Chapter 8 : Chapter 8 A Two-Period Model: The Consumption-Savings Decision and Ricardian Equivalence Slide 2: This chapter focuses on: Intertemporal decisions
(Economic trade-off across period of time)
Ricardian equivalence theorem Slide 3: Intertemporal Decisions Determines the relative price of consumption in the future in terms of consumption in the present By saving, a consumer give up consumption in exchange for assets in the present to consume more in the future.Alternatively, a consumer can dissave by borrowing in the present to gain more current consumption. Slide 4: Assumes: 1-There are N consumers, we can think of N being a large number.2-Each consumer live for two periods –current and future period.3-Consumers do not make a work-leisure decision in either period but simply receive exogenous income.4- y is a consumer real income in the current period and y´ is income in the future period.5-Each consumer pays lump-sum taxes t in the current period and t´ in the future period.6-Income can be different for consumers but all consumers pay the same taxes.7-Consumers saving in the current period is S. Budget constraint
in current period Consumer is a lender Consumer is a borrower Disposable income 8- Consumer start the current period with no assets.9- Financial asset that is traded in the credit market is a bound.10- All bonds are indistinguishable. because consumers never default on their debts. There is no risk.11- Bonds are traded directly in the credit market.12- The borrowing and lending rates of interest are the same. : 8- Consumer start the current period with no assets.9- Financial asset that is traded in the credit market is a bound.10- All bonds are indistinguishable. because consumers never default on their debts. There is no risk.11- Bonds are traded directly in the credit market.12- The borrowing and lending rates of interest are the same. Slide 6: The Consumer’s Lifetime Budget Constraint (8-2) Consumer's Lifetime Budget Constraint : (8-4) Consumer's Lifetime Budget Constraint Slide 8: The Consumer’s Preferences 1-More is always preferred to less.2-The consumer likes diversity in his consumption bundle.3-Current and future consumption are normal goods.(this implies that if there is a parallel shift to the right in the consumers budget constraint, then current and future consumption both increase). indifferent curves are:1- convex 2-downward-sloping3-MRSc,c´ is negative At point B the consumer has small quantity of current Consumption and large quantity of future consumption, and he needs to be given a large quantity of future consumption to give up a small Quantity of current consumption (minus the slop of the indifference curve is large) so the consumer doesn't like the large differences in consumption between the two periods. Slide 9: Consumer Optimization Figure 8.3 A Consumer Who Is a Lender Figure 8.4 A Consumer Who Is a Borrower The optimal consumption bundle here is determined by where an indifference curve is tangent to the budget constraint. Slide 10: An Increase in Current-Period Income Suppose t, t’, r and y’ are constant Figure 8.5 The Effects of an Increase in Current Income for a Lender Slide 11: Figure 8.6 Percentage Deviations from Trend in GDP and Consumption, 1947–2003 If all consumers smooth their consumption relative to their income, then aggregate consumption should be smooth relative to aggregate income. But empirically there is some excess variability aggregate consumption relative to aggregate income for two reasons: There are imperfections in credit market
When all consumers are trying to smooth consumption in the same way, this change market prices. Consumption on durables is much variable than GDP, which is much more variable than consumption of nondurables and services. The consumption smoothing behavior is clearly reflected in the behavior of nondurables and services. Slide 12: An Increase in Future Income Figure 8.7 An Increase in Future Income Suppose t, t’, r and y are constant The budget constraint shifts to the right
c and c’ both increase Although the increase in y’ is the distance AD, but the increase in c’ is AF so Slide 13: Figure 8.8 Temporary Versus Permanent Increases in Income Friedman Permanent Income Hypothesis: A primary determinant of a consumer’s current consumption is his permanent income which is closely related to the concept of lifetime wealth in our model. Changes in in income that are temporary yield small changes in permanent income which have small effects on current consumption whereas changes in income that are permanent have large effects on permanent income and current consumption. So there need not be an increase in saving and current consumption could increase as mach as or more than does income. A temporary increase in income is an increase in current income. with the budge constraint shifting from AB to DE and the optimal consumption bundle changing from H to j. When there is a permanent increase in income ,current and future income both increase ,and the budget constraint shift from AB to FG, with the optimal consumption bundle changing from H to K. An Increase In the Real Interest Rate : An Increase In the Real Interest Rate Figure 8.11 An Increase in the Real Interest Rate Budget constraint steeper
