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The full dynamic short-run model

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The full dynamic short-run model

A nice new addition to Mankiw.

Combines

- IS

- LM (changed to reflect central bank targeting)

- Phillips curve

Closed economy

Short-run of business cycles

Keynesian rather than classical

Taylor rule:

i t = πt + θπ(πt - π*) +θY (Yt - Y* )

Rationale: a rule that incorporates both real and inflation targets

But, also one that has good stability properties

Derived from minimizing loss function such as

L = θπ(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.]

Fedfunds* = pi +2 + .5*(pi – 2) - .25*(u – nairu)

pi = 4 quarter PCE core inflation

Why is rate below target today?

Key equations:

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

2. Cost of capital: rt = it – πe t + risk premium

3. Phillips curve: πt = πe t + φ(Yt - Y* ) + vt

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

5. Monetary policy: i t = πt + θπ(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

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

AS: πt = πt-1 + φ(Yt - Y* ) + vt

NOTE:

AD is like IS-LM equilibrium except is substitutes the Fed response for a fixed money supply

AS is Phillips curve with substituting for expected inflation

Note that we have moved up one derivative from intro AD-AD because of Phillips curve.

π

AS

πt*

AD

Yt*

Y = real output (GDP)

AS

π

AS

AD

Y = real output (GDP)

Y*

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.]

- Supply shocks (e-sup = 1)
- Financial crisis (shock r = 1)
- Inflation targeting without output targets: much deeper recessions with demand shocks (ECB)
- Unstable monetary policy where insufficient response to shocks (Great Inflation discussion)
- Liquidity trap

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?