1

The full dynamic short-run model

Chairman Bernanke J. M. Keynes

2

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

4

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

6

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 = πte + 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.

7

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 ) ( πte

+ ηt )

This is derived by substitution. Check my algebra.

8

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 ) ( πte

+ 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

9

Federalfunds rate

Yt = real output (GDP)

IS(πe, G , εt , σt )

Yt

MP(πe, π*, r*, ηt )

The graphics of dynamic IS-MP

it*

10

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.

11

IS shock (as in fiscal expansion)

i

Y = real output (GDP)

IS(G)

MP

IS(G’)

12

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

tipl

ier f

rom

G,T

on

GD

P

13

Inflationary shock

i

Y = real output (GDP)

IS

MP(ηt = 0)

Yt**

it**

MP(ηt > 0)

14

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 )

15

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.

16

IS shock (Fed v. ECB)

i

Y = real output (GDP)

IS(G)

MP (Fed)

IS(G’)

MP (ECB)

17

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

18

What about in the “liquidity trap” or “zero interest rate bound”

19

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)

20

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.

21

Japan short-term interest rates, 1994-2012

Liquidity trap from 1996 to today: 16 years and counting.

22

Fiscal policy in liquidity trap r = real interest rate

Y = real output (GDP)

IS

re

IS’MP

23

Monetary expansion in liquidity trap r = real interest rate

Y = real output (GDP)

IS

re

MP’MP

24

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

25

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.