Trade Reform with a Government Budget Constraint

Transcription

1 Trade Reform with a Government Budget Constraint James E. Anderson Boston College and NBER 11/1/96 Preared for the International Economic Association conference on Trade Policy and the Pacific Rim, Sydney, July Forthcoming in International Trade Policy and the Pacific Rim, J. Piggott and A. Woodland, eds., London: Macmillan for the IEA, Abstract: The standard theory of trade reform uses a assive government budget constraint, in which changes in tariff revenue are offset by changes in lum sum transfers. This aer offers a general framework for the analysis of trade reform when the government budget constraint is active, meaning that tariff revenue cuts must be offset by distortionary fiscal olicy changes --- ublic good suly cuts or alternative tax increases. Useful and simle new exressions characterizing welfare imroving trade reform comare the Marginal Cost of Funds (MCF) of trade taxes with the MCF of consumtion taxes. The MCF exressions rovide an intuitive index number which is oerational with Comutable General Equilibrium models. The theoretical analysis and an alication to Korean data in 1963 both cast doubt on the desirability of tariff cuts in convex cometitive economies with active government budget constraints.

2 1. Introduction Practical trade olicy advice must usually recognize that trade taxes hel raise government revenue required for other fiscal uroses. In contrast, the theory of trade olicy analysis tyically uses the simlifying assumtion that tariff revenue is assively redistributed, so a fall in revenue is offset by a fall in the lum sum transfer from the government to the rivate sector. The assive transfer assumtion was erhas an aroriate simlification in OECD economies in the era of raid growth, but it is clearly inaroriate to the resent concern over ublic debt along with resistance to tax increases or ublic good cuts. 1 The assive transfer assumtion was never aroriate for develoing nations which are tyically deendent on tariff revenue. The standard case against taxing trade is based on the assive budget constraint. This aer shows that cuts in trade taxes may well be inefficient in the standard convex cometitive model with an active government budget constraint, along which changes in distortionary fiscal instruments must be made. Thus trade reform is robably better argued from the benefits of the international division of labor, the stimulation of cometition, and the reduction of rent seeking behavior. The analysis offers simle and useful sufficient conditions under which trade reform matched by revenue neutral sending cuts or tax increases will raise welfare. The elements of the analysis differ fundamentally from those of a assive budget constraint, in ways not reviously areciated in the trade literature or in the related ublic finance literature. The key concet is the (comensated) Marginal Cost of Funds or MCF of a given class of taxes. The MCF is comared to the marginal benefit of the funds in terms of goods and services so financed, or in terms of the marginal benefit of reductions in other taxes, equal to their MCF. 1 For examle, the current US government budget rocess requires that revenue cuts be matched by sending cuts or other revenue increases. This requirement temorarily threatened the NAFTA obligations.

3 November 1, 1996 Trade reform with a government budget constraint 2 The analysis also oints to oerationality, as the MCF is a very useful summary index number of the roerties of tariff and tax systems. As a demonstration, the aer concludes with calculations of the MCF for tariffs and for consumtion taxes from a CGE model of Korea in With more exerience on reasonable values of MCF for tariffs and for domestic taxation from simulations of other Comutable General Equilibrium (CGE) models, it may be ossible to make trade reform recommendations with confidence, and erhas even extraolate to countries where no CGE model is available. The theoretical analysis and its alication in this aer both cast doubt on the general desirability of tariff cuts matched with consumtion tax rises within the class of convex cometitive models. The theoretical conditions which guarantee welfare imrovement are imlausibly stringent, and the simulation results show that even with higher initial tariffs than indirect taxes, welfare falls with a cut in tariffs combined with a revenue neutral rise in consumtion taxes. The analysis ties the theory of rotection together with the theory of ublic finance. The two literatures have develoed somewhat searate terminologies, and integration based on a dual aroach roves useful. The standard theory of rotection assumes that a benevolent welfare maximizing government seeks a welfare imroving tariff reform subject to unsecified constraints which make imossible the move all the way to free trade (Bertrand and Vanek, 1972, Bruno, 1972, Lloyd, 1974, Hatta, 1977). The government budget constraint is assive, as the fall in distortionary tax revenue is offset in the budget by a fall in the lum sum transfer from the government to the rivate sector. The theory of ublic finance in contrast uses the active budget constraint in which the rovision of goods and services by the government sector (hereafter termed ublic goods for convenience) 2 is aid for by distortionary taxation. In the marginal analysis of this roblem, the MCF lays a key role. The MCF is usually develoed in an uncomensated (real income variable) form, often in the context of a rather 2 There is no difference between ublic goods and government rovided goods in a reresentative consumer economy.

