A Dynamic Model of Aggregate Demand and Aggregate Supply

A Dynamic Model of Aggregate Demand and Aggregate Supply

Chapter 14 of Macroeconomics, 7th edition, by N. Gregory Mankiw

ECO62 Udayan Roy

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Inflation and dynamics in the short run

• So far, to analyze the short run we have used– the Keynesian Cross theory, and– the IS-LM theory

• Both theories are silent about inflation and dynamics

• In this chapter, that silence will end• This chapter presents a dynamic model of

aggregate demand and aggregate supply (DAD-DAS)

Introduction

• The dynamic model of aggregate demand and aggregate supply (DAD-DAS) gives us more insight into how the economy behaves in the short run.

• This theory determines both real GDP (Y) and the inflation rate (π)

• This theory is dynamic in the sense that the outcome in one period affects the outcome in the next period– like the Solow-Swan model, but for the short run

• Instead of representing monetary policy by an exogenous money supply, the central bank will now be seen as following a monetary policy rule that adjusts interest rates automatically when output or inflation are not where they should be.

Introduction

Introduction

Keeping track of time

• The subscript “t ” denotes a time period, e.g.– Yt = real GDP in period t – Yt − 1 = real GDP in period t – 1– Yt + 1 = real GDP in period t + 1

• We can think of time periods as years. E.g., if t = 2008, then – Yt = Y2008 = real GDP in 2008– Yt − 1 = Y2007 = real GDP in 2007– Yt + 1 = Y2009 = real GDP in 2009

The model’s elements

• The model has five equations and five endogenous variables: – output, inflation, the real interest rate, the

nominal interest rate, and expected inflation.

• The first equation is for output…

Output: The Demand for Goods and Services

( )t t t tY Y ra r e= - - +

0, 0a r> >output natural level of output

real interest

rate

Assumption: There is a negative relation between output (Yt) and interest rate (rt). The justification is the same as for the IS curve of Ch. 10.

Assumption: There is a negative relation between output (Yt) and interest rate (rt). The justification is the same as for the IS curve of Ch. 10.

Output: The Demand for Goods and Services

( )t t t tY Y ra r e= - - +

demand shock,

random and zero on average

measures the interest-rate sensitivity of

demand

“natural rate of interest”

Note that in the absence of demand shocks,

t tY Y= when tr r=

The demand shock is positive when C0, I0, or G is higher than usual or T is lower than usual.

This is the long-run real interest rate we had calculated in Ch. 3

IS Curve = Demand Equation

Yt

r

Y

rt

IS

Yt

r

Y

rt

IS The long-run real interest rate of Ch. 3 is now denoted by the lower-case Greek letter ρ.

IS Curve = Demand Equation

Yt

r

Y

rt

IS

Yt

r

Y

rt

IS

The Real Interest Rate: The Fisher Equation

1t t t tr i E p += -

nominal interest

rate

expected inflation rate

ex ante (i.e. expected)

real interest rate

Assumption: The real interest rate is the inflation-adjusted interest rate. To adjust the nominal interest rate for inflation, one must simply subtract the expected inflation rate during the duration of the loan.

The Real Interest Rate: The Fisher Equation

1t t t tr i E p += -

nominal interest

rate

expected inflation rate

ex ante (i.e. expected)

real interest rate

increase in price level from period t to t +1, not known in period t

expectation, formed in period t, of inflation from t to t +1

1tp + =

1t tE p + =

We saw this before in Ch. 4

Inflation: The Phillips Curve

1 ( )t t t t t tE Y Yp p f n-= + - +

previously expected inflation

current inflation

supply shock,

random and zero on average indicates how much

inflation responds when output fluctuates around

its natural level

0f >

Phillips Curve

• Assumption: At any particular time, inflation would be high if– people in the past were expecting it to be high– current demand is high (relative to natural GDP)– there is a high inflation shock. That is, if prices are

rising rapidly for some exogenous reason such as scarcity of imported oil or drought-caused scarcity of food

π t=E t−1 π t+φ⋅(Y t−Y t)+ν t

Phillips Curve

π t=E t−1 π t+φ⋅(Y t−Y t)+ν tMomentum

inflationDemand-

pull inflation

Cost-push inflation

Expected Inflation: Adaptive Expectations

1t t tE p p+ =

Assumption: people expect prices to continue rising at the current inflation rate.

