WORKING PAPER SERIES COMPARING SHOCKS AND FRICTIONS IN US AND EURO AREA BUSINESS CYCLES A BAYESIAN DSGE APPROACH NO. 391 / SEPTEMBER 2004

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1 WORKING PAPER SERIES NO. 39 / SEPTEMBER 24 COMPARING SHOCKS AND FRICTIONS IN US AND EURO AREA BUSINESS CYCLES A BAYESIAN DSGE APPROACH by Frank Smes and Raf Wouers

2 WORKING PAPER SERIES NO. 39 / SEPTEMBER 24 COMPARING SHOCKS AND FRICTIONS IN US AND EURO AREA BUSINESS CYCLES A BAYESIAN DSGE APPROACH by Frank Smes 2 and Raf Wouers 3 In 24 all publicaions ill carry a moif aken from he banknoe. This paper can be donloaded ihou charge from hp://.ecb.in or from he Social Science Research Neork elecronic library a hp://ssrn.com/absrac_id= We hank seminar paricipans a he firs orkshop of he Euro Area Business Cycle Neork held in Madrid on 28 February, he Tinbergen Week Conference inroerdam on April and De Nederlandsche Bank for useful and simulaing commens. The vies expressed in his paper are our on and do no necessarily reflec hose of he European Cenral Bank or he Naional Bank of Belgium. 2 European Cenral Bank, CEPR and Universiy of Ghen, Frank.Smes@ecb.in 3 Naional Bank of Belgium, Rafael.Wouers@nbb.be

3 European Cenral Bank, 24 Address Kaisersrasse Frankfur am Main, Germany Posal address Posfach Frankfur am Main, Germany Telephone Inerne hp://.ecb.in Fax Telex 4 44 ecb d All righs reserved. Reproducion for educaional and noncommercial purposes is permied provided ha he source is acknoledged. The vies expressed in his paper do no necessarily reflec hose of he European Cenral Bank. The saemen of purpose for he Working Paper Series is available from he ebsie, hp://.ecb.in. ISSN 56-8 (prin) ISSN (online)

4 CONTENTS Absrac 4 Non-echnical summary 5 Inroducion 7 2 The linearised DSGE model 8 3 Comparing he parameer esimaes 2 3. The prior disribuion of he parameers The poserior disribuion of he parameers 3 4 Comparing sources of business cycle flucuaions in he US and he euro area 6 5 Propagaion of shocks in he euro area and he US 8 6 Hisorical decomposiion of he business cycles 8 7 Conclusions 9 Daa appendix 2 References 22 Tables and graphs 24 European Cenral Bank orking paper series 33 Working Paper Series No. 39 Sepember 24 3

5 Absrac This paper esimaes a DSGE model ih many ypes of shocks and fricions for boh he US and he euro area economy over a common sample period (974-22). The srucural esimaion mehodology allos us o invesigae heher differences in business cycle behaviour are due o differences in he ype of shocks ha affec he o economies, differences in he propagaion mechanism of hose shocks or differences in he ay he cenral bank responds o hose economic developmens. Our main conclusion is ha each of hose characerisics is remarkably similar across boh currency areas. Keyords: DSGE models; business cycle flucuaions JEL classificaion: E-E3 4 Working Paper Series No. 39 Sepember 24

