Review of Economic Dynamics

Transcription

1 Review of Economic Dynamic Conen li available a ScienceDirec Review of Economic Dynamic Invemen-pecific echnology hock and inernaional buine cycle: An empirical aemen Federico S. Mandelman a, Pau Rabanal b, Juan F. Rubio-Ramírez c,a,d,, Diego Vilán e a Federal Reerve Bank of Alana, Reearch Deparmen, 1000 Peachree Sree, N.E., Alana, GA , Unied Sae b Inernaional Moneary Fund, Reearch Deparmen, h Sree, N.W., Wahingon, DC 20431, Unied Sae c Duke Univeriy, 213 Social Science Building, P.O. Box 90097, Durham, NC , Unied Sae d FEDEA, Calle de Jorge Juan, 46, 28001, Madrid, Spain e Univeriy of Souhern California, 3620 Souh Vermon Avenue, Kaprielian Hall, Lo Angele, CA 90089, Unied Sae aricle info abrac Aricle hiory: Received 30 November 2009 Revied 30 July 2010 Available online 27 Augu 2010 JEL claificaion: E32 F32 F33 F41 Keyword: Inernaional buine cycle Coinegraion Invemen-pecific echnology hock In hi paper, we fir inroduce invemen-pecific echnology IST hock o an oherwie andard inernaional real buine cycle model and how ha a houghful calibraion of hem along he line of Raffo 2009 uccefully addree he quaniy, inernaional comovemen, Backu Smih, and price puzzle. Second, we ue OECD daa for he relaive price of invemen o build and eimae hee IST procee acro he U.S. and a re of he world aggregae, howing ha hey are coinegraed and well repreened by a vecor error correcion model VECM. Finally, we demonrae ha when we fi uch eimaed IST procee in he model inead of he calibraed one, he hock are acually no a powerful o explain any of he four menioned puzzle Elevier Inc. All righ reerved. 1. Inroducion Sandard inernaional real buine cycle IRBC model only driven by oal facor produciviy TFP hock fail o accoun for a lea four imporan feaure of he daa. Fir, cro-counry conumpion correlaion are generally imilar o or lower han cro-counry oupu correlaion in he daa, wherea exiing model ypically produce much higher conumpion correlaion han oupu correlaion he quaniy puzzle. Second, invemen and employmen end o be poiively correlaed acro counrie, wherea he model predic a negaive correlaion he inernaional comovemen puzzle. Third, he andard eup predic ha he real exchange rae RER i poiively linked o he raio of conumpion acro he wo economie, while inead he correlaion in he daa i negaive or cloe o zero he Backu Smih puzzle. Fourh, model generae far le volailiy in he erm of rade and he RER han in he daa he price puzzle. We hank Marín Uribe, Jeper Lindé, an anonymou referee, and eminar paricipan a SCIEA a he Federal Reerve Bank of Dalla for very helpful commen and uggeion. Beyond he uual diclaimer, we mu noe ha any view expreed herein are hoe of he auhor and no necearily hoe of he Federal Reerve Bank of Alana, he Federal Reerve Syem, FEDEA, or he Inernaional Moneary Fund. Finally, we alo hank he NSF for financial uppor. * Correponding auhor a: Duke Univeriy, 213 Social Science Building, P.O. Box 90097, Durham, NC , Unied Sae. addree: federico.mandelman@al.frb.org F.S. Mandelman, prabanal@imf.org P. Rabanal, juan.rubio-ramirez@duke.edu J.F. Rubio-Ramírez, vilan@uc.edu D. Vilán /$ ee fron maer 2010 Elevier Inc. All righ reerved. doi: /j.red

2 F.S. Mandelman e al. / Review of Economic Dynamic Rik haring acro counrie induce rong poiive cro-counry conumpion correlaion in he IRBC framework. Thi reul ill hold even when he complee marke aumpion i replaced by incomplee marke. The efficien repone o a emporary TFP hock involve increaing facor inpu invemen and labor upply in he more producive counry and reducing facor inpu in he le producive counry. The model alo dicae ha domeic houehold conume more relaive o heir foreign counerpar when heir conumpion bake i relaively cheap i.e., when he RER increae. Finally, ince model produce highly correlaed conumpion level, heir raio how low volailiy. Since he RER i direcly aociaed wih hi raio, he RER i no very volaile. The accumulaion of hee effec creae he four puzzle decribed above. The lieraure ha been energeically rying o fill hi gap beween heory and daa on ome of hee dimenion, wih ome ucce. For example, Chari e al how ha a moneary economy wih monopoliic compeiion and icky price can olve he price puzzle if a high degree of rik averion i aumed. They alo how ha in a model wih moneary policy hock only he Backu Smih puzzle canno be olved regardle of he ae marke rucure in he model and of he preence of oher nominal or real rigidiie. Corei e al. 2008a, 2008b how ha inroducing nonraded good help reconcile heory wih daa on he price and Backu Smih puzzle dimenion. Anoher alernaive i o inroduce ae hock a in Sockman and Tear 1995 and Heahcoe and Perri In paricular, Heahcoe and Perri 2007 how how hi ype of demand hock can uccefully addre he Backu Smih puzzle. However, i i difficul o meaure ae hock in he daa. Raffo 2009 inead conider invemen-pecific echnology IST hock, along he guideline pecified in Greenwood e al and he empirical work of Fiher 2006, and he uccefully addree he four puzzle. In fac, hi ype of hock ha wo appealing feaure: i reemble a demand hock given ha i direcly affec he relaive price of capial good and i ha a clear link o he daa. Raffo 2009 cleverly ake advanage of he fir feaure bu doe no conider he econd. Inead of uing he daa o parameerize he law of moion of he IST hock, he houghfully calibrae hem o mach ome oher obervable commonly ued in he IRBC lieraure. Our paper follow an alernaive approach. Fir, uing daa from he OECD, we provide evidence ha IST procee for he Unied Sae U.S. and a re of he world R.W. aggregae have a uni roo and are coinegraed. Moivaed by hi empirical finding, we eimae a vecor error correcion model VECM for he IST procee of he U.S. and he R.W. Second, we add IST hock ha follow he eimaed VECM proce ino an oherwie andard wo-counry, wo-good model wih TFP alo following a VECM proce a decribed in Rabanal e al Our model hould be conidered an exenion of Heahcoe and Perri 2002 o conider IST hock a in Raffo, 2009 and coinegraed hock Rabanal e al., In ha ene, our model i cloely relaed o Ireland 2009, who conruc a wo-counry ochaic growh model wih coinegraed TFP and IST hock o analyze he macroeconomic performance of boh he U.S. and he Euro area. Finally, we imulae he model and analyze he reul. Our reul indicae ha while a calibraion of he IST hock along he line of Raffo 2009 would uffice o addre he above-menioned puzzle, he daa i le upporive. The eimaed proce for he IST hock help in improving model fi along ome of hee dimenion, bu i i unable o fully olve hem. Raffo 2009 calibrae he variance of he IST procee o be almo hree ime he one characerizing he TFP proce. In ha cae, he IST hock accoun for abou wo-hird of he variaion in oupu. Inead, our eimaion reul indicae ha he variance of he IST proce i abou he ame ize a he variance of he TFP innovaion, making he IST hock quaniaively le effecive. 1 Our finding do no change even when we conider addiional inernal amplificaion mechanim uch a endogenou capial uilizaion, which faciliae invemen demand boom; or GHH preference, which uppre he wealh effec reponible for dampening he repone of he labor upply o produciviy innovaion and change in he erm of rade. In addiion o he above-decribed aociaion wih he IRBC lieraure, our work i alo relaed o he growing lieraure analyzing he uefulne of IST hock in explaining buine cycle flucuaion. A in Alig e al and Schmi-Grohé and Uribe 2008, we find ha eimaed IST hock play a minor role in driving buine cycle flucuaion. In addiion o Raffo 2009 paper, he lack of hru of he IST hock i in conflic wih ome oher udie. For example, Juiniano e al eimae ha IST hock are reponible for more han 50 percen of oupu flucuaion in he U.S. and repor a andard deviaion of heir IST proce ha i more han four ime larger han ha of i empirical equivalen. Noe, however, ha here i a relevan difference beween our work and Schmi-Grohé and Uribe 2008 work, and ha of Juiniano e al and Raffo While boh our paper and Schmi-Grohé and Uribe eimae he law of moion for IST hock uing he oberved relaive price of invemen, he paper of Juiniano e al. and Raffo do no. Hence, he IST hock can be freely parameerized o fi he properie of oher oberved macroeconomic variable. Bu clearly hi exra freedom ha ome empirical implicaion ha are a odd wih he daa. The re of he paper i organized a follow. In Secion 2 we preen he model wih coinegraed hock. In Secion 3 we decribe our daa and repor eimae for he law of moion of hee procee of he U.S. and a R.W. aggregae. In Secion 4 we preen he main finding from imulaing he model, leaving Secion 5 for concluding remark. 1 Behind our exercie lie he aumpion ha baic IRBC model do a good job fiing he daa. Some auhor doub i. For example García-Cicco e al. forhcoming repor ha he RBC model doe a poor job a explaining buine cycle in emerging counrie. They alo find ha only a richer model wih counry premium hock and financial fricion can accoun for he buine cycle in emerging marke.

