Estudos e Documentos de Trabalho. Working Papers

Transcription

1 Esudos e Documenos de Trabalho Working Papers THE MONETARY TRANSMISSION MECHANISM FOR A SMALL OPEN ECONOMY IN A MONETARY UNION Bernardino Adão Fevereiro 2009 The analyses, opinions and findings of hese papers represen he views of he auhors, hey are no necessarily hose of he Banco de Porugal or he Eurosysem. Please address correspondence o Bernardino Adão Economics and Research Deparmen Banco de Porugal, Av. Almirane Reis no. 7, Lisboa, Porugal; Tel.: , badao@bporugal.p

2 BANCO DE PORTUGAL Ediion Economics and Research Deparmen Av. Almirane Reis, 7-6 h Lisboa Pre-press and Disribuion Adminisraive Services Deparmen Documenaion, Ediing and Museum Division Ediing and Publishing Uni Av. Almirane Reis, 7-2 nd Lisboa Prining Adminisraive Services Deparmen Logisics Division Lisbon, February 2009 Number of copies 70 ISBN ISSN Legal Deposi No 3664/83

3 The Moneary Transmission Mechanism for a Small Open Economy in a Moneary Union Bernardino Adão February 2009 Absrac This paper develops a model of a small open economy inegraed in a moneary union. The model incorporaes he sandard nominal and real fricions in he lieraure. The parameers of he model are calibraed o he Poruguese daa and he e ecs of he sandard moneary policy shock are sudied. Key words: Small open economy; Moneary union; Moneary ransmission mechanism; Local deerminacy; Impulse response funcion; JEL classi caion: E2; E22; E32; E42; E6; F4; F42. I would like o hank Ana Crisina Leal, João Sousa, Nuno Alves and Mário Ceneno for useful commens and Gabriela Casro, Ricardo Félix, José Maria and Nuno Ribeiro for help wih he daa.

4 . Inroducion This paper develops a sylized model of a small open economy inegraed in a moneary union. Since he small counry rades wih counries inside and ouside of he moneary union here are hree economies in he model. The small open counry, he economy represened by all he remaining counries ha belong o he moneary union oo, and he one ha includes all counries ha do no belong o he moneary union. The Taylor principle, which says ha he ineres rae rule should be such ha he response of he ineres rae o a uniary change in in aion should be larger han uniy, is a necessary condiion o have local deerminacy in he model. If he in aion in all counries of he union, excep in he small counry, was aken as exogenous he Taylor principle would be violaed. The reason is easy o undersand. The ineres rae relevan for he small counry is he one se by he cenral bank of he moneary union. The cenral bank of he moneary union follows an ineres rae rule ha is a funcion of he union s in aion and oupu. If hose union aggregae variables were aken as exogenous hen he Taylor principle would be violaed. A change in he small counry s in aion would imply a negligible change in he ineres rae, since he small counry conribues lile o he union s in aion. Thus, o guaranee local deerminacy he variables associaed wih he counries ouside he union can be assumed exogenous, bu no he variables associaed he oher counries in he union. To guaranee ha he model possesses he local uniqueness propery we adoped a sraighforward ad-hoc speci caion of wo blocks of equaions, each conaining hree equaions, ha specify he behavior of some aggregae variables inside and ouside of he union. One block conains hree reduced form equaions, an IS curve, a Phillips curve and an ineres rae rule ha describe he behavior of oupu, of in aion and of he ineres rae for he counries ouside of he union. These hree variables are deermined enirely inside his block. The oher block of equaions conains hree oher similar reduced form equaions, regarding he behavior of in aion, oupu and ineres rae in he union. This block of equaions conains hree equaions and ve variables. These variables are: he in aion rae and he oupu in he small open economy and in he remaining counries of he union, and 2

5 he ineres rae in he moneary union. The argumens in his block of equaions associaed wih he small open economy are scaled down in accordance wih he dimension of he small counry in he union. These ve variables inerac wih he oher variables in he model, and are deermined ogeher wih hem. This paper can be seen as an exension o he paper by Adolfson e al (2007), as i considers ha he small open economy is inegraed in a moneary union. Adolfson e al (2007) developed a model of a small open economy aking as exogenously given foreign in aion, foreign oupu and foreign ineres rae. Following heir work and he lieraure, we consider various nominal and real fricions, such as sicky wages, sicky prices, variable capial uilizaion, capial adjusmen coss, habi persisence and volume premium on he foreign ineres rae. Adolfson e al (2007) calibraed and esimaed heir model using he Euro area daa. This paper presens a model designed o assess he ransmission of moneary policy shocks in a small counry in a moneary union. As Porugal can be hough as a such an economy, we used he Poruguese daa o calibrae he parameers of our model. We assume ha afer he moneary shock, in aion, oupu and ineres rae ouside of he union are unchanged and ha in aion, oupu and ineres rae inside he union change according o he referred hree equaion block, conaining an IS curve, a Phillips curve and an ineres rae rule. More speci cally, in he quaniaive exercise performed we consider parameers for he IS curve, Phillips curve and ineres rae rule ha generae responses of hese variables o he ypical Euro area moneary shock ha mimic he pahs of he responses of hese variables in he general equilibrium model of Adolfson e al (2007) o he same shock. Some of he model parameers are calibraed o he seady sae values of he Poruguese economy variables, for ohers we do no have informaion and hey correspond o he esimaes obained (or values assumed) by Adolfson e al (2007) for he Euro area. The shape and sign of he impulse responses of he main macro variables o an unanicipaed emporary decrease in he nominal ineres rae are well in line wih he lieraure. When compared wih he Euro area, oupu, invesmen and real wage in Porugal increase more and in aion in Porugal adjuss quicker and reacs slighly more on impac. On he oher hand, consumpion in Porugal has a behavior almos 3

