1

The full dynamic short-run model

2

The Dynamic Model

A nice new addition to Mankiw.Combines

- IS- LM (changed to reflect central bank targeting)- Phillips curve

Closed economyShort-run of business cyclesKeynesian rather than classical

3

Monetary policy rule

Taylor rule:

i t = πt + θ π (πt - π*) +θY (Yt - Y* )

Rationale: a rule that incorporates both real and inflation targets

But, also one that has good stability propertiesDerived from minimizing loss function such as

L = θ π (πt - π*) 2 +θY (lnYt - lnY* ) 2

[This version has loss function the same as the Taylor run. It seems more likely that the optimal Y* would be above potential output.]

4

0

4

8

12

16

20

1980 1985 1990 1995 2000 2005 2010

Federal funds rateTaylor rule rate

Fedfunds* = pi +2 + .5*(pi – 2) - .25*(u – nairu)pi = 4 quarter PCE core inflationWhy is rate below target today?

5

Algebra of Dynamic AS-AD analysis

Key equations:

1. Demand for goods and services: Yt = Y* - α (rt –r*) + μG + εt

2. Cost of capital: rt = it – π e t + risk

premium 3. Phillips curve: π t = π e

t + φ(Yt - Y* ) + vt

4. Inflation expectations: π e t = π t-1

5. Monetary policy: i t = πt + θ π (πt - π*) +θY (Yt - Y* )

Notes:• Equation (1) is just our IS-LM solution• Phillips curve substitutes output by Okun’s Law• Mankiw uses slightly different version of (4)• Mankiw doesn’t consider risk premium, so ignore for now• We have added “G” to show the impact of fiscal policy

6

Solve for AS and AD

AD: Y t = -[α θ π /(1+ α θ Y )] π t + μ /(1+ α θ Y )] G +…

AS: π t = π t-1 + φ(Yt - Y* ) + vt

NOTE:AD is like IS-LM equilibrium except is substitutes the

Fed response for a fixed money supplyAS is Phillips curve with substituting for expected

inflationNote that we have moved up one derivative from

intro AD-AD because of Phillips curve.

7

π

Y = real output (GDP)

AD

Yt*

AS

The graphics of dynamic AS-AD

πt*

8

Inflationary shock

π

Y = real output (GDP)

AD

Y*

AS

AS

9

Example by simulation model

This will be available on course web page.You might download and do some experiments to

see how it works.New kind of economics: computerized modeling.[The screen shots are ones that were used in class.

The model posted on the course web site is slightly changed from that version.]

10

11

Parameters

Parametersalpha 1 dY/drphi= 0.25 d(pi)/dY

Taylor rule:pi*= 2 Inflation targetr*= 2 Natural rate of interestcoef(i,pi)= 0.5 Taylor coeff on inflationcoef(i,Y)= 0.5 Taylor coeff on output

Shocks to systeme-sup 1 Supply (inflation) shockseps-d 0 Demand (G, NX, I) shocksshock r 0 Financial crisis shocks (+ is financial crisis)

12

Numerical simulation in base run

t r pi Y-Y* e-s i e-d e-r-2 2 2 0 0 0 0-1 2 2 0 0 4 0 00 2 2 0 0 4 0 01 2 2 0 0 4 0 02 2 2 0 0 4 0 03 2 2 0 0 4 0 04 2 2 0 0 4 0 05 2 2 0 46 2 2 0 47 2 2 0 48 2 2 0 49 2 2 0 4

10 2 2 0 4

13

Graph of base case

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

r piln(Y/Y*) e-supi e-dem

14

Very big negative demand shock

-3

-2

-1

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

r piln(Y/Y*) e-supi e-dem

15

Other examples

1. Supply shocks (e-sup = 1)2. Financial crisis (shock r = 1)3. Inflation targeting without output targets: much

deeper recessions with demand shocks (ECB)4. Unstable monetary policy where insufficient

response to shocks (Great Inflation discussion)5. Liquidity trap

16

Summary

This now finishes our treatment of closed-economy business cycles.

Key elements are- IS elements in I, C, fiscal policy, and trade- Financial markets and monetary policy- Inflation dynamics

Can we abolish the business cycle?