4 November 1, 1996 Trade reform with a government budget constraint 3 oaque rimal analysis. In contrast, the comensated version develoed here with dual methods is necessary for a clean analysis of the MCF of trade taxes vs. the MCF of consumtion or other taxes. 3 The only systematic treatment of the gradual reform of tariffs in the resence of an active government budget constraint is in two aers by Abe (1992, 1995). 4 This aer generalizes and simlifies Abe s results, considers some additional structures and cleans u his (1992) treatment of marginal changes in ublic goods suly. Related work by Diewert, Turunen-Red and Woodland (1989, 1991) analyzes sufficient conditions for tariff reform to imrove roductivity and Pareto efficiency. Commodity tax changes relace transfers as a means of comensating households, but since all goods can be taxed, lum sum transfers in effect are back in their model. This aer uses a limited set of commodity tax changes, working in the second-best tradition of the gradual reform and ublic finance literatures. Significantly, the two most famous results in second-best ublic finance are extended here to the gradual reform context. The Ramsey (1927) inverse elasticity otimal tax rincile is to tax every taxable good in inverse roortion to its elasticity of demand. This suggests trade should be taxed. The Diamond and Mirrlees (1971) otimal commodity tax rincile is to reserve roductive efficiency. This imlies that a small (rice-taking) country should not discriminate between foreign and domestic suly of identical roducts. 5 The gradual reform extension of the Ramsey rincile is the wider base intuition that it is efficient to at least begin taxing differentiated trade a bit. The gradual reform extension of the Diamond and Mirrlees rincile (that it ays to cut trade taxes and raise consumtion taxes) alies only under quite stringent conditions which restrict substitution. 3 Anderson and Martin (1995) argue that the comensated version of the MCF is a much cleaner concet and avoids the otential errors which have often croed u with use of the uncomensated MCF. 4 Panagariya (1992) treats a revenue neutral switch among tariffs in a 3 final good, one imorted inut model. Falvey (1994) considers conditions under which tariff cuts may both raise welfare and raise revenue. 5 A large country achieves roductive efficiency with a tariff structure which equates the domestic marginal rates of transformation with the marginal rates of transformation in trade.

5 November 1, 1996 Trade reform with a government budget constraint 4 The olitical reasons for gradualism as oosed to a move all the way to constrained otimal taxes are left outside the analysis, in common with all the gradual reform literature. Endogenous choice of gradualism is easy to derive by embedding the resent analysis in a olitical suort function analysis (Hillman, 1989). In lanning its trade reform and fiscal olicy the government trades off general welfare (reresenting the interests of informed but unorganized interests) against the interests of informed and organized factions (the source of funds usable for winning the suort of uninformed and unorganized interests which lose from increases in taxes or cuts in government sending)). Whether the welfare increase from a reform ackage analyzed in this aer is large enough to offset the loss of the secial interests deends on the weights of the olitical suort function. A more comlete analysis requires a develoment along the lines of Grossman and Helman (1994) which endogenizes that ortion of the olitical suort function which relates olicies offered to contributions given. The aer focuses on efficiency while ignoring distributive issues by using the reresentative agent model. (Grossman and Helman submerge distributive issues by using the secial case in which utilities are directly transferable.) For analysis of trade reform in a model where the benevolent government engages in redistribution, including via the rovision of ublic goods, see Diewert, Turunen-Red and Woodland (1989,1991). Section 2 develos the intuition of the analysis. Section 3 sets out the basic structure of the model and relates it to the classic analysis of trade reform with redistribution. Section 4 considers tariff reform matched by ublic goods suly cuts. Trade reform is welfare imroving if ublic goods are over-sulied in an intuitive and useful sense. Section 5 shows that with substitutability, marginal relacement of trade taxes with consumtion taxes on traded goods is welfare imroving --- the marginal reform version of the Diamond and Mirrlees theorem. Section 6 considers the relative efficiency of the taxation of nontraded goods, showing that some taxation of both traded and nontraded goods is efficient. From given interior ositions of taxes and

6 November 1, 1996 Trade reform with a government budget constraint 5 tariffs, it is not generally ossible to rank the MCFs. Section 7 illustrates the estimation of MCF for trade taxes and for nontraded good consumtion taxes. 2. Intuitive Sketch of the Analysis The general method of analysis of trade or tax reform is founded on the concet of the Marginal Cost of Funds (MCF). The MCF of a tax (say tariffs) is comared to the marginal benefit of the funds raised by the tax. The marginal benefit is equal either to the marginal value of the goods and services financed by the tax (tariff) or to the MCF of the taxes which are reduced as a resonse to the rise in tariff revenue. MCF is often not cleanly develoed and may be unfamiliar to trade theorists, so this section discusses its intuition in detail. In contrast, all readers will be familiar with the concet of marginal dead weight loss and may have the imression that this is the key concet for understanding the desirability of trade reform. This indeed is the focus of all textbook analysis of trade reform and all the classic gradual reform aers are based on it. If trade reform takes lace along an active government budget constraint, however, the concet of marginal dead weight loss is generally irrelevant. It characterizes only the secial case in which the only role of government is to levy trade taxes and redistribute them in a lum sum. The grahical analysis here will drive this oint home. MCF for any tax is defined here as the ratio of the marginal comensation required to maintain real income as the tax rises to the comensated marginal tax revenue raised by the tax increase. In other words, it gives, at the margin, the comensation required er dollar of revenue raised. The ublic finance literature also (more often) resents an uncomensated, or money metric utility version of MCF, and this version is the usual one reorted in comutations. See Anderson and Martin for an argument as to why this is not an aroriate definition. The general method of this aer is to comare MCF for a given tax with the marginal benefit of the revenue raised --- either of the government sending or of the reduction in other taxes (valued at their MCF) which it