Assumption: people expect prices to continue rising at the current inflation rate.

Examples: E2000π2001 = π2000; E2010π2011 = π2010; etc.

Monetary Policy Rule

• The fifth and final main assumption of the DAD-DAS theory is that

• The central bank sets the nominal interest rate

• and, in setting the nominal interest rate, the central bank is guided by a very specific formula


it=π t+ ρ+θπ⋅(π t−π t¿)+θY⋅(Y t−Y t )

Nominal interest rate, set each period by the central bank

Current inflation rate

Natural real interest rate

Parameter that measures how strongly the central bank responds to the inflation gap

Parameter that measures how strongly the central bank responds to the GDP gap

Inflation Gap: The excess of current inflation over the central bank’s inflation target

GDP Gap: The excess of current GDP over natural GDP

Example: The Taylor Rule• Economist John Taylor proposed a monetary policy rule

very similar to ours:

iff = + 2 + 0.5 ( – 2) – 0.5 (GDP gap)

where

– iff = nominal federal funds rate target

– GDP gap = 100 x

= percent by which real GDP is below its natural rate

• The Taylor Rule matches Fed policy fairly well.…

Y Y

Y

-

CASE STUDYThe Taylor Rule

Taylor’s rule

actual Federal

Funds rate

SUMMARY OF THE DAD-DAS MODEL

The model’s variables and parameters

• Endogenous variables:

tY =

tr =

tp =

1t tE p + =ti =

Output

Inflation

Real interest rate

Nominal interest rate

Expected inflation


• Exogenous variables:

• Predetermined variable:

tY =*tp =

te =

tn =

1tp - =

Natural level of output

Central bank’s target inflation rate

Demand shock

Supply shock

Previous period’s inflation


• Parameters:a =

r =f =

pq =

Yq =

Responsiveness of demand to the real interest rate

Natural rate of interest

Responsiveness of inflation to output in the Phillips Curve

Responsiveness of i to inflation in the monetary-policy rule

Responsiveness of i to output in the monetary-policy rule

The DAD-DAS Equations

Y t=Y t−α⋅(rt−ρ )+εtrt=it−E t π t+1π t=E t−1 π t+φ⋅(Y t−Y t)+ν tEt π t+1=π tit=π t+ ρ+θπ⋅(π t−π t

¿)+θY⋅(Y t−Y t )

Demand Equation

Fisher Equation

Phillips Curve

Adaptive Expectations


THE LONG RUN EQUILIBRIUM

The DAD-DAS model’s long-run equilibrium

• This is the normal state around which the economy fluctuates.

• The economy is in long-run equilibrium when:– There are no shocks:

– Inflation is stable:

0t te n= =

1t tp p- =


Et π t+1=π tEt−1π t=π t−1

π t=E t−1 π t+φ⋅(Y t−Y t)+ν tπ t=π t−1+φ⋅(Y t−Y t )+ν t

Recall that the long-run equilibrium requirements are:

0t te n= = 1t tp p- =


Phillips Curve

DAS Curve


Y t=Y t−α⋅(rt−ρ )+εt Demand Equation

Recall that the long-run equilibrium requirements include:

0t te n= =


rt=it−E t π t+1Et π t+1=π t

rt=it−π tFisher Equation


Therefore, in the DAD-DAS theory, the (ex ante) real interest rate is the current nominal interest rate minus the inflation rate just observed.


rt=it−E t π t+1Et π t+1=π t

rt=it−π tρ=it−π tρ+π t=it




• To summarize, the long-run equilibrium values in the DAD-DAS theory are essentially the same as the long run theory we saw earlier in this course:

t tY Y=

tr r=*

t tp p=*

1t t tE p p+ =*

t ti r p= +

SHORT-RUN FLUCTUATIONS AROUND THE LONG RUN

Recap: Dynamic Aggregate Supply

π t=E t−1 π t+φ⋅(Y t−Y t)+ν tEt π t+1=π t

Phillips Curve


π t=π t−1+φ⋅(Y t−Y t )+ν t DAS Curve

Et−1π t=π t−1

The Dynamic Aggregate Supply Curve

DAS slopes upward: high levels of output are associated with high inflation.

