Download Optimal Inflation Targets, ЕConservativeG Central Banks, and

Forthcoming in American Economic Review
Byline: Optimal In‡ation Targets
First version: April 1995
This version: November 1996
Optimal In‡ation Targets,
‘Conservative’ Central Banks,
and Linear In‡ation Contracts
Lars E.O. Svensson*
Abstract
In‡ation target regimes (like those of New Zealand, Canada, United Kingdom and
Sweden) are interpreted as having explicit in‡ation targets and implicit employment
targets. Without employment persistence, an ‘in‡ation target-conservative’ central
bank eliminates the in‡ation bias, mimics an optimal in‡ation contract, and dominates a Rogo¤ ‘weight-conservative’ central bank. With employment persistence, a
state-contingent in‡ation bias and a stabilization bias also arises. A constant in‡ation
target and a constant in‡ation contract are still equivalent. A state-contingent in‡ation
target combined with a weight-conservative central bank can achieve the equilibrium
corresponding to an optimal rule under commitment. (JEL E42, E52, E58)
Keywords: Monetary Policy, Commitment, Discretion, Rules
1
Recently a number of countries—New Zealand, Canada, United Kingdom, Sweden,
Finland, Australia and Spain—have introduced explicit in‡ation targeting monetary
policy regimes.1 This paper attempts at understanding in‡ation targeting and its properties in relation to the literature on commitment and 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 shortrun bene…t from surprise in‡ation (for instance, taxes or unemployment bene…ts make
the natural rate of unemployment ine¢ciently high). The …rst-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 second-best equilibrium
can still be achieved if the natural rate is accepted as the employment target. If that
is infeasible, for political or other reasons, discretionary policy leads to a fourth-best
equilibrium with an in‡ation 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, fn. 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 in‡ation bias can be eliminated by
reducing the weight on unemployment stabilization to zero. Kenneth Rogo¤ (1985)
suggested delegation of monetary policy to an independent appropriately ‘conservative’ central bank, where ‘conservative’ means ‘weight-conservative’, having less (but
still positive) weight on employment stabilization than society. This reduces the in‡ation 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 in‡ation 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-conservative central banks by Su2
sanne Lohmann (1992). These also lead to third-best equilibria. 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 in‡ation contract,” consists of adding a linear cost of in‡ation to
the central bank’s loss function.
The study of commitment and discretion in monetary policy has been extended
beyond the standard static framework to the realistic situation with persistence in
output and employment. Such persistence introduces lagged e¤ects of monetary policy,
requires monetary policy to be conducted with a view to the future, and substantially
a¤ects the equilibria. Results in Ben Lockwood and Apostolis Philippopoulos (1994),
Gunnar Jonsson (1995), and Lockwood, Marcus Miller and Lei Zhang (1995) imply
that discretion then leads to a state-contingent in‡ation bias relative to the secondbest equilibrium. The average in‡ation bias is then larger than without persistence.
Also, under discretion there is a stabilization bias, in that in‡ation variability becomes
too high, and employment variability too low, relative to the second best. David Currie,
Paul Levine and Joseph Pearlman (1995) and Lockwood, Miller and Zhang (1995) have
examined third-best Rogo¤ delegation of monetary policy to a central bank which puts
more weight on in‡ation stability than society does; the latter has also shown that a
state-contingent linear in‡ation contract can achieve the second-best equilibrium when
there is persistence.
This paper examines the performance of in‡ation target regimes relative to these
previous results, with and without persistence in employment. This then requires a
theoretical representation of a stylized in‡ation target regime. An in‡ation target
regime is here interpreted as a principal-agent arrangement, where society, the principal, delegates monetary policy 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, say in
the form of a loss function over macroeconomic outcomes. More precisely, the delega3
tion of monetary policy has three components: (1) Society assigns, for instance with
a legislated price stability goal, a loss function to the central bank. (2) The central
bank is given independence to minimize the assigned loss function without interference
from the government or other interests. (3) 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 in‡ation targets, the commitment to the target appears to be
weaker and there is less accountability and independence of the central banks. These
di¤erences are discussed further in Svensson (1996b).
For concreteness, let me follow the literature and assume that society has preferences over in‡ation and employment that correspond to a quadratic social loss function
over in‡ation, ¼ t , and (the) employment (rate), lt , in period t;
L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸) =
i
1h
(¼ t ¡ ¼ ¤ )2 + ¸(lt ¡ l¤ )2 .
2
(1)
The loss function is characterized by three parameters: ¼ ¤ is the socially desirable
in‡ation rate, l¤ is the socially desirable employment rate, and ¸ > 0 is the social
weight on employment stabilization relative to in‡ation stabilization.
An in‡ation target regime is then interpreted as the delegation of monetary pol³
icy to the central bank as above, with an assigned loss function L ¼ t ; lt ; ¼ b ; lb ; ¸b
´
with the three parameters ¼ b , an explicit announced in‡ation target, lb , an implicit
but known employment target, and ¸b > 0; an implicit but known relative weight on
employment stabilization. These parameters may di¤er from the corresponding parameters of the social loss function. The interpretation of in‡ation target regimes as
having a loss function involving both in‡ation and employment targets is supported
by several circumstances (see the contributions in Leiderman and Svensson (1995)):
(1) Actual in‡ation target regimes (with the exception of Finland and Australia) have
explicit tolerance bands around the target level, indicating that some variability of
4
in‡ation around the target is acceptable. (2) No central bank with an explicit in‡ation
target seems to behave as if it wishes to achieve the target at all cost, regardless of
the employment consequences. (3) A prominent central banker, Mervyn King (1995),
has interpreted in‡ation target regimes precisely in this way. Thus, an in‡ation target
regime is not interpreted as corresponding to ¸b = 0, what King (1995) calls the case of
an “in‡ation nutter.” An in‡ation target regime need not have explicit escape clauses
for supply shocks in order to incorporate some preference for employment stabilization,
counter to the interpretation in Fischer (1995).3
In the in‡ation target regimes to be discussed below, it will in the standard case
be assumed that the central bank has the same employment target as society, and the
same relative weight on employment stabilization, although I shall also report results
for di¤erent employment targets and di¤erent relative weights. Society’s employment
target is above the natural rate of employment, because of, for instance, distortions
in the labor market make the natural rate of unemployment ine¢ciently high. The
role of this employment target in the analysis is to introduce a bene…t from a surprise
in‡ation. As noted in the literature, such bene…ts 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 the central bank will in the standard case have an ‘overambitious’ employment target which, under discretion, results in an in‡ation bias. A
more rational delegation of monetary policy would assign an employment target corresponding to the natural rate. Such a rational delegation is assumed infeasible in the
standard case, for instance, because of political di¢culties (say that a powerful labor
movement prevents an employment target less than full employment), or di¢culties
in verifying the delegation of a natural employment rate, or lack of unanimity of estimates of the natural employment rate. The assumption re‡ects 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 we shall see, however,
even if the employment target were to be …xed at the long-run natural rate level, if
there is persistence only the average in‡ation bias is eliminated. The state-contingent
5
in‡ation 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, considers empirical predictions, and
concludes. The appendix reports technical details.
