Macroeconomic Themes:19 1

Interest Rate Determination Rule: Test of the Taylor Rule in the UK

November 2002

Macroeconomic Themes:19 2

Background Literature

General Literature on Role of Money in the Economy

Keynes (1936), Hicks (1937), Bailey(1956) Phillips (1958), Friedman(1968), Phelps (1968),Tobin (1969)) Taylor (1972). Taylor (1993), Laidlerand Parkin (1975) Kydland and Prescott (1977), Phelps and Taylor (1977)Aghevli (1977), Gordon (1983), Barro and Gordon (1983), Sargent (1986)Goodhart (1989), Nickell (1990), Buiter and Patel (1992), Ball and Romer(1990) Dornbusch (1992), MPC (1999), Lockwood Miller and Zhang(1998), MPC (1999).

Natural Rate of Unemployment Hypothesis

Friedman (1968), Phelps (1968)

Macroeconomic Themes:19 3

Research in Time Inconsistency, Policy Co-ordination and Time inconsistency

Kydland and Prescott (1977), Phelps and Taylor (1977),Gordon (1983), Barro and Gordon (1983)Lockwood Miller and Zhang (1998), Rogoff (1985), Millerand Salmon (1985)),

Policy Co-ordination at National and InternationalLevel

Krugman (1979), Barro and Gordon (1983), Canzoneri M.B. and J A Gray (1985), Cukierman (1994), Goodhart(1994), Nardhaus (1994) Eijffinger SCW and J.D. Haan(2000)

Money in General Equilibrium

Tobin (1969) Altig D E, C.T. Carlstrom and K.L. Lansing(1995), Lockwood Miller and Zhang (1998), Holly andWeale (2000), Corsetti and Pesenti (2001), Benigno(2002)

Macroeconomic Themes:19 4

Friedman (1966, 1968) and Phelps (1967) natural rate of unemployment hypothesis

etNutut

w h e r e 0 ( 2 )

w h e r e t i s t h e a c t u a l i n f l a t i o n , et i s t h e e x p e c t e d i n f l a t i o n Nu i s

t h e n a t u r a l r a t e o f u n e m p l o y m e n t t h a t i s g r o u n d o u t b y t h eW a l r a s i a n s y s t e m o f t h e g e n e r a l e q u i l i b r i u m , a n d tu i s t h e a c t u a l

u n e m p l o y m e n t r a t e .

S i n c e

Nutuett a n d 0 t h e i n v e r s e r e l a t i o n

b e t w e e n u n e m p l o y m e n t a n d i n f l a t i o n i m p l i e s

*

*

*

yty

yty

yty

Nutuett

Nutuett

Nutuett

( 3 )

Macroeconomic Themes:19 5

Aggregate Supply and Demands

A g g r e g a t e S u p p l y tNtY i n l o g s tnty ( 6 )

L a b o u r d e m a n d : tptw

tNtNtY

1 t a k i n g l o g i t c a n b e

w r i t t e n a s

tnln1ααlntptw ( 7 )

A g g r e g a t e D e m a n d : tYtktP

tM w h e r e tk i s a m o n e t a r y p o l i c y

p a r a m e t e r tetk

w h e r e t i s a r a n d o m v a r i a b l e . N o w t a k i n g

l o g o f t h i s d e m a n d tyktptm

ln o r

tyttptm ( 8 )

Macroeconomic Themes:19 6

Labour Market Equilibrium and Aggregate Supply

S o l v e ( 4 ) f o r t h e w a g e r a t e tw a n d s u b s t i t u t e t h e r e s u l t f o r

t h e tw t e r m i n ( 2 ) .

tptEstntw *

11

tntptptEs

tn 1ln*1

1

ln*111

tptEtptn l e t

11

ln*

11

tptEtptn a n d

ln*

1 tptEtpty

( 1 1 )

Macroeconomic Themes:19 7

ln1 *

1

tttt pEpn ( 7 )

a n d o u tp u t

ln*1

tttt pEpy (8 )

D 0 D 1

A S :

ln*1

tttt pEpy

cP r ic e ttt pEp *

1 D 2 b a

ttt pEp *1

d A D : tttt pmy

ttt pEp *1 f

*yy t

ln*

y *yy t

O u tp u t

Impact of Monetary Policy in the Short and the Long Run

Macroeconomic Themes:19 8

Policy Rule, Discretion, Cheating and Time Inconsistency in Economic Policy Making

yy

1 :

