Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
K C
Key
Concepts
t and
d Id
Ideas
Business Cycles
Econ 402
Professor Yamin Ahmad
• Incorporating dynamics into the AD-AS model we
previously studied
• Using the dynamics of the AD-AS model to
illustrate long-run economic growth
Lecture 8:
• An introduction to
Dynamic
y
Stochastic
General Equilibrium
Modeling
• Impulse Response Functions: Using the
dynamics
y
AD-AS model to trace out the effects
over time of various shocks and policy changes on
key variables like output and inflation, as well as
other endogenous variables
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
I t d ti
Introduction
I t d ti
Introduction
• The dynamic model of aggregate demand and
aggregate supply gives us more insight into how the
economy works in the short run.
• The dynamic model of aggregate demand and
aggregate supply is built from familiar concepts, such
as:
 the IS curve, which negatively relates the real interest rate
and demand for goods & services
 the Phillips curve, which relates inflation to the gap between
output and its natural level, expected inflation, and supply
shocks
 Adaptive expectations
expectations, a simple model of inflation
expectations
• It is a simplified version of a DSGE model,
used
d iin cutting-edge
tti
d macroeconomic
i research.
h
(DSGE = Dynamic, Stochastic, General Equilibrium)
Note: These lecture notes are incomplete without having attended lectures
2
3
Note: These lecture notes are incomplete without having attended lectures
4
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
How the dynamic AD-AS model is different from
the standard model
K
Keeping
i ttrackk off time
ti
• The subscript
p “t ” denotes the time p
period,, e.g.
g
• Instead of fixing the money supply, the central bank
follows a monetary policy rule that adjusts interest rates
when output or inflation change.
Yt = real GDP in period t
Yt -1 = real GDP in period t – 1
Yt +1 = real GDP in period t + 1
• The vertical axis of the DAD-DAS diagram measures the
inflation rate, not the price level.
• We can think of time periods as years
years.
E.g., if t = 2008, then
• Subsequent time periods are linked together:
Changes in inflation in one period alter expectations of
future inflation, which changes aggregate supply in
future periods, which further alters inflation and inflation
expectations.
Note: These lecture notes are incomplete without having attended lectures
Yt = Y2008 = real GDP in 2008
Yt -1 = Y2007 = real GDP in 2007
Yt +1 = Y2009 = real GDP in 2009
5
Professor Yamin Ahmad, Business Cycles – ECON 402
6
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Professor Yamin Ahmad, Business Cycles – ECON 402
Equation
q
1: - Output
p
The Demand for Goods and Services
K El
Key
Elements
t off The
Th Model:
M d l
• The model has five equations and five endogenous
variables:
Yt  Yt   (rt   )   t
 output,
 inflation,
 the real interest rate,
 the nominal interest rate and
 expected inflation
inflation.
output
• The equations may use different notation
notation, but they are
conceptually similar to things you’ve already learned.
natural
level
e e o
of
output
real
interest
rate
  0,   0
Negative relation between output and interest rate,
same intuition as IS curve.
• The first equation is for output…
Note: These lecture notes are incomplete without having attended lectures
7
Note: These lecture notes are incomplete without having attended lectures
8
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
Equation
q
1: - Output
p
The Demand for Goods and Services
Equation
q
2: - The Real Interest Rate
The Fisher Equation
Yt  Yt   (rt   )   t
measures the
interest-rate
sensitivity of
demand
““natural
t l rate
t off
interest” –
in absence of
demand shocks,
Yt  Yt when rt 
ex ante
(i.e. expected)
real interest
rate
demand
shock,
random and
zero on
average
 t 1 

rt  it  Et  t 1
nominal
interest
rate
expected
inflation rate
increase in p
price level from p
period t to t +1,,
not known in period t
Et  t 1  expectation, formed in period t,
of inflation from t to t +1
9
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Professor Yamin Ahmad, Business Cycles – ECON 402
current
inflation
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
Equation
q
3: - Inflation
The Phillips Curve
Equation
q
4: - Expected
p
Inflation
Adaptive Expectations
 t  Et 1  t   (Yt  Yt )   t
Et  t 1   t
previously
expected
inflation
  0 indicates how much
10
supply
shock,
random and
zero on
average
For simplicity,
p y we assume p
people
p
expect prices to continue rising at
the current inflation rate.