7 November 1, 1996 Trade reform with a government budget constraint 6 ermits. If the marginal benefit exceeds the MCF of the tax which must be raised, the rosective change is welfare imroving. The marginal benefit is also defined at constant real income. The MCF has a clear and intuitive structure and readily extends to aggregation in the many tax case and to incororate other fixed distortions MCF Illustrated To illustrate the concets in the scalar case, consider an imorted good with quantity denoted m selling at rice wedged above its international rice * by a tariff. A small change in the tariff results in the following key elements: md, the external comensating transfer at the margin, and [ m+ ( *) m ] d, the revenue change at the margin. The ratio of these defines the Marginal Cost of Funds: MCF md m = =, [ m+ ( *) m ] d MR the comensation cost er dollar of revenue raised at the margin via d. The earlier tradition of trade reform analysis (and ublic finance tax incidence analysis) relied on the concet of marginal dead weight loss, equal to ( *) m d. Marginal dead weight loss alies only in the case of a lum sum redistribution of the revenue (in which case the MCF of the lum sum tax is equal to one and the marginal gain of a switch from distortionary tax to lum sum tax is equal to the marginal dead weight loss). The analysis below shows that the marginal dead weight loss and the MCF have no tight relationshi to each other, and an examle is rovided in which the marginal dead weight loss and the MCF are negatively correlated both as the tax rises and as the strength of the substitution effect (the resonsiveness of demand to rice) increases. Figure 1 illustrates the concets of MCF and dead weight loss. MR is the marginal revenue schedule based on the imort demand schedule. The tax is set at level t. The areas of rectangles a and b, and of triangle d are the

8 November 1, 1996 Trade reform with a government budget constraint 7 basic building blocks for the standard welfare analysis. a+b is the revenue raised, while a+b+d is the consumer surlus lost. The net welfare effect of a tariff t with revenue redistributed in a lum sum is the dead weight loss of triangle d. The average version of the MCF idea, the comensation cost er dollar raised, is equal to (a+b+d)/(a+b). In this form, dead weight loss d aears to be the central concet. In contrast, MCF = tb / ta = ( a + b)/ a ( a+ b+ d) /( a+ b).

9 November 1, 1996 Trade reform with a government budget constraint 8 The marginal version of MCF is the central concet of tax analysis, as the formal analysis below shows. Only in the secial case of a lum sum redistribution does a further cancellation of terms ermit reducing the roblem so that marginal dead weight loss, ( *) m d (the area of the shaded thin vertical traezoidal section of the triangle d) is relevant MCF vs. Marginal Dead Weight Loss It is clear both from the diagram and the algebra that while MCF has some relationshi to marginal dead weight loss, the relationshi is highly nonlinear and the two concets are fundamentally different. They share a roerty in that MCF differs from 1 and marginal dead weight loss differs from zero due to the existence of the substitution effect. 6 However, varying the strength of the substitution effect or the size of the tax can affect the two concets in oosite directions. To see this, note that MCF in the scalar case can be reduced to: 1 1 MCF = = 1 + ( *) m / m τ 1 1+ τ ε where ε is the elasticity of demand and τ is the ad valorem tax rate. In contrast the negative of the marginal dead weight loss formula is: τ MDWL = m 1 + τ ε. For the constant elasticity case, m = µ ( 1 + τ) ε, MCF is everywhere increasing in τ, while the negative of MDWL is first increasing and then decreasing in τ. Moreover, MCF is everywhere increasing in ε while the negative of MDWL is first increasing and then decreasing in ε. Alternatively, for the linear case the negative of MDWL varies linearly with the secific tax, while MCF is first increasing and then decreasing in the tax. 6 For an inelastic demand curve, MR and the demand curve coincide, MCF is equal to one and the dead weight loss is equal to zero.

10 November 1, 1996 Trade reform with a government budget constraint 9 The difference in the two concets means that the general analysis of distortionary tax tradeoffs based on MCF is fundamentally different from the classic secial case analysis of distortionary vs. nondistortionary tradeoffs based on the marginal dead weight loss concet. MCF is the basic concet, while the marginal dead weight loss only alies to a secial case. 3. Formal Elements of the Analysis The key relationshis of the model are the rivate sector budget constraint and the ublic sector budget constraint. For any exogenous fiscal olicy change there must be an endogenous fiscal olicy change to balance the government budget. The two fiscal changes then imly a change in welfare along the rivate sector budget constraint. To demonstrate the method of this aer and its relation to the earlier literature, this section reviews the standard analysis of a tariff cut offset by a rise in lum sum taxes. The model throughout is of a cometitive economy with no distortions other than fiscal distortions. All tradable goods face fixed international rices. Nontradable goods lay an imortant role. Where necessary for clarity and shar results, further restrictions on tastes and technology will be emloyed, esecially as regards nontraded goods. Substitutability assumtions will be introduced as needed. Finally, for simlicity, the model is static. This assumtion is aroriate for a credit constrained government and economy, and is also rationalized by olitical agreements which constrain the government budget deficit. For a treatment of the comlexities of intertemoral tax structure issues, see Anderson and Young (1992). The basic building blocks of the model are the reresentative consumer's exenditure function and the gross domestic roduct function. The consumer s exenditure function e(,π,u) gives the minimum value of exenditure on rivate goods at rice vector and ublic goods at marginal valuation π required to suort utility level u. The gross domestic roduct function g(,π*,v) gives the maximum value of roduction of rivate goods at rice and ublic goods at rice π* using the vector of rimary inuts v in a convex technology. The value g also measures the total ayments to factors. (If necessary, a diminishing returns technology can be augmented by dummy

