Lecture 8

Central Banks - The Issue of Credibility and Reputation

• This lecture addresses two issues:• Credibility• The distinction between rules and discretion• a) credible commitments• b) rules can be learned by private agents, discretion

cannot

Lucas v Tinbergen

• Tinbergen paradigm - discretionary policy can be used to meet set objectives.

• If there are ‘n’ targets we need ‘n’ independent instruments to satisfy targets

• Lucas critique - very act of discretion undermines its effectiveness

• A modest policy of rules would be more effective

The Leader - Follower paradigm

• Lucas approach treats the economy as a collection of optimising agents

• But the government is also an optimising agent

• The government can be treated as a leader

• private agents are followers

• Leader-follower game (Stackelberg)

Illustration of leader - follower game

• At each date a speculator can raise domestic currency which is sold for foreign currency.

• He pays a fixed charge of ‘c’ per transaction• Assume that there is a limit to which the

speculator can sell in each period - transactions or liquidation costs

• If a devaluation occurs the benefit is ‘π’ per unit of domestic currency

leader - follower continued

• If a devaluation occurs - profit is π - ct; t=1,2,.. and ct is the opportunity cost

• Government has reserves of $R

• It is forced to devalue when it runs out of reserves

Assumptions

• For a given level of reserves, the government prefers maintaining the exchange rate to devaluation

• For a given exchange rate it prefers more reserves to less

• 2 < $R < 3

• π/2 < c < π

Stackelberg GameGd nd

End P

s ns

GG

d nd d nd

P

sns

P

s ns

Possible equilibrium

• Speculators will sell until the government decides to devalue

• Thus the government devalues immediately• delaying devaluation can occur only until t=3 • But suppose government can pre-commit not

to devalue until all reserves are gone• devaluation does not occur

Conclusions

• Solution concepts matter. Nash, Stackelberg, perfect equilibrium etc.

• Even if it is accepted that the government is a leader, the inability to make self binding commitments may reduce the leaders power

• without binding commitments there may be more than one solution.

Time consistency

• Objective function V=V(x1,x2, 1, 2)

• xs are targets and s are instruments

• x1=f1(1)

• x2=f2(x1, 2, 1)

• In period 1 maximise w.r.t. 1

• In period 1 maximise w.r.t. 2

• In period 2 maximise w.r.t. 2 same as period 1

Period 2 optimisation in time consistent case

022

2

2

Vx

x

V

Rational expectations and time inconsistency

),,(

),(

),,,(

21122

2111

2121

xfx

fx

xxVV

Optimising in period 1 for period 2

022

1

12

1

1

2

2

2

2

Vx

x

Vx

x

xx

x

V

But optimising in period 2 for period 2

022

2

2

Vx

x

V

Inflation - Unemployment illustration

U

A

BC

Barro and Gordon

...)1()1()1(

2

33

221

2

r

z

r

z

r

zzEZ

ba

z

tttt

e

Three types of policies

• Discretionary policy - Nash

• Policy rule

• Cheating policy

Discretionary policy

a

bz

a

b

baz

2

2

1ˆ

ˆ

02

2

Policy rule

• Ex-ante optimal policy

• time inconsistent

• but if CB can pre-commit = e

= 0 = *

• cost z = 0 = z*

Cheating policy

a

bz

a

b

2

2

1~

~

Ranking of policies

• Cheating is first best

• policy rule is second best

• discretion is third best

Enforcement rules

• Credibility enhancing t-1 = et-1

• distrust and Nash enforcing t-1 et-1

• Thus the gain from cheating (reneging) must be judged against the costs of loss of reputation

Temptation to cheat

2

22

2

22)0(

2

)~*(

a

ba

a

bb

bab

a

zzE

T

T

T

Cost of cheating

22

11

21

1

*ˆ1

1

a

ba

r

zzEr

c

ttc

Costs and benefits of commitment

b2/2a

b2/2a(1+r)

Enforceable range

Best enforceable rule

0

Ideal rule

b/a

rb/a(2+r)

Minimum cost rule

r

r

a

b

2*

Insights

• The most important insight is that a superior policy to Nash is enforceable when reputation is a criterion

• A policy is only credible if people can see that the costs of cheating is greater than the benefits

• The most limiting aspect of the study is that reputation effects last only for 1 period

Backus and Driffil

• Modification of Barro-Gordon result with introduction of asymmetric information

• Agents are unaware of CB or governments cost function parameters

• Let e = {0,1}• weak government inflates - plays =1• strong government is sound money - plays

=0

Information asymmetry

• Private sector assigns a probability pt each period that the government is strong

• pt is revised periodically

• First, government avoids inflating = e=0

• Government still plays =0 but private sector assigns >0

• At some point the government plays =1

Conclusion

• Contrary to Barro-Gordon there will exist a period during which a zero inflation policy is credible because it pays even a weak government to build up a stock of good reputation.

Insights

• Two-sided uncertainty leads to Stackelberg warfare

• Strong private sector may induce a stronger government to be tougher than necessary to convince them that they are strong

• Even a strong government may abandon =0 if costs of disinflation are large