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The full dynamic short-run model

Chair-nominee Janey Yellen J. M. Keynes

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Paper topic• Last problem is short paper (1000 words + tables,

figures)• Due in reading week (exact date to follow)• Broad latitude on particular topic, but must be

macro• Get approval from TF or me for topic• Examples (verbally, but will be in posted

assignment)• Good style is important• References must be acceptable (not Internet junk)• Don’t wait until last moment

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The full Keynesian model of the business cycle

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IS-MP

Y

Potential output = AF(K,L)

Ypot

u

πe

π

i r

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The Dynamic Model

This is state-of-the-art modern Keynesian modelCombines

- IS- MP- Phillips curve

Closed economyShort-run model of business cyclesKeynesian rather than classical

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LMxBid farewell, hopefully never to see again…

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Monetary policy rule with inflation

Taylor rule:

i t = πt + ρ + θ π (πt - π*) +θY yt

Notation:

ρ = “natural rate of interest” = interest rate when output = potential (natural) output when there are no shocks. = Mankiw's ( - )

, = coefficients of y and in monetary policy rule.

p

y

y Y Y Y Y

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Algebra of Dynamic AS-AD analysis

Key equations:

1. Demand for goods and services: yt = - α (rt –ρ) + μG + εt

2. Business cost of capital: rt = it – π e t+1 + σt

3. Phillips curve: π t = π e t + φ yt + ηt

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

5. Monetary policy: i t = πt + ρ + θ π (πt - π*) +θY yt , i > 0

Notes:• Equation (1) is our IS curve• Phillips curve substitutes y for – ½u by Okun’s Law• Business interest rate is real short rate plus risk and term

premium (σt )• Mankiw leaves out risk premium and G

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Solve for Dynamic AS and AD

NOTE:AD is like IS-MP equilibriumAS is Phillips curve with substitution for expected

inflationNote that we have moved up one derivative from

prices to inflation from introductory AS-AD because Phillips curve related to inflation (see arrow on next page).

1 2 3 4

1

– *   :    , or

1

:        

( )

*  ( )

:      

( )

t t t tt

Y

t t t t t

t t t t

GAD y

AD y k k k

d

AS y

k G

an

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π

y = Y – Y p

AD(π* , G , εt , σt )

yt

AS(πt-1 , ηt )

The graphics of dynamic AS-AD

πt

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Inflationary shock (η)

π

AD

AS

AS’

y = Y – Y p

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Financial shock or cut in G

π

AD

AS

AD’

y = Y – Y p

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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.

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ParametersParametersα 1 dln(Y)/drφ 0.25 d(pi)/dYcontant= -5Taylor rule:π* = 2 Inflation targetr*= 1 Natural rate of interestcoef(i,pi)= 0.5 Taylor coeff on inflationcoef(i,Y)= 0.5 Taylor coeff on outputG multiplier= 1.5Shocks to systemε-sup [Given] Supply (inflation) shocksε-d [Given] Demand (G, NX, I) shocksε-r [Given] Financial crisis shocks (+ is a financial crisis)

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Numerical simulation in base run

rπ

(Y-Y*)/Y* ε-s i-ff ε-d ε-r G*

2004 3.76 2.63 -0.82 0.00 1.35 -2.18 5.00 -3.412005 2.75 3.31 0.23 0.00 3.21 -1.26 3.00 -2.832006 3.31 3.17 0.54 0.00 4.96 -0.08 1.00 -2.622007 3.65 2.83 -0.09 0.00 5.02 0.66 1.00 -1.932008 3.71 3.74 -2.69 0.00 1.93 -3.24 5.00 -2.842009 7.62 -0.32 -7.44 0.00 0.16 -9.39 7.00 -6.382010 4.41 1.63 -6.44 0.00 0.18 -9.61 6.00 -5.052011 2.57 3.09 -6.15 0.50 0.10 -11.62 4.00 -5.362012 2.89 2.05 -5.12 0.50 0.10 -8.86 3.00 -4.412013 1.47 1.57 -3.95 0.50 0.52 -5.50 3.00 -2.012014 1.81 1.36 -2.81 0.50 0.37 -4.00 3.00 -2.002015 2.28 1.30 -2.28 0.50 0.64 -3.00 3.00 -2.002016 2.51 1.42 -1.51 0.50 0.80 -2.00 3.00 -2.002017 2.95 1.68 -0.95 0.50 1.37 -1.00 3.00 -2.002018 3.36 2.09 -0.36 0.50 2.04 0.00 3.00 -2.002019 3.86 2.62 0.14 0.50 2.95 1.00 3.00 -2.002020 4.38 3.03 -0.38 0.50 4.00 1.00 3.00 -2.00