3 138 F.S. Mandelman e al. / Review of Economic Dynamic The model In hi ecion, we preen a andard wo-counry, wo-good IRBC model imilar o he one decribed in Heahcoe and Perri The main difference wih repec o he andard IRBC lieraure i he incluion of IST hock and he definiion of coinegraed procee for boh IST and TFP hock. Following Raffo 2009, and for comparion purpoe, we alo inroduce endogenou capial uilizaion a in Greenwood e al and a quadraic adjumen co in he capial ock. In mo of he exiing lieraure, produciviy procee IST and TFP are aumed o be aionary or rend aionary in log, and hey are modelled a a VAR in level. 2 In hi paper, we inead conider log procee ha are coinegraed of order C1, 1. Thi implie ha he log procee are inegraed of order one bu a linear combinaion i aionary. According o he Granger repreenaion heorem ee Engle and Granger, 1987, our C1, 1 aumpion i equivalen o defining a VECM for he law of moion of he fir log difference of he echnology procee. I i he cae ha our C1, 1 aumpion ha rong daa implicaion. In Secion 3.3 we provide empirical evidence ha uppor our hypohei. In each counry, a ingle final good i produced by a repreenaive compeiive firm ha ue inermediae good in he producion proce. Thee inermediae good are imperfec ubiue for each oher and can be purchaed from repreenaive compeiive producer of inermediae good in boh counrie. Inermediae good producer ue local capial and labor in he producion proce. The final good can only be locally conumed or inveed by conumer; hence, all rade beween counrie occur a he inermediae good level. In addiion, conumer rade acro counrie an unconingen inernaional one-period rikle bond denominaed in uni of home-counry inermediae good. We hu aume incomplee marke. In each period of ime, he economy experience one of many finie even.wedenoeby = 0,..., he hiory of even up hrough period. The probabiliy, a of period 0, of any paricular hiory i π and 0 i given. In he remainder of hi ecion, we decribe he houehold problem, he inermediae and final good producer problem, and he VECM procee. Then, we deail marke clearing and equilibrium. Finally, we dicu he condiion for he exience of a balanced growh pah. In Appendice A.1 and A.2, we explain how o ranform he variable in he model o achieve aionariy Houehold We decribe he deciion problem faced by home-counry houehold. The problem faced by foreign-counry houehold i imilar, and hence, i i no preened becaue of pace conideraion. The repreenaive houehold of he home-counry olve max β π [ U C, L ] 1 {C,L,X,K,D,u } =0 ubjec o he following budge conrain: P [ C + X ] + P H Q D P [ W L + u R K 1] + { P H D 1 Φ [ D ]} 2 and he law of moion for capial: K = { 1 δ [ u ]} K 1 + V { X φ 2 X 1 V 1 V [ X V ] 2 } X 1 V 1 Λ X. 3 U[C, L ] i he period uiliy funcion, 3 β 0, 1 i he dicoun facor, L 0, 1 i he fracion of ime allocaed o work in he home-counry, C 0 are uni of conumpion of he final good, X 0 are uni of invemen, and K 0 i he capial level in he home-counry a he beginning of period + 1. P i he price of he home final good, which will be defined below. W i he hourly wage in he home-counry and R i he home-counry renal rae of capial, where boh are meaured in uni of he final good. P H i he price of he home inermediae good. The depreciaion of he ock of capial, δ[u ], i a funcion of i uilizaion rae u. Following Greenwood e al we aume ha: δ [ u ] = δ + b 1 + ε u 1+ε, 2 Some imporan excepion are Rabanal e al. 2010, Ireland 2009, and Engel and Maumoo I i alo imporan o menion ha Baxer and Crucin 1995 paper wa he fir paper o conider permanen hock and he poibiliy of coinegraion in he conex of hi cla of model. The reaon hey did no purue he VECM pecificaion wa ha he evidence of coinegraion wa mixed for he bilaeral pair hey udied. 3 We will conider wo ype of uiliy funcion when analyzing he reul in Secion 4. The andard Cobb Dougla cae, a in Heahcoe and Perri 2002, and he GHH preference a in Raffo 2009.

