Lecture 8 Rules versus Discretion

Lecture 8

Rules versus Discretion

Prof. Dr. Johann Graf Lambsdorff

Anticorruption and the Design of Institutions 2012/13

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Barro, R. and D. Gordon (1983), A Positive Theory of Monetary Policy in a Natural Rate Model, The Journal of Political Economy, Vol. 91 (4): 589-610.

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 and 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. The reason for this apparent paradox is that economic planning is not a game against nature but, rather, a game against rational economic agents.”

They state that the social welfare function is not maximized by determining the optimal use of instruments in a given economic situation. 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 p: being the rate of inflation; p*: expected rate of inflation (which is formed in the previous period for the current period); : 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:

,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, employers’ profits increase. This induces firms to increase production.


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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 from 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?


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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.


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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.


http://www.uni-goettingen.de/de/document/download/563cc22ac1e3bda7badb238afb144aef.pdf/discuss_16.pdf



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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 l, its employment preference:

We call central bankers with a small l “conservative”. Those with a large l 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:


22 ˆ .rK Y Y l

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 would 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.


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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.


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


22 * .K z l

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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:


r rRY Y

2.RK zl

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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:


2 2 * 0.dK d z l

2 2 0.dK d z l

0.1C zl

l

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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:


* .1

r r rC CY Y z Yl

l

2 22

1 1 1CK z z z zl l lll l l

2 2.1C RK z K zl l

l

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RK

rr YY

rY

*

CK

*

C


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.


2 2 * 0.dK d z l

1 * .z l l

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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, l, and the more desired production exceeds potential production, z.

Due to * production equals its potential level, .


1 * .Dz z zl l l l

r rDY Y

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RK

rr YY

rY

*

CK

D

DK

*

D

C

(1 ) ( * )z l l


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”:


2 21 .D RK z K zl l l

.1D Cz zl l

l

2 2 21 .DK z z zl l l l

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.


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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 ones 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.


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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.


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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.


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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.


2 2 2 21 1 .R CK K z z zl l l l l

2 2 2 2(1 ) .D RK K z z zl l l l

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The central bank will stick to its promise of zero inflation if

This implies:

Apparently, this is achieved with l 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:


2 2 22 2

2 ... .1 1 1 1 s

z z zzr r r

l l lll

2

1 1 1 1... .1 1 1 1 sr r rl

1 1 .1 1

rr

ll

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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.


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The result for l 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.


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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.


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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 =0. 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


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.


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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:


)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.


.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).


2 2( * ) .K w z l

2 2( ).RE K z sl

2 2 2( ) ( 2 ) .E K E w z E w wz zl l

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:


2 2( * ) .K w z l

2 2 ( * ) 0.dK d w z l

( * ).1

w zl l

( * ).1

E zl l

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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:


* ( * ) * .1

E z zl ll

2 2 ( ) 0

1 1 0.dK d z w z

w z l l

l l l l

.1D z wl l

l

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From this we can determine production. Due to -*=l/(1+l)·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.


r rDY *+Y w

1 .1 1

r r rDY w Y w Y wl

l l

11

22

r r r r rD D DV Y E Y E Y E Y w Y

l

2

2

1 11 1

2

E w sl l

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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 l/(1+ l).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.


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In case of discretion we obtain:

Inserting yields:

Due to E(w)=0 we obtain:


2 2( ) ( * ) .D D DE K E E w z l

2 2

( )1 1DE K E z w E w w zl ll l

l l

22 2 2

2( ) 21 1

DE K E z z w wl ll ll l

2 2

2 2 .11

w wz zl l lll

2 2 2 2( ) .1DE K z z sll l

l

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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 (l is small),

a small difference between desired and potential production (z is small).


2 2 2 2 2 2.1

z z s z sll l l ll

2 2 2 2 21 1 .1

z s s z sl ll

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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 rule 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:


, 0, 0FR a bw a b

2 2( ) ( )E K E a bw bw w zl 2 2 2 2 2 2( 1) .E a b w b w zl l

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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.


.1FR wl

l

( ) 2 0 0.E K a aa

2 2( ) 2 2 ( 1) 0 .

1E K bs b s bb

lll

1 .1

r rFRY Y w

l

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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.


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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=2lz. 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


2 2( * ) 2 .K w z z l l

2 2 ( * ) 2 0.dK d w z z l l

* 0 1 ( * ) 0.wl l

1 .w l l

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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 the 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 to exercising such a contract.


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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 (lk>0).

The central banker’s preference should be lower than that of the government (lk<l).

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.


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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, AER 1992).

This policy can be represented by the following curve:


w

* (1 ) w l l

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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 (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).


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Different Rules - Overview


w

Discretion

Flexible Rule

Rule

Conservative Central Banker

Rule with Exception

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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 0 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

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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 its own. Determine the new solutions in case of rule, cheating and discretion. Is the firing of the old central bankers a good idea?

Exercise

2 2 2 ( 16) .rK Y

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f) Determine the costs and benefits of temptation in case of infinite repeated play!

g) What is the discount rate that guarantees price stability? Assume that private agents sanction the central bank for one period (s=1)?

h) If s→∞, and r=1.5, will price stability result if l=0.2 or l=0.8? Interpret your results.

i) The parameter l obtains the value 2/3. How many periods of sanctioning, s, are required to induce price stability if r=1.5.

Exercise

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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, 24 the desired level for production and 16 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) .2

rK Y

* ( 16)rY w

Exercise

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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 l=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

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Lecture 8 Rules versus Discretion