In their classic textbook, Musgrave and Musgrave (1989)

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1 Integrating Expenditure and Tax Decisions Integrating Expenditure and Tax Decisions: Te Marginal Cost of Funds and te Marginal Benefit of Projects Abstract - Tis paper seeks to clarify te extent to wic te rule for providing public goods ougt to correct for te distortionary cost of raising funds We argue tat, in evaluating public projects, te marginal cost of funds (MCF) concept must be supplemented by a symmetrical concept, wic we label te marginal benefit of public projects, or MBP, wic indicates te value to individuals of te dollars spent Eac of tese concepts can be decomposed into two separate components, one reflecting efficiency and te oter caracterizing te distributional impact of te project itself or its financing We conclude tat efficiency of te financing cannot be ignored, tat distributional considerations are also relevant, and tat te availability and optimality of tax instruments is critical for evaluating te appropriateness of proceeding wit a public good cum financing project However, one can construct special cases, as in Kaplow (1996), were te simple cost benefit criterion applies Joel Slemrod University of Micigan, Ann Arbor, MI Slomo Yitzaki Department of Economics, Hebrew University, Jerusalem, 91905, Israel National Tax Journal Vol LIV, No 2 INTRODUCTION In teir classic textbook, Musgrave and Musgrave (1989) lament te disconnection between te expenditure and tax sides of public finance: Altoug good economic analysis calls for joint consideration of bot aspects, te practice is to deal wit tem separately (p 211) One notable exception to tis disconnection is te issue of to wat extent an analysis of public goods ougt to correct for te distortionary cost of raising te funds for te project Pigou (1947) discusses te subject, and te modern analytical treatment of te subject is well illustrated by Atkinson and Stern (1974), wo derive te tax modified Samuelson rule for public good provision and te marginal cost of funds encefort (MCF) Muc recent work as extended tis analysis, but apparent contradictions remain For example, Kaplow (1996) argues tat te decision about weter to provide a public good sould be made witout taking into account te marginal welfare cost of taxation and tat it is optimal to supply te public good wen te simple cost benefit test is satisfied Tis surprising result apparently contradicts Atkinson and Stern (1974) as well as a long line of literature using distributional weigts in evaluating public goods (eg, Harberger, 1978, 1980; Squire, 1980; Brent, 1984) 189

2 Te aim of tis paper is to generalize tis literature and, in so doing, clarify te recent contributions Te generalization includes allowing for evasion, avoidance, and administrative costs of taxation We maintain tat te concept of MCF sould continue to serve as te basic rule for evaluating te revenue side However, in evaluating public projects, te MCF concept sould be supplemented by a symmetrical concept, wic we will refer to as te Marginal Benefit from Public projects, ereafter MBP, wic indicates te value to te individuals in te community of a dollar spent on a public project Te calculations of cost benefit analysis sould compare te MBP to MCF, wit a recommendation to accept te project if te MBP is greater tan te MCF We also argue tat, in general, distributional considerations sould not be ignored To directly deal wit distributional considerations, te MCF concept is decomposed into two separate components: Marginal Efficiency Costs of public Funds (Maysar and Yitzaki, 1995, MECF ereafter) and Feldstein s (1972) Distributional Caracteristic of te tax base (DC) Similarly, for eac parameter affecting te spending on a public project, te MBP can be decomposed into a marginal efficiency benefit of funds (MEBP) and a distributional caracteristic of te public good (also DC) Te MEBP indicates te (equivalent of) monetary value (ie, te willingness to pay) to te individuals of spending an additional dollar by te government, and te DC evaluates its effect on social welfare Finally, we stress te critical importance of te assumptions made about te availability of tax instruments, and weter te tax structure is assumed to be optimal Te paper proceeds as follows We first discuss te MCF, DC, and MECF concepts for a cange in one indirect tax, and address te MBP and MEBP concepts; next, we extend te analysis to any parameter 190 NATIONAL TAX JOURNAL in te tax law To illustrate te metodology, te paper ten applies te analytical framework to te structure of a linear income tax We ten discuss optimal public good provision in te presence of a non optimal tax system Finally, we comment on recent contributions to tis literature, in particular Kaplow (1996), in te ligt of te framework presented ere, and offer some concluding comments THE MCF AND MECF CONCEPTS We first address te problem in a setting in wic avoidance, evasion and administrative costs do not exist, and