The neoclassical approach to fiscal policy (5)

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1 The neoclassical approach to fiscal policy (5) Manuel Wälti September 2003 Contents 1 Introduction 2 2 Some facts and figures Governmentpurchases Taxes Publicdebt Analysis of government consumption financed by lump-sum taxes Assumptions Graphicalrepresentationofthemodel Shockstogovernmentconsumption Atemporarychange Apermanentchange Empirical Evidence: Wars and real interest rates Analysis of distortionary taxation Introduction Assumptions Changes in government consumption and distortionary taxes Wealthandsubstitutioneffects Permanent changes (in distortionary taxes only): Long-run effects Temporary changes: Dynamic effects Department of Economics, University of Bern, Gesellschaftsstrasse 49, CH-3012 Bern, Switzerland. manuel.waelti@vwi.unibe.ch, Homepage: 1

2 5 Budget deficits and public debt Assumptions Ricardianequivalenceofdebtandtaxes Digression:Thestandardview CriticismsoftheRicardianresult Thetimingoftaxes Digression:Optimaltaxation Conclusion Introduction In this summary, we extend the market-clearing model to include a government sector. In Section 2, we look at the data on government purchases, marginal tax rate, and public debt. In Section 3, we begin by assuming that government consumption is financed with lump-sum taxes and that the government sector always runs a balanced budget. We use this framework to analyze the macroeconomic effects of changes in the level of government consumption. Section 4 extends the analysis to allow for distortionary taxation. In a final section, we introduce deficit finance and the public debt and discuss the Ricardian equivalence theorem for taxes versus debt. This summary draws on Barro [3], Chapter 12, 13, and 14, on Barro [2], and on Baxter and King [4]. 2 Some facts and figures 2.1 Government purchases In the U.S., government purchases are broken into two parts: government spending on capital goods (or government investment) and government consumption expenditures. Barro [3], Figure 1.11, shows that government consumption expenditures and gross investment are about as volatile as GDP, with a standard deviation of This component is, however, negligibly related to detrended GDP: the correlation is only Thus, although the government component of GDP is large and moderately variable, the lack of correlation with GDP indicates that this component is acyclical and has little to do with the typical pattern of business fluctuations. Barro [3], Figure 1.12, shows the long-run evolution of government purchases (expressed as ratios to nominal GDP) in the U.S. Government purchases rose most sharply during WW II and the Korean War. We observe a substantial rise in state and local spending until the mid-1970s, whereas the spending for the military dropped sharply. Total spending rose steadily roughly until the mid- 1980s. 2

3 2.2 Taxes Figure 1: Long-run behavior of government receipts and average marginal income tax rate (Baxter and King [4], Figure 1.A) The expanding influence of government over the past 70 years has generated increases in taxation. Figure 1 shows two comprehensive measures of taxation: total government receipts as a fraction of GNP, and average marginal personal income tax rate 1, as generated by Barro and Sahasakul (1986) 2. In the main, the upward movements in the average marginal tax rate parallel the increase in overall federal spending. Two interesting examples of reductions in tax rates are the Kennedy-Johnson cuts ( ) and the Reagan tax cuts ( ). 2.3 Public debt Finally, we look at the long-term history of interest-bearing U.S. public debt. Barro [3], Figure 14.1, shows the ratio of public debt to nominal GNP (GDP since 1959) from 1780 to The two main positive influences are wartime and major economic contractions. During peacetime, non-recession years, the ratio of public debt to GNP tends to decline. 3 Analysis of government consumption financed by lump-sum taxes 3.1 Assumptions Recall the neoclassical model from Summary 2. In this model there is a representative, infinite-lived consumer, and production is neoclassical with variable capital and labor. Let s now extend this model to include a government sector. The most important assumptions are: There is a government sector. We abstract from public production. Hence, in every period the government buys the quantity of public goods, G t, from private producers in the form of final goods. It follows that output can now be labelled either as consumables, capital goods, or public services. 1 The marginal tax rate is the tax rate on an additional dollar of income, in other words, the fraction that the government takes form an additional dollar of income. The average tax rate, in contrast, denotes the ratio of taxes to the gross income. Total revenue equals the average tax rate multiplied by the total amount of income. 2 Barro, Robert and Chaipat Sahasakul (1986), Average marginal tax rates from social security and the individual income tax, Journal of Business, 59,

