Lecture 7 Rules versus Discretion Prof. Dr. Johann Graf Lambsdorff Anticorruption and the Design of Institutions 2008/09
Dec 22, 2015
Lecture 7
Rules versus Discretion
Prof. Dr. Johann Graf Lambsdorff
Anticorruption and the Design of Institutions 2008/09
ADI 2008/09
Blinder, A. (1998), Central Banking in Theory and Practice: 36-51.
Jarchow, H.-J.: Theorie und Politik des Geldes, Band 1: Geldtheorie,
11. neu bearb. und wesentl. erw. Aufl., Göttingen: UTB, 2003. S. 279-
303.
Kydland und Prescott (1977), Rules Rather than Discretion, Journal
of Political Economy, Jg. 85: 473-91.
Literature
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Rational economic policymaking was often approached in a
technocratic manner: policymakers start by analyzing the functioning
of an economic system. This embraces how this system will react to
stimuli, which can be controlled by the policymaker. It also embraces
finding out societies preferred goals. Once (rational and benevolent)
policymakers understand these two issues, they must weigh the costs
and benefits of using stimuli and bring these in line with society‘s
preferences.
In this perspective, policymaking is the maximizing of a social welfare
function (or minimizing a cost function) given the known constraints.
Rational policymaking
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Against this widely held view, Kydland und Prescott (1977) argued:
“Even if there is an agreed-upon, fixed social objective function and
policymakers know the timing and the magnitude of the effects of
their actions, discretionary policy, namely, the selection of that
decision which is best, given the current situation and a correct
evaluation of the end-of-period position, does not result in the social
objective function being maximized. that the social welfare function is
not maximized by determining the optimal use of instruments in a
given economic situation.”
The reason for this seemingly paradox statement is that economic
planning is not a game against nature but a game against other
rational economic actors.
The following model for optimal central bank policy helps us
understand this argument.
Rational policymaking
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The supply side is characterized by a Philipps-curve:
with : being the rate of inflation; : expected rate of inflation (which is formed in the previous period for the current period); Yr : real domestic product; : potential domestic production where labor is employed to an extent that does not induce changes in wages and inflation. For the sake of simplicity we omitted a coefficient preceding the output gap.
In case of rational expectations, economic subjects utilize all
available information and know the model. If they are not surprised by
unanticipated shocks we obtain:
rY
,r r= *+ Y -Y
Output gap
The time inconsistency model
= *.
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Inserting this into the supply side yields: . The central bank
has thus no possibility of influencing production in the long run.
If the central bank, in the short run, manages to set inflation larger
than the level that is expected by private agents, production increases
above its potential level.
This can be justified by the wage setting process. Wages are
negotiated based on expected inflation.
But if inflation increases above this level, employer’s profits
increase. This induces firms to increase production.
The time inconsistency model
r rY =Y
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In our model, the central bank directly controls the inflation rate. This
is certainly a simplification. We disregard the problem that inflation is
only indirectly controlled by influencing macroeconomic demand by
setting the interest rate.
Thus, in our model the central bank can reduce inflation without
temporarily reducing macroeconomic demand.
But the central bank faces another major problem: its announcement
of zero inflation may not be credible.
Private agents must anticipate inflation well in advance. Lenders, for
example, would suffer form inflation unless they well anticipate its
magnitude. Should private agents trust the central bank’s
announcements? May the central bank have reason to mislead private
agents?
The time inconsistency model
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In reality we find many reasons why central banks fail to stick to their
announcements. Why else are many central banks announcing
inflation rates lower than those who are finally achieved?
One reason relates to the government being a net borrower.
Unanticipated inflation helps the government reduce its debt. The
government also profits from central banks that excessively print
money, without giving due consideration to the subsequent risk of
inflation.
The central bank may even profit itself from printing money – there
are cases of outright corruption among central bankers or the
politicians who control central banks.