6 idenical o he one of he Euro area. The rade wih he wo areas responds di erenly. Trade wih counries ouside of he Euro area changes subsanially more han he rade wih counries inside of he Euro area. Boh expors and impors o and from he Euro area increase, wih expors change less. Impors from ouside of he Euro area decrease iniially and expors o ouside of he Euro area increase. The paper is organized as follows. In secion 2 he model is explained. Secion 3 describes how he model is solved. Secion 4 shows how he model is calibraed. Secion 5 sudies he e ecs of a moneary shock on he Poruguese economy. The las secion, secion 6, provides some conclusions. 2. Model The model has 3 economic areas: he small open counry, he oher counries inside he moneary union and he counries ouside of he moneary union. We are concerned wih he small open economy and believe he developmens in he small open economy have lile e fecs over he remaining economic areas. As such, in he model he small open economy is described in deail, bu he oher economic areas are no. 2.. Households There is a represenaive household in he small open economy, whose preferences over sochasic sequences of consumpion C ; real money M P ; and labor L are represened by he uiliy funcion X E 0 =0 log (C bc ) + log M P L+ +! () where E 0 is he condiional expecaion operaor, 2 (0; ) is he discoun facor, and b is a parameer ha conrols he habi persisence. This uiliy funcion is similar o he one used by Chrisiano e al (2005) and Adolfson e al (2007). The aggregae consumpion is a bundle given by a CES index of domesically produced 4

7 and impored foreign goods: C = ( $ o;c $ u;c ) c C h c c c + ($ o;c ) c (C o ) c c + ($ u;c ) c (C u ) c c c ; (2) where C h denoes consumpion of he home good, C o denoes consumpion of he good produced ouside of he union, C u denoes consumpion of he good produced inside of he union, $ o;c is he share of impored consumpion from ouside of he union in oal consumpion, $ u;c is he share of impored consumpion from inside of he union in oal consumpion and c is he elasiciy of subsiuion beween he hree consumpion goods. Thus, consumers derive uiliy from he consumpion of domesically produced goods as well as from he consumpion of goods produced ouside and inside of he union. The price of aggregae consumpion (de ned as he minimum expendiure required o buy one uni of C ) is given by P c = h i ( $ o;c $ u;c ) (P ) c + $ o;c (P o ) c + $ u;c (P u ) c c ; where P is he price of he domesically produced good, P o is he price of he ouside of he union impored good and P u is he price of he inside of he union impored good. All hese prices are in unis of he domesic currency. Consumers choose quaniies of each of hese hree goods ha for a given expendiure maximize aggregae consumpion. The individual demands for each good ha maximize (2) subjec o P C h + P o C o + P u C u = P c C, are c C h P = ( $ o;c $ u;c ) P c C ; P C o o c = $ o;c P c C ; and C u P u c = $ u;c P c C : 5

8 Also, he aggregae invesmen is a bundle given by a CES index of domesically produced and impored foreign goods: I = ( $ o;i $ u;i ) i I h i i i + ($ o;i ) i (I o ) i i + ($ u;i ) i (I u ) i i i ; where I h denoes he home good invesmen, I o denoes ouside of he union invesmen good, I u denoes inside of he union invesmen good, $ o;i is he share of ouside of he union invesmen good in oal invesmen, $ u;i is he share of inside of he union invesmen good in oal invesmen and i is he elasiciy of subsiuion beween he hree invesmen goods. The price of aggregae invesmen is equal o P i = h i ( $ o;i $ u;i ) (P ) i + $ o;i (P o ) i + $ u;i (P u ) i i : The individual demands for each invesmen good are I h = ( $ o;i $ u;i ) P P i i I ; P I o o i = $ o;i P i I ; and I u P u i = $ u;i P i I : Each household is a monopoly supplier of is own labor and can se is wage according o he mechanism described in Calvo (983). The wage can be adjused a exogenously random periods. In order o guaranee ha his fricion does no cause households o become heerogeneous we assume complee domesic nancial markes agains he 6

9 oucomes of his fricion. As a resul all households have he same budge consrain: P c C + P i I + M + D + S B o + B u = P w L + P (r u a(u ))K + M + D R +S R o o ( B z )B o + R u u ( B z )B u + T + z (3) he erms on he lef hand side of he equaliy show how he households use heir income and he erms on he righ hand side he various sources of ha income. Here, M are money holdings, D are deposis ha pay nominal gross ineres rae R, B o are holdings of foreign bonds denominaed in foreign currency ha pay a nominal gross ineres rae R o o, S is he nominal exchange rae, B u are holdings of foreign bonds denominaed in domesic currency ha pay a nominal gross ineres rae R u u and w is he real wage. The erm P r u represens he household s earnings from supplying capial services. The funcion a(u )K denoes he cos of seing he uilizaion rae of capial o u. We assume a(u ) is increasing and convex. These assumpions capure he idea ha he more inensely he sock of capial is uilized, he higher are mainenance coss. We assume ha u = in seady sae and ha a() = 0; a 0 > 0; and a 00 > 0. The expression R o o ( B z ) is he level-adjused gross ineres rae on foreign bonds denominaed in foreign currency, B SBo +Bu P : The erm z is a uni roo echnology shock o be described laer. The funcion i ( B z ) for i = o; u, is assumed o be sricly decreasing in B and o saisfy i (B) =, where B is he seady sae value of B z. This funcion depends on he real holdings of he aggregae foreign asses. This means ha domesic households ake he funcions i (:) as given when deciding on he individual opimal holdings of he foreign bonds. Funcions i ry o capure imperfec inegraion in he inernaional nancial markes. If he domesic economy as a whole is borrowing above is seady sae, domesic households are charged a premium on he foreign ineres raes, if borrowing below is seady sae, domesic households pay less. The inroducion of his premium is needed in order o ensure a well-de ned seady-sae in he model (see Schmi-Grohë and Uribe, 7

10 2003, for furher deails). Wihou his premium, he sock of bonds and consumpion would no be saionary. The remaining variables are T which is a lump-sum ransfer, and z ha sands for he pro s of he rms in he economy. Invesmen I induces a law of moion for capial I K = ( ) K + V I ; (4) I where is he depreciaion rae and V is an adjusmen cos funcion such ha V [ i ] = V 0 [ i ] = 0; and V 00 > 0, where i is he growh rae of invesmen along he balanced growh pah. The household chooses fc ; L ; M ; D ; B o ; B u ; u ; K ; I g o maximize expeced lifeime uiliy () subjec o consrains (3), (4) and iniial values for M 0 ; D 0, B o 0;and B u 0. The Lagrangian is: X E 0 = >< >: M log (C bc ) + log P L+ + P c P C + P i P I + M+D+SB P (r u a(u ))K M +R D +S R o w L o( B z )B o +Ru u( B z )B u P n h i o I Q K ( ) K V I I T P z P 9 >= >; where and Q are Lagrange mulipliers. Ignoring he choices of M and L he rs order condiions are: (C bc ) E (C + bc ) b = P c P P + E + P + R = 0 S P + E + S + P + ()R o = 0 P + E + P + ()R u = 0 8