DAS slopes upward: high levels of output are associated with high inflation.

Y

π

DASt

1 ( )-= + - +t t t t tY Yp p f n

Y t

π t−1+νt


Y

π

DAS2011

1 ( )-= + - +t t t t tY Yp p f n

Y 2011

π2010+ν2011

If you know (a) the natural GDP at a particular date, (b) the inflation shock at that date, and (c) the previous period’s inflation, you can figure out the location of the DAS curve at that date.


Y

π

DAS2015

1 ( )-= + - +t t t t tY Yp p f n

Y 2015

π2014+ν2015

If you know (a) the natural GDP at a particular date, (b) the inflation shock at that date, and (c) the previous period’s inflation, you can figure out the location of the DAS curve at that date.

Shifts of the DAS Curve

Y

π

DASt

1 ( )-= + - +t t t t tY Yp p f n

Y t

π t−1+νt

Any increase (decrease) in the previous period’s inflation or in the current period’s inflation shock shifts the DAS curve up (down) by the same amount


Shifts of the DAS Curve

Y

π

DASt

1 ( )-= + - +t t t t tY Yp p f n

Y t

π t−1+νt



Any increase (decrease) in natural GDP shifts the DAS curve right (left) by the exact amount of the change.

Any increase (decrease) in natural GDP shifts the DAS curve right (left) by the exact amount of the change.

The Dynamic Aggregate Demand Curve

( )t t t tY Y ra r e= - - +

1( )+= - - - +t t t t t tY Y i Ea p r e

Fisher equationFisher equation

rt=it−E t π t+1

( )= - - - +t t t t tY Y ia p r eadaptive

expectationsadaptive

expectations

Et π t+1=π t

The Demand Equation


( )= - - - +t t t t tY Y ia p r e

*[ ( ) ( ) ]= - + + - + - - - +t t t t t Y t t t tY Y Y Ypa p r q p p q p r e

monetary policy rulemonetary policy rule

*[ ( ) ( )]= - - + - +t t t t Y t t tY Y Y Ypa q p p q e


We’re almost there!

Dynamic Aggregate Demand*[ ( ) ( )]= - - + - +t t t t Y t t tY Y Y Ypa q p p q e

Y t=Y t−αθ π⋅( π t−π t¿)−αθY Y t+αθY Y t+εt

Y t+αθY Y t=Y t−αθπ⋅(π t−π t¿)+αθY Y t+ε t

(1+αθY )⋅Y t=(1+αθY )⋅Y t−αθπ⋅( π t−π t¿)+εt

Y t=Y t−αθ π1+αθY

⋅(π t−π t¿)+11+αθY

εt

Y t=Y t−A⋅( π t−π t¿)+Bε t

This is the equation of the DAD curve!


DAD slopes downward:When inflation rises, the central bank raises the real interest rate, reducing the demand for goods and services.

DAD slopes downward:When inflation rises, the central bank raises the real interest rate, reducing the demand for goods and services.

Y

π

DADt

*A( ) B= - - +t t t t tY Y p p e

Note that the DAD equation has no dynamics in it, because it only shows how simultaneously measured variables are related to each other


Y

π

DADtB

*A( ) B= - - +t t t t tY Y p p e

π t¿

Y t+Bε t


Y

π

DADtB

*A( ) B= - - +t t t t tY Y p p e

π t¿

Y t+Bε t

When the central bank’s target inflation rate increases (decreases) the DAD curve moves up (down) by the exact same amount.

DADtA


Y

π

DADtB

*A( ) B= - - +t t t t tY Y p p e

π t¿

Y t+Bε t

When the natural rate of output increases (decreases) the DAD curve moves right (left) by the exact same amount.

When there is a positive (negative) demand shock the DAD curve moves right (left) .

A positive demand shock could be an increase in C0, I0, or G, or a decrease in T.

DADtA


Y

π

The DAD curve shifts right or up if: (a) the central bank’s target inflation rate goes up, (b) there is a positive demand shock, or (c) the natural rate of output increases.

