The Long (and Short) on Taxation and Expenditure Policies

Zsolt Becsi Economist Te Long (and Sort) on Taxation and Expenditure Policies O ne of te central issues in te 1992 presidential campaign was ow best to promote economic growt Because muc of te growt debate concerned fiscal policy, taxation and expenditure plans came under intense public scrutiny At issue were bot te level of taxation and te proper mix of taxes Similarly, voters were concerned wit te composition as well as te level of government expenditures Wile voter interest was ig, te various programs put fort grew so detailed tat teir long- and sort-run effects became difficult to evaluate and compare Wat distinguised te 1992 campaign was a fiscally sober post Cold War reassessment of te government s economic priorities All major candidates argued for cuts in defense spending and agreed tat te resources saved te peace dividend sould be spent on enancing te nation s productivity Tis productivity enancement was to come from some combination of public investment and a more investment-friendly business tax structure Wile te candidates broad visions were similar, tey disagreed on ow muc public investment to allocate to uman capital (suc as education and training) versus pysical capital (suc as roads, bridges, mass transit, and so on) Proposals also differed on ow to cange business taxation to promote investment, altoug all called for lower costs of private capital Most candidates did not openly acknowledge tat promoting growt usually entails a current sacrifice for future public and private consumption Tis article presents an analytical and grapical framework for evaluating te long- and sort-run effects of a broad range of fiscal policies Except for two simplifying assumptions on te structure of preferences and te production process, te model is fairly general Te model is well-suited for insigts into te dynamic effects of some of te 1992 fiscal policy proposals, and it can easily be expanded to analyze distributional, educational, and industrial policy questions 1 To set te stage, I focus first on te effects of canges in factor income taxation Factor income taxes are te main components of an income tax Factor income taxes also ave a simple connection to most tax proposals, and tis article sows ow tey relate to consumption and corporate taxes Lastly, to frame te debate on wat to do wit te peace dividend, I analyze te effects of canges in government defense and investment expenditures Description of te model Tis section presents a simple growt model tat can be used to analyze te macroeconomic effects of alternative fiscal policies Te model consists of tree sectors Te ouseold sector determines current and planned future levels of I wis to tank my reviewer, Evan Koenig, for elpful suggestions and my readers, Steve Brown, Ping Wang, and Mark Wynne, for teir comments Of course, any remaining errors are my own 1 Te analytical model used is a variant on Ascauer (1988, 1989) and Barro (1989) Te grapical exposition is based on and complements tat of Wynne (1991) Tis framework is extended by Becsi (1991) to deal wit eterogeneity and distributional concerns For extensions to an endogenous growt framework wit education and industrial policies, see, for example, Barro and Sala-I-Martin (1992) Economic Review Tird Quarter 1993 51

consumption, labor, and savings Tese plans are optimal in te sense tat ouseolds coices maximize lifetime utility subject to after-tax budget constraints In te production sector, firms maximize after-tax profits Tis is accomplised by coosing optimal pats for output and for capital and labor inputs In te government sector, tax receipts from various sources are used to finance government consumption and investment Equilibrium occurs wen factor and goods markets clear in every period 2 Te ouseold sector is represented by an average ouseold tat values te amount of consumption, c, and leisure it obtains in eac period of its life 3 Individuals ave a certain number of ours, H, per year to allocate to leisure and labor Let, were 0 H, be te number of ours devoted to market labor Tus, H is te amount of time devoted to leisure For simplicity, preferences between any two time periods are described by U(c, H ) + (1 + ρ) 1 U(c +1, H +1 ) 4,5 Te 52 2 For simplicity, te model abstracts from money and uncertainty It also does not consider market imperfections and intergenerational issues 3 Te representative ouseold is assumed to live infinitely long An infinite lifetime can be viewed as dynastic families tat care about te welfare of future generations Or, it can be viewed as a useful abstraction of long lives Time begins in period one, at wic point te individual is endowed wit k 1 units of capital 4 From time to time, it will be convenient to assume, additionally, tat utility is separable between consumption and labor, so tat U(c, H ) = u(c) + v( H ) 5 Alternatively, one could easily expand utility to include composite consumption, were composite consumption is defined as private consumption plus te consumption services derived from public spending Te services of suc spending as ealt care, education, food stamps, and transportation enter individual utility as substitutes for private consumption Similarly, services from some government expenditures may substitute or complement private inputs into production Tus, te only difference between public consumption and public capital is tat te latter takes time to be productive and depreciates over time I abstract from tese considerations by assuming tat te consumption services from public spending enter utility separably, and tat only public investment as productive services However, in several footnotes below, extensions are considered pure rate of time preference tat discounts future utility is given by ρ > 0 An increase in tis