11 r = a 0 (u ) Q + E Q + ( ) + E + (r + u + a(u + )) = 0 P i I + Q V P I V 0 I I I I 2 + E Q + V 0 I+ I+ = 0 I I The labor used by he inermediae good producers, o be described below, is supplied by a represenaive compeiive rm ha hires labor o each family j: This rm aggregaes he di ereniaed labor of households according o he producion funcion, Z l d = 0 l w w j w w dj where w is he elasiciy of subsiuion beween he di eren ypes of labor and L d is he aggregae labor demand. This rm maximizes pro s aking as given he labor wages w j and aggregae labor wage w : Is maximizaion problem is: max w L d L j Z 0 w j L j dj: The rs order condiions imply: w j w i = Lj L i w or w j L j = w i L w i L w w j ; 8j; i: Inegraing ou his condiion and using he fac ha pro s in perfec compeiion are zero, w L d = R 0 w jl j dj; we ge ha L j = w wj w L d ; 8j: 9

12 We plug in he zero pro condiion he inpu demand funcions o nd ou he aggregae wage, Z w = 0 (w j ) w w dj : As referred above households se heir wages according o a Calvo s seing, Calvo (983). In each period, a fracion w of households can change heir wages. All he oher households can only parially index heir wages o pas in aion and pas produciviy growh. Indexaion o pas in aion is conrolled by he parameer w ; and indexaion o pas produciviy growh by he parameer p : Boh assume values in he inerval [0; ]. Thus, a household ha could no change her wage for s periods has real wage s = w w + z p z p + + w j, where is gross in aion of he domesic good in period, is he seady sae domesic in aion, z is gross produciviy growh in period and z is he seady sae produciviy growh. When seing he wage he relevan par of he Lagrangian for he household is, max w j X E s=0 ( w ) s L+ j+s + + j+s s = w w + z p z p + + w j L j+s! subjec o L j+s = 0 s = w w + z p z p + + w +s w j C A w L d +s; 8j: The rs order condiion of his problem is X E s=0 0 ( w ) s 0 w w s + z p z p + = w j + w j w +s + ( w ) j+s s = A w (+ ) L d + +s w w + z p z p w w + wj + w +s L d +s = 0 C A All households se he same wage because complee markes allow hem o hedge he risk of he iming of he 0

13 wage change. Thus, we drop he subscrip from he wage se by household j ( w ) w = E X s=0 w E X s=0 ( w ) s s = ( w ) s j+s s = w w + z p z p + +! w w w + z p z p + w +! w w (+ ) w +s w +s L d +s + : w L d +s In each period a fracion w of he households se w as heir wage while he remaining fracion index heir price by pas in aion. w w = w w w z p z p w! w + ( w ) (w ) w 2.2. Final Good Producer There is one domesic nal good ha is produced wih inermediae goods: Z Y = 0 d y d j; d d dj where d is he markup in he domesic goods marke. The inpu demand funcions of he nal producer are y j; = d pj; P Y ; and he price of he nal home good is Z P = 0 p d j; d dj :

14 2.3. Inermediae Producers There is a coninuum of inermediae good producers. Each one has he following echnology y j; = A k j; l j; %z ; where A is a oal produciviy echnological shock ha follows an auoregressive process: A = A exp ( A + z A; ) ; where z A; = A " A; ; " A; N (0; ) and z = A : The parameer % corresponds o he xed cos of producion o guaranee ha economic pro s are zero in he seady sae. We have z = z exp ( z + z z; ), where z z; = z A; and z = A Inermediae producers solve wo problems. Firs, given w and r ;hey ren labor and capial in perfec compeiive markes in order o minimize real expendiure. Le be he Lagrangian muliplier. Assuming an inerior soluion, he rs order condiions of his problem are w = ( ) A k j; l j; r = A k j; l j; : 2

15 These wo condiions imply ha u K = w : L r The real marginal cos, mc d, is given by he expression mc d = w r A : The second problem inermediae producers mus solve is o choose he price ha maximizes expeced discouned real pro s. Firms se prices according o a Calvo se-up. In each period, a fracion of rms can choose opimally heir prices. The price chosen in period is denoed by p : We suppressed he rm s indexaion because all rms ha have he opporuniy o choose he price se he same price. The remaining rms canno choose he price hey se. In period hese rms updae heir price o p j; d d, where p j; is he price rm j was charging in period ; is pas in aion of he domesic good, is he seady sae domesic in aion and d is an indexaion parameer. The indexaion parameer, d ; assumes values in he inerval [0; ]. Each rm uses he sochasic discoun facor () o compue he value of is pro s. The erm is he marginal uiliy of he households, evaluaed in unis of he domesic good, in period, which is exogenous o he rms. When a rm can choose is price a dae is problem is: max p E s=0 ( X () s +s s = d d + P +s p mc d +s! y j;+s ) subjec o y j;+s = s = d d + P +s p! d Y +s Where P is de ned as he minimum expendiure in inermediae inpus o produce one uni of nal oupu. 3

16 If he demand funcion is subsiued in he objecive funcion we obain, max p E s=0 0 X () s B +s! s = d d + p s = + P mc d +s s = d d + s = + P p! d C A Y+s: A rs order condiion of he problem above is X E s=0 0 () s +s d s = d d + s = + P d mc d +s s = d d + s =+ P d p d + d p d C A Y +s = 0: 2.4. Cenral Bank The cenral bank ses he nominal ineres raes according o he Taylor rule: R R = " R R u R u &! & Y u Y u &! & Y # ( R ) Y exp(m ) Y where m is a random shock o he moneary policy ha follows m = m " m; ; where " m; N (0; ). Variable u is he arge level for he in aion in he union, which is equal o he seady sae in aion in he union, u is he in aion in period in he union wihou including he small open counry, Y u is he seady-sae oupu in he union, Y u is he oupu in period in he union wihou including he small open counry. The parameer & is he weigh of he small open counry in he union, while R, and are he usual parameers of he Taylor rule. 4