were te only tax instruments are commodity taxes It is assumed tat te government evaluates its actions wit reference to a social welfare function of te following form: [1] W(V 1 (G 1,G 2,,G J,q 1,q n,y 1 ),,V H (G 1,,G J,q 1,q n,y H )), were G j is a pure public good ( j = 1,,J), q i (i = 1,,n) is te price of a private good tat te consumer faces, and y is te given lump sum income of individual ( = 1,,H) It is assumed tat te vector of producer prices (including wages), p, is given and tat t i = q i p i are te commodity tax rates (A non linear income tax will be introduced at a later stage) Government actions are constrained by te budget constraint [2]: Σ J Σ n j=1 [2] R 0 = G R = P j G j t i X i, i=1 were G is total expenditures in te budget and R is total revenue Te per unit price of producing G j is P j We use X i = Σ x i to denote te aggregate quantity (or expenditures in te case of ad valorem taxes) of commodity i, and x i is te quantity of te private good i consumed by individual

3 Integrating Expenditure and Tax Decisions In wat follows we do not assume tat te government is at all times maximizing te social welfare function Instead, we presume only tat tere exists a particular tax system tat satisfies te budget constraint, and tat te government is considering increasing tax revenue by $1 in order to finance an increase in te supply of a public good Te issue at and is weter te government, wic is interested in increasing social welfare, sould proceed We first consider weter it is social welfare increasing to increase te production of G j by one dollar and to finance it troug an increase in t i To evaluate weter tis package of expanded public goods wit a specified financing sceme is wort proceeding wit, one as to compare te increase in social welfare from increasing te supply of te public good to te reduction in te social welfare due to te increase in taxes Equation [3] presents te comparison: [3] Σ H =1 W V V G j (?<)0 dg j (P j R)dG G j j Σ H =1 W V R ti V t i dt i dt i Equation [3] is derived from rearranging te derivatives of te social welfare function [1] and te revenue constraint [2] wit respect to bot G j and t i Te numerators in bot terms of [3] are, respectively, te direct effect of increasing G j and te direct effect of increasing t i, on social welfare Te denominators represent te impact of increasing G j and te impact of increasing t i on te budget constraint of te government, respectively Since te budget constraint is given, te denominators are equal to eac oter Te first term on + te left and side is te increase in social welfare per (net) dollar spent by te government on G j Te second term represents te decrease in social welfare per dollar increase in revenue collected troug an increase in t i Terefore, te project increases social welfare, and is wort pursuing if [3] is positive In oter words, te first term of equation [3] evaluates, on te margin, te benefit to te society of increasing te production of te public good per dollar of net expenditure by te government Te second term evaluates te cost to te society, at te margin, of increasing te tax rate on commodity i suc tat te net revenue received by te government increases by one dollar Tis project sould proceed if te first term, wic we will refer to as te Marginal Benefit from Public Goods (MBP), is greater tan te cost to te society of raising te funds necessary to finance te project, ereafter te Marginal Cost of Funds, or MCF We next consider more closely te MCF, a concept tat as been discussed extensively in te literature 1 Wit producer prices given, and denoting te social evaluation of te marginal utility of income as β = ( W/ V ) ( V / y ), ten using Roy s identity one can rewrite te rigt and side of equation [3] as: X i Σ [4] MCF i = MR β s i i were s i = x i /X i is te sare of individual in te consumption of commodity i and MR i is te marginal revenue wit respect to t i Formally, we can write: n [5] MR i = R X X i + t k t i Σ k k=1 t i 1 Te derivation of te MCF, and te MECF discussed later, is based on Slemrod and Yitzaki (1996), wo rely on Maysar (1990), Wildasin (1984), and Maysar and Yitzaki (1995) 191

4 NATIONAL TAX JOURNAL Te rigt and side of [4] can be decomposed into two terms Te first term is defined as: [6] DC i = Σ β s i, wic is Feldstein s (1972) Distributional Caracteristic of a commodity, and is a weigted average of te social evaluation of te marginal utility of income, weigted by te sare of eac individual in te burden of raising te tax revenue It describes te incidence of a dollar burden of taxes, raised troug te cange in t i Te iger is DC i, te less progressive is te cange in te tax on commodity i Te second term on te rigt and side is caracterized in Maysar and Yitzaki (1995) as te Marginal Efficiency Costs of Funds, or MECF, were: [7] MECF i = An extended interpretation of te MECF is given in Slemrod and Yitzaki (1996) Briefly, te MECF measures te ratio of te cost to taxpayers of funds raised to te value of te funds received by te