Chairman Bernanke J. M. Keynes
1

The full Keynesian model of the business cycle i r
IS-MP
Y
π e u
Potential output =
AF(K,L)
Y pot
π
2
2

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
3

1. John Taylor suggested the following rule to implement the dual mandate:
(TR) i t
= π t
+ r* + θ
π
(π t
- π*) +θ
Y y t
Here r* is the equilibrium real interest rate, π inflation rate, π* is inflation target, y is output gap (Y - Y*), θ
π and θ
Y are parameters.
2. Has both normative* and predictive** power.
____________________
*Theoretical point: Can be derived from minimizing loss function such as
L = λ
π
(π t
- π*) 2 + λ
Y
(lnY t
- lnY* ) 2
** We showed this last time with empirical Taylor rule, predictions and actual (see next slide).
4

Actual and Taylor rule federal funds rate
10
8
6
4
2
0
-2
-4
Actual
Taylor rule
-6
88 90 92 94 96 98 00 02 04 06 08 10
5

Key equations:
1. Demand for goods and services: y t
2. Business real interest rate: r t b
3. Phillips curve:
4. Inflation expectations:
5. Monetary policy:
= -
= i
α t r t b
– π
+ μ*G t t e + σ t
+ ε
= r t
π
π e t i t
= π t e + φ y t t
= π
= π t t-1
+ r* + θ
+ η t
π
(π t t
+ σ t
- π*) +θ
Y y t
, 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 (σ t
• Jones uses simplified version of these: no risk and other.
• Jones solves for AS-AD as function of inflation; we stick with interest rates.
)
6

Solution of equations:
(IS) y t
= μ*G t
α ( i t
– π t e + σ t
) + ε t
(MP) i t
= [φ (1+ θ
π
) + θ
Y
] y t
+ r* - θ
π
π* + (1+ θ
π
) ( π t e + η t
)
This is derived by substitution. Check my algebra.
7

(IS) y t
= μ*G t
α ( i t
– π t e + σ t
) + ε t
(MP) i t
A
= [φ (1+ θ
π
) + θ
Y
] y t
B
+ r* - θ
π
π* + (1+ θ
π
) ( π t e + η t
)
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.
8

Federal funds rate
The graphics of dynamic IS-MP
MP(π e , π*, r*, η t
) i t
*
Y t
IS(π e , G , ε t
, σ t
)
Y t
= real output (GDP)
9

1. What are the effects of fiscal policy?
• A fiscal policy is change in purchases (G) or in taxes (T
0,
τ), holding monetary policy constant.
• In normal times, because MP curve slopes upward, expenditure multiplier is reduced due to crowding out.
10

i
IS shock (as in fiscal expansion)
MP
IS(G)
IS(G’)

Multiplier Estimates by the CBO
3.0
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
Bus Tax
Congressional Budget Office, Estimated Impact of the ARRA, April 2010 12

Inflationary shock i
MP(η t
> 0)
MP(η t
= 0) i t
**
IS
Y t
**

Taylor rule for ECB versus the Fed:
(Fed) i t
= π t
+ r* + θ
π
(π t
- π*) +θ
Y y t
(EBC) i t
= π t
+ r* + θ
π
(π t
- π*)
Therefore MP curve steeper for ECB:
(MP) i t
= [φ (1+ θ
π
) + θ
Y
] y t
+ r* - θ
π
π* + (1+ θ
π
) ( π t e + η t
)
14

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.
15

i
IS shock (Fed v. ECB)
MP (Fed)
MP (ECB)
IS(G’)
IS(G)

7
6
5
Fed interest rate
ECB interest rate
4
3
2
1
0
01 02 03 04 05 06 07 08 09 10 11 12
17

18

US short-term interest rates, 1929-45 (% per year)
6
5
4
3
2
1
0
1930 1932 1934 1936 1938 1940 1942 1944
Liquidity trap in US in
Great
Depression
19

20
16
12
Federal funds rate (% per year)
Policy has hit the
“zero lower bound” four years ago.
8
4
0
1975 1980 1985 1990 1995 2000 2005 2010
20

Japan short-term interest rates, 1994-2012
Liquidity trap from 1996 to today:
16 years and counting.
21

r = real interest rate
Fiscal policy in liquidity trap
IS
IS’
MP r e
Y = real output (GDP)
22

Monetary expansion in liquidity trap r = real interest rate
IS
MP
MP’ r e
Y = real output (GDP)
23

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
24

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.
25