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Baseline forecast

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-6

-4

-2

0

2

4

6

82004 2006 2008 2010 2012 2014 2016 2018 2020

Percen

t

r π (Y-Y*)/Y* i

Forecast

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Some policy approaches

What should the Fed do today?Has run out of conventional bullets.Unconventional tools are “quantitative easing” (QE),

Operation Forward Guidance, Operation Pancake

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Fed chair nominee Janet Yellen (2011)General stance: “Since the onset of the financial crisis, the Federal Reserve has employed a wide array of policy tools to foster our statutory objectives of maximum employment and price stability. In particular, with conventional policy having pushed short-term nominal interest rates close to zero, the FOMC … has provided additional monetary accommodation by modifying our forward policy guidance and by adjusting our securities holdings.”

Forward guidance: “At our August meeting, the FOMC decided to provide more-specific information about the likely time horizon by substituting the phrase 'at least through mid-2013' for the phrase 'for an extended period.'

This clarification appears to have reduced market uncertainty about the Committee's current policy expectations.”

Pancake: “At our recent September meeting, the FOMC announced that we intend to extend the average maturity of our securities holdings over coming months by selling $400 billion of short-term Treasury securities and purchasing an equivalent amount of long-term Treasury securities. This maturity extension program should exert downward pressure on longer-term interest rates, thereby supporting a stronger economic recovery. “

http://www.federalreserve.gov/newsevents/speech/yellen20111021a.htm

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Some policy approaches

What should the Fed do today?

Has run out of conventional bullets.

Unconventional tools are “quantitative easing” (QE), Operation Pancake, Operation Risk Reduction, Operation Forward Guidance.

Impact:- Remember, r = i – π + Expected future i + risk and term premiums- Point of QE is to lower term and risk premium- Estimates are in the range of 50 basis points maximum on long-term

rates.

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Quantitative easing (lowers r by 50 basis points)

Forecast (base + QE)

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What about raising inflation target?

Some have argued that Fed should raise target (Krugman in his scholarly writings)

Would keep i at zero for longer period.These results suggest that it would have small

effect (see below).

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Impact of higher inflation premium*

Forecast (base + raise inflation target to 3 percent)

* Works by lowering the expected future short rates through Taylor rule and then building that into current long rates by expectations theory.

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DeflationDeflation = falling price levelThis seldom occurs in modern economy, but sometimes

have near-zero inflation (Japan for two decades, US today).

Problems:- If full-employment interest rate < 0, have liquidity trap- Unstable dynamics: since r = i – π, as π falls have higher real interest rate, lower I, lower Y, and “low-level trap”

Some of the issues involved are discussed in Bullard, Seven Faces. Very interesting discussion!

But this is uncharted territory in modern macro!

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Balance the budget

One of the perennial concerns is budget deficits.

Many conservatives have proposed constitutional amendment to ensure balanced budget.

European governments are pursuing tight fiscal policies to reduce deficits in current global recession.

What would be the effect of attempting to aim for slight budget surplus over next two years? (For simplicity, I use the full-employment budget.)

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-8

-6

-4

-2

0

2

4

6

82004 2006 2008 2010 2012 2014 2016 2018 2020

Percen

t

r π (Y-Y*)/Y* i

Forecast

Balanced surplus (2% structural)

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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

We now move on to long-run growth theory next week.