February 3 Preliminary, no for quoaion MACROECONOMIC ADJUSTMENT TO STRUCTURAL CHANGE (*) Gabriel Fagan Research Deparmen European Cenral Bank Frankfur am Main, Germany Email: gabriel.fagan@ecb.in Vior Gaspar Research Deparmen European Cenral Bank Frankfur am Main, Germany Email: vior.gaspar@ecb.in Alfredo Pereira Deparmen of Economics The College of William and Mary Williamsburg, VA 333, USA Email: ampere@wm.edu Absrac In his paper we address he issue of macroeconomic adjusmen o srucural change for a small open economy caching up in he EU. The issue is paricularly imporan for he EU new Member Saes. In fac, successful inegraion will mean, for hese counries, ha boh nominal convergence (macroeconomic adjusmen) and real convergence (srucural change) will occur simulaneously and synergisically. We use a dynamic general equilibrium model wih wo secors producing raded and non-raded goods. We consider an overlapping generaion se-up and sickiness in wages and he price of non-raded goods. We focus on boh he ransiional and long-erm effecs of srucural changes on he allocaion of resources and ulimaely on pah of he real exchange rae. We consider a package of sylised srucural changes, which include changes in oal facor produciviy in he raded goods secor, financial inegraion, and srucural ransfers. We show ha his package generaes a se of long-erm effecs and macroeconomic adjusmens, in paricular on he real exchange rae, which differ in imporan respecs from he sandard saic Balassa- Samuelson ype of effecs. In paricular, we find a sizeable fron-loading of he effecs due o wealh effecs on consumpion and labour supply. We hen show ha he presence of price and wage sickiness is crucial for he iming of macroeconomic adjusmen o he srucural changes. Finally, we show ha a swich from a regime of fixed exchange raes o a regime of nominal exchange rae floaing wih he objecive ensuring domesic price sabiliy does no maerially change he macroeconomic adjusmen o srucural change. We inerpre his finding as illusraing he absence of a radeoff beween nominal convergence and real convergence. Keywords: Macroeconomic adjusmen, srucural changes, nominal rigidiy, exchange rae regimes. JEL Classificaion: E6, F4, F43, O, O4, and O4. (*) This paper was prepared for presenaion in he Conference organised by he Naional Bank of Hungary on "Moneary Sraegies for Accession Counries" o be held in Budapes on February 7-8, 3. The views expressed in his aricle are hose of auhors and do no necessarily reflec hose of he insiuions o which hey are affiliaed.
MACROECONOMIC ADJUSTMENT TO STRUCTURAL CHANGE. Inroducion Ten counries - Cyprus, Czech Republic, Cyprus, Esonia, Hungary, Lavia, Lihuania, Poland, Slovakia and Slovenia - were acceped o become new members of he European Union on May 4. The hisorical agreemen on EU enlargemen was reached a he European Council, held in Copenhagen, on -3 December. The Accession Treay will be signed, in Ahens, on 6 April 3. Subsequenly, he accession counries and he 5 curren members of he will raify he Treay. From May 4 on, he new members will be Member Saes wih a derogaion in he sense of aricle, paragraph, of he European Union Treay. According o he acquis communauaire, price sabiliy should be he primary goal of moneary policy, in all Member Saes. Aricle 4 of he Treay esablishing he European Communiy, sipulaes ha, when conducing heir economic policies, he Member Saes and he Communiy mus follow he guiding principles of sable prices, sound public finances and moneary condiions and a susainable balance of paymens. Gradual and susainable disinflaion owards low and sable inflaion, as in he euro area, is normally referred o as nominal convergence. Such process of nominal convergence is accompanied by a downward adjusmen in nominal long-erm ineres raes, o levels approaching hose prevailing in he euro area, reflecing boh declining inflaion expecaions and a diminuion of risk premiums. Moreover, he new Member Saes will become, evenually, and in accordance wih he imeables and procedures in he Treay, members of he euro area. All of hese en counries have GDP per capia well below he EU average. Specifically, hey range from 3 per cen (Lavia) o 88 per cen (Cyprus), of he EU average, in erms of GDP per capia, valued in erms of purchasing power pariy sandards. Successful inegraion of he new enrans ino he EU will be associaed wih a caching up process, defined as convergence in he levels of oupu per capia and produciviy, reflecing a number of srucural changes. In he summary of he ECB Seminar on he Accession Process, held in Helsinki, in November 999, one of he key poins underlined was ha nominal and real convergence should be pursued in parallel. By modifying heir economic srucures in line wih hose prevailing wihin he EU and by implemening appropriae srucural reforms, accession counries will speed up he process of "caching up", whereby heir living sandards will progressively evolve owards levels closer o hose of he EU (real convergence). Hisorical experience shows ha his process
should go hand in hand wih he achievemen and mainenance of price sabiliy and sound public finances (nominal convergence). Progress owards fulfilling he Maasrich crieria as a condiion for adopion of he euro is herefore fully compaible wih srucural reform. The desired parallelism beween nominal convergence and real convergence makes macroeconomic adjusmen and srucural change criical issues in he conex of European inegraion. The en accession counries have made considerable progress in erms of disinflaion and mos of hem have experienced growh raes above he EU average. Furhermore, mos of hese counries have also experienced significan real appreciaion of heir currencies vis-à-vis he euro area. Their moneary and exchange rae policy regimes cover he full range of possibiliies. From inflaion argeing cum floaing adoped in he Czech Republic and Poland, for example, o currency boards, followed, for example, in Esonia and Lihuania. Hungary, in urn, allows he exchange rae of he forin o floa inside /- 5 per cen flucuaion bands agains he euro. Srucural change and real convergence in hese counries will be associaed wih adjusmens in relaive prices. One relaive price, which is paricularly relevan in he conex, is he real exchange rae, defined as he price of non-radable goods relaive o he price of radable goods. The real exchange rae, as a relaive price, adjuss o changes in relevan variables including condiions