The Welfare Gains of Trade Integration in the European Monetary Union

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1 The Welfare Gans of Trade Inegraon n he European Moneary Unon Séphane Auray, Aurélen Eyquem, Jean-Chrsophe Pouneau To ce hs verson: Séphane Auray, Aurélen Eyquem, Jean-Chrsophe Pouneau. The Welfare Gans of Trade Inegraon n he European Moneary Unon. Workng Paper GATE 9-7. Workng Paper GATE <halshs-464> HAL Id: halshs-464 hps://halshs.archves-ouveres.fr/halshs-464 Submed on 6 Mar HAL s a mul-dscplnary open access archve for he depos and dssemnaon of scenfc research documens, wheher hey are publshed or no. The documens may come from eachng and research nsuons n France or abroad, or from publc or prvae research ceners. L archve ouvere plurdscplnare HAL, es desnée au dépô e à la dffuson de documens scenfques de nveau recherche, publés ou non, émanan des éablssemens d ensegnemen e de recherche franças ou érangers, des laboraores publcs ou prvés.

2 GATE Groupe d Analyse e de Théore Économque UMR 584 du CNRS DOCUMENTS DE TRAVAIL - WORKING PAPERS W.P. 9-7 The Welfare Gans of Trade Inegraon n he European Moneary Unon Séphane Auray, Aurélen Eyquem, Jean-Chrsophe Pouneau Décembre 9 GATE Groupe d Analyse e de Théore Économque UMR 584 du CNRS 9 chemn des Moulles 69 Écully France B.P Écully Cedex Tél. + () Fax + () Messagere élecronque gae@gae.cnrs.fr Serveur Web :

3 The Welfare Gans of Trade Inegraon n he European Moneary Unon? Séphane Auray a;, Aurélen Eyquem b, Jean-Chrsophe Pouneau b a GREMARS, Unversé de Llle and CIRPEE, Mason de la Recherche, Domane Unversare du Pon de Bos, BP 49, 5965 Vlleneuve d Ascq cedex, France b CREM, Unversé de Rennes, 7, place Hoche, 565 Rennes Cedex, France Frs Verson: June 6. Ths verson: January 9 Absrac Ths paper evaluaes he welfare gans arsng from a deeper rade negraon n he European Moneary Unon. To do hs, he European Moneary Unon s represened n a realsc way by an neremporal general equlbrum model wh ncomplee nancal markes, scky prces and home bas boh n prvae consumpon and producon. The model s esmaed and globally no rejeced by he daa. Two man resuls emerge : () an ncrease n vercal (nermedae goods) rade mples welfare gans whle () an ncrease n horzonal rade mples welfare losses. Keywords: rade negraon, n aon d erenals, welfare analyss, opmal currency areas. J.E.L. Class caon: F, F4, F47. Inroducon Ths arcle nvesgaes he welfare e ecs of a deeper horzonal or vercal rade negraon n he European Moneary Unon (EMU). Independenly of s long-run consequences, welfare gans of rade negraon usually res upon he ncreased correlaon of busness cycles and he mproved overall adequacy of he common moneary? We would lke o hank James Anderson, as well as parcpans of he ESEM n Budapes, he RIEF Meeng n Rome, and he 4h Symposum n Money, Bankng and Fnance n Rennes for helpful commens. The radonal dsclamer apples. Correspondng auhor. Emal: sephane.auray@unv-llle.fr

4 polcy o naonal suaons. Ths paper shows ha he mpac of rade negraon s more conrased when assumng ha nancal markes are ncomplee and mperfecly negraed. We lay ou an esmaed wo-counry DSGE model of he European Moneary Unon (EMU) ha accouns for he mperfec negraon of boh goods and nancal markes. As n Rcc (997), he model encompasses real and moneary argumens for he coss of conducng a sngle moneary polcy n a moneary unon characerzed by busness cycles asymmeres and n aon d erenals. Indeed, he model feaures home bas n prvae consumpon and producon echnology, ncomplee and mperfecly negraed prvae nancal markes, Calvo ype scky prces, and..d. producvy and publc spendng shocks. These assumpons are also se up o be conssen wh he curren economc suaon of he EMU, characerzed by perssen asymmeres n busness cycles and sgn can n aon d erenals (see Camacho, Perez-Quros and Saz, 6 and Lane, 6 for dscussons). In hs racable framework, asymmerc shocks and/or shocks mply asymmeres n busness cycles and n aon d erenals ha can no be addressed by he cenral bank of he moneary unon. These busness cycles asymmeres and n aon d erenals ranslae no welfare coss, buldng on wo mans sources: nomnal nera and mperfec rsk-sharng combned o a cosly access o nancal markes. The role of nomnal nera n a moneary unon, as well as means o reduce he assocaed coss, have already been exensvely suded n he leraure (see among ohers Bengno, 4; Beesma and Jensen, 5 and Gal and Monacell, 8). Less aenon has been pad o welfare losses relaed o mperfecly negraed nancal markes n a moneary unon. In lne wh Carré and Collard (), we show ha mperfec rsk-sharng crucally a ecs he welfare coss of busness cycles asymmeres and he sze, sgn and srucure of welfare gans generaed by rade negraon. Frs, we show ha an ncrease of horzonal or vercal rade negraon, modeled as a reducon of home bas n consumpon or n producon, ncreases he correlaon of busness cycles hrough an ncrease of muual rade ows. The overall adequacy of he common moneary polcy o naonal suaons s hus clearly mproved. The volaly of naonal n aon raes decreases, whch sgn canly mproves he aggregae welfare n he moneary unon. These resuls are n he spr of hose of Romer (99), bu he mechansms ha lead o hese e ecs are d eren. Second, vercal and horzonal rade have oppose e ecs on he paern of exernal adjusmen o asymmerc shocks. Vercal rade negraon reduces he overall need for exernal adjusmen,.e. he volaly of he curren accoun whle horzonal rade ncreases. Because nancal markes are ncomplee and mperfecly negraed, a hgher (respecvely lower) volaly of he curren accoun ncreases (respecvely Accordng o Romer, loose moneary polces become less appealng when openness ncreases.