11 November 1, 1996 Trade reform with a government budget constraint 10 factors to receive the residual returns.) There are also some untaxed tradable goods with unit rice which are suressed as active arguments, so that is a relative rice vector. 7 Untaxed nontraded introduce no essential element and so are suressed for simlicity. The level of ublic good roduction G is set by the government, so it is convenient to work with quantity restricted rivate behavioral functions. Thus, define the rivate goods exenditure and rivate goods GDP functions as: (3.1) e(, G, u) = max {e(, π,u) - πg} π (3.2) g(, G, v) = min {g(, π*,v) - π* G}. π * See Anderson and Neary (1992) for a similar develoment and further details. The net exenditure on rivate goods at domestic rices is defined as (3.3) E( Guv,,, ) = e( Gu,, )- g( Gv,, ). Conventionally, subscrited variable labels denote artial differentiation. Then from the roerties of (3.1)-(3.3), EG = eg+ gg= π π*, the ga between the virtual rice of the ublic goods π and the marginal resource cost of ublic goods π*. E is the vector of excess demands. The next ste is to build the rivate and government budget constraints. The rivate budget constraint is: (3.4) EGuv (,,, ) + Gg ( Gv,, ) ρ =0. G The second (negative) term is needed because rivate consumtion is covered by factor ayments received from ublic as well as rivate roduction. The third term ρ, the lum sum transfer from the government to the rivate agent, is to connect with the earlier literature. The government budget constraint is: (3.5) ( *)' E (, G, u, v) + Gg (, G, v) ρ = 0. G The first term is the government (distortionary tax) revenue, the second term is minus the government exenditure on the ublic good and the third term 7 This convention is necessary in order to study a model in which distortionary taxation is necessary.

12 November 1, 1996 Trade reform with a government budget constraint 11 is the transfer to the rivate sector. (If lum sum taxation is allowed, ρ can be negative.) A tariff reform is equivalent to a change in the domestic rice vector. It is convenient to incororate various classes of tariff reforms in the convention d i i = W dt, where dt is a scalar and W i is a diagonal matrix and the suerscrit i denotes a further restriction on W, i being a member of an index set. For examle, the uniform radial cut rule imlies that the elements of the rincial diagonal of W are equal to the initial tariff rates on the domestic base, so that d = ( *) dt. The classic treatment of tariff reform (Hatta, 1977 and others) considers the effect on the differential of system (3.4)-(3.5) of an exogenous change in d solved for the endogenous change in the redistribution dρ and the welfare change du. Illustrating the method, analyze a uniform radial change dt. Differentiate the government budget constraint and solve for dρ/dt: dρ E E Gg E du = ' ( *) + ( *)' ( *) + G ( *) + ( *)' u. dt dt Substitute into the differential of the rivate budget constraint, isolating terms in du on the left hand side: (3.6) ( 1 ( *)' E / E ) E du dρ u u u = ( E' ( *) + GgG( *) )+ u dt dt 1 = ( E '( *) + Gg ( *) ) 1 + G. t MCF On the left hand side, the change in money metric utility is multilied by a term which is ositive in the normal goods case (Hatta, 1977). On the right hand side, the first bracketed term is a scale effect, the lum sum comensation required to offset a 1% rise in taxes on the reresentative agent. The second, square bracketed term on the right hand side of (3.6) contains the essential welfare analysis. MCF is defined by: (3.7) MCF E ' ( *) + Gg ( *) = E ' ( *) + ( *)' E ( *) + Gg ( *). t G G Note that (3.7) roerly generalizes the ratio (a+b)/a in Figure 1. The -1 term under the square bracket reresents the direct effect of the rise in tax on

13 November 1, 1996 Trade reform with a government budget constraint 12 welfare; a one dollar increase in tax ayments requires a one dollar increase in comensation. The second, ratio term reresents the offsetting effect of endogenous fiscal olicy coming through the government budget constraint. For each dollar raised and redistributed, the benefit is one dollar, the numerator, but each dollar raised through distortionary tax comes at a marginal cost of MCF, the denominator. According to this analysis, the roblem with raising tariffs in order to redistribute the resulting funds is that the MCF for tariffs is greater than one, which is the marginal benefit of the cut in lum sum taxes. The structure of the right hand side exression allows a further simlification: ( ) + E' ( *) + GgG( *) ( *)' E t ( *) 1 1 MCF =, where the right hand side is the familiar marginal dead weight loss term. Here, it aears that the roblem with distortionary taxation vs. nondistortionary taxation is the existence of the substitution effect, as agents avoid distortionary tax. The existence of the substitution effect is the essential reason that MCF lies above 1 as well. However, the argument above in the linear case shows that there is no necessary relation between MCF and marginal dead weight loss; the magnitude of the substitution effect directly affects marginal dead weight loss while it has no unambiguous effect on MCF. The usual treatment of this case first solves (3.5) for the government exenditure, then substitutes into (3.4) to obtain the social budget constraint (3.8) EGuv (,,, ) ( *)' E( Guv,,, ) = 0, and then analyzes the link between d and du at constant G. Redistributive fiscal olicy thus makes the government budget constraint assive. 4. TARIFF REFORM WITH SPENDING CUTS A simle story with ractical imortance is the analysis of trade reform where government budgetary balance imlies that sending cuts must offset tariff revenue cuts. Formally, G must change endogenously as a result of the change in. What rules can deliver welfare imrovements along the ath to the otimal tariffs?

