Documents de travail. «Financial Integration and Fiscal Policy Efficiency in a Monetary Union» Auteurs. Gilbert KOENIG, Irem ZEYNELOGLU

Transcription

1 Documens de ravail «Financial Inegraion and Fiscal Policy Efficiency in a Moneary Union» Aueurs Gilber KOENIG, Irem ZEYNELOGLU Documen de Travail n Mars 2007 Faculé des sciences économiques e de gesion Pôle européen de gesion e d'économie (PEGE) 6 avenue de la Forê Noire F Srasbourg Cedex Secéaria du BETA Chrisine DEMANGE Tél. : (33) Fax : (33) demange@courno.u srasbg.fr hp://courno.u-srasbg.fr/bea CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

2 Efficacié Budgéaire dans une union monéaire en cas d inégraion financière imparfaie Gilber Koenig - Đrem Zeyneloglu Résumé Ce aricle se place dans le cadre de la nouvelle macroéconomie inernaionale en proposan un modèle d équilibre général en concurrence imparfaie. Ce modèle décri une union monéaire qui, comme l UEM, n a pas réalisé une inégraion financière complèe malgré l adopion d une monnaie unique. Il es uilisé pour analyser l impac du degré d inégraion financière sur l efficacié e sur les canaux de ransmission des chocs budgéaires. A cee fin on inrodui une inégraion financière imparfaie dans la version du modèle de Obsfeld e de Rogoff (995, 996) décrivan des pays soumis à un régime de changes fixes e on l adape à la descripion d une union monéaire. On se place ainsi dans le prolongemen des ravaux iniiés par Suherland (996) e desinés à décrire les cas des économies en régime de changes flexibles. Mais on se disingue de ces ravaux en subsiuan à leurs résulas numériques des soluions analyiques. Les résulas monren que dans le cas d une expansion budgéaire financée par impôs dans un pays membre de l union, une hausse du degré d inégraion financière rédui la volailié du aux d inérê e de la consommaion à cour erme dans les deux pays. Ce effe es inversé à long erme. Par conre, le bien-êre es indépendan du degré d inégraion financière. Classificaion JEL: F4, E44, E62 Mos-clés: Nouvelle macroéconomie inernaionale, poliique budgéaire, inégraion financière, union monéaire.

3 Financial Inegraion and Fiscal Policy Efficiency in a Moneary Union Gilber Koenig - Đrem Zeyneloglu Absrac The gap beween he ineres raes of differen members of he European Moneary Union (EMU) poins ou o an imperfec degree of financial inegraion despie he common currency. This paper develops a wo-counry New Open Economy Macroeconomics (NOEM) model wih imperfec financial inegraion in a moneary union in order o analyze fiscal policy efficiency and he impac of financial inegraion on he inernaional ransmission of fiscal policy shocks. For his, we inroduce imperfec financial inegraion ino he fixed exchange rae version of Obsfeld-Rogoff (995, 996). We show ha a higher degree of financial inegraion decreases shor run consumpion and ineres rae volailiy in boh counries while i increases he volailiy in he long run following a balanced-budge increase in governmen spending in one of he counries. In erms of welfare, he degree of financial inegraion is irrelevan since i has no effec on he uiliy of he members. JEL Classificaion: F4, E44, E62 Keywords: New open economy macroeconomics, fiscal policy, financial inegraion, moneary union 2

4 Financial Inegraion and Fiscal Policy Efficiency in a Moneary Union Gilber Koenig - Đrem Zeyneloglu. Inroducion According o he definiion given by he European Cenral Bank (ECB), he marke of a given se of insrumens and services is fully inegraed if all poenial marke paricipans face he same rules, have equal access o he marke and are reaed equally when hey ake acion in he marke (Schmiedel and Schönenberger (2005)).The exisence of a common currency has allowed an imporan increase in financial inegraion beween he members in he European Moneary Union. However, despie he common currency, no all he condiions are me in Europe in order o achieve full financial inegraion. This imperfec characer of he financial marke in EMU is refleced by he ineres rae gaps beween similar bonds (ECB (2003)). The degree of financial inegraion maers mosly o moneary auhoriies as hey consider he imperfec inegraion as an obsacle o he ransmission of moneary policy. Bu i can also have implicaions on he conducion of fiscal policies in he member counries as well as on heir welfare. In he radiional Mundell-Fleming ype models, fiscal policy analysis in a moneary union frame considers generally he perfec financial inegraion case. Indeed, he exisence of a common currency is ofen hough o lead auomaically o full financial inegraion. Neverheless, he degree of financial inegraion is analyzed by he radiional lieraure under fixed exchange raes which is close o moneary union case. In he fixed exchange rae seup, an increase in he degree of financial inegraion improves fiscal policy efficiency. The ineremporal general (dis)equilibrium models, developed beginning from he 80s (Van der Ploeg (994), Frenkel e Razin (2002)), have paid lile aenion on he relaion beween fiscal policy and financial inegraion in a wo counry seup. One excepion is Glick and Huchinson (990) according o which, a higher financial inegraion in Europe reduces he impac of fiscal policy in he implemening counry while increasing is effecs on he oher counry. Nous remercions F. Dufour e E. Spyrimiros pour leurs commenaires d une première version de ce aricle. 3