5 dampens) he welfare coss relaed o he mperfec negraon of nancal markes and mperfec rsk-sharng. The resul bulds on he followng mechansm. Usng nancal markes (he curren accoun) more nensvely o smooh her wealh over me, households ncrease (respecvely decrease) her labor supply when conracng debs (respecvely accumulang asses) o respec her neremporal budge consran. Snce we consder a closed moneary unon, debs conraced by he represenave household of a counry are necessarly equal o he cumulaed asses of he represenave household of he oher counry. As a resul, ncreased movemens of he curren accoun are me by oppose changes n labor supples. In he equlbrum, he dsance of relave hours, relave wages and nermedae erms-of-rade o her naural equlbrum pah (characerzed by complee nancal markes) ncreases, whch generaes welfare losses. The welfare gans of vercal rade negraon are consequenly renforced, whle he welfare gans of horzonal rade negraon are reduced or urn no welfare losses, dependng on parameerzaons. Quanavely speakng, we hghlgh ha vercal rade negraon leads o mporan welfare gans for he whole range of possble parameers of he model. In he baselne esmaon, we show ha a % ncrease of vercal rade mples an average welfare gan equvalen o a.76% rse of permanen consumpon for a consan labor e or. On he oher hand, horzonal rade generaes lower welfare gans or welfare losses, dependng on he paramerzaon. In he baselne esmaon, a % ncrease of horzonal arde mples an average welfare loss equvalen o a.9% drop of permanen consumpon. A sensvy analyss shows ha horzonal rade can lead o welfare gans, especally when he welfare coss of nomnal rgdes ncrease or when he welfare coss of mperfec nancal negraon decrease. The remanng of he paper s organzed as follows. Secon descrbes a wo-counry model of an mperfecly negraed moneary unon. Based on EMU daa, Secon provdes esmaes for he srucural parameers of he log lnear approxmaon of he model. The dynamcs properes of he model are analyzed n Secon 4. Secon 5 provdes an exensve welfare analyss of an ncrease n rade negraon and presens some sensvy analyss. A las secon o ers some concludng remarks. An mperfecly negraed moneary unon The model descrbes a wo-counry world wh a common currency. Each naon represens half of hs moneary unon. I s populaed by N n nely-lvng households, a governmen, rms producng nermedae and nal goods, and mporers assemblng Ths ncrease s he acual consensus concernng he e ec of he EMU on nrazone rade (see Baldwn, 6).

6 consumpon goods. All goods are raded. Moneary polcy s delegaed o he cenral bank of he moneary unon whch conrols he neres rae. The nernaonal nancal marke s ncomplee and agens only rade one-perod compose bonds.. Households and naonal governmens In each counry he number of n nely-lvng households s normalzed o one. The represenave household j [; ] of naon fh; fg maxmzes a welfare ndex, subjec o, ( X C E (j) = N (j) + + ) ; () B +(j) R B (j) = W N (j) + (j) P C (j) T (j) P ; AC (j); () and he followng ransversaly condon, n lm T! T s=rs E B T + (j) o = : In Eq. (), he subjecve dscoun facor,, s equal o (+), s he neremporal elascy of subsuon of prvae consumpon and s he nverse of he Frsch elascy. The aggregae consumpon bundle of agen (j) n counry s called C (j) and he quany of labor ha hs agen supples on he labor marke N (j). Money holdngs are no nroduced n he uly funcon snce he money marke plays no role for he dynamcs when he nomnal neres rae s he moneary polcy nsrumen (see Beesma and Jensen, 5). In Eq. (), B(j) s he amoun of one-perod nomnal bonds hold by he represenave agen of counry a he end of perod, ha pays a gross nomnal rae of neres R beween perods ( ) and. The consumer prce ndex (CPI) n counry s called P whle P ; corresponds o he producer prce ndex (PPI) n counry. W s he nomnal wage n counry n perod, (j) = R (k; j)dk s he amoun of pro s pad by monopolsc nal goods producers, and T (j) s a lump-sum ransfer. Fnally, n he budge consran, AC(j) s a quadrac porfolo adjusmen cos ha households have o pay o nancal nermedares o access nancal markes. The cos s de ned accordng o, AC (j) = h B + (j) B (j) ; Nomnal exchange rae ssues per se as well as he analyss of he condons underlyng he adopon of a common currency are beyond he scope of he paper. 4

7 where B (j) s he seady sae level of ne foregn asses. The Euler condon ha solves Eqs. ()-() s a eced by porfolo adjusmen coss snce, R + + P ; (B +(j) B (j)) E ( P C(j) ) = : () P+C +(j) The porfolo adjusmen cos parameer () a ecs he sensvy of wealh s accumulaon o a varaon of he neres rae, as becomes more or less cosly o smooh consumpon by accessng nancal markes. For nsance, when decreases, s less cosly for he households o access o he nancal markes. The labor supply funcon s based on he radonal consumpon/lesure arbrage, N (j) C(j) = W : (4) P. Governmens Governmens choose he amoun of publc spendng on he nal goods marke and balance her budge usng lump-sum ransfers. The budge consran of he governmen s gven by, Z T (j)dj + Z P ; (k)y (k)dk = P ; G ; where s a proporonal subsdy o rms. Mxng monopolsc compeon and Calvo saggered prce conracs on nal goods markes nroduces several dsorons wh respec o he Pareo e cen equlbrum. Nomnal rgdes mply ne cen ucuaons of boh equlbrum n aon and oupu whle he assumpon of monopolsc compeon a ecs he seady sae. Whle moneary and/or scal polcy may address he rs ssue, an opmal subsdy s able o address he second ssue and resores he rs-bes allocaon n he seady sae (see Bengno and Woodford, 5). Naonal publc spendng are enrely home based,.e., Z G = G (k) dk ; where he level of aggregae publc spendng evolves accordng o, G + = g G + g G + g;+: where g; s an..d. nnovaon. 5

8 . Frms.. Inermedae goods producers The producon of nal goods consss n a wo-sep process. Frs, n each counry, a connuum of dencal rms (normalzed o one) produce he same nermedae good and sell on on a compeve marke. The producon funcon of hese rms s gven by, X = A L ; where L s he labor demand and A s he level of labor producvy evolvng accordng o, A + = ( a ) A + a A + a;+: where a; s an..d. nnovaon... Fnal goods producers Second, nermedae goods are raded whn he moneary unon and combned by monopolsc nal goods producers k [; ]. Inermedae goods are sold a her margnal cos W =A and nermedae erms-of-rade are, = W f =A f : W h =A h The producon funcon of nal goods producer k locaed n counry s gven by, Y (k) = ( ) X h; (k) + ( ) X f; (k) : (5) In hs expresson, X h;(k) s he consumpon of nermedae goods produced n counry h of rm k locaed n counry. The parameer ( ) h ; s he home bas n he producon of nal goods. In he producon funcon (5), s he elascy of subsuon beween nermedae goods. The companon nomnal margnal cos of rm k n counry ; MC (k); s gven by, MC (k) = ( ) W h =A h + ( ) W f =A f : Fnal goods prces are governed by sandard Calvo conracs. Each perod, only a fracon ( ) of randomly seleced rms locaed n counry fh; fg are allowed o se new prces. Assumng ha rms do no dscrmnae among markes hey adress, 6

