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EC213 Macroeconomics Dr Aidan Kane

EC213 Macroeconomics Dr Aidan Kane. Topic 2: Intertemporal budget constraints Chapters 3,4 Burda + Wyplosz. Outline. The consumer’s intertemporal budget constraint …private sector Public sector budget constraints Consolidated public and private sector constraints

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EC213 Macroeconomics Dr Aidan Kane

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  1. EC213 MacroeconomicsDr Aidan Kane Topic 2: Intertemporal budget constraints Chapters 3,4 Burda + Wyplosz

  2. Outline • The consumer’s intertemporal budget constraint …private sector • Public sector budget constraints • Consolidated public and private sector constraints • The Ricardian Equivalence proposition • National Intertemporal budget constraints • Optimal Consumption/Consumption smoothing • Impact of temporary vs. permanent changes in income on savings • Impact of changes in interest rates on savings

  3. Budget constraints • Real analysis • Microeconomic foundations • Intratemporal vs. intertemporal • ‘Robinson Crusoe’ model: Two time periods Income in both periods (endowment) Y Ability to lend or borrow at rate r

  4. See Figure 3.1 p.48 Period 2 0 Period 1

  5. See Figure 3.1 p.48 Period 2 0 Y1 Period 1

  6. See Figure 3.1 p.48 Period 2 Y2 0 Y1 Period 1

  7. See Figure 3.1 p.48 Period 2 A Y2 0 Y1 Period 1

  8. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 0 Y1 Period 1

  9. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  10. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  11. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  12. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 Borrowing in Period 1 C1 > Y1 B 0 Y1 Y2/(1+r) Period 1

  13. See Figure 3.1 p.48 Period 2 D Y1(1+r) A Y2 Borrowing in Period 1 C1 > Y1 C2 B C1 0 Y1 Y2/(1+r) Period 1

  14. See Figure 3.1 p.48 Period 2 D Saving in Period 1 C1 < Y1 Y1(1+r) A Y2 Borrowing in Period 1 C1 > Y1 C2 B C1 0 Y1 Y2/(1+r) Period 1

  15. See Figure 3.1 p.48 Period 2 D C2 Saving in Period 1 C1 < Y1 Y1(1+r) A Y2 Borrowing in Period 1 C1 > Y1 C2 B C1 0 Y1 Y2/(1+r) C1 Period 1

  16. See Figure 3.1 p.48 Period 2 D OD = Y2 + Y1(1+r) Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  17. See Figure 3.1 p.48 Period 2 D OD = Y2 + Y1(1+r) OB = Y1 + Y2/(1+r) Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  18. See Figure 3.1 p.48 Period 2 D OD = Y2 + Y1(1+r) OB = Y1 + Y2/(1+r) -OD/OB = -(1+r) Y1(1+r) A Y2 B 0 Y1 Y2/(1+r) Period 1

  19. Intertemporal budget constraint • First period: Y1 income, C1 • Savings/borrowings: Y1- C1 • Second period: C2 = Y2 + (Y1- C1)(1+r) C1(1+r) + C2 = Y1(1+r) + Y2 C1 + C2 /(1+r) = Y1 + Y2/(1+r)

  20. Lifetime income(wealth) constrains consumption • C1 + C2 /(1+r) = Y1 + Y2/(1+r) • present value of consumption = present value of income • = wealth  • = OB

  21. Discounting and present values • An example • bond pays £100 in 1 year’s time • interest rate is 5% • price of bond now i.e. present value • B(1 + 0.05)=100 • B = 100/(1.05) = £95.24 • For 2 year bond, B = 100/(1.05)2 = £90.7

  22. More generally... • A stream of payments a1, a2, ...., an • Present value = • a1/(1+r) + a2/(1+r)2 + ....+ an/(1+r)n • when payment = a for ever, • present value = a/r

  23. The public sector buget constraint • Assume two period, no initial debt • Spending G1 and G2 • Taxation T1 and T2 • All debts must be paid off (government does not default) • T2 = G2 +(G1 - T1)(1 + rG) • G1 + G2/(1 + rG) = T1 + T2 /(1 + rG)

  24. Deficits and primary deficits • Given initial debt D0, and interest payments rG D0 • Total deficit = (G1 - T1 ) + rG D0 • i.e. primary deficit + interest payments • Then.. • D0 + (G1 - T1 ) + (G2 - T2) /(1+rG)=0