I.
Commitment and 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,
lt = ½lt¡1 + ®(¼ t ¡ ¼ et ) + ²t ;
(2)
where 0 · ½ < 1, where lt is (the) employment (rate) (the log of the share of actual
employment in full employment) in period t, ® is a positive constant, ¼ t is the (log of
the gross) in‡ation rate, ¼ et denotes in‡ation expectations in period t¡1 of the in‡ation
rate in period t, and ²t is an i.i.d. supply shock with mean 0 and variance ¾ 2 . The
private sector has rational expectations,
¼ et = Et¡1 ¼ t ;
(3)
where Et¡1 denotes expectations conditional upon the realization of all variables up to
and including period t ¡ 1, as well as the constant parameters of the model.
The autoregressive term in the Phillips curve can arise in a number of di¤erent
ways, for instance, in wage setting models where trade unions set nominal wages one
period in advance, disregard non-union 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
6
optimal rule under commitment, linear in‡ation contracts and in‡ation targets. The
equilibrium under discretion has been studied by Lockwood and Philippopoulos (1994)
for the in…nite-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, Miller and Zhang (1995) for the in…nite horizon case.5
The (long-run) natural rate of employment, which I identify with the unconditional
mean of employment, E[lt ], 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
V = E0
"1
X
t=1
¯
#
t¡1
¤
¤
L (¼ t ; lt ; ¼ ; l ; ¸) ,
(4)
with the “period” loss function (1) and the discount factor ¯, 0 < ¯ < 1. The (log of
the) socially desirable employment rate, l¤ , is assumed to exceed the natural rate of
employment and hence ful…lls l¤ > 0.
The central bank is, for simplicity, assumed to have perfect control over the in‡ation rate ¼ t . It sets the in‡ation rate in each period after having observed the current
supply shock ²t .6
A.
Commitment to an optimal rule
Consider …rst the situation when the central bank is directly controlled by the
government, so the government can choose the in‡ation rate in each period, conditional
upon the supply shock in the period. Assume temporarily that the government can
commit to a state-contingent rule for the in‡ation rate.
As in Lockwood, Miller and Zhang (1995), the optimal rule under commitment
can conveniently be derived from the Bellman equation
¤
V (lt¡1 ) = mine Et¡1
¼ t ;¼ t
½
¾
i
1h
(¼ t ¡ ¼ ¤ )2 + ¸ (lt ¡ l¤ )2 + ¯V ¤ (lt )
2
(5)
subject to (2) and (3). Thus the government chooses ¼ t , which may depend on lt¡1
and ²t , and in‡ation expectations ¼ et , which may only depend on lt¡1 , subject to the
7
condition that in‡ation expectations are rational. Put di¤erently, the government
internalizes the e¤ects of its decision rule on expectations. This problem di¤ers from
the standard commitment problem in that lagged employment enters as a state variable.
The …rst-order conditions with respect to ¼ t and ¼et result in
(¼ t ¡ ¼ ¤ ) + ¸®(lt ¡ l¤ ) + ¯®Vl¤ (lt ) ¡ Et¡1 [¸®(lt ¡ l¤ ) + ¯®Vl¤ (lt )] = 0;
(6)
where the Lagrange multiplier of (3) has been eliminated. The …rst term is the marginal current loss from increasing in‡ation, the second is the marginal current loss from
the resulting increase in employment (normally negative since employment is normally
below l¤ ), 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 bene…cial), and the fourth is the marginal loss of the resulting increase in
expected in‡ation (normally positive since increased in‡ation expectations reduce employment).
Taking expectations at t–1 of (6) gives
Et¡1 ¼ t = ¼ ¤ ;
(7)
the expected in‡ation rate equals the socially desirable in‡ation rate and is independent
of the employment level.
Since the problem is linear-quadratic, we know that V ¤ (lt¡1 ) must be quadratic.
Then I can write
1
V ¤ (l) = ° ¤0 + ° ¤1 l + ° ¤2 l2 ;
2
(8)
where the coe¢cients ° ¤0 , ° ¤1 and ° ¤2 need to be determined (I will only be interested in
° ¤1 and ° ¤2 ). Substitution of (2), (3), (7) and (8) into (6) results in a decision rule
¼ t = ¼¤ ¡ b¤ ²t
with
b¤ =
®(¸ + ¯° ¤2 )
.
1 + ®2 (¸ + ¯° ¤2 )
8
(9)
(10)
Employment will then ful…ll
lt = ½lt¡1 + (1 ¡ ®b¤ )²t .