9 hese rms choose he followng opmal prce P ; (k); P v= P ; (k) = ( ) ( ) P v= ( ) v Y E +v (k)mc+v P+v C +v (j) ( ) v E Y +v (k) P +v C +v (j) : Aggregang among nal rms and assumng behavoral symmery of monopolsc producers, he average producer prce level of nal goods n counry fh; fg s, P ; = h P ; (k) + P; :.. Imporers A connuum of mporers buld uns of consumpon goods % usng domesc and foregn nal goods accordng he followng producon funcon, Z Z (%) = 4( ) ( ) Zh;(%; k) ( ) Z dk + Zf;(%; k) and sell hem on perfecly compeve markes a he followng prce, ( ) ( ) dk 5 ; P (%) = P = Z 4( ) P h; (k) dk + Z P f; (k) dk 5 ; or equvalenly, P = ( ) (Ph; ) + (P f; ) : In hese expressons, ( ) h ; s he home bas n he producon of consumpon goods, s he elascy of subsuon among naonal varees and s he elascy of susbuon beween domesc and foregn nal goods. Fnally, we de ne nal erms-of-rade n he moneary unon as, S = P f; P h; : I has now become sandard o regard home bas parameers, such as or as a relevan measures of goods marke openness. Indeed, n equlbrum, and are he share of mpored goods n he producon of nal and consumpon goods respecvely (see Corse, 6 and Galí and Monacell, 5). In he remander of he paper, we hus consder and drecly as parameers measurng horzonal and vercal rade openness. 7

10 .4 Moneary polcy A common cenral bank conrols he nomnal neres rae whn he moneary unon, R + = ( r ) R + r R + ' ( u u ) ; where u = h + f and = P =P. Ths rule s commonly used n he leraure (see among ohers Taylor, 99; Clarda, Galí and Gerler, 998 and Rudebusch and Svensson, 999). Furhermore, s a far approxmaon of he moneary polcy of he European Cenral Bank wh respec o s msson,.e. he sablzaon of aggregae n aon n he EMU. Fnally, a large emprcal leraure hghlghs he smoohness of he nomnal neres rae varaons n he euro area (see among ohers Peersman and Smes, 999 and Gerlach and Schnabel, )..5 Markes equlbrum We solve he model assumng ha each counry s he mrror mage of he oher on he goods marke. Posng h = and h = we smply ge f = ( ) and f = ( ). A compeve equlbrum s de ned as a sequence of quanes, fq g = = n C h ; C f ; N h ; N f ; Y h ; Y f ; Z h ; Z f ; L h ; L f ; B h +; B f +; AC h ; AC f o, and a sequence of prces, such ha: fp g = = n P h; (k) ; P f; (k) ; P h; ; P f; ; P h ; P f ; W h ; W f ; R + o, () For a gven sequence of exogenous shocks fs g = = n A h ; A f ; G h ; G f o and prces fp g =, fq g = respecs households rs order condons and maxmzes he pro s of consumpon, nal and nermedae goods producers. () For a gven sequence of shocks fs g = and quanes fq g =, fp g = clears consumpon, nal and nermedae goods markes, labor markes, and nancal markes, Z N = Z B h (j)dj + N (j)dj = L ; Z B f (j)dj = : In he equlbrum, ne foregn asses evolve as follows, B h + B h = (R ) B h + P f C f P h C h + MC f Y f DP f MC h Y h DP h ; 8

11 where DP s he dsperson of nal goods producon prces n counry. Esmaon We esmae he log lnear verson of he model usng he Smulaed Mehod of Momens (SMM) of Hansen (98). 4 In he symmerc compeve exble prce seady sae, we assume ha A = A = and ha = ( ). Oher seady sae relaons are gven by, Y = ( ) N = ( ) + ; C = ( ) + ; G = ( ) + ; + ; W=P = and R = : We use quarerly daa from EMU counres (OECD Economc Oulook quarerly daabase) poseror o he German reun caon,.e. rangng from 99 o 6. Aggregaes are convered n he same currency and we focus on he followng seasonally adjused seres: GDP (whou nvesmen), prvae consumpon, employmen, GDP de aor, rade balance and curren accoun balance (as a percenage of GDP). We also ake no accoun he evoluon of he average nomnal shor-erm neres rae n he EMU. We buld wo regons based on he levels of nomnal rgdes of EMU counres (see Bengno, 4). Table ndcaes he percenage of goods prces n he consumer prce ndex changng every monh n EMU counres (daa are borrowed from Alvarez e al., 6). We consder ha counres n whch less han 5% of CPI goods prces change every monh belong o he group of hgh nomnal rgdes and counres n whch more han 5% of CPI goods prces change every monh belong o he group of low nomnal rgdes. Consequenly, n he rs group (regon h n he model), we have Germany, Span and Ialy and n he second group (regon f n he model), we have all remanng counres. 5 Once boh regons of he moneary unon are de ned, we aggregae seres gven he relave me-varyng weghs of counres n erms of GDP n he regon. In aon raes are compued usng GDP de aors. Fnally, we ake he log of GDP, consumpon and employmen and derend all seres usng he HP- ler. We esmae he model usng a large sample of second order momens. We focus on hree ypes of momen: sandard devaons (absolue or relave o sandard devaon of oupu), rs-order auocorrelaons and cross-correlaons. Sandard devaons and auocorrelaons concern all 4 The log lnear approxmaon of he model s presened n Table A. n he appendx. 5 Ausra, Greece and Ireland are no aken no accoun because daa are unavalable or no relable. 9