5 The relaion beween fiscal policy and financial inegraion has been reconsidered, in a new open economy macroeconomics (NOEM) seup, by Suherland (996) and Pierdzioch (2004). However, hey analyze his relaion in a flexible exchange rae framework providing only numerical soluions. A limied number of research considering a moneary union or fixed exchange raes assume, generally, full financial inegraion (Koenig and Zeyneloglu (2006)). The paper presens a wo-counry NOEM model wih imperfec compeiion on goods markes where he fiscal policy efficiency crierion is considered o be he welfare. I aims o analyze he impac of financial inegraion on he effecs of fiscal policy, implemened in one of he union s members, on he union s welfare. For his, we exend he fixed exchange rae version of Obsfeld and Rogoff (995, 996) analyzed by Caselli (200) and Couinho (2005) by inroducing imperfec financial inegraion. We adap heir fixed exchange rae seup o a moneary union framework and exend heir full financial inegraion seup o he imperfec financial inegraion framework. In designing he imperfecion of financial marke inegraion, we follow Suherland (996) whose seup inspired also Senay (998), Pierdzioch (2004, 2005) and Cenesiz and Pierdzioch (2006). In conras o hese papers where he exchange rae is considered o be flexible, we offer analyical soluions which allow o specify he impac of financial inegraion on fiscal policy efficiency as measured by is capaciy o increase welfare raher han is capaciy o improve naional income. The paper is organized as follows: secion 2 describes he seup while secions 3 and 4 derive log-linear versions of he model in he long run and in he shor run. Secions 5 and 6 give, respecively, he shor run and long run effecs of fiscal policy on real and financial secors. Secion 7 analyses he welfare effecs of fiscal policy. Finally secion 8 concludes. 2. The Model There are wo idenical counries of equal size, which we will call as home and foreign, inhabied by a coninuum of infiniely lived agens wih perfec foresigh. Agens in home counry are indexed by j [0, 2 ] while foreign agens are indexed by j ( 2,]. Each agen produces a single differeniaed good ha is an imperfec subsiue o oher goods and consumes a baske of all home and foreign goods. The wo counries form a moneary union wih a common currency. 2.. Consumer Preferences All agens in he world have idenical preferences so ha we will focus on he represenaive agen in each counry. The preferences of he represenaive home agen j are given by he following uiliy funcion: 4

6 j j s j M s κ j 2 U s = β logcs + χ log ( ys ) ; χ, κ > 0 ; 0< β < () s= Ps 2 The funcion (), whereβ denoes he subjecive discoun facor, implies ha a represenaive domesic agen j derives uiliy in period s and from individual real money balances defined by = from privae consumpion j M P where j C P is he aggregae home currency price index while he las componen represens he disuiliy he agen bears because of labour effor. The consumpion index in equaion () is a CES ype aggregaion of all available goods in he world: θ θ j θ θ ( ) 0 ; θ> (2) j C = c z dz j where c ( z ) is agen j s consumpion of good z and θ is he elasiciy of subsiuion beween goods produced in he world. The corresponding price index is defined as he minimum expendiure required for consuming one uni of he composie consumpion good C and is given as: θ ( ) θ 0 P = p z dz (3) where p(z) is he price of good z. Wihou impedimens o inernaional rade, he price of each good is equalized across counries by he law of one price. Knowing ha preferences are idenical across counries and assuming a common currency, we can rewrie equaion (3) and is foreign analogue as follows: 2 θ ( ) ( ) = = + 0 = 2 ( ) + 2 ( ) 2 θ θ θ θ θ (4) P P p z dz p z dz p h p f h 0, 2 and f ( 2,]. In equaion (4), P and where [ ] p ( f ) denoe respecively, he foreign overall price index and he foreign currency price of a foreign good a ime. We assume he same price rigidiy as in Obsfeld and Rogoff (996). All prices are fixed during he acual period bu hey adjus o heir flexible price level in he following period, wihou a new shock. The relaions concerning he foreign counry are idenical wih aserisks denoing foreign variables. 5

7 2. 2. Goods Demand Each producer saisfies he privae and public demand addressed o his own good. The domesic consumer maximizes equaion (2) under he simple fixed nominal budge consrain for consumpion which gives he individual demand for a ypical good z as follows: θ j p ( z) c ( z) = C P j We assume ha governmen has he same composiion of real per capia consumpion index G as he privae agens given in equaion (2) so ha here is no home bias. Then he public demand for a single good z is given by: (5a) θ p ( z) g ( z) = G P The demand by foreign public and privae agens are similar. (5b) d Aggregaing (5a) and (5b) along wih foreign analogues gives he oal demand y ( z ), faced by he producer of a single home good z where we dropped he index j assuming ha all agens are symmeric: θ d p ( z) w w y ( z) = ( C + G ) P (6) where he upper index w indicaes union aggregaes: C = C + C, and G = G + G. w 2 2 w 2 2 The demand addressed o a ypical producer of a foreign good is similar Financial Marke Srucure We assume ha domesic agens hold hree ypes of asses: domesic money balances, domesic real bonds D paying reurn r, and foreign real bonds F paying reurn r. Foreign agens can also hold hree ypes of asses: foreign money balances, real bonds of heir own counry F and real bonds of he oher counry D. In order o characerize he imperfec financial inegraion, we simply assume ha home and foreign agens are no reaed equally when buying he bonds of he oher counry. All agens in all counries have free access o he foreign financial marke bu he residens of one counry mus bear a cos when buying he bonds of he oher counry whereas he purchases of naional bonds do no include any coss. We know ha, in realiy, agens incur addiional coss even when buying he bonds of heir own counry bu since hese coss are negligible compared o he coss born when buying foreign bonds, we can assume, wihou loss of 6

8 generaliy, ha he coss for foreign bond purchases are posiive while home bonds require no addiional coss. Following Suherland, we define he ransacion coss incurred by he domesic and foreign agens, denoed by Z and Z respecively, by he following relaions : Z 2 ( I ) 2 = γ (7a) Z = γ ( I ) (7b) 2 2 In he above expressions, a posiive value of he parameer γ implies imperfec financial inegraion. I and I denoe respecively he funds, in real erms, ransferred from domesic o foreign financial marke and from foreign o domesic financial marke. In oher words, hey denoe, respecively, he variaions in home counry s claims on he foreign counry and he variaions in foreign counry s claims on home counry: I = F + r F (8a) + ( ) I = D + + r D (8b) ( ) We assume ha he ransacion coss born by domesic (foreign) agens are colleced by a domesic (foreign) insiuion in he form of profis so ha he assumpion of inermediaion coss does no aler he resource consrain of he home (foreign) counry Comsumer s Maximisaion Home individual maximizes his uiliy given in equaion () under he following budge consrain: p y PZ PT PC + M M = PD P ( + r ) D + P F P ( + r ) F (9) j j j j j j j j j + + where r is he real pay off of home bonds beween - and, r is he real pay off of foreign bonds and j j T sands for lump-sum axes. D + and F + denoe home and foreign bond holdings in period reaching mauriy in period +. We absrac from he possibiliy of governmen deb and assume ha public spending is financed by lump-sum axes. Then, public budge consrain can be wrien as: G = T (0) Foreign privae and public budge consrains are similar. The maximizaion of uiliy (equaion ), under budge consrain (8) aking ino accoun he goods demand given in equaion (6) and he ransacion cos given in (7a), wih respec o See Suherland (996) for alernaive explanaions of he ransacion coss. 7