4 F.S. Mandelman e al. / Review of Economic Dynamic where b 0 and ε > 0. The parameer ε repreen he elaiciy of marginal depreciaion wih repec o he uilizaion rae, and b and δ pin down he rae of uilizaion and he depreciaion rae in he eady ae. In order o gain ome inuiion of he effec of each of he conidered feaure, when analyzing he reul we will conemplae model wihou IST hock, adjumen co in he capial ock, or an endogenou capial uilizaion. In paricular, when we conider model wihou a uilizaion rae of capial, u will be e a 1 and δ[u ]=δ1 = δ + 1+ε b for all and all. The parameer φ conrol he elaiciy of he adjumen co in he capial ock o change in invemen. When we conider model wihou co of adjumen in he capial ock, φ will be e o zero. V i he IST hock. In a compeiive equilibrium, V 1 i inerpreed a he relaive price of capial good wih repec o he price of conumpion good. We will alo conider model wihou IST hock when analyzing he reul. In ha cae, we will e V = 1forall and all. The preence of wo uni roo make he model non-aionary a non-aionary TFP hock will be inroduced laer. Hence, we recale he adjumen co o accoun for he long-run gro rae of growh of invemen along he balanced growh pah: Λ X alo o be defined laer. D denoe he holding of he inernaionally raded rikle bond ha pay one uni of he home-counry inermediae good minu a mall co of holding bond, Φ inperiod + 1 regardle of he ae of naure. Q i i price, meaured in uni of he home inermediae good. Finally, he funcion Φ i he arbirarily mall co of holding bond meaured in uni of he home inermediae good. 4 Following he exiing lieraure, we aume ha Φ ake he following funcional form: Φ [ D ] = ς 2 Z 1[ D ] 2. Z 1 We need o include Z 1 in he adjumen co funcion, boh dividing D and muliplying [ D Z 1 ]2 where Z = A 1 α 1 V 1 α α and A i he home-counry TFP hock. The reaon i ha D will grow a he rae of growh of Z 1 along he balanced growh pah, making he raio D aionary. Alo, ince he home-counry inermediae Z 1 good will alo grow a he ame rae of Z 1 along he balanced growh pah, we need o make he adjumen co meaured in uni of he home inermediae good grow a ha rae in order o induce aionariy Firm Final good producer The final good in he home-counry, Y, i produced uing home inermediae good, Y H, and foreign inermediae good, Y F, wih he following echnology: Y = [ ω θ 1 Y H θ 1 θ + 1 ω θ 1 Y F θ 1 ] θ θ θ 1 4 where ω denoe he fracion of home inermediae good ha are ued for he producion of he home final good and θ repreen he elaiciy of ubiuion beween home and foreign inermediae good. Therefore, he repreenaive final good producer in he home-counry olve he following problem: max P Y P H Y H P F Y F Y 0,Y H 0,Y F 0 ubjec o he producion funcion 4, where P F i he price of he foreign inermediae good in he home-counry Inermediae good producer The repreenaive inermediae good producer in he home-counry ue home labor and capial in order o produce home inermediae good and ell her produc o boh he home and he foreign final good producer. Taking price of all good and facor inpu a given, he maximize profi. Hence, he olve: [ Max P H Y H + Y L 0,K 1 H 0 ] P [ W L + u R K 1] ubjec o he producion funcion: GDP = Y H + Y H = A [ u K 1] α L 1 α where Y H i he amoun of home inermediae good old o he home final good producer, Y H i he amoun of home inermediae good old o he foreign final good producer, and A i he TFP hock, which we will characerize below. GDP i he home-counry gro domeic produc or home-counry oupu. Through he ex we ue he concep oupu or GDP o refer o he GDP variable. 5 4 The Φ co i inroduced o enure aionariy of he level of D in IRBC model wih incomplee marke, a dicued by Heahcoe and Perri We chooe he co o be numerically mall, o i doe no affec he dynamic of he re of he variable.

5 140 F.S. Mandelman e al. / Review of Economic Dynamic The VECM for IST and TFP hock A menioned above, we depar from he andard aumpion in he IRBC lieraure and conider procee for boh IST and TFP hock ha are coinegraed of order C1, 1 and hence follow a VECM pecificaion. We pecify he following VECM for he law of moion driving he log difference of he IST V and TFP A ochaic procee for boh he home- and he foreign-counrie: log Ϝ log Ϝ = c c + κ κ [log Ϝ 1 γ log Ϝ 1 log ξ ] + ε ε where Ϝ ={V, A}, 1, γ i he coinegraing vecor and ξ i he conan in he coinegraing relaionhip. The hock ε N0, σ and ε N0, σ are correlaed, and i he fir-difference operaor. We reric ourelve o a VECM wih zero lag. Thi aumpion i moivaed by he empirical reul o be preened below Marke clearing The model i cloed wih he following marke clearing condiion which equae he aggregae demand domeic aborpion wih oal producion in he final good marke: C + X = Y and C + X = Y, and he bond marke: D + D = Equilibrium and equilibrium condiion Given our law of moion for hock defined in Secion 2.2.3, an equilibrium for hi economy i a e of allocaion for home conumer, C, L, K, X, u, and D, and foreign conumer, C, L, K, X, u, and D, allocaion for home and foreign inermediae good producer, Y H, Y H, Y F and Y F, allocaion for home and foreign final good producer, Y and Y, inermediae good price P H, P H, P F and P F, final good price P and P, renal price of labor and capial in he home- and foreign-counrie, W, R, W, and R and he price of he bond Q uch ha i given price, houehold allocaion olve he houehold problem; ii given price, inermediae good producer allocaion olve he inermediae good producer problem; iii given price, final good producer allocaion olve he final good producer problem; iv and marke clear Equilibrium condiion I i ueful o define he following relaive price: P H = P H P, P F = P F P and RER = P P. Noe ha P H i he price of home inermediae good in erm of home final good, P F i he price of foreign inermediae good in erm of foreign final good, which appear in he foreign-counry budge conrain, and RER i he RER beween he home- and foreign-counrie. In our model he law of one price hold; hence, we have ha P H = P H and P F = P F. In he model he only ource of RER flucuaion i he preence of home bia. We now deermine he equilibrium condiion implied by he fir-order condiion of houehold, inermediae and final good producer in he home-counry, a well a he relevan law of moion, producion funcion, and marke clearing condiion. The condiion in he foreign-counry are ymmerical and no decribed here becaue of pace conideraion. The marginal uiliy of conumpion and he labor upply are given by: [ U C C, L ] = λ, U L [C, L ] U C [C, L ] = W, where U x denoe he parial derivaive of he uiliy funcion U wih repec o variable x. The fir-order condiion wih repec o capial and invemen deliver: μ = β +1 π +1 { u +1 R +1 λ +1 + μ +1 1 δ u +1} and λ = μ V 1 φ Ω + β +1 π +1 μ +1 V +1[ φ Ω + 1 X+1 X φ 2 V ] 2 Ω + 1 V +1 9