14 November 1, 1996 Trade reform with a government budget constraint 13 The analysis roceeds in three stes. First, totally differentiate the government budget constraint (3.5) with resect to,g and u, and solve for dg/dt under the restriction W i. 8 This yields dg 1 (4.1) E E Gg W E du i = ' [ + ( *)' + G] + ( *)' u, dt γ dt where γ is the marginal fiscal cost of the ublic good: ( G GG G) ( ) * (4.2) γ = g + Gg + ( *)' E = π * + Gπ ( *)' E G G. The first two terms give the marginal cost of G to a monosonistic buyer. The third term ( - *)' E G is the tax revenue change induced by the change in G. 9 Second, totally differentiate the rivate budget constraint (3.4) with resect to exogenous d, and endogenous dg and du using reviously established roerties of E and g : ' * Eudu = ( E + GgG) d + ( π GπG) dg (4.3) ' = ( E + Gg ) d+ πdg. G The second term on the right hand side, π, the marginal net benefit of the ublic good, is equal to the virtual rice minus the net factoral income effect of the change in ublic goods roduction 10. Note that π π when ublic and rivate roduction are substitutes 11. Third, substitute the exression for dg/dt from the differential of the government budget constraint into (4.3), then isolate terms in du on the left hand side of the equation: 8 If G is a vector, the analysis roceeds under some auxiliary rule dg = H j Gdα, where H j is a sending change rule and dα is a marginal change in the exenditure. 9 A common theoretical convenience is to assume this term is equal to zero, a ractice which is likely to be seriously wrong emirically and may be misleading in understating the marginal fiscal cost of the ublic good. E G = 0 requires 'additive searability' in both references and technology. 10 One unit of ublic goods roduction reduces rivate roduction by -π*, and raises the * factoral income received from ublic goods roduction by π * +Gπ G. 11 Public and rivate roduction are substitutes if the marginal cost of ublic goods π* is raised by an increase in any element of : g = g 1 G π* π* gπ* is a ositive vector (matrix in the case of multile ublic goods).

15 November 1, 1996 Trade reform with a government budget constraint 14-1 du ' i π ' i (4.4) µ E u = - (E + Gg G)W + ( E + ( *)' E + GgG) W dt γ where π = 1+ EW ' i, γmcf (4.5) µ 1 1 = 1 ( *)' E u / E u γ and (4.6) MCF ' i ( E + Gg ) W i E + ( *)' E + Gg W G =. ' G ( ) Here, (4.6) generalizes (3.7) to the case where tax changes are not constrained to uniform radial changes. On the left hand side of equation (4.4), the rate of change of money metric utility E u du/dt is multilied by a coefficient, given by (4.5), usually assumed to be ositive, the normal economy assumtion. The inverse of this coefficient, µ, is often called the shadow rice of foreign exchange in the international trade literature, while for fiscal olicy Anderson and Martin (1995) suggest calling it the fiscal multilier. Comaring (4.5) with the left hand side of (3.6), the coefficient will differ in form for each fiscal exeriment while remaining ositive with the normal economy assumtion. On the right hand side of (4.4) are the comensated terms which sign the rate of change of utility. The term outside the brackets is a ositive scalar, by construction. The term in brackets signs the welfare change and is ositive if the ratio of the marginal benefit π to marginal social cost γmcf is greater than one. The term γmcf is the marginal social cost of a unit of the ublic good financed through distorting. The intuition of (4.4) is simle. Assuming a normal economy, (4.4) imlies that welfare rises with tariffs if the marginal benefit of ublic goods π exceeds the marginal social cost of obtaining the ublic good. Thus: Proosition 1 : The Public Goods Suly Proosition. Tariff reductions financed by cuts in government service are welfare

16 November 1, 1996 Trade reform with a government budget constraint 15 decreasing (increasing) in a normal economy with underrovision (overrovision) of ublic goods relative to their cost, or as π 1+ > (<) 0. γmcf More intuition about Proosition 1 follows by relating it to the otimal rovision of ublic goods. With lum sum taxation available and distortionary taxes equal to zero, the differential of the government budget * constraint imlies: dg / dρ = 1 /( π * + π ). G G Public goods rovision will fall with a rise in lum sum transfers ρ. The differential of the rivate budget constraint imlies: * * * Edu u / dρ = 1+ ( π GπG) dg/ dρ = 1 ( π GπG)/( π * + GπG) = 1 π / γ * = ( π π*)/( π * + Gπ ). G Utility is increasing in lum sum tax reductions with no distortions when the * * ratio of the net benefit π = π Gπ G to the marginal fiscal cost γ = π * + Gπ G is less than one. This condition imlies π < π* due to the canceling of terms, as is intuitive. But the fiscal olicy logic of the marginal net benefit to marginal fiscal cost ratio is general. In the lum sum tax exeriment, the MCF for lum sum taxation is imlicitly resent multilying γ, but is identically equal to one. Recognizing this, Proosition 1 roerly generalizes the logic of the first best case by using the aroriate MCF times the aroriate marginal fiscal cost formula in cost ortion of the social benefit-cost ratio. Proosition 1 relates to Proosition 2 of Abe (1992), but is a good deal more intuitive. In contrast to Abe, Proosition 1 does not require any added conditions on cross effects. Because Abe defines marginal cost and marginal benefit of ublic roduction in a highly eccentric way 12, his condition of underrovision of ublic goods is not the same, and he therefore needs auxiliary conditions to sign the welfare change. Moreover, his oversuly 12 In my notation, Abe defines the marginal cost as *' g G and the marginal benefit as *' e G. These exressions bear no articular relation to the marginal cost and virtual rice which are the natural ones used here.

