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The full dynamic short-run model
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The Dynamic Model
A nice new addition to Mankiw.
Combines
- IS
- LM (changed to reflect central bank targeting)
- Phillips curve
Closed economy
Short-run of business cycles
Keynesian rather than classical
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Monetary policy rule
Taylor rule:
i t = πt + θ π (πt - π*) +θY (Yt - Y* )
Rationale: a rule that incorporates both real and inflation
targets
But, also one that has good stability properties
Derived from minimizing loss function such as
L = θ π (πt - π*) 2 +θY (lnYt - lnY* ) 2
[This version has loss function the same as the Taylor run.
It seems more likely that the optimal Y* would be above
potential output.]
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Federal funds rate
Taylor rule rate
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12
8
4
0
1980
1985
1990
1995
2000
2005
2010
Fedfunds* = pi +2 + .5*(pi – 2) - .25*(u – nairu)
pi = 4 quarter PCE core inflation
Why is rate below target today?
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Algebra of Dynamic AS-AD analysis
Key equations:
1. Demand for goods and services:
2. Cost of capital:
3. Phillips curve:
4. Inflation expectations:
5. Monetary policy:
Yt = Y* - α (rt –r*) + μG + εt
rt = it – π e t + risk premium
π t = π e t + φ(Yt - Y* ) + vt
π e t = π t-1
i t = πt + θ π (πt - π*) +θY (Yt - Y* )
Notes:
• Equation (1) is just our IS-LM solution
• Phillips curve substitutes output by Okun’s Law
• Mankiw uses slightly different version of (4)
• Mankiw doesn’t consider risk premium, so ignore for now
• We have added “G” to show the impact of fiscal policy
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Solve for AS and AD
AD: Y t = -[α θ π /(1+ α θ Y )] π t + μ /(1+ α θ Y )] G +…
AS: π t = π t-1 + φ(Yt - Y* ) + vt
NOTE:
AD is like IS-LM equilibrium except is substitutes the Fed
response for a fixed money supply
AS is Phillips curve with substituting for expected inflation
Note that we have moved up one derivative from intro AD-AD
because of Phillips curve.
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The graphics of dynamic AS-AD
π
AS
πt*
AD
Yt*
Y = real output (GDP)
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Inflationary shock
AS
π
AS
AD
Y*
Y = real output (GDP)
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Example by simulation model
This will be available on course web page.
You might download and do some experiments to see how
it works.
New kind of economics: computerized modeling.
[The screen shots are ones that were used in class. The
model posted on the course web site is slightly changed
from that version.]
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Parameters
Parameters
alpha
phi=
Taylor rule:
pi*=
r*=
coef(i,pi)=
coef(i,Y)=
1 dY/dr
0.25 d(pi)/dY
2 Inflation target
2 Natural rate of interest
0.5 Taylor coeff on inflation
0.5 Taylor coeff on output
Shocks to system
e-sup
1 Supply (inflation) shocks
eps-d
0 Demand (G, NX, I) shocks
shock r
0 Financial crisis shocks (+ is financial crisis)
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Numerical simulation in base run
t
r
-2
-1
0
1
2
3
4
5
6
7
8
9
10
pi
2
2
2
2
2
2
2
2
2
2
2
2
2
Y-Y*
2
2
2
2
2
2
2
2
2
2
2
2
2
e-s
0
0
0
0
0
0
0
0
0
0
0
0
0
i
0
0
0
0
0
0
0
e-d
4
4
4
4
4
4
4
4
4
4
4
4
e-r
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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Graph of base case
4.5
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3.5
r
ln(Y/Y*)
i
3
pi
e-sup
e-dem
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
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Very big negative demand shock
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4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17
-1
-2
-3
r
ln(Y/Y*)
i
pi
e-sup
e-dem
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Other examples
1. Supply shocks (e-sup = 1)
2. Financial crisis (shock r = 1)
3. Inflation targeting without output targets: much deeper
recessions with demand shocks (ECB)
4. Unstable monetary policy where insufficient response
to shocks (Great Inflation discussion)
5. Liquidity trap
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Summary
This now finishes our treatment of closed-economy
business cycles.
Key elements are
- IS elements in I, C, fiscal policy, and trade
- Financial markets and monetary policy
- Inflation dynamics
Can we abolish the business cycle?
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