The time inconsistency model
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In 1979 Erwin Blumenthal, who served as an IMF representative in
Zaire and was the central bank’s vice governor there, experienced
such a case. There was no clear dividing line between the state budget
and President Mobutu’s personal account. Equally, the central bank
was largely regarded the personal property of the President and his
cronies. Blumenthal was repeatedly forced to hand out the central
bank’s money for purely private purposes. Once he rejected payment
he was threatened with submachine guns to comply with the orders of
an army general, Lambsdorff and Schinke (2002).
President Fujimori in Peru embezzled gold reserves from the central
bank and transferred them to Japan. The loss in the central bank's net
equity must be compensated somehow, for example by printing
money and disregarding future inflation.
The time inconsistency model
ADI 2008/09 In 1999 surprise inflation was created by a central banker himself in Brazil.
Francisco Lopes headed the Brazilian Central Bank as a governor for only
three weeks. Upon his appointment he devalued the Brazilian currency, the
Real, by eight percent. Such a devaluation increases import prices and, thus,
inflation. Before the devaluation, Lopes gave advance notice of the new
exchange rate to several private Brazilian banks, enabling them to profit from
the “unexpected move” (BBC, April 14, 1999). Furthermore, a few days after
the devaluation, Lopes sold dollars at favorable prices to the same banks. A
Brazilian weekly news magazine quoted Salvatore Cacciola, an owner of one of
the banks, as saying that he had a paid informant within the central bank. This
informant would alert him to important events, such as changes of the interest
rates or currency movements (BBC, April 26, 1999). A raid on Lopes’ house by
the Brazilian police revealed several documents showing that Lopes, while
working as a public servant, had maintained close connections to a private
consulting firm and had more than $1.5 million in a foreign bank account
(BBC, April 26, 1999). One year later, in February 2000, Lopes was charged
with fraud (BBC, February 3, 2000) and with maintaining a foreign bank
account that he had not declared to the tax office or the central bank (BBC,
January 20, 2001). This event is reported in Schinke (2006).
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But even benevolent central banks may have reason to depart from
their announcement. This is best investigated by considering the
central bank‘s cost function. The central bank dislikes inflation and
deviations of production from its desired level. It weights the latter by
, its employment preference:
We call central bankers with a small “conservative”. Those with a
large are called “populist”. The domestic product which is preferred
by society and the central bank alike is denoted by ( ). It is larger
than potential production and the difference is denoted by z:
The time inconsistency model
22 ˆ .rK Y Y
Y
ˆ 0rz Y Y
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A plausible reason relates to unemployment aid. This aid implies
that individual costs of unemployment are lower than social costs. In
an extreme case where unemployment pay equals the regular salary
an individual would not suffer from unemployment, while society at
large but have to bear the full burden.
This cost function assumes that desired inflation is zero (otherwise a
nonzero target rate for inflation would have to be considered).
The cost function entails another plausible assumption: A mixture of
two “evils”, unemployment and inflation, is preferred to being hit
excessively by only one “evil”. For this reason the two terms are
squared, expressing increasing marginal disutilities.
The time inconsistency model
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The game is played by letting private agents act first. They determine
expected inflation. These expectations are used to sign labor
contracts. In case of high expected inflation, high increases in wages
are negotiated. If low levels of inflation are expected, moderate wage
increases result. The central bank acts in the final period by fixing the
true level of inflation.
Private agents expect inflation.
Wages are negotiated
Central bank fixes inflation.
The time inconsistency model
t
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Inserting for z and the supply function into the cost function yields:
The central bank takes * as given, because it is determined at the
beginning of the game.
For the solution of the game three cases must be distinguished:
1. Rule
2. Cheating
3. Discretion
The time inconsistency model
22 * .K z
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Rule
The central bank announces price stability (=0) and the private
agents believe in this announcement, (*=0).
Due to the supply side implies that production equals its
potential level, .
Costs for the central bank amount to:
The time inconsistency model
r rRY Y
2.RK z
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Cheating
When determining actual inflation the central bank observes that
expected inflation is given. All wages are already fixed and will not
react to the central bank’s choice.