12 Table Nomnal rgdes n he EMU % goods n he CPI % of counry s GDP Regon changng prces every monh n he EMU GDP Germany h :5 9: France f :9 :6 Ialy h : 7:7 Span h : : Neherlands f 6: 6:4 Belgum f 7:6 :7 Luxembourg f : Fnland f : : Porugal f : :8 varables and cross-correlaons are hose of oupu wh prvae consumpon, oupu wh hours and prvae consumpon wh hours. Some parameers of he model are calbraed. We se = :988; whch corresponds o an annual real neres rae of 4:7%, conssen wh he average real neres rae over he correspondng perod n he EMU. Followng Roemberg and Woodford (997), he elascy of subsuon beween varees s = 7; mplyng an average 6-7% seady sae mark-up (compensaed a he equlbrum by he opmal subsdy). The average share of publc spendng n he GDP s se o = :5 (see Galí and Monacell, 8). The elascy of subsuon beween nermedae goods s = :5 (see Haraul, ). Fnally, we calbrae parameers of he nomnal neres rae rule usng sandard values for he smoohng parameer r = :7 and for he feedback coe cen on aggregae n aon ' = :5 (see Gerlach and Schnabel, ). Oher parameers are esmaed. The resuls of he esmaon are repored n Table. The es allowed by over-denfyng condons mples a :85% p-value, whch ndcaes ha he model s no rejeced by he daa. Table Esmaed parameers h f a g sd( a; ) sd( g; ) J sa Ov: Id: Sa: p value : 875 (6) :85 : 99% sgn can

13 Parameer values are conssen wh mos esmaes or calbraons repored n he leraure and are sgn can. The nverse of he Frsch elascy s equal o 7:8 and les on he upper bound of he range pu forh by Canzoner, Cumby and Dba (6). Ths value s conssen wh a sluggsh response of labour supply o varous shocks n he EMU. The neremporal elascy of subsuon of prvae consumpon s = :8, close o sandard values (see Bengno, 4). Ths parameer governs boh he nensy of he ransmsson of moneary polcy hrough he sensvy of consumpon o he real neres rae and he arbrage beween lesure and consumpon. Home bas parameers are = :5 and = :7 and deermne he degree of rade openness of nermedae and nal goods markes. These values are conssen wh hose found n Faa (7) and wh sandard openness measures calculaed usng EMU daa. The esmaon of = :9 s no far from Schm-Grohé and Urbe (). I mples ha households have o pay an average annual :6% neres rae premum o access nancal markes. Nomnal rgdes parameers are very close snce h = :54 and f = :5. Our esmaon s lower han usual esmaons, as n Clarda, Galí and Gerler (998), bu maches he values pu forh n Alvarez e al. (6). Fnally, parameers governng shocks processes are a = :955, g = :886, sd( a; ) = :79% and sd( g; ) = :99%. These esmaons are conssen wh mos values found n he RBC leraure. 4 Dynamc properes In hs secon we sudy he dynamc properes of he economy when facng asymmerc producvy and publc spendng shocks. Fgure plos he Impulse Response Funcons (IRFs) o a posve un producvy shock n he home counry. Oupu rses n boh counres, whle more subsanally n counry h; peekng a :7% for a % producvy shock. In counry h, he remang of producvy gans s used o reduce he labour e or, abou :5% on mpac. Ths e ec arses because he wealh e ec domnaes n models wh separable uly funcons and whou physcal capal. The wealh e ec s renforced by he :7% drop of he PPI n aon n he home counry. The ransmsson of he shock n counry f draws boh on rade ows and moneary polcy. Whle agens n counry h susan hgher producon and consumpon levels, hey generae nermedae and nal rade ows whn he moneary unon, whch nduces a posve reacon of he oupu n counry f of abou :% on mpac. The common moneary polcy also favors a posve ransmsson. By reacng o aggregae n aon, he cenral bank lowers s equlbrum nomnal neres rae, whch nduces an ncrease of aggregae consumpon and oupu n counry f: The supply shock n counry h hus ranslaes no a posve demand shock n counry f, whch generaes

14 % devaon % devaon or % of ss consumpon % devaon % devaon % devaon % devaon Fg.. IRFs o a un producvy shock n counry h Oupu PPI nflaon.6 foregn home..5 foregn home Quarers Hours Quarers Consumpon Quarers Terms of rade nermedae fnal Quarers Nomnal neres rae (NIR) Curren accoun (CA) NIR CA Quarers Quarers some PPI n aon, peekng a :% on mpac and reurnng quckly o he seady sae. Snce wages and producon prces drop n counry h and rse n counry f, boh nermedae and nal erms-of-rade mprove n counry h. Fnal goods prces are sluggsh, whch mples an undershoong of nal erms-of-rade wh respec o he ucuaon of nermedae erms-of-rade. Fnally, agens n counry h accumulae ne foregn asses, mplyng an mprovemen of he curren accoun peekng a 6-7% of seady sae consumpon on mpac. Fgure plos he IRFs o a posve un publc spendng shock n he home counry. Oupu ncreases of :5% on mpac n counry h, mplyng a rse of boh home and foregn labor supply, requred o susan he demanded quany of nal goods n counry h. Prvae consumpon drops seadly n boh counres. The drop aans :% n counry h, because of he crowdng-ou e ec and because Rcardan equvalence holds. The drop s more genle n counry f, reachng :8% on mpac. Snce global demand drops n counry f, oupu clearly falls of :7% on mpac whle reurnng

15 % devaon % devaon or % of ss consumpon % devaon % devaon % devaon % devaon Fg.. IRFs o a un publc spendng shock n counry h Oupu PPI nflaon.5..5 foregn home.4... foregn home Quarers Hours Quarers Consumpon Quarers Terms of rade Quarers Nomnal neres rae (NIR) Curren accoun (CA)....4 nermedae fnal 4 NIR CA Quarers Quarers very quckly o he seady sae. Mechansms behnd he negave ransmsson of a publc spendng shocks n counry h buld on a radonal beggar-hy-neghbor e ec and hghlgh he role of home bas n publc spendng n a rs approach. However, hs e ec also reles () on he fall of prvae consumpon n counry h, mplyng a drop of counry h mpors from counry f and () on he ncrease of nomnal neres rae mpled by he reacon of he cenral bank o he n aon of counry h. The posve demand shock n counry h hus ranslaes no a negave demand shock n counry f. Exernal adjusmen mples a seady deeroraon of nal and nermedae erms-ofrade and an accumulaon of ne foregn lables n counry h. The correspondng de c of he curren accoun peeks a 4:5-5% of seady sae consumpon on mpac.