(11)
In order to …nd b¤ , ° ¤2 has to be determined. Substitution of (8)-(11) into (5) and
2
identi…cation of the coe¢cients of lt¡1 and lt¡1
results in
° ¤1 = ¡
¸½l¤
1 ¡ ¯½
Using this in (10) result in
b¤ =
and ° ¤2 =
¸½2
.
1 ¡ ¯½2
(12)
¸®
.
1 + ¸®2 ¡ ¯½2
(13)
Setting ½ = 0 results in the standard static commitment equilibrium. Examining
(13) we see that the optimal in‡ation response to employment shocks is larger under
persistence than without. Since the employment shock has future as well as current
e¤ects on employment it becomes more important to stabilize employment; hence in‡ation is allowed to ‡uctuate more.
B.
Discretion
Assume now that the government retains direct control of the central bank, but
that the government cannot commit to a state-contingent rule. Instead it acts under
discretion. Then the decision problem of the government/central bank can be written
½
¾
i
1h
¤ 2
¤ 2
V (lt¡1 ) = Et¡1 min
(¼
+ ¯V (lt ) ;
t ¡ ¼ ) + ¸ (lt ¡ l )
¼t
2
(14)
where the minimization in period t is subject to (2) but is done for given in‡ation
expectations ¼ et (since the minimization is done for each t after observing the supply
shock, min¼t can be moved inside the expectations operator). The government/central
bank thus no longer internalizes the e¤ect of its decisions on in‡ation expectations,
although it takes into account that changes in current employment will a¤ect current
expectations of future in‡ation (this is incorporated in V (lt ), which in turn incorporates
future behavior of the government/central bank).
9
The …rst-order condition will be
¼ t ¡ ¼ ¤ + ¸®(lt ¡ l¤ ) + ¯®Vl (lt ) = ¼ t ¡ ¼ ¤ + (¸ + ¯° 2 )®lt ¡ (¸l¤ ¡ ¯° 1 )® = 0, (15)
where I exploit that V (l) must be quadratic as in (8) and let the discretion case have
coe¢cients ° 0 , ° 1 and ° 2 without an asterix. The marginal loss of increased in‡ation
expectations have vanished from the …rst-order condition. We see that the decision
rule can be written as a feedback rule for in‡ation 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 decision rule will also be a function
of past employment.
Taking expectations of (15) gives
Et¡1 ¼ t = ¼ ¤ + (¸l¤ ¡ ¯° 1 )® ¡ (¸ + ¯° 2 )®½lt¡1 .
(16)
Combining (15) and (16), using (2) and (3), gives a decision rule (a; b; c) of the form
¼ t = a ¡ b²t ¡ clt¡1 ;
(17)
with
a = ¼ ¤ + ®(¸l¤ ¡ ¯° 1 );
b=
®(¸ + ¯° 2 )
1 + ®2 (¸ + ¯° 2 )
and c = ®½(¸ + ¯° 2 ).
(18)
Employment will then ful…ll
lt = ½lt¡1 + (1 ¡ ®b)²t :
(19)
In order to determine a, b and c, ° 1 and ° 2 have to be determined. This can be
done by substituting (17)-(19) into (14) and identifying the coe¢cients for lt¡1 and
2
lt¡1
. In the appendix it is shown that this results in
¸®l¤
a=¼ +
;
1 ¡ ¯½ ¡ ¯®c
¤
¸® + ¯®c2
,
b=
1 + ¸®2 ¡ ¯½2 + ¯®2 c2
(20)
where c is given by
c=
·
¸
q
1
1 ¡ ¯½2 ¡ (1 ¡ ¯½2 )2 ¡ 4¸®2 ¯½2 ¸ 0
2®¯½
10
(21)
and an existence condition, detailed in the appendix, must hold.
For ½ = 0 (without persistence), we have c = ° 1 = ° 2 = 0 and the standard
discretion equilibrium occurs.
Comparing the decision rules under commitment, (9), and discretion, (17), we see
that under discretion there is an in‡ation bias, a ¡ clt¡1 ¡ ¼ ¤ . We can decompose
the in‡ation bias into a constant average in‡ation bias, a ¡ ¼ ¤ and a state-contingent
in‡ation bias, ¡clt¡1 . With employment persistence, the average in‡ation bias is larger
than 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 in‡ation bias. With
employment persistence, there is also a state-contingent in‡ation bias, whereas the
in‡ation bias is constant without persistence. The reason is that with employment
persistence the gap between the employment target, l¤ , and the short-run natural
rate of employment, ½lt¡1 , is state-contingent. Comparing (20) and (13) we see that
with persistence there is also a stabilization bias under discretion, in that the in‡ation
response to employment shocks is larger than under commitment, b > b¤ : Since under
discretion the future in‡ation bias depends on current employment, it becomes even
more important to stabilize employment, which requires a larger in‡ation response.
Thus employment will be too stable, whereas in‡ation will be too variable, relative to
the commitment case.
Thus, discretion results in a fourth-best equilibrium with too high in‡ation. With
persistence, in‡ation 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 …rst-best equilibrium. If the distortions cannot be removed, a
commitment to an optimal state-contingent rule 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 shall now
consider how such improvements can be achieved by delegating policy to an instrument11
independent central bank with di¤erent assigned objectives.
II.
Improvements of the discretion equilibrium
A.
Delegation to a weight-conservative central bank
For the case without persistence, Rogo¤ (1985) has shown that the discretionary
equilibrium can be improved if monetary policy is delegated to a weight-conservative
central bank. In the literature, this has mostly been interpreted as the government delegating monetary policy to a central bank with both goal and instrument independence,
and that the government can observe potential Governor’s or Board’s preferences and
can select a Governor or Board with the desired preferences. Alternatively, it can be
interpreted as a delegation to an instrument-independent central bank that is assigned
a particular loss function. This is the interpretation given here.
