Macroeconomic theory and policy phần 5 pot

If consumer spending is an increasing function of disposable income e.g., c = a + by − τ as in Appendix 4.B, then a cut intaxes will increase the disposable income of the household secto

0 c1

c2

FIGURE 5.1 Individual Choice with Lump-Sum Taxes

‘Fried-T For example, Figure 5.1 depicts two after-tax endowment profiles that result

in the same after-tax wealth; endowment B features high current taxes (but lowfuture taxes), while endowment C features low current taxes (but high futuretaxes) In either case, consumer demand remains at point C On the other hand,

if individuals live in a ‘Keynesian’ world (i.e., if they are debt constrained), thenthe same conclusion will generally not hold (again, see Appendix 4.B) The im-portance of this distinction will become apparent shortly In the meantime, wewill operate under the assumption that individuals are not debt constrained

5.4 The Ricardian Equivalence Theorem

In this section, we ask two related questions First, how does a cut in taxesaffect consumer demand? Second, does a large government budget deficit poseany sort of ‘problem’ for the economy? These two questions are related becausecutting taxes generally implies increasing the deficit, at least, to the extent thatprogram spending (g1, g2) is left unaltered Another way to ask the questionbeing posed here is: What are the likely effects of a deficit-financed tax cut?Deficit-financed tax cuts are sometimes recommended by policy advisorswhen the economy is in recession The reasoning here runs something as fol-

5.4 THE RICARDIAN EQUIVALENCE THEOREM 115

lows First, we know that increases in consumer demand are often followed byperiods of economic expansion If consumer spending is an increasing function

of disposable income (e.g., c = a + b(y − τ) as in Appendix 4.B), then a cut intaxes will increase the disposable income of the household sector, leading to anincrease in consumer demand and therefore future GDP

Let us investigate the logic of this argument within the context of our model.Take a look at the government’s budget constraint (5.3) If we hold the pattern

of government spending (g1, g2) fixed, then a tax-cut today ∆τ1< 0 must imply

a future tax increase This is because the deficit incurred today must be repaid(principal and interest) at some point in the future The government budgetconstraint makes it clear that future taxes must rise by the amount ∆τ2 =

−∆τ1R > 0

The key question here is how the deficit-financed tax cut affects the after-taxwealth of the household sector Since gross wealth W is fixed by assumption,after-tax wealth can only change if the present value of the household sector’stax liability T changes The change in the tax liability is given by:

∆T = ∆τ1+∆τ2

R .Observe that since ∆τ2= −∆τ1R, it follows that ∆T = 0

Because the deficit-financed tax cut leaves the after-tax wealth position of thehousehold unchanged, we can conclude that this program will have absolutely

no effect on aggregate consumer demand Another way to state this result is toassert that ‘deficits do not matter.’ The intuition behind this result is straight-forward While the current tax cut increases current disposable income of ourmodel households, these households are also forecasting a future tax hike andhence a reduction in their future disposable income The consumption smooth-ing motive tells us that households would want to react to such a change in theintertemporal pattern of their disposable income by increasing their current de-sired saving By doing so, they can shift the current tax windfall to the future,where they can use it to pay for the higher taxes in that period Since after-taxwealth is left unchanged, households increase their desired saving dollar-for-dollar with the decrease in public sector saving; i.e., ∆sP = −∆sG = ∆bG Inother words, all the new bonds that are issued by the government are willingpurchased by the household sector at the prevailing interest rate, leaving desirednational saving unchanged When these bonds mature in the future, they areused by households to pay off the higher tax bill

The conclusion that ‘deficits do not matter’ is a result implied the dian Equivalence Theorem Loosely speaking, the Ricardian Equivalence Theo-rem asserts that under some conditions (that we will talk about shortly), taxesand deficits are equivalent ways of financing any given government expenditurestream That is, since deficits simply constitute future taxes, the theorem alter-natively asserts that the timing of taxes do not matter Another way of statingthe same thing is that the household sector should not view its government bond

Ricar-holdings as net wealth since such bonds simply represent a future tax obligation(Barro, 1974).1

