Download Chapter 14: Dynamic AD-AS

11/6/2013
Introduction
 The dynamic model of aggregate demand and
Chapter 14: Dynamic AD-AS
aggregate supply gives us more insight into how
the economy works in the short run.
 It is a simplified version of a DSGE model,
used in cutting
cutting-edge
edge macroeconomic research
research.
(DSGE = Dynamic, Stochastic, General
Equilibrium)
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Dynamic AD-AS Model
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 The dynamic model of aggregate demand and
bank follows a monetary policy rule that adjusts
interest rates when output or inflation change.
 The vertical axis of the DAD-DAS diagram
measures the inflation rate, not the price level.
 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.
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Dynamic AD-AS Model
Keeping track of time
The model’s elements
 The subscript “t ” denotes the time period, e.g.
 Yt = real GDP in period t
 Yt -1 = real GDP in period t – 1
 Yt +1 = real GDP in period t + 1
 We can think of time periods as years.
 The model has five equations and five
 The equations may use different notation
notation,
but they are conceptually similar to things
you’ve already learned.
 Yt = Y2008 = real GDP in 2008
 Yt -1 = Y2007 = real GDP in 2007
 Yt +1 = Y2009 = real GDP in 2009
Dynamic AD-AS Model
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endogenous variables:
output, inflation, the real interest rate, the
nominal interest rate, and expected inflation.
E.g., if t = 2008, then
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 Instead of fixing the money supply, the central
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, a simple model of
inflation expectations
Dynamic AD-AS Model
Dynamic AD-AS Model
How the dynamic AD-AS model is
different from the standard model
Introduction
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 The first equation is for output…
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Dynamic AD-AS Model
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Output:
The Demand for Goods and Services
Output:
The Demand for Goods and Services
Yt  Yt   (rt   )   t
Yt  Yt   (rt   )   t
output
natural
level of
output
real
interest
rate
  0,   0
measures the
i t
interest-rate
t t
sensitivity of
demand
Negative relation between output and interest rate,
same intuition as IS curve.
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Dynamic AD-AS Model
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Dynamic AD-AS Model
rt  it  Et  t 1
 t  Et 1  t   (Yt  Yt )   t
nominal
interest
rate
expected
inflation rate
current
inflation
previously
expected
inflation
  0 indicates how much
increase in price level from period t to t +1,
not known in period t
Dynamic AD-AS Model
supply
shock
shock,
random and
zero on
average
inflation responds when
output fluctuates around
its natural level
of inflation from t to t +1
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Dynamic AD-AS Model
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Expected Inflation:
Adaptive Expectations
The Nominal Interest Rate:
The Monetary-Policy Rule
Et  t 1   t
it   t     ( t   t* )  Y (Yt  Yt )
nominal
interest rate,
set each period
by the central
bank
For simplicity, we assume people
expect prices to continue rising at
the current inflation rate.
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Inflation:
The Phillips Curve
Et  t 1  expectation, formed in period t,
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
The Real Interest Rate:
The Fisher Equation
ex ante
(i.e. expected)
real interest
rate
 t 1 
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“natural rate of
interest” –
in absence of
demand shocks,
Yt  Yt when rt 
demand
shock
shock,
random and
zero on
average
Dynamic AD-AS Model
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central
bank’s
inflation
target
natural
rate of
interest
Dynamic AD-AS Model
  0, Y  0
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CASE STUDY
The Nominal Interest Rate:
The Monetary-Policy Rule
The Taylor Rule
 Economist John Taylor proposed a monetary
it   t     ( t   t* )  Y (Yt  Yt )
policy rule very similar to ours:
iff =  + 2 + 0.5 ( – 2) – 0.5 (GDP gap)
measures how much
the central bank
adjusts the interest
rate when inflation
deviates from its target
where
measures how much the
central bank adjusts the
interest rate when
output deviates from
its natural rate
 iff
= nominal federal funds rate target
 GDP gap = 100 x
Y Y
Y
= percent by which real GDP is below its
natural rate
 The Taylor Rule matches Fed policy fairly well.…
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Dynamic AD-AS Model
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CASE STUDY
13
 Endogenous variables:
10
9
actual
Federal
Funds rate
8
7
Yt  Output
t 
6
Inflation
rt  Real interest rate
5
4
it  Nominal interest rate
3
Et  t 1  Expected inflation
Taylor’s
rule
2
1
0
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
The model’s variables and parameters
Central bank’s target inflation rate
t 
Demand shock
t 
Supply shock
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the real interest rate
 
 
 Predetermined variable:
 t 1  Previous period’s inflation
Dynamic AD-AS Model
Dynamic AD-AS Model
 Parameters:
  Responsiveness of demand to
Yt  Natural level of output
 t* 
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The model’s variables and parameters
 Exogenous variables:
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Dynamic AD-AS Model
The model’s variables and parameters
The Taylor Rule
Percen
nt
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Natural rate of interest
Responsiveness of inflation to
output in the Phillips Curve
 
Responsiveness of i to inflation
in the monetary-policy rule
Y 
Responsiveness of i to output
in the monetary-policy rule
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The model’s long-run equilibrium
The model’s long-run equilibrium
 The normal state around which the economy
 Plugging the preceding conditions into the
model’s five equations and using algebra
yields these long-run values:
fluctuates.
