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1 reearc paper erie Gloaliation an Laour Market Programme Reearc Paper 00/7 Cumulative Cauation, Capital Moility an te Welfare State By H. Molana an C. Montagna Te Centre acknowlege financial upport from Te Leverulme Trut uner Programme Grant F4/BF

2 Te Autor Haan Molana i Profeor of Economic an Catia Montagna i Senior Lecturer in te Department of Economic Stuie, Univerity of Dunee. Acknowlegement We are grateful to Saal Lairi, Peter Neary, Tony Venale, Tierry Verier, participant at te EEA Congre in Lauanne, at te ETSG in Bruel an eminar participant at te Univerity of St Anrew for elpful comment an uggetion. Te uual iclaimer applie.

3 Cumulative Cauation, Capital Moility an te Welfare State y H. Molana an C. Montagna Atract Witin a mall open economy wit vertical linkage, welfare tate policie trigger a virtuou circle of cumulative cauation tat will lea to iger level of economic activity y improving te eploitation of potential aggregate cale economie. Capital moility i typically foun to reinforce ti mecanim an te ue of capital taation to finance reitriution policie i not foun to alter tee concluion. Tee reult, conitent wit te evience tat welfare tate an ta uren ave not ignificantly reuce in OECD countrie, callenge te conventional wiom tat gloaliation unermine government aility to purue income reitriution. Outline. Introuction. Te Moel 3. General Equilirium 4. Te Effect of Welfare Policie 5. No Capital Moility 6. Concluing Remark

4 Non-Tecnical Summary We argue tat a retrencment of welfare tate i not an inevitale conequence of gloaliation. Ti counter te conventional wiom accoring to wic () welfare tate, y itorting firm cot, iner ucceful competition in worl market, an () economic integration reuce national government aility to inepenently ape teir policie. In particular, te creile treat of relocation of capital i een a leaing to a rinking ta ae an to preure to ift te uren of taation on to le moile factor uc a laour, a government compete wit eac oter to attract/retain international invetment. Real worl evience, owever, i omewat at o wit te normative implication of ti conventional wiom. Market integration, in fact, oe not appear to ave le to eiter a reuction of ta uren or to any ytematic retrencment of welfare tate in avance inutrial economie. Accoring to ome, ti can e acrie to te increaing nee for ocial inurance an income reitriution tat reult from internationally generate rik an economic ilocation (te o calle compenation ypotei). In ti paper we ientify te prouction tructure an in particular te eitence of aggregate cale economie a an aitional factor aping te relationip etween ocial protection an gloaliation. Contrary to te conventional wiom, we conten tat economic integration oe not lea to a reuction of te revenue-raiing capacity of government an to a eterioration of firm competitivene. Intea, we ow ow welfare tate policie may complement rater tan e in conflict wit international openne in improving economic performance, tu enancing te aility of government to utain programme of pulic epeniture. Te core of our argument i tat ocial ecurity policie may improve te eploitation of aggregate cale economie. Ti cannel i particularly relevant in mature inutrial countrie were unpreceente ept of iviion of laour reult in ignificant prouction eternalitie, woe acknowlegment i tu eential for any meaningful aement of te utainaility of welfare tate. Te iviion of laour witin te economy i moelle y mean of vertical linkage etween final goo ector an a monopolitically competitive uptream inutry, reulting in aggregate increaing return to cale to te range of intermeiate varietie. In ti contet, imperfectly competitive laour market an capital moility interact wit government policie in affecting market tructure an te availaility of intermeiate, tu influencing te ept of te iviion of laour witin te economy, aggregate efficiency an te pattern of international pecialiation. We ow tat, y enancing te eploitation of aggregate cale economie, a more generou welfare tate trigger a virtuou circle of cumulative cauation tat will increae aggregate welfare regarle of te ta intrument ue to offet te policy ock. Capital moility typically reinforce ti mecanim an te ue of capital taation to finance reitriution policie wic we fin oe not necearily lea to an outflow of capital oe not alter tee concluion.

5 Introuction Ti paper tuie ow welfare tate policie in te form of unemployment enefit affect economic performance in an open economy in te preence of international capital moility an aggregate increaing return to cale. Inutrialiation a een accompanie worlwie y an increae in te ue of fical reitriution. However, uring te 980 an 990, te role of government in te economy a come uner eriou preure. Welfare tate policie in particular ave een attacke for teir itortionary effect on te economy an are often eeme reponile for ig unemployment an low growt rate. Tee concern ave een eigtene y economic gloaliation. On te one an, welfare programme are een a aving an avere effect on firm cot, tu inering teir aility to uccefully compete in gloal market (e.g. Aleina an Perotti, 997). On te oter an, economic integration i perceive a reucing national government aility to inepenently ape teir economic an ocial policie. Te increaing egree of capital moility currently caracteriing te worl economy lie at te core of ti argument. Te creile treat of eit of capital an firm i een a reucing national control over ot volume an tructure of te ta revenue y leaing to a rinking of te ta ae an to preure to ift te uren of taation on to le moile factor uc a laour, a government compete wit eac oter to attract/retain international invetment. Conitently wit te normative implication of ti conventional wiom, attempt to roll ack te welfare tate in wetern emocracie in te lat twenty year wic ave not een limite to centre-rigt government ave often een portraye a an inevitale anwer to te preure of an increaingly integrate worl economy. Two tylie fact, owever, are omewat at o wit ti conventional wiom. Firt, overall uren of taation in avance inutrial economie etween te mi-960 an te mi-990 o not appear to ave ignificantly reuce a a reult of market integration an, altoug laour tae a a proportion of government revenue ave grown fater tan capital taation, te average effective ta rate on capital ave increae in OECD countrie (OECD 996, Balwin R. an Krugman, 000; Garrett an Mitcell, 00; Swank, 00). Secon, no trong evience can e foun tat te increae etent of goo an capital market integration a contriute ytematically to te retrencment of evelope welfare tate (ee for intance, Rorik, 997; Garrett, 998; Swank, 00).

6 Reform ave generally een limite to a retructuring of epeniture an wilt ome area of ocial protection ave moetly ecline, oter ave eperience low growt or taility. Ti can partly e acrie to te reitance attempt to reforming te welfare tate ave met in wetern ocietie. A ome autor e.g. Garrett (998) an Rorik (997, 998) ave pointe out, increaing integration of goo an capital market migt eigten te nee for ocial inurance an income reitriution in repone to internationally generate rik an economic ilocation. More generally, owever, te effect of te gloaliation of market on countrie economic performance an on teir aility to retain control on ometic policie will e ape y a comple et of circumtance, many of wic will e country pecific. Political cientit (e.g. Garrett, 998; Swank, 00) argue convincingly tat te etent to wic te economic an political preure temming from gloaliation are tranlate into welfare tate retrencment epen on te intitutional feature of ot te ocio-political repreentation ytem (e.g. type of electoral an interet repreentation) an te welfare tate (e.g. it egree of univeralim). In ti paper, we ientify te prouction tructure an in particular te eitence of aggregate cale economie a an aitional factor tat contriute to aping te relationip etween welfare tate police an economic gloaliation. Contrary to wat te conventional wiom ugget, we conten tat economic integration oe not inevitaly require a rolling ack of te ytem of ocial protection via a reuction of te revenueraiing capacity of government an a eterioration of firm competitivene. Intea, we ow ow welfare tate policie may complement rater tan e in conflict wit international openne in improving economic performance, tu enancing te aility of government to utain programme of pulic epeniture. Te central iea of our argument i tat ocial ecurity programme may lea to iger level of economic efficiency y improving te eploitation of potential aggregate economie of cale. Ti cannel i particularly relevant in mature inutrial countrie ue to te ig compleity of teir economic ytem tat tem from unpreceente ept of te iviion of laour an reult in prouction eternalitie woe effect on te economy In Acemouglu an Simer (000), unemployment inurance improve te allocation of reource y enaling worker to purue rikier an more prouctive option.

