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 Depa amen o de Teo ía Económica y Economía Polí ica Uni e sidad de Se illa Se illa 9, 10 de eb e o de 1995 PONENCIA The o igin p incipie and he wel a e gains om indi ec ax ha moniza ion. Miguel Ángel LÓPEZ GARCÍA Depa amen o de Economía Aplicada. Uni e sidad Au ónoma de Ba celona. In oduc ion The li e a u e dealing wi h he coo dina ion o economic policies among coun ies o g oups o coun ies in an in eg a ed wo ld s ands ou as one o he mos p ominen de elopmen s o he las ew yea s. Al hough no he only one, a clea applica ion o he esul s eme ging om his li e a u e is associa ed wi h he ax app oxima ion e o s ha ha e been ca ied ou in he Eu opean Union, and, wi hou any doub , he abo e-men ioned de elopmen canno be unde s ood wi hou a e e ence o hese eal wo ld e en s. One o he issues mos ac i ely esea ched has p obably been ha o indi ec axa ion, s imula ed by he Eu opean Comission p oposals aimed a ha monizing alué added axes and excises. In pa icula , some ques ions ela ed o ax compe i ion ha e been analyzed in di e en con ex s [Min z and Tulkens (1986), de C omb ugghe and Tulkens (1990), Sinn (1990), Lockwood (1993), Kanbu and Keen (1993)] as well as he wel a e e ec s o indi ec ax ha moniza ion policies [Keen (1987,1989.a,1989.b), Tu unen-Red and Woodland (1991), Keen and Lahi i (1993)]. The amewo k o he analysis o he impac o ha monizing e o ms has been he des ina ion p incipie, i.e., he p incipie ha in e na ionally aded commodi ies a e axed a he a es o (and he e enue acc ues o) he coun y in which inal consump ion akes place. The al e na i e o he des ina ion p incipie is he o igin, o sou ce, p incipie, unde which commodi ies en e ing in ema ional ade a e axed a he a es p e ailing in he coun y whe e hey a e p oduced ( his being he one which collec s he e enue). Al hough he des ina ion p incipie has been he cen al idea go e ning he ha monizing e o s o indi ec axa ion ha ha e been ca ied ou by he Eu opean Comission, he aboli ion o bo de con ols has ende ed i unsus ainable. The de ini i e sys em, o be enac ed a he s a o 1997, main ains he des ina ion sys em o ansac ions be ween i ms bu c oss-bo de pu chases by indi iduáis will be axed on an o igin basis, hus appea ing as a mixed sys em. The pu pose o his pape is o es ablish a pa allelism be ween he analyses in Keen (1987,1989.a) e e ed o indi ec ax ha moniza ion when axes a e le ied acco ding o he des ina ion p incipie and i s coun e pa when axes a e imposed on an o igin basis. Using a simple wo-coun y model o in ema ional ade i is a gued ha indi ec ax ha moniza ion unde he o igin p incipie, conside ed as a mo emen o domes ic axes owa ds an app op ia ely designed "a e age" ax s uc u e, is po en ially Pa e o imp o ing, in he sense ha he wel a e o a gi en coun y can be inc eased p o ided ha he o he coun y's wel a e is kep unchanged wi h he aid o an in ema ional ans e . In he same ein, i is shown ha i he ini ial posi ion is a Nash equilib ium, he e a e si ua ions unde which he abo e-men ioned 1 e o m may gené a e an ac ual Pa e o imp o emen , so ha bo h coun ies imp o e hei wel a e wi hou any need o a compensa ing in ema ional ans e . As s a ed abo e, he de ini i e sys em will be a mixed one, so ha he pu é o igin case is no he mos ealis ic amewo k om a policy poin o iew. Howe e , i may be use ul in yielding indica ions ha , coupled wi h he esul s ha ha e been ob ained unde he des ina ion p incipie, p o ide insigh s on he e ec s o he de ini i e sys em. In he same way as Keen (1987,1989.a) cons uc s his ha monizing e o m unde he des ina ion p incipie in such a way ha (neglec ing income e ec s) wo ld p oduce p ices a e unchanged, he coun e pa o his analysis unde he o igin p incipie does no a ec wo ld consume p ices. This pa alellism ansla es in o modi ying he common a ge owa ds which coun ies ha monize hei indi ec ax s uc u es, which does no depend on local demand esponses bu on local supply esponses. The s uc u e o he pape is as ollows. In sec ion 1 he basic model is se