Macro theory: A quick review

Giovanni Di Bartolomeo

giovanni.dibartolomeo@uniroma1.it

Sapienza University of Rome

Department of economics and law

Advanced Monetary Theory and Policy EPOS 2013/14

Theory: Big view

Keynesian

Cross

Theory of

Liquidity

Preference

IS

curve

LM

curve

IS-LM

model

AD

curve

AS

curve

Model of

AD/AS

Business

Cycle

fluctuations

Phillips

curve

The downward-sloping AD curve

Y

P

AD

• The aggregate demand curve shows the relationship

between the price level and the quantity of output

demanded. It can be derived from the IS/LM model

A

B

Y1 Y2 Y

r

Y

P

IS

LM(P1)

LM(P2)

AD

P1

P2

Y2 Y1

r2

r1

Intuition for slope

of AD curve:

P (M/P )

LM shifts left

r

I

Y

Intuition: Deriving the AD curve

A

B

Shifting the AD curve

Y

P

AD

• An increase in the money supply shifts the AD curve to

the right

AD2

C D

Y

P

IS

LM(M2/P1)

LM(M1/P1)

AD1

P1

Y1

Y1

Y2

Y2

r1

r2

The Fed can increase

aggregate demand:

M LM shifts right

AD2

Y

r

r

I

Y at each

value of P

Intuition: Monetary policy and the AD curve

C D

Neoclassical view

• The economy works well on its own

• “Invisible hand”: the idea that if there are free markets

and individuals conduct their economic affairs in their

own best interests, the overall economy will work well…

• Wages and prices adjust rapidly to get to equilibrium

– Equilibrium: a situation in which the quantities

demanded and supplied are equal

– Changes in wages and prices are signals that

coordinate people‟s actions

• Result: Government should have only a limited role in

the economy

Quantitative theory in the AD/AS model

• Neo-classic economists: Money is a veil and monetary

policy useless

Y

P

AD1

LRAS

Y

An increase in M

shifts AD to the

right.

P1

P2 In the long run, this

raises the price

level…

…but leaves output

the same.

AD2

Determined by real factors

Do markets work?

The effects of a negative demand shock

PSRAS

LRAS

AD2

Y

P

Y

P2

Y2

A B

C AD1

AD shifts left,

depressing output and

employment

in the short run

Over time, prices fall

and the economy

moves down its

demand curve toward

natural employment

JM Keynes

Keynesian view

• The Great Depression: Classical theory failed because

high unemployment was persistent

• Keynes: Persistent unemployment occurs because

wages and prices adjust slowly, so markets remain out

of equilibrium for long periods

– Indeed Keynes (and Kalescki) argues that prices and

wages may do not adjust at all

– Anyway the long run is very far: In the long run we

are all dead (J.M. Keynes)

• Conclusion: Government should intervene to restore full

employment

“Keynesian” world (fixed prices)

• Keynesian economists: Money is not neutral (it affects

output)

Y

P

AD1

In the short run when

prices are sticky…

…causes output to rise.

PSRAS

Y2 Y1

…an increase in

aggregate demand…

AD2

Y

LRAS

Samuelson and Solow in the 1960s

• Between (fully) flexible and fixed price models

Y

P

AS

AD1

AD2

2P

P1

A

B

Y1 Y2

JFK

AD/AS and the policy menu

u 0

4 7

B

A

6

2

Y 8,000 7,500 0

106

102

P

A

B

u=4% u=7% Y=8000

Y=7500

AS

AD2

AD1

Policy menu

Unemployment rates associated to output values

(Okun Law)

The Phillips Curve is just an alternative way

of describing the Aggregate Supply Curve

The estimated Phillips curve: - a u + C

Unemployment rate (u)

Inflation rate ()

1968

1966

19611962

1963

1967

19651964

0 1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

C

-a

In the interview, Robert Solow said “Paul Samuelson

asked me when we were looking at these diagrams (of

inflation and unemployment) for the first time, „Does

that look like a reversible relation to you?‟ What he

meant was „Do you really think the economy can move

back and forth along a curve like that?‟ And I answered

„Yeah I‟m inclined to believe it,‟ and Paul said „Me too‟”

Robert Solow

Paul Samuelson

Government loss function: L = b2+u2

Unemployment rate (u)

Inflation rate ()

0 1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

First best

L1

L2

L3

L0

[,u] =[0,0]

L3>L2>L1>L0

Optimal policy (Tinbergen-Theil approach )

Unemployment rate (u)

Inflation rate ()

0 1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

First best

L1

L2

L3

L0

E

A B

optimal policy rule

Formal representation of the problem

• The Government (Central bank)‟s flexible-target problem

𝑀𝑖𝑛 𝐿 = 𝛽𝜋2 + 𝑢2 s.t. 𝜋 = −𝛼𝑢 + 𝐶

• How can we solve it? (many ways)