7 3 may not e eaily preicte. We argue tat te acknowlegment of tee eternalitie i eential for any meaningful eate aout te utainaility of welfare tate programme. Te iviion of laour witin te economy i moelle y mean of an input-output prouction tructure werey final goo ector ue intermeiate input prouce y a monopolitically competitive uptream inutry. Te vertical linkage etween ector reult in aggregate increaing return to cale to te range of intermeiate varietie. By allowing for ot final goo an capital to e internationally moile, we contriute to aeing te view tat factor moility poe an aitional treat to te utainaility of te welfare tate. International capital flow, wic are clearly affecte y reitriution policie an teir financing, repreent an aitional cannel troug wic economic policy can influence te ept of te iviion of laour witin te economy an te country pattern of international pecialiation. Te nature of te interaction etween capital moility an fical policy in te preence of increaing return, owever, i not oviou an may give rie to counterintuitive reult. We ow tat, y enancing te eploitation of aggregate cale economie, a more generou welfare tate increae overall welfare regarle of te ta intrument ue to offet te ock. In particular, te effect on aggregate income can e poitive even wen te increae in te welfare ill i finance troug an increae in capital taation tat lea to a capital outflow. We alo fin tat a iger capital ta rate oe not necearily lea to an outflow of capital. Tee fining, wic clearly callenge te view tat capital moility unermine government aility to purue income reitriution, are conitent wit an elp eplain te two tylie fact mentione aove. Te ret of te paper i organie a follow. Section outline te moel, Section 3 ecrie te general equilirium an Section 4 carrie out te policy analyi. Section 5 provie an etenion of te moel an Section 6 raw ome concluion. Te Moel.. Te teoretical framework Since international economic integration i perceive a reucing te economic ie of countrie an teir monopoly power in worl market, we all analye te effect of

8 4 welfare tate policie on economic performance witin a mall open economy framework an aume free international trae an capital moility. Given tat welfare tate are primarily a efining feature of avance inutrial countrie, we all aume tat a i typical of tee countrie our mall open economy a () a government tat purue reitriutive policie finance troug itortionary taation, () unionie laour market, an (3) a prouction tructure caracterie y interectoral linkage tat give rie to aggregate economie of cale. It i now wiely accepte tat a typical implication of inutrial evelopment i te increaing compleity an inirectne of prouction procee, wit final goo ector relying more an more on igly pecialie intermeiate input. We terefore aume an input-output tructure wit one uptream monopolitically competitive inutry an two owntream perfectly competitive ector proucing two omogenou final goo ( Y an Y ). Te output of te uptream inutry (X) come in a continuum of oriontally ifferentiate varietie tat can e tougt of a coniting of igly pecialie proucer ervice an oter intangile input uc a knowlege. Te larger te numer of intermeiate, te iger i te egree of pecialiation in prouction an te reulting aggregate efficiency. Tu, to te etent tat government policie influence market tructure an te availaility of intermeiate, tey will affect aggregate prouctivity, te economy trae performance an te irection of international capital flow... Conumer Te repreentative iniviual, wo i enowe wit one unit of laour upplie inelatically, a utility function U Y Y µ µ µ µ ( µ ) µ ~ ( ξ) V, () For imilar moel ee for eample Rorik (996) an Rorigue-Clare (996). Eiting empirical evience reveal important inter-inutry connection leaing to eternal return to cale in manufacturing (e.g. Caallero an Lyon, 99; Bartelman, Caallero an Lyon, 994). Te teoretical importance of vertical linkage a a ource of economy-wie increaing return to cale a een wiely acknowlege, e.g. Eitier (98), Matuyama (995), Venale (996).

9 5 an i employe if ξ an unemploye if ξ 0. In (), Y (,) are te quantitie conume of final goo an V ~ i te utility of leiure. Contraine optimiation of () yiel te eman function Y Y µ M P, ( µ ) M P, () were P (,) are te price of te two goo an M i nominal ipoale income (to e efine later)..3. Proucer Tere are tree primary input in te economy tat we call laour (L), lan (Z), an capital (K) woe rate of return are repectively enote y w, q, an r. Wilt laour (wic i pecific to te intermeiate ector) an lan are internationally immoile, capital moility i initially allowe for (te implication of relaing ti aumption are icue in Section 5). We all treat K a pyical capital ut, a we all argue, te reult of te analyi woul not e qualitatively affecte y auming K to e uman capital intea. Te owntream inutrie prouce two omogenou conumer goo Y an Y wic are freely trae in worl market an wic we all lael ig-tec an low-tec repectively. Laour i not irectly require a a primary factor in te prouction of eiter goo. Intea, ot commoitie are otaine uing Z, K an a aket X of intermeiate input. For a given et of intermeiate, ot final goo are prouce wit a contant α α return to cale Co-Dougla tecnology ( ) Y α K Z X (,), were 0 < α <, 0 < < an α. It i plauile to aume tat te ig-tec goo i relatively more intenive in te intermeiate an at leat a intenive in capital a te low-tec goo, wic i intea relatively more intenive in factor Z 3. Hence, α < <. α 3 In aition to it tecnological relevance, ti aumption elp limit te comination of poile cae wen etermining te effect of a policy ock. Te reult woul not e qualitatively affecte if we aume capital to e ue mot intenively in te low-tec ector.