L u c a s s u p p l y f u n c t i o n

D

C

R B y – y *

O p t i m a l i n f l a t i o n l i n e

*yy

I s o - c o s t c i r c l e s : 22*

22

1

yy

F o u r e q u i l i b r i u m p o i n t s

B : A b l i s s p o i n t i s w h e r e a c t u a l o u t p u t e q u a l s i t t a r g e t , *yy , a n d n o

i n f l a t i o n 0 . D : o p t i m a l d i s c r e t i o n w h e r e d e v i a t i o n o f o u t p u t i s z e r oR : R a t i o n a l e x p e c t a t i o n w i t h z e r o i n f l a t i o n a r y e x p e c t a t i o nC : C h e a t i n g p o i n t f o r t h e g o v e r n m e n t

Macroeconomic Themes:19 9

Fiscal and Monetary Policy Game in a Diagram

This model can be illustrated by means of the above diagram.

Policy Co-ordination between Monetary and Fiscal Authorities (Nardhaus (1994) Model)

MBudget Surplus, S

Fiscal Policy MB: monetary bliss

o F Interest rate, monetary policy

Budget Deficit FB

Nash

M FIndifference curve of fiscal authority

Indifference curve of monetary authority

Macroeconomic Themes:19 10

*

11*

ti

tidtyty 0d ( 9 )

w h e r e ti a n d *ti a r e a c t u a l a n d n a t u r a l l e v e l o f o u t p u t , ti i s

t h e a c t u a l r a t e o f i n t e r e s t i n p e r i o d t , i i s t h e i n t e r e s t t a r g e to f t h e m o n e t a r y a u t h o r i t y .

O n e p e r i o d l a g i s a s s u m e d b e t w e e n t h e i n t e r e s t r a t ed e c i s i o n a n d t h e c h a n g e i n t h e o u t p u t .

*

11*

ty

tyctt 0c ( 1 0 )

w h e r e t a n d *t a r e a c t u a l a n d t a r g e t i n f l a t i o n r a t e s .

***ttbtytyatiti 0a ; 0b ( 1 1 )

Three Equations of the Interest Determination Rule: Taylor Rule

Macroeconomic Themes:19 11

Reduced Form Equation of the Interest Determination Model

*22

*11

*titibcdtitiadtiti

*2

*1

*21 tbcditadititbcditaditi ( 1 2 )

*2

*1

*0 tbcditaditi , a n d ad1 a n d bcd2 .

R e d u c e d f o r m : 02211 tititi ( 1 3 )

S t e a d y S t a t e : ntitititi ...21 :

Macroeconomic Themes:19 12

Natural rate of Interest: Steady State

Natural Rate of Interest: 211

*2

*1

*

tbcditaditii ;

bcdadtbcditaditii

1

*2

*1

*with flexible targets and

bcdadtbcditaditii

1

***with fixed targets (14)

Macroeconomic Themes:19 13

General Solution of the Interest Rule Model

22

4211

1

t a n d

22

4211

2

t .

itAtAti 2211

( 1 6 )

i

t

A

t

Ati

2242

1122

24211

1

( 1 7 )

i

tbcdadadA

tbcdadadAti

242

2242

1 ( 1 8 )

Macroeconomic Themes:19 14

Convergence or Divergence from the Steady State

R e d u c e d f o r m :0

2211

ti

titi ( 1 5 )

( a ) r e a l a n d d i s t i n c t r o o t i f 02421

( b ) r e a l a n d e q u a l r o o t s c a s e i f 02421

( c ) c o m p l e x r o o t s c a s e i f 02421 . T h e g e n e r a l

s o l u t i o n s o f t h e m o d e l i n t h e s e t h r e e d i f f e r e n t c a s e sa r e :

itAtAti 2211

( 1 6 )