up. Sec ion 2 conside e ax ha moniza ion as a po en ial Pa e o imp o emen . Sec ion 3 poses he ques ion whe he he speci ic kind o ha monizing e o m being analyzed can also esul in an ac ual Pa e o imp o emen . Sec ion 4 includes some addi ional commen s. 1. The model The basic amewo k is a s anda d model o in ema ional ade [Dixi and No man (1980)] in which wo coun ies, labelled as "home" and "ab oad", ade in N commodi ies. Each coun y's a iables a e ep esen ed by lowe case and uppe case le e s espec i ely, and he e is a single consume in each o hem. The only dis o ions a e due o consump ion axes, le ied on an o igin basis, so ha commodi ies a e axed a he a es p e ailing in he coun y in which hey a e p oduced, his being he coun y which collec s he ax e enue. Since, assuming away anspo cos s, he applica ion o he o igin p incipie implies ha consume p ices in each coun y a e he same, we ha e he ollowing ela ionship be ween consume p ices, q-Q, p oduce p ices in each coun y, p and P, and he ax ins umen s, and T: [1] P = q- P=q-T whe e axes a e exp essed in speci ic e ms.1 1 Since he applica ion o he o igin p incipie implies ha expo s a e axed and impo s a e exemp ed, he home (ab oad) coun y's consume mus be indi e en , in equilib ium, be ween payingp + (P + T) o domes ically- p oduced goodsand P + T (p + ) o impo ed goods. Thus, consume p ices a e equalized ac oss coun ies, i.e., q = Q. On he wo king and consequences o he o igin p incipie see Cnossen and Shoup (1987) and Keen (1990,1993). 2 The home and o eign consume s can be cha ac e ized by hei expendi u e unc ions, e{q,ü) and E(q, U), whe e u and U s and o he u ili y le éis achie ed by he consume in each coun y. Tax e enue is e u ned o he indi iduáis as a lump sum paymen . As o he p oduc ion side, i is assumed ha bo h coun ies beha e compe i i ely, and hei beha iou can be esumed in he e enue unc ions (p) and R(P).2 Since he pa ial de i a i es o he expendi u e and e enue unc ions yield, espec i ely, he compensa ed demand and supply unc ions, he wo ld ma ke -clea ing condi ions o he N commodi ies a e gi en by: [2] e¿q,u) + E¿q, U) = p(p) + Rp(P) whe e he subindices deno e he ( ec o o ) pa ial de i a i es o he ele an unc ions. Consume expendi u e in each coun y equals na ional income a domes ic p ices plus ax e enue. Using he sign' o deno e ansposi ion, he budge cons ain s in each coun y can be w i en as: [3] e(q,u) = (p) + ' p(p) + qxz [4] E(q,U) = R(P) + T'R iP)-qlz whe e ' p(p) and T' R (P) exp ess ax e enue in each coun y. The e m z ep esen s a ans e o commodi y 1 om he o eign coun y o he home one. I s pu pose is o cha ac e ize e o ms en ailing a po en ial Pa e o imp o emen , in he sense ha u can be inc eased o a gi en alué o U. The ole o z is jus ha o assu ing ha he o eign u ili y le el does no change. On he o he hand, z = 0 in [3] and [4] when he ocus is on cha ac e izing an ac ual Pa e o imp o emen , i.e., a si ua ion in which bo h « and U inc ease wi hou any need o an in ema ional ans e . As a ma e o no maliza ion, commodi y 1 is aken o be he nume ai e (so q = 1) and is assumed o be un axed in bo h coun ies (i.e., = T = 0). In o de o a oid excessi e no a ion, ec o p ices will he ea e be in e p e ed as being oiN- dimensión. By Wal as' Law one o he N+2 equa ions in [2]-[4] can be d opped, so we can d op he equilib ium condi ion o commodi y 1. The e o e he sys em in [2]-[4] can be desc ibed as N+l independen equa ions wi h N+l a iables. In he sea ch o a po en ial Pa e o imp o emen he la e a e N-l ela i e consume p ices, q, he home u ili y le el, u, and he size o he in ema ional 2 The e enue (o GNP) unc ion, exp essing he alué o p oduc ion a gi en p oduce p ices (and amoun s o he p ima y ac o s), is ex ensi ely discussed in Dixi and No man (1980, ch. 2). 