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Macroeconomics

This lecture explores the Keynesian theory of savings and consumption, limitations of the theory, consumption smoothing, and the permanent income theory of consumption and savings in macroeconomics.

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Macroeconomics

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  1. Macroeconomics LECTURE SLIDES SET 3 Professor Antonio Ciccone Macroeconomics SLIDE SET 3

  2. II. ECONOMIC GROWTH WITH ENDOGENOUS SAVINGS Macroeconomics SLIDE SET 3

  3. 1. Household savings behavior Macroeconomics SLIDE SET 3

  4. 1. “Keynesian theory” of savings and consumption 1. The Keynesian consumption (savings) function • So far we assumed a “Keynesian” savings function • where s is the marginal propensity to save. Macroeconomics SLIDE SET 3

  5. Because of the BUDGET CONSTRAINT this implies the “Keynesian” consumption function where c is the marginal propensity to consume. Macroeconomics SLIDE SET 3

  6. 2. Limitations CONCEPTUAL The consumption behavior is assumed to be “mechanic” and “short-sighted”: • Are households really only looking at CURRENT income when deciding consumption? Not really. Many households borrow from banks in order to be able to consume more today because they know they will be able to pay the money back in the future. • If people save, presumably they are doing this for future consumption. Hence, savings is a FORWARD-LOOKING decision and must take into account what happens in the future. Macroeconomics SLIDE SET 3

  7. Assuming savings as a function of current income therefore appears to contradict the use that households make of their savings. EMPIRICAL “Consumption smoothing:” • Empirically, we observe that households smooth consumption. To put it differently, the income of households is often more volatile than their consumption. This suggests that households look forward and try to stabilize consumption (their standard of living) as much as they can. Macroeconomics SLIDE SET 3

  8. FIGURE 1: CONSUMPTION SMOOTHING: A VOLATILE INCOME PATH HOUSEHOLD INCOMEOF FARMER time Macroeconomics SLIDE SET 3

  9. FIGURE 2: INCOME AND "KEYNESIAN CONSUMPTION" HOUSEHOLD INCOMEOF FARMER HOUSEHOLD CONSUMPTIONOF FARMER (“KEYNESIAN” theory) time Macroeconomics SLIDE SET 3

  10. FIGURE 3: CONSUMPTION SMOOTHING HOUSEHOLD INCOMEOF FARMER HOUSEHOLD CONSUMPTIONOF FARMER (EMPIRICAL OBSERVATION) time Macroeconomics SLIDE SET 3

  11. FIGURE 4: SAVINGS AND DIS-SAVINGS IN CONSUMPTION SMOOTHING MODELS HOUSEHOLD INCOME CONSUMPTION SMOOTHING DIS-SAVE TO MAINTAIN CONSUMPTION LEVELS SAVE FOR “RAINY DAYS” time Macroeconomics SLIDE SET 3

  12. INTERESTINGLY: The Keynesian theory of consumption seems to do better at the aggregate level than at the level of individual households. For example: • Keynesian theory does well in describing relationship between consumption and income of a country at different in different years • Theory does also well in describing relationship between consumption and income across different countries Macroeconomics SLIDE SET 3

  13. A PUZZLE? CONSUMPTION AGGREGATE LEVEL Germany 1980 Or Country 3 INDIVIDUAL HOUSE- HOLD LEVEL Ms B Ms D Mr C Mr A Germany 1960 Or Country 2 Germany 1950 Or Country 1 INCOME Macroeconomics SLIDE SET 3

  14. 2. The permanent income theory of consumption and savings 1. Basic idea and two-period model Households make consumption decisions: • LOOKING FORWARD to future • USING SAVINGS AND LOANS from BANKS to maintain their living standards STABLE in time to the extent possible Macroeconomics SLIDE SET 3