4 We abstract from publicly owned capital and, hence, from public investment. It follows that G t in our model corresponds in the national accounts almost to the category government consumption. 3 For the time being we assume that the government s budget constraint is given by G t = T t i.e., the government sector always runs a balanced budget. Taxes are lump-sum, that is, the household s real tax liability is independent of that household s level or type of income. The government uses its outlays, G t, to provide services to households and firms. We assume that the government provides these services free of charge to the users. We allow for two types of public services: Thefirsttypeprovidesutility to households. Examples are libraries, school lunch programs, and subsidized health care. An important feature of these services is that they may substitute closely for private consumer spending. The second type of service is an input to private production. Examples include the provision and enforcement of laws, aspects of national defense, fire and police services, and various regulatory activities. In some cases these services are close substitutes for private inputs of labor and capital. The representative household s life-time utility is given by t=1 βt u (c t + ηg t,l t )+... where η represents a parameter for direct substitution of public services for consumer spending, G t denotes government consumption per person, and... stands for an additively separable term which captures any additional effects of public services; since such a term has no bearing on household s choice of consumption or leisure we forget about. 4 We can say that government consumption, G t, appears as part of the composite consumption flow c t = c t + ηg t 3 The only difference is that, since the major revision implemented in 1996, government consumption in the national accounts includes an estimate of depreciation on stocks of public capital. 4 As hitherto there is no difference between capital letters (which stand for aggregate variables) and lower case letters (which stand for variables on the level of the representative agent). It is only for reasons of convenience that we used G t and T t (instead of g t and t t ) in the utility function and the budget constraint of the representative household. 4

5 An increase in G t by one unit reduces contemporaneous private spending, c t,byη units. We assume that the substitution parameter satisfies the condition 5 0 <η<1 The representative household s budget constraint for each period is 1 b t+1 + c t = w t n t + b t T t 1+r t where T t can be replaced by G t (compare the government s budget constraint). The household holds the amount of real asset b t at the end of period t, where a negative value signifies borrowing. Assets pay the real rate of return r t in period t+1. Moreover, in period t the household supplies work effort n t. The real wage rate for period t is given to the household as the amount w t. From the household s budget constraint for each period we can derive the present-value lifetime budget constraint (PVBC) b 0 + p tw t n t p tg t = p tc t t=1 t=1 t=1 where b 0 is given and p t denotes the present value factor as defined in Summary 2. The PVBC includes the present value of per capita government consumption, t=1 p tg t, as a negative item. This makes sense because the goods, G t, that the government buys represents a part of the output stream that is not available for households. To include effects of public services on production is straightforward as long as the quantity of public services does not influence the marginal products of capital and labor. Therefore let s assume that public services do not affect the schedule for capital s and labor s marginal product, i.e., there is no direct impact of government consumption on private investment demand and labor supply. Let θ be the marginal product of public services: if the inputs of labor and capital do not change, then an increase in G by one unit raises the aggregate supply of goods by θ units. Moreover, we assume that 0 <θ<1 Diminishing marginal productivity of public services suggests that θ would tend to decline as G rises, for given inputs of capital and labor. Usually we assume that the direct substitution for contemporaneous consumption, η, plus the effect on contemporaneous private output, θ, is less than unity η + θ<1 5 The greater the parameter η, the more closely public services substitute for a unit of contemporaneous private spending. For example, η would be close to unity for school lunch programs, but close to zero for national defense. 5