³
´
Thus, the central bank is given the period loss function L ¼ t ; lt ; ¼ ¤ ; l¤ ; ¸b ; where
¸b di¤ers from ¸ in the social period loss function (1). Rogo¤’s result is then that there
exists a ¸b , 0 < ¸b < ¸; that achieves a lower value of (1) than under discretion. For the
case without persistence, the central bank’s decision rule (17), has a = ¼ ¤ + ¸b ®l¤ ; b =
¸b ®
1+¸b ®2
and c = 0: Compared to the optimal rule (9) there is still an in‡ation bias, ¸b ®l¤ ,
but the in‡ation bias is lower. Without persistence there is no initial stabilization bias,
however. Since the in‡ation response to the supply shock is decreasing in ¸, the weightconservative central bank will let the in‡ation response be lower, and the employment
response be smaller, than under commitment; hence introduce a stabilization bias.
Thus, the lower in‡ation 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, Miller and Zhang (1995). Since there is an initial
stabilization bias towards too high in‡ation variability and too low employment variability, a lower weight on employment stabilization reduces both the average and the
12
state-contingent in‡ation bias and the stabilization bias (since both b and c are increasing in ¸), and hence brings three bene…ts. Nevertheless, it is clear that a weightconservative central bank cannot achieve the second-best equilibrium. Eliminating the
average and state-contingent in‡ation bias requires ¸b to be zero, but then there is
no in‡ation response at all. The initial stabilization bias has then been reversed to a
strong stabilization bias towards too low in‡ation variability and too high employment
variability.
Thus, with or without persistence, a weight-conservative central bank can at best
achieve a third-best equilibrium.
B.
A constant linear in‡ation contract
For the case without persistence, Walsh (1995) has shown that a simple linear
in‡ation contract for the central bank can achieve the second-best equilibrium. The
contract adds a linear cost to in‡ation to the social period loss function. Let the central
bank be assigned the period loss function L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸) + f (¼ t ¡ ¼ ¤ ). Using the
Bellman equation as above, the …rst-order condition will be
¼ t ¡ ¼ ¤ + f + (¸ + ¯° 2 )®lt ¡ (¸l¤ ¡ ¯° 1 )® = 0:
This di¤ers from the …rst-order condition (15) only in that ¼ ¤ is replaced by ¼ ¤ ¡ f . It
follows that the only change in the equilibrium is that the decision rule (17) will have
a = ¼¤ ¡ f +
¸®l¤
:
1¡¯½¡¯®c
Hence, by choosing
f =¡
¸®l¤
1 ¡ ¯½ ¡ ¯®c
(22)
the average in‡ation bias can be eliminated, and the decision rule will be (¼ ¤ ; b; c).
A constant linear in‡ation contract can eliminate the average in‡ation bias. It
does not a¤ect the stabilization bias and the state-contingent in‡ation bias. It follows
that without persistence, it achieves the second-best equilibrium. With persistence, it
can only achieve a third-best equilibrium.
13
A linear in‡ation contract is a very elegant way to remove the average in‡ation bias.
It has been noted in the literature that it faces both practical and political di¢culties,
though. One practical di¢culty is that the linear cost is presumably a monetary cost,
whereas the rest of the loss function is in some utility units. Thus the constant f
must translate monetary costs into utility, and hence incorporate the Governor’s or
Board’s marginal utility of money. A political di¢culty is that the contract stipulates
higher monetary rewards to the Governor or Board when in‡ation is low, which may
be provocative to the public if correlated with higher unemployment (Goodhart and
José Viñals (1994, p. 153)).
C.
A constant in‡ation target
Consider now assigning an explicit in‡ation target ¼ b to the central bank. The
target may di¤er from the socially desirable in‡ation rate. Furthermore, let this assignment be with the understanding that the employment target and the weight on
employment stabilization are the same as in the social loss function. The central bank
³
´
is then assigned the period loss function L ¼ t ; lt ; ¼ b ; l¤ ; ¸ rather than (1).
The …rst-order condition under discretion will now di¤er from (15) only in that ¼ ¤
is replaced by ¼ b . It is immediately obvious that only average in‡ation, a, is a¤ected in
¤
¸®l
the decision rule (17), according to a = ¼ b + 1¡¯½¡¯®c
: Hence, by selecting an in‡ation
target that ful…lls
¼b = ¼¤ ¡
¸®l¤
;
1 ¡ ¯½ ¡ ¯®c
(23)
the decision rule will be (¼ ¤ ; b; c) and the average in‡ation bias has been eliminated.
The state-contingent in‡ation bias and the stabilization bias remain. A constant linear
in‡ation contract and a constant in‡ation target are hence equivalent.
It is easy to see that an optimal in‡ation target (23) is equivalent to a optimal
linear in‡ation contract (22), since
³
´
1
L ¼ t ; lt ; ¼ b ; l¤ ; ¸ = L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸) + (¼ ¤ ¡ ¼ b )(¼ t ¡ ¼ ¤ ) + (¼ ¤ ¡ ¼ b )2 .
2
14
³
´
Hence, the in‡ation target loss function, L ¼ t ; lt ; ¼ b ; l¤ ; ¸ di¤ers from the social loss
function, L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸), by a term that is linear in ¼t and a constant. When ¼ b
ful…lls (23) that linear term is the same as for an in‡ation contract with (22).
Without persistence, an optimal constant in‡ation target results in the second-best
equilibrium. Then, delegating monetary policy to an ‘in‡ation-target-conservative’
central bank with an explicit in‡ation 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 Rogo¤ weight-conservative central bank
with relative less weight on employment stabilization.7
D.