10 6 Te intermeiate input, aume to e non-trae 4, conit of a ma N of oriontally ifferentiate varietie tat are aemle into a CES compoite input X i i, i N were i i te quantity of a typical variety i an i te elaticity of utitution etween varietie. We aume >, wic mean tat no ingle variety i an eential input per e. Ti CES tecnology implie tat tere are increaing return to te range of availale varietie, ince te prouctivity of te intermeiate aket rie in N. Alo note tat te increae in te average prouctivity of te intermeiate temming from a given increae in N will e iger te maller i. Te intermeiate varietie are prouce y an enogenouly etermine (via free-entry an eit) ma of ientical firm. Te eitence of a fie prouction cot, y giving rie to internal increaing return to cale an to an incentive to pecialiation, lea to a one-toone correponence etween te ma of firm an tat of availale varietie. Laour i te only factor of prouction, ue a ot fie an variale input. Te laour requirement of a typical firm i i l δ γ, (3) i i were δ >0 an γ >0 are te marginal an fie input coefficient. Te firm profit i π p w l, (4) i i i i i were workforce. i an p i are te firm output an price an w i i te wage rate it pay it Te price ine for te intermeiate varietie, ual to te CES aket efine aove, i P pi i. (5) i N Given te owntream ector prouction tecnology, te minimum total cot of proucing Y i 4 Te non-traaility of intermeiate i commonly aume in te literature to capture te importance of geograpical proimity of te intermeiate ector to final goo inutrie (e.g. Rorigue-Clare, 996, an Rorik, 996). Note, owever, tat in te preence of inter-ectoral linkage, ti aumption oe not imply tat uptream ector proucer are iele from international competition.

11 7 C α ( r q P ) Y,,. (6) Since tee two inutrie are perfectly competitive, teir prouction level i etermine y te equality etween price an average cot: P r q. (7) α P Te mall open economy an free trae aumption imply tat final goo price are etermine in worl market. Te contant return to cale tecnology an te perfect competition aumption imply tat input eman in te two final goo inutrie are X Z K Y Y α Y P, P P, q P. r, (8) Finally, a ytem of eman equation for te varietie of te intermeiate goo y owntream proucer can e otaine, given (5), y applying Seppar Lemma to (6): ( X X ) pi i. (9) P.4. Factor market In te market for lan an capital, wic are aume to e perfectly competitive, factor price (q an r) aut to atify te market clearing reource contraint: Z Z Z, (0) K K K K, () were Z an K are te economy enowment of tee factor. Wit capital moility, te tock of availale capital can iffer from te country enowment y an amount tat enote te capital inflow/outflow. K Te laour market in te intermeiate ector i unionie, wit union aving monopoly over wage an firm etermining employment level 5. We aume tere to e J ymmetric 5 Te laour market i moelle a in Aleina an Perotti (997).

12 8 union, wit a large (mall) J inicating a large (mall) numer of mall (large) union. A typical union emrace te worker of an et te wage for a ma of firm N N/J an will terefore ave a ma of memer L L / J, were L i te total laour enowment of te country. Hence, w w. Note, tat alternatively an equivalently, one coul i N tink of te union tructure a coniting of a ma N of firm pecific union groupe in a icrete numer J of cluter of union, wit union witin eac group etting te cooperative wage for te N/J firm tey cover an eaving non-cooperatively wit repect to te oter cluter. Wit unioniation, laour income tae will ave itortionary effect on te economy even if te iniviual laour upply i perfectly inelatic, ince union will tranfer part of te uren of taation on to employer via iger wage. Te egree of itortion, owever, i known to epen on te intitutional etting of te laour market 6. Ti i ecaue renteeking union face a trae-off etween te eploitation of firm monopoly power (wic work in te irection of iger wage), an te acknowlegement of te negative eternalitie of iger wage on employment an real ipoale income (wic generate incentive for wage retraint). A teir ie an/or te egree of coorination of teir action increae, te etent to wic union internalie te effect of teir wage eciion on te macroeconomic contraint rie. To capture te fact tat union eaviour cange a tey ecome larger an/or more coorinate, we follow Aleina an Perotti (997) an conier two icrete cae, wic we all refer to a te non-internaliation an internaliation. In te firt cae, te numer of union i ufficiently large an te typical union i ufficiently mall for it not to internalie te conequence of it action for te government uget contraint. In te econ, te numer of union i ufficiently mall an te typical union i ufficiently large for it to internalie te conequence of it action for te government uget contraint. In ot cae, union will take into account te effect of teir wage etting eciion on te intermeiate inutry price ine. Unioniation implie tat involuntary unemployment perit in equilirium an tat eac union will ave ome unemploye memer 7. Te oective function of a typical union can e otaine from () an i given y te epecte utility of it typical memer, 6 7 See, for intance, Calmfor an Driffill (988); Summer, Gruer an Vergara (993) an Rama (994). We follow te literature in auming tat unemploye worker from oter union cannot e employe in a

13 9 V L L ( τ ) w L L L L P L P L ~ V, () were L i te union employe memerip, µ µ P i te conumer price ine, τ P P an are repectively te laour income ta an te unemployment enefit rate. Te latter, wic we aume not to e tae, i a net tranfer. A we all eplain later, te union will cooe w to maimie () uect to te relevant contraint..5. Government Te government provie welfare protection in te form of unemployment enefit, finance troug te taation of te primary factor income. We ue te ource principle a a ta rule, o tat income generate y te inflow of capital i tae efore it i repatriate. Noting tat L J L L J L, te government uget contraint i terefore given y: ( L L) J ( L L ) J τ w L ρ r( K K ) φ qz, (3) were φ an ρ are repectively te lan an capital income ta rate. Finally, aggregate income (M) i etermine y total return to primary factor an tranfer etween te pulic an private ector 8 : M J [( τ) w L ( L L )] ( ρ) rk ( φ qz ). (4) 8 given union ector efore te latter unemploye memer are ire. Equation (3) an (4) reflect te aumption tat K i pyical capital. Were K to repreent uman capital (e.g. kille laour), te return to te factor woul e pent were it i locate. It i traigtforwar to ow tat, given our mall open economy aumption, treating K a uman capital (an auming tat perap ue to it international moility it i not unionie) woul not ave any qualitative effect on te reult (te only effect eing a ift in income rougt aout y te nonrepatriation of te return to te factor).

14 0.6. Foreign ector S S Te alance of payment equation i P ( Y Y ) P ( Y Y ) ( ρ ) rk 0. Auming perfect utitutaility an full moility of capital, aritrage in te international capital market enure tat te interet parity conition ol ( ) r r ρ, (5) were te left-an-ie i te net of ta ometic interet rate an te rigt-an-ie i te (eogenou an net) foreign rate of interet. 3 General Equilirium Given equation (3), (4) an (9), an taking a given te wage et y te union, te optimal price rule for a typical firm i covere y union will e given y pi N p δ w. Aopting for implicity te normaliation δ, firm optimal price etting rule can e written a p w. Equilirium wage are etermine y te monopoly union. In te non-internaliation cae te typical union maimie () uect to te laour eman function it face, given y L i l i, an taking account of (3), (5) an firm mark-up rule p w. In te N i internaliation cae, in aition to te aove, te union alo take into account te government uget contraint in (3). Note tat in maimiing teir oective function union take te ma of firm an te government policy variale a given, wic i equivalent to auming tat entry into te inutry an te government coice of policy intrument occur prior to union etting of wage. Denoting te non-internaliation an te internaliation of te government uget contraint wit te upercript NI an I repectively, te correponing wage etting equation tat reult from union optimiation in te two cae will e w NI ~ PV ( τ ) ε, (6a)