in he res of he world, produciviy rends, rade barriers, axaion, migraion flows, financial flows, inernaional ransfers, insiuional and behavioural characerisics of produc and labour markes and much else. In fac, he lis of facors poenially affecing he equilibrium real exchange rae and is adjusmen pah owards equilibrium coincides wih he lis of facors, which may affec relaive prices in a dynamic general equilibrium conex, for an open economy. I includes all facors influencing he relaive supply and demand for non-radable goods. Therefore, he real exchange rae is unlikely o be consan over ime (see, for example, Neary (988) and Edwards (989)). For he counries joining he EU, many of he above facors are likely o play a relevan role in deermining he real exchange rae and is evoluion over ime. One popular explanaion of rend real exchange rae appreciaion is inspired in he Balassa-Samuelson effec (Balassa (964) and Samuelson (964)). The basic idea is very simple. Caching up implies convergence in produciviy levels. The scope for produciviy increase is much greaer in he producion of raded goods (e.g. manufacuring goods) han non-raded goods (e.g. services). Therefore, counries caching up will experience sronger relaive produciviy gains in he producion of raded goods. Wih he ineres rae deermined in he world capial marke and a compeiive domesic labour marke, his implies an increase in he relaive price of non-raded goods. There are many esimaes available of he acual and likely magniudes of Balassa-Samuelson effecs
boh for he euro area and for accession counries (see, for example, Pelkmans, Gros and Nunez- Ferrer,, Bundesbank,, Coricelli and Jazbec,, Halpern and Wyplosz,, Sinn and Reuer,, Eger,, Fisher,, Mihaljek, and MacDonald and Wojcik, ). In his paper we develop a wo-secor dynamic general equilibrium model wih price and wage sickiness. We consider an overlapping generaion se up on he household side (see, for example, Blanchard, 985, and Yaari, 965). In he lieraure on open economies, his seup is usually preferred o he infinie horizon Ramsey approach, since i leads o a deerminae seadysae level of foreign deb. The producion side of he economy considers wo final goods secors: raded and non-raded goods secors. The non-raded goods secor and he labour markes are characerised by monopolisic compeiion (see, for example, Dixi and Sigliz, 977). Furhermore, he accumulaion of capial is subjec o real adjusmen coss while he price of he non-raded good and he wage rae are subjec o nominal adjusmen coss (see, for example, Kim, ). We calibrae and numerically simulae his model using a sylised daa and parameer se inspired in he cases of wo of he euro area counries, which have undergone significan caching up, Ireland and Porugal. We do so o capure he main feaures of a ypical counry engaged in he process of caching up o he EU sandards of living. Our reading of he experiences of Porugal and Ireland leads us o focus on produciviy growh, financial inegraion, unilaeral public ransfers associaed wih EU srucural policies. This is clearly a simplificaion. Neverheless, i allows us o capure some main feaures of he srucural changes associaed wih a caching up process in he EU. In he conex of he dynamic general equilibrium model, he equilibrium real exchange rae will be one of he relaive prices o be deermined in equilibrium. I will be shown ha rend produciviy differenials lead o rend relaive price changes. However, in he shor run he adjusmen in relaive prices is unlikely o follow produciviy differenials closely and we find ha here is a sizeable fron-loading of he impacs on he real exchange rae. Srucural change and macroeconomic adjusmen are likely o inerac in complex ways. I may be ha price and wage sickiness will make adjusmen owards equilibrium very slow. Indeed, Blanchard and Mue (993). Their focus was on he lengh of ime i would ake for he real exchange rae o reurn o is equilibrium following a process of disinflaion based on a fixed exchange rae regime. However, since hey were focusing on he German mark versus he French franc, hey, quie reasonably, assumed ha he equilibrium real exchange rae ha was consan over ime. For accession counries he analysis of he behaviour of he economy under alernaive price norms, when he real exchange rae changes endogenously seems o be a more relevan case 3
o look a. An alernaive view, is ha, in he conex of a model wih forward looking agens, he impacs of anicipaed srucural changes on he real exchange rae and oher macroeconomic variables will be fron-loaded as a resul of immediae wealh effecs on consumpion and labour supply. This paper is organised as follows. In he second secion, we describe he dynamic general equilibrium model and we briefly address parameerisaion and calibraion issues, while leaving he full deails for an Annex. In he hird secion, we simulae he model under specific srucural changes o deermine he relevance of price sickiness and exchange rae regimes on he long-erm changes in he real exchange rae as well as on he ransiional converge o such longerm changes. Finally, in he fourh secion, we summarise he main resuls of he paper and highlighing heir policy implicaions.. The dynamic general-equilibrium model An overview of he model is presened in Char while deails are provided in Table. All variables and parameers are defined in Tables and 3, respecively. We consider a decenralized economy in a dynamic general-equilibrium framework. All privae secor agens maximize uiliy or profis, aking, unless oherwise indicaed, goods and facor prices as given. In addiion, all agens have perfec foresigh. This means ha agens fully anicipae fuure prices and oher exogenous variables. Therefore, heir planned fuure acions are deermined and implemened wihou he need for any changes. The economy is inhabied by households, firms producing in wo differen secors and a governmen. The wo producion secors are a raded goods secor and a non-raded goods secor. The raded goods secor is compeiive. The price of raded goods is he exogenous world price, adjused for he nominal exchange rae, which, under a small open economy assumpion, is independen of domesic raded goods oupu. In conras, he non-raded secor is characerized by monopolisic compeiion wih firms acing as price seers. As regards he households, we follow he convenional overlapping-generaions specificaion of Yaari (965), Blanchard (985), Buier (988) and Weil (989). Households, faced wih a finie probabiliy of deah, maximise a uiliy funcion, which depends on consumpion of boh raded and non-raded goods and leisure. As regards he labour marke, we inroduce imperfec compeiion and a se of wage seing insiuions (unions) ino he framework. 4