17 2.5. Governmen The budge consrain of he governmen in he small open economy is: P G + T = M M ; where G is governmen consumpion, which includes only domesic produced goods and we ake as exogenous Evoluion of Ne Foreign Asses The evoluion of ne foreign asses a he aggregae level sais es: S B o + B u = S R o o ( B z )B o + R u u ( B z )B u + T B : The rade balance is T B = P X u + P X o P u M u P o M o : The oal impors from he union are M u ouside of he union are M o $ u;u P P u u;x Y u P u = $ u;c P c c C + $ u;i P u P o c P o = $ o;c P C c + $ o;i P i and he oal expors o ouside of he union are X o = $ o;o $ o;o are shares, and u;x and o;x are elasiciy parameers. The variables Y u P i i I and he oal impors from i I. The oal expors o he union are X u = o;x P P o and Y o Y o, where $ u;u and denoe he oupu of he oher counries in he union and he oupu of he counries ouside of he union, respecively. The variables Y u and Y o have growh raes z u and z o ; respecively Relaive Prices When deciding heir consumpion and invesmen baskes agens in he small open economy use he following relaive prices: c;d P c P and i;d P i P : To decide impors consumers use wo relaive prices: he relaive price 5

18 beween impors from he union and he domesically produced good u;d P u P and he relaive price beween impors from ouside of he union and he domesically produced good o;d From he de niions of prices we have, P o P : c;d c = ( $ o;c $ u;c ) + $ o;c o;d c + $ u;c u;d c ; i;d i = ( $ o;i $ u;i ) + $ o;i o;d i + $ u;i u;d i ; 2.8. Aggregaion The aggregae demand in he small open economy is Y = C h + I h + a(u )K + G + X ; where C h and I h denoes consumpion and invesmen of he home good. Thus, he demand for each inermediae good producer is: y i; = C h + I h + a(u )K d p i; + G + X ; 8i P and using he producion funcion is: A ki; l i; %z = C h + I h d p i; + a(u )K + G + X : P Since all rms have he same opimal capial-labor raio, k i; l i; = w R 0 l i; = L ; R 0 k i; = u K, hen ki; l i; = uk L : Also, A k i; l i; = A uk L r ; and since marke clearing implies li; : Inegraing ou, 6

19 R 0 A uk L li; di = A uk R L 0 l i;di = A (u K ) L : Thus, A (u K ) L %z = C h + I h + a(u )K + G + X # : where # = R d pi; 0 P di: 2.9. Res of he World As already referred, he res of he world is composed by wo regions: he remaining counries in he union and he counries ouside of he union. We assume ha he demands from he oher counries for he produc produced domesically have he same funcional form as he demands by he domesic consumers: X i = i;d i;x Y i ; for i = u; o. The oupu, in aion and he ineres rae in he union and ouside of he union are given by wo blocks one for each region i, each conaining hree equaions: an IS equaion, a Phillips equaion and an ineres rae equaion, Y i = fy i Y i ; Y+; i i + ; i = f i i ; i +; Y i + ; and R i = f i R(R i ; i ; Y i ); for Y i = Y o or Y i = ( &) Y u + &Y, i = o or i = ( &) u + &, and R i = R o or R i = R : The parameer & is he size of he domesic counry in he union. 7

20 2.0. Equilibrium The de niion of equilibrium for his economy is sandard. I is a vecor of prices, policy variables and quaniies ha sais es cerain condiions. These condiions are he following: The rs order condiions of he households; The rs order condiions of he rms; The governmen s budge consrain; The budge consrain wih he foreign secor, The IS, Phillips and ineres rae equaions for each region, The markes clearing condiions. 3. Solving he model 3.. Saionary Equilibrium We wan o solve he sysem of equilibrium equaions. However, here are wo main di culies in deermining he soluion. Firs, since here is growh in he model, here are variables ha are growing and ohers ha are saionary. Thus, o solve he model we need o make he variables saionary. Second, he equilibrium equaions are non-linear di erence equaions and ypically heir soluion is no rivial. The usual procedure involves simplifying each equaion of he sysem. Each equaion of he sysem is approximaed by a linear equaion. More speci cally each equaion is replaced by is rs order Taylor approximaion. Tha approximaion is aken around he equilibrium seady sae. We sar by rede ning he variables o obain a sysem in saionary variables. Le he saionary variables have a upper bar. Thus, C = C z ; = z ; r = r, q = q Q ; I = I z ; w = w z ; K = K z ; Y = Y z, 8

21 S + S = + ; B o = SBo z P ; and B u = Bu z P : The ransformaion of he original sysem of equaions ino a sysem of equaions wih saionary variables is rivial, bu involved, and i will no be described here. Nex, we compue he seady equilibrium. More noaion needs o be inroduced, we adop he convenion ha he value of a variable a is seady sae does no have subscrip. For insance C is he seady sae value of C : Le z = exp( z ); and A = exp( A ): In order o nd he seady sae we need o give funcional forms o a (:), V (:) and (:): Le a (u) = (u ) (u ) 2 : Since in he seady sae we have u = ; hen a () = 0 h i h i 2 and a 0 () = : The invesmen adjusmen cos funcion is given by V I I = I 2 I I : Thus, in he seady sae, V [ I ] = V 0 [ I ] = 0: Finally he volume premium facor is given by i (B ) = exp( i B B ); a he seady sae i (B) = for i = u; o. Addiionally, here are saionary processes zu z = z u and zo z = z o. The process z u measures he degree of asymmery beween he domesic shock and he res of he union shock, and z o measures he degree of asymmery beween he domesic shock and he ouside of he union shock. In he seady sae zu z = zo z =. Using hese funcional forms he sysem of equaions ha deermines he seady sae can be wrien as: equaion : R = z equaion 2: r = equaion 3: r q = h i z ( ) equaion 4: i;d = q 9

22 equaion 5: mc = d d ; equaion 6: i;d = ( $ o;i $ u;i ) + $ o;i o;d i + $ u;i u;d i i : equaion 7: c;d = ( $ o;c $ u;c ) + $ o;c o;d c + $ u;c u;d c c ; equaion 8: w = = ( ) mc h mc (r) r i equaion 9: C = w w w b z c;d L b z equaion 0: K = w r z L equaion : z ( ) I = K z 20

23 equaion 2: X u = u;d u;x z u z Y u equaion 3: X o = o;d o;x z o z Y o equaion 4: B B o + B u = o nx u + X o u;d M u o;d M o equaion 5: M u = $ u;c u;d c;d! c C + $ u;i u;d i;d! i I equaion 6: M o = $ o;c! o;d c c;d C + $ o;i o;d i;d! i I equaion 7: Y = ( $ o;c $ u;c ) c;d c C + ( $ o;i $ u;i ) i;d i I + G + X u + X o equaion 8: A z K L % # = Y wih # = 2