parameter reflects an increase in te individual s desire for early gratification Te representative individual cooses tose feasible time streams of consumption and labor tat maximize lifetime utility Feasibility is determined by te individual s period-by-period budget constraint Te budget constraint requires tat purcases of consumption goods and purcases of assets (wic are eld until te next period) not exceed current period after-tax income Aftertax income is defined as te sum of after-tax labor income, after-tax income from assets, and lumpsum transfers Savings are put into interest-earning productive capital Te budget constraint for eac period is summarized by () 1 c + ( k k) = ( 1 t ) w + ( 1 t ) rk + l, + 1 w were l is te lump-sum transfer (or tax), k is te pysical capital accumulated up to te current period, and k +1 k is te net purcase of capital Te pretax real wage and real interest rate are given by w and r, wile te t i (i = w, r) are te tax rates on wage and interest income For example, te wage tax encompasses payroll taxes for social security and te salary component of personal income taxes Te interest income tax is a tax on te real returns to capital including dividends, capital gains, and so on Houseolds coose feasible streams of consumption, labor, and savings tat maximize utility Tis leads to well-known optimality conditions for constrained utility maximization: te marginal rate of substitution (MRS ) wic equals te rate at wic te ouseold is just willing to trade one good for anoter is equated to te price ratio of te two goods Te price ratio is te rate at wic te two goods can be substituted and still satisfy te budget constraint Witin a time period, ouseolds adjust private consumption and labor until te MRS between consumption and leisure is equal to te ratio of te after-tax wage to te price of consumption goods, tat is, is equal to te after-tax real wage: () 2 MRS(, c H ) = ( 1 t ) w Te MRS between consumption and leisure tells w r

ow muc additional consumption is required to compensate for a reduction in leisure (an increase in labor) Since a reduction in leisure lowers utility, consumption must rise to increase utility to its original level However, as leisure falls, a unit of leisure becomes more valuable to individuals, so tat progressively more consumption is required to compensate for a unit loss of leisure In oter words, te additional consumption required as compensation for lost leisure rises as leisure falls Tus, te MRS is negatively related to leisure (positively related to labor) and, by te same logic, positively related to consumption From te budget constraint, increasing labor by one our of work increases te ouseold s take-ome pay by (1 t w )w units Tis allows consumption purcases to rise by (1 t w )w, wic is te ratio of te price of leisure to te price of consumption If te MRS is smaller tan tis price ratio, consumers require less consumption to make up for te disutility of working tan tey actually can get Tus, ouseolds find it desirable to work more, because utility rises wen work effort (and consumption) are increased Since te MRS is positively related to consumption and labor, as ouseolds increase teir labor and consumption te MRS rises until condition 2 is satisfied Wen ours of labor are plotted on te orizontal axis and private consumption on te vertical axis, one can trace te trade-offs between consumption and labor for a given level of utility (Figure 1) Tese indifference curves are convex to te origin and curve upward because an increase in labor requires an increase in consumption to keep utility constant Te slope of te indifference curve is te MRS and increases wit labor and consumption Higer indifference curves represent iger levels of utility Te budget constraint also slopes upward and as as its slope te after-tax real wage rate Te vertical intercept of te budget line is nonlabor ouseold income suc as capital income and transfers Houseold plans for consumption and labor are determined by te tangency of ouseold indifference curves and budget constraints at point I in Figure 1 At point A te MRS is below te after-tax real wage rate Since te slope of te indifference curve is less tan te slope of te budget line, te ouseold can increase its utility wile staying on its budget line Te ouseold Figure 1 Optimal Consumption Labor Combination c A I moves to a iger indifference curve by substituting leisure for consumption or increasing labor and consumption Consumption and leisure are assumed to be normal goods: a good is said to be normal wen consumption of te good increases for a parallel upward sift of te budget line Reducing te after-tax wage rate is equivalent to a flattening of te budget line Wen consumption and leisure are normal goods, tis will move te individual to point I were consumption and labor are lower Houseolds adjust consumption and savings across time until te MRS between consumption in adjacent periods equals te price of current consumption in terms of future consumption: ( 3) MRS( c + 1, c) = 1+ r + 1( 1 t r ) I (l t w )w Te MRS tells ow muc next period s consumption must rise to compensate for te fall in lifetime utility tat occurs wen current consumption is reduced Wen current consumption is low relative to future consumption, its value is relatively ig for te individual Tus, te compensation required for a fall in current consumption rises as current consumption is reduced In turn, progressively more future consumption is required to compensate for a unit loss of current consumption Tus, te MRS is negatively related to current consumption Similarly, it is positively related to future Economic Review Tird Quarter 1993 53