(slope of it is –(1+r)) Decrease in lifetime wealth (we) Slide 15: A change in real interest rate results in a change in the relative prices of consumption in the current and future periods. An increase in r cause future consumption to become cheaper rather than to current consumption. also has income and substitution effects in its influence on consumption in the present and future as we mentioned before we will have two effects, income and substitution effects. Figure 8.12 An Increase in the Real Interest Rate for a Lender : Figure 8.12 An Increase in the Real Interest Rate for a Lender An Increase in the Real Interest Rate
for a Lender An increase in the r makes saving more attractive, because the relative price of future consumption is lower (SE), but it makes saving less attractive as there is positive IE on period 1 consumption, which tends to reduce saving. Figure 8.13 An Increase in the Real Interest Rate for a Borrower : Figure 8.13 An Increase in the Real Interest Rate for a Borrower An Increase in the Real Interest Rate for a Borrower The Demand for Current Consumption Goods : The Demand for Current Consumption Goods From the above analysis. we know that an individual’s demand for current consumption goods increase with either current or future income. If intertemporal substitution effect of increasing real interest rate, dominated when a consumer is a lender ,then increasing r always cause the consumer demand for C of goods to fall. Figure 8.15 A Consumer's Demand for Current Consumption Goods, cd, as a Function of Current Income The demand for C is cd, slope of it is less than 1,that called MPC and MPC=∆C/∆Y Figure 8.16 A Shift in a Consumer's Demand for Current Consumption : Figure 8.16 A Shift in a Consumer's Demand for Current Consumption The cd curve shifts up with a decrease in the real interest rate or an increase in future income. Government : Government G: government current purchases
G’: government future purchases
N: number of consumers
t: current tax
t’: future tax
T: aggregate current tax (T=Nt)
T’: aggregate future tax (T’=Nt’)
B: government bonds Government current
budget constraint (8-17) Government was a lender
to the private sector Current period
government deficit Government spending is financed through taxes and the issue of bonds. Current period government deficit, G-T is financed by issuing bonds. So in the future period the government budget constraint is: (8-18) Slide 21: Government present-value budget constraint Competitive Equilibrium : Competitive Equilibrium Government Consumers Credit
Market r r Competitive Equilibrium Conditions in tow-period Economy 1.Each consumer choose first-and second consumption and savings- optimally given the real interest rate r.
2.The government present value budget constraint hold
3.The credit market clears. Net quantity that consumers want to lend is equal to the quantity that government wishes to borrow Aggregate
private saving Government
saving In Equilibrium (8-20) (8-21) (8-22) (8-23) (8-17) Slide 23: The Ricardian Equivalence Theorem DEFINATION: If current and future government spending are held constant, then a change in current taxes with an equal and opposite change in the present value of future taxes leaves the equilibrium real interest rate and the consumption of individuals unchanged. The logic of the Ricardian equivalence theorem is that:
a tax cut is not a free lunch A change in the timing of taxes by government is neutral Slide 24: rearranging (8-25) Government present-value
budget constraint The consumer’s lifetime
budget constraint Ricardian
Theorem (8-4) (8-19) In equilibrium for a given r, each consumer chooses c and c’, respectively, to make himself well
off as possible subject to the lifetime budget constraint, (8-26), the present-value government budget constraint, (8-19), hold, and the credit market clear, so Y=C+G. Slide 25: If current taxes change by Δt for each consumer, with future taxes changing by so that the government budget constraint continues to hold, From (8-24). Then, From (8-26) there is no change in the consumer’s lifetime wealth, the right hand side of (8-26), given r, because y, y’, N, G and G’ remain unaffected. Because the consumer’s lifetime wealth is unaffected, then given r the consumer makes the same decisions, choosing the same quantities of c and c’. This is true for every consumer, so given r aggregate consumption C is the same. Thus, Y=C+G, so the credit market clears. So a change in the timing of taxes has no effect on consumption, welfare or real interest rate. But there are effects on private saving and government saving, because: The logic of Ricardian Equivalence : The logic of Ricardian Equivalence Consumers are forward-looking, know that a debt-financed tax cut today implies an increase in future taxes that is equal – in present value – to the tax cut.