9 C, M, D +, y and j j j j index j: j F + gives he following firs order condiions where we dropped he M P + i + = χ C i+ + + (a) C = β ( + r ) C (b) θ+ w θ θ w θ y = ( C + G ) C (c) θκ ( + r )( + γ I ) = ( + r )( + γ I ) (d) In equaion (a), home nominal ineres rae i + is defined by he following relaion: P + + i + = (+ r + ) P Equaion (a) is he usual money demand equaion implying ha agens mus be indifferen beween consuming a uni of consumpion good and saving he same amoun of money in he period, while deriving uiliy from cash holdings, in order o spend in he nex period. Equaion (b) is he consumpion Euler equaion showing he consumpion smoohing behaviour. Equaion (c) is he labor-leisure rade-off equaion which simply saes ha he marginal disuiliy of producing an exra uni of oupu mus equal he exra uiliy coming from spending he revenue ha exra uni of producion brings. Equaion (d) expresses he inernaional financial equilibrium condiion wih he ransacion cos aken ino accoun. Indeed, imposing γ = 0 leads o he equaliy of ineres raes across counries as implied by he uncovered ineres rae pariy condiion. Foreign agens have similar relaions wih aserisks denoing foreign variables. For he equilibrium we also need he following ransversaliy condiion: ( R, + T D+ T R, + T F+ T M, + T) lim + = 0 (2) T where R, + T is defined as + T v= + ( + r ) v wih R, T 2.5. Exernal Equilibrium and Money Supply + being he foreign analogue. The exernal equilibrium condiions can be expressed in he following way for he wo counries: p ( h) y ( F F ) ( D D ) = r D + r F + C G (3a) + + P 8

10 p ( f ) y ( D D ) ( F F ) = r D r F + C G (3b) + + P According o (3a and b), exernal equilibrium is achieved when he curren accoun balance (righ-hand side of he equaions above) is equal o he capial accoun balance (lef-hand side of he equaions above) in each counry. The laer equals o he difference beween he variaion in foreign counry s claims on home counry ( D+ D ) and he variaion in home counry s claims on foreign counry ( F + F ). Money supply says consan on he union level while i adjuss o money demand in each counry. 3. Long Run Equilibrium In order o provide analyical soluions o his non-linear model, firs, we have o define a seady-sae where prices are flexible. logarihmic deviaions from his seady-sae. 3.. The Iniial Seady Sae Then, we will rewrie he variables in erms of We consider a symmeric seady-sae where an overbar denoes he consan seady-sae values and where we drop he indexes and j. In a seady sae where all endogenous variables are consan, he consumpion Euler equaion given in (b) implies preferences. r β = r = where β β = β because of idenical In he seady sae, oal income coming from financial operaions and from producion mus be equal o oal consumpion. Remembering ha seady-sae ineres raes are equal across counries, he seady-sae versions of equaions (3) become: p( h) y C = r ( F D ) + G (4a) P p ( f ) y C = r ( F D ) + G (4b) P Anoher way o have equaion (4a) is o inegrae he individual budge consrain given in equaion (9) over ime and hen o impose he governmen budge consrain given in equaion (0) as well as he ransversaliy condiion in (2). 9

11 Assuming ha, iniially, counries financial claims on each oher as well as governmen spending in boh counries are equal o zero, equaions (4) imply p ( h) p ( f ) = = and 0 0 P0 P0 hence C = C = C = y = y where he subscrip 0 indicaes he preshock iniial seady sae. w Since here are no capial movemens in his iniial seady-sae, ransacion coss Z and Z are also absen. Inroducing his relaion ino he labor-leisure rade off equaion in (c) gives: y θ = y = θκ Noe ha his level of producion is subopimal because of monopoly power. As he iniial seady sae level of consumpion and producion are equal, we can use equaion (5) o derive he following iniial seady sae levels of money demand in boh counries: M P M χ θ = = β θκ P Log-linearizaion of he Long run Equaions When a permanen fiscal shock his he iniial seady-sae, he economy moves immediaely o a new seady-sae where prices are flexible. In order o deermine he long run impac of his shock, we have o log-linearize he long run versions of he model s equaions around he iniial seady-sae. The long run model consiss of long run curren accoun equaions, price equaions, goods and money demand and consumpion-leisure rade-off equaions. The long run log deviaion of a variable x from he iniial seady sae is indicaed by an over bar and a ilde so ha x ( x x0 ) / x0. Since he iniial value of public spending and foreign bond holdings are assumed o be zero, he deviaions of hese variables are defined wih respec o he iniial seady-sae value of consumpion so ha G = dg / C0, G dg C, = / 0, I = di / C0 0 (5) (6) I = di / C. Since he economy reaches is new seady sae immediaely afer he shock his, in wha follows we can drop ime subscrips. Using he definiion of he variaion in home s claims on he foreign counry given in equaions (8), i is possible o wrie he log linear versions of he long run curren accoun equaions given in (3) which give he following expressions for he consumpion deviaion in he wo counries: 0

12 (7a) C = r ( I I ) + p( h) + y P G C = r ( I I ) + p ( f ) + y P G (7b) In he equaions above I ~ and counry on he oher. ~ I represen he shor run deviaions of he claims of each Assuming symmery among each counry s producers, he log linear version of he price index equaion given in (4) and is foreign analogue is given by: 2 ( ) ( ) (8) P= P = p h + p f The long run log linear version of goods demand equaion given in (6) and is foreign analogue are given as: w w y = θ P p ( h) + C + G (9a) w w y = θ P p ( f ) + C + G (9b) Taking a populaion weighed average of equaions (9a) and (9b) and adding hem making use of equaion (8) gives he world goods marke equilibrium condiion: w w w y = C + G (20) The labour-leisure rade off given in equaion (c) and is foreign analogue become: w w ( θ + ) y = θc + C + G (2a) w w ( θ + ) y = θc + C + G (2b) Noe ha equaions (2a) and (2b) hold only in he long run because wih monopoly power and sicky prices, supply will be demand deermined in he shor run and producers will mee exra demand violaing he opimaliy condiion for labour supply. Money demand equaion given in (a) and is foreign analogue ake he following form: M P = C β r (22a) M P = C βr (22b) 3.3. Union Aggregaes and Counry Differences for Long Run Consumpion and Producion Union aggregaes and counry differences will urn ou o be useful in solving for he individual variables. In order o define long run home and foreign consumpion as well as long run home and foreign producion, we begin by deriving he deviaions in unionwide

