Download A Dynamic Model of Aggregate Demand and Aggregate Supply

A Dynamic Model of Aggregate
Demand and Aggregate Supply
Chapter 14 of Macroeconomics, 7th
edition, by N. Gregory Mankiw
ECO62 Udayan Roy
Inflation and dynamics in the short run
• So far, to analyze the short run we have used
– the Keynesian Cross theory, and
– the IS-LM theory
• Both theories are silent about inflation and
dynamics
• In this chapter, that silence will end
• This chapter presents a dynamic model of
aggregate demand and aggregate supply
(DAD-DAS)
Introduction
• The dynamic model of aggregate demand and
aggregate supply (DAD-DAS) gives us more insight
into how the economy behaves in the short run.
• This theory determines both real GDP (Y) and the
inflation rate (π)
• This theory is dynamic in the sense that the
outcome in one period affects the outcome in the
next period
– like the Solow-Swan model, but for the short run
Introduction
• Instead of representing monetary policy by an
exogenous money supply, the central bank will
now be seen as following a monetary policy rule
that adjusts interest rates automatically when
output or inflation are not where they should be.
Introduction
Keeping track of time
• The subscript “t ” denotes a 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.
E.g., if t = 2008, then
– Yt = Y2008 = real GDP in 2008
– Yt − 1 = Y2007 = real GDP in 2007
– Yt + 1 = Y2009 = real GDP in 2009
The model’s elements
• The model has five equations and five
endogenous variables:
– output, inflation, the real interest rate, the
nominal interest rate, and expected inflation.
• The first equation is for output…
Output:
The Demand for Goods and Services
Yt  Yt   (rt   )   t
output
natural
level of
output
real
interest
rate
  0,   0
Assumption: There is a negative relation between
output (Yt) and interest rate (rt). The justification is the
same as for the IS curve of Ch. 10.
Output:
The Demand for Goods and Services
Yt  Yt   (rt   )   t
measures the
interest-rate
sensitivity of
demand
“natural rate of
interest”
This is the long-run real
interest rate we had
calculated in Ch. 3
Note that in the absence of demand shocks,
Yt  Yt when rt  
demand
shock,
random and
zero on
average
The demand shock is
positive when C0, I0, or G
is higher than usual or T
is lower than usual.
IS Curve = Demand Equation
r
rt
IS
Y
Yt
r
rt
The long-run real interest rate of Ch. 3 is now
denoted by the lower-case Greek letter ρ.
IS
Yt
Y
IS Curve = Demand Equation
r
rt
IS
Y
Yt
r
rt
IS
Yt
Y
The Real Interest Rate: The Fisher Equation
ex ante
(i.e. expected)
real interest
rate
rt  it  Et  t 1
nominal
interest
rate
expected
inflation rate
Assumption: The real interest rate is the inflation-adjusted
interest rate. To adjust the nominal interest rate for inflation, one
must simply subtract the expected inflation rate during the
duration of the loan.
The Real Interest Rate: The Fisher Equation
ex ante
(i.e. expected)
real interest
rate
 t 1 
rt  it  Et  t 1
nominal
interest
rate
expected
inflation rate
increase in price level from 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
We saw this before in Ch. 4
Inflation: The Phillips Curve
 t  Et 1  t   (Yt  Yt )   t
current
inflation
previously
expected
inflation
  0 indicates how much
inflation responds when
output fluctuates around
its natural level
supply
shock,
random and
zero on
average
Phillips Curve
 t  Et 1 t    Yt  Yt   t
• Assumption: At any particular time, inflation
would be high if
– people in the past were expecting it to be high
– current demand is high (relative to natural GDP)
– there is a high inflation shock. That is, if prices are
rising rapidly for some exogenous reason such as
scarcity of imported oil or drought-caused scarcity
of food
Phillips Curve
 t  Et 1 t    Yt  Yt   t
Momentum
inflation
Demandpull
inflation
Cost-push
inflation
Expected Inflation: Adaptive Expectations
Et  t 1   t
Assumption: people expect
prices to continue rising at the
current inflation rate.
Examples: E2000π2001 = π2000; E2010π2011 = π2010; etc.
Monetary Policy Rule
• The fifth and final main assumption of the
DAD-DAS theory is that
• The central bank sets the nominal interest rate
• and, in setting the nominal interest rate, the
central bank is guided by a very specific
formula
Monetary Policy Rule
Current
inflation
rate
Parameter that
measures how
strongly the
central bank
responds to the
inflation gap

