The full dynamic short-run model
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The full dynamic short-run model. The Dynamic 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. Monetary policy rule. Taylor rule:

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The full dynamic short-run model

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The full dynamic short run model

The full dynamic short-run model


The dynamic model

The Dynamic 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


Monetary policy rule

Monetary policy rule

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.]


The full dynamic short run model

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

pi = 4 quarter PCE core inflation

Why is rate below target today?


Algebra of dynamic as ad analysis

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 – 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


Solve for as and ad

Solve for AS and AD

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.


The graphics of dynamic as ad

The graphics of dynamic AS-AD

π

AS

πt*

AD

Yt*

Y = real output (GDP)


Inflationary shock

AS

Inflationary shock

π

AS

AD

Y = real output (GDP)

Y*


Example by simulation model

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.]


Parameters

Parameters


Numerical simulation in base run

Numerical simulation in base run


Graph of base case

Graph of base case


Very big negative demand shock

Very big negative demand shock


Other examples

Other examples

  • 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


Summary

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?


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