Intermediate Macroeconomics

Transcription

1 Intermediate Macroeconomics Lecture 10 - Consumption 2 Zsófia L. Bárány Sciences Po 2014 April

2 Last week Keynesian consumption function Kuznets puzzle permanent income hypothesis life-cycle theory of consumption two-period model the effect of an increase in income, in interest rate borrowing constraints the pull of instant gratification

3 This week 1. Ricardian equivalence 2. credit market imperfections 3. social security programs

4 The Ricardian equivalence the Ricardian Equivalence theorem states that a change in the timing of taxes by the government has no effect on consumption example: reduce taxes today less government revenue, but the same spending have to increase taxes in the future key message is that a tax cut is not a free lunch this is true under certain conditions

5 Introduce the government in the two-period model the government s current period budget constraint is G = T + B G gov spending, T taxes collected, B bonds issued (borrowing) the government s future period budget constraint is G + (1 + r)b = T the gov has to repay its borrowing in this period: (1 + r)b the government s present-value budget constraint is: G + G 1 + r (1 + r)b + =T + B+ T 1 + r 1 + r

6 Introduce the government in the two-period model the government s current period budget constraint is G = T + B G gov spending, T taxes collected, B bonds issued (borrowing) the government s future period budget constraint is G + (1 + r)b = T the gov has to repay its borrowing in this period: (1 + r)b the government s present-value budget constraint is: G + G 1 + r =T + T 1 + r

7 Competitive equilibrium three conditions have to be satisfied in a competitive equilibrium: 1. consumers choose current and future consumption optimally given their BC 2. the gov present-value BC holds 3. credit market equilibrium: total private saving is equal to the quantity of government bonds issued in the current period S p = B

8 remember that before the credit market clearing: S = I where S = S p + S g, and I is investment here there is no capital, or capital accumulation I = 0 S p = S g = B the gov and consumers interact in the credit market: they borrow and lend effectively trade current for future consumption goods relative price: 1 1+r but the total amount of goods in each period is fixed: Y credit market clearing through Walras law implies that the income-expenditure identity holds: Y = C + G

9 Assume that there are N identical consumers: T = Nt Plugging this into the government s present value budget constraint: G + G ) (t 1 + r =N + t 1 + r We can use this in the consumer s present value lifetime wealth: w = y + y ) (t 1 + r + t = y + y 1 + r 1 + r 1 (G + G ) N 1 + r

10 Assume that there are N identical consumers: T = Nt Plugging this into the government s present value budget constraint: G + G ) (t 1 + r =N + t 1 + r We can use this in the consumer s present value lifetime wealth: w = y + y ) (t 1 + r + t = y + y 1 + r 1 + r 1 (G + G ) N 1 + r remember: all that matters for the consumer in choosing c and c is wealth, w, and the interest rate, r in particular the timing of his income does not matter the timing of government spending, or the timing of the taxes that finance it does not matter, as long as its present value is the same

11 The effect of a cut in current taxes for a borrower lower current taxes, t current net income higher higher future taxes, t future net income lower E 1 E 2 BUT the consumer s wealth does not change, just the endowment point the BC does not change

12 Credit market clearing S P (r) is the total saving by all consumers, private supply of credit upward sloping here: assume that substitution effect is stronger than the income effect across all consumers t, t current net income, future net income for a given interest rate each consumer s saving increases by exactly his tax cut (r) shifts to the right by B 2 B 1 to S P 2 (r) S P 1 credit demand shifts: B 1 to B 2 the equilibrium interest rate is unchanged

13 Does the Ricardian equivalence always hold? NO What assumptions are needed? 1. tax burden equally shared among consumers if not: the change could be unequally shared as well gov can redistribute wealth 2. lump-sum taxes if the consumer has a labor supply choice and taxes are lower might change the labor supply thus overall output in a given period if taxes are distortionary, they change the incentives to work

