The full dynamic short-run model
Chair-nominee Janey Yellen
J. M. Keynes
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Paper topic
• Last problem is short paper (1000 words + tables,
figures)
• Due in reading week (exact date to follow)
• Broad latitude on particular topic, but must be macro
• Get approval from TF or me for topic
• Examples (verbally, but will be in posted assignment)
• Good style is important
• References must be acceptable (not Internet junk)
• Don’t wait until last moment
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The full Keynesian model of the business cycle
i
r
IS-MP
Y
πe
u
Potential
output =
AF(K,L)
Ypot
π
3
3
The Dynamic Model
This is state-of-the-art modern Keynesian model
Combines
- IS
- MP
- Phillips curve
Closed economy
Short-run model of business cycles
Keynesian rather than classical
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Bid farewell, hopefully never to see again…
LM
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Monetary policy rule with inflation
Taylor rule:
i t = πt + ρ + θ π (πt - π*) +θY yt
Notation:
ρ = “natural rate of interest” = interest rate when output =
potential (natural) output when there are no shocks.
y  Y  Y p = Mankiw's (Y - Y )
 y ,  = coefficients of y and  in monetary policy rule.
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Algebra of Dynamic AS-AD analysis
Key equations:
1. Demand for goods and services:
2. Business cost of capital:
3. Phillips curve:
4. Inflation expectations:
5. Monetary policy:
yt = - α (rt –ρ) + μG + εt
rt = it – π e t+1 + σt
π t = π e t + φ yt + ηt
π e t+1 = π t
i t = πt + ρ + θ π (πt - π*) +θY yt , i > 0
Notes:
• Equation (1) is our IS curve
• Phillips curve substitutes y for – ½u by Okun’s Law
• Business interest rate is real short rate plus risk and term premium (σt )
• Mankiw leaves out risk premium and G
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Solve for Dynamic AS and AD
 ( t –  *)  t   Gt   t
AD : yt 
, or
(1  Y )
AD : yt   k1 t  k2 t  k3 *  k4 (  Gt   t )
and
AS :  t   t 1   yt  t
NOTE:
AD is like IS-MP equilibrium
AS is Phillips curve with substitution for expected inflation
Note that we have moved up one derivative from prices to
inflation from introductory AS-AD because Phillips curve
related to inflation (see arrow on next page).
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The graphics of dynamic AS-AD
π
AS(πt-1 , ηt )
πt
AD(π* , G , εt , σt )
yt
y=Y–Yp
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Inflationary shock (η)
π
AS’
AS
AD
y=Y–Yp
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Financial shock or cut in G
π
AS
AD
AD’
y=Y–Yp
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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.
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Parameters
Parameters
α
1
φ
0.25
contant=
-5
Taylor rule:
π* =
2
r*=
1
coef(i,pi)=
0.5
coef(i,Y)=
0.5
G multiplier=
1.5
Shocks to system
ε-sup
[Given]
ε-d
[Given]
ε-r
[Given]
dln(Y)/dr
d(pi)/dY
Inflation target
Natural rate of interest
Taylor coeff on inflation
Taylor coeff on output
Supply (inflation) shocks
Demand (G, NX, I) shocks
Financial crisis shocks (+ is a financial crisis)
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Numerical simulation in base run
r
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
(Y-Y*)/Y*
3.76
2.75
3.31
3.65
3.71
7.62
4.41
2.57
2.89
1.47
1.81
2.28
2.51
2.95
3.36
3.86
4.38
π
2.63
3.31
3.17
2.83
3.74
-0.32
1.63
3.09
2.05
1.57
1.36
1.30
1.42
1.68
2.09
2.62
3.03
-0.82
0.23
0.54
-0.09
-2.69
-7.44
-6.44
-6.15
-5.12
-3.95
-2.81
-2.28
-1.51
-0.95
-0.36
0.14
-0.38
ε-s
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
i-ff
1.35
3.21
4.96
5.02
1.93
0.16
0.18
0.10
0.10
0.52
0.37
0.64
0.80
1.37
2.04
2.95
4.00
ε-d
-2.18
-1.26
-0.08
0.66
-3.24
-9.39
-9.61
-11.62
-8.86
-5.50
-4.00
-3.00
-2.00
-1.00
0.00
1.00
1.00
ε-r
5.00
3.00
1.00
1.00
5.00
7.00
6.00
4.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
G*
-3.41
-2.83
-2.62
-1.93
-2.84
-6.38
-5.05
-5.36
-4.41
-2.01
-2.00
-2.00
-2.00
-2.00
-2.00
-2.00
-2.00
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Baseline forecast
2004
2006
2008
2010
2012
2014
2016
2018
2020
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Forecast
6
4
Percent
2
0
-2
-4
-6
-8
r
π
(Y-Y*)/Y*
i
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Some policy approaches
What should the Fed do today?