government, ignoring distributional issues Te difference in value between te numerator and denominator is caused by leakages (as in Okun s (1975) leaky bucket ) from te tax base caused by taxpayers tat are maximizing utility in te presence of taxation Te direct burden on taxpayers of increasing t i is X i At te oter end of te transfer, te government receives only MR i, and te MECF i is te ratio of te burden on te individuals to te dollar amount collected by te government If t i is a lump sum levy, and all oter tax rates are equal to zero, ten te MECF equals one But in general, as pointed out X i X i MR = i X Xi + Σ n t k k k=1 t i in Maysar (1990), wen te starting point is an arbitrary tax system, ten te MECF of a lump-sum levy can be lower or iger tan one 2 As discussed in Slemrod and Yitzaki (1996), one needs only to be able to forecast te revenue generated from a cange in eac tax rate to calculate te MECF Combining equations [4], [5] and [6] we ave sown tat te rigt and side of [3] can be restated as [8] MCF i = DC i MECF i Te first term reflects te distributional impact of raising funds via an increase in t i, wile te second reflects te efficiency costs of raising te funds Altoug a value of one for te MECF as a natural interpretation, tis is not true for te MCF unless β is someow normalized For example, Atkinson and Stiglitz (1980) normalize by setting te unweigted mean value of β to one Anoter possibility is to set sup (β ) to one, wic implies tat 1 β > 0, wit β being one for te poorest person Te type of normalization used affects te value of te MCF, but does not affect te decision of weter to approve a public project Slemrod and Yitzaki (1996) define te MECF in a more complicated setting tat includes avoidance activity, evasion and administrative costs Tis same setting can be repeated ere However, instead of redeveloping it ere we will only explain te logic and te interested reader is referred to te above mentioned paper In te more general setting, te numerator of equation [7] is te additional tax tat would ave been collected if tere were no beavioral response on bealf of te taxpayer Tis tax represents te additional burden on te taxpayer imposed by te canges in te parameters in te tax system Te denominator is te additional tax collected by te government, taking 2 A negative value of te MECF indicates tat te tax system is on te declining portion of te Laffer curve 192

5 Integrating Expenditure and Tax Decisions into account te beavioral response Te ratio of te two is te additional burden per additional dollar collected Te ratio of te tax tat would ave been collected to te actual additional tax collected is te MECF To derive tis interpretation, note tat te difference between te numerator and te denominator is te result of te substitution effect Assuming tat te taxpayer is at an interior solution and tat te cange in te tax rate is small, it is easy to see tat, on te margin, a taxpayer will be ready to sacrifice a dollar value of utility to save a dollar of taxes Hence, te numerator represents te burden on te taxpayer (wic is composed of additional tax collected plus taxes avoided by substitution) wile te denominator represents additional tax collected Extending tis logic to include evasion and avoidance opportunities as well as administrative costs leads to te following expression: γ (X [7 ] MECF i = i MR i ) + C i + MR i, MR i A i were γ is te social evaluation of te dollars tat te taxpayer is sacrificing at te margin in order to save a dollar of tax, 3 C i is te marginal compliance cost associated wit te cange in te it instrument, A i is te marginal administrative costs, and MR i A i is te net revenue collected at te margin Te intuitive interpretation of te expression is te same as before, wit some qualifications Te potential tax is X i, (X i MR i ) is leaked at a social cost of γ per dollar, MR i is collected by te government, and C i is te additional involuntary compliance cost Hence, te total burden on society is te sum of tose (X and C) components Of te MR i collected by te government, A i is spent on administration, leaving MR i A i in te coffers MECF is te burden on society divided by wat is collected net of te cost of doing business Tis yields te marginal efficiency cost of a dollar collected Te extension of te analysis into canging several tax rates is also straigtforward Te MECF of a cange in several tax rates is te weigted average of te MECF of individual tax rates weigted by teir sare in te revenue raised 4 THE MBP AND MEBP CONCEPTS We turn next to te first term on te left and side of [3], wic pertains to te value to te society of a (net) dollar spent by te government on a public good We sow tat a decomposition similar to te one applied earlier to te MCF is useful in interpreting te decision to invest in a public good Let b j = V / Gj V be te willingness to pay of individual for public y good G j, expressed in terms of lump sum income 5 Following te same procedure used for te derivation of te MCF, we can rewrite te left and