  15. SIMPLEST POSSIBLE formal model (2 PERIODS) INGREDIENTS: • Household lives 2 periods and tries to maximize INTERTEMPORAL utility • Understands that will earn LABOR income Lw[0] in period 0 and Lw[1] in period 1 • Starts with 0 WEALTH • Can save and borrow from bank at interest rate r Macroeconomics SLIDE SET 3

  16. MATHEMATICAL MAXIMIZATION PROBLEM: by choosing C0 and C1 subject to S=Lw0-C0 C1=Lw1+(1+r)S DISCOUNT APPLIED TO FUTURE UTILITY NOTE that S can be NEGATIVE (which means the household is BORROWING or DISSAVING) Macroeconomics SLIDE SET 3

  17. MATHEMATICAL FORMULATION Maximize INTERTEMPORAL UTILITY by choosing C subject to INTERTEMPORAL BUDGET CONSTRAINT C1=Lw1+(1+r)S= Lw1+(1+r)(Lw0-C0) Macroeconomics SLIDE SET 3

  18. INTERTEMPORAL BUDGET CONSTRAINT can also be written: IMPORTANT TERMINOLOGY: PERMANENT INCOME (PI) PRICE OF FUTURE CONSUMPTION RELATIVE TO CURRENT CONSUMPTION Macroeconomics SLIDE SET 3

  19. GRAPHICALLY: INCOME LEVELS AND CONSUMTION C[1] Lw[1] Lw[0] C[0] Macroeconomics SLIDE SET 3

  20. THE INTERTEMPORAL BUDGET CONSTRAINT C[1] Lw[1] 1+r Lw[0] C[0] Macroeconomics SLIDE SET 3

  21. INTERTEMPORAL UTILITY MAXIMIZATION C[1] Lw[1] 1+r Lw[0] C[0] Macroeconomics SLIDE SET 3

  22. C[1] Lw[1] C[1] 1+r C[0] Lw[0] C[0] Macroeconomics SLIDE SET 3

  23. BORROWING FOR CURRENT CONSUMPTION C[1] Lw[1] REPAY C[1] BORROW 1+r C[0] Lw[0] C[0] Macroeconomics SLIDE SET 3

  24. 2. Closed form solution in a simple case SUPPOSE THAT INTEREST RATE is ZERO: r = 0 FUTURE UTILITY DISCOUNT is ZERO: MAXIMIZATION PROBLEM BECOMES: with respect to C subject to Macroeconomics SLIDE SET 3

  25. C1 FIRST ORDER MAXIMIZATION CONDITIONS: First-order conditions can be obtained from with respect to C0 where we have substituted the budget constraint. TAKE DERIVATIVE WITH RESPECT TO C[1] AND SET EQUAL ZERO: OR Macroeconomics SLIDE SET 3

  26. EQUALIZE MARGINAL UTILITY AT DIFFERENT POINTS IN TIME THIS IMPLIES  “PERFECT CONSUMPTION SMOOTHING” Using the INTERTEMPORAL BUDGET CONSTRAINT yields consumption as a function of PERMANENT INCOME Macroeconomics SLIDE SET 3

  27. "CONSUMPTION FUNCTION" C[0] 0.5*Lw[0]+0.5*Lw[1] 0.5*Lw[1] Lw[0] Macroeconomics SLIDE SET 3

  28. THE EFFECT OF AN INCREASE IN INITIAL-PERIOD INCOME ON C[0] “TEMPORARY” INCREASE IN INCOME C[0] 0.5*Lw[0]+0.5*Lw[1] 0.5*Lw[1] INCREASE In first-period income Lw[0] Macroeconomics SLIDE SET 3

  29. THE EFFECT OF AN INCREASE IN INITIAL AND FUTURE INCOME “PERMANENT” INCREASE IN INCOME C[0] 0.5*Lw[0]+0.5*Lw[1] INCREASE Lw[1] INCREASE Lw[0] Lw[0] Macroeconomics SLIDE SET 3