 Two conditions required for long-run equilibrium:
 There are no shocks:  t   t  0
 Inflation is constant:
Yt  Yt
rt  
 t   t*
 t 1   t
Et  t 1   t*
it     t*
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Dynamic AD-AS Model
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19
The Dynamic Aggregate Supply Curve
The Dynamic Aggregate Supply Curve
 t   t 1   (Yt  Yt )   t
 The DAS curve shows a relation between output
π
and inflation that comes from the Phillips Curve
and Adaptive Expectations:
 t   t 1   (Yt  Yt )   t
Dynamic AD-AS Model
DASt
(DAS)
DAS slopes upward:
high levels of output
are associated with
high inflation.
DAS shifts in response
to changes in the
natural level of output,
previous inflation,
and supply shocks.
Y
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Dynamic AD-AS Model
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The Dynamic Aggregate Demand Curve
21
result from previous slide
Yt  Yt   ( it  Et  t 1   )   t
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
using the
expectations eq’n
using monetary
policy rule
Yt  Yt   [  t     ( t   t* )  Y (Yt  Yt )   t   ]   t
Yt  Yt   ( it  Et  t 1   )   t
Dynamic AD-AS Model
Dynamic AD-AS Model
The Dynamic Aggregate Demand Curve
 To derive the DAD curve, we will combine four
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Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
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Dynamic AD-AS Model
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The Dynamic Aggregate Demand Curve
The Dynamic Aggregate Demand Curve
Yt  Yt  A( t   t* )  B t
result from previous slide
π
Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
DAD slopes downward:
When inflation rises, the central bank
raises the real interest rate, reducing
the demand for g
goods & services.
combine like terms, solve for Y
Yt  Yt  A( t   t* )  B t ,
where
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(DAD)

1
A
 0, B 
0
1  Y
1  Y
Dynamic AD-AS Model
DADt
Y
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The short-run equilibrium
π
DASt
πt
A
DADt
Y
Yt
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π
πt
= πt
πt + 1
πt + 2
πt – 1
Y
DASt
DASt +1
DASt +2
B
C
D
DASt -1
A
Yt Yt + 2 Yt –1
Dynamic AD-AS Model
Y
25
Yt +1
A
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DASt +1
B
DADt
26
DAD
CHAPTER 14
Yt
Yt
A shock to aggregate supply
πt
Dynamic AD-AS Model
DASt
In the eq’m
shown here at A,
output is below
its natural level.
Dynamic AD-AS Model
π
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Long-run growth
In each period, the
intersection of DAD
and DAS determines
the short-run eq’m
values of inflation
and output.
Yt
DAD shifts in response
to changes in the
natural level of output,
the inflation target, and
demand shocks.
DADt +1
Yt +1
Y
DAS
Period
t: shifts
initialbecause
eq’m at A
economy can
produce more
g&s
Period t + 1 :
Long-run
New
eq’m
eq m at B,
B
DAD shifts
growthgrows
income
because
increases
but
inflation the
higher income
naturalstable.
rate
remains
raises
of output.
demand
for g&s
Dynamic AD-AS Model
27
Parameter values for simulations
Periodtt+
:– 121::
Period
initial
eq’m
at A
Supply
shock
Supply
shock
As
inflation
falls,
(νover
> 0)(shifts
is
ν = 0)
inflation
DAS
upward;
but
DAS
doesfall,
not
expectations
inflation
rises,
return
to its
initial
DAS
moves
central bank
position
due to
downward,
responds
by
higher
inflation
output
rises.
raising
real
expectations.