24 3.2. Loglinear Approximaions Now we loglinearize he sysem of equilibrium condiions for he saionarized variables around he deerminisic seady sae. The variables wih an ha denoe logdeviaions from he deerminisic seady sae. All variables are wrien in logdeviaions excep he ne foreign asses which are wrien in deviaions insead, since i can be assumed ha is seady sae is zero. Thus, he sysem of linear sochasic di erence equaions ha needs o be solved is he following: Equaion : br + u bu = 0: where u = 2 : Equaion 2: ( ) z K b + ( ) z bi ( ) bz K b = 0 z Equaion 3: ( ) bw + br cmc d = 0 Equaion 4: bu + br + b K b L bw bz b = 0: Equaion 5: Y b Y Y b A + Y bz Y bu Y b K ( ) Y b L = 0 where Y = A z uk L : 22

25 Equaion 6: ( $ o;c $ u;c ) c;d c d C c c;d + C b + ( $ o;i $ u;i ) i;d i d I i i;d + b I + K z bu + GG b + X u cu X + X o co X Y Y b = 0 Equaion 7: B b = Ro b z B + X u cx u + X o cx o u;d M u d u;d + d M u o;d M o d o;d + d M o + R u B u R [ u ub b B b bz + Ro B o R [ o o bb b + z z b b bz If in seady sae boh of he foreign debs, B o and B u ; are zero hen we have B b = Ro b z B + X u cx u + X o cx o u;d M u d u;d + d M u o;d M o d o;d + d M o Equaion 8:! M u M du u;d c = $ u;c C c;d! u;d i $ u;i I i;d c d u;d i d u;d d c;d + C c + d i;d + I b 23

26 Equaion 9:! M o M do o;d c = $ o;c C c;d! o;d i $ o;i I i;d c d o;d i d o;d d c;d + C c + d i;d + I b Equaion 0: c X u = u;x d u;d + c Y u + c z u Equaion : X c o = o;x d o;d + Y co + z b o Equaion 2: c;d c \ c;d = $ o;c o;d c \ o;d + $ u;c u;d c \ u;d ; Equaion 3: i;d i \ i;d = $ o;i o;d i \ o;d + $ u;i u;d i \ u;d ; Equaion 4: is he loglinearizaion of u;d = u;d u or d u;d = du;d + b u b Equaion 5: d o;d = do;d + b o b + b 24

27 Equaion 6: is he cenral bank ineres rae rule, br = R b R + ( R ) h ( &) b u + & b i + ( R ) Y ( &) c Y u + & b Y + bm Equaion 7: E b z( b z ) C b + b2 z 2 b z bc + b=z C b + b z b=z bz b z d c;d + b n o b z = 0 Equaion 8: 0 = ( w )( w ) (+ w ) h b + w bw + b L d i + w E + w b + bz + p bz w w b + bz p bz + w bw + w E bw + + ( w ) 2 bw ] Equaion 9: E n b+ + b R b + bz + b o = 0 Equaion 20: E n b+ bz + + c R u u c B b + b o = 0: Equaion 2: E n b+ bz + + b + + c R o o c B b + b o = 0: Equaion 22: E b+ b + ( ) E bq z + + ( ) E br + bq z = 0 25

28 Equaion 23: E bq + z 2 E b I+ z 2 ( + ) b I + z 2b I z 2 d bz i;d = 0: Equaion 24: b d b = E + b d b ( ) ( ) + cmc d d bd : Equaion 25: ( &) c Y u + & b Y = ( &) [ Y u + & b Y + ( )E ( &) [ Y u + + & b Y E ( &) [ u + + & b + + c" Y Equaion 26: ( &) c u + & b = 3 ( &) [ u + & b + 4 E ( &) [ u + + & b E ( &) [ Y u + + & b Y + + c" The exogenous processes are bz ; c z u ; b z o ; bm ; c Y o ; b R o ; b o ; c" Y ; c" : 3.3. Soluion There are a few available algorihms designed o solve he ype of di erence equaions sysem described in he previous subsecion. We used he one developed by Uhlig (995). Le sae denoe he vecor of endogenous sae variables and nsae denoe he vecor of endogenous non-sae variables. Uhlig s algorihm enables us o wrie all variables as linear funcions of he vecor sae, and a vecor of exogenous variables exo which are given a dae. More formally, i gives us marices P, Q, R and S so ha he equilibrium described by he recursive 26

29 equilibrium law of moion sae = P sae + Q exo and nsae = R sae + S exo is sable. 4. Calibraion Mos of he parameers can be relaed o he seady sae values of he variables in he model and herefore, can be calibraed so as o mach he sample mean of hese. Ohers were aken from he lieraure. Whenever here were various alernaives for he parameers we ook he one used by Adolfson e al (2007). Proceeding in ha way we minimized he dimensions in which Porugal is di eren from he Euro area. Tha makes i easier o idenify he causes for he di erences beween he resuls obained for Porugal and he ones for he Euro area obained by Adolfson e al (2007). Many of he parameers were calibraed using he "Quarerly Series for he Poruguese Economy" daa se, which refers o he period 77:Q-07:Q4. This daa se is included in he Economic Bullein of he Bank of Porugal, Summer 2008, and is available online. For he period ha sars in 999, he year in which Porugal enered he European Moneary Union, and ends in 2007, per capia Privae Consumpion grew a 0:29 percen quarerly, per capia Public Consumpion grew a 0:32 percen quarerly, per capia Invesmen grew a 0: percen quarerly, per capia GDP grew a 0:25 percen quarerly, per capia Expors grew a :05 percen quarerly and per capia Impors grew a 0:79 percen quarerly. We considered he average growh rae of z o be 0:25 percen quarerly, which is he growh rae of real GDP per capia in he period 99:Q-07:Q4. The sock of capial was compued using daa on he di eren ypes of invesmen, a se of depreciaion raes, 27

