Consumption-Savings Decisions and Credit Markets

Transcription

1 Consumption-Savings Decisions and Credit Markets Economics Intermediate Macroeconomics Aaron Hedlund Baylor University Fall 2013 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

2 Introduction So far, we have only looked at static consumer optimization or exogenously specified dynamic behavior. Now we look at intertemporal decisions. Just a few issues that we will investigate: Consumption-savings decisions and investment behavior. Ricardian equivalence and fiscal policy. The determination of real interest rates. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

3 A Two Period Model Two period endowment economy with endowments y 1 and y 2. Lump sum taxes t 1 and t 2. Real interest rate r. The consumer s budget constraints are given by c 1 + s 1 = y 1 t 1 c 2 = y 2 + ()s 1 t 2 The lifetime budget constraint combines both constraints to equate lifetime wealth with the present value of consumption. c 1 + c 2 = y 1 t 1 + y 2 t 2 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

4 A Two Period Model Time separable preferences U(c 1, c 2 ) = u(c 1 ) + βu(c 2 ). Standard assumptions: u > 0 and u < 0. The discount factor β (0, 1) measures the household s degree of patience. Consumers make consumption/savings decisions to maximize utility, max c 1,c 2 u(c 1 ) + βu(c 2 ) subject to c 1 + c 2 = y 1 t 1 + y 2 t 2 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

5 A Two Period Model Optimality conditions: u (c 1 ) βu (c 2 ) = MRS c 1,c 2 = c 1 + c 2 = y 1 t 1 + y 2 t 2 A lender if c 1 < y 1 t 1 and a borrower if c 1 > y 1 t 1. y2 t2 c2 c2 c2 c2 y2 t2 c1 y1 t1 y1 t1 c1 c1 c1 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

6 Comparative Statics: Changes in Current Income How do c 1, s 1, and c 2 respond to changes in y 1? c 1 = ()2 βu (c 2 ) > 0 y 1 c 2 = ()u (c 1 ) > 0 y 1 where = u (c 1 ) () 2 βu (c 2 ) > 0. Lastly, s 1 = 1 c 1 = u (c 1 ) > 0 y 1 y 1 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

7 Comparative Statics: Changes in Current Income Consumers use part of the increase in y 1 to augment consumption and the rest to increase savings. Thus, c 1 < y 1. This behavior is called consumption smoothing. In the data, households smooth their consumption, but not by as much as theory predicts. Consumption exhibits excess variability. Possible reasons: 1 Credit market imperfections. 2 Consumer durables are more like investment. 3 General equilibrium effects. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

8 Consumption Variation Durable goods consumption is much more volatile than nondurable goods/services because it is economically a form of investment. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

9 Comparative Statics: Changes in Future Income How do c 1, c 2, and s 1 respond to changes in y 2? c 1 = 1 c 1 > 0 y 2 y 1 c 2 = 1 c 2 > 0 y 2 y 1 s 1 = c 1 < 0 y 2 y 2 Consumers use a portion of the expected increase in future income to augment consumption today (requiring a decrease in savings) and the rest to augment consumption in the future. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

10 The Permanent Income Hypothesis Consumers respond differently to temporary changes in income than they do to permanent changes in income. Examples of temporary changes: unemployment, bonuses, etc. Examples of permanent changes: occupation changes, disability, etc. The permanent income hypothesis states that consumers base their consumption decisions on their discounted lifetime income. W = y + y + y () 2 + = y r ( W temp = y + y + y ) +... W = y ( W perm = y + y + y + y ) +... W = y r Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

11 Consumption Smoothing and the Stock Market Stock price movements are closer to permanent shocks, implying that consumption should respond noticeably to such changes. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

12 Comparative Statics: Changes in The Real Interest Rate How do c 1 and c 2 respond to changes in r? c 1 r c 2 r = βu (c 2 ) ()βu (c 2 )(y 1 t 1 c 1 ) Substitution effects: c 1 r = βu (c 2 ) < 0, subst = ()βu (c 2 ) u (c 1 )(y 1 t 1 c 1 ) s 1 r = c 1 r c 2 r = ()βu (c 2 ) subst > 0 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

13 Comparative Statics: Changes in The Real Interest Rate Income effects: c 1 r = c 1 inc r c 1 r = ()βu (c 2 )(y 1 t 1 c 1 ) subst c 2 r = c 2 inc r c 2 r = u (c 1 )(y 1 t 1 c 1 ) subst The signs of the income effects depend on the sign of y 1 t 1 c 1. The income effect of a higher real interest rate is negative for borrowers and positive for lenders. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

14 Comparative Statics: Changes in The Real Interest Rate weh(h) c2 c2 weh(h) wel(l) wel(l) weh wel weh wel c1 c1 The effect of an increase in the real interest rate for a lender (left) and a borrower (right). Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

15 The Government Suppose the government levies lump-sum taxes T 1 = Nt 1 and T 2 = Nt 2 and issues initial debt B 1 (S g 1 = B 1) to finance spending G 1 and G 2. The government s budget constraints are G 1 = T 1 + B 1 G 2 + ()B 1 = T 2 Substituting out for B 1 gives the present-value government budget constraint G 1 + G 2 = T 1 + T 2 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