A state-contingent linear in‡ation contract
Consider next more complex arrangements, …rst a state-contingent linear in‡ation
contract, where the added cost of in‡ation has a marginal cost of in‡ation that depends
on lagged employment. The loss function will be L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸)+(f0 +f1 lt¡1 )(¼ t ¡¼ ¤ );
where f0 and f1 are constant. With the corresponding Bellman equation, the …rst-order
condition will be
¼ t ¡ ¼ ¤ + f0 + f1 lt¡1 + (¸ + ¯° 2 )®lt ¡ (¸l¤ ¡ ¯° 1 )® = 0:
(24)
Taking expectations we see that
Et¡1 ¼ t = ¼ ¤ + (¸l¤ ¡ ¯° 1 )® ¡ f0 ¡ [(¸ + ¯° 2 )®½ + f1 ] lt¡1 :
Hence, by selecting f0 = ®(¸l¤ ¡¯° 1 ) and f1 = ¡®½(¸+¯° 2 ) we can eliminate both the
average and the state-contingent in‡ation bias, Et¡1 ¼ t = ¼ ¤
and c = 0: Substitution
of this into the Bellman equation and identi…cation of ° 1 and ° 2 results in (12) as in
the optimal rule. Combining (12) with the values of f0 and f1 above, we see that
f0 =
¸®l¤
1 ¡ ¯½
and f1 = ¡
¸®½
1 ¡ ¯½2
results in the optimal decision rule under commitment (¼ ¤ ; b¤ ; 0).
15
(25)
Thus, the average and the state-contingent in‡ation bias and the stabilization
bias vanish. A state-contingent linear in‡ation contract can achieve the second-best
equilibrium under persistence, as has been shown by Lockwood, Miller and Zang (1995).
E.
A state-contingent in‡ation target
³
´
Next, consider a state-contingent in‡ation target, with the loss function L ¼ t ; lt ; ¼ bt ; l¤ ; ¸ ,
where
¼ bt = g0 + g1 lt¡1
(26)
and g0 and g1 are constant.
The …rst-order condition for the Bellman equation will be
¼ t ¡ g0 ¡ g1 lt¡1 + (¸ + ¯° 2 )®lt ¡ (¸l¤ ¡ ¯° 1 )® = 0:
(27)
Taking expectations of (27) gives
Et¡1 ¼ t = g0 + ®(¸l¤ ¡ ¯° 1 ) + [g1 ¡ ®½(¸ + ¯° 2 )] lt¡1 ;
where I have used (8). Hence, by selecting g0 = ¼ ¤ ¡ ®(¸l¤ ¡ ¯° 1 ) and g1 = ®½(¸ +
¯° 2 ), we can eliminate the average and state-contingent in‡ation bias, Et¡1 ¼ t = ¼ ¤ .
It is shown in the appendix that this implies that ° 1 and ° 2 are the same as under
discretion, rather than as under commitment. This in turn implies that g0 and g1 ful…ll
g0 = ¼ ¤ ¡
¸®l¤
1 ¡ ¯½ ¡ ¯®c
and g1 = c;
(28)
where c is given by (21), and that the resulting decision rule will be (¼ ¤ ; b; 0) with b
given by (20) rather than (10). Hence, the average and state-contingent in‡ation bias
can be eliminated, but the in‡ation response to the supply shock will be the same as
with a constant in‡ation target and hence the stabilization bias remains.
Why cannot a state-contingent in‡ation target induce the optimal rule when a
state-contingent linear in‡ation contract can? Compare the …rst-order condition for
16
the linear in‡ation contract, (24), and for the in‡ation target, (27). It appears that by
selecting
¼bt = ¼ ¤ ¡ f0 ¡ f1 lt¡1
(29)
it should be possible to induce the second-best equilibrium. This appearance is misleading, though. We can understand this by comparing the loss functions in the two
cases, assuming (29). With a linear in‡ation contract, we have
L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸) + (f0 + f1 lt¡1 )(¼ t ¡ ¼ ¤ ),
(30)
and with an in‡ation target
³
´
1
L ¼ t ; lt ; ¼ bt ; l¤ ; ¸ = L (¼ t ; lt ; ¼ ¤ ; l¤ ; ¸) + (f0 + f1 lt¡1 )(¼ t ¡ ¼ ¤ ) + (f0 + f1 lt¡1 )2 . (31)
2
We see that the loss functions di¤er by the third term in (31). The fact that this
employment-dependent term enters with an in‡ation target means that it will be more
important to stabilize employment, and hence to let in‡ation react more vigorously
to supply shocks. Taking this into account, (29) with f0 and f1 given by (25) is not
enough to eliminate the average and state-contingent in‡ation bias; instead (26) with
g0 and g1 given by (28) is required. The coe¢cients ° 1 and ° 2 are indeed di¤erent for
the two cases. With a constant in‡ation contract and a constant in‡ation target, the
third term in (31) is constant and the two loss functions result in the same equilibrium.
F.
A state-contingent in‡ation target and a weight-conservative
central bank
The second-best equilibrium can be achieved with an a state-contingent in‡ation
target, if combined with a Rogo¤ weight-conservative central bank. By (20) b is decreasing in ¸ (note that c by (21) is decreasing in ¸). Then there exists a ¸b < ¸ such
that the corresponding b 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 ¸b < ¸
and the state-contingent in‡ation target (28) that corresponds to that relative weight,
the optimal rule (¼¤ ; b¤ ; 0) will result.
17
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 in‡ation target will eliminate the average and state-contingent
in‡ation bias, and hence restore the second-best equilibrium.
Thus, in‡ation target regimes should not only have low and possibly state-contingent
in‡ation targets. They should also put extra weight on in‡ation stabilization. Rogo¤’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 di¤erent!
It is to eliminate the stabilization bias, rather than to reduce the in‡ation bias.8
G.
A rational employment target
The maintained hypothesis so far is that monetary policy inherits society’s em-
ployment target. If feasible, it would be more rational for society to delegate a lower
employment target to monetary policy, and reserve society’s high employment target for other policies that may be able to deliver increased average employment, for
instance structural measures that make the labor market work more e¢ciently. For
completeness I shall also report the results for two regimes with alternative employ³
´
ment targets, where the central bank has the period loss function L ¼ t ; lt ; ¼¤ ; ltb ; ¸ .
That is, the central bank has an in‡ation target equal to the socially desirable in‡ation
rate ¼ ¤ and an employment target equal to ltb . The results below follow easily from the
analysis above.
