Lecture 8
Central Banks - The Issue of
Credibility and Reputation
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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 Game
G
d
nd
End
P
s
ns
G
d
s
G
nd d
nd
P
P
ns 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
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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
V x2 V

0
x2  2  2
Rational expectations and
time inconsistency
V  V ( x1 , x2 ,  1 ,  2 )
x1  f1 ( 1 ,  2 )
x2  f 2 ( x1 ,  1 ,  2 )
Optimising in period 1 for
period 2
V  x2 x2 x1  V x1 V

0
 

x2   2 x1  2  x1  2  2
But optimising in period 2
for period 2
V x2 V

0
x2  2  2
Inflation - Unemployment
illustration

A
C
B
U
Barro and Gordon

a 2
e
z     b   
2



zt 1
zt  2
zt  3
Z  E  zt 


 ... 
2
3
(1  r ) (1  r ) (1  r )


Three types of policies
• Discretionary policy - Nash
• Policy rule
• Cheating policy
Discretionary policy
z
2 a

b  0

2
b
 
 ˆ
a
2
1b
ˆ  
z
2 a
Policy rule
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•
•
•
•
Ex-ante optimal policy
time inconsistent
but if CB can pre-commit  = e
 = 0 = *
cost z = 0 = z*
Cheating policy
b
~
  
a
2
1b
~
z  

2 a




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
T  E ( z * ~z )
2

 a
 a  b 
 b 
T  
 b(0)      b   
 a 
 2
  2  2 
2
ab 
T     
2a 
2
Cost of cheating
1
c 
E zˆt 1  z *t 1 
1 r
2


1 a b
2
c 
      
1  r  2   a 

Costs and benefits of
commitment
b2/2a
Best enforceable rule
b2/2a(1+r)
rb/a(2+r)
Ideal
rule
0
b/a
Enforceable range

Minimum cost rule
b r 
*  

a  2r 
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