1

The full dynamic short-run model

Chairman Bernanke J. M. Keynes

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The full Keynesian model of the business cycle

2

IS-MP

Y

Potential output = AF(K,L)

Ypot

u

πe

π

i r

3

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).

5

-6

-4

-2

0

2

4

6

8

10

88 90 92 94 96 98 00 02 04 06 08 10

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

1.5

2.0

2.5

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

0

1

2

3

4

5

6

7

01 02 03 04 05 06 07 08 09 10 11 12

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

0

1

2

3

4

5

6

1930 1932 1934 1936 1938 1940 1942 1944

US short-term interest rates, 1929-45 (% per year)

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US in current recession

0

4

8

12

16

20

1975 1980 1985 1990 1995 2000 2005 2010

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.