Parameter that
measures how
strongly the
central bank
responds to
the GDP gap

it   t       t    Y  Yt  Yt 
Nominal
interest
rate, set
each period
by the
central bank
Natural real
interest rate
*
t
Inflation Gap: The
excess of current
inflation over the
central bank’s
inflation target
GDP Gap: The
excess of current
GDP over natural
GDP
Example: The Taylor Rule
• Economist John Taylor proposed a monetary policy rule
very similar to ours:
iff =  + 2 + 0.5( – 2) – 0.5(GDP gap)
where
– iff = nominal federal funds rate target
Y Y
Y
= percent by which real GDP is below its natural rate
– GDP gap = 100 x
• The Taylor Rule matches Fed policy fairly well.…
CASE STUDY
10
9
8
Percent
7
The Taylor Rule
actual
Federal
Funds rate
6
5
4
3
2
1
Taylor’s
rule
0
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
SUMMARY OF THE DAD-DAS
MODEL
The model’s variables and parameters
• Endogenous variables:
Yt  Output
t 
Inflation
rt  Real interest rate
it  Nominal interest rate
Et  t 1  Expected inflation
The model’s variables and parameters
• Exogenous variables:
Yt  Natural level of output

*
t
 Central bank’s target inflation rate
t 
Demand shock
t 
Supply shock
• Predetermined variable:
 t 1 
Previous period’s inflation
The model’s variables and parameters
• Parameters:
  Responsiveness of demand to
the real interest rate
  Natural rate of interest
  Responsiveness of inflation to
output in the Phillips Curve
 
Y 
Responsiveness of i to inflation
in the monetary-policy rule
Responsiveness of i to output
in the monetary-policy rule
The DAD-DAS Equations
Yt  Yt    (rt   )   t
Demand Equation
rt  it  Et t 1
Fisher Equation
 t  Et 1 t    Yt  Yt   t Phillips Curve
Et t 1   t
Adaptive Expectations


it   t       t    Y  Yt  Yt 
*
t
Monetary Policy Rule
THE LONG RUN EQUILIBRIUM
The DAD-DAS model’s long-run
equilibrium
• This is the normal state around which the
economy fluctuates.
• The economy is in long-run equilibrium when:
t   t  0
– There are no shocks:
– Inflation is stable:
 t 1   t
The DAD-DAS model’s long-run
equilibrium
Et t 1   t Adaptive Expectations
Et 1 t   t 1
 t  Et 1 t    Yt  Yt   t
Phillips Curve
 t   t 1    Yt  Yt   t
Recall that the long-run
equilibrium requirements are:
t   t  0
DAS Curve
 t 1   t
The DAD-DAS model’s long-run
equilibrium
Yt  Yt    (rt   )   t
Recall that the long-run equilibrium
requirements include:
Demand Equation
t   t  0
The DAD-DAS model’s long-run
equilibrium
Fisher Equation
Adaptive Expectations
rt  it  Et t 1
Et t 1   t
Therefore, in the DAD-DAS theory, the
(ex ante) real interest rate is the
current nominal interest rate minus
the inflation rate just observed.
rt  it   t
The DAD-DAS model’s long-run
equilibrium
rt  it  Et t 1
Et t 1   t
rt  it   t
  it   t
   t  it