side of equation [3] as: [9] MBP j = DC j MEBP j, were [10] MEBP j = B j /(P j Σ i t i ( X i / G j )) In expression [9], DC j = Σ β s, j s = j b / j B j, and B j =Σ b In words, B is te aggregate benefits (willingness to pay) to te j j society from increasing te public good G j by one dollar, and s is te sare of individual in te aggregate benefits Te j MEBP is te ratio of te (equivalent of) monetary benefits to te individuals to te 3 Te value of a dollar saved can be less tan a dollar if te taxpayer is at a corner solution As an example of being in a corner solution, consider te case of a taxpayer wo evades all is income 4 For a derivation of tis result, see Slemrod and Yitzaki (1996) 5 If free disposal exists, ten te relevant willingness to pay is Max [0, b j ] If free disposal is not allowed ten b j may be negative, and it will represent te willingness to pay to get rid of G j 193

6 NATIONAL TAX JOURNAL dollars spent by te government Te distributional caracteristic DC j describes te distribution of te benefits among te population For a given sum of willingness to pay, te larger te effect on tose wit iger social marginal utility of income, te iger te DC of te public good Tis is because te iger te marginal utility of te individual, te iger will be te distributional caracteristic parameter for a given sum of b Note tat j te MEBP is formally similar to te MECF, because bot refer to te ratio of direct costs or benefits to individuals to te (net) cost to te government If te public good as no effect on tax revenue, ten MBP j = DC j (B j ) Tis implies tat te MEBP of a public good depends bot on its revenue effect and on te intrinsic value of te public good, and suggests tat te MEBP j can be furter decomposed as: [11] MEBP j = (B j )(1/(1 Σ i (t i ) ( X i / G j )) (B j )MRCP j Te (B j ) term measures te ratio between te value to te individuals of te public good and te cost to te government Te MRCP j (te Marginal Revenue Cost of Public projects) term measures te cost (or benefit) of a public good due to its effect on tax revenues Using te decompositions of MCF and MBP, we can now rewrite [3] as follows, implying tat a public project is wort doing if: [3 ] DC j (B j ) (MRCP j ) > DC i MECF i It is instructive to note te formal similarity between te MBP and te MCF, te only difference being tat in te former te willingness to pay substitutes for te quantity consumed Imposing a tax (subsidy) is similar to reducing (increasing) te production of a public good: in bot cases te government affects all individuals troug a cange in a price or in a quantity Te cange in te public good canges te welfare of te individuals by teir willingness to pay, witout affecting te prices te individuals face, wile te cange in te tax affects te prices Roy s identity, wic connects te willingness to pay wit te marginal utility of income, is responsible for te similarity 6 Te extension of te analysis to canging te provision of several public goods simultaneously is similar to te extension on te tax side to multiple tax instruments OTHER TAX INSTRUMENTS So far we ave considered a tax system wic as only commodity taxes as tax instruments However, it is important to note tat te analytical structure involving te MCF and MBP is quite general, and can be applied to any parameter tat affects te tax system It can be extended, for example, to parameters of te tax enforcement system, suc as te fraction of tax returns tat are audited It can address a uniform lump sum tax or a differential lump sum tax It can deal wit complicated tax structures suc as tose tat caracterize te income tax, including suc features as allowances, exemptions, and income brackets Eac parameter is 6 Note tat, because te social welfare function affects only te distributional caracteristic, te MECF and te MEBP are still useful for a government wit an objective oter tan maximizing social welfare For example, if te government is a maximizer of votes (Hettic and Winer, 1997,1999, c 6), so tat te target function is P(U 1 (),U H ()) is te probability of voting for te government as a function of te utility level of te individuals, ten all we ave to do to adapt our concepts is to substitute voting caracteristic for distributional caracteristic wic will be a weigted average of te government evaluation of te cange in probability to vote for te government of te t individual weigted by te burden imposed on im Tat is, instead of β = ( W/ V ) ( V / y), one can use β * = ( P/ U ) ( U / y) in te definition of te DC of te commodity 194

