Ch4: Consumption, Saving, and Investment

1. Ch4: Consumption, Saving, and Investment Abel & Bernake: Macro Ch3 Mankiw: Macro Ch3

2. Chapter Outline Appendix: micro-foundation of Macro Consumption and Saving Investment Goods Market Equilibrium

3. Aggregate Demand:Demand for goods & services Assume a closed economy: NX=0, NFP=0 Components of aggregate demand: AD = Cd+Id+G+NX = Cd+Id+G • Desired consumption (Cd) • Desired investment (Id)

4. Consumption C Traditional: Keynesian setup • Disposable income total income minus total taxes: Yd ≡ Y – T. • Consumption function: C = C(Yd) = a+bYd assume Yd C • Marginal propensity to consume (MPC)

5. Appendix: Intertemporal analysis utility maximization over-time • With micro-foundation: Cd = optimal C* = C (lifetime wealth, real interest rate) = C (current income, future income, real interest rate) • Desired consumption and saving: function of r Sd = Y – Cd – G (4.1)

6. Saving is for future consumption Trade-off between current consumption and future consumption The price of 1 unit of current consumption is (1 + r) units of future consumption, where r is the real interest rate Consumption-smoothing motive: the desire to have a relatively even pattern of consumption over time

7. Consumption and Saving S≡Y-C If C=Y, S=0 If C<Y, S>0 If C>Y, S<0 C=a+Y: no-borrowing, no-lending C< a+Y: lender, with interest income C< a+Y: borrower, with interest payment

8. Effect of changes in current income Increase in current income (IE): both consumption and saving increase Marginal propensity to consume (MPC) MPC≡ (△C/△Y), 0≦MPC≦1 Aggregate level: When current income (Y) rises, Cd rises, but not by as much as Y, so Sdrises

9. Effect of changes in expected future income Higher expected future income leads to more consumption today, so saving falls.

10. Application: The Idiosyncrasy of Singapore Aggregate Consumption Does consumption spending remain stable over time? Table 4.1 shows that APC remains stable for all countries except Singapore Consumption ratio in Singapore falls steadily as income increases (Fig 4.1) 2 explanations: the rise in loans and withdrawals from the Central Provident Fund (CPF) to finance housing and car purchases This is cause for policy concern as it means that consumption will not be able to play its role as stabilizer and Singapore will become more susceptible to experience cyclical fluctuations of larger amplitude.

11. Table 4.1 Average Propensity to Consume (APC) in selected economies

12. Fig 4.1 APC in Singapore(1960–2008)

13. Saving S = S (r) r↑: 2 opposing effects ISE: Positive effect on saving, since rate of return is higher; greater reward for saving elicits more saving IE: For a saver (lender): Negative effect on saving, since it takes less saving to obtain a given amount in the future (target saving) For a borrower: Positive effect on saving, since the higher real interest rate means a loss of wealth Empirical studies have mixed results; probably a slight increase in aggregate saving

14. Taxes and the real return to saving Expected after-tax real interest rate: ra-t= (1 – t)i – e (4.2)

15. Table 4.1 Calculating After-Tax Interest Rates

16. In touch with data and research: interest rates different interest rates, default risk, term structure (yield curve), and tax status Since interest rates often move together, we frequently refer to “the” interest rate Yield curve: relationship between life of a bond and interest rate 殖利率曲線:零息債券的殖利率與其到期日的關係 橫軸為各到期期限(time to maturity)， 縱軸為相對應之到期殖利率(yield to maturity)， 用以描述兩者之關係。

17. In Touch Yield Curve

18. Fiscal policy 財政政策: △G, △T  △Sd Directly affects desired national saving, Sd = Y – Cd – G Affects desired consumption through changes in current and expected future income Assume △Y=0: may need revision

19. Fiscal policy: Government purchases (temporary G↑) Higher G financed by higher current taxes reduces after-tax income, lowering desired consumption Even true if financed by higher future taxes, if people realize how future incomes are affected Since Cd declines less than G rises, national saving (Sd = Y – Cd – G) declines So government purchases reduce both desired consumption and desired national saving.

20. Fiscal policy: Tax cut (T↓, △G=0)Ricardian equivalence proposition (Appendix) Lump-sum tax cut today, ?? If tax change affects only the timing of taxes, not their ultimate amount (present value) no change in consumption (Ricardian equivalence proposition) ???

21. Ricardian equivalence proposition In practice, people may not see that future taxes will rise if taxes are cut today; then a tax cut leads to increased desired consumption and reduced desired national saving.

22. Application: How consumers respond to tax rebates The government provided a tax rebate in 2008, hoping to stimulate the economy. 2008年5月美國國稅局 (IRS)會有特別退稅 （個人300-600元，17歲以下小孩每位300元)： 美國振興經濟(Economic Stimulus Act of 2008)法案的一部分 Research by Shapiro and Slemrod suggests that consumers did not increase spending much in 2001, when the government provided a similar tax rebate.

23. Application: How consumers respond to tax rebates New research by Agarwal, Liu, and Souleles have different findings from their study on credit-card payments, purchases, and debt over time. People getting the tax rebates initially made additional payments on their credit cards, paying down their balances; but after nine months they had increased their purchases and had more credit-card debt than before the tax rebate. Younger people, who were more likely to face binding borrowing constraints, increased their purchases on credit cards the most of any group in response to the tax rebate. People with high credit limits also spent less, behaved more in the manner suggested by Ricardian equivalence.