inflation responds when
output fluctuates around
its natural level
Note: These lecture notes are incomplete without having attended lectures
11
Note: These lecture notes are incomplete without having attended lectures
12
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The Nominal Interest Rate:
The Monetary-Policy Rule
The Nominal Interest Rate:
The Monetary-Policy Rule
it   t     ( t   t* )  Y (Yt  Yt )
it   t     ( t   t* )  Y (Yt  Yt )
nominal
interest rate,
set each period
by the central
bank
central
bank’s
i fl ti
inflation
target
natural
rate of
interest
measures how much
the central bank
adjusts the interest
rate when inflation
deviates from its target
  0, Y  0
Note: These lecture notes are incomplete without having attended lectures
13
Professor Yamin Ahmad, Business Cycles – ECON 402
CASE STUDY:
STUDY The
Th Taylor
T l Rule
R l
• Economist John Taylor proposed a monetary
policy rule very similar to ours:
CASE STUDY:
STUDY The
Th Taylor
T l Rule
R l
10
9
8
iff =  + 2 + 0.5 ( – 2) – 0.5 (GDP gap)
7
Perrcent
where
= nominal federal funds rate target
Y Y
 GDP gap = 100 x
Y
= percent by which real GDP is below its natural rate
actual
Federal
Funds rate
6
5
4
3
2
• The Taylor Rule matches Fed policy fairly well.…
Note: These lecture notes are incomplete without having attended lectures
14
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
iff
measures how much the
central bank adjusts the
interest rate when
output deviates from
its natural rate
1
15
Taylor’s
rule
0
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
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16
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
S
Summary:
Th
The model’s
d l’ variables
i bl
S
Summary:
Th
The model’s
d l’ variables
i bl
• Endogenous variables:
• Exogenous variables:
Yt  Output
t 
Yt  Natural level of output
 t* 
Central bank’s target inflation rate
rt  Real interest rate
t 
Demand shock
it  Nominal interest rate
t 
Supply
pp y shock
Inflation
Et  t 1  Expected inflation
• Predetermined variable:
 t 1 
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Professor Yamin Ahmad, Business Cycles – ECON 402
Previous period’s inflation
Note: These lecture notes are incomplete without having attended lectures
18
Professor Yamin Ahmad, Business Cycles – ECON 402
S
Summary:
Th
The model’s
d l’ Parameters
P
t
• Parameters:
 
 
 
Responsiveness of demand to
the real interest rate
Natural rate of interest
Responsiveness of inflation to
output
t t in
i the
th Phillips
Philli C
Curve
 
Responsiveness of i to inflation
i th
in
the monetary-policy
t
li rule
l
Y 
Responsiveness of i to output
i th
in
the monetary-policy
t
li rule
l
Note: These lecture notes are incomplete without having attended lectures
SOLVING THE MODEL
19
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20
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The model’s long-run
g
equilibrium:
q
Steady State
Th model’s
The
d l’ llong-run equilibrium
ilib i
• Plugging the preceding conditions into the model’s five
equations and using algebra yields these long-run
values:
Steady State:
• Def: The normal state around which the economy
fluctuates.
Yt  Yt
rt  
 t   t*
• Two conditions required for long-run equilibrium:
 There are no shocks:
t   t  0
 Inflation is constant:
 t 1   t
Et  t 1   t*
it     t*
21
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The Dynamic Aggregate Supply Curve
Th Dynamic
The
D
i A
Aggregate
t S
Supply
l C
Curve
π
• The DAS curve shows a relation between output and
inflation that comes from the Phillips Curve and
Adaptive Expectations:
 t   t 1   (Yt  Yt )   t
22
Note: These lecture notes are incomplete without having attended lectures
 t   t 1   (Yt  Yt )   t
DASt
(DAS)
DAS slopes upward:
high levels of output
are associated with
high inflation.