17 November 1, 1996 Trade reform with a government budget constraint 16 condition roduces the anomaly that tariff increases may raise welfare even with ublic goods oversulied under his definition. Proosition 1 also relates to the extensive literature on roject evaluation based on the concet of the shadow rice of ublic goods (see for examle Squire, 1989). The shadow rice of G is the net marginal social benefit to the economy of a gift of the foreign exchange needed to buy one unit of G:σ = [ π + MCF ( *)' E ]. Welfare falls with a tariff reduction if, maniulating (4.4): ( G) * σ MCF π * + Gπ > 0. G That is, tariff cuts hurt welfare if ublic goods are undersulied, where the undersuly condition, alternatively to Proosition 1, is that the shadow rice of ublic roduction exceeds the roduct of the direct marginal outlay needed times the marginal cost of funds raised through distortionary trade taxation. The bracketed underrovision of ublic goods term in Proosition 1 is neat and intuitive, but in ractice assessing its sign is comlicated. Possibly the marginal fiscal cost γ and more robably MCF will be high in develoing nations where the marginal benefit of ublic goods is also high. Emirical work must rovide the assessment, and indeed there exist a number of estimates of MCF for various fiscal olicies in a number of countries. While data is lacking for many develoing nations, there is now available a set of Comutable General Equilibrium (CGE) models which can be tweaked to rovide some simulated values of γ and MCF. The most roblematic variable is the marginal benefit of ublic goods. In some lausible models, such as the deendent economy model in which external rices entirely determine internal (nontraded good and factor) rices, the factoral income effect of ublic goods is equal to zero so the marginal benefit reduces to the unobservable virtual rice of ublic goods π. Even here, for some imortant kinds of ublic goods such as education there are at least useful lower bounds available from observable data.

18 November 1, 1996 Trade reform with a government budget constraint TARIFF REFORM WITH CONSUMPTION TAXES A basic rincile of ublic finance is that otimal revenue taxation should reserve roduction efficiency (Diamond-Mirrlees, 1971), which among other things means it should not discriminate between foreign and domestic sources of roduction for the same good. In this sense, trade should not be taxed (Anderson, 1994). In dearting from a subotimal tax structure, under what conditions is it ossible to state a gradual reform result that it ays to reduce tariffs and increase consumtion taxes? This section shows that the olicy of uniform radial reductions in tariffs matched by uniform radial increases in consumtion taxation, or uniform radial relacement, cannot be guaranteed to be welfare imroving without further substitutability restrictions between rivate and ublic goods, along with non-subsidization conditions. One sufficient condition is the nonsubsidized deendent economy case where there are at least as many traded goods and factors as there are nontraded goods and factors in a constant returns technology. This case imlies a owerful general equilibrium zero substitutability restriction in the excess demand system. Let q denote consumer rices and denote roducer rices of tradable goods, both taxed or subsidized away from international rices *. No traded inuts are taxed in this section, for simlicity. Nontradable rivate goods are untaxed, with market clearing rices h. It is convenient now to dro the notation for lum sum transfers ρ. The net exenditure function is now derived as: (5.1) E( qgu,,, ) = max eqhgu (,,, ) g( hg,, ) h { } where the restricted exenditure and gross domestic roduct functions are obtained by extending (3.1) and (3.2) in the obvious way to incororate rivate nontraded goods. Then E q = x, the vector of final goods subject to tax or subsidy, and E = -y, minus the vector of suly subject to tax or subsidy. The ublic sector budget constraint is (5.2) ( *)' E + ( q q*)' E + g G = 0. q G The rivate sector budget constraint is:

19 November 1, 1996 Trade reform with a government budget constraint 18 (5.3) EqGu (,,, )+ gg G = 0. The exogenous fiscal olicy is a change in trade taxes, offset for revenue neutrality by an endogenous change in consumtion taxes, now with constant ublic good suly. To secialize the fiscal olicy to the uniform radial relacement case, it is assumed that: (5.4) d = ( *) dτ dq = d + ( q *) dθ. The meaning of (5.4) is simlest in the case of initial ure trade taxation, =q. With dθ = 0, dτ is a standard uniform radial change in trade taxes. The change in θ modifies this with an additional uniform radial change in the consumer tax vector. As a reliminary ste in what follows, denote the (utility and ublic good constant) rivate marginal cost of the tax changes as q ' R = E ( q *) + Gg ( q *) q Gq for the consumtion tax and q ' R = R + E ( *) + Gg ( *) G for the trade tax. These exressions are obtained from differentiating (5.3) and using (5.4). R q and R give the lum sum transfer needed to maintain u at constant G under the consumtion and trade tax changes resectively. They combine the direct marginal cost with the indirect marginal cost through changing factoral income from ublic goods roduction. The fiscal olicy change must meet the government budget constraint, imlying by totally differentiating (5.2) and using (5.4) that: θ q τ (5.5) dθ/ dτ = MCF / R { R / MCF + [( *)' E + ( q *)' E ] du}, where MCF θ = q R q R + l q MCF τ = R q R+ l + l q l = ( q *)' E ( q *) + ( *)' E ( q *) qq l = ( q *)' E ( *) + ( *)' E ( *). q Here, l q and l are familiar dead weight loss terms, while MCF j stands for the Marginal Cost of Funds raised by a small change in the suerscrit variable j. q u qu