consumption 6 An impatient ouseold as a ig rate of time preference, ρ Tis means tat an impatient ouseold requires a iger return of future consumption for a sacrifice of current consumption tan a patient ouseold Tus, te MRS will tend to be iger te more impatient te individual is From te budget constraint, decreasing current consumption by one unit allows te ouseold to increase savings by one unit In turn, tis increased saving allows future consumption to rise by [1 + r +1 (1 t r )] Tus, te after-tax interest rate affects ow muc additional future consumption one can ave for a unit reduction of current consumption As long as te MRS exceeds tis relative price, te individual requires more future consumption to keep utility constant for a sacrifice of current consumption tan te budget constraints allow Tus, ouseolds will ave an incentive to raise current consumption relative to future consumption As current consumption rises relative to future consumption, te MRS falls until equality in equation 3 is reestablised 54 6 Wen utility is separable in consumption and leisure, te intertemporal MRS as te following form: MRS( c, c) = + 1 u () c 1 u ( c+ 1) 1+ ρ In steady state, consumption is constant across time, so tat te MRS equals 1 + ρ 7 Constant returns to scale means tat if all inputs are scaled up by te same proportion, output will rise by te same scaling factor 8 To simplify te analysis, public capital is assumed to enter production separably Tus, public capital does not raise (or lower) te marginal product of a private input Empirical evidence suggests tat tis is an oversimplification For instance, Lynde and Ricmond (1992) estimate tat a constant-returns-to-scale production function wit a positive marginal product of capital is plausible However, tey find tat public capital raises te marginal product of private capital and lowers te marginal product of labor Teir evidence on te complementarity in production of private and public capital is consistent wit previous findings 9 Equation 6 is inoperative in te sort run wen te capital stock is fixed Given te stock of public capital, k, te representative firm cooses two inputs, labor and private capital, to maximize its after-tax profit from selling its final output, y Te firm s profits are given by ( ) y w ( r + δ ) k ( k k), 4 + 1 were δ is te pysical rate of depreciation of capital, and (r + δ ) is te cost of capital I assume tat te output production function is constant returns to scale in all inputs and given by y = f (k,) + g (k ) 7 In oter words, total final output is te sum of output produced by private inputs and output produced by public inputs 8 Profit maximization by te firm implies tat te firm adjusts private inputs until teir marginal products equal teir factor costs: 9 () 5 f (, k ) = w, and ( 6) fk ( k, ) = r +δ If te marginal product of labor is greater tan te cost of labor, an additional our of labor will add more to revenues tan to costs Tus, firms can increase profits by iring more labor As labor is increased, eac additional unit of labor becomes less productive Te marginal product of labor falls until equality in equation 5 is reestablised Similarly, if te cost of capital is greater tan te marginal product, firms will cut back on capital to raise te marginal product of capital For a given stock of private capital, te production sector s plans for output and labor are determined by te point on te firm s production function were te slope te marginal product of labor equals te ratio of te after-tax wage cost to te after-tax output price Increasing labor increases output at a decreasing rate so tat te production function is concave to te origin In oter words, te slope decreases as labor is increased Point F in Figure 2 gives te profit maximizing labor output combination for a given stock of capital Increasing public capital causes a parallel upward sift in te production function, and te firm s optimal combination of labor and output moves from F to F An increase in private capital causes te production function to twist upward

Tis causes te firm s labor and output to move from F to F Also, an increase in wage costs increases te slope of te tangency line and causes point F to move down te production function Te public sector purcases consumption and investment goods It finances its expenditures and lump-sum transfers wit tax revenues For simplicity, in te model te government s budget is balanced in eac period In tis case, te revenue constraint of te government is described by ( ) d + [( k k ) + k ] + l = t w + t rk, 7 + 1 δ were d denotes defense expenditures Tis is a compreensive revenue constraint tat aggregates federal, state, and local levels of te government 10 Finally, te goods, factor, and asset markets are assumed to clear in all periods In particular, equilibrium in te goods markets is w r Figure 2 Optimal Output Labor Combination y g(k ) F F F f(k,)+g(k ) ( 8) c + ( k+ 1 k) + δk + d + ( k+ 1 k) + δk = f (, k ) + g( k) A dynamic equilibrium occurs wen all markets clear Also, ouseolds and firms must be beaving optimally subject to teir feasibility constraints and te government s actions 11 Graping te model In tis model, te sort run is defined as te amount of time it takes to adjust te capital stock Te sort-run equilibrium can be described by equations 2, 5, and 8 and by te fact tat te capital stock is constant To study te long-run effects of fiscal policies, one needs te steadystate version of equations 2, 3, 5, 6, and 8 In a steady state, all variables are constant troug time Tus, time subscripts may be dropped In particular, tis means tat te net increments to capital are zero Te only investment is replacement investment to offset pysical depreciation Te optimality conditions can be jointly analyzed by combining Figures 1 and 2 Subtracting private investment and public spending from output gives te amount of output available for private consumption Tis is equivalent to a parallel downward sift of te production function and