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Consumption & Savings

Consumption & Savings. Romer Chapter 7. Topics. What is savings? Consumption, savings and income Savings and the Interest Rate Uncertainty and Savings. The Data.

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Consumption & Savings

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  1. Consumption & Savings Romer Chapter 7

  2. Topics • What is savings? • Consumption, savings and income • Savings and the Interest Rate • Uncertainty and Savings

  3. The Data • Data on Expenditure Categories are typically obtained from the National Income and Product Accounts gathered by the statistical authorities. • USA: Bureau of Economic Analysis, Dept. of Commerce • The national income and product accounts provide an aggregated view of the final uses of the Nation's output and the income derived from its production; two of its most widely known measures are gross domestic product (GDP) and gross domestic income (GDI). BEA also prepares estimates of the Nation's stock of fixed assets and consumer durable goods.

  4. Data • In HK, data is collected by the Census and Statistics Department: NIPA Tables • The U.N. maintains statistical databases for a wide variety of countries UN Main Aggregates Database

  5. Consumption in HK • Four consumption categories • Food • Non-Durables: Clothes, Toys • Durables: White Goods, Electronics • Services: Health, Rental Source: CEIC Database

  6. Categories ofSpending BEA NIPA Table 2.3.5

  7. HK Short-term: Year to year growth Theory of consumption best explains non-durables, services and food consumption. HK NIPA Table 038

  8. Savings • Output which is not devoted toward current consumption Gross Savings = Income – Personal Consumption Expenditure – Government Consumption Expenditure BEA NIPA Tables

  9. Personal Savings vs.Gross Savings What’s Missing? BEA NIPA Tables Retained Earnings and Depreciation are not counted in Personal Savings

  10. Gross Saving Bureau of Economic Analysis

  11. Two Consumption Theories • Keynesian: Consumption is dependent on current income. • Permanent Income Theory: Consumption decision is a savings decision so households take into account future income as well as outstanding financial wealth.

  12. Keynesian Consumption Function • Consumption Function C = A + mpc×[GDP – TAX] • C = Household Consumption Expenditure • A = Autonomous Consumption { Consumption not dependent on current income} • mpc = Marginal propensity to consume • {Fraction of extra income will be spent on consumption} • mpc will be smaller than consumption to GDP ratio if A is positive.

  13. Why do Chinese Save so Much? Why do Americans Save so Little? UN Main Aggregates Data Base

  14. East Asian Savings Rates • As a region, East Asia has high savings rates. These high savings rates have helped finance high rates of capital accumulation and growth. • Why have East Asian savings rates been so high? Culture? Luck? • Will it last? UN Main Aggregates Data Base

  15. Cultural Reasons • mpc simply depends on cultural factors and not economic factors. • Hayashi, 1989 Japan's Saving Rate: New Data and Reflections • Japan: 1960-1990 Savings Rate averaged about 30% • Japan 1880-1935 Savings Rate average less than 15%!

  16. Japanese Gross Saving Rate 1994-2004Source: CEIC Database

  17. Income and Savings

  18. Present Discounted Value • Life cycle consumption functions assume that households consider not just the current flow of income but the present value of lifetime income. • Consider a stream of income received over time {y0, y1, …, yT}. This is equivalent in value to a certain amount of current income, pvy < y0+ y1+ …+yT. • Funds available today are worth more than equivalent funds which are not available until the future.

  19. Present value • Reason: Today can earn interest. • Q: How much do you need today to have yt in t periods. • Answer: • A future payment discounted by the interest rate raised by the number of periods that must be waited until the payment is made is called the present value.

  20. Present value of a stream of payments • Households earn a stream of income over their lifetime. {y0, y1, …, yT}. • Present value of an income stream is the sum of the present values of each payment.

  21. Consumption, Savings, and Future Consumption • The decision of the household to spend money on goods is a simultaneous decision not to save this money in the form of financial assets. • A decision not to save money for the future is simultaneously a decision not to have that wealth available in the future to purchase consumption goods. • The consumption decision is based on a trade-off between the welfare gained from consumption today and welfare from consumption based in the future.

  22. Why do People Save? • Life Cycle Motives – Income is Not Smooth Across Time. Households save, in part, to transfer income from high income periods to low income periods. • Precautionary Motives – Households like to achieve a buffer stock of wealth in the case of a possible bad outcome. If households have a buffer stock of saving, bad outcomes in terms of income don’t result in really bad outcomes in terms of consumption.