14 Does the Ricardian equivalence always hold? 3. perfect credit markets if there are credit market imperfections, then credit-constrained consumers might benefit from a current tax cut 4. any debt issued by the gov is paid off during the lifetime of the people who were alive when the debt was issued, i.e. who enjoyed the tax cut if not, there might be inter-generational tax cuts, i.e. those some benefit from lower taxes, have higher wealth, others suffer the higher taxes, and have lower wealth

15 Credit market imperfections 1. credit market imperfections and consumption 2. asymmetric information and the financial crisis would-be borrowers know more about their characteristics than do lenders classic adverse selection: the market for lemons by Akerlof in limited commitment and the financial crisis borrowers may choose to default lender can overcome limited commitment with collateral

16 Credit market imperfections and consumption Type 1: interest rate spread for the consumers the lending and borrowing interest rates are not the same r l < r b for the government they are the same and equal to the lending interest rate: r l the Ricardian equivalence does not hold

17 Lifetime budget constraints for a lender c < y s > 0 second period income y + (1 + r l )s c+s+ c = y+ y + s(1 + r ) l) (t + t 1 + r l 1 + r l 1 + r l 1 + r l for a borrower c > y s < 0, b = s second period income y (1 + r b )b

18 Lifetime budget constraints for a lender c < y s > 0 second period income y + (1 + r l )s c + c = y + y ) (t + t 1 + r l 1 + r l 1 + r l for a borrower c > y s < 0, b = s second period income y (1 + r b )b

19 Lifetime budget constraints for a lender c < y s > 0 second period income y + (1 + r l )s c + c = y + y ) (t + t 1 + r l 1 + r l 1 + r l for a borrower c > y s < 0, b = s second period income y (1 + r b )b c+ c = y+b+ y b(1 + r ) b) (t + t 1 + r b 1 + r b 1 + r b 1 + r b

20 Lifetime budget constraints for a lender c < y s > 0 second period income y + (1 + r l )s c + c = y + y ) (t + t 1 + r l 1 + r l 1 + r l for a borrower c > y s < 0, b = s second period income y (1 + r b )b c + c 1 + r b = y + y 1 + r b (t + t 1 + r b )

21 Different borrowing and lending rates AEB would be the BC if r = r l (= r 1 ) for borrower and lender DEF would be the BC if r = r b (= r 2 ) for borrower and lender if r = r l for s > 0 AE if r = r b for s < 0 EF the BC becomes AEF how does this compare to the borrowing constrained consumer s BC?

22 The effect of a tax cut a change in the timing of taxes: G + G 1 + r l = T 1 + T r l = T 2 + T r l T = T 1 + r l for the consumer this implies t = T N = T N(1 + r l ) = t 1 + r l (1 + r l ) t = t a current tax cut and future tax decrease moves his endowment along the AEB line, since the government s borrowing and lending rate is r l the consumer s BC CHANGES

23 The effect of a tax cut assume that the consumer initially consumes his endowment point the consumer is credit constrained: he d prefer c > y, but borrowing is too expensive the entire tax cut is spent on current consumption: c = t, s = 0 very diff from no credit market imperf: the consumer saves the entire tax cut to pay the higher future taxes: c = 0, s = t

24 Asymmetric information lending carried out through banks deposit rate at banks is r l, loan rate is r b (these are endogenous) fraction a of borrowers never defaults fraction 1 a always defaults bank cannot distinguish the good borrowers from the bad ones bad borrowers mimic good borrowers each borrows L

25 the bank s profit on a loan of amount L is: π = al(1 + r b ) L(1 + r l ) in equilibrium profits must be zero (why?) as long as a < 1, r b > r l π = r b = 1 + r l a there is a default premium: r b r l > 0

26 Link to the current financial crisis the fraction of good borrowers in the population decreases the credit market imperfection becomes more severe a the default premium increases even the good borrowers face higher loan rates consumption falls for all borrowers this matches the observations from the current financial crisis increase in credit market uncertainty, reduction in lending, decrease in consumption expenditures

27 Fraction of good borrowers decreases lower a higher r b BC shifts in on the borrowing part consumption for all borrowers falls