6 Non-echnical summary The creaion of a single currency, he euro, in January 999 has grealy simulaed he analysis of aggregae macro-economic developmens in he ne currency area. Because his aggregae analysis necessarily relies o a large exen on a sample period before he acual esablishmen of EMU, he conclusions ha can be dran from such an analysis should be reaed ih some cauion. Hoever, one of he robus and someha surprising findings has been ha in many cases he business cycle behaviour of aggregae euro area macro variables such as oupu, inflaion and ineres raes has been very similar o ha observed in he Unied Saes (ha has been a large currency area for a longer ime period). For example, i has been shon ha he variances of he main macro-economic ime series and heir cross-covariances ih oupu sho very similar paerns in he euro area and he Unied Saes. Similarly, he esimaed effecs of moneary policy shocks in he euro area appear o be very similar o hose found in he Unied Saes. Finally, also srucural esimaions of he Ne-Keynesian Phillips curve for he euro area and he US daa have shon ha he esimaed parameers, including he degree of price sickiness, are comparable in boh areas. Building on previous ork, his paper provides furher evidence of he similariies and differences in he srucural characerisics of he economy in he o larges currency areas in he orld by esimaing a fully specified dynamic sochasic general-equilibrium (DSGE) model for boh areas over he same sample period. The model used feaures a relaively large number of fricions and shocks, hich are designed o capure he ime series properies of he main macro-economic daa. The fricions include sicky nominal price and age seing ih parial backard indexaion, habi formaion in consumpion and adjusmen coss in invesmen ha creae humpshaped reacion profiles in aggregae demand, and variable capial uilisaion and fixed coss in producion ha generae an elasic supply and smooh marginal cos responses o various srucural shocks. The dynamics is driven by en orhogonal shocks including produciviy, labour supply, invesmen, preference, cos-push and moneary policy shocks. The DSGE model is esimaed for he euro area and he Unied Saes separaely ih Bayesian economeric echniques and using seven key macro-economic daa series: real GDP, consumpion, invesmen, prices, real ages, employmen and he nominal ineres rae. The baseline esimaion period is from 974 ill 22. Hoever, in order o invesigae he sabiliy of he resuls e also esimae he model over a shorer sample period from 983 o 22. One advanage of our srucural mehodology over more reduced-form approaches is ha e are able o direcly compare boh he srucural parameers and he sources of business cycle developmens across he o currency areas. This allos us o invesigae heher differences in Working Paper Series No. 39 Sepember 24 5

7 business cycle behaviour are due o differences in he ype of shocks ha affec he economy, differences in he propagaion mechanism of hose shocks or differences in he ay he respecive moneary auhoriies respond o hose economic developmens. Of course, he more srucure is imposed on he esimaed model, he more he resuls ill be coloured by he seleced heoreical specificaion. Therefore, i is imporan o adop a heoreical srucure ha is no srongly rejeced by he daa. The model ha is used in his paper has a marginal likelihood ha is comparable o ha of unconsrained and lo-order Bayesian VARs. Our main conclusion is ha i is indeed difficul o deec significan differences in eiher he srucure of he economy or he sources of business cycle flucuaions across he o currency areas. Differences in acual business cycle developmens are mainly due o similar ypes of shocks affecing he o economies a differen imes. Regarding he sources of business cycle flucuaions our main resul is ha, hile demand and moneary policy shocks play some role in he shor run, i is mainly produciviy and labour supply shocks ha drive oupu developmens a business cycle frequencies. This is rue in boh he euro area and he Unied Saes. Regarding he srucure of he economy, e find ha in boh economies a subsanial degree of nominal and real fricions are necessary o capure he dynamics of he main macro variables discussed above. We esimae considerable nominal rigidiies in boh goods and labour markes. If anyhing, e find ha nominal age rigidiy is greaer in he Unied Saes han in he euro area. Also he real fricions such as he degree of habi persisence, he coss of adjusmen in invesmen, variable capaciy uilisaion and fixed coss in producion are esimaed o be significan and comparable in size in he o areas. Finally, e find no evidence of significan differences in he ay moneary auhoriies have responded o oupu and inflaion developmens. Shor-erm ineres raes respond someha sronger and faser o changes in he oupu gap and inflaion in he Unied Saes, bu hey are more persisen in he euro area. 6 Working Paper Series No. 39 Sepember 24