16 5 The welfare gans of rade negraon In hs secon, we measure he welfare gans arsng from a deeper horzonal of vercal rade negraon n he EMU. 5. Welfare ndcaors We bul an explc welfare ndcaor on a second-order approxmaon of he aggregae uly funcon. The welfare measure can be expressed as a dscouned sum of uly ows,! = q X E f`g + ::p + O : = where q = ( ) ( ) +, ::p gahers erms ndependen of he problem and O are erms of order or hgher. In hs expresson, he nsan welfare conrbuon ` s a quadrac funcon of devaons of key economc varables from her naural equlbrum pah, k ( h h; e h; ) + k ( f f; e f; ) + ( ) + (y u ey u ) ( ) + ( ) & (s es ) + & ( e ) + ( ) (c r ec r ) + (n r s en r s) ; (6) ` = where k = ( )( ). In Eq. (6), a lde denoes he pah of varables n he naural equlbrum, de ned as he equlbrum under exble prces and complee and perfecly negraed asse markes,.e. h = f = and =. Superscrps u and r respecvely sand for aggregae and relave varables. The welfare measure! penalzes naonal PPI n aon raes, he aggregae oupu gap, he relave consumpon gap, he relave hours gap and erms-of-rade gaps. The weghs a eced o naonal n aon raes are sensve o he degree of prce sckness hrough he values of k. Parameer k depends negavely on he degree of prce rgdes, so ha hgher weghs are deferred o n aon raes when prces are scker. We compue he consumpon equvalen welfare loss. As n Beesma and Jensen (5), s de ned accordng o, = " # ( ) ( ) ( + ( )) (!! ) ; (7) where! measures he welfare for a gven reference suaon. convers he welfare gans assocaed o a pareo-superor equlbrum! no a szable yardsck n erms of permanen ncrease of consumpon for an unchanged work e or. 4

17 5. Baselne scenaro Runnng smulaons usng he baselne esmaon, Table conrass he welfare gans or losses ( ) arsng from a deeper horzonal or vercal rade negraon conssen wh he evdence documened by Baldwn (6),.e. a % ncrease of or. The able also deals he evoluon of he volaly of varables enerng n he welfare loss funcon. Table The welfare gans of a % deeper horzonal () or vercal () rade negraon Sandard devaon (%) (%) b h; b f; by u bs b bc r bn r Baselne :88 :9 :47 :7 :95 : :8 = :97 :8 :86 :87 :47 :665 :96 :8 : V araon(%) :5 :49 : 9: :98 :64 :7 = :74 :9 :85 :87 :47 :7 :786 :996 : V araon(%) :5 :54 : :8 7: :56 :54 Noe: varables wh a ha denoe devaons from naural equlbrum On one hand, a % ncrease of generaes large welfare gans, equvalen o an average :9% ncrease of permanen consumpon. The overall volaly of erms enerng he loss funcon s clearly dampened. When vercal rade ncreases, he composon of nal goods produced becomes more smlar, whch mples ha shocks a ecng he producon process of nermedae goods asymmercally have more smlar e ecs on oupu and margnal coss. Ths mechansm also conrbues o lower he PPI naonal n aon raes, as llusraed by he new keynesan Phllps curves. If margnal coss, he drvng force behnd he PPI n aon raes, are more correlaed, hen he PPI n aon raes are a eced n he same way. The adequacy of he common moneary polcy o naonal n aon raes and busness cycles ncreases, whch mproves s e ecveness and reduces he volaly of naonal n aon raes. Fnally, by he same reasonng, he volaly of nermedae erms-of-rade, relave hours and relave consumpons gaps s reduced, whch ranslaes no aggregae welfare gans. On he oher hand, n he baselne scenaro, a % ncrease of horzonal rade measured by a % ncrease of, mples an average welfare loss equvalen o a :8% fall of permanen consumpon. A close examnaon of volales shows ha he dsance of naonal n aon raes and nal erms-of-rade from her naural equlbrum pah s clearly reduced (respecvely by :5% n average and 9:%), whch has welfare mprovng consequences. Snce he composon of he CPI n aon raes and prvae consumpon bundles becomes more smlar, for a gven moneary polcy rule, moneary polcy becomes more e ecve and s ably o sablze naonal PPI n aon raes ncreases. These lower naonal PPI 5

18 n aon raes resul n a lower pressure on nal erms-of-rade, whch clearly reduces her volaly. However, whle exernal adjusmen reles less on he nal erms-of-rade, he volaly of he curren accoun s enhanced, whch leads o welfare losses ha more han compensae he prevous welfare gans. These losses are mpuable o he ncreased dsance of hours and nermedae erms-of-rade o her naural level. The fac ha agens use he curren accoun more nensvely o adjus asymmerc shocks mples ha labor supples and wages become less correlaed and ha he volaly of nermedae erms-of-rade, based on relave wages, ncreases. These e ecs arse because debor (resp. credor) households need o mprove (resp. lower) her labor supply n order o ncrease (resp. decrease) her earnngs and repay her debs (resp. lower her savngs) n he medum run. The nensy of hs e ec clearly depends on he level of coss leved by nancal nermedares, ha ncreases he sensvy of consumpons, labor e ors and equlbrum wages o varaons of ne foregn asses or lables. A corollary o he ncreased volaly of relave labor e ors and nermedae erms-of-rade s he ncreased volaly of relave consumpons. Because he composon of consumpons becomes more smlar, relave consumpons should be less volale. However, he consequences of he greaer use of he curren accoun dampen hs rs e ec, mplyng ha relave consumpons gaps are more volale, whch s also cosly n erms of welfare. Summng up, an ncrease n horzonal rade reduces he nensy of ne cences caused by nomnal rgdes bu magn es ne cences relaed o he mperfec negraon of nancal markes. For he baselne scenaro, welfare losses are hgher han welfare gans. Our resuls mach hose of oher sudes ha quanfy he welfare gans assocaed o he reducon of varous dsorons n he economy. Canzoner e al. (6) esmae ha he welfare coss of nomnal nera can reach 4% o 5%, mosly dependng on he degree of perssence n he economy. In our model, he value of he Frsch elascy s low, he assumpon of mperfec rsk-sharng adds an mporan source of perssence, and he esmaed perssence of shocks s que hgh. The overall perssence s hus mporan and, conssenly wh Canzoner e al. (6), nomnal nera s que cosly n erms of welfare n our model. Several sudes also quanfy he welfare gans of nancal markes negraon, buldng on hgher rsk-sharng and consumpon smoohng. For example, Van Wncoop (999) nds ha he welfare gans from rsksharng range from % o more han 7% of consumpon. Those welfare gans could acually be much hgher accordng o prevous sudes usng alernave mehods o measure nancal markes negraon (see Lews, 996). More recenly, Demyanyk and Volosovych (8) documen ha he welfare gans of nancal markes negraon range from % of permanen consumpon for EMU members o more han 8% for new European Unon members. In our model, boh sources of welfare losses (nomnal nera and mperfec rsk-sharng) are combned and o yeld mporan welfare losses. 6

