The origin principle and the welfare gains from indirect tax harmonization

P.S.P. 2 /10-2-96 I I I ENCUENTRO DE ECONOMIA PUBLICA Departamento de Teoría Económica y Economía Política Universidad de Sevilla Sevilla 9, 10 de febrero de 1995 PONENCIA The origin principie and the welfare gainsfrom indirect tax harmonization. Miguel Ángel LÓPEZ GARCÍA Departamento de Economía Aplicada. Universidad Autónoma de Barcelona. Introduction The literature dealing with the coordination of economic policies among countries or groups of countries in an integrated world stands out as one of the most prominent developments of the last few years. Although not the only one, a clear application of the results emerging from this literature is associated with the tax approximation efforts that have been carried out in the European Union, and, without any doubt, the above-mentioned development cannot be understood without a reference to these real world events. One of the issues most actively researched has probably been that of indirect taxation, stimulated by the European Comission proposals aimed at harmonizing valué added taxes and excises. In particular, some questions related to tax competition have been analyzed in different contexts [Mintz and Tulkens (1986), de Crombrugghe and Tulkens (1990), Sinn (1990), Lockwood (1993), Kanbur and Keen (1993)] as well as the welfare effects of indirect tax harmonization policies [Keen (1987,1989.a,1989.b), Turunen-Red and Woodland (1991), Keen and Lahiri (1993)]. The framework for the analysis of the impact of harmonizing reforms has been the destination principie, i.e., the principie that internationally traded commodities are taxed at the rates of (and the revenue accrues to) the country in which final consumption takes place. The alternative to the destination principie is the origin, or source, principie, under which commodities entering intemational trade are taxed at the rates prevailing in the country where they are produced (this being the one which collects the revenue). Although the destination principie has been the central idea governing the harmonizing efforts of indirect taxation that have been carried out by the European Comission, the abolition of border controls has rendered it unsustainable. The definitive system, to be enacted at the start of 1997, maintains the destination system for transactions between firms but cross-border purchases by individuáis will be taxed on an origin basis, thus appearing as a mixed system. The purpose of this paper is to establish a parallelism between the analyses in Keen (1987,1989.a) referred to indirect tax harmonization when taxes are levied according to the destination principie and its counterpart when taxes are imposed on an origin basis. Using a simple two-country model of intemational trade it is argued that indirect tax harmonization under the origin principie, considered as a movement of domestic taxes towards an appropriately designed "average" tax structure, is potentially Pareto improving, in the sense that the welfare of a given country can be increased provided that the other country's welfare is kept unchanged with the aid of an intemational transfer. In the same vein, it is shown that if the initial position is a Nash equilibrium, there are situations under which the above-mentioned 1 reform may genérate an actual Pareto improvement, so that both countries improve their welfare without any need for a compensating intemational transfer. As stated above, the definitive system will be a mixed one, so that the puré origin case is not the most realistic framework from a policy point of view. However, it may be useful in yielding indications that, coupled with the results that have been obtained under the destination principie, provide insights on the effects of the definitive system. In the same way as Keen (1987,1989.a) constructs his harmonizing reform under the destination principie in such a way that (neglecting income effects) world producer prices are unchanged, the counterpart of his analysis under the origin principie does not affect world consumer prices. This paralellism translates into modifying the common target towards which countries harmonize their indirect tax structures, which does not depend on local demand responses but on local supply responses. The structure of the paper is as follows. In section 1 the basic model is set up. Section 2 considere tax harmonization as a potential Pareto improvement. Section 3 poses the question whether the specific kind of harmonizing reform being analyzed can also result in an actual Pareto improvement. Section 4 includes some additional comments. 