6 Why does this make sense? If η + θ>1, then the typical household would benefit from an increase in public services, paid for by an increase in taxes. That conclusion follows because the amount that the typical household gets back exceeds the additional taxes. Then it is plausible that the government would grow larger, and this expansion tends to reduce the values of η and θ. It would, in particular, be popular for the government to expand at least until the condition η + θ < 1 was satisfied. Sometimes we simplify matters by pretending η = θ = 0 (an assumption which appears implicitly in many macromodels). 3.2 Graphical representation of the model We incorporate the various effects from government consumption into the condition for clearing the aggregate commodity market. (Recall that the clearing of the commodity market ensures by Walras law that the credit market clears.) The condition for period 1 (the current period) is C d (r 1,G 1 ) (,... + I d r 1,... ) + G 1 = Y s ( r 1,G ),... The aggregate demand for commodities, Y d 1, consists of private consumption demand, C d 1, gross private investment demand, I d 1, and government consumption, G 1. An increase by one unit in G 1 reduces consumer demand by η units. Since there is assumed to be no effect on private investment demand, an increase by one unit in government consumption raises aggregate demand by 1 η units. Moreover, an increase in G 1 by one unit raises the supply of goods by θ units. For a graphical representation compare Figure Shocks to government consumption A temporary change Impact effect Suppose that the economy begins with the steady state level of government consumption. Then consider a temporary increase of government consumption per person, G t. The assumption is that the increase in G t is a surprise but as soon as it occurs is known to last for 1 period; after period 1, spending returns to its steady state level. Since the increase in government consumption is temporary, the present value of government consumption rises by only a small amount. The corresponding effects on the representative household s wealth and, thus, consumption demand and labor supply are small. To analyze the macro effects in the current period (period 1) we focus on the commodity market (compare Figure 2). For simplicity we abstract from the small wealth effects associated with a temporary increase of government consumption. At the original level of government consumption, the market clears at the real 6

7 interest rate r 1. Then the rise in G 1 increases the aggregate quantities of goods demanded and supplied. But since (1 η) >θ, the rightward shift of the aggregate demand curve exceeds that of the supply curve. Therefore, at the real interest rate r 1 there is now excess demand for commodities. We conclude that the real interest rate increases to the value (r 1). Figure 2: Temporary increase in G (taken from Barro [3], Figure 12.3) Consider the composition of output. We know that government consumption rises. But private uses of output - for consumption and investment - decline. Consumer demand falls for two reasons. First, there is the substitution of public services for private spending. Second, the higher real interest rate induces households to postpone their expenditures. This second effect accounts also for a drop in private investment demand. We say that government consumption crowds out private spending. In Summary 2, we noted that investment demand is especially sensitive to variations in the real interest rate. Therefore, unless the direct substitution of public services for consumer spending is strong, we predict that the temporary increase in government consumption will mostly crowd out private investment, rather than consumption. Since private consumption and investment decrease, the rise in total output is smaller than the increase in government consumption. Hence, the ratio of the change in output to the change in government consumption, Y 1 / G 1,is positive but less than one. We say that there is no multiplier. 6 What about saving? The increase in spending, financed by a temporary increase in taxes, implies a temporary decline in household s disposable income. Since the shortfall in income is temporary, the marginal propensity to consume is small. Households therefore reacts mainly by reducing desired saving. (Thus, when desired saving falls and investment demand does not shift, the real interest rate must increase.) Dynamic effects Baxter and King [4] study the equilibrium effects of a temporary fiscal-policy disturbance within a full-fledged RBC model; 7 their findings are summarized in Figure 3. Although their model differs from the one presented here in several respects, their findings are still useful for our purposes as an illustration of the general mechanics. They find that the dynamic response to a 6 If the ratio were greater than one, then we would say that a change in government consumption has a multiplicative effect on output. We do not get this sort of multiplier in our model. That is because the economy typically operates to buffer shocks rather than to magnify them. In particular, the rise in government consumption leads to decreases in private demands for consumption and investment and to an increase in work effort. Each of these responses serves to alleviate the initial excess demand for goods. 7 The same experiment can be done within the non-stochastic neoclassical growth model. For the case where n t = n =1andη = θ = 0 in a continuous time setting see Romer [6], Section