20 November 1, 1996 Trade reform with a government budget constraint 19 Substituting (5.5) into the differential of the rivate budget constraint (5.3) and isolating terms in du on the left hand side of the equation: 1 (5.6) µ E du dτ where µ MCF MCF θ u = 1 τ R, 1 θ = 1 MCF [( *)' Eu + ( q *)' Equ]/ Eu. As always, µ is assumed to be ositive. If trade is not subsidized, and if trade is a substitute for ublic goods roduction, R is ositive. Then the sign of the welfare change from a uniform radial relacement of tariffs with consumtion taxes (dτ<0) is ositive if the bracket term is ositive, or MCF θ τ < MCF, the marginal cost of funds raised through consumtion taxation is less than the marginal cost of funds raised through trade taxation. Condition (5.6) is entirely intuitive, and easy to aly based on simulations of MCF from CGE models. What theoretical restrictions are able to guarantee the condition? Note that if R q MCF τ. As for R R> 0, and l q and l are both negative, MCF θ is indeed smaller than q R> 0, this holds if: ublic and rivate goods are substitutes in roduction, meaning that g * * = π > 0 and g = π > 0; G Gh h traded goods and home goods are substitutes, meaning that h q >0; ' ' trade is not subsidized, E ( *) + E ( q *) >0; ' and consumtion is not subsidized, E ( q *) >0. The restriction on l q and l is far more roblematic. The sum of l q and l is necessarily negative. However, as for l q and l searately, a cross effect arising through the nontraded good revents signing them from theory, even under strong assumtions such as substitutability. Shar results come with the deendent economy roduction and trade structure. Technology is subject to constant returns to scale and there are at least as many homogeneous (erfect substitutes with domestic roducts) traded goods and factors as there are nontraded goods and factors. In these circumstances the nontraded goods roducer rices are determined by the q q

21 November 1, 1996 Trade reform with a government budget constraint 20 traded goods and factors roducer rices, indeendently of the consumer rices. Thus E q = E q = 0 and g ' Gq θ τ = g = 0. Then MCF < MCF if R q R> 0. G Proosition 2: the Marginal Diamond-Mirrlees Proosition. A uniform radial marginal relacement of trade taxes with consumtion taxes is welfare imroving in a normal deendent economy, rovided trade and consumtion are not initially subsidized. These are of course oversufficient conditions. Nevertheless, a art of the significance of Proosition 2 is negative: even quite restrictive conditions do not suffice to guarantee that a relacement of trade taxation with consumtion taxation at the margin will be welfare imroving. Proosition 2 contrasts with Abe (1995), who considers welfare imroving tariff and consumtion tax changes in a deendent economy when both tariffs and taxes change exogenously according to a derived rule, and the suly of ublic goods changes endogenously along with the level of utility. Abe sets the rule such that the net welfare effect of the change in and q is equal to zero, with the welfare effect of the change coming through the increase in ublic goods roduction which is enabled by the revenue increase. In contrast to Proosition 2, Abe s roosition requires a great deal of information to form the weights in the linear tax rule. In further contrast, Diewert, Turunen-Red and Woodland (1989), Theorem 7 and Corollary 7.1 rovide conditions under which uniform tariff cuts combined with unsecified commodity tax changes will suffice for Pareto imrovement. The resent analysis uses a uniform radial increase to balance the government budget, but more imortantly, it allows taxation of only the non-numeraire goods. In

22 November 1, 1996 Trade reform with a government budget constraint 21 allowing taxation of all goods, Diewert, Turunen-Red and Woodland in effect allow lum sum taxation. 13 As in section 4, a simle and useful condition signing the welfare effect of the revenue neutral tariff reform is resented. However, art of the significance of Proosition 2 is negative: fairly strong qualifications are needed to guarantee that uniform radial relacement is beneficial. 6. TAXATION OF NONTRADED VS. TRADED GOODS The first great result of ublic finance is the Ramsey inverse elasticity rincile. It imlies that domestic and imorted goods should generally be taxed differently, and if imort taxes should be higher due to elasticities of demand being lower, liberal trade obligations conflict with fiscal efficiency. Moreover, otimal tax rates will differ across broad roduct categories, hence there are fiscal inefficiencies in the uniform tariff structure advocated by the World Bank and in trade negotiations. In contrast, the logic of the receding section alies when domestic and imorted goods are erfect substitutes: foreign and domestic suliers of the same good should face the same tax; i.e. trade should be untaxed. This section attemts to rovide some theoretical insight into how costly is the decision to bind tariff levels in a WTO deal, or a regional trade agreement. First, a simle counter-examle is develoed in which trade taxation is efficient and the otimal home good tax rate is equal to zero. Second, a general formula for evaluating the relacement of trade taxes with home good taxes is offered. Intuitively, as in (5.6), it comes down to the MCF of home goods taxation vs. the MCF of trade taxation. These are comlex exressions, so only very secial cases can be signed from theory alone An efficient trade tax examle Efficient inut taxes seem likely to exceed efficient final goods taxes on inverse elasticity reasoning, since inuts are likely to be more inelastically demanded than are final goods, and since many develoing or small 13 A uniform tax on all goods, including the numeraire, is equivalent to a lum sum tax. I thank Peter Neary for this observation on Diewert, Turunen-Red and Woodland.

23 November 1, 1996 Trade reform with a government budget constraint 22 countries have no substitutes for their imorted inuts. The examle shows a case where the government collects and redistributes a given revenue from either a consumtion tax or a traded inut tax, and the trade tax dominates. The left hand anel of the Figure shows a roduction function with constant returns to the variable imorted inut m u to a caacity constraint at P. National aggregate final activity is both consumed and exorted, exorts of ZY being used to ay for imorted inuts m. The right hand anel shows that net final activity is slit into two goods, y and x, according to a linear transformation function running from Y through C and C'. Under the inut tax, after aying for imorts at the international rice given by the sloe of PY, net national revenue of Y still remains, the sum of the new national income Y' and the tariff revenue R which is returned to the consumer in a lum sum. The consumtion oint is C. Under a consumtion tax (on consumtion of good y) which raises as much revenue, C' is the consumtion oint, which is clearly inferior to C.