The model also incorporaes a highly simplified governmen secor. As regards links o he res of he world, we assume a high, bu no perfec, degree of capial mobiliy where he domesic ineres rae equals he foreign rae plus exogenous and endogenous risk premiums, he laer depending on he sock of ne foreign asses relaive o oupu. In cases where he nominal exchange rae is allowed o floa, we assume ha a sandard uncovered ineres pariy condiion applies. A noable feaure of our framework, in conras o much of he earlier lieraure exploring he impacs of long-run srucural changes, is ha we incorporae a number of imporan fricions ino he model. We assume price sickiness in a conex of monopolisic compeiion in he marke for he non-raded goods and in he labour marke. In regard o he labour markes his is achieved by including in he model a se of agens which ac as wage seers, specifically rade unions. Our seup means ha he price of non-raded goods and he wage rae are boh subjeced o price mark-ups and o nominal adjusmen coss. Nominal sickiness in hese markes is modeled in erms of quadraic adjusmen coss, following Kim () raher han he Calvo (983) scheme, mainly for reasons of analyical convenience. Moreover, as shown by Roemberg (987), he wo approaches yield equivalen price equaions. An addiional fricion in boh he raded and he nonraded goods secors sems from invesmen adjusmen coss which are again modeled by means of a quadraic adjusmen cos erm. The general equilibrium is defined as pahs for he endogenous variables such ha budge consrains and he firs order condiions of firms and households are saisfied simulaneously and a all poins in ime given he pahs of he exogenous variables.. The raded goods secor The raded good secor comprises a se of idenical firms, each of which acs in a compeiive manner in oupu and facor markes. On he basis of a small open economy assumpion, he price of raded goods is deermined by he exogenous world price - which is independen of he levels of raded oupu of he individual firms and he economy as a whole - along wih he nominal exchange rae. Oupu, YT, is produced wih a Cobb-Douglas echnology as in equaion (T.) in Table, exhibiing consan reurns o scale in labour, d L, and privae capial, K, where θ LT is he labour share and AT is oal facor produciviy in he raded secor. Capial accumulaion is characerized by (T.) where physical capial depreciaes a a rae of δ. Invesmen is subjec o adjusmen coss as in Chrisiano e al, (). These coss 5
comprise learning and insallaion coss and are mean o reflec rigidiies in he accumulaion of capial owards is opimal level. These adjusmen coss are inernal o he firm and are modeled as a loss in capial accumulaion and are, herefore, included in equaion (T.). Adjusmen coss are assumed o be non-negaive, monoonically increasing, and sricly convex. In paricular, we assume adjusmen coss o be quadraic in invesmen per uni of insalled capial. The invesmen good in he raded secor comprises a Cobb-Douglas aggregaion of raded and nonraded goods (as shown in T.7). A ime, he firms' ne cash flow, represens revenues from sales ne of wage paymens and invesmen spending. NCFT, (see equaion T.3), Traded goods firms are assumed o maximise he discouned value of ne cash flow by choosing pahs for labour inpu and invesemen (broken down ino raded and non-raded goods), subjec o he producion funcion and he capial accumulaion equaion. The firs order condiion for labour is given by equaion (T.4), a sandard condiion whereby he marginal produc of labour is equal o he real produc wage. Because of capial adjusmen coss, he firs order condiions for capial and invesmen are more complex. The relevan erms of he Lagrangian are: p AT( LT q r { ) d θ LT θ LT ( δ w LT ) d pi IT q IT µ IT IT } {... ( δ ) IT µ IT IT } where q is he shadow price of he insalled privae capial sock, which evolves according o (T.6), while r is he domesic nominal ineres rae. Differeniaing his expression wih respec o IT and yields equaions (T.5) and (T.6), he firs of which expresses invesmen as a funcion of he shadow price (q raio) while he second gives he law of moion for he shadow price. Finally, he invesmen good in he raded secor is a Cobb-Douglas composie of raded and non-raded goods, ITT and ITN, respecively, given by equaion (T.7), where i is he share of invesmen expendiures in raded goods and s is a scale facor. Accordingly, he firm faces a dual invesmen price index, pi which is given by equaion (T.8). The opimal choice of ITT and ITN yields he sandard condiion by which he nominal expendiure share for raded goods in oal raded-secor invesmen expendiure is equal o i. 6
. The non-raded goods secor The se-up in he non-raded goods secor differs in a number of respecs from ha of he raded goods secor. In paricular, he non-raded goods secor is embedded in a monopolisic compeiion framework and he price of he non-raded goods is subjec o nominal adjusmen coss. These feaures mean ha he firs order condiions differ from hose of he raded secor by incorporaing erms in mark-ups and also erms reflecing cosly price adjusmen... Firms in he non-raded goods secor and he aggregaor The model se-up we employ for he non-raded secor has now become sandard in he New Neoclassical Synhesis lieraure (see, for example, Chrisiano, Eichenbaum and Evans,, Erceg, Henderson and Levin, 999, and Smes and Wouers, ). Specifically, we assume ha he composie non-raded good is produced by a single firm, he non-raded goods aggregaor. This single firm uses inpus supplied by an infinie number of firms locaed along a coninuum in [,]. The inroducion of he aggregaor, which behaves in a compeiive manner, ino he seup is for reasons of analyical convenience. The alernaive approach whereby he individual firms sell heir oupu direcly o consumers would no aler he properies of he model, bu would increase he complexiy of he soluions. Each inermediae good firm produces and supplies o he aggregaor a differeniaed good. In a conex of monopolisic compeiion hese inermediae goods firms are price seers in he marke for heir oupu bu are price akers in he facor markes.. The inermediae goods supplied by he differen firms, YN (s), where s ε [,], are assumed o be imperfec subsiues. The composie non-raded good, is produced by he aggregaor using he following Dixi-Sigliz echnology: εn /( ε ) ( εn) / εn YN = ( ) YN s ds () where ε n is he absolue value of he elasiciy of demand for he inermediae good produced by firm s, his elasiciy being equal for all s. Leing (s) denoe he price of he oupu of firm s, he aggregaor s profi funcion is: 7