The central bank will minimize its costs. A cost minimum requires:
Assuming that private agents trusted the central bank (*=0), we
obtain:
The central bank will thus fix the following inflation rate:
The time inconsistency model
2 2 * 0.dK d z
2 2 0.dK d z
0.1C z
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In spite of its announcement of price stability the central bank
chooses a positive rate of inflation.
Production increases to the following level:
Due to surprise inflation the central bank is thus able to increase
production and lower unemployment towards a level preferred by
society. The costs amount to
These costs are lower as compared to the rules based solution:
The time inconsistency model
* .1
r r rC CY Y z Y
2 22
1 1 1CK z z z z
2 2.1C RK z K z
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RK
rr YY
rY
*
CK
*
C
The time inconsistency model
Y
0 r r= + Y -Y
R
C
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Discretion
Rational private agents will anticipate the central bank’s temptation
to cheat.
This will increase their expected level of inflation. But by how much?
Rational private agents know the central bank‘s calculus and the
model. They thus know that the central bank maximizes according to
Solving for yields the central bank’s reaction function,
Inflation, , thus increases with expected inflation and z.
The time inconsistency model
2 2 * 0.dK d z
1 * .z
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Rationality now assumes that private actors will not make systematic
errors when anticipating the level of inflation. Since there are no
stochastic shocks, this implies that they will not err: *. Inserting
this into the reaction function yields
Due to a lack of central bank credibility private agents and the
central bank bias upwards the level of inflation (“inflation bias“).
This inflation bias is the higher the higher the central bank‘s
preference for employment, , and the more desired production
exceeds potential production, z.
Due to * production equals its potential level, .
The time inconsistency model
1 * .Dz z z
r rDY Y
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RK
rr YY
rY
*
CK
D
DK
*
D
C
(1 ) ( * )z
The time inconsistency model
Y
r r= *+ Y -Y
0 r r= + Y -Y
R
C
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Graphically the equilibrium is reached where both, the supply curve
and the isocost-curve intersect with the -curve and have the
same slope.
The costs in the discretionary solution are given by:
As expected, inflation has increased relative to the cheating solution:
Costs are also higher as in “rules”:
The time inconsistency model
2 21 .D RK z K z
.1D Cz z
2 2 21 .DK z z z
rr YY
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To conclude, economic policy should not be carried out by
determining an optimal use of instruments in specific situations.
Instead, politics should strive to impose rules on its own conduct.
Politics must strive to make these rules binding, so that decision
makers can sustain the temptations when they arise.
This viewpoint is parallel to that of Ulysses and the Sirens. Ulysses
was curious to hear the Sirens' songs but mindful of the danger. He
ordered his men to stop their ears with beeswax and ties himself to
the mast of the ship. He orders his men not to pay attention to his
cries while they pass the Sirens. He anticipated his irrational behavior
and bound himself to a commitment mechanism (i.e. the mast) to
survive.
The time inconsistency model
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Problems of time inconsistency not only arise with central bank
policy.
Taxation is another widely used example. Investors are sometimes
promised preferential taxation in an attempt to attract their capital.
Once these commit their capital, the advantages from increased
capital are reached. Suddenly it is no longer optimal to stick to
promise of reduced taxation.
The same also applies to issues of regulation, for example on
environmental issues.
Investors value the governments announcements on its future policy
when assessing the attractiveness of a country. But along with their
content, they focus on the credibility of these announcements.
The time inconsistency model
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In reality, the central bank’s temptation to surprise with a high level
of inflation may be less severe, (Blinder 1998).
But this may relate to the fact that most central banks already
operate under conditions that ameliorate our problem.
One such condition is that central banks operate repeatedly with
private agents and thus can establish a reputation of trustworthiness.
In order to better understand the resulting game, we must investigate
the impact of repeated play.
Current inflation is likely to impact on expected inflation in
subsequent periods. The short term gains from reduced
unemployment would then be seen against the long term losses from
increased expected inflation.
Repeated play and reputation
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A first theoretical conclusion is that this disciplining effect arises
only if there is no final period (or if private agents do not know when
there might be one).