8 four-year shift in government consumptions financed by lump-sum taxation are broken into two phases. During the period of high government spending, there are reduced opportunities for private consumption, leisure, and investment due to the increased government absorption of resources. Then, after government consumption has returned to its steady-state level, investment is above its long-run level as the economy works to rebuild the capital stock. Private consumption and leisure are correspondingly low along this transition path. Labor input increases more in the initial phase - when government spending is high - than it does along the transition path. Interest rate rises immediately and then gradually falls back to its steady state level. Figure 3: Dynamic response to a four-year shift in G (taken from Baxter and King [4], Figure 3.A) A permanent change Suppose that the economy begins with no government consumption at the steady state. Then consider a one-and-for-all increase of government consumption per person from 0 to the amount G. The assumption is that this change was unexpected beforehand but is perceived as permanent once it occurs. If the change in public consumption is perceived to be permanent, then the new element is that the representative household anticipate a sizable increase in the present value of taxes. The resulting fall in wealth reduces consumer demand and raises labor supply. Impact effect We, first, analyze the impact effect of a permanent change in government consumption. To begin with, consider a simplified setting in which public services are useless (η = θ = 0) and labor supply is fixed. In this case, a permanent increase by one unit in government consumption effectively subtracts one unit from the household s disposable income in each period. As with a permanent shift in the production function, the marginal propensity to consume is close to one in this situation. Consumer demand therefore declines by about one unit; that is, one additional unit of public expenditure directly crowds out one unit of private consumer spending. Since government consumption is higher by one unit, the aggregate demand for goods does not change. With fixed labor supply and nonproductive public services, the supply of goods also does not change. Therefore, a permanent increase in government consumption leaves the aggregate demand for goods equal to the supply. Figure 4: Permanent increase in G (taken from Barro [3], Figure 12.5) This result turns out to hold even if government services are productive (η 0 or θ 0) and/or labor supply is allowed to vary. 8

9 Dynamic effects Let us now turn to the dynamic response to a permanent change in government consumption, still financed by lump-sum taxes. The relevant IRF from Baxter and King [4] are contained in Figure 5. 8 Individuals respond to the negative wealth effect described above by decreasing consumption and leisure, so that steady-state labor supply increases. Because the increase in labor input shifts up the marginal product schedule for capital, there are important short- and long-run effects on investment and capital accumulation. In the short run, an accelerator mechanism operates to generate a strong increase in investment. In the long run, to which the economy rapidly converges, there will be higher capital and labor input, but the capital-labor ratio is unchanged. Along the transition path, the one-period real interest rate is high but declining: at early dates, its high value encourages labor supply and postponement of consumption, enabling the investment boom to take place. (Note that regarding the behavior of the real interest rate, Baxter and King s [4] result contradicts Barro s [3] analysis. This is due to differences in the model specification.) The increase in labor supply raises the marginal product of capital schedule, which stimulates capital accumulation until the initial steady-state capital-labor ratio is restored. (This amplification effect of endogenous capital supply means that it is possible for the long-run multiplier to exceed 1.) Figure 5: Dynamic response to a permanent change in G (taken from Baxter and King [4], Figure 2.A) 3.4 Empirical Evidence: Wars and real interest rates Figure 6: Military spending and the real interest rate in the UK (taken from Romer [6], Fig. 2.10) An empirical test of the proposition that temporary increases in government consumption raise real interest rate requires a data set in which some changes in public purchases are identifiable ex ante as temporary. Empirically, the clearest examples of such changes are the variations in military spending during wartime. This considerations makes wartime experiences attractive for tests of theories about the effects of temporary government consumption. However, this advantage is offset by the many other aspects of war that can affect real interest rates: (i) Negative effects on productive capacity, notably the destruction of capital; (ii) widespread use of rationing to hold down private demands for goods; (iii) military draft, confiscation of property, and appeals to patriotism to stimulate work and production. These mechanisms are examples of direct controls, which 8 The same experiment could be done within the non-stochastic neoclassical growth model. For the case where n t = n =1andη = θ = 0 in a continuous time setting see Romer [6], Section