The DAD curve shifts right or up if: (a) the central bank’s target inflation rate goes up, (b) there is a positive demand shock, or (c) the natural rate of output increases.DADtB

DADtA

Y t=Y t−αθπ1+αθY

⋅( π t−π t¿)+

11+αθY

εt

Summary: DAD-DAS Slopes and Shifts

DAS• Upward sloping• If natural output increases,

shifts right by same amount• If previous-period inflation

increases, shifts up by same amount

• If there is a positive inflation shock (νt > 0), shifts up by same amount

DAD• Downward sloping• If natural output increases,

shifts right by same amount• If target inflation increases,

shifts up by same amount• If there is a positive demand

shock (εt > 0), shifts right

DAD-DAS EQUILIBRIUM

Yt

The short-run equilibrium

In each period, the intersection of DAD and DAS determines the short-run equilibrium values of inflation and output.

In each period, the intersection of DAD and DAS determines the short-run equilibrium values of inflation and output.

πt

Yt

Y

π

DADt

DASt

AIn the equilibrium shown here at A, output is below its natural level. In other words, the DAD-DAS theory is fully capable of explaining recessions and booms.

In the equilibrium shown here at A, output is below its natural level. In other words, the DAD-DAS theory is fully capable of explaining recessions and booms.

DAD-DAS PREDICTIONS

Long-Run Growth

Recap: DAD-DAS Slopes and Shifts


shifts right by same amount

• If previous-period inflation increases, shifts up by same amount



shifts right by same amount

• If target inflation increases, shifts up by same amount

• If there is a positive demand shock (εt > 0), shifts right

Long-run growth Period t: initial equilibrium at APeriod t: initial equilibrium at A

Y

π

DASt

Yt

DADt

A

Yt

Period t + 1: Long-run growth increases the natural rate of output.

Period t + 1: Long-run growth increases the natural rate of output.

Yt +1

DASt +1

DADt +1

Bπt + 1

πt

=

DAS shift right by the exact amount of the increase in natural GDP.

DAS shift right by the exact amount of the increase in natural GDP.

DAD shifts right too by the exact amount of the increase in natural GDP.

DAD shifts right too by the exact amount of the increase in natural GDP.New equilibrium at B. Income grows but inflation remains stable.

New equilibrium at B. Income grows but inflation remains stable.

Yt +1

Long-Run Growth

• Therefore, starting from long-run equilibrium, if there is an increase in the natural GDP,– actual GDP will immediately increase to the new

natural GDP, and– none of the other endogenous variables will be

affected

Inflation Shock

• Suppose the economy is in long-run equilibrium

• Then the inflation shock hits for one period (νt > 0) and then goes away (νt+1 = 0)

• How will the economy be affected, both in the short run and in the long run?

A shock to aggregate supply

Period t – 1: initial equilibrium at APeriod t – 1: initial equilibrium at A

πt – 1

Yt –1

Period t: Supply shock (νt > 0) shifts DAS upward; inflation rises, central bank responds by raising real interest rate, output falls.

Period t: Supply shock (νt > 0) shifts DAS upward; inflation rises, central bank responds by raising real interest rate, output falls.

Period t + 1: Supply shock is over (νt+1 = 0) but DAS does not return to its initial position due to higher inflation expectations.

Period t + 1: Supply shock is over (νt+1 = 0) but DAS does not return to its initial position due to higher inflation expectations.

Period t + 2: As inflation falls, inflation expectations fall, DAS moves downward, output rises.

Period t + 2: As inflation falls, inflation expectations fall, DAS moves downward, output rises.

Y

π

DASt -1

Y

DAD

A

DASt

Yt

Bπt

DASt +1

C

DASt +2

D

Yt + 2

πt + 2

This process continues until output returns to its natural rate. The long run equilibrium is at A.

A shock to aggregate supply: one more time

π2000 = π2001

Y01

Y

π

DAS2001

Y

DAD

A

DAS2002

Y02

Bπ2002

DAS2003

CD

DAS2004

Y03

π2003

π2001 + ν2002

π2004

Y04

ν2002

Inflation Shock

• So, we see that if a one-period inflation shock hits the economy,– inflation rises at the date the shock hits, but then

returns to the unchanged long-run level, and– GDP falls at the date the shock hits, but then

returns to the unchanged long-run level

• What happens to the interest rates i and r?