  25. Consolidated private and public budget constraints C1 + C2 /(1+r) = (Y1-T1) + (Y2 -T2) /(1+r) G1 + G2/(1 + rG) = T1 + T2 /(1 + rG) (C1 + G1) + (C2 + G2)/(1+r)=Y1 + Y2/(1+r) • present value of domestic spending = present value of domestic income • leads to Ricardian equivalence proposition

  26. Ricardian Equivalence Given: (C1 + G1) + (C2 + G2)/(1+r)=Y1 + Y2/(1+r) (1) private sector internalises public sector budget constraint: deficits have no real effects (2) public debt is not net wealth for the private sector Contrast with Keynesian ‘multiplier’ effect Ireland 1987-88: an ‘Expansionary Fiscal Contraction’?

  27. Example: a tax cut • C1 + C2 /(1+r) = (Y1-T1) + (Y2 -T2) /(1+r) • = C1 + C2 /(1+r) = Y1+ Y2 /(1+r) - [T1+ T2 /(1+r)] DT1 = DT DT2 = (1+r)DT change in PV of taxes = DT + (1+r)DT/(1+r) = 0

  28. Period 2 Ricardian Equivalence See Figure 3.11 p.59 0 Period 1

  29. Period 2 Ricardian Equivalence See Figure 3.11 p.59 A Y2 0 Y1 Period 1

  30. Period 2 Ricardian Equivalence See Figure 3.11 p.59 A Y2 0 Y1 Period 1

  31. Period 2 Ricardian Equivalence See Figure 3.11 p.59 A Y2 A´ Y2- G2 0 Y1- G1 Y1 Period 1

  32. Period 2 Ricardian Equivalence See Figure 3.11 p.59 A Y2 A´ Y2- G2 0 Y1- G1 Y1 Period 1

  33. Problems with Ricardian Equivalence • Different time horizons • Different interest rates • Liquidity contraints

  34. Public and private interest rates Table 3.1 p.60 % p.a. 1995 Treasury Bonds Corporate Bonds Belgium 6.83% 7.33%

  35. Public and private interest rates Table 3.1 p.60 % p.a. 1995 Treasury Bonds Corporate Bonds Belgium 6.83% 7.33% France 7.17% 7.60%

  36. Public and private interest rates Table 3.1 p.60 % p.a. 1995 Treasury Bonds Corporate Bonds Belgium 6.83% 7.33% France 7.17% 7.60% Italy 11.51% 10.09%

  37. Different interest rates If r > rG consolidated budget constraint:

  38. Different interest rates If r > rG consolidated budget constraint: C1 + C2 (1+r) =

  39. Different interest rates If r > rG consolidated budget constraint: C1 + C2 (1+r) = (Y1 - G1) + (Y2 - G2) + (1+r)

  40. Different interest rates If r > rG consolidated budget constraint: C1 + C2 (1+r) = (Y1 - G1) + (Y2 - G2) + (1+r) (r - rG ) [G1 - T1] (1+r)

  41. Liquidity constraints Liquidity constraints: • inability to borrow against future income at any interest rate • credit rationing • a form of market failure e.g. in human capital market

  42. Period 2 Liquidity constraints See Figure 3.13 p.61 A Y2- G2 0 Y1- G1 Period 1

  43. Period 2 Liquidity constraints See Figure 3.13 p.61 A Y2- G2 0 Y1- G1 Period 1

  44. Period 2 Liquidity constraints See Figure 3.13 p.61 A Y2- G2 0 Y1- G1 Period 1

  45. National intertemporal budget constraint • Open economy not limited by domestic income • (S-I) + (T-G) = CA • Given F, net asset position with rest of world • and r, return on net assets • CA = Primary Current Account + net investment income • CA = PCA + rF • Ignoring any initial assets in a two-period model: • PCA1 + PCA2/(1+r) = 0

  46. Optimal consumption • Preferences: indifference curves • Consumption smoothing

  47. Period 2 See Figure 4.2 p.77 0 Period 1

  48. Period 2 See Figure 4.2 p.77 0 Period 1

  49. Period 2 See Figure 4.2 p.77 0 Period 1

  50. Period 2 See Figure 4.2 p.77 R 0 Period 1

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