Monetary Policy Rule
it   t       t    Y  Yt  Yt 
*
t
The DAD-DAS model’s long-run
equilibrium
• To summarize, the long-run equilibrium values in the
DAD-DAS theory are essentially the same as the long
run theory we saw earlier in this course:
Yt  Yt
rt  
*
t  t
Et  t 1  
*
it     t
*
t
SHORT-RUN FLUCTUATIONS
AROUND THE LONG RUN
Recap: Dynamic Aggregate Supply
 t  Et 1 t    Yt  Yt   t
Et t 1   t
Et 1 t   t 1
 t   t 1    Yt  Yt   t
Phillips Curve
Adaptive Expectations
DAS Curve
The Dynamic Aggregate Supply Curve
 t   t 1   (Yt  Yt )   t
π
DAS slopes upward:
high levels of output
are associated with
high inflation.
DASt
 t 1  t
Y
Yt
The Dynamic Aggregate Supply Curve
 t   t 1   (Yt  Yt )   t
π
DAS2011
 2010  2011
If you know (a) the
natural GDP at a
particular date, (b) the
inflation shock at that
date, and (c) the
previous period’s
inflation, you can figure
out the location of the
DAS curve at that date.
Y
Y2011
The Dynamic Aggregate Supply Curve
 t   t 1   (Yt  Yt )   t
π
DAS2015
 2014  2015
If you know (a) the
natural GDP at a
particular date, (b) the
inflation shock at that
date, and (c) the
previous period’s
inflation, you can figure
out the location of the
DAS curve at that date.
Y
Y2015
Shifts of the DAS Curve
 t   t 1   (Yt  Yt )   t
π
Any increase (decrease)
in the previous period’s
inflation or in the
current period’s inflation
shock shifts the DAS
curve up (down) by the
same amount
DASt
 t 1  t
Y
Yt
Shifts of the DAS Curve
 t   t 1   (Yt  Yt )   t
π
Any increase (decrease)
in the previous period’s
inflation or in the
current period’s inflation
shock shifts the DAS
curve up (down) by the
same amount
DASt
 t 1  t
Any increase (decrease)
in natural GDP shifts the
DAS curve right (left) by
the exact amount of the
change.
Y
Yt
The Dynamic Aggregate Demand Curve
The Demand Equation
Yt  Yt   (rt   )   t
rt  it  Et t 1
Fisher equation
Yt  Yt   ( it  Et  t 1   )   t
Yt  Yt   ( it   t   )   t
Et t 1   t
adaptive
expectations
The Dynamic Aggregate Demand Curve


it   t       t    Y  Yt  Yt 
*
t
monetary policy rule
Yt  Yt   ( it   t   )   t
Yt  Yt   [  t     ( t   t* )  Y (Yt  Yt )   t   ]   t
Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
We’re almost there!
Dynamic Aggregate Demand
Yt  Yt   [ ( t   t* )  Y (Yt  Yt )]   t
Yt  Yt    ( t   )  Y Yt  Y Yt   t
*
t
Yt  Y Yt  Yt    ( t   )  Y Yt   t
*
t
(1  Y )  Yt  (1  Y )  Yt    ( t   )   t
*
t

1
*
Yt  Yt 
 ( t   t ) 
t
1  Y
1  Y
Yt  Yt  A  ( t   )  B t
*
t
This is the
equation of
the DAD curve!
The Dynamic Aggregate Demand Curve
π
Yt  Yt  A( t   )  B t
*
t
DAD slopes downward:
When inflation rises, the central bank
raises the real interest rate, reducing the
demand for goods and services.
DADt
Y
Note that the DAD equation
has no dynamics in it, because
it only shows how
simultaneously measured
variables are related to each
other
The Dynamic Aggregate Demand Curve
π
Yt  Yt  A( t   )  B t
*
t
 t*
DADtB
Yt  B t
Y
The Dynamic Aggregate Demand Curve
π
Yt  Yt  A( t   )  B t
*
t
When the central bank’s target inflation rate
increases (decreases) the DAD curve moves up
(down) by the exact same amount.
 t*
DADtA
DADtB
Yt  B t
Y
The Dynamic Aggregate Demand Curve
π
Yt  Yt  A( t   )  B t
*
t
When the natural rate of output increases
(decreases) the DAD curve moves right (left)
by the exact same amount.
 t*
DADtA
When there is a positive (negative) demand
shock the DAD curve moves right (left) .
DADtB
Yt  B t
Y
A positive demand shock
could be an increase in C0,
I0, or G, or a decrease in T.
The Dynamic Aggregate Demand Curve
π