This
process
interest rate,
continues
until
outputreturns
falls. to
output
its natural rate.
LR eq’m at A.
Yt  100
 t*  2.0
  1.0
  2.0
  0.25
  0.5
Y  0.5
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Thus, we can interpret Yt – Yt
as the percentage deviation of
Central bank’s inflation
output from its natural level.
target
is 2 percent.
A 1-percentage-point
increase
The
following
graphs are
called
in
the
real
interest rate
reduces
impulse response
functions.
output
p show
demand
by
y1p
percent
of
They
response
Th natural
The
t lthe
rate
t “response”
off interest
i t
t of
is
i
its natural
level. variables to
the
endogenous
2 percent.
When output is 1 percent
the “impulse,” i.e. the shock.
above its natural level, inflation
rises by 0.25 percentage point.
These values are from the Taylor
Rule, which approximates the actual
behavior of the Federal Reserve.
Dynamic AD-AS Model
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The dynamic response to a supply shock
The dynamic response to a supply shock
t
t
A oneperiod
supply
shock
affects
output for
many
periods.
Yt
t
The dynamic response to a supply shock
The dynamic response to a supply shock
t
t
The real
interest
rate takes
many
periods to
return to
its natural
rate.
rt
it
πt + 5
DASt +5
DASt +4
DASt +3
DASt +2
Y
F
G
E
DASt + 1
D
C
πt
DASt -1,t
B
πt – 1
DADt ,t+1,…,t+4
A
DADt -1, t+5
Yt + 5
CHAPTER 14
Yt –1
Yt
Dynamic AD-AS Model
Y
The
behavior
of the
nominal
interest
rate
depends
on that
of the
inflation
and real
interest
rates.
The dynamic response to a demand shock
A shock to aggregate demand
π
Because
inflation
expectations
adjust
slowly,
l l
actual
inflation
remains
high for
many
periods.
:t–+1+
Period
Period
Periods
516:::2
Periods
Period
ttt+t+
Positive
initial
at Ain
DAS
is4eq’m
higher
and
higher:
Higher
inflation
to
t+
:
demand
shock
togradually
higher
DAS
tdue
raised
inflation
Higher
inflation
(ε previous
> 0)down
shifts
inflation
in as
shifts
in
expectations
ADt +to1the
right;
preceding
period,
inflation
and
period
,raises
for
output
and up
but
inflation
ademand
o DAS
inflation
shifting
up.
inflation
rise.
shock
expectations
ends
and
fall,
expectations,
Inflation
rises
DAD
economy
to
shiftsreturns
DAS up.
more,
output
falls.
its
gradually
initial position.
Inflation
rises,
Eq’m
recovers
atfalls.
G.
until
output
reaching
LR eq’m at A.
t
Yt
The
demand
shock
raises
output for
five periods.
When the
shock ends,
output falls
below its
natural
level, and
recovers
gradually.
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The dynamic response to a demand shock
t
t
The
demand
shock
causes
inflation
to rise.
Wh the
When
th
shock ends,
inflation
gradually
falls toward
its initial
level.
The dynamic response to a demand shock
t
it
The
behavior
of the
nominal
interest
rate
depends
on that
of the
inflation
and real
interest
rates.
The dynamic response to a demand shock
t
rt
A shift in monetary policy
 t*
Yt
Y
π
πt – 1 = 2%
πt
A
B
πfinal = 1%
Subsequent
Period
t t–t+
Period
:1:1 :
Period
periods:
target
inflation
Central
bank
The
fall
in
πt
This
lowers
rate
π*process
= target
2%,
reduced
continues
until
inflation
initial
at
A
to π*eq’m
= 1%,
output
expectations
raises returns
real
to
its
for
t +natural
1,, rate,
interest
DASfinal shifting
rate
DAS
shiftsand
DAD
inflation
downward.
leftward.
reaches
its new
Output
Outputrises,
and
DADt – 1
target.
inflation
inflationfalls.
fall.
DASt -1, t
DASt +1
C
Z
DADt, t + 1,…
Yt
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The dynamic response to a reduction in
target inflation
The
demand
shock
raises the
real interest
rate.
After the
shock ends,
the real
interest
rate falls
and
approaches
its initial
level.