30 one for each ype of capial and equaions for he law of moion of he di eren ypes of capial, K j;, given by K j; = ( j; ) K j; + I j; : The per capia aggregae sock of capial, obained according o his mehod, grew in he period 78:Q-07:Q4 a he rae of 0:77 percen quarerly. The quarerly depreciaion rae,, obained was 0:0. For many reasons i is di cul o deermine he seady sae real ineres rae relevan for he represenaive Poruguese consumer. The average real ineres rae measured by he di erence beween he 3 monh money marke ineres rae and he realized in aion rae was 0:04 percen quarerly in he period 99:Q-07:Q4. The usefulness of his real ineres rae is problemaic as i implies a discoun facor,, larger han one. As such we discarded i and considered alernaives. The oher available nominal ineres rae series are implici ineres raes. They are obained eiher by dividing ineres received on bank deposis by bank deposis or by dividing ineres received on bank loans by he bank loans. The ineres raes on deposis we discard as hey also imply a discoun facor larger han one oo. Among he ineres raes on credi, he morgage ineres rae is our preferred, as i is he lowes and he mos relevan for he represenaive consumer. The average real ineres rae measured by he di erence beween he implici morgage ineres rae and he realized in aion rae was 0:46 percen quarerly in he period 99:Q-07:Q4. These values ogeher wih he values assumed for he growh rae of z imply a value of equal o 0:998. This value of is high, bu Adolfson e al (2007) consider an even higher value of for he euro area, 0:999. Following Adolfson e al (2007), we se he labor supply elasiciy,, o and he habi parameer o 0:65. Chrisiano e al (2005) consider similar values for hese parameers. The consan in he labor desuiliy funcion, ; is chosen so ha in he seady sae agens work 30 percen of heir ime. Adolfson e al (2007) assume agens work 30 percen of heir ime while Chari e al (2002) assume agens work 25 percen of heir oal ime in seady This money marke ineres rae series is he 3-monh EURIBOR, and he in aion used was he GDP de aor growh. 28

31 sae. We considered labor income o be he sum of "Remunerações do Trabalho" plus "Conribuições para a Segurança Social" and capial income o be all he remaining domesic income. 2 We ook as he value of, he sample mean of he raio beween non-labor income and domesic income, which for he period 99:07 is 0:27. The value ha Adolfson e al. (2007) consider o be he share of capial for EMU is 0:29. The share of impors in he main componens of he domesic expendiure were obained from he naional inpu-oupu marices of INE. Tha calculaion, which is involved, was only done for he period During ha period he average share of privae consumpion ha was impored was 27 percen and for he same period he average percenage of invesmen ha was impored was 33 percen. The sample mean, for he period 99:- 07:4, of he share of impors from he euro area was 66 percen and he share of impors from counries ouside of he euro area was 34 percen. The percenage of impored consumpion from he union was assumed o be proporional o he raio beween oal impors from he Euro area and aggregae impors. Thus, he share, $ u;c, was calibraed o mach he sample mean, 0:8. Under his assumpion, he oher parameers, $ u;i, $ o;c ; and $ o;i, were se o 0:22, 0:09 and 0:. For he period, 99:-07:4, he raio beween he price of invesmen and he GDP de aor and he raio beween he price of consumpion and he GDP de aor, which we denoed by i;d and c;d ; averaged 0:98 and 0:99. For he oher relaive prices o;d and u;d we do no have informaion. Thus, we canno use equaions 6 and 7 o deermine he values of c and i. Sudies seem o indicae ha for he Unied Saes he elasiciy beween home goods and foreign goods is beween and 2, and values in his range are generally used in empirical rade models. (See, for example, he survey by Sern e al (976).) For Europe, ha seems o be he case also. (See, for example, he discussions of Collard and Dellas (2002), Whalley (985, Ch. 5) and Deardor and Sern (990, Ch. 3).) For he Unied Saes Chari e al. (2002) and Backus e al (994) se he subsiuion elasiciy beween foreign and domesic invesmen goods equal o :5. For Europe Chriso el 2 As he naional accouning daa of GDP includes ne indirec axes, hese need o be subraced o he GDP o obain he domesic income. 29

32 e al (2008) esimae c = :9 and i = :6. In view of he above we se c = :5 and i equal o :6, which are he esimaes obained by Adolfson e al (2007) for he euro area. We se boh u;x and o;x equal o :5. The resuls are robus o changes of he s wihin he inerval [; 2]. The evidence from survey daa, as described in Fernando Marins (2006), indicaes ha he frequency of price changes by Poruguese rms is :9 imes per year. And of hose rms ha change prices only abou 42 percen use curren and fuure informaion o se heir price. This implies ha in each quarer abou 20 percen of he rms change heir prices opimally. This value is higher han he one esimaed by Smes and Wouers (2003) and Adolfson e al (2007) which is around 0 percen, bu lower han he one esimaed by Chrisiano e al (2005), 40 percen. Following Adolfson e al (2007) we se he mark-up equal o 6 percen. 3 We se he indexaion parameer, d, equal o 0:22, which is he value esimaed by Adolfson e al (2007) for he euro area. Following Adolfson e al (2007) and Chrisiano e al (2005), he markup power in wage seing is se o :05. Following Adolfson e al (2007), he indexaion of wages, parameer, w, is se o 0:50; and he probabiliy of no being able o change he wage, w, is se equal o 0:69. Under our assumpions, he seady sae of he model is independen of he adjusmen cos funcions, bu he dynamics depend on hem. The esimaes in he lieraure concerning he adjusmen coss of invesmen, capial uilizaion and foreign deb di er subsanially. Chrisiano e al (2005) nd esimaes of 2:48 and 0:0 for V 00 and 2, respecively. Alig e al (2003) nd a value of 0:049 for 2 : Adolfson e al (2007) esimae a value of a 8:67 for V 00 and esimae a value of 0:252 for b. 4 We ook he values repored in Adolfson e al (2007). I is common in he lieraure, including Adolfson e al (2007), o assume ha in he seady sae expors are equal o impors, and he ne foreign deb is zero. For Porugal he ne value of expors has been consisenly negaive. The average ne value of expors was 0 percen of he GDP value for he period , and for he 3 Chari e al (2005) have a mark-up of %: 4 These divergen resuls in he lieraure are due o he fac ha he daa ses are divergen and o he di eren esimaion echniques used. Adolfson e al (2007) use Bayesian esimaion echniques while Chrisiano e al (2005) mach he impulse response funcions of he ideni ed shocks. 30