YN ( s) YN ( s) ds () Assuming ha he aggregaor behaves compeiively, i.e. acs as a price aker on boh he purchasing and selling side, maximizaion of his expression wih respec o each aggregaor s demand for each inermediae good: YN, yields he n [ ( s) ] ε YN YN ( s) = / (3) Simple manipulaions of he previous expressions and using he zero profi condiion for he aggregaor, yields he following expression for he price of he composie non-raded good supplied by he aggregaor: = ( s) ε n /( εn ) (4).. Inermediae goods firms Each inermediae goods producer (s) aims o maximise discouned cash flow by choosing a level of is oupu price and labour and invesmen subjec o hree consrains: ) he producion funcion (T.9), ) he capial accumulaion equaion incorporaing quadraic adjusmen coss as in he raded secor (T.), and 3) he demand funcion for heir specific good (equaion (3), above). An imporan feaure of our model is ha inermediae goods firms price seing is subjec o nominal adjusmen coss. This means ha i is cosly for he firm o adjus prices o he oherwise ideal level. Nominal adjusmen coss for firm s are given, following Kim () by a quadraic funcion of he percenage price change: ( s) s ) p YN ( s) ( s) µ ( (5) 8
where µ (s) p reflecs he degree of price sickiness for firm s or he cos of changing prices from he previous levels. (A value of zero for his parameer would correspond o perfec price flexibiliy). Noice ha, nominal adjusmen coss incurred by he firm depend on he amoun of oupu which is acually supplied, which is in iself a funcion of he prevailing price. We have, herefore, modelled nominal adjusmen coss as per uni coss. Inermediae goods firms are herefore assumed o choose pahs for (s), KN(s), IN(s) and LN(s) so as o maximise he expeced discouned value of he firm: d R( ){( µ p ) YN w LN pin IN} T (6) = where R() is a discoun facor defined in he usual way, e.g. R()=, R()=/(/r ), R()= /((r )(r )) ec. The maximisaion is subjec o hree consrains: he demand for he firms oupu from he aggregaor given by equaion (3) above; he producion funcion (T.9); he capial accumulaion equaion (T.). The laer wo equaions are defined in an analogous way o he raded secor. The firs order condiions for his problem can be derived in a sraighforward, if edious, manner. To move from individual o aggregae behaviour, we noe ha firms are assumed o have idenical echnologies, budge consrains and demand funcions for heir oupu. Therefore, he equilibrium in his monopolisically compeiive se-up will be symmeric. Thus, oupu levels, prices, invesmen, capial and labour inpus will be idenical across firms. Imposing hese condiions, using () and (4), yields a se of aggregae firs order condiions for he non-raded secor which are shown in equaions (T.3) o (T.9). Equaions (T.3) and (T.4) show he aggregae firs order condiions for labour inpu. This differs from he sandard case (e.g. as in he raded secor) in wo key respecs. Firs, i includes a mark-up erm, reflecing he monopolisic naure of he marke. Secondly, i includes erms in curren and discouned fuure price changes, reflecing he impac of cosly price oupu adjusmen. Noe ha his would collapse o he sandard marginal produciviy condiion for labour as e n? 8 and µ p? (i.e. in he absence of marke power and price adjusmen coss). The same feaures apply o he marginal condiion for capial (T.5). The invesmen equaion (T.6) and he law of moion for he shadow price of non-raded capial sock (T.7) are, apar from he differen definiion of he marginal produciviy of capial, he same as in he raded good secor. Finally, given he definiion of he composie invesmen good in he non-raded 9
secor (T.8) and is dual price index (T.9), he inraemporal choice of raded and non-raded goods in invesmen is deermined by condiions idenical o hose in he raded secor..3 The household secor Populaion is normalised o be equal o and assumed o be consan. Each household/generaion faces he same uiliy funcion wih idenical ineremporal discoun raes and survivor raes. Households are price akers in all markes. In addiion, for reasons ha will become apparen in he nex secion, we assume ha each generaion comprises an infinie number of workers disribued uniformly along a coninuum [,] of skills or professions. This implies ha each generaion comprises workers of differen skills/professions wih he proporions of each profession equal across generaions and ha, furher, he disribuion of workers in each skill class (s) across generaions is equal across skill classes. A convenional overlapping generaions specificaion following Yaari (965), Blanchard (985), Buier (988) and Weil (989) was adoped here. See Frenkel and Razin (996) for a deailed discussion of his ype of household model. In his framework, he planning horizon is finie bu in a non-deerminisic fashion. A large number of idenical agens are faced wih a probabiliy, γ (,), of surviving hrough o he nex period. The assumpion ha γ is consan over ime and across age-cohors yields he perpeual youh specificaion by which all agens face a life expecancy of /( γ ), and he probabiliy of being alive j periods ahead is simply Since populaion is normalized o uniy, per capia and aggregae values are equal. The household, aged a a ime, has o choose presen and fuure consumpion and leisure sreams ha maximize uiliy, equaion (T.), subjec o he consolidaed budge consrain, equaion (T.). The objecive funcion is lifeime expeced insananeous uiliy subjecively discouned a he rae of β. Preferences, u a v v j γ.,, are addiive separable in privae consumpion and leisure, and ake on he CES form where B is a size parameer and σ is he consan elasiciy of subsiuion. In pracice, we will assume a Cobb-Douglas uiliy funcion ( σ =). The effecive subjecive discoun facor can be wrien as γβ meaning ha a lower probabiliy of survival reduces he effecive discoun facor making he household relaively more impaien. The budge consrain, equaion (T.), reflecs he fac ha he households' expeced consumpion expendiure sream discouned a he marke real ineres rae should no exceed he households' oal wealh, TW,, evaluaed a ime. The marke real ineres rae is, bu a r v