6 F.S. Mandelman e al. / Review of Economic Dynamic where Ω = X V X 1 V 1 Λ X, and π +1 = π+1 i he condiional probabiliy of +1 given. When we conider π model wihou an adjumen co of capial, Eq. 9 will be ubiued by: λ = μ V. When we conider model wihou IST hock we will e V = 1forall and in eiher Eq. 9 or Eq. 10 depending on wheher we are conidering model wih or wihou an adjumen co of capial. The fir-order condiion wih repec he capial uilizaion rae i: λ R = μ δ u where, if we ake ino accoun he paramerizaion of δu, wehave: 10 λ R = bμ u ε. 11 When we conider model wihou a capial uilizaion rae, hi fir-order condiion will no be conidered and we will e u = 1forall and. Alo, when hi i he cae, δu will be e equal o δ1 for all and in Eq. 8. The opimal choice by houehold in he home-counry wih repec o he rikle bond deliver he following expreion for i price Q = β π +1 λ+1 P H +1 Φ [ λ D ]. 12 P H +1 The rik-haring condiion i given by he opimal choice of he houehold of boh counrie for he rikle bond: π +1 [ λ +1 P H +1 RER λ P H RER +1 λ+1 P H +1 ] = Φ [D ]. λ 13 P H β +1 We aume ha foreigner do no face porfolio adjumen co. From he inermediae good producer maximizaion problem, we obain he reul ha labor and capial are paid heir marginal produc, where he renal rae of capial and he real wage are expreed in erm of he final good in each counry: W = 1 α P H A [ u K 1] α L α 14 and R = α P H A [ u K 1] α 1 L 1 α. 15 From he final good producer maximizaion problem, we obain he demand of inermediae good, which depend on heir relaive price: Y H = ω P H θ Y 16 and Y F = 1 ω P F RER θ Y. 17 Finally, he good, inpu, and bond marke clear. Thu: and C + X = Y, Y = [ ω θ 1 Y H θ 1 θ + 1 ω θ 1 Y F θ 1 ] θ θ θ 1, 19 Y H + Y H = A [ u K 1] α L 1 α, D + D = The law of moion of he level of deb i: P H Q D = P H Y H P F RER Y F + P H D 1 P H Φ [ D ], 22 and i i obained uing 2 and he fac ha inermediae and final good producer a home make zero profi. Finally, he law of moion for hock are a defined in Secion

7 142 F.S. Mandelman e al. / Review of Economic Dynamic Balanced growh and he rericion on he coinegraing vecor Eq. 6 o 22 and he VECM procee defined in Secion 2.2.3, ogeher wih analogou condiion for foreign-counry houehold, inermediae and final good producer, characerize he equilibrium in hi model. Since we aume ha boh pair log A, log A and log V, log V are coinegraed procee, we need o normalize he equilibrium condiion in order o obain a aionary yem more amenable o udy. The baic idea i o divide mo of he home-counry variable ha have a rend by Z 1, where Z = A 1 α 1 V 1 α α, and he foreign-counry variable by Z 1, where Z = A 1 α 1 V 1 α α. One excepion i he capial ock, which are inead divided by Z 1 V 1 and Z 1 V 1 repecively. In Appendice A.1 and A.2, we deail he full e of normalized equilibrium condiion for he Cobb Dougla and he GHH cae. For he model o have balanced growh we require ome rericion on preference, producion funcion, and he law of moion of he hock. The rericion on preference and echnology of King e al are ufficien for he exience of balanced growh in a cloed economy real buine cycle RBC model. However, in our wo-counry model, an addiional rericion on he coinegraing vecor i needed if he model i o exhibi balanced growh. In paricular, we need he raio Z 1 /Z 1 o be aionary. For example, if he raio Z 1 /Z 1 were o be non-aionary, he raio beween Y F and Y F would alo be non-aionary, and conequenly, he balanced growh pah would no exi. A ufficien condiion o guaranee he aionariy of Z 1 /Z 1 i o check for he aionariy of boh A 1 /A 1 and V 1 /V 1. Rabanal e al indeed how ha he fir raio TFP procee i aionary. In wha follow we focu he analyi on he IST hock. When analyzing he reul in Secion 4, we will alo conider model in which boh IST and TFP hock are aionary. Thi i neceary o compare our reul wih hoe in he exiing lieraure. In hi cae, we will no need o normalize he equilibrium condiion 6 o 22. When hi i he cae, he VECM procee defined in Secion will have o be replaced. In Secion 4 we will define he alernaive aionary procee o be conidered. 3. Eimaion of he VECM for IST hock We preen eimae of our VECM for IST and TFP hock in hi ecion. Fir, we ue erie for he relaive price of invemen for he U.S. and he R.W. o build our IST hock. Then, we how ha our aumpion ha he IST procee are coinegraed of order C1, 1 canno be rejeced in he daa. Nex, we how ha he rericion ha he parameer γ V be equal o one canno be rejeced in he daa. Rabanal e al how ha ame concluion apply o he TFP procee. Conequenly, he fac ha γ V and γ A are boh aiically no differen from one implie ha we canno rejec he exience of balanced growh. For pace conideraion in hi ecion we briefly dicu he daa and repor he poin eimae of he parameer of he VECM for he TFP hock. We popone o Appendix A.3 oher deail Daa for he IST hock In order o eimae our VECM for log IST hock we ue daa for he U.S. and an aggregae for he R.W. The R.W. i compoed of he U.S. mo ignifican rading parner: he 15 counrie of he Euro area, Canada, Japan, he Unied Kingdom, Auralia and Souh Korea. Our ample period goe from 1982:4 o 2007:4. Boh for he U.S. and for he R.W., we aim o build V uing daa on invemen and conumpion deflaor. In paricular, for he U.S. he IST hock i defined a V = PCE U.S. /PI U.S. where PCE U.S. i he peronal conumpion expendiure deflaor, and PI U.S. i he invemen deflaor. For he R.W. aggregae, we define he IST hock a: V = PCE w i i PI i i where i idenifie he counry in he e {15 counrie of he Euro area, Canada, Japan, he Unied Kingdom, Auralia and Souh Korea} and w i i he rade weigh of a paricular counry i a ime. The weigh are he currency weigh ued in he Broad Index of he Foreign Exchange Value of he dollar calculaed by he U.S. Federal Reerve. In Fig. 1 we plo he reuling erie. The paricular deflaor being ued are now decribed. For he U.S. we ue he Peronal Conumpion Expendiure PCE deflaor a our conumpion deflaor and he Gro Domeic Invemen deflaor a our invemen deflaor. Boh erie are derived direcly from he Naional Income and Produc Accoun NIPA and provided by he Bureau of Economic Analyi BEA. For Japan, we employ he Privae final conumpion expendiure and he Privae-ecor capial formaion deflaor erie obained from he Cabine Office. In he cae of Canada, we ue he Peronal expendiure on conumer good and ervice deflaor and he Buine gro fixed capial formaion deflaor erie. Boh erie can be obained from Canada aiical agency, Saiic Canada. For he UK, we ue he Final conumpion expendiure deflaor and he Gro fixed