• Exercise 5.1 If the Ricardian Equivalence Theorem holds, then thetiming of taxes ‘do not matter’ in the sense that there is no effect onconsumer demand, desired national saving, the current account and (in aclosed economy) the real rate of interest However, the timing of taxes doeshave implications for the composition of desired national saving (betweenthe private and public sectors) Explain how

• Exercise 5.2 True, False or Uncertain and Explain The RicardianEquivalence Theorem states that government spending ‘does not matter.’(Hint: the answer is False)

The conclusions of the Ricardian Equivalence Theorem are both striking andcontroversial, so let us take some time now to examine the assumptions under-lying these results The theorem makes an number of important assumptions(that happen to hold true in our model economy) These assumptions are statedbelow:

1 Perfect financial markets That is, individuals are free to save and borrow

at the market interest rate In particular, if some individuals are constrained, then the theorem does not hold On the other hand, if only

debt-a smdebt-all number of people debt-are debt-constrdebt-ained, then the debt-assumption ofperfect financial markets might serve as a reasonably good approximation

2 ‘Rational’ households In particular, households must be ‘forward looking’and understand the government budget constraint While it is easy toimagine that there may be ‘irrational’ households operating in the realworld, one would have to question whether these households influenceaggregate expenditure in a quantitatively important way It is equallyapparent by the fact that households save that they are forward looking.And judging by the political controversy generated by budget deficits,

it seems hard to believe that households are generally not aware of thegovernment budget constraint

3 Lump sum taxes In particular, the theorem does not hold if the ment only has access to distortionary taxes Since distortionary taxes arethe norm in reality, this assumption is potentially a serious one

govern-4 Long-lived households What we literally need here is that the planninghorizon of the household is as long as the government’s planning horizon.Since governments typically live much longer than individuals, one mightquestion the empirical relevance of this assumption To see what can ‘gowrong’ if households have short planning horizons, consider the case of

1 See also: www.garfield.library.upenn.edu/ classics1992/ A1992GX22600001.pdf

5.5 GOVERNMENT SPENDING 117

an individual in retirement If the government cuts this person’s taxestoday and increases taxes at some point in the distant horizon, then ourretired individual is unlikely to ‘be around’ to settle the higher future taxbill (he will have cleverly escaped his tax obligation by dying) For such

an individual, a deficit-financed tax cut constitutes an increase in wealth

On the other hand, while individuals do not live forever, it is conceivablethat households do Barro (1974) has pointed out that to the extent thatpeople care about their children, they may want to save the tax cut andbequest it to their children (who can then use it to pay for the highertaxes they will face)

The Ricardian Equivalence Theorem clearly makes some strong assumptions,most of which are literally not true in reality However, whether an assumption

is literally true or not is not the relevant issue The relevant question is whetherthe set of assumptions serve as good approximations to reality Whether aset of assumptions serve as good approximations or not can only be judged bysubjecting the theory to empirical testing

As it turns out, empirical tests of the Ricardian Equivalence Theorem reportare mixed (try performing a search on Google) Many empirical studies find that

an increase in budget deficits (a decrease in public sector saving) is met by anincrease in private sector saving, as the theorem predicts However, it is lessclear whether private savings rise dollar for dollar with the decline in governmentsaving (as the theorem also predicts)

Perhaps the main lesson of the theorem for policy makers is as follows Tothe extent that households increase their saving in response to a deficit-financedtax cut, such a policy is not likely to be as stimulative as one might expect (if onewas trained to view the world through the lens of the Keynesian consumptionfunction)

• Exercise 5.3 Explain why the Ricardian Equivalence Theorem is likely to hold in an economy that experiences net immigration flows

un-• Exercise 5.4 Demonstrate, with the aid of a diagram, how the RicardianEquivalence Theorem will not hold for an economy where individuals aredebt-constrained

5.5 Government Spending

It is important to understand that while our model implies that governmentbudget deficits ‘do not matter,’ the same is not true of government spending Inour model, changes in the government expenditure program (g1, g2) will matter,

at least, to the extent that it alters the after-tax wealth position of the householdsector