he one-period loan rae a which households borrow and lend among hemselves in a perfecly compeiive marke is / γ imes greaer. In effec, he probabiliy of dying, γ, acs as a perceived defaul rae. To ensure a before-ax reurn of (. r v )/ γ> r v wih cerainy, crediors charge r v For he household of age a a ime, oal wealh, TW,, equaion (T.3), is age-specific a and is composed of human wealh, HW,, ne financial worh, a FW,, and he presen marke a value of he firms, PVF. Human wealh, equaion (T.4), represens he presen discouned value of he household's fuure labour income minus lump sum axes (LST) sream. Financial wealh comprises governmen deb minus foreign deb (T.5). Noe ha fuure labour earnings have o be discouned a a higher rae reflecing he probabiliy of survival, since human wealh is household-specific and canno be ransferred a he ime of deah. Income ne of spending adds o ne financial wealh, as in equaion (T.5). Household's income is augmened by profis disribued by corporaions, ransfers such as emigrans' remiances, NCFT, and NCFN, inernaional R, and public ransfers such as old-age pensions, TR. Loans among households cancel ou upon he consolidaion of households' financial asses, and are hus are omied. On he spending side, debs o foreigners are serviced, axes are paid and consumpion expendiures are made. Under he assumpion ha no bequess are made, households are born wihou any financial wealh. Noe also ha oal wealh is age-specific on accoun of age-specific labour supplies and consumpion sreams. Assuming a consan real ineres rae and ha he consolidaed budge consrain is binding, he household's ineremporal opimizaion problem can be formulaed as a sandard saic program. Furhermore, under our simplifying assumpions, he marginal propensiy o consume ou of oal wealh is age independen and aggregaion over age cohors is grealy simplified. Aggregae consumpion demand as a funcion of he aggregae sock of oal wealh is given by equaion (T.7). In our seup, as explained in he nex secion, employmen will be demand deermined given he wage raes se by unions. Finally, aggregae consumpion spending is a Cobb-Douglas composie of expendiure in raded and non-raded goods, CT and CN, respecively, and is given by equaion (T.8), where c, is he share of invesmen expendiures in raded goods and sc is a scale facor. Accordingly, he households face a dual consumer price index, pc which is given in equaion (T.9).
.4 Wage Sickiness and he Labour Marke The now sandard way of inroducing wage sickiness in o dynamic general equilibrium models is o use a seup where represenaive households hemselves face a downward demand for heir labour and ac as wage seers (see Erceg, Henderson and Levin, 999). In he curren se-up, his approach canno be applied direcly since households in he presen model are no homogenous. They are differeniaed by levels of wealh (due o age effecs) and accordingly differ in regard o heir consumpion. Labour marke decisions, such as he seing of wages, would no, herefore, be idenical across households if households hemselves were wage seers. In addiion, problems would arise in dealing wih newly arrived households who previously would no have se a wage. In order o incorporae wage sickiness in our se-up while overcoming his problem, he approach aken is o add an addiional se of agens o he labour marke. These addiional agens called for convenience unions ac as agens for he labour marke decisions of households and se he wage rae charged o firms by heir members so as o maximise he uiliy of a represenaive union member. Given his wage, he righ o manage model applies, and he level of employmen is deermined by he firms labour demand funcions. A labour aggregaor purchases labour inpus of differen skill classes from unions/households and supplies a single composie labour o he raded and non-raded goods firms..4. The labour aggregaor The specificaion of he behaviour of he aggregaor is now relaively sandard (see Erceg e al, 999). I is assumed ha a represenaive aggregaor supplies a composie labour inpu L o firms by combining differeniaed ypes of labour inpu, differeniaed by professions/skills. The differen labour inpus are supplied by unions locaed along a coninuum, wih unions represening household members of a specific skill ype. The labour services supplied by he differen unions, L(s), where s ε [,], are assumed o be imperfec subsiues. The composie labour supplied o firms is produced using he following Dixi-Sigliz echnology: L = ( ) L s ( εw) / εw ds εw /( εw) (7) Leing W(s) denoe he wage rae for labour of ype s and w he wage rae charged by he aggregaor o he firms in he raded and non-raded secors, he aggregaor s profi funcion is:
w L w( s) L( s) ds (8) Assuming ha he aggregaor behaves compeiively, i.e. acs as a price aker on boh he purchasing and selling side, maximisaion of his expression wih respec o each L(s), yields he aggregaor s demand for each ype of labour inpu: w [ w ( s) w] ε L L ( s) = / (9) ε w is he (absolue value of) he elasiciy of demand for labour for he members of union s, his elasiciy being equal for all s by virue of (7). Subsiuing (9) ino (8) and imposing he zero profi condiion for he aggregaor, yields he following expression for he wage rae for he composie labour supplied o firms: w w ( s) = ε w /( εw) ().4.3 Unions Each ype of labour, L(s), is supplied exclusively o he aggregaor by a union locaed along he coninuum of unions. Unions ac as agens for heir members, seing a wage rae for is specific ype of labour so as o maximise he uiliy of a represenaive member. Given his wage rae, he union (s) supplies as much labour of ype (s) as is demanded by he aggregaor. On he oher side, members of he union agree ha, in reurn for receiving he union wage, hey will supply as much labour as required, wih each member of he union working he same hours and receiving he same wage for is ype of labour. Facing he downward sloping demand curve (9), each union chooses a wage rae for is ype of labour so as o maximise he following = R( ) U { C ( s),( L L ( s))} µ w w ( s) [ ] λ( pc C ( s) w ( s) L ( s)...) w ( s) represenaive member welfare funcion: () 3