8 F.S. Mandelman e al. / Review of Economic Dynamic Fig. 1. Log IST hock. Table 1 Uni roo e for IST hock. log TFP U.S. log TFP R.W. Level Fir diff. Level Fir diff. Mehod aiic aiic aiic aiic ADF DF-GLS P T -GLS MZ α MZ MSB Noe: ADF and for augmened Dickey Fuller e. DF-GLS and for Ellio Rohenberg Sock derended reidual e aiic. P T -GLS and for Ellio Rohenberg Sock poin-opimal e aiic. MZ α,mz, and MSB and for he cla of modified e analyzed in Ng and Perron For ADF and DF-GLS we preen -aiic, for P T -GLS we preen P -aiic and for he MZ α,mz,andmsbwepreenheng Perroneaiic. + Denoe null hypohei of uni roo no rejeced a 5 percen level. capial formaion deflaor aken from he UK naional aiic. The deflaor for Auralia are derived from he Auralian Bureau of Saiic. The paricular erie ued were he Houehold final conumpion expendiure and he Gro fixed capial formaion implici price deflaor. For Souh Korea we ue he Final conumpion expendiure deflaor and Gro capial formaion deflaor erie rerieved from he Navi-Daa daabae provided by he Korean Naional Saiical Office. Finally, for he EMU-15 counrie, we employ he Conumpion deflaor and he Gro Invemen deflaor from he AWM Daabae conruced by he European Cenral Bank Inegraion and coinegraion properie of he IST hock In hi ecion, we preen evidence upporing our aumpion ha he log IST procee for he U.S. and he R.W. are coinegraed of order C1, 1. We will fir empirically uppor he uni roo aumpion for he univariae procee and hen we will e for he preence of coinegraing relaionhip uing he Johanen 1991 procedure. Table 1 preen uni roo e reul for he log IST procee for he U.S. and R.W. The lag lengh i choen uing he Schwarz crierion. In each cae a conan and a rend are included in he pecificaion. None of he e can rejec he null hypohei of uni roo a he 5 percen criical value. Uing he ame e, here i alo rong evidence ha he fir difference of he log IST procee for he U.S. i aionary. All he e rejec he null hypohei of a uni roo a he 5 percen criical value. For he R.W. he evidence of aionariy of he fir difference i weaker. Only he ADF e rejec clearly a he 5 percen. The re of he e canno rejec. So, here i rong evidence ha he log IST proce for he R.W. i inegraed, bu i i hard o clarify wheher i i inegraed of order one or wo. Given ha here i rong evidence ha he log IST procee for he U.S. are inegraed of order one and, a we how below, here i alo rong evidence of a coinegraion relaionhip beween he log IST procee for he U.S. and he R.W., we ake he evidence preened here a evidence in favor of he log IST proce for he R.W. being inegraed of order one.

9 144 F.S. Mandelman e al. / Review of Economic Dynamic Table 2 Coinegraion aiic II: Johanen e. Number of vecor Trace p-value Max-eigenvalue p-value Table 3 The VECM for IST. κ V κ V aiic in parenhei. + Denoe ignificance a a 5 percen level. Once we have preened evidence ha indicae ha he log IST for he U.S. and he R.W. i well characerized by inegraed procee of order one, we now focu on preening evidence upporing our aumpion ha he procee are coinegraed. We conider an unrericed VAR wih one lag and a deerminiic rend for he wo-variable yem [log V, log V ] where he number of lag wa choen uing he Schwarz crierion. The abolue value for he wo eigenvalue of he VAR implied by he poin eimae are 0.98 and If log V and log V hare one common ochaic rend balanced growh, he eimaed VAR ha o have a ingle eigenvalue equal o one and all oher eigenvalue have o be le han one. Poin eimae are in accord wih hi predicion. Bu hi i no a formal e of coinegraion. Table 2 repor reul from he unrericed coinegraion rank e uing he race and he maximum eigenvalue mehod a defined by Johanen We aume no VAR inercep bu a conan in he coinegraion relaionhip and zero lag. 5 Clearly, he daa rongly uppor a ingle coinegraion vecor The eimaed VECM for IST hock In he la ubecion, we preened evidence ha log V and log V are coinegraed of order C1, 1. In hi ubecion we how ha he null hypohei of γ V = 1 canno be rejeced by he daa. In fac, he LR e for he null hypohei γ V = 1 i diribued a a Chi-quared wih one degree of freedom and ake value 1.1, clearly maller han he 5 percen criical value of Condiional on hi rericion and auming zero lag, he VECM eimae are repored in Table 4. 6 Finally, he andard deviaion of he innovaion ε V and ε V σ V and σ V are eimaed o be and , repecively. In he imulaion, we will aume ha ε V and ε V are uncorrelaed, ince hi null hypohei canno be rejeced in he daa The eimaed VECM for TFP hock In order o eimae he VECM for he TFP proce, Rabanal e al ue daa for he U.S. and an aggregae for he R.W. For he U.S., hey ue quarerly real GDP daa from he Bureau of Economic Analyi and hour and employmen daa from he Organizaion for Economic Cooperaion and Developmen OECD. Real capial ock daa i alo obained from he OECD. The R.W. aggregae i defined o be he 15 counrie of he Euro area, he Unied Kingdom, Canada, Japan, and Auralia. For he Unied Kingdom, Canada, Japan, and Auralia hey obain nominal GDP, hour, employmen, and real capial ock from he OECD. For he Euro area hey ake nominal GDP, employmen, and real capial ock from AWM. Hour are a repored in Chrioffel e al The ample period goe from 1973:1 o 2006:4, which i when he hour erie for he Euro area end. Deail abou aggregaion of R.W. daa are provided in Appendix A.3. In Fig. 2 we plo he reuling erie. Rabanal e al alo preen evidence upporing our aumpion ha he log TFP procee for he U.S. and he R.W. are coinegraed of order C1, 1 and eimae he rericed VECM wih zero lag correponding o one lag in he VAR a he Schwarz informaion crierion ugge. The eimaed rericed model deliver he parameer eimae repored in Table 4. They ue he likelihood raio e o preen evidence upporing he null hypohei ha he coefficien relaed o he peed of adjumen in he coinegraing vecor are equal and of oppoie ign, i.e., κ A = κ A. I i worh noing ha he coefficien of he peed of adjumen, while ignifican, i quaniaively mall, denoing ha log TFP procee converge lowly over ime. The conan erm c and c are eimaed o be differen. However, hi doe no imply ha he growh rae of boh log TFP procee are differen. Indeed, becaue he coinegraing vecor i 1, 1 hey mu grow 5 The Johanen 1991 e rejec he exience of a coinegraion relaionhip if we allow for a rend in he VAR or we do no allow for a conan in he coinegraion relaionhip. 6 We do normalize he log IST hock o ha he conan ake a value equal o zero. Hence, we do no repor i.

