Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 22: Credibility in economic policy: Rules vs
Discretion
Lecture Outline:
- Credibility and time inconsistency of monetary policy;
Essential reading:
Mankiw: Ch
...
2
Credibility and Dynamic Inconsistency of Optimal Rules
Here we consider the issue of credibility in monetary policy when there are rational
expectations
...
We
model those ideas using the concept of a game played between the policy maker and
the agents
...
The idea can be expressed using this example taken from
Kydland and Prescott (1977)
...
If agents believe that the government will indeed do that policy, then they have
an incentive of invest in more capital and so more capital will be installed in the
economy at the beginning of next year
...
Governments prefer high revenue (more taxes) to less revenue, and when
capital is installed agents cannot change the capital level in a short period of time
...
The important thing here is that when Rational Expectations are taken into
account policy announcements may not have effects simply because agents do not
believe that the announcement is credible
...
If this contract is enforceable then this commitment may make the
announcement of the government credible and the policy once implemented can have
real effects
...

Consider the following version of the Lucas’ aggregate supply in log form:

y = y + α (π − π e ) + ε

1)

where α > 0 and ε is an aggregate supply shock with the property that E (ε ) = 0
...
This is like a
Phillips curve where we used the Okun’s Law to replace unemployment with real
GDP
...

The policy maker is assumed to MINIMISE a social loss function given by:
Ω =

1
β
( y − y*)2 + π
2
2

2

2)

This function says that the policy maker cares about two things: the deviation of real
output from a target y * and inflation (we can assume that the target for inflation is

π * = 0 )
...

When β = 0 the policy maker doe not care about inflation but only about real output,
therefore in order to reach the target of real output is willing to accept any inflation
level
...
This means that negative
deviations from a target have the same weight as positive deviations
...
This means that the target of the policy maker
in terms of real output is greater than the natural level
...
The policy maker can see the shock while
agents must take decisions before the shock is revealed
...


2

Furthermore, this implies that the agents use the model to form their expectations
...
We call
this case the DISCRETIONARY POLICY case because the policy maker chooses the
level of output as it pleases
...
The Lagrangean of this problem is:

Min
π
,y

1
β
L = ( y − y* ) + π 2 + λ y − y − α π − π e − ε
2
2

(

(

) )

where λ is the Lagrange multiplier
...

y* −

β
π = y + α (π − π e ) + ε
α

Solving that expression for the inflation rate:

α 2π e + α ( y * − y − ε )
πD =
α2 +β
This expression tells you that inflation is high when:
i)

Expected inflation in high;

3

3)

ii)

The target in terms of real output y * is high;

iii)

There is a negative supply shock: ε < 0 ;

However, now we need to find the expected inflation
...
Under discretion, they
know that inflation is given by 3)
...
Therefore, equation 3) can be written as:

π De =

α 2π e D + α ( y * − y )
α2 +β

e
where we used the fact that E (ε ) = 0
...
Assume for
simplicity that ε = 0 and define that values of the loss function as: Ω D
...

2) Policy Rule: the policy maker announces that it will take inflation to zero
...
Then the agents will set π e = 0 , the policy is implemented, so the

4

chosen inflation rate is indeed π R = 0 (where the subscript R means the inflation rate
chosen under this policy rule)
...

So the problem seems fairly simple: policy makers should stick to some policy rules
and avoid discretionary policies
...
By that we mean that the policy maker has an incentive over time
to repudiate the announcement and to cheat about the policy chosen
...
Suppose people
believe in the announcement so they form their expectations accordingly
...

Suppose that the announcement is believed by the public and so their expectations are

πe =0
...

From the aggregate supply, the level of output is:

yC =

β
α +β
2

y+

α2
α +β
2

y* +

β
α +β
2

ε

Putting those values into the original loss function, and assuming

ε = 0 for

simplicity, we obtain:

ΩC =

1 β
( y − y* ) 2
2 α2 + β

Notice that this policy has effects ONLY IF the agents believe in the policy
announcement
...
Therefore, this cheating policy will not have effects
...
This fact makes the rule
announced NOT CREDIBLE
...
If we introduce the idea that the game is played over time, then the policy
maker can build some reputation
...
This makes the agents to believe that the
policy maker is credible and that it will implement what is announced
...
In
this case policy rules can be time consistent
...
The problem of time inconsistency
in our example arises because the policy maker wants to boost the level of real
income
...
By
making the central bank independent from the government it is less likely that the
central bank will boost the economy to please the government
...
Another way to increase
this independence is to appoint a Central Banker for a very long time, possibly for his
entire life (obviously he can always resign)
...
This makes less likely for
a central banker to please a particular government for example by using monetary
policy to boost output
...


6

As you can see in countries where the central bank is less independent from the
government the annual inflation rate tends to be higher than in countries where the
Central bank is more independent
...
This implies that in his loss function the weight given to real output is
particularly small compared to the weight given to inflation
...


Examples of Monetary Policy Rules
a) Constant money supply growth rate
This is a rule advocated by monetarists
...
From the quantity theory of money we know that if velocity is constant we
have:

π=

∆M ∆Y
−
or written differently:
M
Y

7

∆Y ∆M
=
−π
Y
M
If the growth rate of money supply is constant so it will be inflation and so it should
the growth rate of output
...

This is what monetary policy can do in the IS-LM model
...
Vice versa if output increases
...

Many countries’ central banks now practice inflation targeting, but allow themselves a
little discretion
...
5 (π – 2) – 0
...

For each one-point increase in π, monetary policy is automatically tightened to raise
the interest rate by 1
...
For each one percentage point that GDP falls below its natural
rate, monetary policy automatically eases to reduce the interest rate by 0
...


8



---