Inflation Shock

• According to the monetary policy rule, the temporary spike in inflation dictates an increase in the real interest rate, whereas the temporary fall in GDP indicates a decrease in the real interest rate

• The overall effect is ambiguous, for both interest rates• We can do simulations for specific values of the

parameters and exogenous variables


it−π t=ρ+θπ⋅(π t−π t¿)+θY⋅(Y t−Y t)

rt= ρ+θπ⋅(π t−π t¿)+θY⋅(Y t−Y t )

Parameter values for simulations100=tY

* 2.0=tp1.0=a

2.0=r0.25=f

0.5=pq0.5=Yq

The central bank’s inflation target is 2 percent.The central bank’s inflation target is 2 percent.

A 1-percentage-point increase in the real interest rate reduces output demand by 1 percent of its natural level.

A 1-percentage-point increase in the real interest rate reduces output demand by 1 percent of its natural level.

The natural rate of interest is 2 percent. The natural rate of interest is 2 percent.

When output is 1 percent above its natural level, inflation rises by 0.25 percentage point.When output is 1 percent above its natural level, inflation rises by 0.25 percentage point.

These values are from the Taylor Rule, which approximates the actual behavior of the Federal Reserve.

These values are from the Taylor Rule, which approximates the actual behavior of the Federal Reserve.

Impulse Response Functions

• The following graphs are called impulse response functions.

• They show the “response” of the endogenous variables to the “impulse,” i.e. the shock.

• The graphs are calculated using our assumed values for the exogenous variables and parameters

The dynamic response to a supply shock

tY

tn

A one-period supply shock affects output for many periods.

A one-period supply shock affects output for many periods.


tp

tnBecause inflation expectations adjust slowly, actual inflation remains high for many periods.

Because inflation expectations adjust slowly, actual inflation remains high for many periods.


tr

tn

The real interest rate takes many periods to return to its natural rate.

The real interest rate takes many periods to return to its natural rate.


ti

tnThe behavior of the nominal interest rate depends on that of inflation and real interest rates.

The behavior of the nominal interest rate depends on that of inflation and real interest rates.

A Series of Aggregate Demand Shocks

• Suppose the economy is al the long-run equilibrium

• Then a positive aggregated demand shock hits the economy for five successive periods (ε > 0), and then goes away (ε = 0)

• How will the economy be affected in the short run?

• That is, how will the economy adjust over time?








shifts up by same amount• If there is a positive

demand shock (εt > 0), shifts right

A shock to aggregate demandPeriod t – 1: initial equilibrium at APeriod t – 1: initial equilibrium at A

πt – 1

Y

π

DASt -1,t

Y

DADt ,t+1,…,t+4

DADt -1, t+5

DASt +5

Yt –1

A

DASt + 1

C

DASt +2

D

DASt +3

E

DASt +4

F

Yt

Bπt

Yt + 5

Gπt + 5

Period t: Positive demand shock (ε > 0) shifts AD to the right; output and inflation rise.

Period t: Positive demand shock (ε > 0) shifts AD to the right; output and inflation rise.

Period t + 1: Higher inflation in t raised inflation expectations for t + 1, shifting DAS up. Inflation rises more, output falls.

Period t + 1: Higher inflation in t raised inflation expectations for t + 1, shifting DAS up. Inflation rises more, output falls.

Periods t + 2 to t + 4:Higher inflation in previous period raises inflation expectations, shifts DAS up. Inflation rises, output falls.

Periods t + 2 to t + 4:Higher inflation in previous period raises inflation expectations, shifts DAS up. Inflation rises, output falls.Period t + 5: DAS is higher due to higher inflation in preceding period, but demand shock ends and DAD returns to its initial position. Equilibrium at G.

Period t + 5: DAS is higher due to higher inflation in preceding period, but demand shock ends and DAD returns to its initial position. Equilibrium at G.

Periods t + 6 and higher:DAS gradually shifts down as inflation and inflation expectations fall. The economy gradually recovers and reaches the long run equilibrium at A.

Periods t + 6 and higher:DAS gradually shifts down as inflation and inflation expectations fall. The economy gradually recovers and reaches the long run equilibrium at A.