13 consumpion and producion. Then, we proceed wih relaive home consumpion and producion. The populaion weighed average of home and foreign labor-leisure rade off equaions given in (2a) and (2b) implies: w w w ( θ+ ) y = ( θ ) C + G (23) Combining equaion (23) wih log linear version of goods marke equilibrium condiion given in equaion (20), we ge: y = G ; C = G (24) w w w w 2 2 According o (24), a permanen increase in unionwide public spending leads o a fall in long run world consumpion while i increases long run world producion. Subracing long run curren accoun equaions (7b) from (7a), he demand equaion (9b) from (9a), labor-leisure rade off equaions (2b) from (2a) gives respecively: C C = 2 r ( I I ) + p ( h) p ( f ) + ( y y ) ( G G ) (25) θ ( ) ( ) (26) y y = p h p f y y θ ( C C = ) θ+ (27) Inroducing equaions (26) and (27) ino (25) gives: C θ+ θ + C = r ( I I ) ( G G ) (28) θ 2θ Combining equaions (28) and (27) gives he long run relaive producion as follows: y y = r ( I I ) + ( G G ) (29) 2 As we will see in a while, he ransacion cos will affec he long run relaive consumpion and producion hrough he effec of ne curren accoun posiion on he ineres rae gap. For ha, we need o deermine he shor run equilibrium. 4. Shor Run Equilibrium In order o evaluae shor run effecs of a fiscal shock, we need o log-linearize he shor run versions of he equaions ha make up he model. Then, as in he long run analysis, we will deermine he deviaions in union aggregaes and relaive consumpion and producion. In he shor run, individual prices are fixed. A fixed exchange rae implies ha he overall price index is also fixed in he shor run. Because prices are higher han he marginal coss due o monopoly power, producers are willing o mee exra demand for he same price. Therefore, supply will be demand deermined in he shor run. 2

14 4.. Log-linearizaion of he Shor Run Equaions The shor run model consiss of goods demand, consumpion Euler equaions, money demand, shor run curren accoun equaions and he inernaional financial marke equilibrium condiion. In wha follows, he shor run log deviaion of a variable x from he iniial seady sae is indicaed by a ilde so ha x ( x x0 ) / x0. Since we look only a one period changes in he economy, we can drop he ime subscrips. Because of price rigidiy, he log-linearized goods demand in he home counry given in equaion (6) and is foreign analogue can be expressed as: y= y = C + G w w (30) The ineremporal consumpion Euler equaion given in (b) and is foreign analogue ake he following log linear forms: C = C + ( β ) r (3a) ( ) (3b) C = C + β r Shor run money demand deviaions in he wo counries are defined as: M = C r P (32a) β β β M C r P (32b) β = β β Since goods supply is demand deermined, labor/leisure rade-off equaion does no hold in he shor run. Anoher difference beween shor run and long run concerns he curren accoun equaions. In conras o he long run, in he shor run curren accoun need no be in equilibrium. Insead, home counry may run a curren accoun surplus or defici which can be expressed as follows afer log linearizaion using he definiion given in equaions (8): (33a) I I = y C G I I = y C G (33b) In he cos-adjused financial equilibrium condiion (d) and is foreign analogue, he long run deviaions in home claims on foreign I and foreign claims on home hese wo equaions ake he following form when log-linearized: I are zero 2. Hence 2 This is because, he economy reaches he new seady-sae in he immediae afermah of a shock. Since foreign bond holdings do no change in he seady-sae by definiion, whaever ne foreign asse socks arise a he end of he firs period become he new seady-sae levels from period 2 on. 3

15 C C r r γ γ = I = I β β 0 0 (34a) Equaion (34) saes ha he ineres rae differenial across counries depends on he capial ransferred o he inernaional bond marke in each counry. Pu differenly, i depends on he ne capial movemen. The deviaion of he gap can be posiive or negaive depending on ha of foreign bond holdings of he wo counries. Equaion (34a) implies : γ C0 r r = ( I I ) 2( β ) (34b) 4.2. Union Aggregaes and Counry Differences for Shor Run Consumpion and Producion In a moneary union wih an independen cenral bank, money marke equilibrium requires ha money supply in he union be equal o he sum of he money demand in he wo member counries. Since we focus on fiscal policy, we will assume ha he cenral bank pursues a passive moneary policy so ha he unionwide money supply will remain unchanged boh in he shor and in he long run. Taking a populaion weighed average of long run money demand equaions given in (22a and b) and plugging he resul in he populaion weighed average of shor run money demand equaions (32a and b) o subsiue for long run price levels gives a relaionship beween deviaions of shor run world consumpion and average ineres rae as follows: w w r + r = C + 2C (35a) β 2 Anoher relaion can be derived from he populaion weighed average of consumpion Euler equaions given in (3a and b): 2 w w ( ) r + r = C C (35b) β Combining he wo relaions implies ha he shor run deviaion of world consumpion from is iniial seady sae is zero. A fiscal expansion does no crowd ou privae consumpion in he shor run because oupu is compleely demand driven. Privae consumpion is no undermined since here are no price changes due o exra demand. Then he shor run equilibrium on goods marke implies w w. y = G For he counry differences, we begin by subracing foreign consumpion Euler equaion (3b) from home given in (3a): 4