• By Lagrangian

𝑀𝑖𝑛*𝜋,𝑢,l+ L = 𝛽𝜋2 + 𝑢2 + l −𝛼𝑢 + 𝐶 − 𝜋

• Or by substitution

𝑀𝑖𝑛*𝜋,𝑢,l+ L = 𝛽𝜋2 +𝐶

𝛼−

𝜋

𝛼

2 (find 𝜋 and then u by PC)

or

𝑀𝑖𝑛*𝜋,𝑢,l+ L = 𝛽𝜋2 + −𝛼𝑢 + 𝐶 2 (find u and then 𝜋 by PC)

• Or …

Optimal policy rule (derivation)

• The Government (Central bank)‟s problem

𝑀𝑖𝑛*𝜋+𝐿 = 𝛽𝜋2 + 𝑢(𝜋)2 s.t. 𝑢(𝜋) =𝐶

𝛼−

𝜋

𝛼

• The operative instrument is 𝜋 (it chooses M, moving the

AD, to get a certain P (i.e. 𝜋) on the AS, Y and 𝑢 follows)

• First order condition

2𝛽𝜋 + 2𝑢𝜕𝐶(𝜋)

𝜕𝑢= 0

• i.e. optimal policy rule (Government minimize the cost):

𝛽𝜋 −1

𝛼𝑢 = 0 𝜋 =

1

𝛼𝛽𝑢

• By using the optimal monetary policy rule and the PC we

obtain the equilibrium for and (a linear system of two

equations in two unknowns)

In the 1970s something changes

• Stagflation; both are u high (out of PC?)

1966

1971

19611962

1963

1967

1968

19691970

19651964

1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

Inflation rate ()

Unemployment rate (u)

1972

19751981

1976

19781979

1980

1973

1974

1977

The 1970s oil shocks

1P SRAS1

Y

P

AD

LRAS

YY2

A

B 2P SRAS2

A

The oil price shock

shifts SRAS up,

causing output and

employment to fall

In absence of further

price shocks, prices will

fall over time and

economy moves back

toward natural level of

employment

Stagflation

1966

1971

19611962

1963

1967

1968

19691970

19651964

1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

Inflation rate ()

Unemployment rate (u)

1972

19751981

1976

19781979

1980

1973

1974

1977

Optimal policy and an (observed) shock

optimal policy rule

C+e

- a u + C + e

A

C

𝝅 =𝟏

𝜶𝜷𝒖

Friedman‟s 1968 AEA Presidential Address

• Milton Friedman argued the following

– Theory (his theory) predicts no stable relationship

between unemployment and inflation

– According to his theory, policymakers do face a short-

term tradeoff between unemployment and inflation

due to the private sector‟s failure to quickly adapt to

changing environments

– long term costs to policymakers of exploiting short

term tradeoff. If policymaker generates temporarily

low unemployment by inflating, in future, higher and

higher unemployment rates will be associated with

each level of inflation. (Phillips curve shifts out)

• This argument was formalized and refined by Lucas

• An attempt to increase Y over LRAS…

From the short to the long run (M > 0)

Y

P

AD1

LRAS

Y

PSRAS

P2

Y2

A

B

C

AD2

Expectations: Phillips Curve and SRAS

• Do shocks only matter?

• How does the economy moves from the short to the long

run position?

• The role of expectations!!!

• SRAS curve: Output is related to unexpected

movements in the price level

• Phillips curve: Unemployment is related to unexpected

movements in the inflation rate

+ - +eY Y P P eSRAS: ( )

- - +( )e nu u a ePhillips curve:

The Phillips Curve and SRAS equivalence

+ - +eY Y P P SRAS: ( )

- - +( )e nu u a ePhillips curve:

- -

+ - -

- - - + -

- - - -

- - +

- - +

( )

( )

( ) ( )

e

e

NP

P

e

e N

e N

Y Y P P

Y Y P P P P

u u

u u

u u

L

L

a

e

1 1

See next slide

Note

• YP and LP are potential output and (full) employment,

thus if Y=YP and L=LP, then 𝑢 =𝐿𝐹−𝐿

𝐿𝐹= 0.

• But in the long run there are some distortions thus the

long rate (natural) output (𝑌 or YN) and employment (𝐿𝑁)

are lower than potentials, and 𝑢𝑁 =𝐿𝐹−𝐿𝑁

𝐿𝐹> 0.

• Consider the Okun law: 𝑌 = 𝜃𝐿, then

• We have that

𝑌 − 𝑌 = 𝜃 𝐿 − 𝐿𝑁 = 𝜃 𝐿 − 𝐿𝐹 − 𝐿𝑁 + 𝐿𝐹 =

= 𝐿𝐹𝜃𝐿 − 𝐿𝐹

𝐿𝐹−

𝐿𝑁 − 𝐿𝐹

𝐿𝐹

• i.e.