33 more recen period, , hey were negaive and on average abou 9 percen of he GDP value. According o his evidence, i would seem ha he seady sae ne foreign asses for Porugal would be a subsanial posiive amoun. However, his is conradiced by he fac ha Poruguese ne foreigns asses have been been negaive and decreasing. In 2007 he ne foreigns responsabiliies were 90 per cen of GDP, being 83 per cen denominaed in euros. Wihou excuses we consider a calibraion in which he ne foreign asses are in seady sae 90 per cen of GDP and ha 83 per cen are denominaed in euros. During he period 99:0-07:04 he share of he expors o counries ouside of he euro area was 0:37, while as referred before, he share of impors from counries ouside he euro area was 0:34: The parameers chosen replicae approximaely hese raios as well as he average sample shares in he GDP of privae consumpion, public consumpion, invesmen, oal expors and oal impors. The behavior of he nominal ineres rae, oupu and in aion in he union is deermined by equaions (6), (24) and (25). The parameers of hese equaions were chosen so ha he impulse response funcion of hese variables o a moneary shock could mimic he impulse response funcion of hese variables o a moneary shock in he model esimaed by Adolfson e al (2007) for he Euro area. The parameers of he ineres rae rule are similar o he ones esimaed for he Euro area by Adolfson e al (2007) and Smes and Wouers (2003). The parameer & re ecs he size of Porugal and is se o 0:05. The parameers in he equaions ha deermine he nominal ineres rae, oupu and in aion ouside he union do no need o be speci ed as we assumed hese variables are no a eced by a moneary policy shock in he union. 5. Impulse Response Funcions Excep for he in aions, nominal ineres rae and ineres rae premium, which are repored as annualized quarerly raes, he graphs associaed wih he impulse response funcions have on he y-axis he percenage deviaions of he variables from heir seady sae values. The shock considered is a whie noise shock o he 3

34 nominal ineres rae. There is a feaure on he impulse response funcions worh noing. As can be seen from Figure, wih he excepion of he variables associaed wih rade, mos of he variables respond in a hump-shaped form, peaking afer 3 or 4 quarers and reurning o he preshock levels afer abou hree years. The excepions are he nominal exchange rae, some relaive prices and he di eren impors and expors. The euro area variables: nominal ineres rae, in aion and oupu replicae closely he pah of he impulse responses of hese variables o a moneary shock in he Adolfson e al (2007) model. On impac he nominal ineres rae drops by 40 basis poins and reurns o he seady sae four years laer. Boh oupu and in aion have hump-shaped responses and achieve heir peaks afer abou one year, around 0:3 percen of he seady sae for he oupu and around 0 basis poins (annualized) for in aion. The small open economy responses o he moneary shock are roughly similar o he ones obained in a closed economy, even hough he model possesses an addiional channel of moneary policy ransmission. We summarize hese responses now. Because prices are sicky, he unexpeced decrease in he nominal ineres rae implies a decrease in he real ineres rae. A lower real ineres rae makes bonds less aracive han invesmen, which leads o an increase in invesmen. As he sock of capial increases he marginal produciviy of labor increases also and rms increase heir labor demand. The emporary lower real ineres rae has ineremporal subsiuion e ecs over consumpion and labor supply. I makes presen consumpion and presen leisure (since nominal wages are sicky) relaively less expensive, which lead households o increase consumpion and decrease labor supply. The changes in he labor supply and labor demand lead o an increase in he real wage. Oupu increases, since consumpion and invesmen increase, and capial uilizaion increases because here are coss in adjusing capial. As consumpion and invesmen increase he demand for impors increases. The addiional channel for he moneary policy ransmission associaed wih an open economy compels rms o 32

35 increase producion oo. In a closed economy households can only smooh ou he pah of consumpion and leisure by varying he pah of invesmen. Bu in an open economy households have anoher alernaive o accomplish ha, he possibiliy of changing he pah of ne expors. The moneary shock considered leads o an increase in he domesic income. In order o smooh heir pah of consumpion and leisure households increase heir ne foreign asses. This behavior of foreign asses implies an increase in ne expors and a furher increase in he oupu. Afer he shock, he sock of ne foreign asses is above is seady sae value for abou four years. There is an addiional income e ec in Porugal ha is absen in he Adolfson e al (2007) calibraed EMU. They assumed ha he ne foreign asses of he EMU in he seady sae were zero, bu we assumed ha for Porugal he seady sae ne foreign asses were negaive, 90 per cen of GDP, and ha 83 per cen were denominaed in euros. Thus, due o he high sock level of he ne foreign asses denominaed in euro, he impac of a drop in he euro ineres rae is favourable for Porugal, bu irrelevan for he EMU. For his reason, i should be expeced ha invesmen and oupu in Porugal would vary more han invesmen and oupu in he EMU. In fac he oupu increases in percenage deviaions from he seady sae a lile more in Porugal han in he Euro area. The impulse response funcion for he oupu in Porugal is almos all he ime above he one for he EMU. For Porugal he maximum response is jus over 0:3 and in he EMU i is jus below 0:3. The invesmen, employmen and real wage in Porugal and in he EMU, as compued by Adolfson e al (2007), have similar shapes bu in Porugal hose variables move considerably more. The impulse response funcions for invesmen, employmen and real wage in Porugal are almos all he ime above he ones for he EMU. For Porugal he maximum response for invesmen is jus abou 0:6; for employmen is abou 0:25, and for he real wage abou 0:, while for he EMU he maximum response for invesmen is abou 0:5; for employmen is abou 0:2 and for he real wage is abou 0:07. Consumpion in Porugal and in he Euro area have almos idenical pahs. In aion in Porugal responds quicker o he shock han he in aion in he Euro area, on impac i increases by more and reurns faser o he seady sae. The maximum increase of in aion in Porugal is 6 basis poins 33

36 while ha maximum in he EMU is around 0 basis poins. This should be associaed wih he fac ha we assumed ha in Porugal each quarer 20 percen of he rms change heir prices opimally, while Adolfson e al (2007) ook ha only 0 percen of he rms in he EMU change heir prices opimally. The relaive price of he Euro area s good is persisenly below he seady sae in response o he shock due o he referred di ereniaed behavior of in aion in Porugal and in he euro area. This fac, ogeher wih he shock having an impac in he oupu relaively higher in Porugal han in he Euro area, implies ha impors from he Euro area increase more han expors o he Euro area, in response o he shock. Consumpion in Porugal and in he Euro area have almos idenical pahs. This resul is very ineresing. I indicaes ha he households in Porugal use he saving insrumens available o hem o oo smooh ou consumpion, and are able o replicae he impulse response pah of heir euro area counerpars, even hough, as we saw above, he e ecs of he shock are sronger in Porugal han in he euro area. Now we inerpre he behavior of he exchange rae. From equaions 9 and 2 we obain he UIP condiion E b + = c R c R o + o c B. The UIP does no resric he depreciaion rae of he euro in he impac period. Apar from he impac period, he nominal exchange rae behavior is he one implied by he UIP. The foreign ineres rae is unchanged and he volume premium changes lile, as he adjusmen coss of he asse socks were assumed o be relaively small. In he iniial periods, jus afer he impac period, he euro appreciaes as he decrease in he ineres rae is larger in absolue value han he decrease in he volume premium on he foreign deb, and in he las periods i depreciaes as he opposie happens. In he impac period he currency depreciaes because, as we observed before, ne expors mus increase. Ne expors o he Euro area did no increase due o he evoluion, described above, of he main aggregae variables in Porugal and in he Euro area. Thus, in order for ne expors o increase, ne expors o ouside of he union mus increase. Tha is possible only if he relaive price of he good produced ouside of he union increases, given ha we assumed ha he main aggregae economic variables ouside of he union were consan. Equaion 34

