Download Sorensen-Chapter 17

Advanced
Macroeconomics
Chapter 17
MONETARY
POLICY AND
AGGREGATE
DEMAND
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THEMES
 Keynes, the Classics and the Great Depression
 Goods market equilibrium and the determinants of aggregate demand
 Monetary policy and the formation of interest rates
 The relationship between short-term and long-term interest rates
 Derivation of the aggregate demand curve
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KEYNES VERSUS THE CLASSICS
The classical economic orthodoxy: If only market forces are allowed to
work, economic activity will quickly adjust to its natural rate determined by
the supply side.
Winston Churchill, British Secretary of the Treasury 1925-1929: ”It is
the orthodox Treasury dogma, steadfastly held, that whatever might be
the political and social advantages, very little employment can, in fact,
be created by state borrowing and state expenditure”.
The Great Depression of the 1930s undermined the Classical orthodoxy
and paved the way for the Keynesian view that aggregate demand plays
an important role in the determination of economic activity.
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THE GOODS MARKET
Condition for goods market equilibrium
Y  C  I G
(1)
Investment demand
I  I (Y , r ,  )
IY 
I
 0,
Y
Ir 
I
 0,
r
I 
I
0

(2)
Consumption demand
C  C (Y  T , r ,  )
0  CY T 
C
C 
C
 1, Cr 
0,
C

0


 (Y  T )
r

(3)
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THE GOODS MARKET
Define
Aggregate private demand
D C+I
We assume a
Balanced public budget
T=G
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THE GOODS MARKET
From (1) through (3) we then get the
Equilibrium condition for the goods market
Y  D(Y , G, r ,  )  G
(4)
Properties of the aggregate private demand
function
D
0  DY 
 CY  IY  1,
Y
D
Dr 
 Cr  I r  0,
r
D
C
DG 

 CY  0,
G
(Y  T )
(5)
D
D 
 C  I   0

(6)
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Percentage of GDP
7
Percent
Private sector savings surplus (left axis)
5
Real interest rate (right axis)
4
3
1
1
-2
-1
-5
-3
-8
-5
-11
1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999
-7
Year
Figure 17.2: The real interest rate and the private
sector savings surplus in Denmark, 1971-2000
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THE GOODS MARKET
In the chapter text we show that (4) may be log-linearized to give the
following
Approximation of the goods market equilibrium condition
y  y  1 ( g  g )   2 (r  r )  v,
y  ln Y ,
y  ln Y ,
g  ln G,
G
,
Y
 
 2  m 
1  m(1  CY ) 
1  0,
g  ln G,
 Dr 
,
Y


2  0
m
(11)
1
1  DY
  D 
v  m
  ln   ln 
Y



Note that the equilibrium real interest rate is determined by the condition for
Long run equilibrium in the goods market
Y  D(Y , G, r ,  )  G
(13)
We now wish to transform (11) into a relationship between y og . For that
purpose we must study
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THE MONEY MARKET
The equilibrium condition for the money market
M
 L(Y , i ),
P
LY 
L
 0,
Y
Li 
L
0
i
(14)
The money demand function
L(Y , i)  kY  e  i ,
k  0,
  0,
 0
(15)
Note: i is the short-term interest rate which is controlled by the central
bank.
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THE MONEY MARKET
Constant money growth rule (Friedman)
lnM - lnM-1 = 
Motivation for the CMG rule: If  is close to 1 and  is close to zero, equations
(14) and (15) roughly imply that
M = kPY
A constant rate of growth of M will then ensure a stable growth in
aggregate money income PY.
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Interest rate policy under the CMG rule
Money market equilibrium under the CMG rule
(1   ) M 1
 kY  e  i
(1   ) P1
(16)
M 1
 L*  kY  e   ( r   )
P1
(17)
Assume that we have
Long run equilibrium in the previous period
Taking logarithms in (16) and (17) and using the approximations
ln(1+)   and ln(1+)   , we get
    ln L*  ln k   y   i
(18)
ln L*  ln k   y   (r   )
(19)
Substitution of (18) into (19) yields
Monetary policy under the CMG rule
 1  
 
(20)
i  r  
(



)

(
y

y
)