10 can substitute for higher real interest rate as instruments for crowding out private spending and for stimulating work and production. Despite these objections, Barro (1987) 9 tests the model s prediction by examining military spending and interest rates in the United Kingdom (UK) from 1729 to The most significant complication he faces is that, instead of having data on short-term real interest rates, he has data only on long-term nominal interest rates. Long-term interest rates should be, loosely speaking, a weighted average of expected short-term interest rates. Thus, since our analysis implies that temporary increases in government consumption raise the short-term rate over an extended period, it also implies that they raise the long-term rate. Similarly, since the analysis implies that permanent increases in government consumption never change the short-term rate (at least in Barro s [3] analysis), it predicts that they do not affect the long-term rate. In addition, the real interest rate equals the nominal rate minus expected inflation; thus, the nominal rate should be corrected for changes in expected inflation. Barro does not find any evidence, however, of systematic changes in expected inflation in his sample period. Figure 6 plots British military spending as a share of GNP (relative to the mean of this series for the full sample) and the long-term interest rate. The spikes in the military spending series correspond to wars; for example, the spike around 1760 reflects the Seven Years War, andthe spike around 1780 corresponds to the American Revolution. The figure suggests that the interest rate is indeed higher during periods of temporarily high government purchases. A formal test supports these findings. The success of the theory is not universal, however. In particular, for the U.S. real interest rates appear to have been, if anything, generally lower during wars than in other periods (those who are interested in the subject: compare Barro s texbook). 4 Analysis of distortionary taxation 4.1 Introduction The previous discussion assumed that government consumption is financed by lump-sum taxes. Now we make the analysis more realistic by allowing for distorting taxation. We assume that public consumption is financed either by an income tax or by capital tax. A tax on labor income implies a substitution effect for work versus leisure (or other nontaxed activities, such as the underground economy). The relevant substitution variable is the marginal tax rate, τ, that is, the increase in tax implied by an addition to labor income: When an individual works an additional hour, he or she raises output and hence income by the marginal product of labor, MPN t. But the individual keeps only the fraction 9 Barro, Robert J. (1987), Government spending, interest rates, prices, and budget deficit in the United Kingdom, , Journal of Monetary Economics, 20 (September),

11 1 τ of his or her extra income. Hence, the after tax marginal product of labor, (1 τ) MPN t, matters for the choice of work and consumption. (With a separate labor market, the after-tax real wage rate, (1 τ) W t, would matter.) An increase in the marginal tax rate, τ, lowers the schedule when measured net of tax. The representative household responds just as it would to a decrease in the schedule for labor s marginal product: it reduces work effort and consumption demand. A tax on capital income has similar effects. The representative household receives real interest at the rate r t, but it pays the fraction τ of its receipts to the government. Hence, when measured net of tax, the household earns after-tax real interest rate r t (1 τ) r t,andtheafter-tax rate of return to capital is (1 τ) (MPK t δ). The condition for the desired capital stock now is (1 τ) (MPK t δ) = r t This implies that we can write the function for the desired stock of capital, ˆk t,as ( ) ˆk t = ˆk r t,τ,... For a given value of r t,ahigherτ lowers the after-tax return from investment. The desired capital stock therefore declines. As before, the desired stock of capital, ˆk t, determines a producer s gross investment demand ( ) i d t = ˆk r t,τ,... (1 δ) k t Assumptions We modify the model of Section 3 as follows: We replace the lump-sum tax by a tax on income and capital. The income tax is a flat-rate tax, which means that the marginal tax rate is the same for all income groups. (A graduated-tax rate or progressive-tax system, in contrast, would impose a higher rate as income rises.) We assume that the tax rate, τ, does not vary over time. 4.3 Changes in government consumption and distortionary taxes Wealth and substitution effects With a balanced budget, an increase in government consumption, G, requires an increase in government revenues. In the actual setting, an increase in revenues requires an increase in the average marginal tax rate, let s say the average 11

