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A dynamic approach to short run economic fluctuations. The DAD/DAS model Part 3 The long run equilibrium & short run fluctuations.
A dynamic approach to short run economic fluctuations. The DAD/DAS
model
Part 3
The long run equilibrium & short run fluctuations.
The DAD-DAS model’s long-run equilibrium
• Recall the long-run equilibrium values in the DAD-DAS theory (in the LR the shocks are zero!):
t tY Y
tr *
t t *
1t t tE *
t ti
In the short-run, the values of the various variables fluctuate around the long-run equilibrium values.
Long run growth
• Suppose that the economy is its long run equilibrium, when…
• …natural (long-run) level of GDP increases
Long-run growth
Y
π
DASt
y t
DADt
A
yt
Period t + 1: Long-run growth increases the natural rate of output.
yt +1
DASt +1
DADt +1
B
πt + 1
πt
=
New equilibrium at B. Income grows but inflation remains stable. yt +1
Period t : Equilibrium:
*
t
tyy
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
Supply Shock
• Suppose the economy is in long-run equilibrium
• The supply shock hits for one period (νt > 0) and then goes away (νt+1 = 0)
• Note that from the definition of a shock, we know that the long run equilibrium values are unchanged
• How will the economy be affected, both in the short run and in the long run?
What is a supply shock anyway?
• A temporary shock to costs of production.
• For an interesting discussion on what is and what isn’t a supply shock, see:
• http://gregmankiw.blogspot.com/2009/04/what-are-supply-shocks.html
A shock to aggregate supply
Period t – 1: initial equilibrium at A
π *= πt – 1
Yt –1
Period t: Supply shock (νt > 0) shifts DAS upward; inflation rises, central bank responds by raising real interest rate, output falls.
Period t + 1: Supply shock is over (νt+1 = 0) but DAS does not return to its initial position due to higher inflation expectations.
Y
π
DASt -1
Y
DAD
A
DASt
Yt
B πt
DASt +1
C
DASt +2
D
Yt + 2
πt + 2
This process continues until output returns to its natural rate. The long run equilibrium is at A.
νt
πt + 1
The dynamic response to a supply shock
tY
t
A one-period
supply shock
affects output
for many
periods.
t
tBecause
inflation
expectations
adjust slowly,
actual inflation
remains high for
many periods.
The dynamic response to a supply shock
ti
t
The behavior
of the
nominal
interest
rate depends
on that
of inflation
and real
interest rates.
The dynamic response to a supply shock
Aggregate Demand Shocks
• Suppose the economy is at the long-run equilibrium
• Then a positive aggregated demand shock hits the economy for one period (εt> 0), and then goes away (εt+1 = 0)
• How will the economy be affected in the short run?
• That is, how will the economy adjust over time?
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One-period demand shock
π*=πt – 1
Y
π
DASt -1,t
Y
DADt
DADt -1,t+1, t+2…
Yt –1
A
DASt + 1
C
DASt +2
D
Yt
B πt
Yt+2
πt+2
Period t: A demand shock(εt>0) shifts DAD. DAS does not change: inflation goes up, the central bank increases the interest rate.
Period t+1: An increase in expected inflation shifts the DAS; while DAD comes back to its previous position (εt+1=0).
-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
1,5
2,0
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
One period demand shock: reaction functions
tY
t
14 99,0
99,5
100,0
100,5
101,0
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
1,5
1,6
1,7
1,8
1,9
2,0
2,1
2,2
2,3
2,4
2,5
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
t
t
15
-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
1,5
2,0
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
One period demand shock: reaction functions
tr
16
3,0
3,5
4,0
4,5
5,0
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
1,5
1,7
1,9
2,1
2,3
2,5
2,7
2,9
t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12
ti
One period demand shock: reaction functions
Aggregate Demand Shocks
• Suppose the economy is at the long-run equilibrium
• Then a positive aggregated demand shock hits the economy for three successive periods (εt= εt+1= εt+2> 0), and then goes away (εt+3 = 0)
• How will the economy be affected in the short run?
• That is, how will the economy adjust over time?