8 . Inroducion The creaion of a single currency, he euro, in elve of he fifeen counries of he European Union in January 999 has grealy simulaed he analysis of aggregae macro-economic developmens in he ne currency area. Obviously, because his aggregae analysis necessarily relies o a large exen on a sample period before he acual esablishmen of EMU, he conclusions ha can be dran from such an analysis should be reaed ih sufficien cauion. Hoever, one of he robus and someha surprising findings has been ha in many cases he business cycle behaviour of aggregae euro area macro variables such as oupu, inflaion and ineres raes has been very similar o ha observed in he Unied Saes, anoher large currency area. For example, Agresi and Mojon (22) compare he cyclical ime series properies of he main macro-economic ime series and heir co-movemen ih oupu in he euro area ih hose in he Unied Saes folloing he mehodology of Sock and Wason (2). They find ha he variances and cross-covariances sho very similar paerns in boh areas. Similarly, Peersman and Smes (22) analyse he effecs of moneary policy shocks in an idenified Vecor Auoregression for he euro area and sho ha he impulse responses are very similar o hose found in he Unied Saes. A final example is he ork by Gali and Gerler (999) and Gali, Gerler and Lopez-Salido (2) and Leigh and Malley (22), ho esimae srucural Ne-Keynesian Phillips curves for he euro area and he US and find again ha he esimaed parameers, including he degree of price sickiness, is comparable in boh areas. Building on our previous ork (Smes and Wouers, 23a and b), his paper provides furher evidence of he similariies and differences in he srucural characerisics of he economy in he o larges currency areas in he orld by esimaing a fully specified dynamic sochasic general-equilibrium (DSGE) model for boh areas over he same sample period. The model used is he one developed in Smes and Wouers (23b). Folloing Chrisiano, Eichenbaum and Evans (2), Alig, Chrisiano, Eichenbaum and Linde (23) and Smes and Wouers (23a), i feaures a relaively large number of fricions and shocks, hich are designed o capure he ime series properies of he main macro-economic daa. The fricions include sicky nominal price and age seing ih parial backard indexaion, habi formaion in consumpion and adjusmen coss in invesmen ha creae hump-shaped reacion profiles in aggregae demand, and variable capial uilisaion and fixed coss in producion ha generae an elasic supply and smooh marginal cos responses o various srucural shocks. The dynamics is driven by en orhogonal shocks including produciviy, labour supply, invesmen, preference, cos-push and moneary policy shocks. The DSGE model is esimaed for he euro area and he Unied Saes separaely ih Bayesian economeric echniques and using seven key macro-economic daa series: real GDP, consumpion, invesmen, prices, real ages, employmen and he nominal ineres rae. The baseline esimaion period is from 974 ill 22. Hoever, in order o invesigae he sabiliy of he resuls e also esimae he model over a shorer sample period from 983 o 22. One advanage of our srucural mehodology over some of he approaches menioned above is ha e are able o direcly compare boh he srucural parameers and he sources of business cycle The main daa se used for his analysis has been developed in Fagan e al (2). Working Paper Series No. 39 Sepember 24 7

9 developmens across he o currency areas. This allos us o invesigae heher differences in business cycle behaviour are due o differences in he ype of shocks ha affec he economy, differences in he propagaion mechanism of hose shocks or differences in he ay he cenral bank responds o hose economic developmens. Of course, he more srucure is imposed on he esimaed model, he more he resuls ill be coloured by he seleced heoreical specificaion. Therefore, i is imporan o have a heoreical srucure ha is no srongly rejeced by he daa. As shon in Smes and Wouers (23a and b), he model ha is used in his paper has a marginal likelihood ha is comparable o ha of unconsrained and lo-order Bayesian VARs. 2 Our main conclusion is ha i is indeed difficul o deec significan differences in eiher he srucure of he economy or he sources of business cycle flucuaions across he o currency areas. Differences in acual business cycle developmens are mainly due o similar ypes of shocks affecing he o economies a differen imes. Regarding he sources of business cycle flucuaions our main resul is very similar o he one found in Shapiro and Wason (989). While demand and moneary policy shocks play some role in he shor run, i is mainly produciviy and labour supply shocks ha drive oupu developmens a business cycle frequencies. This is rue in boh he euro area and he Unied Saes. Regarding he srucure of he economy, e find ha in boh economies a subsanial degree of nominal and real fricions are necessary o capure he dynamics of he main macro variables discussed above. We esimae considerable nominal rigidiies in boh goods and labour markes. If anyhing, e find ha nominal age rigidiy is greaer in he US han in he euro area. Also he real fricions such as he degree of habi persisence, he coss of adjusmen in invesmen, variable capaciy uilisaion and fixed coss in producion are esimaed o be significan and comparable in size in he o areas. Finally, e find no evidence of significan differences in he ay moneary auhoriies have responded o oupu and inflaion developmens. Shor-erm ineres raes respond someha sronger and faser o changes in he oupu gap and inflaion in he US, bu hey are more persisen in he euro area. The res of he paper is srucured as follos. Secion 2 describes he linearised version of he model ha e esimae. For a descripion of he esimaion mehodology e refer o Smes and Wouers (23a). We compare he parameer esimaes and he sources of business cycle flucuaions in boh currency areas in Secions 3 and 4 respecively. Secion 5 discusses he propagaion of some of he main srucural shocks in boh currency areas and Secion 6 concludes he analysis by providing a shor inerpreaion of he hree boom and recession episodes in boh areas. Finally, Secion 7 conains he main conclusions. 2. The linearised DSGE model In his Secion, e describe he log-linearised DSGE model ha e subsequenly esimae using boh euro area and US daa. For a discussion of he micro-foundaions of he model e refer o Smes and Wouers (23b) The ^ above a variable denoes log deviaions from seady sae. The dynamics of aggregae consumpion is given by: 2 See Schorfheide (2) for a discussion of he model evaluaion mehods based on he marginal likelihood concep ihin a Bayesian approach. 8 Working Paper Series No. 39 Sepember 24

