagged employment. In practice, only constant targets may be feasible. Suppose, however, that state-contingent targets are feasible. A state - contingent inflation target then is not equivalent to a state-contingentemployment target or a statecontingent linear inflation contract. Although it eliminates the average and state-contingent inflation bias, a state-contingent inflation target leaves the stabilization bias in place. This points to an interesting combination of a weight-conservative central bank and a state-contingent inflation target. A weightconservative central bank can remove the stabilization bias, whereas a state-contingent inflation target can remove the average and state-contingent inflation bias. A weight-conservative centralbank can also remove the stabilization bias for constant targets. Thus, weight-conservative banks are desirable, though not for eliminating the inflation bias as Rogoff suggested, but for eliminating the stabilization bias. Generally, central banks should be assigned both weight-conservative and inflation-target-conservativetargets. This has practical implications for the width of the tolerance bands for actual inflationtargetingregimes. If the width of the tolerance band indicates the implicit weight on em-

MARCH 1997

ployment stabilization, the bands should be relatively narrow (which they actually seem to be, relative to realistic forecast error variance [see Charles Freedman, 1995; Haldane, 1995]). A general methodological conclusion from this paper for the literature on commitment and discretion in monetary policy is that a quadratic loss function has more than one parameter that may warrant discussion. For reasons that ex post appear arbitrary,the discussion in the literaturehas focused almost exclusively on one parameter of the standard quadratic loss function-the relative weight on inflation stabilization-with the occasional observation that a reduction of the employment target would improve the equilibrium. Discussion of the inflation-targetparameteris of no less (and perhaps of more) practical relevance. Thus, the identification of "conservativeness" with the relative weight on inflation stabilization seems unwarranted.The same can be said about the frequent identification of central-bankindependence with the same relative weight in the literatureon measurement of central-bankindependence. APPENDIX A: THE DISCRETION SOLUTION AND THE EXISTENCE CONDITION

Consider the explicitly recursive problem (Al)

Vt- I((t- 1)

I =Et_-l min I[

_-X*

(-Ft

)2

7r,

+ \(et

-

+ pVt(et)

*)2]

}

instead of (14). Let Vt(et) = yot + yltft + 72e t . The first-ordercondition results in a decision rule of the form 7rt = at- bt-t ltl with (A2)

at = lr* + a(Xe*

-

6yt)

a(X + /Y2t)

1+

a2(A

ct = ap(X

+

+ /Y2t) /Y2t)-

SVENSSON: OPTIMALINFLATIONTARGETS

VOL. 87 NO. I

Substitution of this into (Al) and identification -of the coefficient for EL 1 leads to (A3)

=

Y2,t-I

p2(A +

PY2t)

+ a 2p2(\

+

From (18), (A3), and (A7), one can express both y, and 72 in terms of c: (A8)

= Xcrp + /p2c, + 6a3pc .

c,_

= c=

A stationary solution ct -

c must fulfill

the second-degree equation p

c2 -

(A5)

c +

2a,fp

[1I-

pp2

? V(l

3p2)2

4Xa2/p2] 2

-

0

if, and only if, _

(A6)

'

= (I

p2)2

4a2/p2

is fulfilled. By (A4), it is known that p = 0 implies that c = 0, and that / = 0 implies c = Xap. Then the smaller solution (21) is the relevant one, since only then does c - 0 when p

-

0, and c -+ Xap when

/

-+ 0. Alterna-

tively, one can study the iteration (A4) when t-

-oo and show that the smaller solution is

the stable one. Identification of the coefficient for E,- I in (Al), and considering the stationaryvalues of y, and 72, lead to

(A7)

y

I1

_ p _ ac) <

=

72 -

X*[p e+ a2p(X + /372)] 2(X + /3Y2 6[p

c-Xcap fpap

Ap2 + C2

1-/pp2>0 _

where the stationary version of (A4) has been used to rewrite 72, to facilitate comparison with (12). Clearly, 72 > 0, but in order to ensure that there is a finite solution to 71, one must assume the second existence condition,

3(p + ac)

(A9)

,

which has real solutions

C=

,

3'Y2 )2.

Using the expression for c, in (A2), the equation can be written in terms of ct as (A4)

11]

<

1.