A 3-period shock to aggregate demand
Period t – 1: initial equilibrium at A
πt – 1
Y
π
DASt -1,t
Y
DADt ,t+1,t+2
DADt -1, t+3
Yt –1
A
DASt + 1
C
DASt +2 D
Yt
B πt
Yt +3
G πt + 3
Period t: Positive demand shock (ε > 0) shifts DAD to the right; output and inflation rise.
Period t + 1 (and t+2): Higher inflation in t raised inflation expectations for t + 1, shifting DAS up. Inflation rises more, output falls.
Periods t + 3 : DAD returns to its old level - recession in G.
DASt +3
After the shock
• From point G the economy – by adjustments of the dynamic aggregate supply – returns to the old equilibrium
3-period demand shock.
π1999 = π00
Y
π Y
Y00
A
C
Y01
B π01
D
π02
π03
Y02 Y03 Y05 Y04
π04 π05 F
E
π
unemployment
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USA: Inflation and unemployment
Źródło: https://krugman.blogs.nytimes.com/2012/04/08/unemployment-and-inflation/
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Inflation (upper graph) & GDP growth (lower graphs) after the famous „500+” policy of the Polish government (April 2016) – a shock to DAD?
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500+
• The problem with „500+” program (fiscal policy) is that we probably cannot call it a „shock” – as this change is probably permanent…(no government will have to courage to end this program)
• We will think, what are the likely consequences of a permanent change like „500+” next week
• But for now, we let’s assume that this is a true „shock” (i.e. will go away) and we are in the middle of it (so it is still not zero)
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 long-run equilibrium?
A shift in monetary policy Period t – 1: target inflation rate π* = 2%, initial equilibrium at A
πt – 1 = 2%
Yt –1
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.
Y
π DASt -1, t
Y
DADt – 1
A
DADt, t + 1,…
DASfinal
Yt
πt B
DASt +1
C
Subsequent periods: This process continues until output returns to its natural rate and inflation reaches its new target.
Z πfinal = 1%
,
Yfinal
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 CB increases the nominal interest (according to the
simple monetary policy rule) – 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 long-run level (i = ρ + π*)
The dynamic response to a reduction in target inflation
tY
*
t
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
tr
*
t
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
ti
*
t
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,
Y
π
DADt – 1, t
DASt
DASt – 1
Yt –1
πt –1
Yt
πt
A supply shock
shifts DAS up. 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:
Output variability vs. inflation variability
CASE 2: θπ is small,
Y
π
DADt – 1, t
DASt
DASt – 1
Yt –1
πt –1
Yt
πt
In this case, a
large change in
inflation has only
a small effect on
output, so DAD
is relatively steep.
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 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
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.
• DAD has a negative slope.
(DAD)
(MP rule) *
tttti
tttt
yy
*)(
APPLICATION:
The Taylor Principle
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 & services.
• DAD has a positive slope.
(DAD)
(MP rule)
tttt
yy
*)(
*
tttti
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.
A positively sloped DAD
A positively sloped DAD
• The effect: very unstable, rising inflation (with both demand and supply shocks )
• There is evidence that before the Vockler era (1979), in the US, the response of the Fed to inflation was too weak (the nominal interest rate did not rise „enough”, so that as inflation increases, so did the real interest rate), what has caused a double digit inflation (see the „Case Study” in Mankiw).
• In the 1980’s the reactions of the Fed changed
Anchored expectations
• Ball & Mazumder (2015) argue that inflation expectations were „anchored” at 2%.
• This implies that DAS does not shift and that the relationship between high unemployment and falling inflation is lost (that’s how the aithors explain the shape of the green line on the graph)
USA: Inflation and unempolyment
Źródło: https://krugman.blogs.nytimes.com/2012/04/08/unemployment-and-inflation/
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Conclusions
• Transitory shocks may have longer lasting effects on the economy
• Eventually however, the economy returns to its long run equilibrium; with LR output determined by the factors of production (K, N, A) & target inflation set by the central bank
• The DAD/DAS model is in fact an introduction to DSGE models used by central banks & other institutions to predict & analyze policy changes