Y
Note: These lecture notes are incomplete without having attended lectures
23
Note: These lecture notes are incomplete without having attended lectures
DAS shifts in response
to changes in the
natural level of output
output,
previous inflation,
and supply shocks.
24
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
Th Dynamic
The
D
i A
Aggregate
t D
Demand
dC
Curve
Th Dynamic
The
D
i A
Aggregate
t D
Demand
dC
Curve
Yt  Yt   ( it  Et  t 1   )   t
• To derive the DAD curve, we will combine four equations
and then eliminate all the endogenous variables other
than output and inflation.
Start with the demand for goods and services:
Yt  Yt   ( it   t   )   t
Yt  Yt   (rt   )   t
using the Fisher eq’n
Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
25
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
The Dynamic Aggregate Demand Curve
π
Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
(DAD)

1
 0,
0 B
0
1  Y
1  Y
Note: These lecture notes are incomplete without having attended lectures
Yt  Yt  A( t   t* )  B t
DAD slopes downward:
When inflation rises, the central bank
raises the real interest rate, reducing
the demand for goods & services.
combine like terms,
terms solve for Y
A
26
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
Th Dynamic
The
D
i A
Aggregate
t D
Demand
dC
Curve
where
h
using monetary
policy rule
Yt  Yt   [  t     ( t   t* )  Y (Yt  Yt )   t   ]   t
Yt  Yt   ( it  Et  t 1   )   t
Yt  Yt  A( t   t* )  B t ,
using the
expectations
t ti
eq’n
’
DADt
Y
27
Note: These lecture notes are incomplete without having attended lectures
DAD shifts in response
to changes in the
natural level of output,
the inflation target, and
demand shocks.
28
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
Long-run
Long
run growth
The short
short-run
run equilibrium
π
Yt
DASt
πt
π
In each period, the
intersection of DAD
and DAS determines
the short-run
short run eq
eq’m
m
values of inflation
and output.
A
DADt
Y
Yt
Yt +1
DASt
πt
= πt
πt + 1
In the eq’m
shown here at A,
A
output is below
its natural level.
A
Yt
Professor Yamin Ahmad, Business Cycles – ECON 402
DASt +1
B
DADt
29
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Yt
DADt +1
Yt +1
Note: These lecture notes are incomplete without having attended lectures
Y
30
Professor Yamin Ahmad, Business Cycles – ECON 402
A shock to aggregate supply
Y
π
πt
πt + 2
πt – 1
DASt
DASt +1
DASt +2
B
C
D
Period t – 1:
initial eq’m
q at A
DASt -1
A
DAD
Yt Yt + 2 Yt –11
Note: These lecture notes are incomplete without having attended lectures
Y
This process
continues until
output returns to
its natural rate.
LR eq’m at A.
Impulse Response Functions
SIMULATIONS
31
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32
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a supply shock
P
Parameter
t values
l
for
f simulations
i l ti
Yt  100
  2.0
  11.00
*
t
  2.0
  0.25
t
The following graphs are called
i
impulse
l response functions.
f
ti
They
show the
The natural
rate“response”
of interestof
is
the
endogenous variables to
2 percent
percent.
the “impulse,” i.e. the shock.
Yt
  0.5
Y  0.5
33
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Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a supply shock
t
Note: These lecture notes are incomplete without having attended lectures
34
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
t
A oneone
period
supply
shock
affects
output for
many
periods.
The dynamic response to a supply shock
Because
i fl ti
inflation
expectations
adjust
slowly,
actual
inflation
remains
hi h ffor
high
many
periods.
p
t
rt
35
Note: These lecture notes are incomplete without having attended lectures
The real
interest
rate takes
many
periods to
return to
its natural
rate.