10 () h c C C EC ( ) ( l l h h c ( )( h) h h b ( R E ) ( h) ( h) c c ) Consumpion Ĉ depends on he ex-ane real ineres rae R ) and, ih exernal habi ( E formaion, on a eighed average of pas and expeced fuure consumpion. When h, only he radiional forard-looking erm is mainained. In addiion, due o he non-separabiliy of he uiliy funcion, consumpion ill also depend on expeced employmen groh ( l l ). When he elasiciy of ineremporal subsiuion (for consan labour) is smaller han one ( c ), consumpion and labour supply are complemens. Finally, b represens a preference shock affecing he discoun rae ha deermines he ineremporal subsiuion decisions of households. This shock is assumed o follo a firsorder auoregressive process ih an IID-Normal error erm: b b b b. The invesmen equaion is given by: (2) I I / E I Q here S" depends on he adjusmen cos funcion (S) and is he discoun facor applied by he households. As discussed in CEE (2), modelling he capial adjusmen coss as a funcion of he change in invesmen raher han is level inroduces addiional dynamics in he invesmen equaion, hich is useful in capuring he hump-shaped response of invesmen o various shocks including moneary policy shocks. A posiive shock o he invesmen-specific echnology, I, increases invesmen in he same ay as an increase in he value of he exising capial sock Q. This invesmen shock is also assumed o follo a firs-order auoregressive process ih an IID-Normal error erm: I I I I The corresponding Q equaion is given by: k r Q (3) k Q ( R ) E k Q E k r r r here sands for he depreciaion rae and I k k r for he renal rae of capial so ha /( r ). The curren value of he capial sock depends negaively on he ex-ane real ineres rae, and posiively on is expeced fuure value and he expeced renal rae. The inroducion of a shock o he required rae Q of reurn on equiy invesmen,, is mean as a shorcu o capure changes in he cos of capial ha may be due o sochasic variaions in he exernal finance premium. 3 We assume ha his equiy premium shock follos an IID-Normal process. In a fully-fledged model, he producion of capial goods and he associaed invesmen process could be modelled in a separae secor. In such a case, imperfec informaion beeen he capial producing borroers and he financial inermediaries could give rise o a sochasic exernal finance premium. For example, in Bernanke, Gerler and Gilchris (998), he 3 This is he only shock ha is no direcly relaed o he srucure of he economy. Working Paper Series No. 39 Sepember 24 9

11 deviaion from he perfec capial marke assumpions generaes deviaions beeen he reurn on financial asses and equiy ha are relaed o he ne orh posiion of he firms in heir model. Here, e implicily assume ha he deviaion beeen he o reurns can be capured by a sochasic shock, hereas he seady-sae disorion due o such informaional fricions is zero. 4 The capial accumulaion equaion becomes a funcion no only of he flo of invesmen bu also of he relaive efficiency of hese invesmen expendiures as capured by he invesmen-specific echnology shock: (4) ( )K Î K I Wih parial indexaion o lagged inflaion, he inflaion equaion becomes a more general specificaion of he sandard Ne-Keynesian Phillips curve: (5) p ( E ) ( p p p ( )( ) p p p k a p r ( ) ( ) ) The deviaion of inflaion from he arge inflaion rae depends on pas and expeced fuure inflaion deviaions and on he curren marginal cos, hich iself is a funcion of he renal rae on capial, he real age ŵ and he produciviy process, ha is composed of a deerminisic rend in labour efficiency and a sochasic componen a, hich is assumed o follo a firs-order auoregressive a a a p process: a. is a IID-Normal price mark-up shock. When he degree of indexaion o pas inflaion is zero ( p ), his equaion revers o he sandard purely forard-looking Phillips curve. By assuming ha all prices are sill indexed o he inflaion objecive in ha case, his Phillips curve ill be verical. Announcemens of changes in he inflaion objecive ill be compleely neural even in he shor run. This is based on he srong assumpions ha indexaion habis ill adjus immediaely o he ne inflaion objecive. Wih p, he degree of indexaion o lagged inflaion deermines ho backard looking he inflaion process is or, in oher ords, ho much exogenous persisence here is in he inflaion process. The elasiciy of inflaion ih respec o changes in he marginal cos depends mainly on he degree of price sickiness. When all prices are flexible ( p ) and he price-mark-up shock is zero, his equaion reduces o he normal condiion ha in a flexible price economy he real marginal cos should equal one. Similarly, he indexaion of nominal ages resuls in he folloing real age equaion: 4 For alernaive inerpreaions of his equiy premium shock and an analysis of opimal moneary policy in he presence of such shocks, see Dupor (2). Working Paper Series No. 39 Sepember 24