Has run out of conventional bullets.
Unconventional tools are “quantitative easing” (QE),
Operation Forward Guidance, Operation Pancake
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Fed chair nominee Janet Yellen (2011)
General stance: “Since the onset of the financial crisis, the Federal Reserve has employed
a wide array of policy tools to foster our statutory objectives of maximum employment
and price stability. In particular, with conventional policy having pushed short-term
nominal interest rates close to zero, the FOMC … has provided additional monetary
accommodation by modifying our forward policy guidance and by adjusting our
securities holdings.”
Forward guidance: “At our August meeting, the FOMC decided to provide morespecific information about the likely time horizon by substituting the phrase 'at least
through mid-2013' for the phrase 'for an extended period.' This clarification appears to
have reduced market uncertainty about the Committee's current policy expectations.”
Pancake: “At our recent September meeting, the FOMC announced that we intend to
extend the average maturity of our securities holdings over coming months by selling
$400 billion of short-term Treasury securities and purchasing an equivalent amount of
long-term Treasury securities. This maturity extension program should exert downward
pressure on longer-term interest rates, thereby supporting a stronger economic recovery.
“
http://www.federalreserve.gov/newsevents/speech/yellen20111021a.htm
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Some policy approaches
What should the Fed do today?
Has run out of conventional bullets.
Unconventional tools are “quantitative easing” (QE), Operation Pancake, Operation Risk Reduction, Operation Forward Guidance.
Impact:
- Remember, r = i – π + Expected future i + risk and term premiums
- Point of QE is to lower term and risk premium
- Estimates are in the range of 50 basis points maximum on long-term
rates.
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Quantitative easing (lowers r by 50 basis points)
Forecast (base + QE)
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What about raising inflation target?
Some have argued that Fed should raise target (Krugman
in his scholarly writings)
Would keep i at zero for longer period.
These results suggest that it would have small effect (see
below).
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Impact of higher inflation premium*
Forecast (base + raise
inflation target to 3 percent)
* Works by lowering the expected future short rates through Taylor rule and
then building that into current long rates by expectations theory.
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Deflation
Deflation = falling price level
This seldom occurs in modern economy, but sometimes have
near-zero inflation (Japan for two decades, US today).
Problems:
- If full-employment interest rate < 0, have liquidity trap
- Unstable dynamics: since r = i – π, as π falls have higher real
interest rate, lower I, lower Y, and “low-level trap”
Some of the issues involved are discussed in Bullard, Seven
Faces. Very interesting discussion!
But this is uncharted territory in modern macro!
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Balance the budget
One of the perennial concerns is budget deficits.
Many conservatives have proposed constitutional
amendment to ensure balanced budget.
European governments are pursuing tight fiscal policies to
reduce deficits in current global recession.
What would be the effect of attempting to aim for slight
budget surplus over next two years? (For simplicity, I
use the full-employment budget.)
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Balanced surplus (2% structural)
2004
2006
2008
2010
2012
2014
2016
2018
2020
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Forecast
6
4
Percent
2
0
-2
-4
-6
-8
r
π
(Y-Y*)/Y*
i
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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
We now move on to long-run growth theory next week.
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