Imagine such a final period (t=n). In this period the central bank will
minimize its costs because it does not care about future expectations.
This will be anticipated by private agents who expect ==D. We
obtain the simple discretionary solution in the final period.
Since the result for the last period is already fixed, the central bank
obtains no incentive to try to influence the last period‘s expectations.
Why then should it abstain from a surprise inflation in the penultimate
period (t=n–1)? Indeed, it will also act according to its reaction
function and minimize costs. Private agents will anticipate this again.
By backward induction we observe that the discretionary solution is
obtained in all periods.
Repeated play and reputation
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There are straightforward implications for the design of institutions:
Central banks and similar institutions should not be confronted with a
final period. This can be practically achieved by allowing continuity in
the pursuit of its obligations.
First, employment contracts with central bankers should last for a
long term.
Second, there should be overlapping time horizons for the central
bankers’ employment contract. This introduces the continuity
necessary for the central bank’s tasks and avoids end period
problems that would arise if a complete cohort of central bankers
leaves office.
If, indeed, end period problems are overcome, we can model the
central bank’s problem as one with an infinite time horizon.
Repeated play and reputation
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In case of an infinite time horizon the central bank‘s incentive to
cheat with *=0 is:
Cheating once induces private agents to disbelief in future
announcements of the central bank. They will expect *=D and the
central bank will act accordingly by setting =D. This future inflation
bias goes along with increasing costs:
These costs arise in the future. Their present value depends on the
degree to which central banks discount future costs (r) and the length
(s) by which private agents sanction the central bank‘s malfeasance by
disbelieving in its announcements.
Repeated play and reputation
2 2 2 21 1 .R TK K z z z
2 2 2 2(1 ) .D RK K z z z
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The central bank will stick to its promise of zero inflation if
This implies:
Apparently, this is achieved with and s being large and r being
small. If we assume the special case of s=1, private agents would
sanction the central bank only once and afterwards again believe in an
announcement of zero inflation. We obtain:
Repeated play and reputation
2 2 22 2
2 ... .1 1 1 1
s
z z zz
r r r
2
1 1 1 1... .
1 1 1 1sr r r
1 1.
1 1r
r
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With r being small, future losses are little discounted and thus larger.
This induces the central bank to avoid future sanctions by private
agents.
Suggestions have been made that this discount rate is lower for
independent central banks. Political actors can boost their chances of
being reelected by increasing employment during the electoral
campaign. Inflation would thus increase during electoral cycles – and
they are difficult to reduce afterwards. For politicians r is rather large
during elections. Independent central bankers would act less myopic.
With s being large, malfeasance is heavily sanctioned and thus
becomes unattractive. There are apparent conclusions of this finding
for the design of institutions. Environments with a good memory for
past misbehavior appear better in deterring malfeasance.
Repeated play and reputation
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The result for is paradox. Shouldn‘t a large preference for
employment increase the central bank‘s temptation to cheat? Indeed,
it does so but it also increases the future costs of malfeasance. This
impact on the future costs is even higher.
An employment preferring central banker is aware of the high future
costs of his malfeasance and more deterred to avoid cheating.
This is comparable to a self-help group of anonymous alcoholics.
Those engaging in such a group are well aware of the temptation to
drink. While the temptation is higher for them, they suffer heavier from
malfeasance. One drink alone is likely to put them back on the slope to
addiction. Rational behavior thus induces them to strictly avoid any
alcohol.
Repeated play and reputation
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The likelihood of drunk driving is thus lower for such an alcoholic.
Parents seeking someone to drive back their children after a party may
have good reason to entrust their offspring to such an alcoholic rather
than anyone else.
Our results, however, are valid only for a central banker who is aware
of the future sanctions that follow his malfeasance.
If a populist central banker disbelieves in the private agents
sanctions, he would not be deterred from surprise inflation. The
deterrence effect is thus restricted to central bankers who accept our
model.
Repeated play and reputation
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The model has been deterministic. In reality, shocks are likely to hit
the economy.