16 C C C C β r r = ( ) ( )( ) (36) Equaion (36) capures he effec of he degree of financial inegraion. When inegraion is perfec, he ineres rae gap is zero and he long run home relaive consumpion deviaion is equal o he shor run deviaion. The reason is ha, wih perfecly inegraed markes agens in boh counries face he same ineres rae and hence he counry consumpion profiles are affeced in he same way. However, when asses are imperfec subsiues, he ineres rae differenial ils he home consumpion profile relaive o he foreign. If, for example, home ineres rae increases more han he foreign, shor run home consumpion decreases more han shor run foreign consumpion because home agens are induced o save more wih respec o foreign agens. In he long run, his leads o a higher increase in home consumpion compared o he foreign. A posiive ineres rae differenial decreases relaive shor run home consumpion because home agens pospone consumpion in ime by adjusing curren consumpion downwards while he opposie is rue abroad. 5. Shor Run Effecs of Fiscal Policy In he shor run, a balanced-budge increase in home public spending affecs he consumpion and producion of he wo counries, as well as he ineres raes, inernaional capial movemens and moneary equilibrium. 5.. The Effecs of Fiscal Policy on Consumpion and Oupu In order o solve for individual variaions of he relevan variables we use he Aoki mehod w (98) which relaes a union aggregae x~ and a counry difference ( x ~ ~ x ) o he acual level of a variable x ~ ~ = C, ~ y or ~ ~ x = C, ~ y by he following ideniies : w ( x = x + ) 2 x x or w. x = x ( ) 2 x x In order o assess he effecs of an increase in public spending, financed by lump-sum axes, we need o express shor run aggregae and relaive deviaions in consumpion and producion in erms of public spending deviaion. According o equaions (35a) and (35b), he shor run world consumpion deviaion is w zero : C ~ =0. Then shor run increase in world producion is equal o he increase in world governmen spending: y w = G w I is possible o solve for relaive shor run consumpion deviaion and for ne capial inflow deviaion using he following sysem of wo equaions wih wo unknowns: ( I I ) = 2 ( C C ) + ( G G ) (37) 5

17 2 θ ( θ+ ) (38) 2 r ( θ+ ) + θγ C 2 r ( θ+ ) + θγ C ( I I ) = ( C C ) + ( G G ) 0 0 Equaion (37) is obained by subracing shor run foreign curren accoun equaion (33b) from (33a) aking ino accoun ha shor run deviaion of relaive producion is zero as implied by he goods demand equaion (30). To obain equaion (38), we firs plug he differenial consumpion Euler equaion given in (36) ino equaion (28) o eliminae long run consumpion differenial. Then, we make use of equaion (34b) o eliminae he ineres rae gap. Solving he sysem consising of equaions (37) and (38) gives he following expression for shor run relaive consumpion deviaion: C C { r θ θγ C0} G G θ G G 2Ψ+ θγ C = 2 ( + ) + ( ) + 2( + )( ) (39) Ne capial inflow deviaion 0 ~ ~ I I will be defined laer. Since shor run world consumpion deviaion is zero and relaive shor run consumpion is given by (39), shor run consumpion deviaions in each counry are given as follows: C = { 2 r ( θ+ ) + θγ C0} ( G G ) + 2( θ+ )( G G ) (40a) 2 2Ψ+ θγ C 0 C { r C0} G G G G 2 2Ψ+ θγ C 0 = 2 ( θ+ ) + θγ ( ) + 2( θ+ )( ) (40b) Shor run relaive producion needs no calculaion since equaion (30) implies ha y y = 0. Applying he Aoki formula gives: ( ) 2 y= y = G+ G (4) Following a emporary or permanen increase in home governmen spending, home consumpion decreases and foreign consumpion increases while producion increases in he same way in boh counries. The fall in home consumpion is due o he negaive welfare effec of he ax. Since governmen spending increases more han he fall in privae consumpion, domesic oupu increases. Because of he no home bias assumpion, home public demand expansion has a posiive effec on foreign oupu while he decrease in home privae demand has a negaive effec. However, he ne effec is posiive and foreign oupu also increases in he shor run. Higher income in he foreign counry leads o higher foreign consumpion. Noe ha, in conras o he flexible exchange rae seup, he deviaions of consumpion and producion are of he same magniude in he wo counries. This is because, wih he same 6

18 currency across counries and sicky prices, he expendiure swiching effec of he erms of rade is absen in he shor run. The only effec is he expendiure shifing effec of home public spending which is symmeric across counries. When he fiscal shock is permanen (G = G ), agens anicipae a higher deviaion in heir fuure consumpion compared o he emporary shock, which induces a higher adjusmen of curren consumpion. Therefore, permanen fiscal expansion has a higher impac on shor run consumpion wih respec o emporary fiscal expansion. The effecs of fiscal policy on shor run consumpion are higher when financial inegraion is imperfec. Indeed, an increase in γ, leading o a fall in he degree of financial inegraion, induces an increase in home ineres rae wih respec o foreign. Therefore, home (foreign) agens are induced o adjus heir curren consumpion downwards (upwards) in he anicipaion of higher (lower) fuure consumpion. Noe ha he degree of financial inegraion does no affec shor run oupu because wih fixed prices and a common currency, he shor run supply block of he model is independen of he curren accoun equaion which includes he cos The Effecs of Fiscal Policy on Capial Movemens and Ineres Raes Inroducing he shor run relaive consumpion given in equaion (39) in equaion (37) gives he following resul for he deviaion in ne capial inflow: 2Ψ+ θγ C I I = 2 θ ( G G ) + ( θ+ )( G G ) (42) 0 Equaion (42) saes ha following a emporary or a permanen increase in home governmen spending, foreign bond holdings of home agens fall or domesic deb vis-à-vis he foreign counry increases. In boh cases, equaion (42) implies ha a fiscal shock leads o a ne capial inflow owards he home counry. This inflow is more pronounced when financial inegraion is high (γ is low). Fully inegraed financial markes ( γ = 0) lead o he same resul as Couinho (2005) for he fixed exchange rae version of Obsfeld and Rogoff (996). A permanen fiscal expansion has a lower effec on ne capial movemens wih respec o a emporary shock, because a permanen shock induces a lower curren accoun defici due o is higher effec on home consumpion given in equaion (40a). According o (42), a decrease in he degree of financial marke inegraion, implying a higher γ, reduces he effec of fiscal policy on capial movemens. Indeed, since lower financial inegraion amplifies he fall in home consumpion according o (40a), i reduces he 7