Macroeconomic Themes:19 15

Growth rate of output, interest rate and the the retail price index in UK

-10

-5

0

5

10

15

20

25

30

1970

Q2

1971

Q2

1972

Q2

1973

Q2

1974

Q2

1975

Q2

1976

Q2

1977

Q2

1978

Q2

1979

Q2

1980

Q2

1981

Q2

1982

Q2

1983

Q2

1984

Q2

1985

Q2

1986

Q2

1987

Q2

1988

Q2

1989

Q2

1990

Q2

1991

Q2

1992

Q2

1993

Q2

1994

Q2

1995

Q2

1996

Q2

1997

Q2

1998

Q2

1999

Q2

Quarters

Pe

rce

nt

pe

r a

nn

um

RPI

GGDP

TBILLS

Data Set Used for the Interest Rate Rule

Macroeconomic Themes:19 16

P h i l l i p s ’ C u r v e

U = 9 . 4 2 - 0 . 2 5 0 R P I t - r a t i o s ( 1 8 . 0 5 ) ( 1 8 . 0 5 ) R - S Q U A R E = 0 . 1 5 8 8 D W = 0 . 5 6

O u t p u t a n d t h e i n t e r e s t r a t e *

11185.0* tttt iiyy 0d ( 9 )

t - r a t i o ( - 1 . 5 4 ) R - S Q U A R E = 0 . 0 1 9 9

O u t p u t a n d i n f l a t i o n *

11* 129.0 tttt yy 0c ( 1 0 )

t - r a t i o s ( 0 . 9 8 2 ) R - S Q U A R E = 0 . 0 0 8 2

D U R B I N - W A T S O N = 0 . 1 2 7

I n t e r e s t r a t e r u l e

** 76.270.225.9 ttttt yyi ( 1 1 )

t - r a t i o s ( 3 2 . 0 ) ( 3 . 9 7 ) ( - 3 . 3 8 )

18.02 R D U R B I N - W A T S O N = 0 . 2 0 6 5

Drawbacks of Single Equation Estimation

Macroeconomic Themes:19 17

Better Fit From the Simultaneous Estimation

E s t i m a t i o n o f t h e s e c o n d o r d e r d i f f e r e n c e e q u a t i o n f o r t h e i n t e r e s t r a t e :21 244.0582.0630.1 ttt iii

t - r a t i o s ( 2 . 7 1 ) ( 6 . 4 2 ) ( 6 . 6 9 )

R - S Q U A R E = 0 . 6 2 D U R B I N - W A T S O N = 2 . 0 1 0 4

S i m u l t a n e o u s e q u a t i o n e s t i m a t i o n : V A R m e t h o d

I n t e r e s t r a t e i = 4 . 9 6 9 ( y - y * ) - 5 . 1 8 2 ( p - p * )

( 7 . 7 4 ) ( - 7 . 2 7 )

O u t p u t g a p : y - y * = 0 . 0 8 i + 0 . 5 0 4 ( p - p * )

( 7 . 7 5 ) ( 5 . 2 1 )

I n f l a t i o n : p - p * = - 0 . 0 7 1 i + 0 . 4 2 1 ( y - y * )

( - 7 . 2 7 ) ( 5 . 2 1 )

S Y S T E M R - S Q U A R E = 0 . 8 6 3 7

Macroeconomic Themes:19 18

Actual and Predicted Interest from the Single Equation Method

0

2

4

6

8

10

12

14

16

18

0 20 40 60 80 100 120TIME

PTBIL TBILLS

Macroeconomic Themes:19 19

Actual and Predicted Interest from the Simultaneous Equation Method

-10

-5

0

5

10

15

20

25

0 20 40 60 80 100 120TIME

PTBIL TBILLS

Macroeconomic Themes:19 20

Main Points of this PaperOrigin of the interest determination rule in the literature of thenatural rate of unemployment hypothesis, dynamic timeinconsistency and credibility and policy co-ordination at thenational and international level.

The prominence of the central bank independence and rule basedmonetary policy in 1990s.

A simple model for interest determination and found its analyticalsolution using the second order difference technique.

Estimation of the model using the time series data on treasurybills rate, growth rate of output and inflation rates for the UKeconomy during the last three decades.

An evidence for such a interest rule and the interest changes tohave significant impacts on output, unemployment and inflation inour estimation.

The simultaneous equation technique better than the singleequation technique.

Macroeconomic Themes:19 21

Alesina A, L. H. Summers (1993) Central Bank Independence and Macroeconomic Performance: SomeComparative Evidence Journal of Money, Credit and Banking, Vol. 25, No. 2. May, pp. 151-162.

