1 the full dynamic short-run model. 2 the dynamic model a nice new addition to mankiw. combines - is...
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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 economyShort-run of business cyclesKeynesian 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 propertiesDerived 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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1980 1985 1990 1995 2000 2005 2010
Federal funds rateTaylor rule rate
Fedfunds* = pi +2 + .5*(pi – 2) - .25*(u – nairu)pi = 4 quarter PCE core inflationWhy is rate below target today?
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Algebra of Dynamic AS-AD analysis
Key equations:
1. Demand for goods and services: Yt = Y* - α (rt –r*) + μG + εt
2. Cost of capital: rt = it – π e t + risk
premium 3. Phillips curve: π t = π e
t + φ(Yt - Y* ) + vt
4. Inflation expectations: π e t = π t-1
5. Monetary policy: 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 supplyAS is Phillips curve with substituting for expected
inflationNote that we have moved up one derivative from
intro AD-AD because of Phillips curve.
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π
Y = real output (GDP)
AD
Yt*
AS
The graphics of dynamic AS-AD
πt*
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Inflationary shock
π
Y = real output (GDP)
AD
Y*
AS
AS
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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
Parametersalpha 1 dY/drphi= 0.25 d(pi)/dY
Taylor rule:pi*= 2 Inflation targetr*= 2 Natural rate of interestcoef(i,pi)= 0.5 Taylor coeff on inflationcoef(i,Y)= 0.5 Taylor coeff on output
Shocks to systeme-sup 1 Supply (inflation) shockseps-d 0 Demand (G, NX, I) shocksshock r 0 Financial crisis shocks (+ is financial crisis)
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Numerical simulation in base run
t r pi Y-Y* e-s i e-d e-r-2 2 2 0 0 0 0-1 2 2 0 0 4 0 00 2 2 0 0 4 0 01 2 2 0 0 4 0 02 2 2 0 0 4 0 03 2 2 0 0 4 0 04 2 2 0 0 4 0 05 2 2 0 46 2 2 0 47 2 2 0 48 2 2 0 49 2 2 0 4
10 2 2 0 4
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Graph of base case
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r piln(Y/Y*) e-supi e-dem
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Very big negative demand shock
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r piln(Y/Y*) e-supi 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?