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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.
References-2