Altig D E, C.T. Carlstrom and K.L. Lansing (1995) Computable General Equilibrium Models andMonetary Policy Advice, Journal of Money Credit and Banking, vol. 27, no. 4, Nov., pp. 1472-1493.

Barro R.J. and D. B. Gordon (1983) Rules, Discretion and Reputation in a Model of Monetary Policy,Journal of Monetary Economics, 12: 101-121, North-Holland.

Barro R.J. and D. B. Gordon (1983) A Positive Theory of Monetary Policy in a Natural Rate Model,Journal of Political Economy, vol.91 no. 4, pp. 589-610.

Benigno, Pierpaolo (2002) A Simple Approach to International Monetary Policy Coordination; Journal ofInternational Economics, June 2002, v. 57, iss. 1, pp. 177-96

Bernanke B. S. and F.S. Mishkin (1997) Inflation Targeting: A New Fremework for Monetary Policy,Journal of Economic Perspectives, vol. II, no.2, Spring, pp. 97-116.

Canzoneri M. B. and J A Gray (1985) “Monetary Policy Games and the Consequences of Non-Cooperative Behaviour”, International Economic Review, 26:3: 547-567.

Corsetti, G.; P.Pesenti; (2001) Welfare and Macroeconomic Interdependence; Quarterly Journal ofEconomics, May, v. 116, iss. 2, pp. 421-45

Cukierman A.(1994) Policy Forum: The Banking System and Monetary ControlCentral Bank Independence and Monetary Control The Economic Journal, Vol. 104, No. 427.

November, pp. 1437-1448

Driffil J. (1988) Macroeconomic Policy Games with Incomplete Information: A Survey, EuropeanEconomic Review, 32 (2-3) 513-41.

Eichenbaum (1997) Some Thoughts on Practical Stabilisation Policy, American Economic Review,87:2:236-239.

Eijffinger SCW and J.D. Haan (2000) European Monetary and Fiscal Policy, Oxford University Press.

Friedman, M (1968) The Role of Monetary Policy, American Economic Review, vol. LVIII, March ,58:1:1-17.

Goodhart C. (1989) The Conduct of Monetary Policy, Economic Journal, 99, June, pp. 293-346.

References-1

Macroeconomic Themes:19 22

Julius DeAnne (1998) Inflation and growth in a service economy, Bank of England Quarterly Bulletine,November, pp. 338-346.

Kydland, F. E. and E.C. Prescott (1977) Rules Rather than Discretion: The Inconsistency of OptimalPlans, JPE vol. 85, no. 3, pp. 473-491.

Lockwood, Ben; Miller, Marcus; Zhang, Lei (`998) Designing Monetary Policy When UnemploymentPersists Economica, August, v. 65, iss. 259, pp. 327-45

W. D. Nordhaus (1995) Policy Games: Co-ordination and Independence in Monetary and Fiscal Policeis,Brookings Papers on Economic Activity 2:1994: 139-216.

Miller M and M. Salmon (1985) Dynamic Games and the Time Inconsistency of Optimal Policy in OpenEconomies The Economic Journal, Vol. 95, Supplement: Conference Papers. pp. 124-137.

MPC Bank of England (www.bankofengland.co.uk) The Transmission Mechanism of Monetary Policy.

Phillips A W. (1958) The relation between unemployment and the rate of change ofmoney wage rates in the United Kingdom, 1861-1957.

Phelps E. S. (1968) Money wage dynamics and labour market equilibrium, Journal ofPolitical Economy, 76 , 678-711.

Phelps E. S. and J.B. Taylor (1977) Stabilisation Powers of Monetary Policy underRational Expectations, Journal of Political Economy, vol.85 no. 1, pp. 163-190.

Sargent, T. J. and N. Wallace (1975) “Rational” Expectations, the Optimal Monetary Instrument, andthe Optimal Money Supply Rule, JPE, pp. 41-254.

Taylor J B (1972) Staggered Wage Setting in a Macro Model, American Economic Review, 62, pages 1-18.

Taylor J (1993) Discretion versus policy rules in practice, Carnegie Rochester ConferenceSeries on Public Policy 29 Amsterdam.

Tobin, J (1969), A general Equilibrium Approach to Monetary Theory, JMCB, pp. 15-29, 1969.

Vickers J (1999), Inflation Targeting in the UK, Bank of England Quarterly Bulletin, pp. 368-375.

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