12 marginal income tax rate, τ. While the wealth effect from more G implies more labor supply, the substitution effect from a higher average marginal income tax rate implies less labor supply. Consequently, the overall effect of government consumption on work effort is ambiguous Permanent changes (in distortionary taxes only): Long-run effects Sometimes we shall find it convenient to keep separate the effects of changes in the average marginal tax rate, τ, from those of changes in government consumption, i.e., to focus on the substitution effect and to neglect any effects on wealth. How do we change τ without shifting the level of spending, G, and real tax revenues, T? Recall that the representative household s PVBC involves the present value of real taxes. This present value depends on the present value of government consumption. As long as we hold this last present value fixed, a change in the tax rate does not affect the aggregate present value of taxes and, therefore, would not seem to affect the representative household s wealth. 10 Suppose the change in distortionary taxes is unexpected beforehand but is perceived as permanent once it occurs. To simplify matter we neglect any effects on wealth from changes in the tax rate and pretend that labor supply is fixed. If taxes fall entirely on labor income, then the steady-state real interest rate, r, and steady-state capital-labor ratio, K/N, are invariant with the tax rate. The steady-state capital-labor ratio follows as before the condition MPK δ = r. When the marginal tax rate, τ, applies to all forms of income, including interest income and returns to capital, then the after-tax real interest rate is (1 τ) r t, and the after-tax return to capital is (1 τ) (MPK t δ). A steady state requires equality between (1 τ) r and the rate of time preference, ρ (implicitly defined by β 1/ (1 + ρ)), thus implying that r = ρ 1 τ It follows that an increase in τ leads to a rise in r. As a corollary, the steady-state capital-labor ratio, K/N, declines. Thus, when taxes apply to the earnings from capital, a higher tax rate leads in the long run to a lower capital intensity (and in the short run to less investment) Temporary changes: Dynamic effects Baxter and King [4] examine how the economy responds to an unexpected change in government consumption which is financed by current revenues from distor- 10 For example, the government might increase various exemptions [Steuerbefreiungen] in the income-tax law but then raise all of the tax rates on taxable income to maintain the level of real revenues. However, this example is only approximately right; for a more careful treatment see the box in Barro [3], p

13 tionary taxation and that is known to be temporary. This means that the period of temporary high government purchases also becomes an interval of temporarily high distortionary taxes. Since high taxes imply temporarily low after-tax factor rewards, there is a strong incentive to substitute work effort intertemporally away from the wartime period and also to curtail investment during this period. This means the imposition of tax distortions precisely when society must reduce consumption, leisure, and investment due to temporarily high government consumption. This particularly poor timing of tax distortions would be avoided by the smoothing of taxation over time and the related use of public debt for financing temporarily high consumption (compare Subsection 5.4). 5 Budget deficits and public debt In this final section we introduce deficit finance and the public debt and derive an important result of the neoclassical analysis of fiscal policy (which is directly linked to the name of Barro), referred to as the Ricardian equivalence theorem. The Ricardian equivalence theorem describes assumptions under which the timing of lump-sum taxes does not matter. 5.1 Assumptions The model s assumptions are modified as follows: Suppose now that the government can finance expenditures by issuing interest-bearing public debt. Assume that this debt has a maturity of one period and that the government s interest rate coincides with private rates. Then the government s budget constraint in real terms becomes G t + r t 1 B t 1 = T t +(B t B t 1 ) where G t is real public consumption, B t 1 is the real public debt outstanding at the end of period t 1, r t 1 is the real interest rate on this debt, and T t is real tax revenues. Consider the present value sum of taxes over a finite horizon H H p tt t = H p t [G t + r t 1 B t 1 (B t B t 1 )] t=1 t=1 H p tt t = H p t [G t +(1+r t 1 ) B t 1 B t ] t=1 t=1 H p tt t = H p tg t + H p t (1 + r t 1 ) B t 1 H p tb t t=1 t=1 t=1 t=1 where p t is the market discount factor familiar from Summary Letting 11 Recall that p t [(1 + r 0 )(1+r 1 ) (1 + r t 1 )] 1.Thusp t (1 + r t 1 )=p t 1. 13