19 increase in he domesic curren accoun defici. Therefore, he exernal equilibrium can be achieved hrough a lower deviaion of foreign bond holdings. In order o compue he ineres rae response o a fiscal shock, we firs plug equaion (42) ino equaion (34b) o subsiue for ~ ~ I I. Then we inroduce he value of shor run world consumpion deviaion w consumpion deviaion ( C = 0,5G w C ~ =0, derived from (35a e b), and ha of long run world w ), given in equaion (24), ino equaion (35b) which gives he sum of he ineres raes. In his way we obain wo relaions: one for he gap and one for he sum of he ineres raes. Solving his sysem of wo equaions gives he ineres rae response in boh counries as follows: θγ C 2 Ψ+ (2θ + ) γc γc 2Ψ r = ( G G ) G+ G (43a) 2( β) 2Ψ+ θγ C 0 4( β) 2Ψ+ θγ C 0 4( β) 2Ψ+ θγ C 0 θγ C γc 2Ψ 2 Ψ+ (2θ + ) γc r = ( G G ) + G G (43b) 2( β) 2Ψ+ θγ C 0 4( β) 2Ψ+ θγ C 0 4( β) 2Ψ+ θγ C 0 According o (43a) and (43b), a emporary home fiscal expansion increases home ineres rae because i leads o a curren accoun defici and a deb accumulaion in he home counry. Foreign ineres rae decreases by he same amoun as he increase in home ineres rae. The sum of he ineres raes is zero in his case as implied by equaion (35a) where long run consumpion deviaion is independen of emporary fiscal policy according o equaion (24) and where emporary fiscal expansion has no effec on shor run world consumpion as implied by equaions (40a) and (40b). A low degree of financial inegraion or a high value of γ increases he ineres rae response o a home emporary fiscal expansion. Indeed, wih low capial mobiliy, a higher increase in he ineres rae is needed o induce he same amoun of capial inflow. When he home fiscal shock is permanen, ineres raes fall in boh counries. There are wo mechanisms behind his effec on ineres raes. The firs acs hrough curren accoun defici and deb accumulaion as in he emporary fiscal expansion case: home counry deb accumulaion increases home ineres rae and decreases he foreign rae. The second mechanism acs hrough he long run world consumpion. A emporary fiscal expansion, which reduces long run world consumpion according o equaion (24), leads o a fall in he sum of he ineres rae deviaion according o (35a). Hence, home ineres rae falls. Overall, his negaive effec coming from he consumpion fall dominaes he posiive firs effec caused by he deb accumulaion and he ne effec is a fall in he home ineres rae. The 8

20 foreign ineres rae also decreases following he reducion in world consumpion, which magnifies he fall induced by he home counry deb accumulaion. Overall, foreign ineres rae decreases more han home ineres rae. The effecs of a home fiscal expansion on he ineres raes increase wih γ. In oher words, when he degree of financial marke inegraion is low, fiscal policy has higher effecs on he ineres raes. However, he impac of he degree of financial marke inegraion on ineres raes is less imporan when fiscal policy is permanen compared o he emporary shock case. When he asses are perfec subsiues so ha financial inegraion is perfec (γ = 0), ineres raes are equal across counries and we have only he second mechanism a work (he fall in world consumpion). As in Obsfeld and Rogoff (996), in his case, he ineres rae is affeced only by permanen shocks because world privae spending is no crowded ou in he shor run. Specifically, he fall in home shor run consumpion decreases he home ineres rae by he same amoun he increase in foreign consumpion increases foreign ineres rae. A he end, he ineres rae says unaffeced Fiscal Policy and he Moneary Equilibrium Because of he common currency assumpion money supply adjuss o money demand in each counry. However, on he union level, shor run money supply is consan in nominal and real erms. Shor run union money supply deviaion is derived, as follows, from equaions (32a) and (32b): ~ w w w C ( ~ r ~ = β + r ) P (44) M ~ β ~ β Following a emporary or permanen fiscal shock, shor run union wide consumpion does no move as implied by equaions (40a) and (40b). If he shock is emporary home real ineres rae increases by he same amoun as he fall in he foreign ineres rae implying ha ~ r + ~ r =0 hence agens do no anicipae a variaion in he average level of long run prices in he union. If he fiscal shock is permanen, boh ineres raes fall which implies r + r p 0. The moneary equilibrium is achieved hrough he anicipaion of a higher average price level in he union. 6. Long Run Effecs of Fiscal Policy In he long run, where prices are flexible, he economy reaches a new seady-sae immediaely in he afermah of a balanced-budge increase in public spending. This fiscal 9

21 shock affecs consumpion and oupu in boh counries, as well as prices and moneary equilibrium. 6.. The Effecs of Fiscal Policy on Long Run Consumpion and Oupu In order o assess he long run impac of a balanced-budge increase in home public spending on consumpion and producion in each counry, we use he Aoki (98) formula. For ha we need o define he deviaions of relaive consumpion and producion in erms of public spending deviaion. Given he shor run relaive home consumpion deviaion, we can use he difference of consumpion Euler equaions given in (36) o compue long run relaive home consumpion deviaion. For ha, we firs subsiue equaion (34b) ino (36) o eliminae he ineres rae gap. Then we inroduce he expression for shor run relaive home consumpion deviaion given in equaion (39) and he expression for he ne capial inflow given in equaion (42). This gives he following expression for he long run relaive home consumpion deviaion: r ( ) 4 C C θ+ + γ C = 2( G G ) + ( G G ) (45) 0 2Ψ+ θγ C 0 2r Now we can apply he Aoki formula, using equaion (24) for he union aggregaes and equaion (45) for he counry differences, o solve for he individual consumpion in boh counries as follows: 2( Ψ+ 2θ+ 2) + (2θ + ) γc0 4( θ+ ) 2 Ψ+ γc0 r( θ+ ) ( ) C = G + G G G 4(2 Ψ+ θγ C ) 4(2 Ψ+ θγ C ) 2Ψ+ θγ C (46a) ( θ+ ) 2 Ψ+ γc ) 2( Ψ+ 2θ+ 2) + (2θ + ) γc r( θ+ ) C G G ( G G ) 4(2 Ψ+ θγ C ) 4(2 Ψ+ θγc ) 2Ψ+ θγ C 0 0 = + (46b) Once he relaive long run consumpion is given, i is easy o derive he long run relaive home oupu deviaion from equaion (27). Combining equaions (45) and (27) gives: θr 4+ γ C 0 y y = 2( G G ) + ( G G ) 2Ψ+ θγ C 0 2r (47) Given he counry differences for oupu defined in equaion (47) and unionwide producion defined in equaion (24), we can make use of he Aoki formula o derive long run deviaion of oupu in each counry: Ψ+ 2 θ+ θγ C r ( θ+ ) θr 0 y = G+ G + ( G G ) (48a) 2 2Ψ+ θγ C 0 2 2Ψ+ θγ C 0 2Ψ+ θγ C 0 r ( θ+ ) Ψ+ 2θ + θγ C θr 0 y = G+ G ( G G ) (48b) 2 2Ψ+ θγ C 0 2 2Ψ+ θγ C 0 2Ψ+ θγ C 0 20

