UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1 MACROECONOMICS I UPF LECTURE SLIDES SET 4...

UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1

MACROECONOMICS IUPF

LECTURE SLIDES SET 4

Professor Antonio Ciccone


3. Applications of the Ramsey-Cass-Koopmans (RCK) model

3.1 Government spending, consumption, and interest rates

3.2 Bond versus tax financed government spending



- Comparative “dynamics” in the RCK model

- Permanent, surprise drop in output

- Temporary, surprise drop in output

- Wars, government expenditures and interest rates

- The role of expectations

- Permanent, anticipated drop in output

- Temporary, anticipated drop in output


k

c

k-ISOCLINE: NO CAPITAL GROWTH

c-ISOCLINE: NO CONSUMPTION GROWTH

k*0

The RCK model


k

c



k*0


k

c

NEW k-ISOCLINE: NO CAPITAL GROWTH


k*0

Permanent, surprise fall in output for given k


timePermanent, surprise fall in output

Evolution of consumption


timePermanent, surprise fall in output

Evolution of capital intensity


-- consumption can JUMP at the time new information arrives

-- but consumption must be smooth (follow the first-order condition) from than onward:

There CANNOT BE an ANTICIPATED jump in consumption


k

c



k*0

Temporary, surprise fall in output for given k: PART I



k

c



k*0

Temporary, surprise fall in output for given k: PART II


k

c



k*0

Temporary,surprise fall in output: Equilibrium response


timeSTART of Tempfall in output

END of Tempfall in output

Evolution of the capital intensity




Evolution of real interest rate


Wars and real interest rates

-- Suppose government expenditures associated with wars are surprise, temporary events

-- Study the dynamic response of: capital, interest rates, and consumption to wars

-- Government expenditures associated with wars decrease output available for consumption and investment

( , )F K L G C I

INCREASE G Same effect as temporary fall in output


timeSTART of War END of War

Evolution of real interest rate


k

c



k*0

Permanent, anticipated fall in output: PART I


k

c



k*0

Permanent, anticipated fall in output: PART II


k

c



k*0

Permanent, anticipated fall in output: Equilibrium response


timeINFO of permanent FUTUREfall in output

Evolution of capital intensity

Output actually falls


timeINFO of permanent FUTUREfall in output


Output actually falls


k

c



k*0

Temporary, anticipated fall in output for given k: PART I


k

c



k*0

Temporary, anticipated fall in output for given k: PART II


k

c



k*0

Temporary, anticipated fall in output for given k: PART III


k

c



k*0

Temporary, anticipated fall in output: Equilibrium response


timeINFO of FUTURETemp fall in output


Evolution of the capital intensity

START of FUTURETemp fall in output


time


INFO of FUTURETemp fall in output


START of FUTURETemp fall in output


3. Application of the Ramsey-Cass-Koopmans (RCK) model


3.2 Bond versus tax financed government spending


Government expenditures and taxes

t t tGDEFICIT G T

Government intertemporal budget constraint

0 00 0

t t t t tPV T dt GWEALTH PV G dt


-- Suppose that households believe in government budget constraint

-- The government cut taxes at time t

-- But there is no indication that the government cuts expenditures

00

t tPV T dt

-- WHAT HAPPENS TO DISCOUNTED FLOW OF TAXES?


Nothing, because:

0 00 0

t t t t tPV T dt PV G dt GWEALTH

and the right-hand side of this equation has not changed.

Government will have to compensate current tax cut by tax increase sometime in the future.


Now let’s look at household intertemporal budget constraint:

0 00 0

0 00

t t t t

t t

PV C dt PV T dt

PV w Ldt Q

-- current tax cut does NOT affect this constraint at all as only the DISCOUNTERD PRESENT VALUE OF TAXES MATTERS

-- and present value of taxes remains constant if expenditures do not change


-- TAX CUT DOES NOT CHANGE HH CONSUMPTION

-- AS A RESULT IT DOES NOT CHANGE THE NATIONAL SAVINGS RATE:

t t t tS Y C G

-- DOES NOT AFFECT: - INVESTMENT(!) - AND INTEREST RATES (!)