14 p 0 =1leadsto H H H p tt t = H p tg t + B 0 + H p t (1 + r t 1 ) B t 1 H p tb t t=1 t=1 t=2 t=1 p tt t = H p tg t + B 0 + H p t 1B t 1 H p tb t t=1 t=1 t=2 t=1 p tt t = H p tg t + B 0 p H B H t=1 t=1 Letting H approach infinity leads to p tt t = p tg t + B 0 lim p HB H t=1 t=1 H Recall the transversality condition for an individual s optimization problem which ensures that individuals do not leave over any resources that asymptotically have positive present value. The public debt is held by individuals as part of their assets; so it follows form the same argument that p H B H must approach zero asymptotically. Setting the last term to to zero implies p tt t = p tg t + B 0 t=1 t=1 Taxes are treated as lump-sum. We take the sequence of government consumption, {G t } t=0,asgiven. 5.2 Ricardian equivalence of debt and taxes Suppose for simplicity that n t = n =1andη = θ = 0 (although the analysis can readily be extended to incorporate the work-leisure choice and η 0 or θ 0). The representative household s PVBC is then given by k 0 + B 0 + p tw t p tt t = p tc t t=1 t=1 t=1 Substituting for t=1 p tt t leads to k 0 + B 0 + p tw t p tg t B 0 = p tc t t=1 t=1 t=1 k 0 + p tw t p tg t = p tc t t=1 t=1 t=1 The resulting expression shows that we can express household s PVBC in terms of the present value of government consumption without reference to the division of the financing of those purchases at any point in time between taxes and bonds. This means that wealth is invariant with B 0 and the entire subsequent path of budget deficits (except that the path of debt is constrained to satisfy the condition that p H B H approach zero asymptotically). 14

15 The result implies a version of the Ricardian equivalence theorem on the public debt: Under certain conditions, the economy s path of real interest rates, investment, consumption, and so on is invariant with shifts between taxes and budget deficits or with changes in the initial stock of public debt. Roughly, those conditions are: perfect capital markets, a long planning horizon for households, rational expectations, and non-distorting taxes. If these conditions hold, then people save the entire tax cut, buy the bonds issued by the government, and use the interest on the bonds to pay the higher future taxes. 5.3 Digression: The standard view As you may know from previous macro courses, the Keynesian or standard view differs from the Ricardian result. In the IS-LM model we assume that a deficit financed tax cut stimulates consumer demand. The reasoning is that the tax cut makes people feel wealthier (e.g. because of some short-sightedness on the part of the households or because of liquidity constraints). As a corollary, consumer demand rises and - as long as taxes are lump-sum, the type of taxes that most macromodels assume - labor supply falls. The resulting excess demand for goods leads to a higher real interest rate and, thereby, to lower investment. Thus, this analysis predicts that government deficits raise real interest rate and crowd out private investment. (The decrease in net investment shows up in the long run as a decrease in the stock of capital; some economists refer to this negative effect on the capital stock as a burden of the public debt. Each generation burdens the next one by leaving behind a smaller aggregate stock of capital.) 5.4 Criticisms of the Ricardian result Meaningful criticisms of the Ricardian result amount to deviations from the assumptions set out above. Barro [2] discusses the following arguments that have been raised, while he maintains the assumption of a fixed path of government consumption: (i) Finite time horizons; (ii) imperfect loan markets (or liquidity constraints), (iii) uncertainty about future taxes, and (iv) non-lump-sum taxes. In what follows we focus on the last point The timing of taxes If taxes are not lump-sum, departures from Ricardian equivalence arise. Let us consider the case of an income tax. Suppose the path of government consumption is given and B 0 = 0. Consider the example in which current taxes, T 1, falls by $1, and the public debt rise by $1. Assume further that the government raises next period s taxes, T 2,by$(1+r) to pay off the extra debt. Unless the government has gone beyond the point of maximum tax revenues on the Laffer curve, the changes in taxes collected show up as corresponding changes in the marginal 15