3 ans e , z, gi en he ax pa ame e s and T as well as he o eign u ili y le el, U. Al e na i ely, in he sea ch o an ac ual Pa e o imp o emen he N+l a iables a e q, u and U and he pa ame e s a e / and T. 2. Tax Ha moniza ion as a Po en ial Pa e o Imp o emen Conside i s ax ha moniza ion as a po en ial Pa e o imp o emen , so ha he policy leads o an inc ease in one coun y's wel a e when i is accompanied by an app op ia e in ema ional ans e o he o he coun y so ha i s wel a e le el is kep cons an . We can hus e alúa e in [2]-[4] he wel a e e ec s in e ms o he home coun y's wel a e, du, o an a bi a y ax e o m, {d ,dT}, coupled wi h he ans e , dz, equi ed o hold U unchanged. Di e en ia ing in [2]-[4] wi h dU = 0, we ha e: [5] eq/iu + [eqj + EC í- pp - Rpp]dq + ppd + RPPdT = 0N.i [6] e,¿lu+[eq- p- pp ydq + ' ppd -dz = 0 [7] [Eq-Rp-RPPT],dq+T'Rppd +dz = 0 whe e is he (N-1)- ec o o ze oes. Thus, elimina ing dz in [6] and [7]: du] = -( ' ppd +T'RPPdT) • dq [ -{ ppd + RppdT) whe e A = + Egj - pp - Rpp, i.e, he ma ix o he de i a i es o he compensa ed wo ld excess demand o he non-nume ai e goods wi h espec o he non-nume ai e p ices, is nega i e semi-de ini e. I will be assumed h oughou ha he e is enough subs i u abili y in demand o p oduc ion be ween he nume ai e good and he o he goods o ensu e ha A will be nega i e de ini e.3 The sys em in [8] allows one o ob ain an exp ession o he change in home u ili y, du, as a unc ion o he e o m associa ed wi h d and dT: -{ ' ppd + T' RppdT) -( pp + RPPT)' -( ppd + RppdT) A whe e: 3 See Dixi and No man (1980, ch. 5). [8] -( pp +RPPT)' 'qu [9] du - 4 [10] a = eu + ( pp + RPPT) 'A^e^ and i can be shown ha a is posi i e whene e an inc ease in he home coun y's endowmen o he i s commodi y, a cons an ax a es and o eign u ili y, implies a s ic po en ial Pa e o imp o emen . We will assume his is he case. The no ion o ha moniza ion is usually aken o mean making he ax sys ems mo e "uni o m". This en ails bo h a p ocess o con e gence owa ds a common a ge and he sugges ion o de e mining his a ge as some kind o a e age o he exis ing ax s uc u es. The i s ques ion can be app oached as a p og am o domes ic ax e o ms implying a uni o m p opo iona e con e gence o he ax a es in bo h coun ies owa ds a ce ain common s uc u e H, i.e.: whe e H is a N-l ec o and /3 is a small posi i e scala which measu es he "size" o he e o m. As o he second ques ion, i.e., he choice o he common a ge o which bo h coun ies "ha monize" hei axes, he coun e pa o he p oposi ion shown in Keen (1987) e e s o he pa icula class o ha monizing e o ms [11] which imply a con e gence owa ds he ec o The in e p e a ion o [12] becomes clea e when i is ew i en as: [13] H=<P +(INA-<P)T whe e <P = [ pp + Rpp]'l pp and is he iden i y ma ix o o de N-l, so ha (Ip¡_i - <P) = [ pp + RpP]'1Rpp. As shown in [13], His a ma ix weigh ed a e age o he ax s uc u es in he wo coun ies whe e he weigh s depend on local supply esponses. In pa icula , i hese local supply esponses a e iden ical a he s a ing posi ion, i.e., pp = RPp, [13] becomes H= (l/2)(í+7), and each componen o His loca ed jus midway be ween he co esponding componen s o he ini ial domes ic ax s uc u es and T. Now we can show ha he ha monizing e o m unde examina ion leads o a wel a e imp o emen : [11] [12] H= [ pp + RppY pp + RPPT) 5 P oposi ion 1: When axes a e le ied acco ding o he o igin p incipie, and gi en any a bi a y ini ialposi ionin which * T, he ha monizing e o m in [11]-[13], consis ing in a p opo iona e con e gence owa ds an app op ia e weigh ed a e age o he exis ing domes ic ax s uc u es, gene ales a po en ial Pa e o imp o emen . P oo . The p oo uns pa allel o ha o Keen (1987) and hinges on he ac ha [11]-[13] imply: [14] ppd + RppdT = OAM whose subs i u ion in [9] gi es ise o: [15] du= ±( ' pPd +T'RppdT) = ^-{T- yRPp$(T- )>0 whe e he inequali y ollows om he ac ha he ma ix Rpp<P= Rp [ pp + Rpp' 1 pp = Tpi + Rpp}1 is posi i e de ini e. Q.E.D. Some in ui ion on he esul can be ob ained i we neglec income e ec s o he non- nume a ie goods, i.e., i e^ = 0p¡. . Subs i u ing in [8] and using [14] p o ides dq- OJV-I, so ha wo ld consume p ices do no a y. The e o e, he ha monizing e o m is designed o lea e consume p ices unchanged. As a consequence, wo ld demand, e¿ q,u) + E< q,U), will no change, as