24. Summary 5

25. Investment Investment plays a crucial role in economic growth. Investment fluctuates sharply over the business cycle, so we need to understand investment to understand the business cycle.

26. Firm’s intertemporal analysis: profit maximization over-time (Varian Ch17) St. BC (production function and capital accumulation) • Over-time optimal K = desired capital stock (K*) • Πt ?? Trade-off between dividends over time

27. Desired capital stock (K*) • MB= future benefit of investment = MPKf • MC= user cost of capital = r+d 1. Opportunity cost: interest rate ( r ) 股利原可存銀行賺利息或借錢融資需繳利息 2. Depreciation cost: d the value loss as capital wears out (capital resale price ↓) • Real-side comparison: MPKf = r+d  optimal K* • Earlier: one-time period decision rule:

28. 課本將MPKf視為名目 • 若MPKf視為實質 Nominal-side comparison: uc = PK (r + d) (4.3) P‧MPKf = PK (r + d)  optimal K* If P= PK same as real-side comparison • 以下採用課本：將MPKf視為名目 If MPKf > uc profits rise as K ↑ If MPKfuc profits rise as K ↓ With diminishing MPKf , profits are maximized where MPKf = uc

29. Fig 4.3 Determination of the desired capital stock （Nominal MPKf）

30. Changes in the desired capital stock (△K*) △r, △d, △PK  △uc Technological changes  △MPKf Factors that change user cost of capital (Fig. 4.4) Or factors that shift the MPKfcurve (Fig. 4.5) the desired capital stock to change

31. Fig 4.4 A decline in the real interest rate raises the desired capital stock

32. Fig 4.5 An increase in the expected future MPK raises the desired capital stock

33. △τ(tax rate on capital return)△K* With taxes, MB = (1 – ) MPKf (1 – ) MPKf = uc Or MPKf = uc/(1 – ) = PK (r + d)/(1 – ) (4.4) Tax-adjusted user cost of capital is uc/(1 – ) An increase in τ raises the tax-adjusted user cost and reduces the desired capital stock

34. the effective tax rate In reality, there are complications to the tax-adjusted user cost We assumed that firm revenues were taxed In reality, profits, not revenues, are taxed So depreciation allowances reduce the tax paid by firms, because they reduce profits Investment tax credits reduce taxes when firms make new investments Summary measure: the effective tax rate—the tax rate on firm revenue that would have the same effect on the desired capital stock as do the actual provisions of the tax code Table 4.2 shows effective tax rates for many different countries

35. Table 4.2 Effective Tax Rate on Capital, 2007

36. Application: measuring the effects of taxes on investment Do changes in the tax rate have a significant effect on investment? A 1994 study by Cummins, Hubbard, and Hassett found that after major tax reforms, investment responded strongly; elasticity about –0.66 (of investment to user cost of capital)

37. From the desired capital stock to investment Gross investment It = Kt+1 – Kt + dKt If firms can change their capital stocks in one period, then Kt+1 = K* (the desired capital stock) It = K* – Kt + dKt (4.6) Investment has two parts Desired net increase in the capital stock over the year (K* – Kt) Investment needed to replace worn-out capital (dKt) With adjustment costs  lags ? -- partial adjustment

38. r I(r) I The investment function:r↓ K*↑ Id↑

39. Fig 4.6 Gross and net investment, 1929-2008 Sources: GDP, gross private domestic investment, and net private domestic investment from BEAWeb site, Tables 1.1.5, 5.1, and 5.2.5.

40. Tobin’s q theory of investment V: stock market value of the firm PkK: replacement cost of firm’s capital stock If V < PkK , q < 1  K↓ If V > PkK , q > 1 K↑ If V = PkK , q=> 1 optimal K*

41. Tobin’s q theory of investment • Firms change investment in the same direction as the stock market. • If r↓? , q > 1  K↑ • If Pk↓ ? q > 1  K↑ • MPKf ↑ V ↑  q > 1 K↑ • Data show general tendency of investment to rise when stock market rises; but relationship isn’t strong because many other things change at the same time (Figure 4.7)

42. Fig 4.7 Investment and Tobin’s q, 1987-2009 Source: Investment from St. Louis Fed Web site at research.stlouisfed.org/fred2/series/PNFIC1; Tobin’s from Federal Reserve Flow of Funds Accounts, Table B.102, for nonfarm nonfinancial corporate business, market value plus liabilities divided by assets.

43. Investment in inventories and housing Marginal product of capital and user cost also apply, as with equipment and structures

44. Summary 6

45. Government spending, G • G = govt spending on goods and services. • G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits). • Assume government spending and total taxes are exogenous:

46. Goods market equilibrium • Aggregate demand: • Aggregate supply: • Equilibrium: • The real interest rate adjusts to equate demand with supply.

47. Goods Market Equilibrium The real interest rate adjusts to bring the goods market into equilibrium Y = Cd + Id + G (4.7) goods market equilibrium condition Differs from income-expenditure identity, as goods market equilibrium condition need not hold; undesired goods may be produced, so goods market won’t be in equilibrium.

48. Goods Market Equilibrium Alternative representation for a closed economy: Y= Cd + Id + G Sd = Y – Cd – G,  Sd = Id (4.8) saving-investment diagram (Fig. 4.8)

49. Fig 4.8 Goods market equilibrium

50. Table 4.3 (△r to reach equilibrium)Components of Aggregate Demand for Goods