-- HH SAVINGS INCREASES, BUT IS OFFSET BY AN INCREASE IN GOVERNMENT DEFICIT:

t t t t t tS Y T C T G


Hence, government cuts taxes

Has to issue debt (government bonds)Government ensures that real interest rate on bond mimicsmarket interest rate (before issue of new bonds)Households buy these new bonds with their tax savings

Hence, Household use to buy government bonds what they “save” in current taxes


3. The Diamond model1. Overlapping generations models2 Setup of the Diamond model1. Technology2. Household behavior3. Dynamic equilibrium system

3. Equilibrium growth and optimality4. Applications of the Diamond model1. Government spending, consumption, and

interest rates2. Bond versus tax financed government

spending


-- Discrete time model-- Households live for two periods, and only work in the first

1. Overlapping Generations models


Time 3 Time 4Time 2Time 1

Generation 1

YOUNG:Workand

Consume

RETIRED:Consume

THE LIFE CYCLE OF A SINGLE GENERATION


TIMING

Time 3 Time 4Time 2Time 1

Generation 1

Generation 2

Generation 3


2. Setup of the Diamond model

1. Technology2. Household behavior3. Dynamic equilibrium system


1. Technology

1 t t t tY K A L

Owned/Supplied by RETIRED Supplied by YOUNG

Capital fully depreciates during production: 1


time

t t+1

Born -Earn Wage-Consume-Save

- Earn Interest- Consume

2. Household behavior

GENERATION t

Production usesgeneration t labor

Production usesgeneration t capital


UTILITY of GENERATION t

MAXIMIZATION WITH DISCOUNTING&INTEREST

with respect to C

subject to INTERTEMPORAL BUDGET CONSTRAINT

1

1t

t tt

cc w

r

1max ( ) (1 ) ( )t tU c U c


FIRST-ORDER CONDITIONS FOR GENERATION t

1'( ) (1 )(1 ) '( )t tU c r U c

“EFFECTIVE TIME DISCOUNTING”


Take the following CES utility function:

with

CONSUMPTION PROFILE BECOMES

1 (1 )(1 )tt

t

cr

c


1

1t

t tt

cc w

r

(1 )(1 )

1t t

t tt

c rc w

r

11 (1 ) (1 )t t tc r w

11 (1 ) (1 )t

tt

wc

r

Consumption profile intoBudget constraint


11 (1 ) (1 )t

tt

wc

r

11 (1 ) (1 )t

t t t tt

ws w c w

r

1

1

(1 ) (1 )

1 (1 ) (1 )t

t tt

rs w

r

Consumption and savings of generation t (when young)


s

r

(1 )

1 (1 )t ts w

0


s

r

(1 )

1 (1 )t ts w

t ts w

0


s

r

(1 )

1 (1 )t ts w

0


1

1

1

(1 ) (1 )

1 (1 ) (1 )

t t t t

tt t

t

K I L s

rL w

r

3. Dynamic equilibrium system

Savings per young person


1(1 )t t t t tw MPL K A L

111 1t t t t tr MPK K A L

1 t t t tY K A L

Financed by SAVINGSof the now RETIRED

Supplied by YOUNG


1

11

1

(1 ) (1 )(1 )

1 (1 ) (1 )

t t t t

tt t t

t

K I L s

rK A L

r

11 1t t t tr K A L


1

1 1

1 1

11 1

(1 ) (1 )

1 (1 ) (1 )

t

t t

t t tt t t

t t t t t

K

L A

K A LL A r

L A L A r

11 1t t t tr K A L


1

1

1

(1 ) (1 )1(1 )(1 ) 1 (1 ) (1 )

t

tt

t

k

rk

n a r

1 1t tr k


3. Equilibrium growth and optimality

1

1 (1 )

(1 )(1 ) 1 (1 )

t

t

k

kn a

1


0

1tk

0k

1t tk bk

tk1k BGP


Optimality

• How to weight different generations unclear.

• Is the allocation at least Pareto efficient?


Dynamic Inefficiency

• A situation where the allocation is not even Pareto efficient

• I.e. we can increase consumption of at least one generation without decreasing consumption of all others


Consider case without technological progress a=0.

How much do we need to invest per person at time t to keep capital intensity constant?

11

1 1 1t t t t

tt t

K L i ik

L L n

1t tk k (1 )t ti k n


0 GoldRulek

( )t ty f k

tk

(1 )tk n

Consumption per capita


0

tkGoldRulek

Consumption per capita

1MPK n


11 (1 )

(1 ) 1 (1 )t tk k

n

1 (1 )(1 ) 1 (1 )

k kn

111 (1 )

(1 )1 (1 )BGPk

n

BGP


11 (1 )

(1 )(1 )1 (1 )

BGPMPKn

1(1 )MPK k

1 (1 )(1 ) (1 )

(1 )BGPMPK n

UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1 MACROECONOMICS I UPF LECTURE SLIDES SET 4...

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Transcript of UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1 MACROECONOMICS I UPF LECTURE SLIDES SET 4...