First, suppose the employment target is constant and equal to the natural rate,
ltb = 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 (¼ ¤ ; b; c). The equilibrium is the same third-best equilibrium as for the
constant linear in‡ation contract (22) and the constant in‡ation target (23). That is,
the average in‡ation bias is eliminated but there is a state-contingent in‡ation bias,
and the stabilization bias remains.
18
It is easily shown that the employment target has to equal the state-contingent
“short-run” natural rate of employment, ltb = Et¡1 lt = ½lt¡1 ; in order to achieve the
second-best equilibrium (¼ ¤ ; b¤ ; 0).
III.
Conclusions
An in‡ation target regime is here interpreted as the delegation of monetary policy
to a central bank that is assigned an explicit in‡ation 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 in‡ation bias, in that average in‡ation rate will exceed the in‡ation target. With
employment persistence, also if the employment target equals the long-run natural rate,
there will in addition be a state-contingent in‡ation bias, in that in‡ation will depend
on lagged employment, and a stabilization bias, in that in‡ation variability will be too
high and employment variability too low. The equilibrium will be fourth best.
The results of the paper imply several empirical predictions for in‡ation target
regimes. First, the in‡ation bias implies that realized in‡ation rates should, on average,
exceed the in‡ation target. This prediction remains to be con…rmed, since the period
of in‡ation targets is yet a bit short too draw conclusions about average in‡ation. None
of the in‡ation target regimes has yet been through a complete business cycle. Second,
the in‡ation bias implies that an in‡ation target will normally be imperfectly credible,
since in‡ation expectations will normally exceed the in‡ation target. This prediction is
con…rmed so far, since the in‡ation targets in the existing in‡ation target regimes have
indeed so far been imperfectly credible (see Svensson (1993), Leiderman and Svensson
(1995), Richard T. Freeman and Jonathan L. Willis (1995) and Haldane (1995)).
Third, since lower in‡ation targets result in lower average in‡ation rates, without
any e¤ect on the variability of employment and output, lower in‡ation need not generally be associated with higher output variability. This is in contrast to the empirical
19
implication of Rogo¤ (1985) that lower in‡ation should be associated with increased
employment variability (if that lower in‡ation is the result of more weight-conservative
central banks). The prediction in this paper is con…rmed, since empirical studies have
indeed found that lower in‡ation is not correlated with higher output variability (cf.
Alberto Alesina and Lawrence H. Summers (1993), Debelle and Fischer (1994), Fischer
(1994) and Eric Schaling (1995)). Among possible explanations of this …nding, the literature has suggested that more-independent central banks are better at stabilization
than less-independent banks; that …scal policy is more disciplined in countries with
more central bank independence; or that both in‡ation and employment performance
are primarily a¤ected by shocks that di¤er from country to country. The most obvious,
but nevertheless overlooked, explanation is that lower in‡ation is due to lower in‡ation
targets rather than lower weights on employment stabilization!
An important policy implication is that even if an in‡ation target regime would
exceed its targets and be imperfect credible, that is by itself not a reason for abolishing
the regime. The resulting in‡ation may still be lower than it would have been without
the in‡ation 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 in‡ation bias arises if the natural employment rate, due to some
distortions, falls short of the socially desirable employment rate, the implicitly assigned
employment target. This represents, as outlined in the beginning of the paper, the
unfortunate but 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 …rst-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 bene…ts of surprise
in‡ation (cf. Mats Persson, Persson and Svensson (1996)). If it is infeasible to attack
20
the distortions directly, the equilibrium can instead be improved 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 will usually at best lead to a secondbest equilibrium.
One way to improve the regime is to assign a more rational employment target to
the central bank. Creating mechanisms for rational assignment of employment targets
should generally be a crucial aspect of monetary reform. In this regard it is worth
observing that only without employment persistence is it enough to assign the longrun natural rate as the employment target. Then the second-best equilibrium results.
With persistence, assigning the long-run natural rate still leaves the state-contingent
in‡ation bias and the stabilization bias in place. To remove these and get to the secondbest equilibrium, the employment target should be state-contingent and equal to the
short-run natural 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 in‡ation contracts. The …rst two lead only to third-best equilibria. Linear in‡ation contracts face both practical and political di¢culties. This paper emphasizes the
potential of lower in‡ation target and compares with the other alternatives. Without
persistence, an in‡ation target equal to the socially desirable in‡ation rate less the
in‡ation bias achieves the second-best equilibrium and is equivalent to an employment
target equal to the natural rate or to a linear in‡ation contract. Suppose, for instance,
that the socially desirable in‡ation rate is 2 percent per year (perhaps because a quality
bias in the CPI implies that a quality-adjusted in‡ation rate is zero). If the outcome
with a 2 percent in‡ation target then on average is 4 percent in‡ation, that is, the in‡ation bias is 2 percentage points, the socially desirable in‡ation rate can be achieved
with a zero in‡ation target. Thus, the optimal in‡ation target need not necessarily be
negative, something some may deem infeasible.
21
Would an in‡ation target below the socially desirable in‡ation rate be sustainable?
It seems that a zero in‡ation target that results in 2 percent in‡ation would be no less
sustainable than a 2 percent target that results in 4 percent in‡ation. If a zero in‡ation
target results in actual in‡ation that is above zero but equal the most socially desirable
rate, a zero target may be more sustainable. It requires, though, that the central bank
continues to su¤er disutility, depending on the deviation from zero rather than from
the socially desirable level, that is, that the target remains zero. This requires that
the target’s deviation from the socially desirable in‡ation rate is clearly motivated and
publicly understood to be necessary to counter the in‡ation bias. This requirement
does not appear to distinguish conservative in‡ation targets from conservative weights
on employment stabilization; it seems that a weight-conservative central bank also
requires motivation and public understanding to be sustained.
