macroeconomics

Macroeconomics

LECTURE SLIDES SET 4

Professor Antonio Ciccone

Macroeconomics SET 4

3. Ramsey-Cass-Koopmans (RCK) Model: Applications

3.1Government expenditures, consumption and interest rate

3.2 Financing government expenditures: bonds vs taxes


3.1 Government expenditures, consumption and interest rate

- Comparative dynamics in RCK Model

- Permanent unexpected fall in output

- Temporary unexpected fall in output

-Wars, expenditures and interest rate

-The role of expectations

-Permanent anticipated fall in output

-Temporary anticipated fall in output


k

c

k-ISOCLINE: CONSTANT CAPITAL

c-ISOCLINE: CONSUMSUMPTION CONSTANT

k*0

RCK Model


k

c


c-ISOCLINE: CONSTANT CONSUMPTION

k*0


k

c


k*0

Permanent unexpected fall in output for a given k

NEW k-ISOCLINE: CONSTANT CAPITAL


timePermanent unexpectd fall in output

Consumption evolution


timePermanent unexpected fall in output

Capital intesity evolution


-Consumption can JUMP when new information appears

-- But the evolution of consumption must be smooth from now (following first-order conditions)

There CAN’T be ANTICIPATED jumps in consumption


k

c



k*0

Temporary unexpected fall in output for a given k: PART I



k

c



k*0

Temporary unexpected fall in output for a given k: PART II


k

c


k*0

Temporay unexpected fall in output: Equilibrium response



k

c



k*0

Temporary unexpected fall in output: Equilibrium response


TimeBeginning of temporary fall

End of temporary fall

Capital intensity evolution


Time

Real interest rate evolution

Beginning of temporary fall



Time


Beginning of temporary fall



Wars and real interest rate

-- Supose that the Government expenditures caused by a war are an unexpected and temporary event.

We’ll study capital stock, interest rate and consumption dynamic responses to the war.

-- Public expenditures associated with wars reduce the amount of output avalaible for consumption and investment.

INCREASE IN G Same effect as an output fall

ICGLKF ),(


timeBeginning of war End of war

Real interest rate evolution


Macroeconomics SET 4 Slide 19

Militar expenditures and long run interest rate at The United Kingdom (Barro, 1987)

The role of expectations

- Permanent anticipated fall in output

- Temporary anticipated fall in output


k

c



k*0

Permanent anticipad 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 about the FUTURE permanent fall in output


Permanent fall takes place here


time


INFO about the FUTURE permanent fall in output

Permanent fall takes place here


The role of expectations

- Permanent anticipated fall in output

- Temporary anticipated fall in output


k

c



k*0

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


k

c


k*0

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



k

c



k*0

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


k

c



k*0

Temporary anticipated fall in output: Equilibrium response


timeINFO about the FUTURE temporary fall in output

END of temporary fall in output


START of temporary fall in output


time


INFO about the FUTURE temporary fall in output

END of temporary fall in output

START of temporary fall in output


3. Ramsey-Cass-Koopmans (RCK) Model: Applications

3.1 Government expenditures, consumption and interest rate

3.2 Financing Government expenditures: bonds vs taxes


Government expenditures and taxes

Government intertemporal budget constraint

0 00 0 dtGVPWealthdtTVP tt

GOVttt

ttGOVt TGDeficit


-Suppose that families believe in Governments intertemporal budget constraint

-- Government reduces taxes at moment t

-- But there are no evidence that government will reduce also its expenditures

-- What happens to DISCOUNTED TAXES FLOW?

0 0 dtTVP tt


NOTHING, because:

And nothing has changed in right-side of the equation

GOVERNMENT WILL COMPENSATE THE REDUCTION IN CURRENT TAXES WITH AN INCREASE IN FUTURE TAXES

GOVttttt WealthdtGVPdtTVP

0 00 0


Lets look at families constraint:

-- The reduction in current taxes DOESN’T affect this constraint at all. Only matters the PRESENT DISCOUNTED VALUE OF TAXES

-- and the present value of taxes holds constant if government expenditures don’t change

00 00 0 00 QLdtwVPdtTVPdtCVP tttttt


- TAX REDUCTIONS DOESN’T CHANGE FAMILIES CONSUMPTION

-- AS A RESULT, NATIONAL SAVING RATE DOESN’T CHANGE

-- LLAVORS, NO AFECTA:-- SO, IT DOESN’T AFFECT: - INVESTMENT (!) - INTERES RATE (!)

-- FAMILIES INCREASE THEIR SAVINGS, BUT IT IS CANCELED WITH THE INCREASE IN GONVERNMENT DEBT:

tttt GCYS

)()( tttttt GTCTYS


Hence, if government reduces taxes

It has to issue debt (Bonds) El govern ha d’assegurar-se que el tipus d’interès real dels

títols replica el tipus d’interès de mercat (abans d’emetre nous títols)

The Government has to make sure that bond’s real interest rate replies market interest rate (before issuing new bonds)

Families buy those bonds with their savings.