7 Integrating Expenditure and Tax Decisions treated in a similar way as any commodity tax in te earlier model To see te generality of te approac, consider any tax instrument, z In order to evaluate its MCF, one as to know its direct impact on social welfare, plus its impact on tax revenue Te MCF is simply te ratio of te former to te latter In expression [4] and tereafter, X refers no longer to te amount of good X consumed, but rater to te tax base to wic instrument z applies It reveals te amount of revenue tat would be collected from a cange in z, absent any beavioral response Te effect on te social welfare function can be furter decomposed into te distributional caracteristic and te Marginal Efficiency Cost of Funds components Tis procedure is relevant to every parameter z, be it a marginal tax rate, an income bracket or any oter parameter For example, it can be sown tat in te context of an income tax, expression [7] reduces to 1/(1 e), were e (defined to be a positive number) is te elasticity of taxable income Tis concept is discussed in Feldstein (1997) and Slemrod (1998) Te introduction of a general non linear income tax can be interpreted in te case of a continuous distribution of endowments as introducing an infinite number of tax parameters, or, in te case of a discrete distribution of endowments, as introducing a number of parameters at least as large as te number of individuals, wit eac marginal tax rate being a separate tax parameter Te DC of eac marginal tax rate is calculated as if it was a lump sum tax on all incomes iger tan te income on wic te marginal tax rate is effective Te MECF is determined by te cange in tax revenue of all taxpayers wit income equal to or iger tan te one on wic te marginal tax rate is imposed A final, important, example arises if te government is able to carge eac individual according to is willingness to pay 195 for te public good In tis case, DC j = DC i In tis case one can ignore distributional issues because te project (and its financing) is distributionally neutral If, in addition, MECF equals one, ten according to [3 ], te project sould be done as long as MEPB j exceeds one Tis corresponds to Lindal s solution to te public good provision problem We return to tis example later in our discussion of Kaplow (1996) Before moving on, we pause ere to make an important observation At te margin, weter or not to proceed wit a given public good project depends on te financing sceme tat accompanies it It may be sensible to proceed wit a given project under one financing sceme, but not wit anoter OPTIMAL TAX SYSTEMS AND OPTIMAL PUBLIC GOOD PROVISION To tis point we ave not assumed tat, wen considering weter to undertake a public good cum financing package, te existing tax system is in any sense optimal We now turn to consider ow tis would cange our analysis An optimal tax system is tat structure wic maximizes [1], subject to [2], over te set of available tax instruments, olding te vector of public goods fixed For some instruments, suc as commodity taxes, tere is no constraint on te value of te tax rate: a negative tax is simply a subsidy In oter cases, suc as te amount of resources devoted to auditing, a negative setting is not feasible, so tere is a non negativity constraint It is straigtforward to sow tat in te optimal tax structure all tax instruments tat are utilized ave an equal value of MCF i = DC i MECF i To illustrate te implications of tis, we consider te problem analyzed by Wilson (1991) and Sandmo (1998), in wic te government as only two tax instruments: a uniform lump sum tax (or demogrant), and a

8 NATIONAL TAX JOURNAL single marginal income tax Assume tat te linear income tax can be caracterized as: [12] T = a + t w L, wit w being te wage rate and L is ours worked Assume tat tere is a zero revenue requirement Ten, te linear tax may ave two possible structures: (a > 0 and t < 0) were te tax is composed of a lump sum tax and a subsidy for labor income, or (a < 0 and t > 0), tat is, a lump sum subsidy and a positive tax rate We will consider only te second structure because, as sown later, te first can never be optimal Let DC a be te distributional caracteristic of te lump sum tax 7 Ten: [13] DC a = (1/H)Σ β and [14] DC t = Σ s β, were s =(w L ) / (Σ w L ) is te sare of individual in labor income and (1/H) is effectively te sare of eac individual in an equal per capita ead tax Te MECFs are: 1 [15] MECF a =, 1 + t Σ n L w a and [16] MECF t = We first sow tat, provided tat te social evaluation of te marginal utility of income declines wit labor income, ten: =1 Σw L L Σ w L + t Σ t [17] DC a DC t = Σ β (1/H s ) > 0 To see tat expression [17] is positive, arrange te population in declining order of β (By assumption, tis will also be in increasing order of labor income) Since s increases wit, it must be tat te term in brackets decreases wit Since, by definition, Σ (1/H s ) is zero, it must be tat te term in te brackets is positive for small, and negative for large Since β is positive and declines wit, it follows tat DC a DC t > 0, and so DC a > DC t If tese two instruments are used optimally, ten DC a MECF a = DC t MECF t, so tat MECF t > MECF a If, on average, leisure is a normal good (ie, Σ w ( L / a) > 0), ten MECF a 1; tus, MECF a differs from one (only) because of income effects Note tat, wen te tax system is optimal, te coice of weter at te margin to proceed wit a public good project does not depend on any assumed financing sceme, because witin te set of feasible taxes all scemes ave