15 w I ~ PV ε. (6) Te numerator in (6a) an (6) give te repective reervation wage an ε L w w L i te wage elaticity of laour eman facing a typical union an provie an invere meaure of it monopoly power. It can e own tat ε ε ( ) / J (ee te Appeni A.) from wic follow tat uner eac unioniation regime, w w. 9 Te mark-up over te reervation wage, ε /( ε -), i negatively relate to ε an terefore fall in J. Hence, ceteri pariu, a union ecome larger, teir monopoly power an teir wage eman increae. In (6a) te wage rate i poitively relate to ot te ta an unemployment enefit rate. A ceteri pariu increae in τ, y reucing te after ta wage, inuce te union to i up te nominal wage. A iger y reucing te utility ifference etween eing employe an unemploye allow te union to increae teir wage eman. However, wen union are large enoug to internalie te effect of teir action on te government uget contraint te wage i inepenent of ot income ta an unemployment enefit rate. It follow tat, for a given J, w I < w NI alway ol. More generally, if a i plauile te numer (ie) of union i maller (larger) in te internaliation tan in te nointernaliation cae (i.e. J I <J NI ), ten w I < w NI if τ an are ufficiently large. Note tat letting J an ε, te wage in equation (6a) wic ecome inepenent of J ten to it lower oun ( w ). It i traigtforwar to ow tat ti limiting cae correpon to te very ecentralie ituation in wic union are o mall tat tey even iregar te effect of teir action on te inutry price ine. It ten follow tat our moel conform wit te umpe-ape relationip etween te wage rate an te egree of wage etting centraliation foun in te literature, ecaue w< w NI an te latter, wic rie wit union ie, i typically larger tan w I. 0 9 Note tat union firt orer conition are erive efore impoing ymmetry etween union wage. 0 Te umpe-ape relationip etween te egree of ometic coorination an wage level i own in te literature to e flattene y foreign competition, ecaue te more open i te economy te lower will e te impact on conumer price ine (CPI) of ometic wage cange, given tat te latter will e more eavily epenent on foreign price. In te limit, a in te mall open economy wit free trae µ µ icue in ti moel, te CPI, P P P, i fully eogenou. A a reult, te relationip etween

16 Note tat te ymmetry of wage in equilirium (i.e. w w ) implie tat p p. Hence te optimal price rule will e for all firm to et p w. (7) In te free-entry equilirium, eac firm will reak even. Sutituting from (3) into (4), etting te reulting equation equal to ero an uing (7) an te normaliation δ, we otain te equilirium output cale of a typical firm in te intermeiate goo inutry, wic, in te ymmetric equilirium, will e γ, (8) wic i contant an oe not epen on market ie. Ti i ue to te contant elaticity of utitution aumption an te lack of trategic interaction etween firm, werey te etent to wic eac firm eploit internal increaing return to cale epen only on te elaticity of utitution etween varietie. Hence, cange in te ie of te market o not affect te mark-up an te optimal output cale of firm ut only work troug cange in te prouct range N. Te general equilirium of te moel ecrie aove conit of te following equation were (5), (6a) an (6) are repeate for convenience: ( ) r r ρ, (5) eiter or ~ PV w NI, (6a) ( τ ) ε ~ PV w I, (6) ε P ( P P ) r, (9) q ( P P ) r, (0) wage an union power an egree of internaliation coul even e monotonic. To ee ti recall tat w NI < w I i poile for certain value of τ,, J NI an J I. By Walra law, te alance of payment equation can e otaine from (3), (4) an te oter market equilirium conition.

17 3 P N w, () L γ N, () P X wl, (3) r ( K K ) qz P X, (4) ( K K ) φqz ( L L) τ wl ρ r. (5) Equation (9) an (0) are otaine y rearranging (7), were ( α α ) ( α α ) / <0, / >0, an >0; () i otaine from (5) an (7) in te ymmetric equilirium; () i te total laour eman otaine y aggregating (3) an (8); (3) i te ero profit conition otaine y etting te aggregate verion of (4) equal to ero; (4) i te overall reource contraint otaine y eliminating Y an Y from (8), (0) an () (ee Appeni A.); an (5) i te government uget contraint in (3). For given parameter (α, α,,,,, γ, ) an eogenou variale ( Z, K, L, P, P, r,, V ~, ε, J), te aove equation can e olve to etermine te enogenou variale q, r, w, P, K, L, X, N, an one of te ta rate τ, ρ, or φ wic te government will allow to vary to alance it uget. For implicity, let φ e te enogenou ta rate. It i ten eay to ow tat te moel can e olve recurively: w an r are etermine y (6) an (5), an (9)-(5) ten etermine q, P, N, L, X, K an φ in tat orer. Before analying te conequence of a move to a more generou welfare ytem, it i ueful to igligt te main caracteritic of te working of ti economy y coniering te effect of an eogenou increae in te wage rate (e.g. ue to a fall in J) an auming for implicity tat φ i te enogenou ta rate. Given te mall open economy aumption, for a given ρ, te interet parity conition an te eogeneity of final goo price imply tat r, q, an P are ultimately etermine regarle of te ret of te moel ee equation (5), (9), (0). It follow from equation () an () tat ceteri pariu increae in te wage rate are aociate wit a larger ma of firm an a iger aggregate employment, a long a ecee unity an i finite.

18 4 Te poitive relationip etween te wage rate an te numer of firm an employment i not intuitively oviou an critically ret on te eitence of increaing return to te range of availale intermeiate wic implie tat te equilirium ma of varietie (an firm) may e u-optimal. In tee circumtance, a iger wage may contriute to alleviating market inefficiencie. For a given ma of firm N, te immeiate impact of an increae in w will e to raie te marginal prouction cot in te uptream ector. Firm in te ector will react y auting price upwar. A a reult, te inutry price ine P will initially go up, leaing in ot final goo ector to a utitution away from X an towar K an Z, ence eerting an upwar preure on tee factor price an leaing to an incipient inflow of capital. On te wole, ti firt effect will entail lower profit for intermeiate proucer an will clearly work towar a reuction of te ma of firm in te inutry. However, te iger wage will alo crucially imply a iger ipoale income tu triggering an aggregate eman effect tat i eentially Keyneian in nature. By timulating conumption of final goo, te iger wage will lea to a iger eman for all factor of prouction. In particular, te iger eman for X will foter entry into te uptream ector an contriute to counteract te avere effect of te increae in firm marginal cot on te ma of availale varietie. Te furter increae in te eman for K (an Z) y trengtening te upwar preure on te ometic interet rate will reinforce te capital inflow until te interet parity conition i retore. Te larger capital tock will in turn increae te marginal prouct of te oter factor, tu ooting te eman for X. Te overall effect of tee force will e a net increae in te eman for te uptream goo, a larger ma of firm in te inutry an a eeper iviion of laour witin te economy. A a reult of te epanion in te range of intermeiate, average prouction cot will ecline in ot owntream inutrie ut particularly o in te prouction of Y wic i relatively intenive in te intermeiate input. Reource will ift from te lowtec to te ig-tec ector, ut te contraction of te former will releae le intermeiate (an le capital, if te ig-tec goo i alo relatively intenive in capital i.e. if α /α >) tan te ig-tec ector require at te given factor price. Te ece eman See for intance Devereu, Hea an Lapam (000).