𝑌 − 𝑌 = −𝐿𝐹𝜃 𝑢 − 𝑢𝑁

Key Questions

• How are expectations formed?

• How fast do they adjust?

• Two theories

– Adaptive expectations (Friedman, …)

– Rational expectations (Sargent, Lucas, …)

Phillips curve: e nu u - - +( ) b

Friedman and Phelps

• The Phillips curve states that depends on

– cyclical unemployment: the deviation of the actual

rate of unemployment from the natural rate

– supply shocks

• It can also depend on

– The expected inflation rate, e (for instance, in wage

bargaining operators are interested in the real wage

so AS should depend on the expected real wage)

– Note that as long as is the operational instrument of

the central bank, one can think that e should also

depend on the expectations about monetary policy!

• Friedman assume that e = -1 (lagged inflation)

Friedman Phillips Curve

• Friedman adjustment based on past price to form current

expectations, e = -1, it follows

• Consider an increase of money growth, not all producers

adjust prices (imperfect information, no one knows if the

increase in demand is relative to his product or to all), output and prices increase → short run

• But afterward, one that everybody realizes that the

observed increase in the demand was general all will adjust prices → long run

• As results output will finally not increase and inflation

increase will be instead permanent

- - - +

1( )nu u a e

• Friedman adjustment based on past price to form current

expectations

Y

P LRAS

SRAS1

SRAS2

AD1

AD2

2P

2Y

Friedman and adaptive expectation

P1

P3

A

B C

Expectation-driven shifts in the Phillips curve

• People adjust their expectations over time, so the

tradeoff only holds in the short run

u

nu

+1

e e

+2

e e

E.g., an increase in e

shifts the short-run P.C.

upward. So if the central

bank tries to increase ,

in the long run the effect

will be offset by an equal

change in e

A

B C

( )e nu u b - - +

Policy menu in the long-run

Natural rate of unemployment

LR Policy menu

0

Phillips Curve

B

A

YN 0

P2

P1

AD1

LRAS

AS/AD Model

P

AD2

u Y

1966

1971

19611962

1963

1967

1968

19691970

19651964

1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

Inflation rate ()

Unemployment rate (u)

1972

19751981

1976

19781979

1980

1973

1974

1977

Short- and long-run Phillips curves

Long run Phillips curve

Short rune Phillips curves

A

The Lucas critique

• The Phillips curve states that depends on

– cyclical unemployment: the deviation of the actual

rate of unemployment (u) from the natural rate (uN)

– supply shocks, e

• Thus, - a u + C implies C= a uN + x + e

• Estimations from the past give unbiased values for a and

uN, but what does it occur if the shifter contains a policy

related term x( )?

• Estimating the theoretical equation (bold are estimated

parameters by OLS):

- a u - uN) + e

• We obtain a biased estimation as uN is correleted with

Neo-classical economics

• New Classical Theories were an attempt to explain the

apparent breakdown in the 1970s of the simple inflation-

unemployment trade-off predicted by the Phillips curve

– They argue that traditional models have assumed that

expectations are formed in naïve ways

– But naïve expectations are inconsistent with the

assumptions of microeconomics/rationality

– Expectations are rational (RE) so adjustment is

immediate

• No effect for monetary policy (unless surprise but then

usefulness or even counter-productive)

• But we do not need it as markets are efficient (on

average)

Neo-classical economics

• Micro-foundation → No Lucas critique (based on deep

parameters, which do not depend on the policy regime)

• Assumptions

– Perfect markets (flexible prices)

– Rational expectations hypothesis (REH)

• Expectations are rational so adjustment is immediate

– RE → disequilibrium exists only temporarily as a result of

random, unpredictable shocks

– No effect for monetary policy (unless surprise, but then it is

usefulness or even counter-productive)

– But, on average, all markets clear and there is natural

employment. No need for government stabilization

Rational expectations

• Naïve expectations: inconsistent with rationality as they

are associated with systematic errors

• The REH assumes that people use available information

efficiently, including how the economy works (Muth).

– People know the “true model” of the economy and that

they use this model to form their expectations of the future.

By “true” model we mean a model that is on average

correct in forecasting inflation

– People can make mistakes, but they do not make

systematic forecasting errors

• The forecast errors of expectations will be random with a

mean of zero, unrelated to those made in previous

periods, revealing no discernible pattern, and have the

lowest variance compared to other forecasting methods

From New Classicals to RBC and NK theory

• The New Classical Economics challenged Keynesian

theory, and stimulated the development of Real

Business Cycle (RBC) and New Keynesian (NK) Theory

• RBC theory accepts the REH, but views cycles arising in

frictionless, perfectly competitive economies with

complete markets. It argues that cycles arise through the

reactions of optimizing agents to real disturbances, such

as random changes in technology or productivity

• NK theory accepts the REH, but emphasizes the

importance of imperfect competition, costly or impeded

price adjustments, and externalities. It argues that

nominal shocks are the predominant cause of business

cycles