Where R() is a discoun facor defined in he usual way, e.g. R()=, R()=/(r ), R()= /((r )(r )) ec. The funcional form of U(C,-L) is he same as for he individual household. The consumpion erm enering he union s objecive funcion (C(s)) is he average consumpion of members. Given our earlier assumpion ha he disribuion of union members across generaions is idenical, average consumpion of he members of union (s), C(s), will in fac be equal o average consumpion in he economy as a whole. I is ineresing o noe ha in basing is choice on average consumpion, he union is implicily assigning a higher weigh o older (and herefore richer) members, a ype of senioriy principle. In seing he wage, he union also akes ino accoun he fac ha hours worked by members will be deermined by he labour demand funcion of he aggregaor, (9). The quadraic erm in change in he union wage in he welfare funcion reflecs and assumed disuiliy of changing he nominal wage rae. This erm, reflecing psychic adjusmen coss, can be moivaed by he idea ha changing nominal wages involves considerable negoiaing effors in he union, reducing members uiliy. Finally, in choosing he wage rae, he union akes ino accoun he budge consrain of is members and heir decisions regarding he choice of consumpion level. This is shown in he final erm in he objecive funcion above. Given he households firs order condiion for consumpion, λ will equal he marginal uiliy of consumpion of he represenaive member divided by he consumer price index. This erm is aken as given in he union s opimisaion problem. Subsiuing he labour demand funcion (), differeniaing wih respec o w (s) and subsiuing he marginal uiliy condiion for consumpion for λ, yields he following Euler equaion for he wage rae of union (s): L L ( εw ) U C εw U pc w ( s) µ ( ) w w s == w( s) w( s) L µ ( w ( s) w ( s) r ) w ( s) w ( s) w () In order o inerpre his equaion, noe ha along a zero wage growh seady sae, he las wo erms in he above expression will be zero. This implies ha he seady sae real wage rae of he union will be given by: ( s) = ε w pc ε w U U w L C 4
(3) The second erm on he righ of his equaion is an expression for he real wage ha would be saisfied under perfecly compeiive labour marke condiions. Thus he real wage charged by he union in he long-run is hus a mark-up on he wage ha would have prevailed if he labour marke had been operaing under perfec compeiion, wih he size of he mark-up depending on he elasiciy of demand for he union s labour services. Wih his in mind, he firs wo erms of he Euler equaion herefore represen a non-linear error-correcion erm in he deviaion of he curren union wage from is long run equilibrium level. The remaining erms reflec a (forward-looking) adjusmen o his long run level resuling from he quadraic erm in he uiliy funcion. The Euler equaion herefore has he usual inerpreaion, where he union balances he coss of being away from is equilibrium agains he coss of adjusmen which arise when changing nominal wages. To move from he wage rae of individual unions o he aggregae wage rae, we noe ha under our assumpions, a symmeric equilibrium will apply. Specifically, he elasiciy of he aggregaors demand for each ype of labour (e w ) and all of he oher parameers and funcional form of he union s objecive funcion are equal across unions. By our assumpions on he disribuion of union members across generaions, average consumpion will also be equal across unions. This implies ha he soluion o he firs order condiion will be idenical across unions. The equilibrium in he labour marke will herefore be symmeric, implying ha w(i)=w(j) and L(j) = L(i) for all i,j. This implies ha he aggregae wage rae mus saisfy an economy-wide Euler given by (T.). From he aggregaor s demand for labour funcion (9), hours worked per member will also be equal across unions. Since union membership is equally disribued across generaions, his implies, in urn, ha hours worked will also be he same across generaions. Given he wage raes se by he unions, and he resuling aggregae wage rae (equaion ()), oal labour inpu will be deermined by firms labour demand funcions (equaions T.4 and T.3)..5 Public Secor The model includes a relaively simplified public secor. We assume ha in all periods, a balanced budge rule is followed.. Accordingly, he budge for he public secor is given by equaion (T.3). In his equaion CGT and CGN, are public consumpion of raded and nonraded goods, respecively, rpd, are ineres paymens on exising public deb, LST are lump 5
sum axes levied on he households, and TR are public ransfer o he households. Finally, are foreign ransfers o he Governmen in foreign currency (e.g. EU ransfers), which are convered ino domesic currency using he nominal exchange rae of FT ner. The proceeds are spen immediaely on addiional non-raded goods, accouning for he appearance of his erm on boh sides of he budge consrain. Governmen consumpion is assumed o be exogenous in real erms. In paricular, public consumpion of raded and non-raded goods boh grows a given rae. Naurally, o he exen ha here are changes in he nominal exchange raes or in he price of he non-raded goods, governmen consumpion changes in nominal erms. Lump sum axes adjus according o he balanced budge condiion above..6 Furher equilibrium condiions and he deerminaion of prices and ineres raes In addiion o he firs order condiions and budge consrains discussed earlier, a number of whole economy consrains are saisfied. The ineremporal budge consrain for our open economy is given by equaion (T.3). This saes he balance of paymens condiion ha he change in foreign deb (he financial accoun) is equal o he curren accoun defici (nominal spending on raded goods and ineres paymens on he foreign deb minus domesic producion of raded goods and inernaional ransfers). In urn, he equilibrium in he non-raded goods marke is given by equaion (T.3). Here he only relevan poin is ha i is assumed ha inernaional ransfers are, as menioned in he previous secion, exclusively spen on non-raded goods. Equaion (T.33) shows ha oal labour inpu is he sum of labour inpus in he raded and nonraded secors. Finally, he definiion of household financial wealh is given by equaion (T.34). In his model, we assume ha he domesic economy is a small open economy, i.e., a price aker in he raded good markes as well as he financial markes. This means ha domesic agens ake he price of he raded good and he ineres rae as exogenous. In he deerminaion of he domesic price of raded goods we sar by assuming a regime of fixed exchange raes. In his case, he nominal exchange rae and he inernaional price of non-raded goods pw, are exogenous. The domesic price of raded goods, p, is given by (T.35). Alernaively, we assume a regime of flexible exchange raes in which he auhoriies arge consumer price sabiliy. In his case he nominal exchange rae will evolve so as o ensure a pah for raded goods prices which generaes a sable overall consumer price level. Via an 6