1. The central bank may stochastically err in setting the inflation rate.
It aims at a certain level but misses this level. For example, after
aiming at =D import prices drop suddenly or macroeconomic
demand declines and produce = As long as private agents observe
the shocks, the impact on the model are minor. We do not further
investigate this here.
2. Another type of shock relates to the supply side. These shocks are
problematic for the central bankers because they confront him with a
dilemma. Should he stick to his rigid rules or prefer some flexibility
that is responsive to the shock?
Stochastic Supply Shocks
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rr YY
rY
D
Y
r r= *+ Y -Y w
R
0 r r= + Y -Y w R
D
Stochastic Supply Shocks
C
A Negative Supply
Shock
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Should we worry about shocks? They might be good or bad!
Indeed, we should care about shocks: inflation and the output gap
enter the cost function with quadratic terms. Extreme deviations are
particularly bad. In case of a large shock, the desire to balance one
disutility with another may become stronger.
Imagine Ulysses and the Sirens again. His strict commitment helped
him survive. But what would have been the outcome if his ship sank?
His solution of tying himself to the mast would turn out to be dreadful
and he may have preferred to somewhat cope with the Sirens instead.
Stochastic Supply Shocks
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The game is played only once. A shock, w, is normally distributed
with expected mean E(w)=0 and variance V(w)=s2 . If w>0 inflation
rises. This is equal to saying that production drops.
The game is played according to the following sequence:
Stochastic Supply Shocks
)r r= *+(Y -Y w .r rY *+Y w
Private agents expect inflation.
Wages are negotiated
Central bank fixes inflation.
t
Nature determines shock
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If the central bank is strictly bound by a rule (=0), it cannot
recognize the shock‘s impact on production.
We obtain R =*=0 and
The variance of production is determined by:
Since we obtain
To see this, observe that and E(w)=0.
Stochastic Supply Shocks
.r rRY Y w
.2
r r rR R RV Y E Y E Y
r rRE Y Y
2.2r r r
RV Y E Y w Y s 2 ( )
2s E w E w
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For the costs we obtain:
For expected costs we obtain due to R=*=0:
Due to and E(w)=0
As compared to the deterministic model costs increased due to the
shock because situations of reduced production are particularly
painful (variations of production enter the costs function in squared
form).
Stochastic Supply Shocks
2 2( * ) .K w z
2 2( ).RE K z s
2 2 2( ) ( 2 ) .E K E w z E w wz z
2 2s E w
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In case of discretionary policy the central bank observes the shock,
w, prior to determining its policy. It will minimize:
A cost minimum requires:
The central bank sets inflation according to:
On average the following inflation rate can be expected:
Stochastic Supply Shocks
2 2( * ) .K w z
2 2 ( * ) 0.dK d w z
( * ).1
w z
( * ).1
E z
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Due to rational expectations private agents know this calculus of the
central bank. They cannot be systematically misled and expect
inflation equal to the mean inflation set by the central bank, *= E().
This implies:
Inserting this into the central bank’s calculus, we obtain:
Inflation in case of discretion is thus:
Stochastic Supply Shocks
* ( * ) * .1
E z z
2 2 ( ) 0
1 1 0.
dK d z w z
w z
.1D z w
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From this we can determine production. Due to -*=/(1+)·w:
Variance of production is:
This is smaller than s2. This reveals that the impact of shocks on
production is dampened in case of a discretionary policy.
Stochastic Supply Shocks
r rDY *+Y w
1.
1 1r r rDY w Y w Y w
1
1
22
r r r r rD D DV Y E Y E Y E Y w Y
2
2
1 1
1 1
2
E w s
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This advantage, however, comes at a cost: average inflation
increases due to an increased inflation bias.
Another downside effect is that variation of inflation has increased.
While it was zero in case of a rules-based policy, variation of inflation
now amounts to /(1+ )w.
Strict rules avoid the inflation bias. But they also disallow a more
flexible reaction towards supply shocks. Shocks would impact
completely on production, without any dampening reaction.