This condition does not follow from (A6), but has to be assumed separately. The condition has a natural interpretation: the expression f3(p + ac) is the discounted total increase in employment in period t of a unit increase in employment in period t - 1, when inflation in period t is held constant. The total effect consists of the direct effect, p, and the indirect effect through reduced inflation expectations, ac. If this discounted effect is above unity, the present value of the effect in all future periods will be unbounded.Note that (A9) is only relevant when e* * 0. From (A9) and (21), it follows that the second existence condition is equivalent to the condition (AIO)

1-2p

+ x < V(1-X)2-4Xa2x,

where 0 < x = /p2 < p2. If 1 - 2p + x < 0 (that is, if 2 < p < 1 and 0 0 (that is, if 2p - 1 < x < p2), (AIO) is equivalent to

(All)

X < X2

(1 - p)(p -x) 2 azx (1

-

p)(p _ a2/p2

,6p2)

THE AMERICAN ECONOMIC REVIEW

112

Indeed, it can be shown that (Al 1) is at least as restrictive as (A6), that is, X2 Z XI. To see this, note that

(1 _

6p2)2

-

(1

x)2 -

4(1 - p)(p

-

4(1 - p)(p _ 4,6a 2p 2 -

APPENDIX B: A STATE-CONTINGENT INFLATION TARGET

x)

4(1 Study the numerator,z = (1 - x)2p)(p - x). It is easy to show thatz 2 0 for 0 < x < p2 and0 < p < 1, andthatz = 0 if, and only if, x = 2p - 1. Thus, for t* * 0 the existence condition depends on the values of 6 and p. The existence condition can be summarized as

XAXI for

1 0

<

2p - 1I/p2 = -1.25 (0.94), so (A14) applies. Then X2 = 0.98 (0.06). If a instead equals 0.2, the corresponding X2 values are 25 times larger, that is, 24.5 (1.58). The corresponding values for XI are 1.18 (0.06) for a = 1, and 29.6 (1.58) for a = 0.2.

,6p2)

4a 2x

(A12)

MARCH 1997

<2

2

It is known that b is given by (18). Substitution of (27) into the Bellman equation and identification of the coefficient for e 2_ gives 72

=

p2(X + PY2)

+ gI

Because g, = ap(X + 6Y2), this is the same equation as the stationary version of (A3). This means that y, and 72 are given by (A8) with c given by (21) if, and only if, the existence condition (A12)-(A14) holds. Thus, with (28), the decision rule will be (r*, b, 0), with b given by (20). REFERENCES Alesina, Alberto and Summers, Lawrence H.

(A13)

X
for

1 __p < 1 I

22

p-

"Central Bank Independence and Macroeconomic Performance:Some Comparative Evidence." Journal of Money, Credit, and Banking, May 1993, 25(2), pp. 151-62. Ammer, John and Freeman, Richard T. "Infla-

2

[O
(A14)

X
2

1 2


For t* = 0, only (A6) needs to be fulfilled, since then 'yI = 09 '0 If a in (2) equals unity, as in Lockwood and Philippopoulos ( 1994) and in Lockwood et al. ( 1995 ), the existence condition appearsrather restrictive. If 6 = 0.95 and p = 0.4 (0.8), then

9 In the analysis of Lockwood and Philippopoulos ( 1994), only (A6) appears, since they assume that 4 * = 0. '?An early working-paper version of this paper erroneously reports that (A14) must hold regardless of the values of 63and p.

tion Targeting in the 1990s: The Experiences of New Zealand, Canada and the United Kingdom." Journal of Economics and Business, May 1995, 47(2), pp. 16592. Barro, Robert and Gordon, David. "A Positive

Theory of Monetary Policy in a Natural Rate Model." Journal of Political Economy, August 1983, 91(4), pp. 589-610. Currie, David; Levine, Paul and Pearlman,

Joseph. "Can Delegation Be Counterproductive? The Choice of 'Conservative' Bankers in Open Economies." Centre for Economic Policy Research (London) Discussion Paper No. 1148, March 1995. Debelle, Guy and Fischer, Stanley. "How Inde-

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VOL. 87 NO. I

Boston, MA: Federal Reserve Bank of Boston, 1994, pp. 195-221. Duguay,Pierre."Some Thoughts on Price Stability versus Zero Inflation." Working paper, Bank of Canada, March 1994. Faust,Jon W. and Svensson,Lars E. 0. "When Credibility Matters: Monetary Policy with Unobserved Goals." Working paper, Institute for International Economic Studies, Stockholm, 1997. Fischer, Stanley. "Modem Central Banking," in ForrestCapie, Charles Goodhart,Stanley Fischer,andNorbertSchnadt,eds., Thefuture of central banking. Cambridge:Cambridge UniversityPress, 1994, pp. 262-308. __.