causes points F and I to coincide Were te two points coincide is depicted as point O in Figure 3 At point O, te (downward-sifted) production function and te indifference curve intersect at teir points of tangency wit teir respective budget lines Tus, point O determines te profit and utility maximizing aggregate consumption and labor levels Point O is optimal for individual ouseolds and firms However, it is suboptimal for te economy as a wole as long as te slope of te indifference curve does not equal te slope of te production function If firms increased labor by one unit, te additional output produced would increase utility for te ouseold sector However, te tax structure makes tis move unprofitable for 10 As a point of reference, defense expenditures averaged 184 percent of total government expenditures, transfers to te private sector were 358 percent, and gross public investment averaged around 68 percent for te period 1986 90 (See Aktar and Harris [1992] and Council of Economic Advisers [1992] Also, see footnote 15) 11 A perfect foresigt equilibrium is defined as sequences of optimal ouseold consumption, labor, and savings plans and sequences of optimal firm plans of output and inputs tat perfectly forecast te time pat of all prices and government variables Tese optimal plans also clear product and factor markets Economic Review Tird Quarter 1993 55

te firms In fact, te difference between te intercepts of te two tangency lines is a measure of te aggregate distortion from te tax system Tis distortion is termed te aggregate tax wedge Figure 3 can be augmented to sow te long and sort-run equilibrium levels of consumption and labor First, market equilibrium is given by equation 8 In steady state, tis equation reduces to Figure 3 Combining Intratemporal Optima c,y f(k,) k k ( 9) c + d + k = f, 1 gk ( ) δ δ + Also, combining ouseold and firm optimality conditions and imposing steady state yields k ( 10) MRS( c, H ) = ( 1 tw) f, 1 Since consumption in steady state is constant across time, te MRS between two adjacent consumptions only depends on te individual s impatience for early consumption: k ( 11) ρ = ( 1 ), 1 δ tr fk Since te rate of time preference is te required rate of return to compensate for te individual s impatience, te MRS in steady state equals te constant ρ Equation 11 determines te marginal product of private capital, and it also pegs te private capital labor ratio to te rate of time preference 12 Raising te tax rate on interest income reduces te after-tax marginal product of private capital below its long-run equilibrium level To restore it to its long-run level, te steady-state marginal product of capital must rise, and te capital labor ratio must, in turn, fall Te market equilibrium condition, equation 9, determines te long-run market equilibrium relationsip of consumption and labor for a given capital labor ratio and for a given level of government expenditures In te long run, equilibrium consumption is positively related to equilibrium employment Tis is graped as te line MML in Figure 4 Consumption and labor are linearly related because te capital labor ratio is fixed Wen te capital labor ratio increases, labor is more productive at all levels of employment Tis causes line MML to twist upward from its intercept As will be discussed below, canging government expenditures causes a parallel sift of line MML Figure 4 Sort- and Long-Run Equilibria c Aggregate tax wedge g(k ) (k t1 k) δk d (k t1 k ) δk OOS O MML OOL MMS 12 Tis is because of te omogeneity properties of te production function and because public capital enters separably Tus, te capital labor ratio is not affected by wage taxation and government consumption and investment See footnote 20 on ow te analysis canges wen public capital is not separable in production c* * H 56

In te sort run, te capital stock is fixed and te market equilibrium condition is given by equation 8 Te sort-run equilibrium relationsip between consumption and labor is represented by line MMS Tis line is just te parallel-sifted production function from Figure 3 Note tat as labor increases beyond *, output will increase more in te long run tan in te sort run Tis is because an increase in labor lowers te capital labor ratio in te sort run, wic as a partially offsetting effect on output In te long run, tis partial offset does not occur because capital and labor move togeter Equation 10 determines te aggregate tradeoff between private consumption and labor One can use tis equation to trace all intersections of te indifference and production functions in Figure 3 tat are compatible wit utility and profit maximization In oter words, one can trace all possible points O in Figure 3 for parallel sifts in te tangency lines for te production function and te indifference curves Given te private capital labor ratio, tese points constitute te line OOL in Figure 4 Line OOL gives all te desired steadystate combinations of consumption and labor for a given wage rate In essence, line OOL traces ow consumption and labor respond to canges in wealt, olding relative after-tax prices constant 13 For a given tax system, tere are an infinite number of similar lines associated wit different capital labor ratios (or wage rates) Te pats lying above and to te rigt of OOL are associated wit iger after-tax wages or a iger capital labor ratio For a constant capital labor ratio, a lower output tax or a lower consumption tax also causes OOL to sift up and to te rigt Tus, sifts of line OOL represent substitution effects on labor and consumption Wen capital rater tan te capital labor ratio is eld fixed, equation 10 gives te desired sort-run combinations of labor and consumption Tis is graped as OOS in Figure 4 OOS is steeper tan OOL, because as labor is reduced from * te capital labor ratio and, ence, te wage rate, rises