The limits to stabilization policy. IAM Ch 22.
Ragnar Nymoen
Department of Economics, UiO
5 October 2009
ECON 3410/4410: Lecture 7
Limits to stabilization policy
Fine tuning the economy to avoid large and persistent deviation
from full employment is a di¢ cult task, also in the case where full
employment is the only steady-state of the economy (as the PCM
implies). Ch 22 in IAM identi…es three types of assumptions that
have been implicit so far:
1
No information lags. The policy maker knows the state of the
economy (the initial situation). There are no serious
measurement problems.
2
There are no adjustments lags in policy decisions— and policy
instruments can be adjusted “both up and down”.
3
The announced policy is credible.
IAM Ch 22 contains in-depth discussions of all three. Here we
concentrate on 3.
ECON 3410/4410: Lecture 7
Rule based equilibrium
We simplify the AD-AS model by assuming
vt = st = 0, gt = g ,
= 0 and
= 1:
And we assume rational expectations, RE.
From Ch 21, the RE equilibrium under a Taylor-rule with
= 0, as in
rt = r + h t + b(yt y );
and with the above simpli…cations, is
yt = y ;
t
=0
e
tjt 1
= 0.
ECON 3410/4410: Lecture 7
(1)
(2)
(3)
Central bank objective function (social loss function)
Assume that the central bank minimizes the loss-function
SL = (yt
y )2 +
2
t
(4)
where
y = y + !, ! > 0:
! is a parameter that re‡ects labour and product market
distortions/ine¢ ciencies.
y is the e¢ cient level of output that is attainable, given the
degree of permanent distortions represented by !.
Formally, (4) is like a ordinary (dis)utility function. The
marginal rate of substitution, between the two “goods” is
MRS =
which (for non-negative
t)
d t
y
=
dyt
yt
t
has its sign determined by yt .
ECON 3410/4410: Lecture 7
(5)
The value of social loss under the Taylor-rule
Insertion of the RE solution (1) and (2) gives
SLR = (yt
y )2 + 0 = ! 2 > 0
for the value of the social loss function under the rule based
policy.
Is this the minimum social loss?
ECON 3410/4410: Lecture 7
The “cheating” equilibrium I
Express the SL function as
SL = f(yt
Since
y ) + (y
y )g2 +
2
t
= 1, we have the PCM
t
e
tjt 1
= yt
y
and therefore the SL can be written as
n
o2
e
SL = ( t
)
+
(y
y
)
+
tjt 1
(6)
2
t
(7)
Assume that the central bank has led the public to believe
that it will ensure price stability, so etjt 1 = 0 as in the rule
based RE solution.
What is the optimal
its rule?
t
if the central bank can deviate from
ECON 3410/4410: Lecture 7
The “cheating” equilibrium II
The “cheating” in‡ation rate is de…ned by
c
t
= minf(
t
= minf(
t
The closed form expression for
c
t
Insertion of
e
tjt 1
!+
y ))2 +
+ (y
!)2 +
2
tg
2
tg
c
t
is obtained from the 1oc:
c
t
=0
c
t
=
!
1+
>0
= 0 into the Phillips curve (6) gives
ytc = y +
!
:
1+
ECON 3410/4410: Lecture 7
The “cheating” equilibrium III
These “cheating values” of the rate of in‡ation and output
give zero SLC < SLR , The e¤ect from distortions ! on output
are reduced.
An alternative mathematical derivation: Consider …nding the
minimum of (4):
SL = fyt
y g2 +
2
t
given the Phillips curve (6) with etjt 1 = 0 imposed, i.e.
conditional on expectations being …xed at zero in‡ation.
ECON 3410/4410: Lecture 7
The “cheating” equilibrium IV
First, form the Lagrangian function:
L = fyt
y g2 +
2
t
(
t
yt
y)
and obtain the two …rst order conditions
@L
= 0 () y
yt =
@yt
@L
= 0 () t =
@ t
These two conditions entails
MRS = 1:
The derivation using the Lagrangian function therefore brings
out that the cheating equilibrium is where the slope of the
Phillips curve with etjt 1 = 0 is a tangent to one of the
indi¤erence curves of the social loss function.
This is useful for the graphical illustration of the solution.
ECON 3410/4410: Lecture 7
Graphical solution
π
LRAS
SRAS (
SRAS (
ω /κ
E
π
e
= 0)
E
R
ER is the Taylor
rule equilibrium
EC is the
cheating
equilibrium.
D
ω /(1 + κ )
E
π e = ω /κ )
C
E
*
y
*
'
y
ECON 3410/4410: Lecture 7
ED is the
time-consistent
equilibrium.
Time-consistent equilibrium I
The “cheating policy” is however self-defeating, since agents,
after having being cheated once, will take account of the
cheating behaviour. This is called the time-inconsistency
problem after Kydland Precott (1977).
Speci…cally rational in‡ation expectations will be formed from
(
t
e
tjt 1
!) +
t
=0
(8)
which is the 1oc for minimization of the cheating loss function
(7). Alternatively: obtain it from the 1ocs for the Lagrangian
function.
Taking expectations on both sides of (8) gives
(
e
tjt 1
e
tjt 1
!) +
!+
e
tjt 1
e
tjt 1
= 0
= 0
ECON 3410/4410: Lecture 7
Time-consistent equilibrium II
So the in‡ation expectations that take account of the central
bank’s cheating becomes:
e
tjt 1
=
!
=
t
(9)
The last “=” sign in (9) re‡ects that there is no uncertainty
in the model, ie. after the simpli…cations we did initially.
Insertion of (9) in the Phillips curve (6) gives
yt = y
(10)
(9) and (10) de…ne the time-consistent RE equilibrium.
In‡ation is higher than in the Taylor-rule equilibrium.
Therefore loss of credibility in monetary policy can be said to
lead to an in‡ation bias.
ECON 3410/4410: Lecture 7
In‡ation bias and credibility loss
That loss of credibility in monetary policy can lead to an
in‡ation bias is a result which has been very in‡uential in
practice.
For example: One of the main rationale for credibility
building, which often involves delegation of monetary policy
and central bank independence.
Compare Sweden’s Riksbank. On 15 January 1993, the
Riksbank announced that monetary policy would be conducted
with a view to achieving price stability. But because of high
in‡ation expectations, it was also stated that the target for
monetary policy would not begin to apply until 1995.
One interesting point made in IAM, is that the case for
central bank independence with a strict mandate for in‡ation
stabilization is strongest when demand shocks dominate.
With dominating supply shocks, the results may be excess
variability in output. Compare Ch 21.
ECON 3410/4410: Lecture 7