1
*
Yt  Yt 
 ( t   t ) 
t
1  Y
1  Y
DADtA
DADtB
The DAD curve shifts right or
up if:
(a) the central bank’s target
inflation rate goes up,
(b) there is a positive demand
shock, or
(c) the natural rate of output
increases.
Y
Summary: DAD-DAS Slopes and Shifts
DAS
• Upward sloping
• If natural output increases,
shifts right by same amount
• If previous-period inflation
increases, shifts up by same
amount
• If there is a positive inflation
shock (νt > 0), shifts up by
same amount
DAD
• Downward sloping
• If natural output increases,
shifts right by same amount
• If target inflation increases,
shifts up by same amount
• If there is a positive demand
shock (εt > 0), shifts right
DAD-DAS EQUILIBRIUM
The short-run equilibrium
π
Yt
DASt
πt
A
In each period, the
intersection of DAD and
DAS determines the shortrun equilibrium values of
inflation and output.
DADt
Yt
Y
In the equilibrium
shown here at A,
output is below its
natural level. In other
words, the DAD-DAS
theory is fully
capable of explaining
recessions and
booms.
DAD-DAS PREDICTIONS
Long-Run Growth
Recap: DAD-DAS Slopes and Shifts
DAS
• Upward sloping
• If natural output increases,
shifts right by same
amount
• If previous-period inflation
increases, shifts up by same
amount
• If there is a positive inflation
shock (νt > 0), shifts up by
same amount
DAD
• Downward sloping
• If natural output increases,
shifts right by same
amount
• If target inflation increases,
shifts up by same amount
• If there is a positive demand
shock (εt > 0), shifts right
Long-run growth
Yt
π
πt
=
πt + 1
A
DASt +1
B
DADt
Yt
Period t + 1: Long-run
growth increases the
natural rate of output.
Yt +1
DASt
Yt +1
Period t: initial
equilibrium at A
DADt +1
Y
DAS shift right by the
exact amount of the
increase in natural
GDP.
DAD shifts right too by
the exact amount of
the increase in natural
GDP.
New equilibrium at B.
Income grows but
inflation remains stable.
Long-Run Growth
• Therefore, starting from long-run equilibrium,
if there is an increase in the natural GDP,
– actual GDP will immediately increase to the new
natural GDP, and
– none of the other endogenous variables will be
affected
Inflation Shock
• Suppose the economy is in long-run
equilibrium
• Then the inflation shock hits for one period (νt
> 0) and then goes away (νt+1 = 0)
• How will the economy be affected, both in the
short run and in the long run?
A shock to
Period t + 2: As inflation falls,
inflation expectations fall, DAS
aggregate supply
moves downward, output rises.
Y
π
πt
πt + 2
B
C
D
DASt
DASt +1
DASt +2
DASt -1
Period t + 1: Supply
shock is over (νt+1 = 0)
but DAS does not return
to its initial position due
to higher inflation
expectations.
Period t: Supply shock (νt > 0) shifts
πt – 1
DAS upward; inflation rises, central
A
bank responds by raising real
DAD interest rate, output falls.
Y This process continues
Yt Yt + 2 Yt –1
until output returns to
Period t – 1: initial
its natural rate. The long
equilibrium at A
run equilibrium is at A.
A shock to aggregate supply: one
more time
Y
π
DAS2002
DAS2003
DAS2004
π2001 + ν2002
π2002
π2003
π2004
B
C
D
π2000 = π2001
ν2002
DAS2001
A
DAD
Y04
Y02 Y03
Y01
Y
Inflation Shock
• So, we see that if a one-period inflation shock
hits the economy,
– inflation rises at the date the shock hits, but then
returns to the unchanged long-run level, and
– GDP falls at the date the shock hits, but then
returns to the unchanged long-run level
• What happens to the interest rates i and r?
Inflation Shock

 