19 5 for X an K implie furter entry of firm in te uptream inutry an of capital into te country. In um, te original wage ock will reult in a virtuou circular cauation proce of riing eman for intermeiate, entry of new firm into te uptream ector, an increae pecialiation in te ig-tec goo tat will amount to an increae in te level of economic activity, i.e. iger employment in te uptream ector an iger output of intermeiate an final goo. Since w NI >w I typically ol, te poitive relationip etween w an N implie tat te ma of firm an aggregate employment will e larger wen union o not internalie te government uget contraint. 4 Te effect of welfare policie Ti ection analye te policy multiplier reulting from an increae in te rate of unemployment enefit, wen ifferent ta intrument are ue to offet te implication of te policy ock for te government uget contraint. In all cae we conier te two type of unioniation icue aove. e e It i analytically convenient to tart from an initial equilirium in wic K Y Y 0, were e Y an Y e are te ece upply of te ig-tec an of te low-tec goo repectively (ee Appeni A3). It i eay to ow tat tee initial conition o not qualitatively affect te reult. All multiplier ave een erive analytically (ee Appeni A5-A6 for etail). For epoitional implicity in wat follow we all concentrate on te main qualitative effect of an increae in unemployment enefit finance via cange in te taation of one of te primary factor of prouction. In te ummary tale elow, te firt column give te ta intrument ue (ητ,φ,ρ).

20 6 4.. Union o not internalie te government uget contraint Tale elow ummarie te reult for te cae in wic union o not internalie te government uget contraint. Wen te ock i offet uing te ta rate on one of te immoile factor, a rie in te rate of unemployment enefit will unamiguouly increae te equilirium wage, te range of intermeiate varietie (i.e. te ept of te iviion of laour), an te country income, an will typically lea to a iger egree of pecialiation in te ig-tec goo. Te policy will alo unamiguouly reult in a capital inflow. To eplain tee reult recall tat a icue in te previou ection te general equilirium of te moel implie tat any eogenou ock tat raie w will increae N, L an X an can alo lea to a capital inflow, if te rigt an ie of (4) rie ufficiently. It follow tat te poitive relationip etween w an in equation (6a) implie tat a iger unemployment enefit rate will reult in a iger level of economic activity. Ti i ecaue in te preence of vertical linkage etween ector, te policy ock y timulating aggregate eman trigger a virtuou circle of iger eman for intermeiate an iger aggregate efficiency. Effectively, terefore, income reitriution from employe to unemploye factor contriute to alleviating te market inefficiencie tat reult from te poitive eternality of te ma of firm in te inutry, tu leaing to an increae in income. Moreover, if te potential aggregate cale economie are ufficiently trong (i.e. i mall), te offetting of te policy ock on te government uget contraint will entail a reuction rater tan an increae in te enogenou ta rate. Tale Qualitative effect of an increae in in cae (NI): non-internaliation () Ta rate ue η w N X L K M Y e q P r WB η τ () (3) φ () (4) ρ (5) (6) (3) (3) () See Appeni A5 an A6 for erivation an analytical epreion. WB i te total unemployment enefit ill an Y e i te ece upply of goo.

21 7 (6) () (3) (4) (5) Te neceary conition for a poitive ign i tat te propenity to conume Y i ufficiently mall. See Appeni A6.. an A6.. for etail. A poitive ign i otaine if an (or) τ are ufficiently mall. See Appeni A6.. for etail. A poitive ign i otaine for ufficiently mall value of. See Appeni A6.. for etail. Tee ign are otaine y numerical imulation wit plauile caliration (ee Appeni A6 for initial value an plot of te multiplier). Ti multiplier can e negative for ufficiently mall value of. Wen te government offet te policy ock y increaing te ta rate on te moile factor, a capital outflow may occur. Figure in te Appeni illutrate te main effect of te ρ-finance policy grapically. Altoug te firt part of te autment proce i unaltere, te immeiate increae in ρ require to finance te policy may lea to a capital outflow tat may more tan compenate te initial inflow. Ti i more likely for mall value of, wen a ig monopoly power of firm implie tat, in repone to te increae in te eman for X, entry will e limite an a mall increae in N will lea to a relatively large increae in te prouctivity of te intermeiate (i.e. to large reuction in P ). A a reult, relative to a ituation caracterie y a larger value of, te etent of factor utitution towar te intermeiate input will e iger, tu limiting te increae in te eman for an te reulting inflow of capital. However, we fin tat for mot parameter value te increae in y triggering te virtuou circle of iger wage, entry into te intermeiate inutry an iger income will lea to a reuction in te ta rate on capital an to a capital inflow, tat will terefore reinforce te poitive proce of cumulative cauation. In ummary, our reult ow tat regarle of te ta intrument ue, a more generou welfare tate (note tat WB will typically increae epite te fall in unemployment) can lea to a iger welfare an to a capital inflow, even in toe circumtance in wic capital flow out of te country a a reult of an increae in it ta rate. 4.. Union internalie te government uget contraint Wen union are large enoug to internalie te link etween taation an unemployment enefit, te wage rate et y eac union, given y equation (6), will not e affecte y te increae in. Te policy multiplier are ummarie in Tale elow.

22 8 Tale Qualitative effect of an increae in in cae (I): internaliation () Ta rate ue η w N X L K M Y e q P r WB η () () (3) (4) τ φ ρ (4) 0 () () () (3) () () () () See Appeni A5 an A6 for erivation an analytical epreion. WB i te total unemployment e enefit ill an Y i te ece upply of goo. Te ufficient conition for ti multiplier to e poitive i >. See Appeni A6..3 for etail. A poitive ign i otaine if i ufficiently large. See Appeni A6..3 for etail. Tee ign are otaine y numerical imulation wit plauile caliration (ee Appeni A6 for initial value an plot of te multiplier). Wen te government offet te policy ock y canging te ta rate on any of te immoile factor, tere will e no effect on te economy. Uing ρ, owever, will irectly impinge on te availaility of capital in te country an, ecept for te wage rate tat oe not cange, te typical effect of te policy on te ept of te iviion of laour an on aggregate income are qualitatively te ame a in te non-internaliation cae. A ρ increae to finance te policy, a net capital outflow will occur (ee Figure in te Appeni). Te fall in K will increae te ometic interet rate an foter factor utitution towar X an Z. Te iger eman for X will trigger te virtuou circle of entry an iger aggregate efficiency icue aove, wic will lea to an increae in iger income an to a larger ig-tec ector. Ti will in turn raie te eman for K (more o if te ig-tec ector i alo relatively intenive in K) tu putting an upwar preure on te interet rate. For mot parameter value, owever, te increae in interet rate i not ufficient to offet te effect on K of a iger ρ. Hence, wen union internalie te ugetary effect of welfare tate policie, wilt taation of immoile factor oe not affect economic performance, capital taation can ave a poitive impact on te country income an on te etent of pecialiation in te ig-tec ector, epite te fact tat a net capital outflow i likely to occur. It may e note tat in ti latter cae, te force at work are qualitatively ientical to tat icue