  23. Household born in period 0 and lives until period T. (T+1 period lives) Household begins with real financial wealth F • Present value of consumption equals present value of financial & human wealth

  24. Combine the period-by-period savings equations. • Present value of consumption equals present value of financial & human wealth

  25. Algebra Trick • If x ≠ 1, then • If x = 1, 1+ x +…+ xT = T+1 • If x ≠ 1 • If x = 1, x+ x +…+ xT = T

  26. Annuities & Annuity Value • Just as any stream of future payments has a present value, so does any current sum have an annuity value. • An annuity is an asset that makes a constant payment every period, for a number of years, T. Such an asset has a present value. • The annuity value of any current amount is the annuity payment generated by an annuity whose present value is equal that current amount.

  27. The real present value of an annuity with payment YP. Off-the-shelf formula for geometric sum Solve for present value of an annuity Y Present Value of an Annuity Payment: Annuity Value of Present Wealth

  28. Annuity Value of a Present Value • If you have some current lump sum, PV, payment and you want to buy a annuity for T periods. • Q: How big an annuity payment Y can you get. • A: Invert Equation 5)

  29. Permanent Income • We define a households, permanent income as the annuity value of its wealth, W. • Conceptually, if the household borrowed on all of its future income and added that to its financial wealth, it could buy an annuity generating perfectly smooth income.

  30. Permanent Income and Average Income • If FW = 0, and r = 0, then YP = W/T • If r > 0, then Annuity Value is a weighted average of lifetime income with larger weights on current income than on income in the far future.

  31. Permanent Income and Current IncomeIf Y grows at constant rate • Yt = (1+g)tY0

  32. Permanent Income and Current IncomeIf Y is mean reverting

  33. Intratemporal Utility Function • A household will exist for t = 0,…,T periods then expire. • Household will enjoy a stream of consumption spending {c0, c1, c2,….cT} • Households preferences over this stream can be defined by a utility function U = U(c0, c1, c2,….cT) • Often a utility function is represented as a weighted sum of utility in each period (called felicity functions).

  34. Example: Felicity • Agents get the same utility from consumption in each period. • Households lifetime utility is a weighted sum of the felicity that they receive in each period. • The per-period utility of the household is called the felicity function, u(ct). • Felicity displays diminishing returns from consumption u’(C) > 0, u’’(C) < 0

  35. Felicity Function u(c) u’(c) c

  36. Example: Time separable utility • Weights are higher in earlier period due to households impatience. Households discount future utility. U = u(c0) + β u(c1) + β2 u(c2) + β3u(c3)+…. • Rate at which the household discounts future utility is time discount rate.

  37. Maximize Discounted Utility • Maximize

  38. Lagrangian Penalty • Assume that there is some utility cost λ of overspending the budget constraint. Maximize utility including this cost and set λ as small as necessary so that people exactly hit their budget constraint.

  39. First-Order Conditions • Budget Constraint Holds • For each period, discounted marginal utility equals discounted cost of spending one more good over the limit.

  40. Euler Equation • The marginal utility of consumption in one period is equal to the marginal benefit of waiting one period which is the consuming the good plus interest times the extra utility gained from extra future consumption discounted by impatience.

  41. Permanent Income • Permanent Income Hypothesis: β(1+r)=1 then c0=c1 • The permanent income theory says that households keep consumption smooth consuming the annuity value of their financial wealth, F, plus the present value of lifetime income, W.

  42. Example • The fraction is referred to as the propensity to consume out of wealth. • A household lives for = 40 periods and the real interest rate is .02. In every period they would consume a fraction of their wealth equal to

  43. Applications: Wealth Effect • Changes in asset prices will change the current value of financial wealth. • The effect of an increase in financial wealth on consumption is called the wealth effect. • According to the PIH, a one dollar increase in the value of a stock portfolio should lead to an increase in consumption equal to the propensity to consume out of wealth. • Econometricians estimate that the wealth effect to be less than $.05 consistent with our theory.

  44. Application: Life Cycle of Saving • Permanent Income Hypothesis suggests that households like to keep a constant profile of consumption over time. • Age profile of income however is not constant. Income is low in childhood, rises during maturity and reaches a peak in mid-1950’s and drops during retirement. • This generates a time profile for savings defined as the difference between income and consumption.

  45. Time Path of Savings C,Y S>0 C S<0 S<0 Y time

  46. East Asian Demographics • Due to plummeting birth rates, East Asia had a plummeting ratio of youths as a share of population • This put a large share of population in high savings years. • Share of prime age adults has hit its peak in most Asian countries and will fall over the next half century.

  47. East Asian Demographics • During last 25 years, East Asian Nations had a sharp decrease in their ‘dependency ratio’. • Dependency ratio is the % of people in their non-working years (children & seniors. • Dependents are dis-savers and non-dependents are savers.

  48. Applied Consumption Function • Optimal consumption is a linear function of human wealth and financial wealth. Both growth part and cyclical part of human wealth is proportional to current income. • Dynamics of consumption expenditure self correct to the optimal level

  49. Interest Rates and Savings

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