      Y  Y 
    Y  Y 
it   t       t   t*  Y  Yt  Yt 
it   t    

rt       t  
t
*
t
*
t
Y
Y
t
t
t
t
• According to the monetary policy rule, the temporary
spike in inflation dictates an increase in the real
interest rate, whereas the temporary fall in GDP
indicates a decrease in the real interest rate
• The overall effect is ambiguous, for both interest rates
• We can do simulations for specific values of the
parameters and exogenous variables
Parameter values for simulations
Yt  100
  2.0
*
t
  1.0
  2.0
  0.25
  0.5
Y  0.5
The central bank’s inflation target is 2 percent.
A 1-percentage-point increase in the real interest
rate reduces output demand by 1 percent of its
natural level.
The natural rate of interest is 2 percent.
When output is 1 percent 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.
Impulse Response Functions
• The following graphs are called impulse
response functions.
• They show the “response” of the endogenous
variables to the “impulse,” i.e. the shock.
• The graphs are calculated using our assumed
values for the exogenous variables and
parameters
The dynamic response to a supply shock
t
A one-period
supply shock
affects output
for many
periods.
Yt
The dynamic response to a supply shock
t
t
Because
inflation
expectations
adjust slowly,
actual inflation
remains high for
many periods.
The dynamic response to a supply shock
t
rt
The real
interest rate
takes many
periods to
return to its
natural rate.
The dynamic response to a supply shock
t
it
The behavior
of the
nominal
interest
rate depends
on that
of inflation
and real
interest rates.
A Series of Aggregate Demand Shocks
• Suppose the economy is al the long-run
equilibrium
• Then a positive aggregated demand shock hits
the economy for five successive periods (ε >
0), and then goes away (ε = 0)
• How will the economy be affected in the short
run?
• That is, how will the economy adjust over
time?
Recap: DAD-DAS Slopes and Shifts
DAS
• Upward sloping
• If natural output increases,
shifts right by same amount
• If previous-period inflation
increases, shifts up by same
amount
• If there is a positive inflation
shock (νt > 0), shifts up by
same amount
DAD
• Downward sloping
• If natural output increases,
shifts right by same amount
• If target inflation increases,
shifts up by same amount
• If there is a positive
demand shock (εt > 0),
shifts right
A shock to aggregate
π
πt + 5
G
πt
πt – 1
Yt + 5
Period t – 1: initial
demandequilibrium at A
Period t: Positive demand
DASt +5
shock (ε
shifts AD
to the
Period
t +>1:0)Higher
inflation
Y
right;
output
and inflation
DASt +4
in
t raised
Periods
t +inflation
2 to t + 4:
rise.
forint +previous
1,
Higher inflation
DASt +3 expectations
F
shifting
DAS up.
Inflation
period
raises
inflation
DASt +2 rises more, output falls.
expectations, shifts DAS up.
E
Period t +rises,
5: DAS
is higher
output
falls.
DASt + 1 Inflation
D
due to higher inflation in
C
DASt -1,t preceding period, but
demand shock ends and
B
DADPeriods
returnstto
initial
+ 6itsand
higher:
position.
Equilibrium
at G.
DAS gradually
shifts
DADt ,t+1,…,t+4 down as inflation and
A
inflation expectations
DADt -1, t+5
fall. The economy
Y
gradually recovers and
Yt –1
Yt
reaches the long run
equilibrium at A.
A 3-period shock to aggregate demand
π
DAS04
Y
DAS03
π03
π02
C
π01
π1999 = π00
DAS02
D
DAS00,01
B
DAD01,02,03
A
DAD00,04
Y00
Y03 Y02Y01
Y
When the demand shock first hits, output and inflation both increase. In the two
following periods, despite the continuing presence of the demand shock, output starts
to fall. Inflation continues to rise.
A shock to aggregate demand
π
DAS04
DAS05
DAS06
Y
π03
π04
π05
π1999 = π00
DAS00,01
A
DAD00,04,05,06
Y04Y05 Y00
Y
On the date the demand shock ends, output falls below the long-run level and inflation
finally begins to fall. After that, output rises and inflation falls towards the initial longrun equilibrium.
A Series of Aggregate Demand Shocks:
4 Phases
1. On the date the multi-period demand shock first
hits, both output and inflation rise above their
long-run values
2. After that, while the demand shock is still
present, output falls and inflation continues to
rise
3. On the date the demand shock ends, output falls
below its long-run value and inflation falls
4. After that, output recovers and inflation falls,
gradually returning to their original long-run
values
• What happens to the interest rates i and r?
Inflation Shock

 

