A dynamic approach to short run economic fluctuations. The...

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A dynamic approach to short run economic fluctuations. The DAD/DAS

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

1t t tE *

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

Period t + 1: Long-run growth increases the natural rate of output.

DASt +1

DADt +1

πt + 1

New equilibrium at B. Income grows but inflation remains stable. yt +1

Period t : Equilibrium:

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.

DASt -1

DASt +1

DASt +2

Yt + 2

πt + 2

This process continues until output returns to its natural rate. The long run equilibrium is at A.

πt + 1

The dynamic response to a supply shock

A one-period

supply shock

affects output

for many

periods.

tBecause

inflation

expectations

adjust slowly,

actual inflation

remains high for

many periods.

The behavior

of the

nominal

interest

rate depends

on that

of inflation

and real

interest rates.

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?

One-period demand shock

π*=πt – 1

DASt -1,t

DADt -1,t+1, t+2…

Yt –1

DASt + 1

DASt +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).

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

14 99,0

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

DASt -1,t

DADt ,t+1,t+2

DADt -1, t+3

Yt –1

DASt + 1

DASt +2 D

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

B π01

Y02 Y03 Y05 Y04

π04 π05 F

unemployment

USA: Inflation and unemployment

Źródło: https://krugman.blogs.nytimes.com/2012/04/08/unemployment-and-inflation/

Inflation (upper graph) & GDP growth (lower graphs) after the famous „500+” policy of the Polish government (April 2016) – a shock to DAD?

• 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.

π DASt -1, t

DADt – 1

DADt, t + 1,…

DASfinal

DASt +1

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

Reducing the

target

inflation rate

causes output

to fall below

its natural

level for a

while.

Output

recovers

gradually.

t Because

expectations

adjust slowly,

it takes many

periods for

inflation to

reach the

new target.

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 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:

CASE 1: θπ is large,

DADt – 1, t

DASt – 1

Yt –1

πt –1

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:

CASE 2: θπ is small,

DADt – 1, t

DASt – 1

Yt –1

πt –1

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:

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.

(MP rule) *

APPLICATION:

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.

(MP rule)

APPLICATION:

• 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

• 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/

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

A dynamic approach to short run economic fluctuations. The...

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