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BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 1
MACROECONOMICSBGSE/UPF
LECTURE SLIDES SET 4Professor Antonio Ciccone
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 4
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
The RCK model
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 5
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 7
timePermanent, surprise fall in output
Evolution of consumption
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 8
timePermanent, surprise fall in output
Evolution of capital intensity
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 9
-- consumption can JUMP at the time newinformation arrives
-- but consumption must be smooth (follow thefirst-order condition) from than onward:
There CANNOT BE an ANTICIPATED jump in consumption
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 14
timeSTART of Tempfall in output
END of Tempfall in output
Evolution of the capital intensity
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 15
timeSTART of Tempfall in output
END of Tempfall in output
Evolution of real interest rate
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 16
timeSTART of Tempfall in output
Evolution of consumption
END of Tempfall in output
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 17
Wars and real interest rates
-- Suppose government expenditures associated withwars are surprise, temporary events
-- Study the dynamic response of: capital, interest rates, and consumption to wars
-- Government expenditures associated with warsdecrease output available for consumption andinvestment
( , )F K L G C I− = +
INCREASE G Same effect as temporary fall in output
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 18
timeSTART of War END of War
Evolution of real interest rate
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 20
- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 24
timeINFO of permanent FUTUREfall in output
Evolution of capital intensity
Output actually falls
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 25
timeINFO of permanent FUTUREfall in output
Evolution of consumption
Output actually falls
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 26
- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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
BGSE/UPF Macroeconomics, 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∞ ∞
+ =∫ ∫
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 36
-- Suppose that households believe in government budgetconstraint
-- The government cut taxes at time t
-- But there is no indication that the government cutsexpenditures
00
t tPV T dt∞
∫
-- WHAT HAPPENS TO DISCOUNTED FLOW OF TAXES?
BGSE/UPF Macroeconomics, 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 taxincrease sometime in the future.
BGSE/UPF Macroeconomics, 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 onlythe DISCOUNTERD PRESENT VALUE OF TAXES MATTERS
-- and present value of taxes remains constant if expendituresdo not change
BGSE/UPF Macroeconomics, 2008-09 SLIDE SET 4 SLIDE 39
-- TAX CUT DOES NOT CHANGE HH CONSUMPTION
-- AS A RESULT IT DOES NOT CHANGE THE NATIONALSAVINGS 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= − − + −
BGSE/UPF Macroeconomics, 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 mimics
market 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