nei he will wo ld supply, p(p) + Rp(P). The only e ec o he policy is he " ealloca ion" o p oduc ion be ween coun ies so ha he agg ega e wel a e loss om dis o ing axes is dec eased. A g aphical explana ion is p o ided in Figu e l.4 I shows he simpli ied case in which he wo coun ies ha e he same supply schedule o a single axed good whose consume wo ld p ice is q. The excess bu den associa ed wi h he axes and T in each coun y is gi en by ABC in coun y 1 and ADE in coun y 2. In his case in which supply esponses a e he same, i he wo coun ies ha monize hei axes a he le el (1/2) ( + T) implied by [12], he educ ion in excess bu den in he high- ax coun y is BCFG, which exceeds he inc ease in he low- ax coun y, DEFG. Since he dis ances y ¿y and y y a e he same, agg ega e supply does no a y. P o ided he app op ia e in ema ional ans e is made, one coun y can imp o e wi hou he o he one expe iencing any wel a e change. Figu e 1 is he eoun e pa in he p esen con ex o he analysis o ha moniza ion unde he des ina ion p incipie in Keen (1990,1993). I am indeb ed o Ben Lockwood o sugges ing his diag am in his discussion o he pape a he Copenhagen mee ing o he HCM esea ch ne wo k on "Fiscal Implica ions o Eu opean In eg a ion". 6 3. Tax Ha moniza ion as an Ac ual Pa e o Imp o emen While he p e ious sec ion has a gued ha he ha monizing e o m [11]-[13] is wel a e imp o ing in he sense ha i inc eases he u ili y le el o a coun y p o ided he o he coun y's wel a e is kep unchanged, he ques ion ha a ises is whe he his e o m may also imply an ac ual Pa e o imp o emen , i.e., a gain in bo h coun ies' u ili y wi hou any need o an in ema ional compensa ion. This is he ques ion discussed in Keen (1989.a) when axes a e le ied acco ding o he des ina ion p incipie unde he assump ion ha he a e no income e ec s o he N-l axed commodi ies (i.e., — Equ - 0#_i in e ms o he p esen model). The analysis can now be ca ied ou o cing z = 0 in [2]-[4] and in e p e ing he N+l a iables as N-l consume p ices, q, and wo u ili y le éis, u and U, o gi en alúes o he ax pa ame e s and T. Di e en ia ing o ally we ob ain: [16] e^/iu + EqUdU + Adq + ppd + RppdT = Oy.i [17] eudu + [eq- p - pp ]'dq + ' ppd = 0 [18] EudU+[Eq-Rp-RpPT]'dq+T'RppdT =0 1 Using [16] o isola e dq, he e ec s on wel a e, du and dU, associa ed wi h an a bi a y e o m {d ,dT} a e he solu ion o he sys em: 5 [19] c« - (eq - p - pp ) 'A' eq4 - {eq - p - pp ) 'A EqU - {Eq-RP- RppT)'A'Xeqi E -(Eq-RP-RPPT)'A'lEqU_ dU} = L dU i - ' ppd + (eq - p - pp ) 'A' ( ppd + RppdT) T'RppdT +{Eq-Rp- RppT)'A~ ppd + RppdT) _ We can now assume, as in Keen (1989.a), ha he e a e no income e ec s o he N-l axed goods, i.e.: [20] Zqu = Equ=0 í-l so ha all income e ec s a e h ough he un axed nume ai e. This allows one o ew i e [19] as: {eq- p- pp yAA [21] eju EudU ' +(eq- p- pp )'A~ (Eq-Rp-RpPT)'A 1 T' +{Eq-Rp-RPPT)'A ppd RppdT Sol ins o du we ob ain: [22] du = M[ ' - (eq - p - pp )']AA ppd - (eq - p - pp ) 'A'lRPPdT} and a simila exp ession o dU. Focusing on he ha monizing e o ms [11]-[13], and ecalling ha hey imply ppd + RppdT = 0#-i, [22] becomes: [23] du= —{ 'S - 'ST) 5 In he pa icula case o he ha monizing e o ms [11]-[13], and using [14], he igh hand side in [19] becomes - í ' ppd , - T'RppdT'] ' - We can obse e ha adding he exp essions o du and dU in [19] we md a weigh ed sum o he wel a e changes expe ienced by bo h coun ies: [eu + { pp + RppT)'Aleq^du + [E + ( pp + RPPT)'A'X Eqjj dU - - (í ' ppd + T 'RppdT) > 0 whe e he weigh s a e a (> 0) in [10] and i s coun e pa A (> 0) o he o eign coun y. Since his is posi i e using he igh hand side in [15], he ha monizing e o m [11]-[13] is wel a e-enhancing in he sense ha i inc eases he alué o a social wel a e unc ion W = au + AU, i.e., an addi i e measu e o wo ld wel a e whe e he weig hs a ached o each coun y a e a and A. Ac ually, his esul is no su p ising when compa ed o ha in sec ion 2, and he p ocedu e in ha sec ion has he ad an age o ocusing on he ole o he in ema ional ans e dz equi ed o du o be posi i e o a gi en alué o U. 8