10 F.S. Mandelman e al. / Review of Economic Dynamic Fig. 2. Log TFP hock. Table 4 VECM model. c A c A κ A aiic in parenhei. + Denoe ignificance a he 5 percen level. Denoe ignificance a he 10 percen level. a he ame rae along he balanced growh pah. Given he parameer eimae, he implied long run growh rae of log TFP procee i 1.44 percen in annualized erm. Finally, hey alo eimae he andard deviaion of he innovaion σ A o be and σ A equal o In our imulaion, we will alo aume ha ε A and ε A are uncorrelaed, ince he null hypohei could no be rejeced in he daa Reul In hi ecion we analyze he reul. We compue he oluion of wo differen model here. In he fir cae we olve he model aking a log-linear approximaion around he eady ae and calibrae IST hock along he line of Raffo 2009 and TFP hock a in Heahcoe and Perri In he econd cae we olve he normalized model aking a log-linear approximaion around he normalized eady ae and hen we will imulae he model uing he paramerized law of moion of hock a decribed in Secion 3. Since in he econd cae he hock in he model are non-aionary, we need o rely on imulaion echnique o obain he relevan momen. A we how below, he implicaion of he wo approache wih repec o he model abiliy o olve he above-menioned four puzzle are differen. While Raffo 2009 approach can eaily accoun for hem, while he alernaive eimaion approach canno. The reaon i ha our eimaed IST hock are much le volaile han Raffo 2009 aume Model parameerizaion We calibrae he model following Heahcoe and Perri 2002 cloely. The dicoun facor β i e equal o 0.99, which implie an annual rae of reurn on capial of 4 percen. We aume a co of bond holding, ς,of1baipoin0.01. Parameer on echnology are fairly andard in he lieraure. Thu, he capial hare of oupu i e o α = 0.36, and home bia for home-counry inermediae good i e o ω = 0.9, which implie he oberved impor/oupu raio in he eady ae for he U.S. A in Raffo 2009, we aume a low value for he elaiciy of ubiuion, θ = Thi value i a bi 7 Rabanal e al ue a model in which echnology innovaion are labor augmening: K 1 α A L 1 α. By definiion, he andard deviaion in hi paper i hu equal o he one repored in Rabanal e al muliplied by he conan 1 α.

11 146 F.S. Mandelman e al. / Review of Economic Dynamic higher han he lower bound ued in Corei e al. 2008b. For model comparion, we alo conider a relaive higher value, θ = 0.85, a in Heahcoe and Perri We conider wo differen period uiliy funcion. Fir, we analyze Cobb Dougla preference a in Heahcoe and Perri 2002: [ U C, 1 L ] = {C τ [1 L ] 1 τ } 1 σ. 1 σ When hi i he cae, we ricly follow Heahcoe and Perri 2002 and fix he conumpion hare, τ,a0.34, which alo erve o pin down he eady-ae value for he houehold labor upply a The coefficien of rik averion, σ, i e equal o 2. Backu e al aume he ame value for he laer parameer. Second, we alo conider he Greenwood, Hercowiz and Huffman GHH quailinear preference pecificaion: [ U C, 1 L ] = {C ψ L ν } 1 σ. 1 σ Here we follow Raffo 2008 and fix ν and ψ, o 8.01 and , o a o obain he ame eady-ae value for he houehold labor upply and he ame labor upply elaiciy a in he Cobb Dougla pecificaion. 8 The value of σ i e o be equal o he Cobb Dougla cae. A i i andard in he IRBC lieraure, when we conider capial adjumen co, we will calibrae φ o ha in he model imulaion, he relaive andard deviaion of invemen wih repec o oupu reemble he value in he U.S. daa. The value of hi parameer will change depending on he verion of he model we are analyzing. We will decribe hedifferenvalueakeninheubecion. Similarly, when we conider he capial uilizaion rae, we will normalize i eady-ae value o 1. The value of b will be e o , ince he fir-order condiion 11 relae b o he eady-ae value of he inere rae. The elaiciy of marginal depreciaion, ε, will be fixed a 1, in line wih Baxer and Farr 2001, who rely on eimae provided by Bau and Kimball Finally, δ will be e o 0.074, uch ha δ1 = Solving he puzzle We ar by howing how he baeline IRBC framework exhibi he aforemenioned puzzle. Then, we replicae Raffo 2009 exercie: we add IST, endogenou capial uilizaion, and GHH uiliy. Thee hree feaure a long a we calibrae he IST hock a in Raffo, 2009 will be ufficien o addre he four puzzle dicued in he inroducion. In order o ay cloe o Raffo 2009 work, in hi ubecion we conider aionary hock. The baeline framework include only aionary TFP hock wih Cobb Dougla preference, a in Heahcoe and Perri In hi cae, neiher IST hock, invemen adjumen co, nor endogenou capial uilizaion i conidered. Mimicking hi paper, we aume he following aionary VAR1 o characerize he aionary TFP proce: A = ρ A A 1 + ρ A A 1 + ε A, A = ρ A A 1 + ρ A A 1 + ε A, where ρ A = 0.97, ρ A = 0.025, Varε A A = Varε = , and corrε A, ε A = The fir wo row of Table 5a, 5b and 5c how Hodrick Preco HP filered momen from he daa along hoe heoreical counerpar from he baeline IRBC model M1. We conruc he RER a a geomeric average of bilaeral CPI-baed RER wih repec o he Euro area, Japan, Canada, he Unied Kingdom and Auralia. We ue he ame weigh ha he Federal Reerve ue o conruc he real effecive exchange rae of he U.S. dollar. Our ample period i 1973:4 o 2006:4. Real GDP, invemen, conumpion, and hour are conruced a decribed in Appendix A.3 o build he TFP erie. When comparing boh row, he four puzzle ha characerize hi framework are eviden. Fir, he baeline model end o predic a relaively high cro-counry conumpion correlaion, wherea he daa indicae ha conumpion correlaion end o be lower han oupu correlaion. Second, he andard model deliver a andard deviaion of he erm of rade and he RER ha i much lower han in he daa. Backu e al refer o hee wo anomalie a he quaniy puzzle and price puzzle, repecively. The inernaional comovemen puzzle Baxer, 1995 addree he cro-counry correlaion of facor inpu. Invemen and employmen are poiively correlaed acro counrie, wherea he model deliver a negaive correlaion. Finally, he Backu Smih puzzle refer o he fac ha while model rong rik-haring 8 1 L[1 τ1 σ ] The labor upply elaiciy for he Cobb Dougla ε CD and GHH pecificaion ε GHH are defined a follow: ε CD = σ, ε L GHH = 1 ν 1,where L i he eady-ae value of L. Noice ha if ν = 1+εCD,weeffecivelyimpoeε CD = ε εcd GHH.Finally,ψ i adjued o obain he deired L, a implied by he eady-ae condiion: W = 1 α K α = ψνl ν 1 L, o ha ψ = W. νl ν 1