      Y  Y 
    Y  Y 
it   t       t   t*  Y  Yt  Yt 
it   t    

rt       t  
t
*
t
*
t
Y
Y
t
t
t
t
• According to the monetary policy rule, an
increase (decrease) in either inflation or output
dictates an increase (decrease) in the real interest
rate
• We can do simulations for specific values of the
parameters and exogenous variables
A Series of Aggregate Demand Shocks:
4 Phases, interest rates
1. On the date the multi-period demand shock first hits,
both output and inflation rise above their long-run
values. So, interest rate rises
2. After that, while the demand shock is still present,
output falls and inflation continues to rise. Now, the
effect on the interest rate is ambiguous
3. On the date the demand shock ends, output falls
below its long-run value and inflation falls. So, the
interest rate falls
4. After that, output recovers and inflation falls,
gradually returning to their original long-run values.
Again, the effect on the interest rate is ambiguous,
but it does return to its original long run value (ρ)
The dynamic response to a demand shock
t
Yt
The demand
shock raises
output for five
periods.
When the
shock ends,
output falls
below its
natural level,
and recovers
gradually.
The dynamic response to a demand shock
t
t
The
demand shock
causes
inflation
to rise.
When the
shock ends,
inflation
gradually falls
toward its
initial level.
The dynamic response to a demand shock
t
rt
The demand
shock raises
the real
interest rate.
After the
shock ends,
the real
interest
rate falls and
approaches 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.
Stricter Monetary Policy
• Suppose an economy is initially at its long-run
equilibrium
• Then its central bank becomes less tolerant of
inflation and reduces its target inflation rate
(π*) from 2% to 1%
• What will be the short-run effect?
• How will the economy adjust to its new longrun equilibrium?
Recap: DAD-DAS Slopes and Shifts
DAS
• Upward sloping
• If natural output increases,
shifts right by same amount
• If previous-period inflation
increases, shifts up by same
amount
• If there is a positive inflation
shock (νt > 0), shifts up by
same amount
DAD
• Downward sloping
• If natural output increases,
shifts right by same amount
• If target inflation increases,
shifts up by same amount
• If there is a positive demand
shock (εt > 0), shifts right
A shift in monetary
Y
π
πt – 1 = 2%
πt
Period t – 1: target
inflation rate π* = 2%,
policy
initial equilibrium at A
DASt -1, t
DASt +1
A
B
C
πfinal = 1%
DASfinal
Z
DADt – 1
DADt, t + 1,…
Yt
Yt –1 ,
Yfinal
Y
Period t: Central bank
lowers target to π* =
1%, raises real interest
rate, shifts DAD
leftward. Output and
inflation fall.
Period t + 1: The fall in
πt reduced inflation
expectations for t + 1,
shifting DAS
downward. Output
rises, inflation falls.
Subsequent periods:
This process continues
until output returns to
its natural rate and
inflation reaches its
new target.
Stricter Monetary Policy
• At the date the target inflation is reduced, output falls
below its natural level, and inflation falls too towards
its new target level
– The real interest rate rises above its natural level (ρ)
– The effect on the nominal interest rate (i = r + π) is
ambiguous
• On the following dates, output recovers and gradually
returns to its natural level. Inflation continues to fall
and gradually approaches the new target level.
– The real interest rate falls, gradually returning to its natural
level (ρ)
– The nominal interest rate falls to its new and lower longrun level (i = ρ + π*)
The dynamic response to a reduction in
target inflation
 t*
Yt
Reducing the
target
inflation rate
causes output
to fall below
its natural
level for a
while.
Output
recovers
gradually.
The dynamic response to a reduction in
target inflation
 t*
t
Because
expectations
adjust slowly,
it takes many
periods for
inflation to
reach the
new target.
The dynamic response to a reduction in
target inflation
 t*
rt
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.
The dynamic response to a reduction in
target inflation
 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:
Output variability vs. inflation variability
• A supply shock reduces output (bad)
and raises inflation (also bad).
• The central bank faces a tradeoff between
these “bads” – it can reduce the effect on
output,
but only by tolerating an increase in the effect
on inflation….
APPLICATION:
Output variability vs. inflation variability
CASE 1: θπ is large, θY is small
π
A supply shock
shifts DAS up.
DASt
DASt – 1
πt
In this case, a small
change in inflation has
a large effect on
output, so DAD
is relatively flat.
πt –1
DADt – 1, t
Yt
Yt –1
Y
The shock has a large
effect on output, but a
small effect on
inflation.
APPLICATION:
Output variability vs. inflation variability
CASE 2: θπ is small, θY is large
π
DASt
πt
DASt – 1
In this case, a large
change in inflation has
only a small effect on
output, so DAD is
relatively steep.
πt –1
DADt – 1, t
Yt Yt –1
Y
Now, the shock has
only a small effect on
output, but a big effect
on inflation.
APPLICATION:
The Taylor Principle
• The Taylor Principle (named after economist 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 (so that the real
interest rate rises). I.e., central bank should set θπ > 0.
• Otherwise, DAD will slope upward, economy may be
unstable, and inflation may spiral out of control.
APPLICATION:
The Taylor Principle

1
*
Yt  Yt 
( t   t ) 
t
1  Y
1  Y
it   t     ( t   t* )  Y (Yt  Yt )
(DAD)
(MP rule)
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 and
services.
• DAD has a negative slope.
APPLICATION:
The Taylor Principle

1
*
Yt  Yt 
( t   t ) 
t
1  Y
1  Y
it   t     ( t   t* )  Y (Yt  Yt )
(DAD)
(MP rule)
If θπ < 0:
• When inflation rises, the central bank increases
the nominal interest rate by a smaller amount.
The real interest rate falls, which increases the demand
for goods and services.
• DAD has a positive slope.
APPLICATION:
The Taylor Principle
• 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).
• Estimates of θπ from published research:
– θπ = – 0.14 from 1960-78, before Paul Volcker 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.