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?