the full dynamic short-run model
DESCRIPTION
The full dynamic short-run model. J. M. Keynes. Chairman Bernanke. The full Keynesian model of the business cycle. i. r. IS-MP. Y. π e. u. Y pot. Potential output = AF(K,L). π. 2. The Dynamic Model. This is state-of-the-art modern Keynesian model Short-run model of business cycles - PowerPoint PPT PresentationTRANSCRIPT
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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
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IS-MP
Y
Potential output = AF(K,L)
Ypot
u
πe
π
i r
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The Dynamic Model
This is state-of-the-art modern Keynesian modelShort-run model of business cyclesCombines
- IS (consumption, investment, fiscal, later trade)- MP (Taylor rule)- Phillips curve
Closed economy
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The Taylor rule1. 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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ActualTaylor rule
Actual and Taylor rule federal funds rate
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Full Dynamic IS-MP analysisKey equations:
1. Demand for goods and services: yt = - α rtb + μ*Gt + εt
2. Business real interest rate: rtb = it – πt
e + σt = rt + σt 3. Phillips curve: π t = πt
e + φ yt + ηt
4. Inflation expectations: π e t = π t-1
5. Monetary policy: 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 analysisSolution 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 ) ( πt
e + ηt )
This is derived by substitution. Check my algebra.
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Interpretation of Dynamic IS-MP
(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 ) ( πt
e + ηt )
A = standard multiplier on spendingB = risk enters in as negative element on investmentC = slope of MP due to inflation and output term in Taylor ruleD = lower inflation target raises Fed interest ratesE = expected inflation or inflation shock raises Fed interest
rate.
A B
C D E
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Federalfunds rate
Yt = real output (GDP)
IS(πe, G , εt , σt )
Yt
MP(πe, π*, r*, ηt )
The graphics of dynamic IS-MP
it*
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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)
i
Y = real output (GDP)
IS(G)
MP
IS(G’)
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Multiplier Estimates by the CBO
Congressional Budget Office, Estimated Impact of the ARRA, April 2010
0.0
0.5
1.0
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3.0
G: Fed G: S&L Trans: indiv Tax: Mid/Low Income
Tax: High Income
Bus Tax
Mul
tiplie
r fro
m G
,T o
n GD
P
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Inflationary shock
i
Y = real output (GDP)
IS
MP(ηt = 0)
Yt**
it**
MP(ηt > 0)
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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
Y = real output (GDP)
IS(G)
MP (Fed)
IS(G’)
MP (ECB)
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Prediction: Fed should respond more to IS shocks such as those of 2001 - 2012
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Fed interest rateECB interest rate
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What about in the “liquidity trap” or “zero interest rate bound”
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Liquidity trap in US in Great Depression
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US short-term interest rates, 1929-45 (% per year)
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US in current recession
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Federal funds rate (% per year)
Policy has hit the “zero lower bound” four years ago.
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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
Y = real output (GDP)
IS
re
IS’MP
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Monetary expansion in liquidity trap r = real interest rate
Y = real output (GDP)
IS
re
MP’MP
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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 ModelThis 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.