12 F.S. Mandelman e al. / Review of Economic Dynamic Table 5a Saionary model reul. SDGDP SDC SDX SDN SDRER ρrer Daa M1 Baeline IRBC M2 M1 IST ρ V = M3 M1 IST ρ V = M4 M3 wih Cap. Uil M5 GHH Denoe relaive o GDP. Table 5b Saionary model reul. CORRGDP, N CORRGDP, C CORRGDP, X CORRRER, C C Daa M1 Baeline IRBC M2 M1 IST ρ V = M3 M1 IST ρ V = M4 M3 Cap. Uil M5 GHH Table 5c Saionary model reul. CORRGDP, GDP CORRC, C CORRX, X CORRN, N Daa M1 Baeline IRBC M2 M1 IST ρ V = M3 M1 IST ρ V = M4 M3 Cap. Uil M5 GHH condiion predic a poiive and very cloe o one correlaion beween he RER and he raio of conumpion beween counrie, he daa indicae ha uch a correlaion i negaive. If TFP hock are aionary, change in permanen income following aymmeric hock are mall, implying lile need for inurance marke. A ingle inernaional ae allow houehold o obain allocaion imilar o hoe when marke are complee. However, a dicued in Heahcoe and Perri 2002, impoing a aionary echnology proce doe no eem o coniue an imporan feaure o judge he quaniaive relevance of he model. Tha i, in principle, near-uni-roo TFP hock wih no pill over o he oher counry can lead o ignifican change in relaive wealh and hu relaive conumpion. In uch a conex, we could expec large difference beween he behavior of he model wih incomplee ae marke following he hock. However, he elaiciy of ubiuion i an imporan addiional deerminan of he exen o which produciviy hock affec relaive wealh. An increae in aggregae produciviy in one counry due o a TFP hock lead o an increae in he relaive world upply of he good ha counry produce. Thi implie an increae in he erm of rade of he oher counry, ince he good i produce become relaively carcer. Sandard rade elaiciy value ued wihin he IRBC framework imply ha movemen in he erm of rade almo exacly offe change in relaive produciviy. The abence of izable change in relaive wealh implie ha a ingle rik-free bond i ufficien o cloely replicae he complee marke allocaion even when near-uni-roo innovaion are in place. The incluion of IST hock break hi logic. The erm of rade do no only reflec he relaive carciy of producion, bu alo he relaive demand for capial good ha hi hock rigger. We fir proceed by imply acivaing he ochaic proce for he IST hock. Le u fir aume a near uni-roo proce hough ill aionary wih no pillover acro counrie, i.e., V = ρ V V + ε V, V = ρ V V + ε V, uch ha ρ V = A Raffo 2009, we aume ha he variance of he IST hock i abou hree ime 3.6 a big a he one characerizing he TFP hock, o ha IST hock explain mo of he flucuaion in he model endogenou variable. Mimicking Raffo 2009, we e he invemen adjumen co o mach he relaive andard deviaion of invemen wih repec o oupu oberved in he U.S. daa φ a We ill do no conider endogenou capial uilizaion. Reul are repored in he hird row M2 of he menioned able. Thi hock appear o be he ilver bulle needed o uccefully addre he four puzzle in he lieraure. 9 In fac, we chooe φ o ha he volailiy of invemen mache he daa when ρ V = 0.97 model M3 o be een nex ince hi i he paramerizaion ha i cloe o Raffo 2009.

13 148 F.S. Mandelman e al. / Review of Economic Dynamic Fig. 3. Impule repone o a aionary IST hock. The inuiion for hi reul i provided in Fig. 3, which plo he impule repone funcion o hi IST hock one andard deviaion increae. A he IST hock hi he home-counry, he domeic invemen demand ignificanly increae. Given he aggregae reource conrain, home-counry conumpion decreae o accommodae he increae in invemen demand. The perien IST hock lead o efficiency gain in he invemen proce which increae oal produciviy a home. Tha i, he invemen boom increae he ock of capial available in he home economy. Thi more capial-inenive echnology reul in he increaing availabiliy of home-counry GDP, which become relaively abundan and furher improve he erm of rade for he foreign economy. A a reul he RER depreciae i.e., RER increae. Foreign houehold feel richer becaue of he improvemen in he erm of rade and unlike o heir home-counry neighbor conume more on impac olving he quaniy puzzle. In addiion, cro-counry relaive conumpion and he RER move in oppoie direcion olving he Backu Smih puzzle. Finally, foreign houehold ake advanage of hi izable erm of rade effec and increae heir labor upply and invemen, magnifying over ime heir join comovemen wih heir home counerpar olving he inernaional comovemen puzzle. On impac, however, hi RER depreciaion a home i ignificanly mued: due o home bia, he increae in he demand for he home inermediae good i relaively ronger a he hock hi and lowly diipae over ime. Such flucuaion in he RER conribue o i increae volailiy in he model imulaion, which help u o beer addre he price puzzle. If IST hock are inead raniory ρ V = 0.97, a in Raffo 2009, he invemen boom i relaively hor-lived and he model fi woren wih repec o M2. The fourh row M3 in he menioned able reflec hi cenario. Fig. 3 graph he correponding impule repone. The quaniy puzzle revive and he Backu Smih puzzle woren again. Raffo 2009 parly olve hi problem by adding endogenou capial uilizaion a in Greenwood e al Refer o he fifh row M4 in he menioned able and Fig. 3. Endogenou capial uilizaion erve a an effecive endogenou propagaion mechanim ha help o improve on he Backu Smih puzzle dimenion. Nonehele, hi new mechanim generae oher new counerfacual and canno olve he quaniy puzzle. Given he reource conrain, a rong invemen boom reduce conumpion in he home economy o ha he correlaion beween conumpion and GDP urn ou o be zero and much lower han in he daa. Cleverly, Raffo 2009 addree hi problem uing a GHH uiliy pecificaion M5, which uppree he wealh effec reponible for dampening he repone of he labor upply o poiive produciviy innovaion. Aben hi wealh effec in he labor upply, agen in boh counrie can increae he labor upply and conumpion in repone o hock. Thi uiliy funcion alo help improving he quaniy puzzle. To conclude, in hi ecion we have hown ha he IST procee are able o improve he four menioned puzzle if hey are calibraed o a o explain mo of he oberved macroeconomic flucuaion. In hi nex ubecion we will how ha when we ue he eimaed VECM procee o imulae he model inead, he model can only parially addre he puzzle.