Yt –1 ,
Yfinal
Y
Dynamic AD-AS Model
39
The dynamic response to a reduction in
target inflation
Reducing
the target
inflation
rate
causes
output to
fall below
its natural
level for a
while.
Output
recovers
gradually.
 t*
t
Because
expectations
adjust
slowly,
it takes
many
periods for
inflation to
reach the
new target.
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The dynamic response to a reduction in
target inflation
The dynamic response to a reduction in
target inflation
To reduce
inflation,
the central
bank raises
the real
interest rate
to reduce
aggregate
demand.
The real
interest rate
gradually
returns to its
natural rate.
 t*
rt
 t*
it
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.
APPLICATION:
APPLICATION:
Output variability vs. inflation variability
Output variability vs. inflation variability
 A supply shock reduces output (bad)
CASE 1: θπ is large, θY is small
and raises inflation (also bad).
π
 The central bank faces a tradeoff between these
A supply shock
shifts DAS up.
DASt
“bads” – it can reduce the effect on output,
b t only
but
l b
by ttolerating
l ti an iincrease iin th
the effect
ff t
on inflation….
DASt – 1
πt
πt –1
DADt – 1, t
Yt
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Dynamic AD-AS Model
44
CHAPTER 14
Yt –1
Dynamic AD-AS Model
Y
In this case, a
small change in
inflation has a
large effect on
output, so DAD
is relatively flat.
The shock has
a large effect
on output, but
a small effect
on inflation.
APPLICATION:
APPLICATION:
Output variability vs. inflation variability
The Taylor Principle
 The Taylor Principle (named after John Taylor):
CASE 2: θπ is small, θY is large
π
DASt
πt
DASt – 1
πt –1
DADt – 1, t
Yt Yt –1
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Dynamic AD-AS Model
Y
45
The proposition that a central bank should
respond to an increase in inflation with an even
greater increase in the nominal interest rate
((so that the real interest rate rises).
)
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
Now, the shock
has only a small
effect on output,
but a big effect
on inflation.
be unstable, and inflation may spiral out of control.
46
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Dynamic AD-AS Model
47
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11/6/2013
APPLICATION:
APPLICATION:
The Taylor Principle

1
( t   t* ) 
Yt  Yt 
t
1  Y
1  Y
The Taylor Principle

1
( t   t* ) 
Yt  Yt 
t
1  Y
1  Y
it   t     ( t   t* )  Y (Yt  Yt )
(DAD)
(MP rule)
it   t     ( t   t* )  Y (Yt  Yt )
(DAD)
(MP rule)
If θπ > 0:
0
If θπ < 0:
0
 When inflation rises, the central bank increases the
 When inflation rises, the central bank increases
nominal interest rate even more, which increases
the real interest rate and reduces the demand for
goods & services.
the nominal interest rate by a smaller amount.
The real interest rate falls, which increases the
demand for goods & services.
 DAD has a negative slope.
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Dynamic AD-AS Model
 DAD has a positive slope.
48
APPLICATION:
relationships: an IS-curve-like equation of the
goods market, the Fisher equation, a Phillips
curve equation, an equation for expected
at o , and
a d a monetary
o eta y po
policy
cy rule.
ue
inflation,
 Estimates of θπ from published research:
 The long-run equilibrium of the model is
 θπ = –0.14 from 1960-78, before Paul Volcker
classical. Output and the real interest rate are
at their natural levels, independent of monetary
policy. The central bank’s inflation target
determines inflation, expected inflation, and the
nominal interest rate.
became Fed chairman. Inflation was high during
this time, especially during the 1970s.
 θπ = 0.72 during the Volcker and Greenspan years.
Inflation was much lower during these years.
Chapter Summary
 The DAD-DAS model can be used to
determine the immediate impact of any shock
on the economy, and can be used to trace out
the effects of the shock over time.
 The parameters of the monetary policy rule
influence the slope of the DAS curve, so they
determine whether a supply shock has a
greater effect on output or inflation. Thus, the
central bank faces a tradeoff between output
variability and inflation variability.
49
 The DAD-DAS model combines five
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).
Dynamic AD-AS Model
Dynamic AD-AS Model
Chapter Summary
The Taylor Principle
 If DAD is upward-sloping and steeper than DAS,
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50
Chapter Summary
 The DAD-DAS model assumes that the Taylor
Principle holds, 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.
9