36
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a supply shock
A shock to aggregate demand
The
behavior
of the
nominal
interest
rate
depends
on that
of the
inflation
and real
interest
rates.
t
it
π
πt + 5
Note: These lecture notes are incomplete without having attended lectures
Period t – 1:
initial eq’m at A
DASt + 1
DASt -1,t
B
πt – 1
DADt ,t+1,…,t+4
A
DADt -1, t+5
Yt + 5
Yt –11
Yt
Y
38
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic
y
response to a demand shock
Yt
E
πt
Professor Yamin Ahmad, Business Cycles – ECON 402
t
F
G
D
C
37
Note: These lecture notes are incomplete without having attended lectures
DASt +5
DASt +4
DASt +3
DASt +2
Y
The dynamic
y
response to a demand shock
The
demand
shock
raises
output for
fi periods.
five
i d
When the
shock ends,
output falls
below its
natural
level, and
recovers
gradually.
d ll
39
t
t
Note: These lecture notes are incomplete without having attended lectures
The
demand
shock
h k
causes
inflation
to rise.
When the
shock ends
ends,
inflation
gradually
f ll ttoward
falls
d
its initial
level.
40
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic
y
response to a demand shock
The dynamic
y
response to a demand shock
The
demand
shock
raises the
real interest
rate
rate.
After the
shock ends,
th reall
the
interest
rate falls
and
approaches
its initial
level.
t
rt
t
it
41
Note: These lecture notes are incomplete without having attended lectures
The
behavior
of the
nominal
interest
rate
depends
on that
of the
inflation
and real
interest
rates.
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a reduction in target inflation
A shift in monetary policy
πt – 1 = 2%
πt
Period t – 1:
target
g inflation
rate π* = 2%,
initial eq’m at A
Y
π
DASt -1,
1 t
DASt +1
A
B
C
πfinal = 1%
 t*
DASfinal
Z
DADt – 1
DADt, t + 1,…
Yt
42
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Yt –1 ,
Yfinal
Note: These lecture notes are incomplete without having attended lectures
Yt
Y
43
Note: These lecture notes are incomplete without having attended lectures
Reducing
the target
inflation
rate
causes
output to
fall below
its natural
level for a
while.
Output
recovers
gradually.
44
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a reduction in target inflation
 t*
The dynamic response to a reduction in target inflation
 t*
Because
expectations
adjust
slowly,
it takes
many
periods for
inflation to
reach the
new target.
t
rt
45
Note: These lecture notes are incomplete without having attended lectures
To reduce
inflation,
the central
bank raises
the real
i t
interest
t rate
t
to reduce
aggregate
gg g
demand.
The real
interest rate
gradually
returns to its
natural rate.
Professor Yamin Ahmad, Business Cycles – ECON 402
Note: These lecture notes are incomplete without having attended lectures
46
Professor Yamin Ahmad, Business Cycles – ECON 402
The dynamic response to a reduction in target inflation
 t*
it
Note: These lecture notes are incomplete without having attended lectures
The initial
increase in
the real
interest rate
raises the
nominal
interest
rate.
As the
inflation
and real
interest
rates fall,
the nominal
rate falls.
APPLICATIONS
47
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48
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
APPLICATION:
APPLICATION: Output variability vs
vs. inflation variability
Output variability vs. inflation variability
CASE 1: θπ is large, θY is small
π
• A supply shock reduces output (bad) and raises
inflation (also bad).
A supply shock
shifts DAS up.
DASt
• The central bank faces a tradeoff between these
“bads”
bads – it can reduce the effect on output
output,
but only by tolerating an increase in the effect
on inflation….
DASt – 1
πt
πt –1
DADt – 1, t
Yt
49
Note: These lecture notes are incomplete without having attended lectures
Professor Yamin Ahmad, Business Cycles – ECON 402
Yt –11
Y
In this case, a
small change in
inflation has a
large effect on
output,
p , so DAD
is relatively flat.
The shock has
a large effect
on output, but
a small effect
on inflation.
