Topic 5 - Dynamics

Question 1

What does the dynamic model of AD and AS give insight into?

Answer 1

• How the economy works in the SR

- Simplified model of a DSGE model (dynamic, stochastic, general equilibrium)

Question 2

What is the dynamic model of AD and AS build off of?

Answer 2

• The IS curve, negatively relates the real interest rate and demand for goods and services
• Phillips Curve, relates inflation to the gap between output and natural lvl
• Adaptive expectations, simple model of inflation expectations

Question 3

How does the dynamic AD-AS model differ from the standard model?

Answer 3

• Instead of fixing the money supply, central bank follows monetary policy rule adjusts interest rates when output or inflation change
• y axis of DAD-DAS diagram measures inflation rate not P
• Subsequent time periods 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.

Question 4

What are the elements of the model?

Answer 4

Five equations (covered later) and 5 endogenous variables

Question 5

What are the 5 endogenous variables of the DAD-DAS model?

Answer 5

Output
Inflation
Real Interest Rate
Nominal Interest Rate
Expected Inflation

Question 6

What is the equation for output in the DAD-DAS model?

Answer 6

Yt = Yt bar - α(rt - p) + εt

SEE IN NOTES

Question 7

What is the equation for real interest rate(fisher equation) in the DAD-DAS model?

Answer 7

rt = it - Et Π t+1

Π t+1 = Increase in price lvl from period t to t+1 not known in period t

Et Π t+1 = Expectation, formed in period t, of inflation from t to t+1

(SEE IN NOTES)

Question 8

What is the equation for inflation (phillips curve) in the DAD-DAS model?

Answer 8

Πt = E t-1 Πt + Φ (Yt - Yt bar) + vt

SEE IN NOTES

Question 9

What is the equation for expected inflation (Adaptive expectations) in the DAD-DAS model?

Answer 9

EΠt+1 = Πt

• We assume that people expect prices to continue rising at the current inflation rate

SEE IN NOTES

Question 10

What is the equation for the nominal interest rate (Monetary Policy rule) in the DAD-DAS model?

Answer 10

it = Πt + P + θΠ ( Πt - Πt*) + θy (Yt - Yt bar)

SEE IN NOTES

Question 11

What is the Taylor rule?

Answer 11

A monetary policy rule around the fed

iff = Π + 2 + 0.5 (Π - 2) - 0.5(GDP Gap)

where:

• iff = Nominal Fed funds rate target
• GDP gap = 100 x Ybar -Y/Y bar = % by which real GDP below its natural rate

Question 12

What is the model’s endogenous variables?

Answer 12

Yt = Output 
Πt = Inflation
rt - Real Interest Rate
it = Nominal Interest Rate
Et Π t+1 = Expected Inflation

Question 13

What are the model’s exogenous variables?

Answer 13

Yt bar = Natural Lvl of output
Π*t = Central Bank’s target inflation rate
εt = Demand Shock
Vt = Supply Shock

Predetermined Variables:
Πt-1 = Previous period’s inflation

Question 14

What are the model’s parameters?

Answer 14

α = Responsiveness of demand to the real interest rate
p = Natural rate of interest
θΠ = Responsiveness of output in the monetary policy rule
θy = Responsiveness of output in the monetary policy rule
Φ = Responsiveness of inflation to output in the Phillip Curve

Question 15

What are the 2 conditions required for long run equilibrium?

Answer 15

No shocks: εt= Vt=0

Inflation is constant: Πt-1= Πt

Question 16

What are the long run values of the DAD and DAS model?

Answer 16

Yt = Yt bar
rt = p
Πt = Πt*
EtΠt+1 = Πt*
it = p + Πt*

Question 17

What is the dynamic aggregate supply (DAS)?

Answer 17

Πt = Πt-1 + Φ (Yt - Yt bar) + vt

Shows relationship between output and inflation

SEE GRAPH IN NOTES

Question 18

Where does the DAS come from?

Answer 18

Phillips Curve and Adaptive Expectations equations

Question 19

How do you derive the DAD (Dynamic Aggregate Demand)?

Answer 19

• Combine four equations and eliminate all endogenous variables other than output and inflation

SEE HOW TO DO IT IN NOTES (NOT TOO HARD TBH)

Question 20

What is the Dynamic Aggregate Demand?

Answer 20

Yt = Yt bar - A(Πt - ΠT*) + Bεt

SEE GRAPH IN NOTES

Question 21

What does the short run equilibrium of DAD-DAS look like?

Answer 21

In each period, the intersection of DAD and DAS determines the SR equilibrium values of inflation and output

SEE GRAPH IN NOTES

Question 22

What does long run growth look like?

Answer 22

As natural lvl of output increases, dynamic AS curve shifts to right and does does AD leading to growth in out and stable inflation

SEE GRAPH IN NOTES

Question 23

What does a shock to aggregate supply do to the economy?

Answer 23

1. Adverse supply shock shifts DAS upwards (DASt-1 to DASt)
2. Causing inflation to rise (Πt)
3. Output to fall (Yt)
4. In later periods inflation falls (ΠT+1)
5. Output slowly recovers (Yt+1)

Process continues until output returns to its natural rate. LR Equilibrium at A
SEE GRAPH IN NOTES

Question 24

What is the dynamic response to a supply shock?

Answer 24

• One period supply shock affects output for many periods
• Because inflation expectations adjust slowly, actual inflation remain high for many periods
• The real interest rate takes many periods to return to its natural rate.
• The behavior of the nominal interest rate depends on that of the inflation and real interest rates.

Question 25

What does a shock to aggregate demand do to an economy?

Answer 25

1. Positive shock to demand (DAD t-1, t+5 to DAD t, t+4)
2. Causes output to increase (Yt)
3. And inflation to rise (Πt)
4. In subsequent periods DAS t+1 through to 5), higher expected inflation shifts DAS curve upward
5. When demand shock disappears and output fall, and the economy begins its return to its inital equilibrium (point G)

SEE GRAPH IN NOTES

Question 26

What is the dynamic response to a demand shock?

Answer 26

-The demand shock raises output for five periods. When the shock ends, output falls below its natural level and recovers gradually.
-The demand shock causes inflation to rise. When the shock ends, inflation gradually falls toward its initial level.
- The demand shock raises the real interest rate. After the shock ends, the real interest rate falls and approaches its initial level.
-

Question 27

What does the behaviour of the nominal interest rate depend upon?

Answer 27

The inflation and real interest rates