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

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Presentation on theme: "UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1 MACROECONOMICS I UPF LECTURE SLIDES SET 4 Professor Antonio Ciccone."— Presentation transcript:

1 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1 MACROECONOMICS I UPF LECTURE SLIDES SET 4 Professor Antonio Ciccone

2 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

3 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

4 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

5 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 5 k c k-ISOCLINE: NO CAPITAL GROWTH c-ISOCLINE: NO CONSUMPTION GROWTH k* 0

6 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

7 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 7 time Permanent, surprise fall in output Evolution of consumption

8 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 8 time Permanent, surprise fall in output Evolution of capital intensity

9 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 9 -- 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

10 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

11 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

12 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

13 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

14 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 14 time START of Temp fall in output END of Temp fall in output Evolution of the capital intensity

15 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 15 time START of Temp fall in output END of Temp fall in output Evolution of real interest rate

16 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 16 time START of Temp fall in output Evolution of consumption END of Temp fall in output

17 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 17 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  INCREASE G  Same effect as temporary fall in output

18 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 18 time START of War END of War Evolution of real interest rate

19 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 19

20 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 20 - The role of expectations - Permanent, anticipated drop in output - Temporary, anticipated drop in output

21 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

22 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

23 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

24 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 24 time INFO of permanent FUTURE fall in output Evolution of capital intensity Output actually falls

25 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 25 time INFO of permanent FUTURE fall in output Evolution of consumption Output actually falls

26 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 26 - The role of expectations - Permanent, anticipated drop in output - Temporary, anticipated drop in output

27 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

28 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

29 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

30 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

31 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

32 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 32 time INFO of FUTURE Temp fall in output END of Temp fall in output Evolution of the capital intensity START of FUTURE Temp fall in output

33 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 33 time Evolution of consumption INFO of FUTURE Temp fall in output END of Temp fall in output START of FUTURE Temp fall in output

34 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

35 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 35 Government expenditures and taxes Government intertemporal budget constraint

36 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 -- WHAT HAPPENS TO DISCOUNTED FLOW OF TAXES?

37 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 37 Nothing, because: 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.

38 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 38 Now let’s look at household intertemporal budget constraint: -- 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

39 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: -- DOES NOT AFFECT: - INVESTMENT(!) - AND INTEREST RATES (!) -- HH SAVINGS INCREASES, BUT IS OFFSET BY AN INCREASE IN GOVERNMENT DEFICIT:

40 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 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

41 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 41 3. The Diamond model 1.Overlapping generations models 2Setup of the Diamond model 1.Technology 2. Household behavior 3. Dynamic equilibrium system 3.Equilibrium growth and optimality 4. Applications of the Diamond model 1. Government spending, consumption, and interest rates 2. Bond versus tax financed government spending

42 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

43 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 43 Time 3Time 4Time 2Time 1 Generation 1 YOUNG: Work and Consume RETIRED: Consume THE LIFE CYCLE OF A SINGLE GENERATION

44 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 44 TIMING Time 3Time 4Time 2Time 1 Generation 1 Generation 2 Generation 3

45 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 45 2.Setup of the Diamond model 1.Technology 2. Household behavior 3. Dynamic equilibrium system

46 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 46 1.Technology Owned/Supplied by RETIRED Supplied by YOUNG Capital fully depreciates during production:

47 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 uses generation t labor Production uses generation t capital

48 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

49 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 49 FIRST-ORDER CONDITIONS FOR GENERATION t “EFFECTIVE TIME DISCOUNTING”

50 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 50 Take the following CES utility function: with CONSUMPTION PROFILE BECOMES

51 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 51 Consumption profile into Budget constraint

52 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 52 Consumption and savings of generation t (when young)

53 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 53 s r 0

54 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 54 s r 0

55 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 55 s r 0

56 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 56 3. Dynamic equilibrium system Savings per young person

57 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 57 Financed by SAVINGS of the now RETIRED Supplied by YOUNG

58 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 58

59 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 59

60 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 60

61 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 61 3.Equilibrium growth and optimality

62 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 62 0 BGP

63 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 63 Optimality How to weight different generations unclear. Is the allocation at least Pareto efficient?

64 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

65 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? 

66 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 66 0 Consumption per capita

67 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 67 0 Consumption per capita

68 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 68 BGP

69 UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 69

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