With employment persistence, a constant in‡ation target, a constant employment
target equal to the natural rate, and a constant linear in‡ation contract, are still
identical. They can eliminate the average in‡ation bias, but not the state-contingent
in‡ation bias and the stabilization bias. To remove the state-contingent in‡ation 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
in‡ation target is then not equivalent to a state-contingent employment target or a
state-contingent linear in‡ation contract. Although it eliminates the average and statecontingent in‡ation bias, in contrast to these it leaves the stabilization bias in place.
This points to an interesting combination of a weight-conservative central bank and a
state-contingent in‡ation target. A weight-conservative central bank can remove the
stabilization bias, whereas a state-contingent in‡ation target can remove the average
and state-contingent in‡ation bias.
Also for constant targets, a weight-conservative central bank can remove the stabilization bias. Thus, weight-conservative banks are desirable, though not for eliminating
22
the in‡ation bias as Rogo¤ suggested, but for eliminating the stabilization bias. Generally, central banks should be assigned both weight-conservative and in‡ation-target
conservative targets.
This has practical implications for the width of the tolerance bands for actual
in‡ation target regimes. If the width of the tolerance band target indicates the implicit
weight on employment stabilization, the bands should be relatively narrow (which they
actually seem to be, relative to realistic forecast error variance, cf. Charles Freedman
(1995) and Haldane (1995)).
A general methodological conclusion for the literature on commitment and discretion in monetary policy from this paper, 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 literature has focused almost exclusively on one parameter of the
standard quadratic loss function, the relative weight on in‡ation stabilization, with the
occasional observation that a reduction of the employment target would improve the
equilibrium. Discussion of the in‡ation target parameter is of no less, and perhaps of
more, practical relevance. Thus, the identi…cation of ‘conservativeness’ with the relative weight on in‡ation stabilization seems unwarranted. The same can be said about
the frequent identi…cation of central bank independence with the same relative weight
in the literature on measurement of central bank independence.
23
Appendix A.
The discretion solution and the existence condition
Consider the explicitly recursive problem
½
¾
i
1h
¤ 2
¤ 2
Vt¡1 (lt¡1 ) = Et¡1 min
(¼
¡
¼
)
+
¸
(l
¡
l
)
+ ¯Vt (lt ) ;
t
t
¼t
2
(A1)
instead of (14). Let Vt (lt ) = ° 0t + ° 1t lt + ° 2t lt2 . The …rst-order condition results in a
decision rule of the form ¼ t = at ¡ bt ²t ¡ ct lt¡1 ; with
at = ¼ ¤ + ®(¸l¤ ¡ ¯° 1t );
bt =
®(¸ + ¯° 2t )
1 + ®2 (¸ + ¯° 2t )
and ct = ®½(¸ + ¯° 2t ).
(A2)
2
leads to
Substitution of this into (A1) and identi…cation of the coe¢cient for lt¡1
° 2;t¡1 = ½2 (¸ + ¯° 2t ) + ®2 ½2 (¸ + ¯° 2t )2 :
(A3)
Using the expression for ct in (A2) the equation can be written in terms of ct as
ct¡1 = ¸®½ + ¯½2 ct + ¯®½c2t .
(A4)
A stationary solution ct¡1 = ct = c must ful…ll the second-degree equation
c2 ¡
1 ¡ ¯½2
¸
c + = 0.
®¯½
¯
(A5)
which has real solutions
·
¸
q
1
2
c=
1 ¡ ¯½ § (1 ¡ ¯½2 )2 ¡ 4¸®2 ¯½2 ¸ 0
2®¯½
if and only if
2
¸ · ¸1 =
(1 ¡ ¯½2 )
4®2 ¯½2
(A6)
is ful…lled.
We know that ½ = 0 by (A4) implies that c = 0, and that ¯ = 0 implies c = ¸®½.
Then the smaller solution (21) is the relevant one, since only then does c ! 0 when
½ ! 0, and c ! ¸®½ when ¯ ! 0. Alternatively, one can study the iteration (A4)
when t ! ¡1 and show that the smaller solution is the stable one.
24
Identi…cation of the coe¢cient for lt¡1 in (A1) and considering the stationary
values of ° 1 and ° 2 lead to
°1 = ¡
¸l¤ [½ + ®2 ½ (¸ + ¯° 2 )]
:
1 ¡ ¯ [½ + ®2 ½ (¸ + ¯° 2 )]
(A7)
From (18), (A3) and (A7) we can express both ° 1 and ° 2 in terms of c,
°1 = ¡
¸l¤ (½ + ®c)
c ¡ ¸®½
¸½2 + c2
> 0;
< 0 and ° 2 =
=
1 ¡ ¯½ ¡ ¯®c
¯®½
1 ¡ ¯½2
(A8)
where the stationary version of (A4) has been used to rewrite ° 2 , to facilitate comparison with (12): We clearly have ° 2 > 0. But in order to ensure that there is a …nite
solution to ° 1 we must assume the second existence condition
¯(½ + ®c) < 1.
(A9)
This condition does not follow from (A6) but has to be assumed separately. The
condition has a natural interpretation: The expression ¯(½ + ®c) is the discounted
total increase in employment in period t of a unit increase in employment in period
t ¡ 1, when in‡ation in period t is held constant. The total e¤ect consists of the
direct e¤ect, ½; and the indirect e¤ect via reduced in‡ation expectations, ®c. If this
discounted e¤ect is above unity, the present value of the e¤ect in all future periods will
be unbounded. Note that (A9) is only relevant when l¤ 6= 0.
From (A9) and (21) follows that the second existence condition is equivalent to
the condition
1 ¡ 2½ + x <
q
(1 ¡ x)2 ¡ 4¸®2 x;
where 0 < x = ¯½2 < ½2 . If 1 ¡ 2½ + x < 0, that is, if
1
2
(A10)
< ½ < 1 and 0 < x < 2½ ¡ 1,
the condition (A10) is always ful…lled. If 1 ¡ 2½ + x > 0, that is, if 2½ ¡ 1 < x < ½2 ,
(A10) is equivalent to
¸ < ¸2 =
(1 ¡ ½)(½ ¡ x)
(1 ¡ ½)(½ ¡ ¯½2 )
.