14 F.S. Mandelman e al. / Review of Economic Dynamic Fig. 4. Impule repone o a non-aionary IST hock IRBC wih he eimaed IST hock In hi ubecion we make wo change wih repec o he la ubecion. Fir, inead of calibraing he IST hock, we imulae he model uing he VECM eimae repored in Secion 3. Alo, inead of uing he aionary TFP hock, a in Heahcoe and Perri 2002, we ue coinegraed TFP hock a eimaed in Rabanal e al Hence, we conider he non-aionary verion of he model where boh TFP and IST hock are coinegraed. We hall how ha when ha i he cae, he fi of he model improve along ome dimenion wih repec o M1, bu i i unable o fully olve he aforemenioned puzzle. The reaon behind he difference in he reul i ha while Raffo 2009 calibrae he variance of he IST procee o be almo hree ime he one characerizing he aionary TFP proce, he eimaed non-aionary IST hock are much le volaile. The fir wo row in Table 6a, 6b, and 6c depic he daa and he momen obained from a andard IRBC wih Cobb Dougla uiliy M1NS ha include only coinegraed TFP hock a eimaed in Rabanal e al A dicued in ha paper, he preence of uni roo procee in TFP wih low convergence acro counrie lead o highly perien difference in produciviy acro counrie. A a reul, he volailiy of he RER increae and he model ge cloer o he empirical evidence and he price puzzle improve wih repec o he M1 model. Alo, houehold in each counry ake advanage of eiher perien produciviy gain or izable improvemen in he erm of rade and joinly increae heir labor upply and invemen. Thi reul i ueful o addre he inernaional comovemen puzzle wih repec o he M1 model. In he previou ubecion, we howed ha an arbirary near-uni-roo IST proce wih no pillover acro counrie wa he ilver bulle needed o olve he four puzzle. Inereingly, our VECM eimae for he IST proce imply imilar dynamic: a IST procee for he U.S. and he R.W. are well-characerized by uni roo and b he eimaed very low peed of convergence κ V, κ V of hee procee omewha mimic he cenario wih no pillover in he aionary cae. Tha i, depie he fac ha he IST procee for boh counrie are coinegraed and co-move in he long run, hee IST procee will converge very lowly when a hock hi one of he counrie. Indeed, he hape of he impule repone o a non-aionary hock ee Fig. 4 confirm hi inuiion, ince he dynamic reemble hoe in Fig. 3. However, a we are abou o how, he quaniaive reul are le encouraging. In he hird row of Table 6a 6c, we conider a cae wih coinegraed IST and TFP hock M2NS. 10 The Backu Smih and he quaniy puzzle, alhough lighly maller, remain well in place. Thi i he by-produc of conumpion decline needed in home o accommodae higher invemen expendiure wih he preence of worening erm of rade in he afermah of IST hock. Thee reul grealy depend on he elaiciy of ubiuion of he final good θ = For inance, he Backu Smih puzzle i fully reored if we lighly increae he degree of ubiuabiliy beween local and impored inpu 10 Noe ha in hi cae we do no conider invemen adjumen co. Since our eimaed IST hock have a maller variance han he one ued by Raffo 2009 we do no need o include hem o dampen he repone of invemen. Acually, zero adjumen co will deliver a relaive andard deviaion of invemen ha i lower han he one oberved in he daa.

15 150 F.S. Mandelman e al. / Review of Economic Dynamic Table 6a Non-aionary model reul. SDGDP SDC SDX SDN SDRER ρrer Daa M1NS Coin. TFP M2NS M1NS IST M2NSb M2NS θ = M3NS M2NS Cap. Uil M3NSb M3NS θ = M4NS M3NS GHH M5NS M3NS High SD Denoe relaive o GDP. Table 6b Non-aionary model reul. CORRGDP, N CORRGDP, C CORRGDP, X CORRRER, C C Daa M1NS Coin. TFP M2NS M1NS IST M2NSb M2NS θ = M3NS M2NS Cap. Uil M3NSb M3NS θ = M4NS M3NS GHH M5NS M3NS High SD Table 6c Non-aionary model reul. CORRGDP, GDP CORRC, C CORRX, X CORRN, N Daa M1NS Coin. TFP M2NS M1NS IST M2NSb M2NS θ = M3NS M2NS Cap. Uil M3NSb M3NS θ = M4NS M3NS GHH M5NS M3NS High SD θ = Thi relaively high elaiciy dampen he decline in he erm of rade in he home-counry and he correponding increae in conumpion and labor effor in he foreign economy in repone o domeic hock. Conequenly, he RER volailiy and he inernaional comovemen are alo ignificanly reduced in uch cenario. Refer o he fourh row M2NSb and Fig. 4. When we include capial uilizaion fifh and ixh row, M3NS and M3NSb, or GHH uiliy evenh row, M4NS pecificaion, reul do no improve. Why do our eimaed IST procee generae uch differen reul depie he fac ha hey lead o dynamic imilar o he one dicued in he aionary cae? A menioned above, in he previou ubecion we followed Raffo 2009 and fixed he andard deviaion of he IST hock o be abou hree ime a large a he one characerizing he TFP hock. Our eimae indicae ha, in he daa, he andard deviaion of boh echnological procee i abou of he ame magniude. Would i be poible o recover Raffo 2009 reul if we increaed he variance of he coinegraed IST hock? The anwer i ye. When non-aionary hock are in place, we need o muliply he andard deviaion of he IST hock by a facor of 7, and e capial adjumen co, φ, equal o 6, in order o properly addre he puzzle. The la row M5NS of hee able depic hi cae. Thi arbirary calibraion produce reul cloed o he one obained wih M5. 5. Concluding remark Sandard IRBC model wih aionary TFP hock fail o accoun for ome imporan feaure of he daa. In paricular, here are four puzzle ha are robu o differen model pecificaion and conradic he empirical evidence. Fir, rik haring induce very rong poiive cro-counry conumpion correlaion, even when only incomplee marke are conidered quaniy puzzle. Second, he RER i much more volaile in he daa han in hee model price puzzle. Third, he equilibrium RER i cloely relaed o he raio of conumpion acro he wo economie, oppoie o he evidence Backu Smih puzzle. Finally, hee model predic a counerfacual negaive cro-counry correlaion of invemen and employmen inernaional comovemen puzzle.