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Macroeconomics

Macroeconomics. LECTURE SLIDES SET 4 Professor Antonio Ciccone. 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.

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Macroeconomics

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  1. Macroeconomics LECTURE SLIDES SET 4 Professor Antonio Ciccone Macroeconomics SET 4

  2. 3. Ramsey-Cass-Koopmans (RCK) Model: Applications 3.1Government expenditures, consumption and interest rate 3.2 Financing government expenditures: bonds vs taxes Macroeconomics SET 4

  3. 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 • Temporaryanticipatedfall in output Macroeconomics SET 4

  4. RCK Model c c-ISOCLINE: CONSUMSUMPTION CONSTANT k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  5. c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  6. Permanent unexpected fall in output for a given k c c-ISOCLINE: CONSTANT CONSUMPTION NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  7. Consumption evolution time Permanent unexpectd fall in output Macroeconomics SET 4

  8. Capital intesity evolution time Permanent unexpected fall in output Macroeconomics SET 4

  9. --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 Macroeconomics SET 4

  10. Temporary unexpected fall in output for a given k: PART I c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  11. Temporary unexpected fall in output for a given k: PART II c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  12. Temporay unexpected fall in output: Equilibrium response c c-ISOCLINE: CONSTANT CONSUMPTION NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  13. Temporary unexpected fall in output: Equilibrium response c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  14. Capital intensity evolution Time Beginning of temporary fall End of temporary fall Macroeconomics SET 4

  15. Real interest rate evolution Time Beginning of temporary fall End of temporary fall Macroeconomics SET 4

  16. Consumption evolution Time Beginning of temporary fall End of temporary fall Macroeconomics SET 4

  17. 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 Macroeconomics SET 4

  18. Real interest rate evolution time Beginning of war End of war Macroeconomics SET 4

  19. Militar expenditures and long run interest rate at The United Kingdom (Barro, 1987) Macroeconomics SET 4

  20. The role of expectations - Permanent anticipated fall in output - Temporary anticipated fall in output Macroeconomics SET 4

  21. Permanent anticipad fall in output: PART I c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  22. Permanent anticipated fall in output:PART II c c-ISOCLINE: CONSTANT CONSUMPTION NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  23. Permanent anticipated fall in output: Equilibrium response c c-ISOCLINE: CONSTANT CONSUMPTION NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  24. Capital intensity evolution Permanent fall takes place here time INFO about the FUTURE permanent fall in output Macroeconomics SET 4

  25. Consumption evolution Permanent fall takes place here time INFO about the FUTURE permanent fall in output Macroeconomics SET 4

  26. The role of expectations - Permanent anticipated fall in output - Temporary anticipated fall in output Macroeconomics SET 4

  27. Temporary anticipated fall in output for a given k: PART I c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  28. Temporary anticipated fall in output for a given k: PART II c c-ISOCLINE: CONSTANT CONSUMPTION NEW k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  29. Temporary anticipated fall in output for a given k: PART III c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  30. Temporary anticipated fall in output: Equilibrium response c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  31. Temporary anticipated fall in output: Equilibrium response c c-ISOCLINE: CONSTANT CONSUMPTION k-ISOCLINE: CONSTANT CAPITAL 0 k k* Macroeconomics SET 4

  32. Capital intensity evolution time INFO about the FUTURE temporary fall in output END of temporary fall in output START of temporary fall in output Macroeconomics SET 4

  33. Consumption evolution time INFO about the FUTURE temporary fall in output END of temporary fall in output START of temporary fall in output Macroeconomics SET 4

  34. 3. Ramsey-Cass-Koopmans (RCK) Model: Applications 3.1 Government expenditures, consumption and interest rate 3.2 Financing Government expenditures: bonds vs taxes Macroeconomics SET 4

  35. Government expenditures and taxes Government intertemporal budget constraint Macroeconomics SET 4

  36. --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? Macroeconomics SET 4

  37. 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 Macroeconomics SET 4

  38. 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 Macroeconomics SET 4

  39. -- 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: Macroeconomics SET 4

  40. 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 Macroeconomics SET 4

  41. 3. Diamond model 1. Overlapping generations model 2. Model specification 1. Technology 2. Families behavior 3. Dynamic equilibrium system 3. Equilibrium growth and optimality 4. Diamond model applications 1. Government expenditures and interest rate 2. Financing government expenditures: bonds vs taxes Macroeconomics SET 4

  42. 1. Overlapping generations model • Model in discret time. • - Families live for two periods, and only work in the first one. Macroeconomics SET 4

  43. GENERATION’S LYFE CICLE Time 1 Time 2 Time 3 Time 4 Generation 1 ACTIVE (or YOUNG): Work and consume RETIRED (or OLD): Only consume Macroeconomics SET 4

  44. TEMPORAL ORGANIZATION Time 1 Time 2 Time 3 Time 4 Generation 1 Generation 2 Generation 3 Macroeconomics SET 4

  45. 2. Diamond model specification 1. Technology 2. Families behavior 3. Dynamic equilibrium system Macroeconomics SET 4

  46. 1. Technology Given by retired Given by actives Capital completly depreciates with production: =1 Macroeconomics SET 4

  47. 2. Families behavior Generation t Productions uses Generation’s t work Production uses Generation’s t capital t+1 t time Born • Earns interest • Consumes • Earns salary • Consumes Macroeconomics SET 4

  48. GENERATION t UTILITY MAXIMIZATION WITH DISCOUNT TAXES AND INTEREST Respect C Subject to: INTERTEMPORAL BUDGET CONSTRAINT Macroeconomics SET 4

  49. First-order conditions for generation t “EFFECTIVE TEMPORAL DISCOUNT” Macroeconomics SET 4

  50. Suppose the following utility function CES (Constant Elasticity of Substitution): Temporal consumption path will be: Macroeconomics SET 4

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