=
®2 x
®2 ¯½2
(A11)
It can indeed be shown that (A11) is at least as restrictive as (A6), that is, ¸2 · ¸1 .
To see this, note that
2
¸1 ¡ ¸2 =
(1 ¡ ¯½2 ) ¡ 4 (1 ¡ ½) (½ ¡ ¯½2 )
(1 ¡ x)2 ¡ 4 (1 ¡ ½) (½ ¡ x)
=
:
4¯®2 ½2
4®2 x
25
Study the numerator, z = (1 ¡ x)2 ¡ 4 (1 ¡ ½) (½ ¡ x). It is easy to show that z ¸ 0
for 0 < x < ½2 and 0 < ½ < 1, and that z = 0 if and only if x = 2½ ¡ 1.
Thus, for l¤ 6= 0 the existence condition depends on the values of ¯ and ½: The
existence condition can be summarized as
¸ · ¸1
for
¸ < ¸1 = ¸2
¸ < ¸2 < ¸1
8
>
<
1
2
<½<1
>
: 0<¯<
8
>
<
for
for
1
2
(A12)
2½¡1
;
½2
·½<1
>
: ¯=
(A13)
2½¡1
;
½2
8
>
< 0<½<1
>
:
2½¡1
½2
(A14)
< ¯ < 1:
For l¤ = 0, only (A6) needs to be ful…lled, since then ° 1 = 0.9
10
If ® in (2) equals unity, as in Lockwood and Philippopoulos (1994) and in Lockwood, Miller and Zhang (1995), the existence condition appear rather restrictive. If ¯
= 0.95 and ½ = 0.4 (0.8), we have
2½¡1
½2
= ¡1:25 (0.94), so (A14) applies. Then ¸2 =
0.98 (0.06), respectively. If ® instead equals 0.2, the corresponding ¸2 values are 25
times larger, that is, 24.5 (1.58). The corresponding values for ¸1 are 1.18 (0.06) for ®
= 1, and 29.6 (1.58) for ® = 0.2.
Appendix B.
A state-contingent in‡ation target
We know that b is given by (18). Substitution of (27) into the Bellman equation
2
and identi…cation of the coe¢cient for lt¡1
gives
° 2 = ½2 (¸ + ¯° 2 ) + g12 :
Because g1 = ®½ (¸ + ¯° 2 ) this is the same equation as the stationary version of (A3).
This means that ° 1 and ° 2 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
(¼ ¤ ; b; 0) with b given by (20).
26
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Notes
* Institute for International Economic Studies, Stockholm University, S-106 91
Stockholm, Sweden. I have bene…ted from comments by Robert Barro, Claes Berg,
Alan Blinder, Alex Cukierman, Jon Faust, Stanley Fischer, Stefan Gerlach, John Green,
Dale Henderson, Berthold Herrendorf, Lars Hörngren, Peter Isard, Gunnar Jonsson,
Mervyn King, Leo Leiderman, Paul Levine, Christian Nilsson, Torsten Persson, Andrew Rose, Paul Söderlind, Guido Tabellini, Carl Walsh, Janet Yellen, the editors,
anonymous referees, and participants in seminars at Bank of England, CEPR Summer
Symposium, Federal Reserve Board, Federal Reserve Bank of San Francisco, IIES, IMF,
Sveriges Riksbank, University of California at Berkeley and University of California at
Santa Cruz. Remaining errors and obscurities are my own. I thank Christina Lönnblad
for secretarial and editorial assistance, and Stefan Palmqvist for research assistance.
1
See the papers in Leonardo Leiderman and Lars E.O. Svensson (1995) and An-
drew 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 in‡ation targeting are discussed in Svensson (1996a). In‡ation targeting, allowing base
drift in the price level, results in price levels that are random walks or more generally
integrated of order one. Price-level targeting, which results in (trend-)stationary price
levels, is discussed and compared to in‡ation targeting in, for instance, Pierre Duguay
(1993) and Svensson (1996c).
2
McCallum (1995b) has criticized the commitment-discretion framework. The
critique is discussed in a longer version of this paper, Svensson (1996b).
3
John W. Faust and Svensson (1996) examines the situation when implicit em-
ployment targets, in contrast to explicit in‡ation 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.
4
Charles A.E. Goodhart (1995, p.1426-1427): ‘Even without political subservience,
there will usually be a case for deferring interest rate increases, until more information
31
on current developments becomes available. Politicians do not generally see themselves as springing surprise in‡ation 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.’
5
Barro and Gordon (1983) included the case of an exogenous persistent natural
(un)employment rate. The only change in the equilibrium is then that the in‡ation
bias is exogenous and persistent. This is very di¤erent from the case of an endogenous
persistent employment rate, where there are substantial changes in the equilibrium
demonstrated below.
6
The results are not a¤ected in any essential way if an error term is added on
in‡ation, indicating imperfect control of in‡ation. Neither are the results a¤ected if
output is considered the control variable; or 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 if a money demand equation is
also added and money supply is the instrument, see for instance Rogo¤ (1985).
7
After the …rst version of this paper was completed, I received a copy of Mus-
catelli (1995), which for the situation without persistence observes that a low in‡ation
target can remove the in‡ation bias and then discusses the consequences of uncertain
preferences of goal-independent central banks.
8
Berthold Herrendorf and Lockwood (1996) consider a few other situations that
result in a stochastic in‡ation bias and show that a weight-conservative central bank
can improve the discretionary equilibrium.
9
In the analysis of Lockwood and Philippopoulos (1994) only (A6) appears, since
they assume that l¤ = 0:
10
An early working paper version of this paper erroneously reports that (A14)
must hold regardless of the values of ¯ and ½.
32