te same MCF 8 In tis case one can speak of te marginal cost of funds tat can be used as a bencmark for any prospective public good project Altoug different alternative financing scemes will in general ave different values of MECF, eac tax instrument used will ave an offsetting value of te DC Te less efficient instruments used, ie, tose wit a ig value of te MECF, will necessarily also ave a low value of te DC tey will raise revenue from individuals wit relatively low social marginal valuations 9 Mirrlees (1971) optimal non linear income tax problem is anoter example of optimization As mentioned above, one can view Mirrlees income tax problem as aving an infinite number of instruments 7 Note tat DC a and MECF a refer to te distributional caracteristic and cost of funds of raising revenue via increasing a 8 Tis is in sarp contrast to te rule tat applies wen te tax system is not optimal, wen project approval sould depend on wat financing package accompanies te project 9 Condition [17] can be used to sow tat te case (a > 0, t < 0) cannot be optimal 196

9 Integrating Expenditure and Tax Decisions If te income tax is set to be optimal, ten te MCF of eac of te infinite number of tax parameters must be equal Te solution to tis problem is complicated, inter alia, because of te simultaneous impact of tose marginal tax rates on te MECF of eac oter In parallel to considering an optimal tax system, one can consider te case in wic te set of public goods is optimized, for a given amount of funds tat may or may not ave been raised optimally If no projects are lumpy, ten it is straigtforward to sow tat at te optimum all projects undertaken will ave te same value of MBP = DC(B/P)(MRCP) Tose projects tat fail to meet tis common value are not undertaken Altoug tere is one common value of te MBP, any marginal project is more likely to be accepted te better is te financing package tat accompanies it, were better means a lower value of te MCF If te set and quantity of bot public goods and tax instruments can be cosen optimally, ten all tax instruments used will ave te same value of MCF = DC MECF, and all te public goods provided will ave te same value of MBP = DC(B/P)MRCP Furtermore, te common value of te MCF will equal te common value of te MBP OPTIMAL PUBLIC GOOD PROVISION IN THE PRESENCE OF A NON OPTIMAL TAX SYSTEM Assuming tat taxes are set optimally is convenient, because it allows us to assume tat te MCFs are equal It is, toug, implausible tat tese conditions are met in practice On te oter and, wen te starting point is non optimal, eac tax parameter in te system may be associated wit a different MCF Tis implies tat associating a project wit one set of taxes may suggest tat it be rejected, wile associating it wit anoter set of taxes may suggest tat it be accepted In 197 tis situation understanding wy te existing tax system is not optimal becomes important In wat follows we consider tree types of explanations: (a) Tere as been a cange in te parameters of te problem since te last time te tax/public expenditure system was reformed, (b) Tere are oter (eg, political) constraints tat ave not been addressed in te model, and (c) Tere exist non convexities or discontinuities in te administrative cost function If a cange in parameters is te culprit, te first best response is to reform te tax system in order to return it to an optimal setting A relatively low MCF does not justify accepting a project, nor does a relatively ig MCF justify not accepting it If te culprit is outside te model constraints, te MCFs redefined to include te sadow prices for tese constraints would again all be equal Because te sadow prices may affect different MCFs differently, te MCFs calculated ignoring tese extra model constraints may differ For example, assume tat te MCF of eliminating te mortgage interest deduction is relatively low, but te (unmeasured) political cost of eliminating it is substantial Ten, applying te MCF of tis impossible to implement tax instrument could justify many projects tat could not be justified if coupled wit oter, feasible, tax instruments How sould a policy maker proceed in tis case? Assuming tat it is certainly feasible to raise additional taxes by proportionally raising all existing tax rates, one can use an average of tese MCFs, weigted by teir marginal tax revenue, as a rule of tumb for te MCF for project evaluation Finally, consider te point empasized in Slemrod and Yitzaki (1996), tat administrative costs tend to be discontinuous and non convex For example, introducing a value added tax will entail a large fixed cost, as a process of reporting and monitoring te tax base of eac firm must be establised Having tis infra-