23 9 in te previou u-ection, ut te etent of te final autment i weakene y te fact tat te wage rate i unreponive to cange in te policy variale A ummary of te reult Our reult o far ugget te following. Firt, y increaing te uptream ector general equilirium wage, a iger welfare protection will eepen te iviion of laour witin te economy an raie ot aggregate income an te etent to wic te country pecialie in te ig-tec ector 3. Wen te government finance te policy y taing immoile factor, ti virtuou circle i unamiguouly reinforce y a capital inflow tat increae te eman for te intermeiate goo an it may trengten te ift of reource towar te ig-tec goo to te etent tat te latter i more intenive in te ue of capital. Hence, contrary to te commonly el view, capital moility (an te enuing rinking of te ta ae) oe not necearily iner te ue of reitriution policie. Secon, te ue of capital taation to offet te policy ock oe not utantially alter te aove reult. A iger unemployment enefit, y leaing to an increae in aggregate efficiency will improve welfare even wen te larger ta rate on te return to capital lea to a capital outflow. A iger capital taation, owever, oe not alway caue a capital outflow: a net inflow may occur tat will reinforce te virtuou circle icue aove. On te wole, our fining cat out on te conventional wiom icue in te introuction. 5 No capital moility Te analyi ugget tat capital moility enance te virtuou circle temming from aggregate cale economie an tu increae te poitive impact of welfare tate policie on economic performance. In orer to gain more inigt into it role, we now aume tat capital i internationally immoile. Te capital market reource contraint in () will now e given y K K K. ( ) Te equilirium propertie of te moel are icue in Appeni A4. It i teiou ut traigtforwar to ow tat in ti cae te eitence of a poitive relationip etween unemployment enefit an te ept of te iviion of laour witin te economy i not unamiguou. A ufficient conition for N/>0 can e foun tat require te elaticity 3 Clearly, te epanionary effect of te policy reuce a te economy laour reource contraint tigten.

24 0 of utitution etween intermeiate varietie not to e too large (ee Appeni A6.). In oter wor, witout capital moility, regarle of te ta intrument ue to finance te policy ock, an increae in unemployment enefit will e more likely to ave poitive welfare effect te tronger i te etent of aggregate cale economie, i.e. te maller i. Tee reult confirm tat factor moility nee not poe a treat to te utainaility of te welfare tate an it migt actually trengten government aility to finance it. Ti i ecaue, y relaing te reource contraint in te economy, capital moility reuce te critical level of aggregate increaing return at wic a poitive link etween welfare tate policie an te ept of te iviion of laour witin te economy occur. 6 Concluing Remark Ti paper a eamine te role of economy-wie increaing return to cale in aping te relationip etween welfare tate policie an economic performance in a worl wit free trae in final goo an international capital moility. Contrary to te conventional wiom, we fin tat a retrencment of welfare programme i not an inevitale conequence of economic integration. Intea, y improving te eploitation of aggregate cale economie, ocial inurance policie an international openne may complement eac oter in increaing welfare. Tee fining wic are conitent wit an elp eplaining te evience tat goo an capital market integration a not le to ignificant reuction in welfare tate an ta uren in OECD countrie crucially ret on te imperfectly competitive nature of te laour market an of te intermeiate ector of te economy. In te former, unioniation reult in equilirium wage eing increaing in te unemployment enefit an income ta rate. In te latter, monopolitic competition lea to te emergence of increaing return to te range of availale varietie. A a reult, te epanionary effect of unemployment enefit an iger wage trigger a virtuou circle of entry in te intermeiate ector, iger aggregate prouctivity, an iger income. We ave own tat ti virtuou circle i typically reinforce y capital moility. Unioniation play an important role in te tranmiion mecanim etween government policie an economic performance. Our reult are roaly conitent wit te relationip etween union monopoly power an egree of itortion of taation foun in te literature. However, a funamental ifference i tat a iger egree of itortion reulting

25 in a iger wage oe not in our moel imply a worening of economic performance. On te contrary, it i wen union are trong enoug to raie wage ignificantly ut are not large enoug to internalie te government uget contraint tat an epanion of te welfare tate will ave a larger poitive effect on aggregate welfare. Ti i ecaue union rent-eeking activity contriute, y increaing income, to trigger a virtuou circle tat reuce te market failure aociate wit te u-optimal proviion of intermeiate varietie. Ti reult eerve cloer crutiny ecaue it appear to counter te common perception tat larger welfare tate are typical of corporatit countrie were encompaing union y ecanging wage moeration for ocial protection limit te itortionary effect of taation. Our teoretical reult can e taken to ugget tat prouction eternalitie affect te impact of ifferent laour market intitution on economic performance. Since tere eit evience (e.g Caallero an Lyon, 990) tat countrie eiit ifferent egree of eternal economie of cale, a fruitful line for future reearc will e to tuy empirically ow eternal economie affect te relationip etween openne an te ie of te pulic ector. It i important to tre, owever, tat unioniation i not neceary for tee reult to emerge. Any form of laour market imperfection (e.g. efficiency wage) giving rie to a poitive link etween wage an policy intrument will lea to imilar concluion. It i of coure alo true tat welfare tate policie are not te only way y wic government may trigger te virtuou proce of cumulative cauation ecrie aove. One leon of economic policy i tat intervention oul e applie a cloely a poile to te eire target. So, given tat in ti cae te market imperfection conit of a uoptimal prouction of varietie, inutrial policy may well e more effective in correcting te itortion. Ti conieration, owever, oe not imini te relevance of our analyi. Te welfare tate a playe a pecific ocial an political role in avance inutrial economie an attempt to retrenc it are eing met y oppoition an may terefore reult in a ackla againt trae an capital market lieraliation. It i terefore relevant to ae te etent to wic openne an ti type of policie are incompatile. Our reult ugget tat ti nee not e te cae. Finally, we woul like to point out tat tee concluion are not qualitatively epenent on te pecific moel et up of te paper. A we ow in Molana an Montagna (00), te

26 funamental force at work in aping te relationip etween welfare tate policie an economic performance are not altere if we rela te aumption of a mall open economy, te non-traaility of intermeiate an te aence of unioniation in final goo ector.