12 (6) L L L hc C h L E E ) ( ) ) ( ( ) )( ( ) ( ) ( ) ( The real age ŵ is a funcion of expeced and pas real ages and he expeced, curren and pas inflaion rae here he relaive eigh depends on he degree of indexaion o lagged inflaion of he non-opimised ages. When, real ages do no depend on he lagged inflaion rae. There is a negaive effec of he deviaion of he acual real age from he age ha ould prevail in a flexible labour marke. The size of his effec ill be greaer, he smaller he degree of age sickiness ( ), he loer he demand elasiciy for labour (higher mark-up ) and he loer he inverse elasiciy of labour supply ( l ) or he flaer he labour supply curve. L is a preference shock represening a shock o he labour supply and is assumed o follo a firs-order auoregressive process ih an IID-Normal error erm: L L L L. In conras, is assumed o be an IID-Normal age mark-up shock. The equalisaion of marginal cos implies ha, for a given insalled capial sock, labour demand depends negaively on he real age (ih a uni elasiciy) and posiively on he renal rae of capial: (7) ) ( k K r L here "() () ' is he inverse of he elasiciy of he capial uilisaion cos funcion. The goods marke equilibrium condiion can be rien as: (8) L r K g I k C g k Y k a G y y y y ) ( ) )( ( ) ( here y k is he seady sae capial-oupu raio, y g he seady-sae governmen spending-oupu raio and is one plus he share of he fixed cos in producion. We assume ha he governmen spending shock follos a firs-order auoregressive process ih an IID-Normal error erm: G G G G. Finally, he model is closed by adding he folloing empirical moneary policy reacion funcion: (9) R p p y p Y Y Y Y Y r r Y Y r r R R ) ) ( ) ( ) ( ) ( )} ( ) ( ){ ( ) ( The moneary auhoriies follo a generalised Taylor rule by gradually responding o deviaions of lagged inflaion from an inflaion objecive and he lagged oupu gap defined as he difference beeen acual and poenial oupu (Taylor, 993). Consisenly ih he DSGE model, poenial oupu is defined as he level of oupu ha ould prevail under flexible price and ages in he absence of he hree cos-push shocks. 5 The parameer capures he degree of ineres rae smoohing. In addiion, here is also a 5 In pracical erms, e expand he model consising of equaions (2) o (9) ih a flexible-price-and-age version in order o calculae he model-consisen oupu gap. Working Paper Series No. 39 Sepember 24