37 5 says ha for he relaive price of he good produced ouside of he union o be persisenly above is seady sae i is necessary ha on impac he euro depreciaes su cienly o compensae is subsequen appreciaion and he persisen domesic in aion. Summing up, in he shor run, lower real ineres raes in he Euro area end o reduce he foreign exchange value of he euro, which lowers he relaive prices of he goods produced in Porugal and in he Euro area. This leads o higher ouside of he union aggregae spending on goods and services produced in Porugal and in he Euro area. The behavior of he ne foreign asses impulse response funcion, which re ecs he evoluion of he ne expors, is a resul of he households choice o smooh ou consumpion hrough ime. I has an hump-shaped paern, achieves is peak afer four quarers a abou 0:8 of he seady sae, and reurns o he seady sae afer 4 years. Wih respec o he impulse response funcions of he expors and impors here is a sriking di erence beween hose o and from inside he Euro area and hose o and from ouside of he Euro area. Expors and impors o and from he Euro area increase bu impors increase more. This behavior is explained by wo facs. Firs, because he oupu in Porugal increases more han in he Euro area. Secondly, because he relaive price of he good produced in Porugal increased due o he fac ha in aion in Porugal is slighly above he Euro area s in aion. The rade wih he counries ouside of he Euro area evolves in a very di eren way and is in par explained by he pah of he relaive price of he good produced ouside of he Euro area, which jumps up on impac and reurns wih some persisence o is seady sae four years afer he shock. Boh expors and impors o and from counries ouside of he Euro area change subsanially. Expors on impac are abou 0:54 percen above he seady sae and impors on impac are abou 0:32 percen below he seady sae. Impors from ouside of he union achieve is maximum when invesmen achieves is maximum, 5 quarers afer he shock. Here he e ecs over he exchange rae are smaller han in Adolfson e al (2007). In our model on impac he euro depreciaes by abou 0:4 from he seady sae, while in Adolfson e al (2007) i depreciaes by abou 0:5 from he seady sae. Mos likely, if we were o change some of he parameers in our model in order o ge ha 35

38 higher value for he depreciaion of he euro, he e ecs over many of he real variables like oupu, invesmen and real wages, which are already bigger in Porugal han in he union, would be furher augmened. 6. Conclusions In his paper we inroduce modi caions in he benchmark open economy moneary business cycle model of Adolfson e al (2007) in order o incorporae a small counry ha rades wih counries inside and ouside of he moneary union o which i belongs. To guaranee local deerminacy he variables associaed wih he counries ouside he union can be assumed exogenous, bu no he variables associaed he oher counries in he union. As he ineres rae rule for he union depends on he in aion and oupu of he union, if we were o ake hese variables as exogenous he ineres rae would be exogenous also and here would no be a unique local equilibrium. We proceeded by assuming ha in aion, oupu and ineres rae inside he union change according o a hree equaion block, conaining an IS curve, a Phillips curve and an ineres rae rule, which parameers were chosen so ha hese equaions ogeher wih he remaining condiions of he model could deliver he impulse response funcions o a moneary shock of he European Union s in aion, oupu and ineres rae obained by Adolfson e al (2007). We use he model o sudy he moneary ransmission mechanism in Porugal. The shape and sign of he responses of he variables are similar o he ones obained in he lieraure for he Euro area. There are wo main ndings. I seems ha some variables in Porugal adjus more or faser. When compared wih he Euro area, he oupu in Porugal expands more on impac and in aion and real wage in Porugal adjus quicker and reac furher on impac. The rade wih he wo areas responds di erenly o he moneary shock. Trade wih counries inside of he Euro area increases, as boh expors and impors increase. Impors from counries ouside of he Euro area change lile and expors o counries ouside of he Euro area increase. I could be worhwhile o conduc more empirical work in he conex of his model. Di eren behaviors for 36

39 he aggregae variables of he counries inside and ouside of he Euro area can be considered. For insance, o assume ha he equaions ha deermine he evoluion of hese variables are he ones given by an esimaed VAR. Anoher dimension ha can be explored is he esimaion of some of he parameers of he model using Bayesian mehods, as Adolfson e al (2007) do. 5 The model has many fricions, bu is simplisic in various dimensions. As such i could be ineresingly exended in various direcions. I could incorporae governmen deb and non-ricardian households so ha scal policy could inerac wih he moneary policy. I could incorporae a nancial secor o sudy he so called nancial acceleraor channel of he moneary policy. I could consider he labor marke as a more complex marke allowing for unemploymen. More secors of producion could be considered, in paricular he nonradable good secor. 7. References Adolfson, M., S. Laseen, J. Linde, and M. Villani (2007), "Bayesian esimaion of an open economy DSGE model wih incomplee pass-hrough", Journal of Inernaional Economics, Elsevier, vol. 72(2), pages 48-5, July. Alig, D., L. J. Chrisiano, M. Eichenbaum, and J. Linde (2003), The Role of Moneary Policy in he Propagaion of Technology Shocks. Manuscrip, Norhwesern Universiy. Backus, D., P. Kehoe, and F. Kydland (994), Dynamics of he Trade Balance and he Terms of Trade: The J-Curve?, American Economic Review, 84, Calvo, G. (983) "Saggered Prices in a Uiliy-Maximizing Framework", Journal of Moneary Economics, vol. 2, p Collard, F. and H. Dellas (2002), "Exchange Rae Sysems and Macroeconomic Sabiliy", Journal of Moneary Economics", 49, p According o Canova (2007) in general he esimaion of his ype of models is ricky for many reasons, bu specially because i is prone o ideni caion problems. 37