22 Equaions (46a and b) and (48a and b) give he effecs of emporary and permanen fiscal shocks on consumpion and producion in each counry. We already said ha a emporary increase in home governmen spending induces a curren accoun defici a home, according o equaion (42), and an increase in ne liabiliies of home agens. Hence, he ineres burden increases a home while financial income increases in he foreign counry. This, in urn, induces a fall in home consumpion by he same amoun as he increase in foreign consumpion. Therefore, marginal uiliy of consumpion increases a home and home agens shif ou of leisure ino work as implied by he labor-leisure rade-off equaion. Home oupu increases, which allows o mee he exra foreign demand for home goods. In he foreign counry, he increase in he foreign consumpion decreases is marginal uiliy. Foreign agens increase heir demand for leisure and foreign oupu decreases. This reducion sems from he fall in home privae demand for foreign goods as well as he fall in foreign privae demand due o he expendiure swiching effec of he long run erms of rade. Long run consumpion and oupu deviaions following a emporary fiscal expansion decrease as γ increases. In oher words, as he degree of financial inegraion decreases, he impac of fiscal policy on long run consumpion and oupu fades. Indeed, according o equaion (43) an increase in γ reduces he shor run effec of fiscal policy on I I, which limis he fall in he long run disposable income a home and is increase abroad. A permanen home fiscal expansion reduces home long run consumpion and foreign oupu while i increases foreign long run consumpion and home oupu. The impac of a permanen fiscal shock on long run consumpion is higher han ha of a emporary shock. Indeed, home agens suffer no only from an increase in deb burden bu also from permanenly higher axes in order o finance he public spending. In he foreign counry, agens enjoy higher ineres revenues along wih higher demand for foreign goods. Since permanen public spending decreases home consumpion more han when he spending is emporary, i leads o a higher increase in home oupu compared o he emporary shock case. However, foreign oupu decreases less following a permanen shock wih respec o he emporary shock alhough is consumpion increases more under he firs case. This resuls from he effec of unionwide demand deviaion on oupu as implied by equaion (2b) The Effec of Fiscal Policy on Moneary Equilibrium and he Terms of Trade From equaions (22a) and (22b), i is possible o derive an expression for he deviaion in money supply and demand which achieves he moneary equilibrium in he union, where he long run ineres rae deviaions are considered o be equal o zero. Subsiuing he value of 2

23 long run unionwide consumpion deviaion given in equaion (24) in he resuling expression gives he following relaion beween real money supply deviaion and ha of permanen public spending: ~ M ~ P ~ G 2 w w w = (49) Since a permanen home fiscal expansion reduces he union consumpion according o equaion (24) and he union s nominal money supply remains unchanged, i has o induce an increase in he union s average price level in order o mainain he long run moneary equilibrium. Noe ha, a emporary fiscal shock does no affec union s real money supply since he union s average price level remains unchanged following emporary shocks. In order o deermine he effecs of fiscal policy on he erms of rade, we plug labor-leisure rade-off equaion given in (27) along wih equaion (28), which we use o eliminae I I, ino equaion (25). In he resuling expression, we subsiue he long run consumpion differenial given in equaion (45). The resul is he following expression giving he long run deviaion of he erms of rade: r 4 C p h p γ f G + G G G (50) 0 ( ) ( ) = 2( ) + ( ) 2Ψ+ θγ C 0 2r According o equaion (50), a emporary home fiscal expansion deerioraes he erms of rade because of is effecs on relaive consumpion and oupu as well as on ne capial movemens. Temporary fiscal policy reduces home prices p(h) by he same amoun i increases he foreign prices p(f), which, as implied by he price index definiion given in equaion (8), leaves he average union price level consan ensuring he moneary equilibrium in he union. The erms of rade deerioraes more when he shock is permanen wih respec o he emporary shock case. However, foreign prices increase more han he decrease in home prices and average price level in he union increases, which re-equilibraes he union s money marke. The effecs of fiscal policy decrease as γ increases. In oher words, he impac of fiscal shocks on he erms of rade is lower under imperfec financial inegraion compared o he perfec inegraion case, which is consisen wih is impac on consumpion and oupu. 22

24 7. Welfare Effecs of Fiscal Policy In order o evaluae he effecs of a fiscal expansion in one counry on he welfare of boh counries, we will consider, as i is now radiional in his lieraure, only he real par of uiliy neglecing he uiliy coming from real balances. Then he home uiliy funcion akes he following form: κ 2 ( log 2 ) s β s s s= U C y ( ) Toally differeniaing he equaion above and evaluaing a he iniial seady sae gives: 2 2 du = C κ y0 y + C κ y0 y r Subsiuing equaion (48a) for long run oupu, (4) for shor run oupu, (46a) for long run consumpion, (42a) for shor run consumpion and plugging in he value of oupu in he iniial seady sae given in equaion (6), we ge: du 2θ 4 2 G 2 G θ = + θ θ 4θ r G + 4θ r G (5) According o (5), a emporary or permanen balanced-budge home fiscal expansion decreases he welfare of domesic agens because of is negaive impac on consumpion and leisure in boh shor and long run. Hence, ax-financed fiscal policy is beggar-hyself. The previous secion shows ha he lower financial inegraion accenuaes he shor run consumpion decrease while i has no effecs on shor run producion. This implies ha shor run home welfare is lower under imperfec financial inegraion wih respec o full inegraion. In he long run, higher saving due o he ineres rae gap reduces he decrease in long run domesic consumpion. Moreover, long run producion increases less under imperfec financial inegraion because of he lower decrease in consumpion and he lower increase in deb accumulaion. Boh of hese effecs improve long run welfare. Equaion (5) shows ha welfare is no affeced by he degree of financial inegraion. Indeed, his expression is he same wih he one derived in Couinho (2005) for he perfec mobiliy case under fixed exchange rae. This implies ha he decrease in shor run welfare due o lower financial inegraion exacly offses he increase in he long run welfare. According o (5), a foreign fiscal expansion increases home welfare because i increases consumpion and decreases producion in he shor run. This posiive effec is miigaed in he long run because of he lower increase in home leisure. A home fiscal expansion increases foreign welfare in he same way. Hence, ax-financed fiscal policy is prosper-hy-neighbor. 23