uncovered ineres pariy erm, his pah will in urn deermine he pah of he domesic ineres rae vis-à-vis he world risk free rae, ir, which is assumed o be consan over ime Apar from UIP consideraions, we assume ha he domesic ineres rae also conains boh exogenous and endogenous risk premiums. The exogenous risk premium, rp, is assumed o reflec a lack of inegraion ino global financial markes and is a parameer which we change in some simulaions. The endogenous risk premium is a funcion of he foreign deb o GDP raio. The purpose of including his raher arbirary elemen is o dampen down flucuaions in ne foreign asses. Puing all hese elemens ogeher, he domesic ineres rae is given by equaion (T.36). We define he seady-sae growh pah as an ineremporal equilibrium rajecory for he economy in which all he flow and sock variables grow a he same rae while marke prices and shadow prices are consan. There are hree major ypes of resricions imposed by he exisence of a seady-sae growh pah. Firs, he exisence of a seady sae deermines he value of criical producion parameers, like adjusmen coss and depreciaion raes given he iniial socks of physical and human capial. These socks, in urn, are deermined by assuming ha he observed levels of invesmen of he respecive ypes are such ha, he capial o GDP raios do no change in he seady sae. Second, he need for consan public deb and foreign deb o GDP raios implies ha he seady-sae public accoun defici and he curren accoun defici are a consan fracion of he respecive socks of deb ha coincides wih he growh rae of he economy. Finally, he exogenous variables, as public ransfers or inernaional unilaeral ransfers, ec., have o grow a he seady-sae growh rae..7 Calibraion The daa and parameers ha are used in simulaing he model are presened in Tables and 3, respecively, and he deails of he calibraion procedure are given in Annex. The calibraion approach is o choose a se of model parameers so as o mach a seady sae daa se which broadly corresponds o he sylised facs of he Irish and Poruguese economies. These feaures mainly relae o shares of raded and non-raded goods in oupu, employmen and demand componens. In addiion, we ake ino accoun informaion of he funcional disribuion of income. The basis informaion sources are inpu-oupu ables and naional accouns for boh counries. On he basis of his informaion, a baseline daa se was consruced and is shown in Table 3, where for convenience, GDP and all prices are normalised o uniy. In deriving his daa 7
se from he raw daa, we have assumed ha he raded secor basically comprises agriculure and manufacuring while he non-raded secor comprises he remainder of GDP. We choose he parameers of he model in way such ha he model, when run on he baseline, reproduces his daa se. This comprises four seps. Firs, some parameer values are assumed on he basis of available lieraure or educaed guesses. These include invesmen adjusmen coss as a percenage of invesmen and mark-up parameers. Second, he values of he share parameers (producion funcion parameers, shares of raded and non-raded goods in invesmen and consumpion) can be deermined sraighforwardly from he respecive shares in he daa. Third, some parameers, specifically he parameers for nominal sickiness and wages and non-raded prices, are chosen o mach empirical evidence from oher sudies. A final subse of parameers, namely he discoun rae, he depreciaion raes in boh secors and he invesmen adjusmen cos parameers are chosen so ha he model reproduces he baseline daa se. 3. Macroeconomic adjusmen o srucural change: simulaion resuls In his secion we seek o characerise macroeconomic adjusmen o srucural changes using he model oulined in earlier secions. To do his we solve he model numerically using he sacked-ime algorihm of Laxon and Juillard (996). This involves sacking he equaions for all periods (in our case years) and solving hem simulaneously subjec o given iniial and erminal condiions, he laer being se o he seady sae values. We examine he response of sandard macroeconomic aggregaes prices, oupu and employmen as well as he allocaion of resources beween he wo secors. We focus especially on he long-erm impac on he real exchange rae as well as on is dynamics of adjusmen owards is long run equilibrium. We explore he exen o which he presence or absence of price and wage sickiness impacs on hese adjusmen processes. Finally, we consider how differen exchange rae regimes affec he macroeconomic adjusmen. In paricular we examine he implicaions for macroeconomic adjusmen of a policy of fixed nominal exchange rae regime as agains a policy orienaed o domesic price sabiliy under floaing raes. 3. Simulaion design 8
In our simulaion experimens we consider he effecs of hree sylised srucural changes, which, as emphasised in he inroducion, are seen as he principal srucural changes associaed wih inegraion ino he EU on he basis of he experience of Porugal and Ireland. The firs srucural change corresponds o a proraced increase of produciviy growh in he raded good secor. I is mean o reflec a sandard source of real convergence conneced wih increased rade inegraion. The magniude of he change is such ha he shock in oal facor produciviy growh in he raded good secor when combined wih he oher wo shocks (see below) accumulaes o a level effec on oal oupu of abou 3% in 5 years. This implies an increase inhe raded secor TFP growh rae of abou percenage poin a year for a period of 3 years. The second srucural change reflecs he process of financial inegraion. I corresponds o a reducion in he ineres rae he domesic economy faces in he inernaional markes. We consider a reducion of he exogenous risk premium of 5 base poins spread over years. The hird srucural change is associaed wih he Communiy s srucural policies. I is modelled as a pure demand shock. We consider an increase in inernaional ransfers, reflecing access o EU srucural funds, corresponding o 3% of he GDP. This change lass for a 5-year period afer which ransfers reurn o baseline. In erms of he differen ses of simulaions o be considered, we sar by considering he effecs of srucural changes under price sickiness and a fixed nominal exchange rae and proceed o deermine he role of boh assumpions. In he firs se of simulaion resuls our objecive is o esablish ha a plausible package of srucural changes leads in our model o reasonable