in te sort-run Houseolds, terefore, require a larger compensation in terms of current consumption tan in te long run wen te wage rate is fixed In sum, te OO lines give desired combinations of labor and consumption, wile te MM Figure 5 Effects of a Higer Wage Tax c OOL OOS E E lines represents tecnologically feasible combinations Te intersection of te curves yields te overall equilibrium for te economy (in te sort and long run) Te effects of tax policies 14 E Wat appens wen te government raises wage taxes? A permanent increase in wage taxes is te analytical counterpart to increasing payroll taxes Wage taxes do not affect te long-run market equilibrium relationsip Tus, line MML is uncanged in Figure 5 Since te after-tax interest rate is pegged to te constant rate of time preference in te long-run, a wage tax does not alter te steady-state capital labor ratio H MMS MML 13 Wen preferences are omotetic, scaling consumption and leisure by te same scaling factor will leave te MRS uncanged Tis implies tat te MRS is constant along OOL and tat OOL is a straigt line 14 To isolate te effect of eac fiscal policy instrument, I assume tat te government uses lump-sum transfers to balance its budget wen tax rates are increased For te same reason, lump-sum taxes are used to finance increases in government expenditures Economic Review Tird Quarter 1993 57

Since te capital labor ratio does not cange, te wage rate before taxes is unaffected But since te after-tax wage rate received by ouseolds falls, ouseolds substitute away from work and consumption towards leisure Tis is equivalent to a downward sift of OOL in Figure 5 Since OOL sifts down and te intersection of OOL and MML determines te long-run effect of te wage tax on consumption and labor, te long-run equilibrium moves from E to E Tus, consumption and labor fall in te long run Because te capital labor ratio is uncanged in te long run, raising te wage tax causes te capital stock to decline proportionately to te fall in labor In turn, output will fall in te long run In te sort run, capital is fixed, and line OOS sifts to te left As ouseolds substitute away from labor, te sort-run capital labor ratio rises Tis causes te wage rate before taxes to rise Tus, te sort-run fall in te after-tax wage rate is less tan te long-run fall Te increase in te sort-run capital labor ratio also affects te market equilibrium line MMS given by equation 8 Since te capital labor ratio is uncanged in te long run, investment must fall over time to return te capital labor ratio to its original level A reduction in investment tends to offset te necessary reduction in consumption, given tat labor and output fall For any level of labor (and output), a reduction of investment means tat tere is more output available for consumption Tus, consumption increases according to equation 8, and MMS sifts upward in te sort run Assuming te effect on OOS dominates, te economy jumps from E to E, and labor and consumption fall in te sort run Wat appens wen te government raises taxes on interest income? Tis tends to reduce te after-tax interest rate received by ouseolds for any given pretax interest rate But since te aftertax interest rate is pegged in te long run, te pretax interest rate must rise To accomplis, tis te long-run capital labor ratio falls in order to increase te marginal product of capital In turn, a fall in te steady-state capital labor ratio will affect lines MML and OOL For any given level of labor, reducing te capital labor ratio means tat labor is less productive Tis reduces long-run output and consumption Tus, MML rotates down and to te rigt At te same time, te after-tax wage rate falls wit a reduction in te capital labor ratio 58 Tus, ouseolds substitute away from work and consumption Tis is equivalent to a leftward sift of OOL Figure 6 sows ow increasing te interest rate tax twists MML and OOL downward Tis causes te equilibrium to move from E to E Consumption falls in te long run Weter labor falls or rises is unclear and depends on ow muc OOL falls relative to MML Noneteless, for all reasonable parametrizations, capital and output will fall in te long run Since te capital labor ratio falls in te long run, investment will fall in te sort run Tus, MMS sifts up and te economy moves from E to E in te sort run To summarize, increasing eiter factor tax will lower labor and output in te sort run and increase te capital labor ratio But a wage tax will lower consumption in te sort run, wile an interest rate tax will raise consumption In te long run, bot taxes depress consumption and output However, tey affect labor and te capital labor ratio differently A wage tax leaves te capital labor ratio uncanged and depresses labor On te oter and, an interest rate tax lowers te capital labor ratio and as an uncertain effect on labor A brief glance at te box titled Equivalence of Permanent Tax Policies, sows ow taxes on consumption and corporations are equivalent to te factor income taxes introduced in tis article In sort, most taxes correspond to taxes on capital or labor Ostensibly, aving a personal and cor- Figure 6 Effects of a Higer Interest Rate Tax c OOL OOS E E E H MML MMS