1. The model The basic framework is a standard model of intemational trade [Dixit and Norman (1980)] in which two countries, labelled as "home" and "abroad", trade in N commodities. Each country's variables are represented by lower case and upper case letters respectively, and there is a single consumer in each of them. The only distortions are due to consumption taxes, levied on an origin basis, so that commodities are taxed at the rates prevailing in the country in which they are produced, this being the country which collects the tax revenue. Since, assuming away transport costs, the application of the origin principie implies that consumer prices in each country are the same, we have the following relationship between consumer prices, q-Q, producer prices in each country, p and P, and the tax instruments, t and T: [1] P = q-t P=q-T where taxes are expressed in specific terms.1 1 Since the application of the origin principie implies that exports are taxed and imports are exempted, the home (abroad) country's consumer must be indifferent, in equilibrium, between payingp + t (P + T) for domesticallyproduced goodsand P + T (p + t) for imported goods. Thus, consumer prices are equalized across countries, i.e., q = Q. On the working and consequences of the origin principie see Cnossen and Shoup (1987) and Keen (1990,1993). 2 The home and foreign consumers can be characterized by their expenditure functions, e{q,ü) and E(q, U), where u and U stand for the utility levéis achieved by the consumer in each country. Tax revenue is returned to the individuáis as a lump sum payment. As for the production side, it is assumed that both countries behave competitively, and their behaviour can be resumed in the revenue functions r(p) and R(P).2 Since the partial derivatives of the expenditure and revenue functions yield, respectively, the compensated demand and supply functions, the world market-clearing conditions for the N commodities are given by: [2] e¿q,u) + E¿q, U) = rp(p) + Rp(P) where the subindices denote the (vector of) partial derivatives of the relevant functions. Consumer expenditure in each country equals national income at domestic prices plus tax revenue. Using the sign' to denote transposition, the budget constraints in each country can be written as: [3] e(q,u) = r(p) + t' rp(p) + qxz [4] E(q,U) = R(P) + T'RfiP)-qlz where t' rp(p) and T' Rf(P) express tax revenue in each country. The term z represents a transfer of commodity 1 from the foreign country to the home one. Its purpose is to characterize reforms entailing a potential Pareto improvement, in the sense that u can be increased for a given valué of U. The role of z is just that of assuring that the foreign utility level does not change. On the other hand, z = 0 in [3] and [4] when the focus is on characterizing an actual Pareto improvement, i.e., a situation in which both « and U increase without any need for an intemational transfer. As a matterof normalization, commodity 1 is taken to be the numeraire (so q\ = 1) and is assumed to be untaxed in both countries (i.e., t\ = T\ = 0). In order to avoid excessive notation, vector prices will hereafter be interpreted as being oiN-\ dimensión. By Walras' Law one of the N+2 equations in [2]-[4] can be dropped, so we can drop the equilibrium condition for commodity 1. Therefore the system in [2]-[4] can be described as N+l independent equations with N+l variables. In the search for a potential Pareto improvement the latter are N-l relative consumer prices, q, the home utility level, u, and the size of the intemational 2 The revenue (or GNP) function, expressing the valué of production at given producer prices (and amounts of the primary factors), is extensively discussed in Dixit and Norman (1980, ch. 2). 