10 NATIONAL TAX JOURNAL structure in place lowers te MECF of furter VAT revenue and may also affect te MECF of oter tax instruments, eg, by providing information tat is relevant for income tax enforcement Altoug te marginal cost of raising te first dollar from a VAT may appear proibitively ig, te marginal cost of raising funds from an existing VAT may be quite low Now consider a country tat does not currently ave a VAT, but for wic at a sligtly iger level of revenue requirement it would make sense to adopt a VAT to raise a substantial fraction of its revenues For deciding weter to proceed wit a public project funded by VAT, it is not appropriate to use te literal marginal cost of raising funds, but instead one sould consider te cost of non discrete canges in te tax system Tese tree explanations for unequal MCFs ave different policy implications To see tis, let us ignore distributional issues and assume a representative consumer economy, so tat we can state te issue in terms of te MECF instead of te MCF Consider te example were te MECF of a specific funding alternative is less tan one Tis implies tat a public project may be adopted even if te marginal benefit of te project is equal to or lower tan one or, loosely speaking, its return is negative; tis is because a ceap way of raising public funds as been identified Under a reformed, optimal, tax system te MECF of tis and any oter funding metod must be greater tan one 10 Tus, te rigt solution is to reform te system and not to adopt te MEBP< = 1 project If, on te oter and, tere are adminstrative cost non convexities, ten it may be appropriate to adopt tis project because te tax system is in a neigborood of a (locally) low marginal cost of raising funds Finally, if tere are un modeled constraints, ten a weigted average MECF of certainly feasible tax instruments may be an appropriate bencmark for evaluating projects RELATIONSHIP TO RECENT LITERATURE Sandmo (1998) addresses similar issues, and reaces conclusions wic are compatible wit tose stated ere However, our approac is more general tan Sandmo s on a number of dimensions First, we allow a general social welfare function, wile Sandmo treats only a utilitarian social objective function Second, our metodology allows for a wider range of beavioral response, including for example avoidance and evasion, and a wider set of instruments Finally, we stress te parallel nature of te optimal taxation and optimal public good provision problems Sandmo, on te oter and, does not restrict te analysis to te margin Ng (2000, p 259) informally makes a similar point to ours in is reconciliation of Feldstein (1997) and Kaplow (1996) He argues tat one must consider te incentive effects of bot te public spending and te accompanying tax, and te net distributional effect of te package He does not, owever, develop an analytical framework for assessing weter to undertake a package of public spending and funding Our analysis is completely consistent wit te tone of Kaplow (1996), but it is inconsistent wit its central conclusion Te tone of Kaplow s paper is well captured by te following statement: Knowledge tat te aggregate reform te public good and te tax adjustment, taken togeter causes distortion tus provides little guidance, because te existence of 10 Tis will obtain in te absence of te kind of non-convexities discussed above As demonstrated in Yitzaki (1979), in tis case te MECF must always be above one 198

11 Integrating Expenditure and Tax Decisions distortion is associated wit greater redistribution (p 520) Tis is completely consistent wit te analysis presented ere In terms of expression [3 ], knowing te terms tat ave to do wit revenue leakage and terefore efficiency, MECF and MRCP, is not sufficient for deciding weter to proceed wit a public good; DC j and DC i, te distributional caracteristics of te public good and te assumed financing, also enter into te decision It does not follow, toug, tat for any given financing mecanism, expression [3 ] reduces to (B j ) > 1, wic is wat is implied by Kaplow s statement tat it is optimal to supply te public good wen te simple cost benefit test is satisfied Yes, in general tere is a tendency for more progressive tax scemes (tose wit a low value of DC i ) to be more distorting (ave a ig value of MECF i ), and similarly for public goods But, outside of an optimum, tere is no necessary link between te distrbutional caracteristic of a tax or public good and te revenue leakage associated wit it Indeed, one can easily imagine tax scemes wic are bot regressive and inefficient, suc as an easily evaded tax on a commodity consumed disproportionately by te poor Moreover, one can imagine two tax scemes tat ave identical distributional caracteristics but are not equally efficient It migt certainly be appropriate to reject a public good wit a value of (B j ) tat exceeds one tat ad to be financed by an inefficient tax, but to accept it if it is financed by an efficient tax If one is willing to assume tat te initial tax system and te financing package are optimal, ten it is correct tat te MECF is irrelevant In tis case at te optimum DC MECF is equal for all financing scemes, so te more distorting instruments are necessarily tose tat cause a more progressive distribution of te burden Tax instruments, suc as tose in te example above, wic are relatively distorting and