19 Ψ Ψ Ψ Ψ As suggesed by Dosey and Ireland (996), hs combnaon of varous frcons may acually resul n mporan welfare losses. 5. Sensvy analyss We nvesgae he robusness of our resuls o a wde range of parameers varaons. The smulaons have been run o evaluae he sensvy of our resuls o he asymmery n he paern of nomnal rgdes. Snce hese smulaons show ha asymmeres n he paern of nomnal rgdes do no play a sgn can role n generang our resuls, hey are no repored bu avalable. Fgure repors he sensvy of welfare gans or losses assocaed o a % ncrease n horzonal rade o d eren varaons n he se of srucural parameers. Fg.. Sensvy of he welfare gans or losses of a % ncrease n horzonal rade σ ψ 4 6 µ φ σ orψ µ orφ χ η h η f η orη h f Fgure one more me hghlghs he neracon beween wo e ecs when horzonal rade negraon ncreases: () welfare gans relaed o he lower coss of nomnal rgdes and () welfare losses caused by he ncreased volaly of he curren accoun. 7

20 Dependng on paramerzaon, he overall welfare e ec of horzonal rade negraon s eher posve or negave. When porfolo managemen coss () fall under a ceran hreshold, beween :9% and :%, or when nomnal rgdes are beyond :6, horzonal rade negraon generaes welfare gans. Ths s he case eher because he enhanced volaly of he curren accoun become less cosly or because he reducon of naonal PPI n aon raes generaes hgher welfare gans. These resuls clearly show ha frcons on nancal markes are a key assumpon o generae our resuls. Ths assumpon nroduces welfare losses relaed o mperfec rsk-sharng among members of he moneary unon. The sensvy analyss reveals ha small frcons ( = :9% mples ha households have o pay an average :6% annual neres rae premum o access nancal markes) are su cen o mgae he welfare gans of lower n aon raes when horzonal rade ncreases. One shall also noce ha he welfare gans of lower naonal n aon raes clearly surpass welfare losses when nomnal rgdes parameers ake sandard values of he leraure (around :7-:75). The sensvy of welfare gans/losses o varaons of he elascy of subsuon beween nermedae or nal goods also llusraes he mechansm behnd welfare gans or losses. As he elascy of subsuon beween nal goods () ncreases, changes n he volaly of nal erms-of-rade mpled by an enhanced horzonal rade negraon are lower. In he equlbrum, he volaly of PPI n aon raes s hus reduced, whle he mpac of on he volaly of he curren accoun s clearly posve (see he equaon governng ne foregn asses dynamcs n Table A.). Welfare gans relaed o lower naonal n aon raes are hus dampened, whle welfare losses caused by he ncreased volaly of he curren accoun ncrease. As a consequence, ne welfare gans of horzonal rade negraon depend negavely on he elascy of subsuon beween nal goods. On he conrary, as he elascy of subsuon beween nermedae goods () ncreases, nermedae erms-of-rade are less requred o ucuae o reach he equlbrum on nermedae goods markes, ceers parbus. As a consequence, he rse of he volaly of nermedae erms-of-rade, relave hours and relave consumpons gaps are reduced when horzonal rade ncreases, whch has a posve mpac on welfare gans. Fnally, he sensvy of welfare gans o he nverse of he Frsch elascy ( ) and he rsk-averson parameer () s also nvesgaed. When he neremporal elascy of labor supply ( ) ncreases, he volaly of hours decreases n he equlbrum. Snce welfare losses relaed o nancal frcons depend on he response of labor supply as documened n he prevous subsecon, lower responses of labor supples mply lower overall welfare losses or hgher overall welfare gans when horzonal rade negraon ncreases. The e ec of he rsk-averson parameer s somehow surprsng. The rskaverson parameer governs he wllngness of households o smooh her consumpon over me when undergong unexpeced asymmerc shocks, whch s assocaed wh an ncreased use of nancal markes, and should lead o hgher welfare losses. However, Fgure ells us ha hese aspecs are more han compensaed by he drop of he 8

21 Ψ Ψ Ψ Ψ volaly of erms-of-rade and of naonal n aon raes. Rsk-averson s hus found o have a posve mpac on he welfare gans generaed by an ncrease n horzonal rade negraon. Second, gure 4 repors he sensvy of welfare gans or losses assocaed o a % ncrease n vercal rade o d eren varaons n he se of srucural parameers. Fg. 4. Sensvy of he welfare gans or losses of a % ncrease n vercal rade σ orψ σ ψ 5 µ φ µ orφ η h χ η h orη f η f Welfare gans generaed by a % deeper vercal rade negraon are clearly ncreasng wh he degree of nomnal rgdes (), snce he reducon of naonal n aon raes s boh enhanced and more weghed n he loss funcon. These gans are bearly sensve o he level of porfolo managemen coss (), whch con rms ha nancal markes do no play an mporan role when rade negraon s vercal. The welfare gans of a deeper vercal rade negraon also clearly decrease wh he degree of subsuably beween goods. Whle he decrease s mporan when he subsuably of nal goods () ncreases (from more han 5% of permanen consumpon when = o % when = 5), welfare gans declne even more when 9

22 he subsuably of nermedae goods () ncreases (from 4% of permanen consumpon when = o % when = 5). In general, hgher subsuably lowers he requred varaons of erms-of-rade volaly when vercal rade ncreases. As a consequence, as subsuably ncreases, changes n nermedae and nal ermsof-rade volaly become very small when rade negraon ncreases, whch mpacs negavely on welfare gans. Ths e ec s much sronger for he subsuably beween nermedae goods because nomnal rgdes bear on nal goods prces whle nermedae goods prces are exble. When he subsuably beween nermedae goods ncreases, he volaly of nermedae erms-of-rade gaps end o become una eced and he mpac of vercal rade negraon on welfare vanshes. Because nal erms-of-rade are saggered, he welfare gans of vercal rade negraon do no compleely fade away. Fnally, an ncrease of he neremporal elascy of subsuon of labor supply ( ) has a negave mpac on he welfare gans of vercal rade negraon for mos plausble values ( > ). In he case of vercal rade negraon, he volaly of he curren accoun decreases. The sofenng e ec of an ncrease of on he volaly of labor supples hus a ecs welfare gans n he oppose drecon. Indeed, n he equlbrum, hgher values of mply lower volales of hours worked, whch slows down he process of reducon of regonal d erences n hours and lowers welfare gans of vercal rade negraon. 6 Concluson Ths paper shows ha horzonal and vercal rade negraon have d eren oucomes n erms of welfare n a moneary unon characerzed by busness cycles asymmeres and n aon d erenals. In boh cases, a deeper rade negraon reduces n aon d erenals by favorng a beer d uson of shocks from one counry o an anoher, hrough ncreased rade ows. Ths ncreased macroeconomc nerdependence helps he common moneary polcy o be n lne wh naonal suaons. Equlbrum naonal n aon raes decrease, and mply ha rade negraon hus generaes welfare gans. However, horzonal rade negraon mproves he volaly of he curren accoun whle vercal rade negraon reduces he overall need for exernal adjusmen n case of asymmerc shocks. As a consequence, horzonal rade negraon mples welfare losses ha mgh exceed he prevous welfare gans. For he baselne esmaon presened n hs paper, horzonal rade negraon produces welfare losses equvalen o an average.8% drop of permanen consumpon and vercal rade negraon generaes welfare gans ha amoun o an average.9% of permanen consumpon. However, an exensve sensvy analyss ndcaes ha he relave mporance of nancal markes frcons and nomnal rgdes plays a key role n he paern of welfare gans or losses.

