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The full dynamic short-run model
Chairman Bernanke
J. M. Keynes
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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
2
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The Dynamic Model
This is state-of-the-art modern Keynesian model
Short-run model of business cycles
Combines
- IS (consumption, investment, fiscal, later trade)
- MP (Taylor rule)
- Phillips curve
Closed economy
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The Taylor rule
1. John Taylor suggested the following rule to implement the dual
mandate:
(TR)
i t = πt + r* + θ π (πt - π*) +θY yt
Here r* is the equilibrium real interest rate, π inflation rate, π* is
inflation target, y is output gap (Y - Y*), θ π and θY are parameters.
2. Has both normative* and predictive** power.
____________________
*Theoretical point: Can be derived from minimizing loss function such as
L = λ π (πt - π*) 2 + λ Y (lnYt - lnY* ) 2
** We showed this last time with empirical Taylor rule, predictions and actual (see
next slide).
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Actual and Taylor rule federal funds rate
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Actual
Taylor rule
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Full Dynamic IS-MP analysis
Key equations:
1. Demand for goods and services:
2. Business real interest rate:
3. Phillips curve:
4. Inflation expectations:
5. Monetary policy:
yt = - α rtb + μ*Gt + εt
rtb = it – πte + σt = rt + σt
π t = πte + φ yt + ηt
π e t = π t-1
i t = πt + r* + θ π (πt - π*) +θY yt , i > 0
Notes:
• Equation (1) is our IS curve from last time with risk.
• Phillips curve in (3) substitutes y for u by Okun’s Law
• Business interest rate is real short rate plus risk and term premium (σt )
• Jones uses simplified version of these: no risk and other.
• Jones solves for AS-AD as function of inflation; we stick with interest
rates.
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Algebra of Dynamic IS-MP analysis
Solution of equations:
(IS)
yt = μ*Gt - α ( it – πte + σt ) + εt
(MP)
i t = [φ (1+ θ π ) + θY ] yt + r* - θ π π* + (1+ θ π ) ( πte + ηt )
This is derived by substitution. Check my algebra.
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Interpretation of Dynamic IS-MP
(IS)
(MP)
yt = μ*Gt - α ( it – πte + σt ) + εt
A
B
i t = [φ (1+ θ π ) + θY ] yt + r* - θ π π* + (1+ θ π ) ( πte + ηt )
C
D
E
A = standard multiplier on spending
B = risk enters in as negative element on investment
C = slope of MP due to inflation and output term in Taylor rule
D = lower inflation target raises Fed interest rates
E = expected inflation or inflation shock raises Fed interest rate.
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The graphics of dynamic IS-MP
Federal
funds rate
MP(πe, π*, r*, ηt )
it *
IS(πe, G , εt , σt )
Yt
Yt = real output (GDP)
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1. What are the effects of fiscal policy?
• A fiscal policy is change in purchases (G) or in taxes (T0, τ),
holding monetary policy constant.
• In normal times, because MP curve slopes upward,
expenditure multiplier is reduced due to crowding out.
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IS shock (as in fiscal expansion)
MP
i
IS(G’)
IS(G)
Y = real output (GDP)
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Multiplier Estimates by the CBO
3.0
Multiplier from G,T on GDP
2.5
2.0
1.5
1.0
0.5
0.0
G: Fed
G: S&L
Trans: indiv
Tax:
Mid/Low
Income
Tax: High
Income
Congressional Budget Office, Estimated Impact of the ARRA, April 2010
Bus Tax
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Inflationary shock
MP(ηt > 0)
MP(ηt = 0)
i
it**
IS
Yt**
Y = real output (GDP)
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Dual mandate v single mandate
Taylor rule for ECB versus the Fed:
(Fed) it = πt + r* + θ π (πt - π*) +θY yt
(EBC) it = πt + r* + θ π (πt - π*)
Therefore MP curve steeper for ECB:
(MP)
i t = [φ (1+ θ π ) + θY ] yt + r* - θ π π* + (1+ θ π ) ( πte + ηt )
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ECB v Fed
Note added after class:
I had the slopes backwards. The Fed is steeper (higher
coefficient). Eating arithmetic humble pie. Note the interest
rate diagram is explained by this.
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IS shock (Fed v. ECB)
i
MP (Fed)
MP (ECB)
IS(G’)
IS(G)
Y = real output (GDP)
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Prediction: Fed should respond more to IS
shocks such as those of 2001 - 2012
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Fed interest rate
ECB interest rate
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What about in the “liquidity trap”
or “zero interest rate bound”
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US short-term interest rates, 1929-45 (% per year)
Liquidity
trap in US in
Great
Depression
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4
3
2
1
0
1930
1932
1934
1936
1938
1940
1942
1944
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US in current recession
Federal funds rate (% per year)
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Policy has
hit the
“zero lower
bound” four
years ago.
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0
1975
1980
1985
1990
1995
2000
2005
2010
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Japan short-term interest rates, 1994-2012
Liquidity trap from 1996 to today:
16 years and counting.
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Fiscal policy in liquidity trap
r = real
interest rate
IS
IS’
MP
re
Y = real output (GDP)
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Monetary expansion in liquidity trap
r = real
interest rate
IS
MP
MP’
re
Y = real output (GDP)
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Can you see why macroeconomists emphasize the
importance of fiscal policy in the current environment?
“Our policy approach started with a major commitment to fiscal
stimulus. Economists in recent years have become skeptical about
discretionary fiscal policy and have regarded monetary policy as a
better tool for short-term stabilization. Our judgment, however, was
that in a liquidity trap-type scenario of zero interest rates, a
dysfunctional financial system, and expectations of protracted
contraction, the results of monetary policy were highly uncertain
whereas fiscal policy was likely to be potent.”
Lawrence Summers, July 19, 2009
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Summary on IS-MP Model
This is the workhorse model for analyzing short-run
impacts of monetary and fiscal policy
Key assumptions:
- Inflexible prices
- Unemployed resources
Now on to analysis of Great Depression in IS-MP
framework.
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