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"The Unending Searchs for Mone-

tary Salvation," in Ben S. Bernanke and Julio J. Rotemberg, eds., NBER macroeconomics annual. Cambridge,MA: MIT Press, 1995, pp. 275-86. Flood, Robert F. and Isard, Peter. "Monetary Policy Strategies." IMF Staff Papers, September 1989, 36(3), pp. 612-32. Freedman,Charles."The CanadianExperience with Targets for Reducing and Controlling Inflation," in LeonardoLeidermanand Lars E. 0. Svensson, eds., Inf lation targets. London: Centre for Economic Policy Research, 1995, pp. 19-31. Freeman, Richard T. and Willis, Jonathan L. "Targeting Inflation in the 1990s: Recent Challenges." Working paper, Board of Governors of the Federal Reserve, Washington, DC, 1995. Goodhart,CharlesA. E. "What Should Central Banks Do? What Should Be Their Macroeconomic Objectives and Operations?" Economic Journal, November 1994, 104 (426), pp. 1424-36. Goodhart,CharlesA. E. and Vifials,Jose. "Strategy and Tactics of Monetary Policy: Examples from Europe and the Antipodes," in Jeffrey C. Fuhrer,ed., Goals, guideliries and constraints facing monetary policymakers. Boston, MA: Federal Reserve Bank of Boston, 1994, pp. 139-87. Haldane, Andrew G., ed. Targeting inflation. London: Bank of England, 1995. Herrendorf, Berthold and Lockwood, Ben.'"Rogoff's 'Conservative'CentralBanker Restored." Working paper, University of Warwick, 1996.

Jonsson, Gunnar. "Monetary

Politics

and

Unemployment Persistence," in Gunnar Jonsson, ed., Institutions and incentives in monetary and fiscal policy, Institute for International Economic Studies Monograph, No. 29. Stockholm: Institute for International Economic Studies, 1995, pp. 87-- 123. King, Mervyn. "Changes in U.K. Monetary Policy: Rules and Discretion in Practice." Unpublished manuscript presented to the Swiss National Bank Conference on Rules versus Discretion in Monetary Policy, Gerzensee, Switzerland, 15-19 March 1995. Kydland, Finn and Prescott, Edward. "Rules

Rather Than Discretion: The Inconsistency of Optimal Plans." Journal of Political Economy, June 1977, 85(3), pp. 473-90. Leiderman, Leonardo and Svensson, Lars E. O.,

eds. Inf lation targets. London: Centre for Economic Policy Research, 1995. Lockwood, Ben; Miller, Marcus and Zhang, Lei.

"Designing Monetary Policy when Unemployment Persists." Working paper, University of Exeter, May 1995. Lockwood, Ben and Philippopoulos, Apostolis.

"Insider Power, Unemployment Dynamics and Multiple Inflation Equilibria." Economica, February 1994, 61(241), pp. 5977. Lohmann, Susanne. "The Optimal Degree of

Commitment: Credibility and Flexibility." American Economic Review, March 1992, 82(1), pp. 273-86. McCallum, Bennett T. "Inflation Targeting in

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Bank Independence." American Economic Review, May 1995b (Papers and Proceedings), 85(2), pp. 207-11. Muscatelli, V. Anton. "Delegation versus Opti-

mal InflationContracts:Do We Really Need Concervative Central Bankers?" Working paper, University of Glasgow, 1995. Persson, Mats; Persson, Torsten and Svensson,

Lars E. 0. "Debt, Cash Flow and Inflation Incentives: A Swedish Example." National Bureau of Economic Research (Cambridge, MA) Working Paper No. 5772, September, 1996.

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Persson, Torsten and Tabellini,Guido. "Designing

Institutionsfor MonetaryStability."CarnegieRochester Conference Series on Public Policy, December 1993, 39, pp. 53-84. Rogoff, Kenneth. "The Optimal Degree

of

Commitment to a MonetaryTarget." Quarterly Journal of Economics, November 1985, 100(4), pp. 1169-90. Schaling, Eric. Institutions and monetary policy. Hants, U.K.: Elgar, 1995. Svensson,Lars E. 0. "The Simplest Test of Inflation Target Credibility." National Bureau of Economic Research (Cambridge, MA) Working Paper No. 4604, December 1993. . "Inflation Forecast Targeting: Implementing and Monitoring InflationTargets."

MARCH 1997

European Economic Review, 1997 (forthcoming). . "Optimal Inflation Targets, 'Conservative' Central Banks, and Linear Inflation Contracts." Working paper (revision of National Bureau of Economic Research [Cambridge, MA] Working Paper No. 5251), 1996a. . "Price Level Targeting vs. Inflation Targeting." National Bureau of Economic Research (Cambridge, MA) Working Paper No. 5719, 1996b. Walsh, Carl. "Optimal Contracts for Independent Central Bankers." American Economic Review, March 1995, 85(1), pp. 150-67.