The tax cut does not make consumers better off, so they do not increase consumption spending.
Instead, they save the full tax cut in order to repay the future tax liability.
Result: Private saving rises by the amount public saving falls, leaving national saving unchanged. Figure 8.17 Ricardian Equivalence with a Cut in Current Taxes for a Borrower : Figure 8.17 Ricardian Equivalence with a Cut in Current Taxes for a Borrower Ricardian Equivalence: A Graph A current tax cut with a future increase in taxes leaves the consumer’s lifetime budget constraint unchanged. And so the consumer’s optimal consumption bundle remains at A. The endowment point shifts from E1 to E2, so that there is an increase in saving by the amount of the current tax cut. The consumer’s consumption-smoothing motive, some of increase in disposable income would be save. Friedman’s permanent income hypothesis would appear to imply that a temporary change in taxes leads to a very small change in current consumption. The Ricardian equivalence theorem carries this logic one step future by taking into account the implications of a current change in taxes for future taxes. Slide 28: Ricardian Equivalence and the Burden of Government Debt Key assumptions of the Ricardian equivalence theorem 1-When taxes change, they change by the same amount for all consumers both in the present and future. Now, if some consumers received higher tax cut than others, this change their consumption choices and change the equilibrium real interest rate. But in the future when the higher debt is paid off through higher future taxes, consumers might share unequally In this taxation so that the burden of the debt might not be distributed equally. 2-Any debt issued by the government is paid off during the lifetimes of the people alive when the debt was issued. If government postpone pay off the debt until long in the future, then the current old receive higher disposable income, but the young have to pay off the debts in the future and it can be a burden on the young. (intergenerational redistribution of wealth). Slide 29: 3- Taxes are lump sum. All taxes cause distortions which represent welfare losses from taxation. One of the trade offs made by the government in setting taxes optimally is the trade off between current and future taxation. ROBERT BARRO shows that the government should act to smooth tax rates over time to achieve the optimal trade off between current and future taxation. 4- There are perfect credit market. It means consumers can lend and borrow as much as they want and they can borrow and at the same interest rate. In practice consumers face constraints on how much they can borrow and the rate of borrowing is higher than rate of lending. So the credit-constrained consumers could be affected beneficially by a tax cut. Slide 30: Social Security Programs Social security programs are government-provided means for saving for retirement. Types of
Programs Pay-As-You-Go (PAYG) Fully Funded (FF) Mix of PAYG and FF Transfer between the young and the old Saving program where the saving of young are used to purchase assets, and the old receive the payoffs on assets that were acquired when were young Slide 31: N: number of old consumers currently alive
N’: number of young consumers currently alive
n : population growth rate
y : young consumer income
y’ : old consumer income
b : benefit of social security
t : young consumer tax
t’ : old consumer tax Social security has no effect on the market real interest (r constant for all time)
Each consumer lives for tow periods (youth and old)
In any period there is a young generation and an old generation
Government spending is zero in all periods
Social security is established at date T and continues forever after
Before date T the taxes on the young and old are zero in each period.