There is a trade off between credibility (rules) and flexibility
(discretion).
Which policy to prefer can be revealed by comparing expected costs.
Stochastic Supply Shocks
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In case of discretion we obtain:
Inserting yields:
Due to E(w)=0 we obtain:
Stochastic Supply Shocks
2 2( ) ( * ) .D D DE K E E w z
2 2
( )1 1DE K E z w E w w z
22 2 2
2( ) 21 1
DE K E z z w w
2 2
2 2 .11
w wz z
2 2 2 2( ) .1DE K z z s
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Comparing this to the costs of rules yields that discretion is
preferable if:
Simplifying this, we obtain:
Discretionary policy should be preferred in case of
a high variance of supply shocks, (s2 is large)
a low preference for employment ( is small),
a small difference between desired and potential production
(z is small).
Stochastic Supply Shocks
2 2 2 2 2 2.1
z z s z s
2 2 2 2 211 .
1z s s z s
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As we observed, rules are preferable with respect to containing
inflation.
Discretion is preferable with respect to stabilizing production.
Is there some optimal policy in between these two extreme cases?
In research four different variants have been discussed:
1. A flexible rule
2. Incentive contracts for central bankers
3. A moderately conservative central banker
4. Rules with exceptions
Optimal Design of Central Bank Policy
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1. A flexible rules for the central bank would be:
a is the long-term desired value for inflation.
b is the central bank‘s flexible reaction towards shocks (w > 0).
Both parameters can be determined so as to minimize costs.
We assume that the flexible rule is binding and announced upfront.
Apparently, we then obtain *=a.
Inserting this and the flexible rule into the cost function, it follows:
Optimal Design of Central Bank Policy
, 0, 0FR a bw a b
2 2( ) ( )E K E a bw bw w z 2 2 2 2 2 2( 1) .E a b w b w z
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Partial differentiation yields:
The optimal flexible rule is thus:
This allows to achieve long-term price stability. At short sight,
deviation from price stability are allowed so as to dampen supply
shocks. Production would be equal to the discretionary value:
With inflation being zero on average, total costs are lower than in
both previous solutions: strict rules or strict discretion.
Optimal Design of Central Bank Policy
.1FR w
( )2 0 0.
E Ka a
a
2 2( )
2 2 ( 1) 0 .1
E Kbs b s b
b
1.
1r rFRY Y w
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Such a solution, however, faces practical problems: How should
private agents distinguish between a central bank that cheats and one
that reacts to a shock? Maybe it cannot! How can the central bank
commit to such a flexible rule, if nobody can observe its adherence to
the rule?
One attempt could be that the central bank upfront identifies various
observable shocks and determines its quantitative reaction to these
shocks. But supply shocks may range from natural catastrophes, oil
price shocks, sudden technological innovations to warfare.
Determining upfront how to react to such crises is not an easy task.
Apart from that, determination of the output gap may contain a high
degree of discretion. Whether a drop in production is due to a
shortage in demand or a decrease in supply is commonly disputed.
A central bank may use its discretion to cheat and private agents
may therefore disbelieve in its announcements.
Optimal Design of Central Bank Policy
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2. An optimal solution can also be achieved by providing incentives to
central bankers. A government that seeks to approach the optimal
solution would confront a central banker with a penalty in case of
excessive inflation.
Assume this penalty to be Kp=2z. The cost function of the central
bankers is then modified to:
A cost minimum requires:
This simplifies to:
Taking expectations on both sides, we observe that and
Optimal Design of Central Bank Policy
2 2( * ) 2 .K w z z
2 2 ( * ) 2 0.dK d w z z
* 0 1 ( * ) 0.w
1 .w
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The solution thus equals that of the flexible rule. The impact of
shocks on production are dampened and inflation is allowed to vary.
The advantage of this solution is that private agents do not have to
verify the magnitude of a shock. Even if the magnitude of a shock is
known only to central bank, the central bank does not obtain an
incentive to cheat.
