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ITFD Growth and Development UPF 2009-2010

ITFD Growth and Development UPF 2009-2010. LECTURE SLIDES SET 3 Professor Antonio Ciccone. II. ECONOMIC GROWTH WITH ENDOGENOUS SAVINGS. 1. Household savings behavior. 1. “ Keynesian theory ” of savings and consumption. 1. The Keynesian consumption (savings) function.

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ITFD Growth and Development UPF 2009-2010

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  1. ITFD Growth and DevelopmentUPF 2009-2010 LECTURE SLIDES SET 3 Professor Antonio Ciccone BGSE Growth and Development, 2009-10 SLIDE SET 3

  2. II. ECONOMIC GROWTH WITH ENDOGENOUS SAVINGS BGSE Growth and Development, 2009-10 SLIDE SET 3

  3. 1. Household savings behavior BGSE Growth and Development, 2009-10 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. BGSE Growth and Development, 2009-10 SLIDE SET 3

  5. Because of the BUDGET CONSTRAINT this implies the “Keynesian” consumption function where c is the marginal propensity to consume. BGSE Growth and Development, 2009-10 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. BGSE Growth and Development, 2009-10 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. BGSE Growth and Development, 2009-10 SLIDE SET 3

  8. FIGURE 1: CONSUMPTION SMOOTHING: A VOLATILE INCOME PATH HOUSEHOLD INCOMEOF FARMER time BGSE Growth and Development, 2009-10 SLIDE SET 3

  9. FIGURE 2: INCOME AND "KEYNESIAN CONSUMPTION" HOUSEHOLD INCOMEOF FARMER HOUSEHOLD CONSUMPTIONOF FARMER (“KEYNESIAN” theory) time BGSE Growth and Development, 2009-10 SLIDE SET 3

  10. FIGURE 3: CONSUMPTION SMOOTHING HOUSEHOLD INCOMEOF FARMER HOUSEHOLD CONSUMPTIONOF FARMER (EMPIRICAL OBSERVATION) time BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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) BGSE Growth and Development, 2009-10 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) BGSE Growth and Development, 2009-10 SLIDE SET 3

  18. INTERTEMPORAL BUDGET CONSTRAINT can also be written: IMPORTANT TERMINOLOGY: PERMANENT INCOME (PI) PRICE OF FUTURE CONSUMPTION RELATIVE TO CURRENT CONSUMPTION BGSE Growth and Development, 2009-10 SLIDE SET 3

  19. GRAPHICALLY: INCOME LEVELS AND CONSUMTION C[1] Lw[1] Lw[0] C[0] BGSE Growth and Development, 2009-10 SLIDE SET 3

  20. THE INTERTEMPORAL BUDGET CONSTRAINT C[1] Lw[1] 1+r Lw[0] C[0] BGSE Growth and Development, 2009-10 SLIDE SET 3

  21. INTERTEMPORAL UTILITY MAXIMIZATION C[1] Lw[1] 1+r Lw[0] C[0] BGSE Growth and Development, 2009-10 SLIDE SET 3

  22. C[1] Lw[1] C[1] 1+r C[0] Lw[0] C[0] BGSE Growth and Development, 2009-10 SLIDE SET 3

  23. BORROWING FOR CURRENT CONSUMPTION C[1] Lw[1] REPAY C[1] BORROW 1+r C[0] Lw[0] C[0] BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 SLIDE SET 3

  27. "CONSUMPTION FUNCTION" C[0] 0.5*Lw[0]+0.5*Lw[1] 0.5*Lw[1] Lw[0] BGSE Growth and Development, 2009-10 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] BGSE Growth and Development, 2009-10 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] BGSE Growth and Development, 2009-10 SLIDE SET 3

  30. DISCOUNTING OF FUTURE UTILITY, AND INTEREST MAXIMIZATION WITH DISCOUNTING&INTEREST with respect to C subject to INTERTEMPORAL BUDGET CONSTRAINT BGSE Growth and Development, 2009-10 SLIDE SET 3

  31. FIRST-ORDER CONDITIONS “EFFECTIVE TIME DISCOUNTING”  CONSTANT CONSUMPTION DISCOUNTING OF FUTURE UTILITY AND POSTITIVE INTEREST RATE JUST OFFSET BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 SLIDE SET 3

  33. AN EXAMPLE Take the following utility function: FIRST-ORDER CONDITION BECOMES or BGSE Growth and Development, 2009-10 SLIDE SET 3

  34. 3. The case of 3 and more periods -- Timing -- Intertemporal budget constraint -- Optimality conditions -- Time consistency BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 SLIDE SET 3

  36. INTERTEMPORAL BUDGET CONSTRAINT BGSE Growth and Development, 2009-10 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 BGSE Growth and Development, 2009-10 SLIDE SET 3

  38. INTERTEMPORAL BUDGET CONSTRAINT BGSE Growth and Development, 2009-10 SLIDE SET 3

  39. OPTIMAL SOLUTION OF CONSUMPTION PROBLEM MAXIMIZE BETWEEN ADJACENT PERIODS • plus BUDGET CONSTRAINT WITH EQUALITY BGSE Growth and Development, 2009-10 SLIDE SET 3

  40. Shortest way from A to B? B A BGSE Growth and Development, 2009-10 SLIDE SET 3

  41. Shortest way from A to B B A BGSE Growth and Development, 2009-10 SLIDE SET 3

  42. Must be the shortest way between ANY two points B C D A BGSE Growth and Development, 2009-10 SLIDE SET 3

  43. Must be the shortest way between ANY two points B C D A BGSE Growth and Development, 2009-10 SLIDE SET 3

  44. INFINITE HORIZON =TIME ZERO (PRESENT) VALUE OF 1 EURO PAID AT (end of) PERIOD t BGSE Growth and Development, 2009-10 SLIDE SET 3

  45. INTERTEMPORAL BUDGET CONSTRAINT NO-PONZI-GAME condition BGSE Growth and Development, 2009-10 SLIDE SET 3

  46. WHAT IF: NO PONZI GAME CONDITION VIOLATED? 0 -e TIME T BGSE Growth and Development, 2009-10 SLIDE SET 3

  47. INTERTEMPORAL BUDGET CONSTRAINT WITH EQUALITY NO-PONZI-GAME condition BGSE Growth and Development, 2009-10 SLIDE SET 3

  48. WHAT IF: e 0 TIME T BGSE Growth and Development, 2009-10 SLIDE SET 3

  49. CAN INCREASE TIME-0 CONSUMPTION  CONSUMPTION PLAN NOT OPTIMAL! NECESSARY FOR OPTIMALITY: BGSE Growth and Development, 2009-10 SLIDE SET 3

  50. TIME CONSISTENCY of HOUSOLD CONSUMPTION PLANS BGSE Growth and Development, 2009-10 SLIDE SET 3

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