13 shor-run feedback from he curren changes in inflaion and he oupu gap. Finally, e assume ha here R are o moneary policy shocks: one is a emporary IID-Normal ineres rae shock ( ) also denoed a moneary policy shock; he oher is a permanen shock o he inflaion objecive ( ) hich is assumed o follo a non-saionary process ( ). The dynamic specificaion of he reacion funcion is such ha changes in he inflaion objecive are immediaely and ihou cos refleced in acual inflaion and he ineres rae if here is no exogenous persisence in he inflaion process. In he empirical exercise, e assume ha his policy rule ogeher ih he process for he sochasic shocks is able o describe he behaviour of moneary auhoriies over he sample period. Especially for he euro area his is a srong assumpion because here as no unified moneary policy during mos of he period under invesigaion. Bu even for he US, he hypohesis of a sable moneary policy rule over he sample period is frequenly rejeced in he lieraure and should be esed empirically. Hoever, he presence of o ypes of moneary policy shocks disinguishes our exercise from many oher sudies on his opic. Equaions () o (9) deermine he nine endogenous variables:, ŵ, K, Q, Î, Ĉ, R, k r, L of our model. The sochasic behaviour of he sysem of linear raional expecaions equaions is driven by a I b L en exogenous shock variables: five shocks arising from echnology and preferences (,,,, G p Q ) hich are assumed o follo an AR() process, hree cos-push shocks (, and ) hich R are assumed o follo a hie-noise process and o moneary policy shocks ( and ). 3. Comparing he parameer esimaes We esimae equaions () o (9) for he US and he euro area separaely using seven key macro-economic ime series: oupu, consumpion, invesmen, hours orked, real ages, prices and a shor-erm ineres rae. The Bayesian esimaion mehodology is exensively discussed in Smes and Wouers (23a) The prior disribuion of he parameers The Bayesian esimaion mehodology requires he specificaion of prior disribuions over he 32 srucural parameers of he log-linear DSGE model. The firs se of columns in Table summarises hose prior disribuions. For comparison ih he resuls on he poserior disribuion e repor he 5 and 95 percenile and he median of he prior disribuion. We assumed he same prior for boh counries and for boh periods for hich he model is esimaed. The priors on he sandard error and he persisence of he exogenous sochasic processes are harmonised as much as possible. The sandard errors of he innovaions are assumed o follo an Inverse-Gamma disribuion ih a mean of.25 (.5 for he permanen inflaion objecive shock) and o degrees of freedom corresponding o a raher loose prior. 6 The Bayesian esimaion mehodology conains five seps. In sep he linear raional expecaions model is solved resuling in a sae equaion in he predeermined sae variables. In sep 2 he model is rien in sae space form by adding a measuremen equaion linking he seven observable variables o he vecor of sae variables. In sep 3 he likelihood funcion is derived using he Kalman filer. Sep 4 involves combining his likelihood funcion ih a prior disribuion over he parameers o form he poserior densiy funcion. The final sep consiss of numerically deriving he poserior disribuion of he parameers using a Mone Carlo Markov Chain (MCMC) algorihm. The specific MCMC mehod used is he Meropolis- Hasings algorihm. 2 Working Paper Series No. 39 Sepember 24

14 The persisence parameers of he AR() processes are assumed o follo a Bea disribuion ih mean of.85 and sandard deviaion of.. The hree mark-up shocks o prices, ages and equiy prices are assumed o be IID hie noise processes. The deerminisic groh rae in echnology is assumed o be Normal-disribued ih mean.4 (quarerly groh rae) and sandard deviaion.. Five parameers are resriced o a poin value prior o he esimaion process. The discoun rae is se a.99, he depreciaion rae is se a.25 (boh on a quarerly basis). For he US, he share of consumpion and invesmen are se a.65 and.7 and he capial income share in he Cobb Douglas producion funcion is fixed a.24. For he euro area, he consumpion and invesmen shares are respecively.6 and.22 and he producion parameer is.3. These values are in line ih hisorical averages for he series used and guaranee a seady sae groh pah. These parameers are hard o esimae unless he means of he ime series are aken ino accoun in he esimaion process. The parameers describing he moneary policy rule are based on a sandard Taylor rule: he long run reacion coefficien o inflaion and he oupu-gap are described by a Normal disribuion ih mean.5 and.25 (corresponding o.5 for annual raes) and sandard errors. and.5. The persisence of he policy rule, deermined by he coefficien on he lagged ineres rae, is assumed o be Normal disribued around.75 ih a sandard error of.. The prior on he shor run reacion coefficiens o inflaion and oupu-gap changes reflec he assumpions of a gradual adjusmen oards he long run. The parameers of he uiliy funcion are disribued as follos. The prior on he ineremporal subsiuion elasiciy is se a (ih a sandard error.375), he habi parameer is assumed o flucuae around.7 (ih a sandard error of.) and he age elasiciy of labour supply is assumed o be around 2 (ih a sandard error of.75). The prior on he adjusmen cos parameer for invesmen is se around 4 ih sandard error 2 (based on CEE 2) and he capaciy uilisaion elasiciy is se a.2 (sandard error. including he. of King and Rebelo, 2). The share of fixed coss in he producion funcion is assumed o be disribued around.25 (he corresponding parameer is defined as.25). All hese priors are described by a Normal disribuion, ih he excepion of he habi persisence parameer, hich follos a Bea disribuion because i is resriced beeen and. 7 Finally here are he parameers describing he price and age seing. The Calvo probabiliy is assumed o be around.75 for boh prices and ages, corresponding o a one-year average conrac lengh. The degree of indexaion on pas inflaion is se a.75, hich corresponds o a significan coefficien (.43) on he lagged inflaion erms in he linearised inflaion and age equaions. 3.2 The poserior disribuion of he parameers The second and hird ses of columns in Table repor he resuls of he poserior sampling. More specifically, hey repor he median and he 5 and 95 percenile of he esimaed poserior disribuion of 7 Addiional jusificaions for he assumed prior disribuions are given in Smes and Wouers (23a,b). Working Paper Series No. 39 Sepember 24 3