Benefit for old consumer must be financed by taxes on the young (t’=-b) supposes (8-27) (8-28) (8-29) Total social security
benefit Total taxes on
the young = From (8-27) & (8-28) Pay-As-You-Go
Social Security Figure 8.18 Pay-As-You-Go Social Security for Consumers Who Are Old in Period T : How do consumers benefit from social security? Figure 8.18 Pay-As-You-Go Social Security for Consumers Who Are Old in Period T The consumers who are old when the program is introduced in period T gain as these consumers receive the social security benefit but don’t have to suffer any increase in taxes when they are young. In the period when social security is introduced the budget constraint of an old consumer shifts from AB to DF and he is clearly better off. Because he is able to choose a consumption bundle on a higher indifference curve. Slide 33: Figure 8.19 Pay-As-You-Go Social Security for Consumers Born in Period T and Later What happens to consumers born in periods T and later? There is no way for people to trade with those who are not born yet, and the young and old can not trade because the young would like to exchange the current consumption for future consumption and the old would like to exchange current consumption for past. So the government is able to bring about intergenerational transfers that may yield the Pareto improvement. Figure 8.20 Fully Funded Social Security When Mandated Retirement Saving Is Binding : Figure 8.20 Fully Funded Social Security When Mandated Retirement Saving Is Binding Fully Funded Social Security With binding mandated retirement saving, the consumer must choose point F rather than D and is, therefore, worse off. At best, fully funded social security is ineffective if the amount of social security saving is not binding or if consumers can undo forced savings by borrowing against their future social security benefits when young. Is a program whereby the government invests the proceeds from social security taxes in the private credit market and social security benefits determined by the payoff the government receives in the private credit market. Figure 8.21 A Consumer Facing Different Lending and Borrowing Rates : Credit Market Imperfections and Consumption c =Current Consumption c’ =Future Consumption Figure 8.21 A Consumer Facing Different Lending and Borrowing Rates Figure 8.22 Effects of a Tax Cut for a Consumer with Different Borrowing and Lending Rates : Figure 8.22 Effects of a Tax Cut for a Consumer with Different Borrowing and Lending Rates A B The consumer receives a current tax cut, with a future increase in taxes, and this shifts the budget constraint from AE1B to AE2F. The consumer’s optimal consumption bundle shifts from E1 to E2, and the consumer consumes the entire cut (contrast this with the Ricardian equivalence result) If credit market imperfection mater significantly, then the people that are helped by current tax cuts are those who are affected most by credit market imperfections so tax policy could be used to increase general economic welfare but it might be to target particular groups of people. Slide 37: Summary 1- A two period macro economic model was constructed to understand the intertemporal consumption- saving decisions of consumers and the effects of fiscal policy choices concerning the timing of taxes and the quantity of government debt. 2- In the model, there are many consumers and each make decisions over a two- period horizon where a consumer’s income in two periods are given, and the consumer pays the lump-sum taxes in each period to the government. 3- The lifetime budget constraint of the consumer states that the present value of consumption over the consumer’s two-period time horizon is equal to the present value of disposable income. 4- A consumer’s lifetime wealth is his or her present value of disposable income. Slide 38: 6- consumption smoothing yields the result that, if income increases in the current period for a consumer , then current consumption increases, future consumption increases, and current saving increases. If future income increases, then consumption increases in both periods and current saving decreases. A permanent increase in income (when current and future income increase) has a larger impact on current consumption than does a temporary increase in income (only current income increases). 5- A consumer’s preferences have the property that more is preferred to less with regard to current and future consumption, there is a preference to diversity in current and future consumption, and current and future consumption are normal goods. A preference for diversity implies that consumers wish to smooth consumption relative to income over the present and the future. 7- If there is an increase in the real interest rate that a consumer faces, then there are income and substitution effects on consumption. Because an increase in the real interest rate causes a reduction in the price of future consumption in terms of current consumption, the substitution effect is for current consumption to fall, future consumption to rise, and current saving to rise when the real interest rate rises. For a lender (borrower), the income effect of an increase in the real interest rate is positive(negative) for both current and future consumption. Slide 39: 10- We explored the role of social security programs when Ricardian equivalence does not hold, and the effects of changes in taxes when there are credit market imperfections. 9- Ricardian equivalence depends critically on the notion that the burden of the government debt is shared equally among the people alive when the debt is issued. The burden of the debt is not shared equally when: (1) there are current distributional effects of changes in taxes; (2) there are intergenerational distributional effects; (3) taxes cause distortions; or (4) there are credit market imperfections. 8- The Ricardian equivalence theorem states that changes in current taxes by the government that leave the present value of taxes constant have no effect on consumers’ consumption choices or on the equilibrium real interest rate. This is because consumers change savings by an amount equal and opposite to the change in current taxes to compensate for the change in future taxes.