  ©The McGraw-Hill Companies, 2005



 
INTEREST RATE POLICY UNDER THE
TAYLOR RULE
Note that  may be interpreted as the central bank’s target inflation rate.
Problem with the CMG rule: A stable growth in total money income cannot be
achieved if the parameters  and  change in an unpredictable way (for
example through financial innovations).
As an alternative to the CMG rule John Taylor proposed the
Taylor rule
i  r    h  (   *)  b  ( y  y ),
h  0,
b0
(21)
Note: It is important for economic stability that the parameter h is positive so
that an increase in inflation triggers an increase in the real interest rate.
Taylor’s proposal for USA
h = 0.5
b = 0.5
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Estimated interest rate reaction
functions of four central banks
Estimate of
h
b
German Bundesbank
1
1
Bank of Japan
U.S. Federal Reserve Bank
European Central Bank2
1
Estimation period
0.31
0.25
1979:3 - 1993:12 (monthly data)
1.04
0.08
1979:4 - 1994:12 (monthly data)
0.83
0.56
1982:10 - 1994:12 (monthly data)
0.74
0.82
1999:1 - 2003:1
(quarterly data)
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Three-month interest rate and the
estimated Taylor rate in the euro area
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FROM THE SHORT RATE TO THE
LONG RATE
The problem: the central bank may control the short-term interest rate, but
aggregate demand mainly depends on the long-term interest rate.
Assumption: Short-term and long-term bonds are perfect substitutes
This implies the
Arbitrage condition
(1  itl )n  (1  it )  (1  ite1 )  (1  ite 2 )  ........  (1  ite n 1 )
(24)
Taking logs on both sides of (24) and using the approximation ln(1+i)  i, we
get
The expectations theory of the term structure of interest rates
1
i  (it  ite1  ite 2  ......  ite n 1 )
n
l
t
(25)
Implication: The current long rate is a simple average of the current short
rate and the expected future short rates.
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FROM THE SHORT RATE TO THE
LONG RATE
Further implications of (25):
 Monetary policy can only have a significant impact on long-term interest
rates by influencing the expected future short-term interest rates
 A change in the current short-term rate which is expected to be
temporary will only have a very limited impact on the long-term interest
rate
 When the market expects a future tightening of monetary policy, the
yield curve is rising
 If the market expects a future relaxation of monetary policy, the yield curve
is falling
 The yield curve is flat when market participants have
Static interest rate expectations
itl  it
iff
ite j  it
for all j  1, 2,..., n  1
(26)
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Effective yield
(percent)
14
12
10
August 1st, 1996
8
August 2nd, 1993
6
January 2nd, 2000
4
2
Term to maturity (logarithms)
0
14 days
1 month
3 months
6 months
1 year
2 years
5 years
10 years
30 years
The term structure of interest rates in Denmark
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Percent p.a.
7
6
10-year government bond
yield
5
4
Federal funds
target rate
3
2
1
Jan.
Feb.
Mar.
Apr.
May.
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Jan.
Feb.
The decoupling of short-term and long-term
interest rates in the United States, 2001-2002
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Percent
14
12
10
8
6
4
2
0
1990
1991
1992
1993
1994
10-year government bond yield
1995
1996
1997
1998
1999
2000
2001
'Signaling' interest rate of the central bank
The ’signalling’ interest rate of the central bank and the
10-year government bond yield in Denmark
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DERIVING THE AGGREGATE DEMAND
CURVE
The ex post real interest rate
1 i
1 r 
1   1
a
 r a  i   1
(27)
Investment and consumption are governed by
The ex ante real interest rate
1 i
e
1 r 

r

i


1
1   e1
(28)
We assume
Static expectations
Equations (28) and (29) imply
 e1  
(29)
r  i 
(30)
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DERIVING THE AGGREGATE DEMAND
CURVE
Recall that
y  y  1 ( g  g )   2 (r  r )  v,
1  0,
i  r    h(   *)  b( y  y ),
h  0,
2  0
b0
(11)
(21)
Inserting (21) and (30) into (11), we get
The aggregate demand curve
r r
y  y  1 ( g  g )   2 [h(   *)  b( y  y )]  v 
y  y   ( *  )  z
2h

0
1   2b
(32)
v  1 ( g  g )
z
1   2b
(33)
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PROPERTIES OF THE
AGGREGATE DEMAND CURVE
 The AD curve has a negative slope: higher inflation induces the central
bank to raise the interest rate, causing aggregate demand to fall
 The AD curve is flatter, the more weight the central bank attaches to
stable inflation compared to output stability (see figure 17.7)
The AD curve shifts upwards in case of more optimistic growth
expectations in the private sector or in case of a more expansionary fiscal
policy
 The AD curve shifts downwards if the central bank reduces its inflation
target
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B
AD (h high, b low)
AD (h low, b high)
y
Figure 17.7: The aggregate demand curve under
alternative monetary policy regimes
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IMPORTANT CONCEPTS AND
RESULTS IN CHAPTER 17
 The goods market equilibrium condition
 Properties of the investment function
 Properties of the consumption function
The relationship between the real interest rate, public consumption,
expectations and aggregate demand
 Money market equilibrium
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IMPORTANT CONCEPTS AND RESULTS
IN CHAPTER 17
 The constant-money-growth rule and its implications for interest rate
policy
 The Taylor rule and its implications for interest rate policy
 The relationship between the short-term and the long-term interest rate:
The expectations hypothesis and the yield curve
 The ex ante versus the ex post real interest rate
 Poperties of the AD curve, including the importance of monetary policy for
the position and the slope of the curve
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