So:

Families buy Government bonds using what they “saved” by the reduction in taxes


3. Diamond model

1. Overlapping generations model2. Model specification 1. Technology 2. Families behavior 3. Dynamic equilibrium system3. Equilibrium growth and optimality4. Diamond model applications 1. Government expenditures and interest rate 2. Financing government expenditures: bonds vs taxes


Model in discret time.- Families live for two periods, and only work in the first one.

1. Overlapping generations model


Time 3 Time 4Time 2Time 1

Generation 1

ACTIVE (or YOUNG):Work and consume

RETIRED (or OLD): Only consume

GENERATION’S LYFE CICLE


TEMPORAL ORGANIZATION

Time 3 Time 4Time 2Time 1

Generation 1

Generation 2

Generation 3


2. Diamond model specification

1. Technology2. Families behavior3. Dynamic equilibrium system


1)( tttt LAKY

Slide 46

1. Technology

Given by retired Given by actives

Capital completly depreciates with production: =1


time

t t+1

Born -Earns salary-Consumes

-Earns interest-Consumes

2. Families behavior

Generation t

Productions uses Generation’s t work

Production uses Generation’s t capital


GENERATION t UTILITY

MAXIMIZATION WITH DISCOUNT TAXES AND INTEREST

Respect C

Subject to: INTERTEMPORAL BUDGET CONSTRAINT

)()1()(max 1 tt cUcU

tt

tt w

r

cc

11


First-order conditions for generation t

“EFFECTIVE TEMPORAL DISCOUNT”

)(')1)(1()(' 1 tt cUrcU


Suppose the following utility function CES (Constant Elasticity of Substitution):

Temporal consumption path will be:

0/11

][])[(

/11

withtC

tCU

/1][])[(' tCtCU

)]1)(1[(1t

t

t rc

c


If we introduce the consumption path into the budget cosntraint we obtain:

1

1

1

)1()1(1

))1()1(1(

1

)]1)(1[(

1

t

tt

ttt

tt

ttt

tt

tt

r

wc

wrc

wr

rcc

wr

cc


Consumtion and saving of Generation t (when young)

1

1

1

1

)1()1(1

)1()1(

)1()1(1

)1()1(1

t

ttt

t

ttttt

t

tt

r

rws

r

wwcws

r

wc


s

r

0

)1(1

)1(

tt ws


s

r

t ts w

0

)1(1

)1(

tt ws


s

r

0

)1(1

)1(

tt ws


3. Dynamic equilibrium system

1

1

1

)1()1(1

)1()1(

t

ttt

tttt

r

rwL

sLIK


Financed with RETIRED SAVINGS

Given by ACTIVES

1)(1

)1(11

1

ttttt

ttttt

LAKPMKr

LAKPMLw

1)( tttt LAKY


1

11

1

)1()1(1

)1()1()()1(

t

tttt

tttt

r

rLAK

sLIK

1)( 11 tttt LAKr


1

11

11

11

1

)1()1(1

)1()1()(

t

t

tt

ttt

tt

tt

tt

t

r

r

AL

LAK

AL

AL

AL

K

1)( 11 tttt LAKr


1

1

1 )1()1(1

)1()1(~

)1)(1(

1~

t

ttt r

rk

ank

1~ 1 tt kr


3. Equilibrium growth and optimality

1

)1(1

)1(~

)1)(1(

1~1

tt kan

k


0

1tk

0k

1t tk bk

tk1k BGP


Optimality

• It’s not clear how different generations should be weighted.

• The resulting assignation is at least Optimal in terms of Pareto?


Dynamic inefficiency

• A situation where resources assignation is not Pareto effcient.

• In other words, a situation where we can increase the consumption of at least one generation without reducing other’s consumption.


Consider the case WITHOUT technological progress a=0

How much is need to invest by person at moment t to hold the capital intensity of use?

n

i

L

iL

L

Kk t

t

it

t

tt

111

11

)1(1 nkikk tttt


0

( )t ty f k

tk

(1 )tk n

Per capita consumption

goldkMacroeconomics SET 4

0

tkgoldk

Per capita consumption

nPMK 1


Steady state or BGP

)1(1

)1(

)1(

11

tt kn

k

1

1

)1(1

)1(

)1(

1

)1(1

)1(

1

1

nk

kn

k

BGP

BGP


1

)1(1

)1(

)1(

1)1(

nPMK BGP

1)1( kPMK


macroeconomics

Documents

outputmacroeconomics

consumptionmacroeconomics

iimacroeconomics set

output fallmacroeconomics

rck modelmacroeconomics

constant capital cisocline

constant consumptionk

timepermanent unexpected