27 3 Appeni A. Derivation of te wage elaticity of laour eman,, in equation (6) Union laour eman i i N L i i N l i. Union take account of firm mark-up rule p w an eploit te ero profit conition wic implie l i i were X p i i, i N, an P P Tu, i taken a given y te union. X PY P Y L w i pi i P pi i p w P p w i N i i. (A.) Noting tat pi w i p i i, p i i ( ), te mark-up rule p i w an ence i P P, we otain from (A.) L w l p P i i ( ) i w P. (A.) p i N i In te ymmetric equilirium internaliation (I) cae P p i L N li. In ot te non-internaliation (NI) an te J i evaluate y partitioning P in equation (5) a P pi i i N i N p i i wic implie tat P p i i N p P i. In te ymmetric equilirium, te latter can e written a P p i N J p P an te price ine will e given y P N pi. Tee are ue in (A.) to otain L w L w an ence ε - ( - )/J for ot cae J (NI) an cae (I). Te only ifference i terefore ue to te numer of union wic i muc maller in cae (I).

28 4 A. Derivation of te overall reource contraint, equation (4) Uing (8), (0), () an noting tat X X X, we otain te following tree reource contraint:.,, Y r P Y r P K K K K Y q P Y q P Z Z Z Y P P Y P P X X X α α (A.) Solving te firt two equation for Y an Y yiel, qz P X Y P, (A.) an X P qz Y P. (A.3) Sutituting tee into te tir equation yiel te overall reource contraint, ( ) X P qz K K r α α α α (A.4) wic i equation (4) in te tet were we ave efine parameter ( ) α α / <0, ( ) α α / >0, an >0 (te ign ol wen α α < < ). Ti equation impoe a retriction on te value of te tree factor an, regarle of te tructure of factor intenitie, oul ol for all Y an Y. A3. Calirating te moel at te initial equilirium. Te moel conit of equation (5), (6) an (9)-(5) an te efinition of total income an te egree of pecialiation in trae meaure y te ece upply of te ig-tec goo. Total income i given y equation (4) wic, upon utitution from te government uget contraint in (3) yiel rk qz rk wl M ρ, (A3.) Te ece upply of te ig-tec goo i e PY PY Y P wic, upon utitution from (A.) an equation () yiel

29 5 ( P X qz )/ µm e P Y. (A3.) For eae of comparion, we calirate te moel at an initial equilirium correponing to te autarkic economy were e e K 0, Y Y Y ) 0, an Y Y Y ) 0 aume tat te ta rate are initially equal, ( e K 0 an Y Y Y ) 0 wit K ck ( (. We alo τ ρ φ. It can e own tat replacing an e Y ( Y Y ) ρ rck will not cange te reult (c i ome contant an te latter equation i otaine from te alance e of payment equation in wic Y Y Y ) 0 an P ince goo i te numeraire). ( Uing tee initial value, we can olve equation (3)-(5) an (A3.) an (A3.) to otain were P X wl qz ψ wl rk ξ wl ( L L) τ ( ξ ψ ) wl M ( ξ ψ ) wl ψ µ µ ( µ ) ( µ ) >0 an ξ µα µ ( µ ) α ( µ ) >0. Finally, we let te enefit rate to e et at te reervation wage, i.e. w NI, or ( τ ) ε (A3.3) ~ PV, wic yiel: w I. (A3.4) ε A4. Equilirium propertie of te moel wit no capital moility. In ti cae te moel i equivalent to equation (6) an (9)-(5) were K 0 i impoe. Te relationip etween w an N in ti cae can e otaine a follow. We olve equation (9)-() an et P (treating goo a te numeraire) to otain an equation for q in term of N an w, q P wn, (A4.) We alo olve equation (3)-(5) to otain an equation for q in term of wl, ( L L) ( τ ρ ) wl q. (A4.) ( φ ρ ) Z

30 6 Equating te rigt-an-ie of (A4.) an (A4.) yiel c wn ( L L ) ( τ ρ ) wl (A4.3) c φ ρ ZP > were ( ) 0 an >0. Noting tat from () LγN, (A4.3) give a relationip etween w an N wic oul ol in equilirium. Differentiating (A4.3) totally, taking account of () an letting ρ τ yiel N w N w c wn c wn ( L ( ) τwl) ( ) τwl Te enominator of te aove i alway poitive. Uing (A4.3) an taking account of te caliration in (A3.3), te conition for te numerator to e poitive i (( ψ ξ) ( )) ( ) > 0 τw Finally, we can ue (A3.4) to replace (/w) in te aove epreion, for eac cae (NI) an (I), an otain te conition tat te parameter (,, ξ, ψ, ), te union ie, an te initial ta rate τ oul atify wen igning te multiplier erive elow. A5. Lineariing te equation of te moel. Starting from te initial equilirium ecrie aove, we tuy te qualitative effect of a cange in finance y one of te ta rate. For implicity, wenever poile, we linearie te moel in term of proportional cange in variale. In te following, a cange an a proportional cange are enote y a ot an a at (^) over a variale repectively. Totally ifferentiating equation (5), (6), (9) to (5), (A3.) an (A3.) we otain ρ r ρ r ρ. (A5.) ητ η w ε ητ P r q r ( ητ ) w τ 0 (A5.) (A5.3) (A5.4)

31 7 N w P L N X w L P rk& τwl (A5.5) (A5.6) (A5.7) (A5.8) r( K K ) r ( qz ) q ( P X )( P X ) ( ) ( τ w L φ qz φ q ) ρr( K K )( ρ r ) ρrk& LL ( L L) 0 M & wl ( L w ) rkr qzq ρrk& P X ( P X ) qzq M& & e µ P P Y Tee equation are olve to erive te policy multiplier. (A5.9) (A5.0) (A5.) A6. Te policy multiplier ue to a cange in. For eae of epoition, were poile we preent te proportional cange rater tan te cange. Recall tat a cange an a proportional cange are enote y a ot an a at (^) over a variale, repectively. WB enote te welfare ill, WB ( L L) an in all te epreion τ i te initial ta rate, given tat initially all ta rate are et equal, i.e. ρφτ. Finally, ue to te compleity of igning te multiplier in ome cae we ave reorte to numerical imulation. In tee cae, we ave given te tree imenional grap wic plot te multiplier againt te crucial parameter an τ, uing te following caliration: α 0.3; µ 0.5; α r 0.3; 0.; ~ 0.05; PV ; 0.5; L ; J 0.5; NI 00; J 0.; I 0; A6.. Moel wit capital moility A6... Policy finance uing te ta rate Cae (NI): Non-internaliation P 0 ; q 0 r ; 0 ; w N >0; L N N ε( ) ( τ )( ε ) >0; X N >0; [ τ ( ( ξ ψ ))] [( ε ) τ ( ε( ))] >0;