A disadvantage is that central bankers commonly earn less than
private bankers. Punishing central bankers would not be feasible, as
they prefer to quit. Another problem is that the contract would be
exercised by the government. But the government faces the same (or
in case of a forthcoming election even a larger) incentive to cheat.
Why should a government punish a central banker for an action that it
considers to be optimal? Due to these incentives the government may
fail in committing the exercising of such a contract.
Optimal Design of Central Bank Policy
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3. Another option arises be employing a central banker who is known
to be moderately conservative.
This central banker should have a nonzero preference for
employment (k>0).
The central banker’s preference should be lower than that of the
government (k<).
This allows for a cost-minimizing mixture of the two disutilities,
inflation and unemployment. A small inflation bias is accepted, while
the impact of the shock on output is a little dampened.
Optimal Design of Central Bank Policy
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4. A final solution arises with a simple rule plus an escape clause. In
case of a large shock the central bank would obtain the chance to shift
to a discretionary policy, (Lohmann 1992).
This policy can be represented by the following curve:
Optimal Design of Central Bank Policy
w
* (1 ) w
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Private agents determine expected inflation by multiplying the
regular inflation bias with the likelihood that the escape clause is
applied (*>0). In normal times, the central bank sticks to =0 and
produces a little unemployment. The larger the horizontal part of the
reaction curve (rule) the lower will be expected inflation, *, and thus
the intercept of the upward sloping part of the curve.
Who should verify the size of the shock? Rather than letting the
central bank try to prove its size it (and provide it with an incentive to
cheat) one may require high efforts among the central bank for using
the escape clause.
One simple idea would be to require a parliamentary approval for
using the escape clause. It would not be the parliament‘s expertise
that makes the difference, but rather the central bank‘s effort required
for convincing parliament (and its unhappiness with delegating
authority to someone else).
Optimal Design of Central Bank Policy
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The central bank’s cost function is:
The supply function is:
with K being costs in the central bank’s calculus, being inflation, *
expected inflation, Yr production, 16 the desired level for production
and 10 potential domestic production.
a) Determine the costs if private agents believe in the central banks
announcement of and the central bank sticks to its announcement
(rule).
b) Contrary to a) the central bank minimizes its cost function after
observing *=0 (cheat). Determine the rate of inflation and the central
bank‘s costs.
2 2 0.5 ( 16) .rK Y
* ( 10)rY
Exercise
ADI 2008/09
c) Private agents observe the central bank’s incentive to cheat and
adjust upward their expectation of inflation to a rational level
(discretion). Determine this level of inflation and the central bank’s
costs.
d) Use your findings from a)-c) to explain what is meant by “time
inconsistency”.
e) A new government has a higher preference for employment
according to The government
considers firing the old central bankers and employ bankers with
preferences equal to those of the government. Determine the new
discretionary solution. Is the firing of the old central banker’s a
good idea?
Exercise
2 2 2 ( 16) .rK Y
ADI 2008/09
The central bank’s cost function is:
The supply function is:
with K being costs in the central bank’s calculus, being inflation, *
expected inflation, Yr production, 10 the desired level for production
and 6 potential domestic production. The shock, w, is normally
distributed with mean E(w)=0 and variance V(w)=s2. Private agents
form expectations for levels of inflation first, nature determines w and
finally the central bank determines the level of inflation.
a) Determine the expected costs if private agents believe in the central
banks announcement of =0 and the central bank sticks to its
announcement (rule).
2 23 ( 24) .
2rK Y
* ( 16)rY w
Exercise
ADI 2008/09
b) Determine the discretionary solution where announcements lack
credibility, the central bank minimizes costs and private agents
rationally anticipate the equilibrium level of inflation. Determine the
central bank‘s expected costs.
c) Compare your findings in b) to those in a). Would you recommend a
strict rule if variance obtains alternative values of s2=100, 200 or 300?
d) The government finds a central banker with an employment
preference =1/2. Assuming s2=100, would it make sense to employ
this central banker?
e) The government penalizes a central bank for excessive inflation.
What level of penalty would you recommend so that price stability
results in the discretionary solution?
Exercise