Note: These lecture notes are incomplete without having attended lectures
50
Professor Yamin Ahmad, Business Cycles – ECON 402
APPLICATION: The Taylor Principle
APPLICATION: Output variability vs
vs. inflation variability
CASE 2: θπ is small, θY is large
π
DASt
πt
DASt – 1
πt –1
DADt – 1, t
Yt Yt –11
Note: These lecture notes are incomplete without having attended lectures
Y
• The Taylor Principle (named after John Taylor):
The proposition that a central bank should respond to an
increase in inflation with an even greater increase in the
nominal interest rate
( th
(so
thatt the
th reall interest
i t
t rate
t rises).
i
)
In this case, a
large change in
inflation has only
a small effect on
output, so DAD
is relatively steep.
i.e., central bank should set θπ > 0.
• Otherwise, DAD will slope upward, economy may be
p
out of control.
unstable,, and inflation mayy spiral
Now,, the shock
has only a small
effect on output,
but a big effect
on inflation.
51
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52
Professor Yamin Ahmad, Business Cycles – ECON 402
APPLICATION: The Taylor Principle

1
Yt  Yt 
t
( t   t* ) 
1  Y
1  Y
it   t     ( t   t* )  Y (Yt  Yt )
Professor Yamin Ahmad, Business Cycles – ECON 402
APPLICATION: The Taylor Principle

1
Yt  Yt 
t
( t   t* ) 
1  Y
1  Y
(DAD)
(MP rule)
it   t     ( t   t* )  Y (Yt  Yt )
(DAD)
(MP rule)
If θπ > 0:
If θπ < 0:
• When inflation rises, the central bank increases the
nominal interest rate even more, which increases
the real interest rate and reduces the demand for
goods & services.
• When inflation rises, the central bank increases
the nominal interest rate by a smaller amount.
The real interest rate falls,
falls which increases the
demand for goods & services.
• DAD has a negative slope
slope.
• DAD has a positive slope
slope.
Note: These lecture notes are incomplete without having attended lectures
53
Professor Yamin Ahmad, Business Cycles – ECON 402
54
Professor Yamin Ahmad, Business Cycles – ECON 402
APPLICATION: The Taylor Principle
Summary
• If DAD is upward-sloping and steeper than DAS, then
the economy is unstable: output will not return to its
natural level, and inflation will spiral upward
(for positive demand shocks) or downward
(for negative ones)
ones).
• The DAD-DAS model combines five relationships: an
IS-curve-like equation of the goods market, the Fisher
equation, a Phillips curve equation, an equation for
expected
p
inflation,, and a monetary
yp
policy
y rule.
• The long-run equilibrium of the model is classical.
Output and the real interest rate are at their natural
levels, independent of monetary policy. The central
bank’s
bank
s inflation target determines inflation, expected
inflation, and the nominal interest rate.
• Estimates of θπ from published research:
 θπ = –0.14 from 1960-78, before Paul Volcker became
Fed chairman.
chairman Inflation was high during this time
time,
especially during the 1970s.
 θπ = 0.72 during
g the Volcker and Greenspan
p yyears.
Inflation was much lower during these years.
Note: These lecture notes are incomplete without having attended lectures
Note: These lecture notes are incomplete without having attended lectures
55
Note: These lecture notes are incomplete without having attended lectures
56
Professor Yamin Ahmad, Business Cycles – ECON 402
Professor Yamin Ahmad, Business Cycles – ECON 402
S
Summary
(cont.)
(
t)
S
Summary
(cont.)
(
t)
• The DAD-DAS model can be used to determine the
immediate impact of any shock on the economy
economy, and
can be used to trace out the effects of the shock over
time.
• The DAD-DAS model assumes that the Taylor
Principle holds,
holds i.e.
i e that the central bank responds to
an increase in inflation by raising the real interest
rate. Otherwise, the economy may become
unstable and inflation may spiral out of control.
• The parameters of the monetary policy rule influence
the slope of the DAS curve
curve, so they determine
whether a supply shock has a greater effect on output
or inflation. Thus, the central bank faces a tradeoff
b
between
output variability
i bili and
d iinflation
fl i variability.
i bili
Note: These lecture notes are incomplete without having attended lectures
57
Note: These lecture notes are incomplete without having attended lectures
58