The results of this section can be summarized briefly First, since we areworking with an endowment economy, changes in (g1, g2) can have no effect onreal output (y1, y2) Any increase in government spending then must ultimatelyimply lower levels of private consumer spending Second, since the RicardianEquivalence Theorem holds in our model, we can without loss of generalityassume that τ1 = g1 and τ2 = g2 That is, since the timing of taxes ‘does notmatter,’ let’s just assume that the government balances its budget on a period

by period basis In this case, domestic saving corresponds to private sectorsaving (since public sector saving will always be equal to zero)

5.5.1 A Transitory Increase in Government Spending

Consider an initial situation in which (g1, g2) = (0, 0) and suppose that holds are initially content with consuming their endowment; i.e., point A inFigure 5.2 (remember that where you place the initial indifference curve doesnot matter) A transitory increase in government spending can be modeled as

house-∆g1> 0 and ∆g2 = 0 We are assuming here that ∆τ1 = ∆g1, but rememberthat whether the government finances this increase with higher current taxes or

a deficit (higher future taxes) will not matter

This fiscal policy shifts the after-tax endowment point to the left (i.e., topoint B) The higher tax burden makes households less wealthy The consump-tion smoothing motive (i.e., the wealth effect) implies that generally speaking,households will react to this fiscal policy by reducing their demand for con-sumption at all dates; i.e., ∆cD

1 < 0 and ∆cD

2 < 0 We can depict this change

in behavior by moving the indifference curve from point A to point C in Figure5.2

5.6 GOVERNMENT SPENDING AND TAXATION IN A MODEL WITH PRODUCTION119

W

W - T

y1

From Figure 5.2, we see that current consumer spending does not decline by

the full amount of the tax increase Therefore, private sector (and domestic)

saving must decline Households react to the transitory increase in spending

(and taxes) by increasing the amount they wish to borrow from foreigners

By (temporarily) increasing the net imports of goods and services, domestic

consumers can smooth their consumption over time Of course, the resulting

current account deficit must be matched in the future by a corresponding current

account surplus (domestic households must export goods and services to the

foreign sector to pay back their debt)

• Exercise 5.5 Demonstrate, with the aid of a diagram, the effects of a

transitory increase in government spending financed by a deficit

• Exercise 5.6 Demonstrate, with the aid of a diagram similar to Figure

5.2, what effect an anticipated increase in future government spending will

have on the current account

5.6 Government Spending and Taxation in a Model

with Production

The analysis above has assumed that the intertemporal production of output

(y , y ) is exogenous We can move a step closer to reality by assuming instead

that the level of production depends on the time-allocation choices made in thelabor market, the way we described in Chapter 2 and Appendix 4.D.

In a two-period model, the preferences of households must be modified toinclude time-dated leisure; i.e., u(c1, l1, c2, l2) If the production function is linear

in labor; i.e., yj = zjnj for j = 1, 2, then using the arguments developed inChapter 2, we know that the equilibrium gross wages in this model economy will

be given by (w∗

1, w∗

2) = (z1, z2) The household’s intertemporal budget constraintthen depends on whether taxes are lump sum or distortionary For lump-sumtaxes, the budget constraint is given by:

When taxes are lump sum, the Ricardian Equivalence Theorem continues to hold

in this environment However, this will not be the case if taxes are distortionary

To see why, consider what happens if the government decides to implement adeficit-financed tax cut In this case, the tax cut today (∆τ1 < 0) stimulatesemployment (and hence, output) today so that ∆n∗1 > 0 and ∆y∗1 > 0 Thetax increase expected in the future (∆τ2 > 0) has the opposite effect, so that

∆n∗

2 < 0 and ∆y∗

2 < 0 Clearly, the timing of taxes does matter here We canalso see why a large deficit today may elicit some concern on the part of thepopulation That is, if people understand that a high deficit today must atsome point be met with higher future taxes, and if these taxes are distortionary,then people will understand that high deficits today will put a drag on futureeconomic activity