16 Competitive Equilibrium A competitive equilibrium in this economy consists of an interest rate r, allocations for the household c 1 and c 2, and allocations for the government G 1, G 2, T 1, T 2 such that: 1 Consumption c 1 and c 2 solve the consumer s optimization problem. 2 The government s present-value budget constraint is satisfied: G 1 + G 2 = T 1 + T 2 3 The credit market clears in the initial period (total savings S 1 = 0): S 1 S p 1 + S g 1 = S p 1 B 1 = 0 S p 1 = B 1 where S p 1 = N(y 1 t 1 c 1 ) and B 1 = G 1 T 1. 4 The goods market clears: Y 1 = C 1 + G 1 and Y 2 = C 2 + G 2 where Y 1 = Ny 1, Y 2 = Ny 2, C 1 = Nc 1, and C 2 = Nc 2. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

17 Walras Law Conditions (1), (2), and (3) automatically imply (4). c 1 + c 2 = y 1 t 1 + y 2 t 2 Thus, C 1 + C 2 = Y 1 T 1 + Y 2 T 2 ( ) S p 1 = Y Y2 T 2 C 2 1 T 1 C 1 = Also, G 1 + G 2 = T 1 + T ( ) 2 B G2 T 2 1 = G 1 T 1 = Credit market clearing S p 1 = B 1 implies Y 1 T 1 C 1 = G 1 T 1 and Y 2 T 2 C 2 = G 2 T 2 Y 1 = C 1 + G 1 and Y 2 = C 2 + G 2 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

18 Ricardian Equivalence Suppose the government leaves G 1 and G 2 unchanged but reduces initial period taxes by t 1 = T 1 N per household. The deficit increases by T 1 and the government must raise second period taxes by T 2 to pay back the increased debt: G 1 = T 1 T 1 + (B 1 + T 1 ), G 2 + ()(B 1 + T 1 ) = T 2 + T 2 Before the tax cut, G 1 + G 2 = T 1 T 1 + T 2 + T 2 G 1 + G 2 = T 1 + T 2 Thus, the required tax increase is T 2 = T 1 (). Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

19 Ricardian Equivalence What are the macroeconomic effects of this deficit-financed tax cut? The consumer s intertemporal budget constraint becomes c 1 + c 2 = y 1 (t 1 t 1 ) + y 2 (t 2 + t 1 ()) c 1 + c 2 = y 1 t 1 + y 2 t 2 Unchanged! The consumer s original c 1 and c 2 are still feasible and optimal. Private savings becomes S p 1,new = Y 1 (T 1 T 1 ) C 1 = Y 1 T 1 C 1 + T 1 = S p 1 + T 1. National saving is (S p 1 + T 1) (B 1 + T 1 ) = S p 1 B 1 = 0. Thus, the credit market is still in equilibrium without requiring a change in r. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

20 Ricardian Equivalence Summary: Holding r fixed, increased household saving exactly offsets decreased public saving, leaving national saving unchanged. Equilibrium c1, c 2, and r are unchanged. The true tax burden is the discounted value of government spending. Deficits are just deferred taxes. S P 1 S P + ΔT1 1 r B1 B1 + ΔT1 Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

21 Assumptions of Ricardian Equivalence Ricardian equivalence relies on four assumptions Taxes change by the same amount for all households, i.e. it is not the case that certain households receive the initial tax cuts and different households pay the future tax increases. The increased government debt is paid off during the lifetimes of the people alive when the debt was issued. Lump-sum taxation. Perfect credit markets. Real world example: the income tax withholding reduction in Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

22 Government Deficits and Debt Government deficits in the U.S. and in Europe. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

23 Government Deficits and Debt Government debt to GDP ratio in the United States. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

24 Can the Government Run a Perpetual Deficit? Consider the following scenario: GDP growth rate g: Yt = Y 0 (1 + g) t. Permanent primary deficit d t G t T t = dy t a fraction d of GDP. Constant real interest rate r. From the government s per period budget constraint, G t + ()B t 1 = T t + B t B t = d t=dy 0(1+g) t {}}{ (G t T t ) +()B t 1 B t = dy 0 (1 + g) t + () { dy 0 (1 + g) t 1 + () [ dy 0 (1 + g) t ]} [ B t = dy 0 (1 + g) t + ()(1 + g) t 1 + () 2 (1 + g) t () t] B [ t B t = Y t Y 0 (1 + g) t = d 1 + ] ()2 ()t g (1 + g) 2 (1 + g) t Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

25 The Arithmetic of Perpetual Government Deficits The debt/gdp ratio is therefore If r > g, Bt Y t B t Y t = d t n=0 ( ) n = d 1 + g 1 + g g r [ 1 in the long run, which is impossible. If r < g, Bt Y t d 1+g g r in the long run. Example: r = 0.01, g = 0.03, d = 0.05 Long run debt/gdp of d 1+g g r = ( ) ] t g Annual (primary deficit + debt service)/gdp of d + rd 1+g g r = These calculations assume that the world is willing to purchase all of this debt at interest rate r. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26

26 European Sovereign Default Crisis Interest rates in Europe. Econ 3307 (Baylor University) Consumption-Savings Decisions Fall / 26