23 The man concluson of he paper s ha nancal frcons, as well as her neracons wh real and nomnal rgdes should carefully be aken no accoun when analyzng busness cycles asymmeres n open economes and/or moneary unons. References Alvarez, L. J., Dhyne, E., Das, D., Ho mann, J., Jonker, N., Lünnemann, H. L. B. P., Rumler, F., Veronese, G. & Vlmunen, J. (6), Prce Seng n he Euro Area: Some Sylzed Facs from Indvdual Consumer Prce Daa, Journal of he European Economc Assocaon 4(-), Baldwn, R. (6), The Euro s Trade E ecs, ECB Workng Paper N o 594. Beesma, R. M. W. J. & Jensen, H. (5), Moneary and Fscal Polcy Ineracons n a Mcro-founded Model of Moneary Unon, Journal of Inernaonal Economcs 67(), 5. Bengno, P. (4), Opmal Moneary Polcy n a Currency Area, Journal of Inernaonal Economcs 6(), 9. Bengno, P. & Woodford, M. (5), In aon Sablzaon and Welfare: The Case of a Dsored Seady Sae, Journal of he European Economc Assocaon (6), Camacho, M., Perez-Quros, G. & Saz, L. (6), Are European Busness Cycles Close Enough o Be Jus One?, Journal of Economcs Dynamcs and Conrol (9-), Canzoner, M., Cumby, R. & Dba, B. (6), The Cos of Nomnal Inera n NNS Models, Journal of Money, Cred and Bankng. Forhcomng. Carré, M. & Collard, F. (), Moneary Unon: A Welfare-based Approach, European Economc Revew 47(), 5 5. Clarda, R., Galí, J. & Gerler, M. (998), Moneary Polcy Rules n Pracce. Some Inernaonal Evdence, European Economc Revew 4, 67. Corse, G. (6), Openness and he Case for Flexble Exchange Raes, Research n Economcs 6(),. Demyanyk, Y. & Volosovych, V. (8), Gans from Fnancal Inegraon n he European Unon: Evdence for New and Old Members, Journal of Inernaonal Money and Fnance 7, Dosey, M. & Ireland, P. (996), The Welfare Cos of In aon n General Equlbrum, Journal of Moneary Economcs 7(), Faa, E. (7), Fnance and Inernaonal Busness Cycles, Journal of Moneary Economcs 54(4), 8 4. Galí, J. & Monacell, T. (5), Moneary Polcy and Exchange Rae Volaly n a Small Open Economy, Revew of Economc Sudes 7, 77 4.

24 Galí, J. & Monacell, T. (8), Opmal Moneary and Fscal Polcy n a Currency Unon, Journal of Inernaonal Economcs. Forhcomng. Gerlach, S. & Schnabel, G. (), The Taylor Rule and Ineres Raes n he EMU Area, Economcs Leers 67, Haraul, J. O. (), Labor-marke Search and Inernaonal Busness Cycles, Revew of Economc Dynamcs 5, Hansen, G. (98), Large Sample Properes of Generalzed Mehod of Momens esmaors, Economerca 5(4), Lane, P. R. (6), The Real E ecs of he Euro, Journal of Economc Perspecves (4), Lews, K. K. (996), Consumpon, Sock Reurns, and he Gans from Inernaonal Rsksharng, Techncal repor, NBER Workng Paper N o 54. Peersman, G. & Smes, F. R. (999), The Taylor Rule, a Useful Moneary Benchmark for he Euro Area?, Inernaonal Fnance (), Rcc, L. A. (997), A Model of an Opmum Currency Area, Techncal repor, IMF Workng Paper N o 97/76. Romer, D. (99), Openness and In aon: Theory and Evdence, The Quarerly Journal of Economcs 8(4), Roemberg, J. & Woodford, M. (997), An Opmzaon-Based Economerc Framework for he Evaluaon of Moneary Polcy, n B. S. Bernanke & J. J. Roemberg, eds, NBER Macroeconomcs Annual. Rudebusch, G. & Svensson, L. (998), Polcy Rules for In aon Targeng, NBER Workng Paper N o 65. Schm-Grohé, S. & Urbe, M. (), Closng Small Open Economy Models, Journal of Inernaonal Economcs 6(), Taylor, J. (99), Dscreon versus Polcy Rules n Pracce, Carnege Rocheser Conference Seres on Publc Polcy 9, Van Wncoop, E. (999), How Bg are Poenal Welfare Gans from Inernaonal Rsksharng?, Journal of Inernaonal Economcs 47, 9 5. Woodford, M. (), Opmal Ineres-rae Smoohng, Revew of Economc Sudes 7(4),

25 APPENDIX A Log lnear approxmaon of he model Table A. A log lnear approxmaon of he model Euler equaons and labor supply E c h + c h = r + E f( ) h;+ + f;+ g ( ) + b h + o E nc f + c f = r + E f( ) f;+ + h;+ g + ( ) + b h + n h + c h = w h p h; s n f + cf = wf p f; + s In aon and erms-of-rade h; = E f h;+ g + ( h )( h ) ( ) w h h a h + w f a f f; = E f f;+ g + ( f )( f ) f ( ) w f a f + w h a h p h; p f; h; = p h; p h; f; = p f; p f; s s = f; h; = w f w h + a h a f Goods marke clearng y h = ( ) ( ) c h + c f + ( ) s + g h y f = ( ) ( ) c f + ch ( ) s + g f a h + n h = ( ) y h + y f + ( ) a f + nf = ( ) yf + yh ( ) Curren accoun b h + b h = b h + Ineres rae rule r + = r r + ' h; + f; hc f c h + ( ( ) ) s + [yf y h + ( ( ) ) ]