resuls which are no in conradicion wih known sylised facs. In he second se of simulaion experimens, we consider he effecs of he same srucural changes in he absence of price and wage sickiness bu sill wih a fixed nominal exchange rae o deermine how he macroeconomic adjusmen would change in absence of such sickiness. The poin is o esablish ha nominal price rigidiies in he conex of monopolisic compeiion are imporan o produce he plausible resuls inroduced before. Finally, in he hird se of simulaion resuls, we consider he effecs of srucural changes under price and wage sickiness bu wih a policy orienaed o domesic price sabiliy under a flexible nominal exchange rae. The idea is o show he effecs of he choice of moneary policy regime, associaed wih nominal exchange rae floaing, on he macroeconomic adjusmen process. For he sake of breviy we will refer o shor erm effecs as effecs happening wihin a en-year period, medium-erm effecs as hose occurring beween en and weny years, and long- See, Pereira (999a,b) and Gaspar and Pereira (995), for specific analysis of his ype of srucural changes in he conex of hese ands oher counries. 9
erm he effecs hereafer. Furhermore, all he references o saus quo refer o he model oucomes before he srucural shocks are imposed and, herefore, refer o he values for our sylised economy ha reflec he long erm rends for he economy in he absence of such srucural shocks. 3. Effecs of srucural changes under marke rigidiies and fixed nominal exchange rae How does our sylised economy adjus o he srucural shocks considered under price and wage sickiness when he nominal exchange rae is fixed? Wha are he effecs on he long-erm allocaion of resources and real exchange rae? Wha are he properies of he adjusmen o he new equilibrium allocaion of resources and real exchange rae? These are some of he quesions we address in his secion. The simulaion resuls for his case are presened in Char. The srucural changes under consideraion lead o a sharp increase of he real exchange in he shor-erm o up 5% above he saus quo level followed by a relaively slow convergence o a new long-erm seady-sae level which is abou 3% above he saus quo. The nominal wage rae and he consumpion price index follow a similar paern wih a sharp increase in he shor erm followed by smooh convergence o a level abou 45% and 5% above he saus quo levels, respecively. As a corollary, he effecs of srucural changes on consumer price inflaion are fron-loaded. Indeed hey virually disappear afer a en-year period. The effecs of he srucural changes on nominal wages and consumpion prices sugges ha real wages increase sharply wihin he firs five years and hen converges slowly o a longerm increase of abou %. The long-erm evoluion of he employmen follows he corresponding paern. I shows a long erms increase of abou.5%, bu in he shor erm he srucural changes lead o an increased employmen on impac. This increase, however, shrinks unil i evenually urns ino a decrease. The recovery oward he long-erm increase sars around 5 years ino he srucural changes. I is ineresing o undersand his shor-erm response paern of employmen o he srucural changes under consideraion. Alhough he real wage rae increases in he shor-erm, his is jus one of he deerminans of labour supply and, ulimaely, employmen. Indeed, hese srucural changes because hey are fully anicipaed by forward-looking households - lead o a subsanial increase in he oal wealh of he households. Recall ha oal wealh includes in addiion o financial wealh (he foreign deb posiion), he forward-looking socks of human wealh and he value of he firms. The srucural changes represen a subsanial gain in he profiabiliy of he producion secors as well as on he discouned wage income of households.
This being he case, he srucural changes induce on impac a major increase in he wealh posiion of he households. They respond, in a sandard fashion, by increasing consumpion (more on his below) and leisure. Hence a shor-erm reducion in desired labour supply. As will be discussed in more deail below, however, he impacs are offse in he very shor run by wage sickiness which prevens an immediae adjusmen of wages o desired levels, resuling iniially in a rise in employmen due o a shif in labour demand. This evoluion in he supply of labour hides a very differen evoluion of employmen in he raded and non-raded goods secors. In fac, he srucural changes lead o a subsanial posiive bu declining effec on employmen on he non-raded goods secor and a negaive shorerm effec in he raded goods secor, which however urns ino a subsanial long-erm gain. This suggess ha he srucural changes induce a shif in he composiion of employmen o he non-raded goods secor in he shor erm bu decisively o he raded goods secor in he medium and long erm. In erms of he capial accumulaion we see ha he srucural changes lead o a long erm increase in he shadow price of capial for boh secors of abou % in boh he raded and nonraded goods secors. The ransiional paerns, however, are very differen beween he wo secors. In he shor and medium erm he shadow price of capial in he raded goods secor increases smoohly o a level of 35% above he saus quo hereby overshooing he new longerm level. In urn, he shadow price in he non-raded goods secor increases on impac o abou 4% over is saus quo level and hen declines smoohly o he new seady sae level. The effecs of he srucural changes on he wo socks of capial follow a corresponding paern. The sock of capial in he raded secor increases srongly iniially and hen smoohly converges o a new seady sae level abou 7% above he saus quo. The sock of capial in he non-raded secor increases a a smooh bu decreasing rae o he new seady-sae level, which is abou.5 above he saus quo level. Again he srucural changes induce a shif in he secor composiion of capial. In he shor run he composiion shifs o he non-raded secor while in he long erm i shifs decisively o he raded secor. I should be poined ou ha his paern of resuls is consisen wih he fac ha ha invesmen in he non-raded goods secor is more dependen on non-rade goods and he price of hese goods increases subsanially in he long erm. Naurally, he evoluion of oupu, boh a he aggregae and he secor level, follow closely he evoluion of employmen and capial accumulaion. In he shor-erm aggregae oupu is only very marginally affeced. The increase in capial formaion is mached by a decline in employmen. In he longer-erm however, as boh employmen and capial accumulaion