A 3-period shock to aggregate demand

π1999 = π00

Y

π

DAS00,01

Y

DAD01,02,03

DAD00,04

Y00

A

DAS02

C

Y01

Bπ01

DAS03

Dπ02

π03

Y02Y03

DAS04

When the demand shock first hits, output and inflation both increase. In the two following periods, despite the continuing presence of the demand shock, output starts to fall. Inflation continues to rise.

A shock to aggregate demand

π1999 = π00

Y

π

DAS00,01

Y

DAD00,04,05,06

Y00

A

π03

Y05Y04

DAS04

π04

DAS05DAS06

π05

On the date the demand shock ends, output falls below the long-run level and inflation finally begins to fall. After that, output rises and inflation falls towards the initial long-run equilibrium.

A Series of Aggregate Demand Shocks: 4 Phases

1. On the date the multi-period demand shock first hits, both output and inflation rise above their long-run values

2. After that, while the demand shock is still present, output falls and inflation continues to rise

3. On the date the demand shock ends, output falls below its long-run value and inflation falls

4. After that, output recovers and inflation falls, gradually returning to their original long-run values

• What happens to the interest rates i and r?

Inflation Shock

• According to the monetary policy rule, an increase (decrease) in either inflation or output dictates an increase (decrease) in the real interest rate

• We can do simulations for specific values of the parameters and exogenous variables


it−π t=ρ+θπ⋅(π t−π t¿)+θY⋅(Y t−Y t)

rt= ρ+θπ⋅(π t−π t¿)+θY⋅(Y t−Y t )

A Series of Aggregate Demand Shocks: 4 Phases, interest rates

1. On the date the multi-period demand shock first hits, both output and inflation rise above their long-run values. So, interest rate rises

2. After that, while the demand shock is still present, output falls and inflation continues to rise. Now, the effect on the interest rate is ambiguous

3. On the date the demand shock ends, output falls below its long-run value and inflation falls. So, the interest rate falls

4. After that, output recovers and inflation falls, gradually returning to their original long-run values. Again, the effect on the interest rate is ambiguous, but it does return to its original long run value (ρ)

The dynamic response to a demand shock

tY

te

The demand shock raises output for five periods. When the shock ends, output falls below its natural level, and recovers gradually.

The demand shock raises output for five periods. When the shock ends, output falls below its natural level, and recovers gradually.


tp

teThe demand shock causes inflation to rise. When the shock ends, inflation gradually falls toward its initial level.

The demand shock causes inflation to rise. When the shock ends, inflation gradually falls toward its initial level.


tr

te

The demand shock raises the real interest rate. After the shock ends, the real interest rate falls and approaches its initial level.

The demand shock raises the real interest rate. After the shock ends, the real interest rate falls and approaches its initial level.


ti

teThe behavior of the nominal interest rate depends on that of the inflation and real interest rates.

The behavior of the nominal interest rate depends on that of the inflation and real interest rates.

Stricter Monetary Policy

• Suppose an economy is initially at its long-run equilibrium

• Then its central bank becomes less tolerant of inflation and reduces its target inflation rate (π*) from 2% to 1%

• What will be the short-run effect?• How will the economy adjust to its new long-

run equilibrium?








shifts up by same amount• If there is a positive demand

shock (εt > 0), shifts right

A shift in monetary policyPeriod t – 1: target inflation rate π* = 2%, initial equilibrium at A

Period t – 1: target inflation rate π* = 2%, initial equilibrium at A

πt – 1 = 2%

Yt –1

Period t: Central bank lowers target to π* = 1%, raises real interest rate, shifts DAD leftward. Output and inflation fall.

Period t: Central bank lowers target to π* = 1%, raises real interest rate, shifts DAD leftward. Output and inflation fall.Period t + 1: The fall in πt reduced inflation expectations for t + 1, shifting DAS downward. Output rises, inflation falls.

Period t + 1: The fall in πt reduced inflation expectations for t + 1, shifting DAS downward. Output rises, inflation falls.

Y

πDASt -1, t

Y

DADt – 1

A

DADt, t + 1,…

DASfinal

Yt

πtB

DASt +1

C

Subsequent periods:This process continues until output returns to its natural rate and inflation reaches its new target.

Subsequent periods:This process continues until output returns to its natural rate and inflation reaches its new target.