3 transfer, z, given the tax parameters t and T as well as the foreign utility level, U. Alternatively, in the search for an actual Pareto improvement the N+l variables are q, u and U and the parameters are / and T. 2. Tax Harmonization as a Potential Pareto Improvement Consider first tax harmonization as a potential Pareto improvement, so that the policy leads to an increase in one country's welfare when it is accompanied by an appropriate intemational transfer to the other country so that its welfare level is kept constant. We can thus evalúate in [2]-[4] the welfare effects in terms of the home country's welfare, du, of an arbitrary tax reform, {dt,dT}, coupled with the transfer, dz, required to hold U unchanged. Differentiating in [2]-[4] with dU = 0, we have: [5] eq/iu + [eqj + ECfírpp - Rpp]dq + rppdt + RPPdT = 0N.i [6] e,¿lu+[eq-rp-rpptydq + t'rppdt-dz = 0 [7] [Eq-Rp-RPPT],dq+T'Rppdr+dz = 0 where is the (N-1)-vector of zeroes. Thus, eliminating dz in [6] and [7]: du] = \-(t'rppdt+T'RPPdT) • dq\ [ -{rppdt + RppdT) where A = + Egj - rpp - Rpp, i.e, the matrix of the derivatives of the compensated world excess demand for the non-numeraire goods with respect to the non-numeraire prices, is negative semi-definite. It will be assumed throughout that there is enough substitutability in demand or production between the numeraire good and the other goods to ensure that A will be negative definite.3 The system in [8] allows one to obtain an expression for the change in home utility, du, as a function of the reform associated with dt and dT: -{t' rppdt + T' RppdT) -(rppt + RPPT)' -(rppdt+ RppdT) A where: 3 See Dixit and Norman (1980, ch. 5). [8] -(rppt+RPPT)' 'qu [9] du - 4 [10] a = eu + (rppt + RPPT) 'A^e^ and it can be shown thata is positive whenever an increase in the home country's endowment of the first commodity, at constant tax rates and foreign utility, implies a strict potential Pareto improvement. We will assume this is the case. The notion of harmonization is usually taken to mean making the tax systems more "uniform". This entails both a process of convergence towards a common target and the suggestion of determining this target as some kind of average of the existing tax structures. The first question can be approached as a program of domestic tax reforms implying a uniform proportionate convergence of the tax rates in both countries towards a certain common structure H, i.e.: where H is a N-l vector and /3 is a small positive scalar which measures the "size" of the reform. As for the second question, i.e., the choice of the common target to which both countries "harmonize" their taxes, the counterpart of the proposition shown in Keen (1987) refers to the particular class or harmonizing reforms [11] which imply a convergence towards the vector The interpretation of [12] becomes clearer when it is rewritten as: [13] H=<Pt+(INA-<P)T where <P = [rpp + Rpp]'lrpp and is the identity matrix of order N-l, so that (Ip¡_i - <P) = [rpp + RpP]'1Rpp. As shown in [13], His a matrix weighted average of the tax structures in the two countries where the weights depend on local supply responses. In particular, if these local supply responses are identical at the starting position, i.e., rpp = RPp, [13] becomes H= (l/2)(í+7), and each component of His located just midway between the corresponding components of the initial domestic tax structures t and T. Now we can show that the harmonizing reform under examination leads to a welfare improvement: [11] [12] H= [rpp + RppY\rppt + RPPT) 5 Proposition 1: When taxes are levied according to the origin principie, and given any arbitrary initialpositionin which t * T, the harmonizing reform in [11]-[13], consisting in a proportionate convergence towards an appropriate weighted average ofthe existing domestic tax structures, generales a potential Pareto improvement. Proof. The proof runs parallel to that of Keen (1987) and hinges on the fact that [11]-[13] imply: [14] rppdt+ RppdT = OAM whose substitution in [9] gives rise to: [15] du= ±(t'rpPdt+T'RppdT) = ^-{T-tyRPp$(T-t)>0 where the inequality follows from the fact that the matrix Rpp<P= Rpf[rpp + Rpp'\1rpp = Tpi + Rpp}1 is positive definite. Q.E.D. Some intuition on the result can be obtained if we neglect income effects for the nonnumerarie goods, i.e., if e^ = 0p¡.