Equivalence of Permanent Tax Policies One can easily expand te model by including ouseold consumption taxes, t c, tat comprise excise and sales taxes In tis case, equation 1 expands to (A) ( 1+ tc) c + ( k+ 1 k) = ( 1 tw) w + ( 1 t ) rk + l r Additionally, various taxes can be levied on te firm so tat after-tax profits are given by (B) ( 1+ to) y ( 1+ t) w ( 1+ tk)( r + δ) k ( k k), + 1 were t o is a tax rate on te output of te firm Also, t is a tax surcarge on firms labor costs, suc as contributions for social insurance Te term t k is te tax surcarge on te rental payments of capital and adds to (or subtracts from) te cost of capital troug alternative tax depreciation scedules, capital consumption allowances, and taxation and deductibility of dividends, debt, and capital gains In tis case, te combined ouseold and firm steady-state optimality conditions generalize to ( 1 tw)( 1 to) k (C) MRS(, c H ) = f, 1, ( 1+ tc)( 1+ t) 1+ t (D) ρ = δ o k ( 1 tr ) fk, 1 1 tk From te optimality conditions, one can sow tat te following taxes are equivalent, in te sense tat teir qualitative effects on aggregate consumption, investment, labor, and output (in te sort run and long run) are te same Te equivalence relationsips sow tat taxes on corporations imitate taxes on ouseolds by ultimately taxing labor and capital It also can be sown tat a consumption tax is equivalent to a tax on labor: 1 A tax on te wage income of ouseolds, t w, is equivalent to a surcarge on te labor costs of firms, t 2 A tax on te interest income of ouseolds, t r, is equivalent to a surcarge on te capital costs of firms, t k 3 A (simple) income tax, t y, is equivalent to taxing ouseolds wage and interest incomes at te same rate tat is, t w = t r 4 An output tax, t o, is equivalent to taxing firms wage and interest costs at te same rate tat is, t = t k 5 An output tax, t o, is equivalent to a (simple) income tax, t y 6 An output tax, t o, is equivalent to a consumption tax plus a tax on interest income tat is, t c = t r Or, a consumption tax is equivalent to a sales tax wit capital costs exempt 7 A consumption tax, t c, is equivalent to a tax on wage income, t w porate income tax implies tat tax rates on labor and capital are equal or tat a simple income tax exists Tis is misleading because of special tax considerations for capital, suc as depreciation scedules, capital gains taxes and so on In fact, tere is evidence tat tax rates on capital far exceed tax rates on labor 15 Tus, it is natural to ask wat are te effects of a reduction in interest rate taxes 15 Marginal tax rates ave been estimated by a number of autors For instance, Hansson s (1985) survey concludes tat te labor tax rate lies between 02 and 03, wile te capital tax rate is bounded above by 05 McGrattan (1991) estimates tat te labor tax rate fell in te interval between 01 and 035, and te capital tax rate ranged between 03 and 06 Economic Review Tird Quarter 1993 59

and an increase in wage taxes Suc a sceme may be considered a variant of te investmentfriendly restructuring of business taxes proposed by te presidential candidates 16 From te analysis above, one sees tat te sort-run effect is to sift OOS leftward However, te individual taxes affect sort-run investment in opposite directions Since te capital labor ratio rises in te long run, it is likely tat investment will increase in te sort run and tat te MMS will sift down However, even if te effects on investment approximately cancel, consumption and labor will fall in te sort run Line MML will sift up in te long run, because te long-run capital labor ratio rises Assuming tat te different effects on line OOL approximately cancel, consumption will increase and labor will fall Also, output will rise in te long run along wit te capital labor ratio Tis exercise is intriguing, because it is possible to get a long-run expansionary effect simply by canging te tax mix from capital to labor taxation However, te sort-run economic costs of suc policies may outweig te long-run benefits 60 16 Reducing te cost of capital can be accomplised by an investment tax credit or by reducing te capital gains tax Te cost of labor would rise if a tax for worker training were instituted, or employer ealt care costs were raised Since consumption taxes and labor taxes are equivalent, one would get te same result by increasing sales taxes 17 Tis policy exercise was analyzed by Wynne (1991) He also considers te aggregate effects of military employment policies 18 Wat if government consumption enters private utility, as in footnote 5? In tis case, te MRS is a function of composite, not private, consumption Also, public consumption enters te market equilibrium condition just like defense expenditures Tese two facts can be attaced to te grapical analysis for defense spending If government consumption falls, lines MMS and MML sift up just as tey do wit a reduction in defense spending However, lines OOS and OOL will also sift down, because private consumption must rise to offset te fall of te MRS induced by public consumption If public and private consumption are less tan perfect substitutes, ouseolds will work more to raise output and to mitigate te negative effect on private consumption In te sort and long run, private consumption will rise, wile te effect on labor is uncertain Te effects of spending policies Suppose tat defense spending falls permanently 17 Since capital tax rates do not cange, te capital-labor ratio is unaffected in te long run Tus, te long-run market equilibrium relationsip MML depends solely on te demand and supply effects of te cange Since defense spending does not enter te production function, tere is only a demand effect Tis means tat more output is left for consumption tan before te sock For all levels of equilibrium labor, consumption rises Tus, line MML sifts up in Figure 7, wile line OOL is unaffected Consequently, te long-run equilibrium moves from E to E, wit private consumption rising and labor falling Also, since te long-run capital labor ratio does not cange, capital must fall proportionately to labor Te sort-run effects are qualitatively similar; only MMS sifts up Private consumption will be crowded in and labor will fall because ouseolds feel wealtier Since te capital labor ratio remains uncanged in te long run, investment will fall Tis reinforces te positive effect on private consumption Since labor falls, output will fall, too 18 Te effects of increased public investment differ from tose of increased