5.7 U.S FISCAL POLICY 1215.6.2 Government Spending Shocks

When taxes are lump sum, any type of positive government spending shockwill simply serve to reduce the after-tax wealth of the household sector Whenwealth declines, the demand for all normal goods declines so that ∆c∗

in economic welfare

When taxes are distortionary, individuals are hit by a ‘double-whammy,’

so to speak Since higher levels of government spending require higher taxes

at some point, not only do households experience a decline in wealth, but theirdecisions become distorted (in an attempt to escape the tax) Since these highertaxes are distortionary, they may very well lead to a decline in employmentand output (again, see Chapter 3) It is for these reasons that ‘supply side’economists are critical of large government spending programs

5.6.3 Barro’s Tax-Smoothing Argument

Suppose that the government’s expenditure program (g1, g2) is fixed in place.When taxes are lump-sum, the government’s finance department faces a trivialdecision: choose any (τ1, τ2) that satisfies the government’s intertemporal bud-get constraint However, when taxes are distortionary, Barro (1979) has pointedout that it would be optimal for the government to smooth taxes over time That

is, the government should choose a tax rate that balances not only the ment’s intertemporal budget constraint, but balances government spending andrevenue on average throughout time This implies a relatively constant tax rateand a budget deficit/surplus that fluctuates over time (but balance out over thelong-run)

govern-By smoothing taxes in this manner, the government is in effect smoothingout (and therefore minimizing) the distortions that its taxes create over time.For example, if the government requires an extraordinarily high (but transitory)level of government purchases in one period (say, to finance a war effort), thetax smoothing argument implies that the government should finance such anexpenditure by issuing bonds rather than by raising taxes to extraordinarilyhigh levels The tax rate should be increased slightly (to minimize distortions)and kept at this higher level until the debt is paid off

5.7 U.S Fiscal Policy

There has been much talk recently of George W Bush’s fiscal policy In a shell, this policy appears to entail: (1) tax cuts (in order to stimulate economic

nut-activity); (2) an increase in government spending on the military (to fight thewar on terror); and (3) a decrease in government spending in other areas Iwill not attempt a full analysis of this fiscal program, but will provide someperspective in the context of the historical pattern of U.S government spendingand taxation Figure 6.3 (should be 5.3) plots U.S government spending andtaxation (as a ratio of GDP) beginning in 1930.

Figure 6.3 U.S Government Spending and Taxation

5.8 SUMMARY 123

Also note the sharp rise in government spending during the second worldwar (most of which was in the form of military spending) While taxes didrise significantly during the war, they did not rise anywhere near to the extentneeded to balance the budget Here, we see Barro’s tax-smoothing argument

at work That is, to the extent that the war was perceived to be transitory, itmade sense to finance the bulk of expenditures by issuing bonds, rather than

by raising taxes

5.8 Summary

The intertemporal approach to government spending and finance emphasizesthe fact that a government with access to financial markets is subject to anintertemporal budget constraint From this perspective, it is clear that currentbudget deficits simply represent future taxes The intertemporal approach alsomakes clear the importance of evaluating fiscal policy as an entire program thatdictates not only current spending and taxation, but the entire future path ofspending and taxation

In some circumstances, it was shown that for a given expenditure program,the timing of taxes is irrelevant as long as the government has access to a lumpsum tax instrument This conclusion, however, is unlikely to hold empiricallybecause taxes are typically distortionary When taxes are distortionary, it makessense to smooth taxes over time and allow budget deficits to grow during reces-sions (or periods when government spending requirements are high), followed

by budget surpluses during periods of economic expansion (or periods whengovernment spending requirements are low)

In the models studied above, government spending has the effect of ‘crowdingout’ private consumption expenditures Certain types of government spendingshocks were also shown to affect the current account position of a small openeconomy In addition to these effects, government spending is often asserted tocrowd out private investment spending and lead to higher interest rates Theseissues can be explored in later chapters once we have an appropriate theory ofinvestment developed