Zπfinal = 1%

,

Yfinal

Stricter Monetary Policy

• At the date the target inflation is reduced, output falls below its natural level, and inflation falls too towards its new target level– The real interest rate rises above its natural level (ρ)– The effect on the nominal interest rate (i = r + π) is

ambiguous• On the following dates, output recovers and gradually

returns to its natural level. Inflation continues to fall and gradually approaches the new target level.– The real interest rate falls, gradually returning to its natural

level (ρ)– The nominal interest rate falls to its new and lower long-run

level (i = ρ + π*)

The dynamic response to a reduction in target inflation

tY

*tp

Reducing the target inflation rate causes output to fall below its natural level for a while. Output recovers gradually.

Reducing the target inflation rate causes output to fall below its natural level for a while. Output recovers gradually.


tp

*tp Because

expectations adjust slowly,

it takes many periods for inflation to reach the new target.

Because expectations adjust slowly,

it takes many periods for inflation to reach the new target.


tr

*tp

To reduce inflation, the central bank raises the real interest rate to reduce aggregate demand.The real interest rate gradually returns to its natural rate.

To reduce inflation, the central bank raises the real interest rate to reduce aggregate demand.The real interest rate gradually returns to its natural rate.


ti

*tp

The initial increase in the real interest rate raises the nominal interest rate. As the inflation and real interest rates fall, the nominal rate falls.

The initial increase in the real interest rate raises the nominal interest rate. As the inflation and real interest rates fall, the nominal rate falls.

APPLICATION:Output variability vs. inflation variability

• A supply shock reduces output (bad) and raises inflation (also bad).

• The central bank faces a tradeoff between these “bads” – it can reduce the effect on output, but only by tolerating an increase in the effect

on inflation….


CASE 1: θπ is large, θY is small

Y

π

DADt – 1, t

DASt

DASt – 1

Yt –1

πt –1

Yt

πt

A supply shock shifts DAS up.A supply shock shifts DAS up. In this case, a small

change in inflation has a large effect on output, so DAD is relatively flat.

In this case, a small change in inflation has a large effect on output, so DAD is relatively flat.

The shock has a large effect on output, but a small effect on inflation.

The shock has a large effect on output, but a small effect on inflation.


CASE 2: θπ is small, θY is large

Y

π

DADt – 1, t

DASt

DASt – 1

Yt –1

πt –1

Yt

πt

In this case, a large change in inflation has only a small effect on output, so DAD is relatively steep.

In this case, a large change in inflation has only a small effect on output, so DAD is relatively steep.

Now, the shock has only a small effect on output, but a big effect on inflation.

Now, the shock has only a small effect on output, but a big effect on inflation.

APPLICATION:The Taylor Principle

• The Taylor Principle (named after economist John Taylor): The proposition that a central bank should respond to an increase in inflation with an even greater increase in the nominal interest rate (so that the real interest rate rises). I.e., central bank should set θπ > 0.

• Otherwise, DAD will slope upward, economy may be unstable, and inflation may spiral out of control.


If θπ > 0:

• When inflation rises, the central bank increases the nominal interest rate even more, which increases the real interest rate and reduces the demand for goods and services.

• DAD has a negative slope.

* 1( )

1 1= - - +

+ +t t t t tY Y

Y Y paqp p e

aq aq(DAD)

*( ) ( )= + + - + -t t t t Y t ti Y Ypp r q p p q (MP rule)


If θπ < 0:

• When inflation rises, the central bank increases the nominal interest rate by a smaller amount. The real interest rate falls, which increases the demand for goods and services.

• DAD has a positive slope.

* 1( )

1 1= - - +

+ +t t t t tY Y

Y Y paqp p e

aq aq(DAD)

*( ) ( )= + + - + -t t t t Y t ti Y Ypp r q p p q (MP rule)


• If DAD is upward-sloping and steeper than DAS, then the economy is unstable: output will not return to its natural level, and inflation will spiral upward (for positive demand shocks) or downward (for negative ones).

• Estimates of θπ from published research:

– θπ = – 0.14 from 1960-78, before Paul Volcker became Fed chairman. Inflation was high during this time, especially during the 1970s.

– θπ = 0.72 during the Volcker and Greenspan years. Inflation was much lower during these years.

A Dynamic Model of Aggregate Demand and Aggregate Supply

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