defense spending Because of te separability of te production function, public investment does not affect te private capital labor ratio Wile iger public investment does not affect OOL, it as two effects on MML Not only does public investment ave a demand effect, it also as a supply effect on te market equilibrium condition If te marginal product of public capital is greater tan te depreciation rate, ten te supply effect will dominate Since tis is likely, output increases relatively more tan demand does, and consumption rises for all levels of labor Tus, line MML sifts up in Figure 8 Terefore, labor, capital, and private output fall in te long run, wile consumption and total output increase Te sort-run effect of public investment does not include a supply effect Tis is because investment takes time to be productive Tus, te demand effect governs te sort-run market equilibrium relationsip For all levels of labor, iger investment means lower consumption Tus, line MMS sifts down in te sort run in Figure 8 Tis means tat at te sort-run equilibrium point E,

Figure 7 Effects of Lower Defense Spending Figure 8 Effects of Higer Public Investment c c MML OOS MML OOL OOS OOL E E E MMS E E E MMS H H labor is iger and consumption lower tan at te point of departure, E Over time, as te economy moves from E to E, consumption will rise and labor fall 19 In sum, in te sort run, more public investment tends to lower consumption and increase labor and output In te long run, public investment raises consumption and output and lowers labor A reduction of defense expenditures will, on te oter and, raise consumption and reduce labor and output in te long run and in te sort run Spending te peace dividend from reduced defense outlays on public investment is equivalent to increasing public investment and reducing defense spending by an equal amount In tis case, demand effects will cancel in te market equilibrium condition MMS Wile tere are no supply effects in te sort run, in te long run tere will be positive demand and supply effects on MML Since te supply effect dominates, MML sifts leftward by more tan if public investment were increased by itself Tus, in te sort run tere is no effect on te aggregate variables However, in te long run private consumption will rise and labor will fall Since public output rises in te long run and private output falls, te effect on total output is indeterminate 20 Finally, wat if te government reduces defense spending and legislates an investment-enancing reduction in capital taxes? Briefly, in te sort run tere are no effects on OOS Tere are offsetting 19 If public capital is not separable in production and production is constant-returns-to-scale in all inputs, ten te public capital to private labor ratio enters equations 9 troug 11 Tus, te private capital labor ratio is not pegged by te constant rate of time preference in equation 11 and will adjust wit canges of te public capital labor ratio Te government can peg te private capital labor ratio to te discount rate by varying te public capital labor ratio (using lump-sum taxes to balance its budget) It ten is free to pursue te policies discussed above wit te same aggregate effects If te government targets a iger public capital labor ratio, te marginal product of private capital rises in te long run, raising te private capital labor ratio In te sort run, public and private investment increase, causing MMS to sift down Assuming tat supply effects dominate demand effects, line MML will sift up Line OOL sifts rigtward because wages rise, wile OOS remains unaffected Tus, te grapical analysis resembles te case of increasing public investment and simultaneously reducing capital taxes 20 Wat if (separable) public capital is raised and public consumption is reduced dollar for dollar? In tis case, line OOS sifts up Since labor rises in te sort run and te capital labor ratio falls, private investment will increase Tus, MMS sifts down Terefore, labor, investment, and output rise in te sort run, wile private consumption may rise or fall Also, line MML will sift upwards because of te supply effect of public investment At te same time, line OOL will sift down wen public consumption is not separable Tus, it follows tat labor and output fall in te long run, but te effect on consumption is uncertain Economic Review Tird Quarter 1993 61

Table 1 Summary of Policy Effects Sort-Run Effects Long-Run Effects Capital Capital Con- labor Invest- Con- labor Policy sumption Labor ratio ment Output sumption Labor ratio Capital Output Higer labor tax + 0 Higer capital tax + +? Higer labor tax and lower capital tax + + + + + Lower defense spending + + + 0 Higer public investment + + + + 0 + Lower defense spending and iger public investment 0 0 0 0 0 + 0? Lower defense spending and lower capital tax????? + + +? effects on investment, so tat te effects on MMS are unclear In te long run, bot MML and OOL will sift upward, except tat te sift of MML will be magnified Since te sort-run effects depend on ow MMS sifts, consumption will move in te opposite direction of labor (and output) In te long run, consumption rises, labor falls, and te effect on output is ambiguous Conclusion In tis article, I ave developed a simple framework to analyze te effects of various fiscal policies Abstracting from distributional considerations, tis model is useful for looking at te sortrun and long-run effects of various taxation and expenditure scemes In particular, I contrast wage income taxation (or taxes on labor) wit interest income taxation (or taxes on capital), and I contrast defense spending wit government investment Te effects of te policy experiments are summarized in Table 1 Tese particular instruments are cosen because tey figured prominently in te 62 fiscal policy debate of 1992 Also, many fiscal policies can be described