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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1
MACROECONOMICS IUPF
LECTURE SLIDES SET 4
Professor Antonio Ciccone
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 2
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 3
3.1 Government spending, consumption, and interest rates
- 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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 4
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
The RCK model
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 5
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 6
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, surprise fall in output for given k
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 7
timePermanent, surprise fall in output
Evolution of consumption
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timePermanent, surprise fall in output
Evolution of capital intensity
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-- 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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 10
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, surprise fall in output for given k: PART I
k-ISOCLINE: NO CAPITAL GROWTH
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 11
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, surprise fall in output for given k: PART II
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 12
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary,surprise fall in output: Equilibrium response
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 13
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary,surprise fall in output: Equilibrium response
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 14
timeSTART of Tempfall in output
END of Tempfall in output
Evolution of the capital intensity
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timeSTART of Tempfall in output
END of Tempfall in output
Evolution of real interest rate
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timeSTART of Tempfall in output
Evolution of consumption
END of Tempfall in output
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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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 18
timeSTART of War END of War
Evolution of real interest rate
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- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 21
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: PART I
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 22
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: PART II
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 23
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: Equilibrium response
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timeINFO of permanent FUTUREfall in output
Evolution of capital intensity
Output actually falls
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timeINFO of permanent FUTUREfall in output
Evolution of consumption
Output actually falls
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- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 27
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART I
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 28
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART II
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 29
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART III
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 30
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output: Equilibrium response
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 31
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output: Equilibrium response
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 32
timeINFO of FUTURETemp fall in output
END of Tempfall in output
Evolution of the capital intensity
START of FUTURETemp fall in output
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 33
time
Evolution of consumption
INFO of FUTURETemp fall in output
END of Tempfall in output
START of FUTURETemp fall in output
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 34
3. Application of the Ramsey-Cass-Koopmans (RCK) model
3.1 Government spending, consumption, and interest rates
3.2 Bond versus tax financed government spending
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 35
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 36
-- 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?
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 37
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.
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 38
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 39
-- 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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 40
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 41
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 42
-- Discrete time model-- Households live for two periods, and only work in the first
1. Overlapping Generations models
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 43
Time 3 Time 4Time 2Time 1
Generation 1
YOUNG:Workand
Consume
RETIRED:Consume
THE LIFE CYCLE OF A SINGLE GENERATION
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TIMING
Time 3 Time 4Time 2Time 1
Generation 1
Generation 2
Generation 3
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2. Setup of the Diamond model
1. Technology2. Household behavior3. Dynamic equilibrium system
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1. Technology
1 t t t tY K A L
Owned/Supplied by RETIRED Supplied by YOUNG
Capital fully depreciates during production: 1
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 47
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 48
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 49
FIRST-ORDER CONDITIONS FOR GENERATION t
1'( ) (1 )(1 ) '( )t tU c r U c
“EFFECTIVE TIME DISCOUNTING”
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 50
Take the following CES utility function:
with
CONSUMPTION PROFILE BECOMES
1 (1 )(1 )tt
t
cr
c
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 51
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 52
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)
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 53
s
r
(1 )
1 (1 )t ts w
0
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s
r
(1 )
1 (1 )t ts w
t ts w
0
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s
r
(1 )
1 (1 )t ts w
0
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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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 57
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 58
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 59
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 60
1
1
1
(1 ) (1 )1(1 )(1 ) 1 (1 ) (1 )
t
tt
t
k
rk
n a r
1 1t tr k
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 61
3. Equilibrium growth and optimality
1
1 (1 )
(1 )(1 ) 1 (1 )
t
t
k
kn a
1
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0
1tk
0k
1t tk bk
tk1k BGP
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Optimality
• How to weight different generations unclear.
• Is the allocation at least Pareto efficient?
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 64
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 65
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
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 66
0 GoldRulek
( )t ty f k
tk
(1 )tk n
Consumption per capita
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 67
0
tkGoldRulek
Consumption per capita
1MPK n
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 68
11 (1 )
(1 ) 1 (1 )t tk k
n
1 (1 )(1 ) 1 (1 )
k kn
111 (1 )
(1 )1 (1 )BGPk
n
BGP
UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 69
11 (1 )
(1 )(1 )1 (1 )
BGPMPKn
1(1 )MPK k
1 (1 )(1 ) (1 )
(1 )BGPMPK n