32 8 M& & K& & εl( τ ) N [( ε ) τ ( ε( ( ξ ψ )))] ( ) ( ) >0; εl( τ) N [( ε ) τ( ε( ( ξ ψ) ))] r Y& e Te neceary conition for & ( ) ( ) >0. εl[ ( τ ) µ ] N [( ε ) τ( ε( ( ξ ψ) ))] 0 < µ < an te ufficient conition for τ τ ( ε )( )( τ) ( ) ε >0 i ε[ ( ξ ψ) ( τ )] N >0 i ( ψ ) ( τ ) < 0 [ τ( ( ξ ψ) )] τ ξ. Cae (I): Internaliation All multiplier are ero in ti cae an τ ξ ψ >0. A6... Policy finance uing te ta rate φ. Cae (NI): Non-internaliation P q r 0 ; 0 ; 0 ; K& & N ( τ) ε L [( ε ) τ( ε( ( ξ ψ) ))] r Te neceary conition for ( ) Y& e >0; >0; ŵ M& & ; L ( ε ) >0; ( ( τ ) µ ) ε [( ε ) τ( ε( ( ξ ψ) ))] 0 < µ < τ, an te ufficient conition for φ ( ξ ψ) ψ ( ) ( ε ( ε )( τ) ) 4ψετ X ( τ ) εl τ( ε( ( ξ ψ) )) >0 i >0; <0 i ( ξ ψ ) < 0. >0. Cae (I): Internaliation All multiplier are ero in ti cae an φ ξ ψ >0. ψ

33 9 A6..3. Policy finance uing te ta rate Cae (NI): Non-internaliation ŵ ; L N ; X an (ii) [ ( ψ ξ ) ] > 0 N N τ are require for an te ufficient conition (i) ( ) > 0 ( ) ε[ ψ ( τ ( )) ( ( ( ψ ξ ) ) τ )] [( ) ( ε τ ( ε( ))) ε ( τ )] εψ ( τ ( )) P N r Ap N Alo, Ap,, were te neceary conition for A q A p N, an >0. ( τ ) ρ τ [( ε τ ( ε( 3 4( ψ ξ ))) ( ε τ ( ε( )))] [ τ ( ( ψ ξ ) )] ψ ( τ ( )) p >0 are ( ε(3 4( ψ ξ ))) τ ( ε( )) A τ p N ε τ P < an conition (i) an (ii) aove, in wic cae, < 0, ε r q ρ > 0, < 0, an > 0. Given te compleity of igning te multiplier in ti cae, following grap provie furter inication., Figure Effect of a ρ-finance increae in : cae (NI), non-internaliation N / / P M & / & K & / &

34 30 Y e & & / ρ / WB / ^ Cae (I): Internaliation 0 w, an > i te ufficient conition for N L >0; N X >0; N P <0; N q ) ( <0; 0 ) ( > N r ; an ( ) ( ) ( ) ( ) [ ] ( ) ( ) N τ εψ ετ ετ ε ψ ξ τε ) )( ( >0. Te ufficient conition for ( ) ( ) ( ) ( ) ( ) N r L K ) ( ) ( ) ( ψ ξ τε ε ψ ε τ & & <0 i < <. Oter multiplier are ( ) ( ) ( ) ( ) ( ) ( ) N L M ) ( ) ( ψ ξ τε ε ψ τ ε & & ; ( ) ( ) ( ) ( ) ( ) C( ) N Y ) ( ) ( ψ µ ψ τ & &, were ( ) ( ) 0 ) ( > ψ ξ τε ε ε L C ; an 0 ) ( ) ( > N ρ τ τ.

35 3 Given te compleity of te igning of te multiplier in ti cae, following grap provie furter inication. Figure Effect of a ρ-finance increae in : cae (I), internaliation M & / & K & / & & / & Y e ρ / ^ WB/ A6.. Moel witout capital moility A6... Policy finance uing te ta rate Cae (NI): Non-internaliation Te neceary conition for N ε ψ ε( ) [ τ ( ( ξ ψ ))][ ψ ( ) ( )] [ ( ) ( τ )] ( τ )( ε )( ) [ ψ ( ) ( ))] > 0

36 3 i ) [ ψ ( ) ( ))] [ ψ ( ) ( )] ( τ )( ε >, i.e. ufficiently mall. If - ε τ N >0, ten P L N ( -) r ( -) w ψ ( -) Finally, & & µ >0; X N >0; - [ ψ ( ) ( )] [ ψ ( ) ( )] ( ) ( ) N ( ) [ ( ) ( )] ψ M& & N <0; ( ψ ( ) ) [ ψ ( ) ( )] εl N >0; ( ) [( ε ) τ ( ε( ( ξ ψ) ))] q ( -) [ ψ ( ) ( )] N >0; an te ufficient conition for >0 i ψ <. < i te neceary conition for Y e µ N C( ( ψ ( ) ) ψ [ ψ ( ) ( )] ) εl C >0. ( ) [( ε ) τ ( ε( ( ξ ψ )))][ ψ ( ) ( )] >0, were Given te compleity of te igning of te multiplier in ti cae, following grap provie furter inication. N <0;

37 33 Figure 3 Effect of a τ-finance increae in : cae (NI), non-internaliation N / w / M & / & / P & / & Y e τ / ^ WB/

38 34 Cae (I): Internaliation All multiplier are ero in ti cae an τ ξ ψ >0. A6... Policy finance uing te ta rate Cae (NI): Non-internaliation w M& & P an, an te ufficient conition for N ( <. Provie tat ti conition ol, ten εl N >0; ( ) [( ε ) τ ( ε( ( ξ ψ) ))] ( -) Finally, & & [ ψ ( ) ( )] r ( -) µ N <0; [ ψ ( ) ( )] ( ψ ( ) ) [ ψ ( ) ( )] ψ ) [ ψ ( ) ( )] [ ψ ( ) ( ( ) )] L N q ( -) N >0. >0; X >0 i N >0; [ ψ ( ) ( )] < i te neceary conition for Y e µ N C( ( ψ ( ) ) ψ [ ψ ( ) ( )] ) εl C >0. ( ) [( ε ) τ ( ε( ( ξ ψ )))][ ψ ( ) ( )] >0, were N >0; Given te compleity of te igning of te oter multiplier in ti cae, following grap provie ome inication.

39 35 Figure 4 Effect of a φ-finance increae in : cae (NI), non-internaliation ^ WB/ φ / Cae (I): Internaliation All multiplier are ero in ti cae an φ ξ ψ ψ >0. A6..3. Policy finance uing te ta rate Cae (NI): Non-internaliation w M& & P an, an te ufficient conition for N ( <. Provie tat ti conition ol, ten εl N >0; ( ) [( ε ) τ ( ε( ( ξ ψ )))] ( -) r [ ψ ( ) ( )] ( -) N <0; [ ψ ( ) ( )] ) [ ψ ( ) ( )] [ ψ ( ) ( ( ) )] q N >0. L N ( -) >0; X >0 i N >0; [ ψ ( ) ( )] N <0;

40 36 ( ( ) ) [ ( ) ( )] ψ ψ Finally, µ < i te neceary conition for ψ & & Y e µ N C( ( ψ ( ) ) ψ [ ψ ( ) ( )] ) εl C >0. ( ) [( ε ) τ ( ε( ( ξ ψ )))][ ψ ( ) ( )] >0, were Given te compleity of te igning of te oter multiplier in ti cae, following grap provie ome inication. Figure 5 Effect of a ρ-finance increae in : cae (NI), non-internaliation ^ WB/ φ / Cae (I): Internaliation All multiplier are ero in ti cae an ρ ξ ψ >0. ψ

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