as a combination of tese four instruments For instance, it is sown tat most corporate taxes are equivalent to personal income taxes in teir effects on macroeconomic aggregates Tis is because corporate and personal income taxes ultimately tax te inputs to production Tis equivalence lies at te eart of economists observation tat te current tax system eavily taxes capital Te model suggests tat increases in taxes on inputs will depress output and consumption in te long run Wile labor taxes tend to lower labor and capital in te long run, capital taxes lower capital but may raise or lower labor in te long run Te model also sows tat a consumption tax is equivalent to a tax on labor Tus, a differential cange in factor taxes may ave been implicit in some of te 1992 campaign proposals for a pro-investment restructuring of business taxes Suppose tat capital taxes are lowered and labor (or consumption) taxes raised suc tat te effect is neutral on government revenues In tis case, it

is likely tat consumption, labor, and output will fall in te sort run In te long run, labor still may fall, but consumption and output will rise Tus, it is possible tat canging te tax mix will ave expansionary long-run effects on te economy and still be revenue neutral However, tese longrun benefits must be weiged against teir sortrun costs 21 On te oter and, te model proposes tat spending te peace dividend from reduced defense spending on public investment will yield long-run benefits and no sort-run costs A reduction in defense expenditures tends to increase consumption and reduce capital, labor, and output in te sort and long run By contrast, public investment will raise labor and output and lower consumption in te sort run; it will reduce labor and raise consumption and output in te long run Tus, if government investment increases and defense spending falls dollar for dollar, consumption, labor, and output are not affected in te sort run, but in te long run, consumption rises and labor and private capital fall Weter output rises depends on te output effects of sifting from private capital to public capital Te model also as implications for wen te peace dividend is used to create a more investment-friendly business tax structure by reducing tax distortions on capital In te sort run, output may rise or fall; owever, consumption and output (and labor) will move in opposite directions in te sort run In te long run, consumption and capital will rise wile labor falls Weter output rises depends on te output effects of sifting from labor to private capital Weter tis last option is preferable to increasing public investment was a principle difference between te major contending fiscal policy platforms However, it turns out tat bot options would be likely to ave very similar qualitative outcomes in te long run And tey also appear to be similar to a sift from capital to labor (or consumption) taxes in teir long-run effects Wile tese tree policies ave qualitatively similar longrun effects, teir sort-run effects are dissimilar Increasing public investment by reducing defense spending dollar-for-dollar clearly dominates a differential tax cange (from a labor tax to a capital tax) in te sort run Weter tis policy also dominates a reduction of defense spending and capital taxes depends on weter output rises or falls And since consumption will move opposite to output, te ranking of te sort-run effects of te last two policies depends on weter te public puts a iger value on movements in consumption or output Currently, te empirical testing of tese models is an active area of researc Tis researc will provide estimates of te sort-run and long-run policy effects and elp in deciding wic policies are implemented 21 Note tat increasing te progressivity of te personal income tax by increasing taxes on te ric (and maybe lowering taxes on te middle class) is a capital tax in disguise Because te sare of capital income increases wit income, taxing te ric taxes capital income (and reducing middle class taxes lowers labor taxes) Tus, increasing te progressivity of te income tax migt offset te pro-investment business tax restructuring discussed above Economic Review Tird Quarter 1993 63

References Aktar, MA, and Etan S Harris (1992), Te Supply-Side Consequences of US Fiscal Policy in te 1980s, Federal Reserve Bank of New York Quarterly Review, Spring, 1 20 Ascauer, David A (1989), Does Public Capital Crowd Out Private Capital? Journal of Monetary Economics 24 (September): 171 88 (1988), Te Equilibrium Approac to Fiscal Policy, Journal of Money, Credit and Banking 20 (February): 41 62 Barro, Robert J, and Xavier Sala-I-Martin (1992), Public Finance in Models of Economic Growt, Review of Economic Studies 59 (October): 645 61 (1989), Te Neoclassical Approac to Fiscal Policy, in Modern Business Cycle Teory, Robert J Barro, ed (Cambridge, Mass: Harvard University Press) Becsi, Zsolt (1991), Fiscal Policy in a Perfect Foresigt Model wit Heterogeneous Consumer/Workers, (PD dissertation, University of Wisconsin Madison) Council of Economic Advisers (1992), Economic Report of te President (Wasington, DC: US Government Printing Office) Hansson, Ingemar (1985), An Evaluation of te Evidence of te Impact of Taxation on Capital Formation, (Paper presented at te Forty-First Conference of te International Institute of Public Finance, Madrid, Spain, Summer) Lynde, Caterine, and James Ricmond (1992), Te Role of Public Capital in Production, Review of Economic Statistics 74 (February): 37 44 McGrattan, Ellen R (1991), Te Macroeconomic Effects of Distortionary Taxation, Institute for Empirical Macroeconomics, Discussion Paper no 37, Federal Reserve Bank of Minneapolis Wynne, Mark A (1991), Te Long-Run Effects of a Cange in Defense Purcases, Federal Reserve Bank of Dallas Economic Review, January, 1 16 64