\. Substituting in [8] and using [14] provides dq- OJV-I, so that world consumer prices do not vary. Therefore, the harmonizing reform is designed to leave consumer prices unchanged. As a consequence, world demand, e¿fq,u) + E<fq,U), will not change, as neither will world supply, rp(p) + Rp(P). The only effect of the policy is the "reallocation" of production between countries so that the aggregate welfare loss from distorting taxes is decreased. A graphical explanation is provided in Figure l.4 It shows the simplified case in which the two countries have the same supply schedule for a single taxed good whose consumer world price is q. The excess burden associated with the taxes t and T in each country is given by ABC in country 1 and ADE in country 2. In this case in which supply responses are the same, if the two countries harmonize their taxes at the level (1/2) (t + T) implied by [12], the reduction in excess burden in the high-tax country is BCFG, which exceeds the increase in the low-tax country, DEFG. Since the distances y ¿y and y\y are the same, aggregate supply does not vary. Provided the appropriate intemational transfer is made, one country can improve without the other one experiencing any welfare change. Figure 1 is the eounterpart in the present context of the analysis of harmonization under the destination principie in Keen (1990,1993). I am indebted to Ben Lockwood for suggesting this diagram in his discussion of the paper at the Copenhagen meeting of the HCM research network on "Fiscal Implications of European Integration". 6 3. Tax Harmonization as an Actual Pareto Improvement While the previous section has argued that the harmonizing reform [11]-[13] is welfare improving in the sense that it increases the utility level of a country provided the other country's welfare is kept unchanged, the question that arises is whether this reform may also imply an actual Pareto improvement, i.e., a gain in both countries' utility without any need for an intemational compensation. This is the question discussed in Keen (1989.a) when taxes are levied according to the destination principie under the assumption that the are no income effects for the N-l taxed commodities (i.e., — Equ - 0#_i in terms of the present model). The analysis can now be carried out forcing z = 0 in [2]-[4] and interpreting the N+l variables as N-l consumer prices, q, and two utility levéis, u and U, for given valúes of the tax parameters t and T. Differentiating totally we obtain: [16] e^/iu + EqUdU + Adq + rppdt + RppdT = Oy.i [17] eudu + [eqrp - rppt]'dq + t'rppdt = 0 [18] EudU+[Eq-Rp-RpPT]'dq+T'RppdT =0 1 Using [16] to isolate dq, the effects on welfare, du and dU, associated with an arbitrary reform {dt,dT} are the solution to the system: 5 [19] c« - (eq - rp - rppt) 'A' eq4 - {eq - rp - rppf) 'A EqU - {Eq-RP- RppT)'A'Xeqi Ev-(Eq-RP-RPPT)'A'lEqU_ \dU} = L dU i - t' rppdt + (eq - rp - rppf) 'A' (rppdt + RppdT) T'RppdT +{Eq-Rp- RppT)'A~\rppdt + RppdT) _ We can now assume, as in Keen (1989.a), that there are no income effects for the N-l taxed goods, i.e.: [20] Zqu = Equ=0fí-l so that all income effects are through the untaxed numeraire. This allows one to rewrite [19] as: {eq-rp-rpptyAA [21] eju EudU t' +(eq-rp-rppt)'A~ (Eq-Rp-RpPT)'A 1 T' +{Eq-Rp-RPPT)'A rppdt RppdT Solvins for du we obtain: [22] du = M[t' - (eq - rp - rppt)']AArppdt - (eq - rp - rppt) 'A'lRPPdT} and a similar expression for dU. Focusing on the harmonizing reforms [11]-[13], and recalling that they imply rppdt + RppdT = 0#-i, [22] becomes: [23] du= —{t'St -t'ST) 5 In the particular case of the harmonizing reforms [11]-[13], and using [14], the right hand side in [19] becomes - í 'rppdt , - T'RppdT'] ' - We can observe that adding the expressions for du and dU in [19] we fmd a weighted sum of the welfare changes experienced by both countries: [eu + {rppt + RppT)'Aleq^du + [Ev + (rppt + RPPT)'A'X Eqjj\dU - - (í 'rppdt + T 'RppdT) > 0 where the weights are a (> 0) in [10] and its counterpart A (> 0) for the foreign country. Since this is positive using the right hand side in [15], the harmonizing reform [11]-[13] is welfare-enhancing in the sense that it increases the valué of a social welfare function W = au + AU, i.e., an additive measure of world welfare where the weigths attached to each country are a and A. Actually, this result is not surprising when compared to that in section 2, and the procedure in that section has the advantage of focusing on the role of the intemational transfer dz required for du to be positive for a given valué of U. 8