5.9 Problems

1 Consider a small open economy as in Figure 5.2 In that figure, we assumedthat the transitory increase in government spending was financed by anincrease in current taxes Suppose instead that the government chooses

to finance the current increase in government spending with an increase

in future taxes Show that the method of finance has no effect on desiredconsumer spending or the current account, but serves simply to alter thecomposition of national saving

2 Consider a closed economy with individuals who have preferences given

by M RS = c2/c1 Show that the equilibrium real interest rate is given by:

3 Consider an economy populated by two types of individuals, A and B.Normalize the total population to unity and let θ denote the fraction oftype A individuals Type A individuals live for one period only; theirpreferences are given by uA(c1) = c1 and they have an endowment y1.Type B individuals live for two periods; their preferences are given by

uB(c1, c2) = ln c1+ β ln c2 and they have an endowment (y1, y2) Thereal rate of interest is fixed at R Imagine that a government decides

to implement a public pension plan The government plans to run thisprogram as follows In period one, it taxes all individuals an amount τand then saves these ‘contributions’ at the interest rate R In period two,the government pays out the proceeds Rτ to all (living) individuals Eachperson living in period two receives a payout equal to s = Rτ /(1 − θ)

If g1= g2= 0, then the government’s intertemporal budget constraint isgiven by:

(1 − θ)Rs = τ

The left hand side of the GBC represents the present value of the ment’s pension liabilities (promises) The right hand side represents thetaxes that are collected in order to cover these liabilities

govern-(a) Assume for the moment that θ = 0 Explain why the governmentpension program has no effect on aggregate consumer demand Hint:use the Ricardian Equivalence Theorem

(b) Now, assume that θ > 0 Show that the aggregate demand for sumption in period one is now increasing in the ‘generosity’ of thepromised payout s Explain Why does the Ricardian EquivalenceTheorem not hold here?

of purchases (or sales) of financial capital Financial capital simply representsclaims against the output of other members in society (e.g., claims against theoutput of individuals, foreigners, or governments) However, in these previouschapters we maintained an important assumption; namely, that output is non-storable The way to think of physical (as opposed to financial) capital is that itrepresents an intertemporal production technology that allows the economy to

‘transport’ output across time The most obvious example of physical capital isinventory But physical capital can also take the form of a factor of production(like labor)

Most of the physical capital in an economy constitutes durable assets thatproduce services that are useful in the production of output (new goods andservices) Examples of such capital include the residential capital stock (whichproduces shelter services) and various forms of business capital (office towers,land, machinery and equipment, inventory, etc.) In most production processes,both labor and capital are important inputs for the creation of goods and ser-vices The goods and services that are produced by these factors of productioncan be classified into two broad categories: consumer goods and investmentgoods Investment goods are treated as expenditures on new capital goods (andinclude additions to inventory) These goods are produced in order to augmentthe existing capital stock When the capital stock increases, more output can

be produced with any given amount of labor In this way, an economy may beable to grow even in the absence of technological progress

127

6.2 Capital and Intertemporal Production

The production function in this model economy takes the form:

yj= zjF (kj, nj),

for j = 1, 2 The function F is increasing and strictly concave in both kj and

nj (see Appendix 2.A) For simplicity, let us assume that the time allocationchoice is fixed (exogenous) at (n∗

1, n∗

2) = (1, 1) Hence, the production functioncan be written as zf (k) ≡ zF (k, 1), where the function f is increasing andstrictly concave All this means is that as we increase the amount of capitalused in production (holding fixed the labor input), the amount of output that isproduced increases The fact that f is concave means that output increases with

k at a diminishing rate (there are diminishing returns to capital accumulation).The slope of the production function is called the marginal product of capital,which we denote here by M P K(k, z) ≡ zf0(k) The M P K(k, z) tells us theextra output that can be produced by increasing capital by a small amountfrom k (given the technology parameter z) If the function f is increasing andconcave, then it follows that the M P K is positive and a decreasing function of

k As well, note that the M P K is an increasing function of z Figure 6.1 depictsthe production technology for two different levels of technology z0 > z Notethat M P K(k, z0) > M P K(k, z) > M P K(k0, z)

0

y

zf(k) z’f(k)

k