Lecture 17 1
Macroeconomic Analysis 2003
Monetary Policy:
Inflation Targeting
Interest Determination
Policy Loss FunctionMankiw ( 18 ) Blanchard (27 ) Miles and Scott (12 )
Lecture 17 2
Learning Objectives
• Inflation Targeting: Rule or Discretion?
• Taylor Rule for Interest Determination
• Inflation Bias of the Government
• Central Bank Independence
• Loss Function for Policy Analysis
Lecture 17 3
Policy Rule vs. Optimal Discretion for Inflation TargetingObjective of a policy maker is to minimise loss function Subject to the aggregate supply constraint.
2*
ayybSMin (1)
Subject to
Ecyy * (2)
where y is actual output y* is the natural level of output
and *yy is the output gap and is the actual inflation rate. Aggregate Supply: Output responds to higher level of inflation Using the value of *yy from the constraint in the objective function
2
aEbcSMin (3)
Lecture 17 4
2
aEbcSMin (3)
Let inflationary expectation of people, E to be a constant. Policy maker have two choices: (1) to stick to a policy rule (2) to use optimal discretion
If they stick to policy rule E ; *yy
2 aS ; 02
aS
Optimal Inflation in the policy rule: 0
Optimal Inflation Under the Policy Rule
Lecture 17 5
2
aEbcSMin (3)
Policy makers choose the inflation rate to minimise the loss function (3).
First order condition of (3) wrt
02
abcS
=> a
bc
2
Conclusion: Inflation rate under discretion is higher than the inflation under the policy rule. This is the main reason for the central bank independence.
Optimal Inflation Under the Discretion
Lecture 17 6
*11
*ti
tidtyty 0d (9)
where ty is actual output *ty is trend output, ti is the actual
interest rate and *ti the basic interest rate,
One period lag is assumed between the interest rate decision and the change in the output.
*11
*ty
tyctt 0c (10)
where t and *t are actual and target inflation rates.
Interest rate rule:
***ttbtytyatiti 0a ; 0b (11)
Interest Determination Rule to Achieve the Inflation Target: Taylor Rule
Lecture 17 7
Reduced Form Equation of the Interest Determination Model
*11
*ti
tidtyty
*11
*ty
tyctt
***ttbtytyatiti 0a ; 0b
(11)
Substituting the output and inflation equations in the interest
rate rule:
*
22*
11*
ti
ticdb
ti
tidatiti
*22
*11
*titibcdtitiadtiti
*2
*1
*21 tbcditadititbcditaditi (12)
Lecture 17 8
Interest Rule: A Numerical ExampleTarget inflation 2.50%
Target interest rate (basic) 5.00%
Initial interest rate 11.00%
Initial output gap 2.00%
Initial inflation 2.00%
a 0.5
b 0.5
c 0.25
d -0.5
ad-square ==> 0.0625
(ad)square >4bcd for stability
4bcd ==> -0.25
Years Output gap Inflation gap
Actual interest rate
1996 0.02000 -0.00500 0.11000
1997 -0.03000 0.00500 0.06250
1998 -0.00625 -0.00750 0.06813
1999 -0.00906 -0.00156 0.06969
2000 -0.00984 -0.00227 0.06895
2001 -0.00947 -0.00246 0.06903
2002 -0.00952 -0.00237 0.06906
2003 -0.00953 -0.00238 0.06905
2004 -0.00952 -0.00238 0.06905
Lecture 17 9
Interest Rate Rule
-0.04000-0.02000
0.000000.02000
0.040000.06000
0.080000.10000
0.12000
Perce
nt
Output gap
Infaltion gap
Actual interest rate
Lecture 17 10
Why Should the Central Bank Be Independent?Inflation Biases of a Government and a Central Bank
Figure 1
G
Preference of government and a conservative central bank regarding inflation and output AS Preference of Government (GP)Inflation A
AS1
B Preference of a CB (CP)
O Yn Output
Lecture 17 11
Inflationary Bias Model-Loss Functions of a Government and a CB and Supply Constraint
G o v e r n m e n t s o b j e c t i v e f u n c t i o n :
t
Min
2*
22
21
tytybt
GL ( 1 )
C e n t r a l b a n k s ’ o b j e c t i v e f u n c t i o n :
t
Min
2*
22
21
tytybt
CBL ( 2 )
A g g r e g a t e s u p p l y C o n s t r a i n t s :
tuettty
( 3 )
Lecture 17 12
Inflation Bias of the Government
2*
22
21
tytu
ett
bt
GL
0*
tytuettbt
t
GL
tubb
tybb
t
1*
1
Lecture 17 13
Inflation Bias of the Central Bank
2*
22
21
tytu
ett
bt
CBL
*1 tytu
ettbt
t
CBL
tubb
tybb
t
1*
1
H ere is the in fla tion aversion fac to r. S ince 0 thecen tra l bank w ou ld choose low er ra te o f in fla tion thanthe governm en t.
Lecture 17 14
Inflation Bias When the Central Bank is under the Spell or when it is Completely Independent
2*
22
211
2*
22
21
tytuett
bttytue
ttb
ttM
2*
21
22
21
21
tytuett
bbttM
2*
22
21
tytuett
bttM
0*1
tytuettbt
ttM
tub
bty
bb
t
1*
1
Lecture 17 15
Lessons for Price Stability From Analysis of the Central Bank Independence
1. Bind the central bank with a zero inflation rate target.
2. Appoint the most conservative central banker.
3. Make the central bank as independent as possible fromthe government.
4. Peg the exchange rate to the currency of a country withone or more of the above characteristics.
Lecture 17 16
Exercises• Target inflation under the policy rule
• Target inflation under the discretion
• Interest rate determination rule
• Examples from the interest determination
• Inflation bias of the government
• Should the Central Bank be Independent?
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