not progressive, will not be part of te optimal tax structure CONCLUSION In determining weter particular new public projects or canges in te tax system are appropriate, neiter te distributional impact of te proposals nor te beavioral response to tem sould be ignored Tis implies tat te primitives of te problem, te concavity of te social welfare function, and te magnitude of te beavioral response all affect te evaluation of proposals for financing new public goods Tere may, toug, be special cases were simpler rules may apply For example, if te distributional caracteristic of te public good is identical to te distributional caracteristic of te tax instrument ten one can use te simple cost benefit rule Our analysis as focused on marginal increases in public spending Altoug marginal evaluations ave te advantage of reducing information requirements, one migt question te applicability of marginal approximations to discrete projects In tis paper, te reliance on marginal derivation is necessary to allow for te evaluation of tree issues: te willingness to pay, te burden of te cange in te tax, and te distributional caracteristics of te tax and te public project Our approac is appropriate wenever a first order approximation does not introduce a large error into te evaluation of te appropriate term Willig (1976) provides some rules of tumbs for te first two approximations to be reasonable Te tird one, concerning te distributional caracteristic of te project, requires tat te social evaluation of te marginal utility of income is not significantly affected by te project Furter researc, along te lines suggested by Willig, migt clarify under wat conditions tis is an appropriate approximation for discrete projects 199

12 NATIONAL TAX JOURNAL Acknowledgments We would like to tank Louis Kaplow, Stanley Winer, te Editor, and two anonymous referees for perceptive comments on earlier drafts REFERENCES Atkinson, Antony, and Nicolas Stern Pigou, Taxation, and Public Goods Review of Economic Studies 4 No 1 (January, 1974): Atkinson, Antony B, and Josep E Stiglitz Lectures on Public Economics New York: McGraw Hill Book Co, 1980 Brent, R J Use of Distributional Weigts in Cost Benefit Analysis: A Survey of Scools Public Finance Quarterly 12 No 2 (April, 1984): Feldstein, Martin S Distributional Equity and te Optimal Structure of Public Prices American Economic Review 62 No 1 (Marc, 1972): 32 6 Feldstein, Martin S How Big Sould Government Be? National Tax Journal 50 No 2 (June, 1997): Harberger, Arnold C On te Use of Distributional Weigts in Social Cost Benefit Analysis Journal of Political Economy 86 No 2 (April, 1978): S87 S120 Harberger, Arnold C Reply to Layard and Squire Journal of Political Economy 88 No 5 (October, 1980): Hettic, Walter, and Stanley L Winer Te Political Economy of Taxation In Perspectives on Public Coice, edited by Dennis C Mueller, Cambridge: Cambridge University Press, 1997 Hettic, Walter, and Stanley L Winer Democratic Coice and Taxation New York: Cambridge University Press, 1999 Kaplow, Louis Te Optimal Supply of Public Goods and te Distortionary Cost of Taxation National Tax Journal 48 No 4 (December, 1996): Maysar, Joram On Measures of Excess Burden and teir Applications Journal of Public Economics 43 No 3 (December, 1990): Maysar, Joram, and Slomo Yitzaki Dalton Improving Tax Reform American Economic Review 85 No 4 (September, 1995): Mirrlees, James An Exploration in te Teory of Optimum Income Taxation Review of Economic Studies 38 No 2 (April, 1971): Musgrave, Ricard A, and Peggy B Musgrave Public Finance in Teory and Practice 5 t ed New York: McGraw Hill Book Company, 1989 Ng, Yew Kwang Te Optimal Size of Public Spending and te Distortionary Cost of Taxation National Tax Journal 53 No 2 (June, 2000): Okun, Artur M Equity and Efficiency: Te Big Trade off Wasington, DC: Brookings Institution, 1975 Pigou, A C A Study in Public Finance London: MacMillan, 1947 Sandmo, Agnar Redistribution and te Marginal Cost of Public Funds Journal of Public Economics 70 No 3 (December, 1998): Slemrod, Joel Metodological Issues in Measuring and Interpreting Taxable Income Elasticities National Tax Journal 49 No 4 (December, 1998): Slemrod, Joel, and Slomo Yitzaki Te Social Cost of Taxation and te Marginal Cost of Funds International Monetary Fund Staff Papers 43 No 1 (Marc, 1996): Squire, Lyn On te Use of Distributional Weigts in Social Cost Benefit Analysis Journal of Political Economy 88 No 5 (October, 1980): Wildasin, David E On Public Good Provision wit Distortionary Taxation Economic Inquiry 22 No 2 (April, 1984):

13 Integrating Expenditure and Tax Decisions Willig, Robert D Consumer s Surplus Witout Apology American Economic Review 66 No 4 (September, 1976): Wilson, Jon D Optimal Public Good Provision wit Limited Lump Sum Taxation American Economic Review 81 No 1 (Marc, 1991): Yitzaki, Slomo A Note on Optimum Taxation and Administrative Costs American Economic Review 69 No 3 (June, 1979):

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