25 The following able resumes he fiscal policy impac on relevan variables under imperfec financial inegraion. The posiive or negaive sign is associaed wih he effec of fiscal policy on he variables while he leers a and m poin ou respecively o an amplificaion or a miigaion of he effecs of fiscal policy following a decrease in financial inegraion (an increase in γ ). The number 0 denoes ha he effec of fiscal policy on he variable is no affeced by he degree of financial inegraion. For example, a permanen home fiscal expansion decreases long run home consumpion and he effec is miigaed as he degree of financial inegraion decreases while he effec on shor run home consumpion is a fall and his effec is amplified by he imperfec degree of financial inegraion. Table : Effecs of fiscal policy under imperfec financial inegraion dg dg >0 C ~ ~ C ~ y ~ y C ~ ~ C ~ ~ y y ~ r ~ ~ ~ r I I du d U Temporary -/a +/a +/0 +/0 -/m +/m +/m -/m +/a -/a -/m -/0 +/0 Permanen -/a +/a +/0 +/0 -/m +/m +/m -/m -/a -/a -/m -/0 +/0 8. Conclusion The paper aims o conribue o he NOEM lieraure by inroducing imperfec financial inegraion in a wo counry general equilibrium model wih opimizing agens. Much of he analysis in he NOEM lieraure is limied o perfec financial inegraion case. Some excepions consider he degree of financial inegraion under flexible exchange raes. Moreover, hey provide only numerical soluions. Since, one of he aims of he NOEM lieraure is o provide an alernaive o he M-F ype of models, we find i imporan o provide analyical soluions. In his aim, we exend he fixed exchange rae version of Obsfeld and Rogoff (995), proposed by Caselli (200) and Couinho (2005), by inroducing imperfec capial mobiliy. In his way, we also exend Suherland (996) and Pierdzioch (200) by assuming fixed exchange rae and by providing analyical soluions. The paper uses his seup o reconsider he implicaions of radiional models. Namely, we show he inefficiency of a balanced-budge fiscal expansion while he same policy proves o be efficien in M-F ype of models. The conras comes from he difference concerning he efficiency crierion beween he radiional and new lieraure. In he NOEM lieraure, efficiency is measured by he welfare while in M-F models i is measured by he oupu or real income. In fac, he difference beween he implicaions of M-F models and our resuls 24

26 depends on he impac of financial inegraion on he effecs of fiscal policy. Indeed, fiscal policy efficiency measured by is effec on oupu is affeced by he degree of financial inegraion while he efficiency measured by is effec on welfare is independen of he financial ransacion coss. Therefore, he quesion of financial inegraion which is imporan for a cenral bank is no crucial for he fiscal auhoriies in a moneary union and for heir fuure members. Fiscal auhoriies may neverheless prefer o improve financial inegraion since higher financial inegraion decreases he volailiy of shor run consumpion and ineres rae following unanicipaed fiscal shocks semming from abroad. We have o noe ha our assumpion of pure wase naure of public spending is crucial for he inefficiency of fiscal policy. Useful governmen spending as in Ganelli (2003) or Corse- Peseni (200) would probably lead o an increase in welfare following a fiscal expansion. However, welfare would be independen of he degree of financial inegraion even wih useful public spending. References ECB (2003), The inegraion of Europe s financial markes, Monhly Bullein of ECB, n 0: Caselli P. (200), Fiscal consolidaion under fixed exchange raes, European Economic Review 45: Cenesiz A. and C. Pierdzioch (2006), Capial mobiliy; labor markes, and macroeconomic Policy, MPRA Paper n 532. Corsei G and P. Peseni (200), Welfare and macroeconomic inerdependence, Quarerly Journal of Economics May: Couinho L. (2005), Fiscal policy in NOEM and prospecs for fiscal policy coordinaion, Journal of Economic Surveys, vol.9, n 5: Frenkel J.A. and A. Razin (2002), Fiscal policies and growh in he world economy, The MIT Press. Ganelli G. (2003), Useful governmen spending, direc crowding-ou and fiscal policy inerdependence, Journal of inernaional money and finance 22: Koenig G. e I. Zeyneloglu (2006), La poliique budgéaire dans la nouvelle macroéconomie inernaionale, Documens de ravail du BETA, n

27 Obsfeld, M. and K. Rogoff (995), Exchange Rae Dynamics Redux, Journal of Poliical Economy,03: Obsfeld, M. and K. Rogoff (996), Foundaions of inernaional macroeconomics, MIT Press Pierdzioch C. (2004), Capial mobiliy and he effeciveness of fiscal policy in open economies, Journal of Macroeconomics 26: Pierdzioch C. (2005), Home-produc bias, capial mobiliy, and macroeconomic volailiy, Oxford Economic Papers, vol.57,n : Schmiedel H. and A. Schönenberger (2005), Inegraion of securiies marke infrasrucure in he euro area, Occasional Paper n 33. Senay O.(998), The effecs of goods and financial marke inegraion on macroeconomic volailiy, The Mancheser School Supplemen: Suherland A. (996), Financial marke inegraion and macroeconomic volailiy, Scandinavian Journal of Economics 98/4: Van Der Ploeg F.(994), Handbook of inernaional macroeconomics, Blackwell, chaper. 26