24 November 1, 1996 Trade reform with a government budget constraint 23 Panagariya (1992) considers inut tariff increases balanced by final goods tariff decreases in a revenue neutral model and obtains ambiguous results in general. While the models are different, his conclusion about ambiguity holds here as well, since the ranking of the two instruments can be reversed by reversing the substitutability assumtion: comlete inelasticity in consumtion while roduction has elastic demand. As inuts are usually thought to be more inelastically demanded than are final goods, the logic is to tax inuts more heavily than final goods, which will imly trade taxation Trade taxation vs. home good taxation When trade taxes are high and home good taxes are very low it usually (but see the counter-examle) ays to switch at the margin. Symmetrically, with low trade taxes and high home good taxes it ays to switch at the margin. The intuition is that a uniform radial relacement olicy lowers the tax needed on each initially taxed good while raising it on each initially untaxed good. Since MCF is quadratic, rising more than in roortion to the tax, the relacement olicy marginally tends to reduce loss. Cross effects qualify the insight with nonzero initial taxation of both sets of goods. The home good consumtion rice vector is h and the home good roducer rice vector is h*. The secific tax t = h-h* is an instrument. The numeraire (including at least one exort good) rice is constant. For simlicity, restricted imorts are confined to final goods only. Under these restrictions, the exenditure function is e(,h,g,u) and the gross domestic roduct function is g(h*,g). Equilibrium in the home good markets determines h*(t,,g,u) as a function of t,,g,u imlicitly in: (6.1) e (, h* + t, G, u) g ( h*, G) = 0. h h The rivate and the government budget constraints are: (6.2) e( hgu,,, ) gh ( *, G) + Gg G = 0 (6.3) [ *]' e + [ h h*]' e + g ( h*, G) G = 0. h G Now consider uniform radial relacement of arametric trade taxes with revenue neutral endogenous home good taxes: (6.4) d = ( *) dα dt = ( h h*) dη

25 November 1, 1996 Trade reform with a government budget constraint 24 In the nontraded good market, dt imlies h* changes by h * t while h changes by I + h * t both obtained by imlicit differentiation of (6.1). Using the same methods as before, 1 (6.5) µ E du u dα η MCF = 1 α R, where MCF MCF α = R R + l, MCF η = h R h h R + l, ' ' * h ' ' ' R = e ( *) + Gg h ( *), R = e ( h h*) + Gg h ( h h*), Gh* h Gh* t ( h ) + ( h + hh ) l = ( *)' * e + e h ( *) ( h h *)' * e e h ( *), h * * l = ( h h*)' e [ I + h ]( h h*) + ( *)' e [ I + h ]( h h*). hh t h t When might MCF η be less than MCF α in (6.5)? Proosition 3: The Wider Base Proosition With consumtion taxes initially equal to zero, a uniform roortional rise in consumtion taxes combined with a uniform radial reduction in trade taxes is welfare imroving rovided traded goods are not erfectly inelastically demanded. For this case, MCF η is equal to one, while MCF α is greater than one. By continuity, welfare should continue to rise with small home goods taxation. The reasoning is symmetrical: a regime with no taxation of imerfectly substitutable imorts can always imrove welfare with at least a bit of trade taxation. Proosition 3 is the formal counterart to the intuitive notion that at the margin it always ays to add new goods to the tax base. General results for switching between trade and home good taxation from interior ositions are not ossible, as the MCF exressions deend on the entire substitution effects matrix interacted with the tax structure. 7. TOWARD OPERATIONALITY This aer stresses the imortance of the MCF of trade taxes relative to that for domestic taxes. Thus it concludes with illustrative estimates of MCF θ and MCF τ for a stylized small scale CGE model of the Korean economy in 1963, found in the ublic domain GAMS (General Algebraic Modeling System) software library. For more details, see Chenery et al. (1986).

26 November 1, 1996 Trade reform with a government budget constraint 25 There are 3 sectors, agriculture, manufacturing and services. Each sector has an imort available at fixed international rice cometing with a domestic roduct which is an imerfect substitute in demand via a CES reference structure. The CES aggregate consumtion bundles are substitutes with each other according to a Cobb-Douglas reference structure. Each sector exorts at fixed international rice a roduct which is an imerfect substitute in suly for the domestic roduct according to a CET joint outut technology. Each sector roduces its outut with intermediate goods with fixed coefficients, while the value added technology has a CES form. Agricultural labor is not mobile and sectoral caital is fixed in the short run. There is in effect a reresentative consumer who receives all sources of income. 14 Government consumtion is modeled as absorbing revenue but not sulying a ublic good. Imorts are subject to tariffs, and indirect taxes aly to all domestic transactions. Income taxes in the model are equivalent to lum sum taxes, as labor suly is inelastic. The model is fully Walrasian. The MCF is a comensated imlicit derivative. It is built u from two searate simulations of the change in money metric utility with resect to a small external transfer. In the first, the government budget is balanced by a uniform radial tax change while in the second it is balanced by a lum sum transfer. The results are not very sensitive to the size of the erturbation or to variation in the size of elasticities of substitution, so the sensitivity analysis is not reorted. The comutational methods are described in the Aendix. The simulation of the model at the base values of the substitution arameters yields the MCF for tariffs of around 1.57 while the MCF for indirect taxes is around (The MCFs are calculated based on a uniform radial change in tariffs and in indirect taxes resectively.) These values aear reasonable, based on two sorts of check. First, reorts of estimates of MCF for income and commodity taxes combined range from 1.32 to 1.47 for the US while an estimate for Sweden is recorded at 2.2 (Devarajan et al, 1995). 14 For the intertemoral asect of the model, there are different marginal roensities to save out of different sources of income. This divergence from the reresentative consumer story does not affect the static roerties of the model.