16 tax rates: today s marginal tax rate, τ 1, declines, and next period s tax rate, τ 2, rises. These changes motivate households to shift their income toward the current period and away from the next period. Specifically, households raise today s work but plan to reduce work in the next period. We conclude that when we consider income taxes there are real effects from fiscal policy. In this situation budget deficits change the timing of income taxes and thereby affect people s incentives to work and produce in different periods. A deficit-financed cut in today s marginal tax rate leads to increases in today s real economic activity. But the responses reverse later when the marginal tax rate is higher than otherwise. In our simple example, the higher future tax rate applies only to period 2. But, more generally, the higher tax rate could be spread over many periods. Then the tendency for real economic activity to decline would also be spread out into the future) Digression: Optimal taxation To sum up, in a world of distorting taxes the government can manipulate its budget deficits to change the relative value of marginal taxes for different periods and thereby influence the relative levels of output at different times (we say it can influence the timing of real economic activity; variations in deficits are nonneutral). This rises new questions: Should tax rates be changed when economic activity is unexpectedly high or low? Or is it desirable to smooth tax rates across time and states of nature? What is the optimal time pattern of taxes, what is the optimal path of the budget deficit? In fact, the theory of debt management becomes a branch of public finance, specifically, an application of the theory of optimal taxation Conclusion What, in the end, should one make of the Ricardian result? To conclude we would like to cite Romer [6], p. 71: Economists take a wide range of positions on the issue. At one extreme is the view that Ricardian equivalence is a theoretical abstraction so unrelated to reality that it is of little interest. At the other extreme is the position that despite the many reasons for it not to hold exactly, it is nonetheless a good first approximation. A reasonable middle ground is that Ricardian equivalence is a useful theoretical baseline but not a useful empirical one. It is valuable as a theoretical baseline because it is so simple and logical. Specifically, any candidate explanation of why governments choices between bonds and taxes affect consumption must spell out precisely how the assumptions underlying Ricardian equivalence fail and why those failures matter. (...) At the same time, it is likely that departures from Ricardian equivalence are quantitatively important. At the very least, the data do not clearly reject the 16

17 importance of any of the potential sources of failure of Ricardian equivalence we have discussed. Thus despite its logical appeal, there does not appear to be strong case for using Ricardian equivalence to gauge the likely effects of government financing decisions in practice. References [1] Abel, Andrew B. and Ben S. Bernanke (1998), Macroeconomics, Addison- Wesley [2] Barro, Robert J. (1989), The Neoclassical approach to fiscal policy, in R.J. Barro, ed., Modern Business Cycle Theory, Harvard University Press, pp [3] Barro, Robert J. (1997), Macroeconomics, The MIT Press [4] Baxter, Marianne and Rober G. King (1993), Fiscal Policy in General Equilibrium, The American Economic Review, vol. 83 no. 3: [5] Mankiw, N. Gregory (1998), Principles of Economics, The Dryden Press [6] Romer, David (1996), Advanced Macroeconomics, The McGraw-Hill Companies 17