28 Interest rate spread in the data measured by: the difference between the interest rates on AAA-rated and BAA-rated corporate debt the spread hikes at the end of recessions as default rate then most recent recession: spread at the beginning cause of recession financial crisis: the degree of asymmetric information increased due to increasing uncertainty in credit markets

29 Limited commitment any loan contract represents an inter-temporal exchange the borrower receives goods and services in the present in exchange for a promise to repay in the future borrowers need incentives not to default on their debts these incentives typically provided by collateral requirements collateral is something that the lender can seize in case of non-payment (default) examples: house is collateral for a mortgage loan or for financing consumption, car is collateral for a car loan

30 Limited commitment Introduce limited commitment into the two-period consumption model H quantity of housing owned by consumer p price of housing assume that housing is illiquid can t be sold in the current period BUT it is possible to borrow against housing wealth, with a collateral constraint loan repayment cannot exceed what the bank can get by selling the house: ph

31 Limited commitment the lifetime BC of the consumer: collateral constraint: using that s = y t c c + c 1 + r = y t + y t + ph 1 + r s(1 + r) ph c y t + ph 1 + r

32 A fall in house prices E endowment point the consumer can only borrow up to the value of the house AEB and then BD a fall in the price of the house implies endowment point shifts down and borrowing limit is lower FG and then GH

33 The evolution of house prices in the US the average selling price of houses divided by the CPI

34 Percentage deviations from trend in consumption in the US house prices do not fall during the 2001 recession consumption also does not decline too much consumers financed their consumption by borrowing against the value of their house

35 Social security programs Pensions pension programs: government provided means for saving for social security helps people smooth consumption over their life cycle why is there a need for this? why can t individuals do it themselves on the credit markets? social security programs can be rationalized by a credit market failure the inability of the unborn to trade with those currently alive there are two important types of social security programs pay-as-you-go: transfer between the young and the old fully funded: a government sponsored savings program where the old receive the payoffs on the assets that were acquired when they were young

36 Pay-as-you-go social security taxes on the working population pay for social security transfers to those who have retired each period assume for simplicity that there are two generations are alive at each date, young and old the young pay social security taxes t, the old receive social security benefits b the population grows at rate n: N = (1 + n)n, where each period, there are N young and N old alive for a balanced social security budget total social security benefits must equal total taxes on the young: Nb = N t t = b 1+n

37 The introduction of a pay-as-you-go social security the effect on those who are old at the time of its introduction they receive benefits b endowment point shifts up E 1 E 2 pure positive income effect

38 The introduction of a pay-as-you-go social security the effect on those who are born at or after the time of its introduction pay tax t when young receive benefits b when old endowment point shifts in and up E 1 E 2 slope: (1 + n) if n > r the BC shifts out and the consumer is better off income effect: w = t + b 1+n + b 1+r = r+n b (1+n)(1+r) b 1+r =

39 Pay-as-you-go social security pay-as-you-go is beneficial only if the population growth rate exceeds the real interest rate interpretation: the population growth rate is the implied rate of return for an individual from the social security system social security is only worthwhile if the return exceeds what could be obtained in private credit markets due to the baby boom in the 50 and 60s, currently (in the US), the social security taxes paid by the working age population can cover social security benefits to the old but when the baby boom generation retires - the social security tax (paid by future young) has to go up - or the benefits have to be cut some European countries are already facing the problem of an aging population and considering a transition to some form of fully funded social security

40 Fully funded social security essentially a mandated savings program where assets are acquired by the young, with these assets sold in retirement E endowment point D optimal point without the pension program mandated savings: y c 1 optimal point with pension program: F consumer worse off due to pension program

41 Fully funded social security the program only matters if it mandates a higher level of saving than the consumer would choose otherwise in such a case the consumer is worse off than without the pension program might be subject to a moral hazard problem government insures a minimum return on retirement savings fund managers might take high risk projects, as they only get the upside so what is the rationale for such a forced saving program? government s inability to commit people know that they won t be left to die when old and without any income pull of instant gratification there is no Pareto optimal transition from PAYG to fully-funded, as someone has to pay to the current retirees.