26 B The welfare loss funcon The welfare creron wres! T = X Z s=t s= s E U s h (j) + U s f (j) dj = X Z s=t s= s E U s h C h s (j) ; Ns h (j) + U s f = X Z s=t h s= s E U u C;s (j) UN;s(j) dj u ; C f s (j) ; N f s (j) dj where, afer usng he symmery among agens, U u C;(j) = U u C; = U u N;(j) = U u N; = C h ( ) + ( ) N h + ( + ) + ( + ) C f ; N f + : We compue welfare dervaons hrough a second order approxmaon of varables o her seady sae values and for second order expressons of shocks equal o zero,.e. [a ] = [g ] =. Before approxmang, we need o sae, hc h hn h h + c f + h n f = [c u ] + [c r ] ; = [n u ] + [n r ] : A second order approxmaon o U u C; wres, UC; u ' C + C c u + [c u ] + [c r ] + O : A second order approxmaon o U u N; wres, U u N; ' N N + " n u + + [n u ] + [n r ] # + O : (B.) 4

27 Recallng ha [a ] = ; a second order approxmaon of nermedae goods markes gves, n h + h a h + n h = ( ) y h + + h y h + + dp h + y f + ( ) + h y f + ( ) + dp f n f + h a f + n f = ( + ::p + O ; + ) y f + h y f + dp f y h ( ) + h y h ( ) + dp h + ::p + O ; where ::p sands for erms ha are ndependen of he problem, and, dp = var (p ;) ; mplyng ha [dp ] O. Combnng he las wo expressons, we ge, n u + [nu ] + [nr ] + ah n h + af n f = y u + [yu ] + [yr ] + ( ) [ ] + 4 var (p h;) + 4 var (p f;) + ::p + O : Combnng wh (B.), we ge, UN; u ' N + fy u + [yu ] + [yr ] ah n h af n f ( ) + [ ] + 4 var (p h;) + 4 var (p f;) + [n u ] + [n r ] g + ::p + O : 5

28 Now urnng o U u C;; we compue a second order approxmaon o nal goods markes condons, whle recallng ha [g ] =, y h + h y h = ( ) ( ) c h + s + h c h + s + ( ) c f + ( ) s + h c f + ( ) s y f + + ::p + O ; h y f = ( ) ( ) c f s + h c f s + ( ) c h ( ) s + h c h ( ) s + ::p + O ; whch allows o deduce, y u + [yu ] + [nr ] = ( ) c u + [cu ] + [cr ] or, ( ) ( ) [s ] + ::p + O ; c u + [cu ] + [cr ] = y u + ( ) [yu ] + [yr ] ( ) [s ] + ::p + O ; U u C; becomes, UC; u ' C f y u + [yu ] + [yr ] ( ) [s ] h c h h 4 c f g 4 + ::p + O : 6

29 Collecng erms, we ge, U u = UC; u UN; u ' C f y u + [yu ] + [yr ] ( ) [s ] [cu ] [cr ] g N + fy u + [yu ] + [yr ] ( ) + [ ] + 4 var (p h;) + 4 var (p f;) ah n h + [n u ] + [n r ] g + ::p + O : af n f Usng he fac ha, we ge, N + = Y A N = Y C = C ( ) ; U u ' C ( ) f ( ) & [s ] & [ ] + ah n h + af n f ( ) [c u ] + [c r ] [n u ] + [n r ] 4 var (p h;) 4 var (p f;)g + ::p + O ; where & = ( ) and & = ( ) : Recallng, we ge, n u = y u a u ; g u c u = yu ( ) ; U u ' C ( ) f ( ) & [s ] & [ ] 4 var (p h;) 4 var (p f;) h [y u ( ) ] y u g u ( ) [c r ] h [y u ] y u a u [nr ] + ah n h + af n f g + ::p + O : Recallng ha, ey u = ( )( + ) ( ) + au + ( ) + gu ; 7

30 he welfare smpl es o, U u ' C ( ) f ( ) & [s ] & [ ] 4 var (p h;) + ( ) [y u ey u ] y u a u + ah n h + af n f ( ) ( ) [c r ] [nr ] g + ::p + O : 4 var (p f;) Smplfyng cross producs wh, we ge, ah n h + af n f = n u a u + n r a r = y u a u + n r a r + ::p U u ' C ( ) f ( ) & + ( ) ( ) + ::p + O : [s ] & [ ] 4 var (p h;) [y u ey u ] + n r a r ( ) [c r ] 4 var (p f;) [nr ] g Usng, ec r = es = e = ( ) $ g r ( ) $ g r ( + ) ( ) ( ) a r $ en r = $ ( ) + & ( + ) $ a r ; ( + ) ( ) $ a r ; $ a r + ( ) ( ) $ g r ; ( ) $ g r where $ = + $ ( ) + & ; and decomposng n r a r, n r a r = ( + ) n r $ a r ( ) g r n r $! + g r $ ( + ) a r ( ) + n r : $ $ {z } en r 8

31 Usng he expressons of n r and y r ; n r a r = ( ) c r ( ) ( ) ( + ) a r ( )! ( ) g r $ $ {z } ( + ) ( ) ( ) & s a r ( )! g r $ $ {z }! ( + ) & a r ( ) g r $ $ {z } e + en r n r : es ec r Smplfyng, n r a r = ( ) ec r c r + en r n r + & e + ( ) & es s ; and pluggng no he welfare expresson, U u ' C ( ) f ( ) & + ( ) ( ) + ::p + O : [bs ] & [b ] 4 var (p h;) [by u ] ( ) [bc r ] [bnr ] g 4 var (p f;) where bx = x ex : Acualzng and summng among perods, we ge, Followng Woodford (), we know ha,! T = X s=t s= s E fu u s g : where k = ( )( ) X s=t s= s var (p ;s ) = P s=t s= s ;s k ; whch yelds he nal form of he welfare funcon, C X s=t! T = ( ) s= s E f( ) & [bs ] + & [b ] + ' h h; + + ( ) + [by u ] + ( ) [bc r ] + [bn r ] g + ::p + O : ( ) ' f f; where & = ( ), & = ( ), ' = ( )( ), and where ::p gahers erms ndependen of he problem and O erms of order or hgher. 9