  30. DISCOUNTING OF FUTURE UTILITY, AND INTEREST MAXIMIZATION WITH DISCOUNTING&INTEREST with respect to C subject to INTERTEMPORAL BUDGET CONSTRAINT Macroeconomics SLIDE SET 3

  31. FIRST-ORDER CONDITIONS “EFFECTIVE TIME DISCOUNTING”  CONSTANT CONSUMPTION DISCOUNTING OF FUTURE UTILITY AND POSTITIVE INTEREST RATE JUST OFFSET Macroeconomics SLIDE SET 3

  32. (1-β)(1+r) > 1 UPWARD SLOPING CONSUMPTION PATHS IN TIME:  INCREASING CONSUMPTION OVER TIME POSITIVE INTEREST MORE THAN OFFSETS UTILITY DISCOUNTING DOWNWARD SLOPING CONSUMPTION PATHS IN TIME:  DECREASING CONSUMPTION OVER TIME UTILITY DISCOUNTING MORE THAN OFFSETS POSITIVE INTEREST (1-β)(1+r) < 1 Macroeconomics SLIDE SET 3

  33. AN EXAMPLE Take the following utility function: FIRST-ORDER CONDITION BECOMES or Macroeconomics SLIDE SET 3

  34. 3. The case of 3 and more periods -- Timing -- Intertemporal budget constraint -- Optimality conditions -- Time consistency Macroeconomics SLIDE SET 3

  35. PRESENT-VALUE INCOME AND CONSUMPTION C[0] C[1] C[2] YOU ARE HERE t=0 t=1 t=2 interest discounting interest discounting interest discounting Q[0] w[0]L w[1]L w[2]L - PERMANENT INCOME - PRESENT VALUECONSUMPTION Macroeconomics SLIDE SET 3

  36. INTERTEMPORAL BUDGET CONSTRAINT Macroeconomics SLIDE SET 3

  37. BUDGET CONTRAINT AND TIME EVOLUTION OF WEALTH t=0 t=1 t=2 C[2] C[0] C[1] Q[0] w[0]L w[1]L w[2]L Macroeconomics SLIDE SET 3

  38. INTERTEMPORAL BUDGET CONSTRAINT Macroeconomics SLIDE SET 3

  39. OPTIMAL SOLUTION OF CONSUMPTION PROBLEM MAXIMIZE BETWEEN ADJACENT PERIODS • plus BUDGET CONSTRAINT WITH EQUALITY Macroeconomics SLIDE SET 3

  40. Shortest way from A to B? B A Macroeconomics SLIDE SET 3

  41. Shortest way from A to B B A Macroeconomics SLIDE SET 3

  42. Must be the shortest way between ANY two points B C D A Macroeconomics SLIDE SET 3

  43. Must be the shortest way between ANY two points B C D A Macroeconomics SLIDE SET 3

  44. INFINITE HORIZON =TIME ZERO (PRESENT) VALUE OF 1 EURO PAID AT (end of) PERIOD t Macroeconomics SLIDE SET 3

  45. INTERTEMPORAL BUDGET CONSTRAINT NO-PONZI-GAME condition Macroeconomics SLIDE SET 3

  46. WHAT IF: NO PONZI GAME CONDITION VIOLATED? 0 -e TIME T Macroeconomics SLIDE SET 3

  47. INTERTEMPORAL BUDGET CONSTRAINT WITH EQUALITY NO-PONZI-GAME condition Macroeconomics SLIDE SET 3

  48. WHAT IF: e 0 TIME T Macroeconomics SLIDE SET 3

  49. CAN INCREASE TIME-0 CONSUMPTION  CONSUMPTION PLAN NOT OPTIMAL! NECESSARY FOR OPTIMALITY: Macroeconomics SLIDE SET 3

  50. TIME CONSISTENCY of HOUSOLD CONSUMPTION PLANS Macroeconomics SLIDE SET 3

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