15 he parameers for boh he US and euro area model, esimaed over o common sample periods. 8 The baseline model is esimaed over he longer period from 974: o 22:2. This sample period is given by he sample size of he euro area daa se. In order o increase he comparabiliy of he US and euro area resuls, e also limied he US sample o he same period. In order o examine he sabiliy of he resuls, Table also repors he esimaion resuls for a shorer period from 983: o 22:2. I has been argued ha paricularly in he Unied Saes here has been a break in he ime series properies and paricularly in heir volailiy in he early 98s. 9 Par of his break may be relaed o a change in moneary policy behaviour as, for example, argued in Clarida, Gali and Gerler (998). Regarding he euro area, i may be argued ha he convergence process o a common moneary policy only seriously sared in he mid- 98s. Also in his case, i is herefore of ineres o analyse o ha exen he resuls over he longer sample period are robus ih respec o he more recen period. In ha follos, e ill focus on he resuls of he longer period and commen on any imporan differences ih he resuls for he shorer sample. The overall finding is ha he parameers are remarkably similar across he o regions. As discussed in he inroducion, his may no be very surprising given he recen findings of Agresi and Mojon (22) and Peersman and Smes (22). The finding of broad similariy across he o regions applies o boh he esimaed sochasic driving processes, he behavioural parameers and he policy rule. Neverheless, here are also some ineresing differences. Turning firs o he esimaed sochasic processes for he srucural shocks, i appears ha he variances of he demand shocks are ypically larger in he US han in he euro area. This is mos sriking for he preference shock hich is almos five imes as variable in he US (.66) han in he euro area (.32). Hoever, he persisence of hose shocks is ypically loer, so ha he difference in he uncondiional variance of he shock variables is less sriking. For example, he auoregressive parameer in he preference shock is only.49 in he US compared o.87 in he euro area. Of he hree demand shocks, he governmen spending process is esimaed o be he mos persisen in boh areas. Also he moneary policy shock has a larger variance in he US han in he euro area. Overall, he larger variabiliy of he demand and moneary policy shocks becomes less sriking in he shorer and more recen sample period. For example, he median sandard deviaion of he preference shock in he US falls from.66 o.4. Similarly, he median sandard deviaion of he moneary policy shocks falls from.24 o.3, hich is much closer o he relaively sable esimae of abou.2 in he euro area. The fall in he variabiliy of he non-sysemaic componen of moneary policy is consisen ih he findings of Boivin and Giannoni (23), ho conclude ha changes in boh sysemaic and non-sysemaic moneary policy have conribued o he loer variabiliy of he US economy in he mos recen period. Regarding he oher shock processes, i urns ou ha he variabiliy of he produciviy shock is someha higher in he euro area han in he Unied Saes. Compared o oher esimaes, he esimaed sandard error of he produciviy shock is on he lo side, bu his is parly due o he inroducion of variable 8 9 The poserior disribuion repored in Table has been generaed by 25 dras for he euro area model and 25 dras for he US model from he Meropolis Hasings sampler (see Geeke, 999). An appendix available from he auhors documens various saisical convergence ess ha sho ha in each case he Markov chains have converged and ha hey can be considered as a valid sample from he poserior disribuion. See, for example, Perez-Quiros and McConnel (2), Sock and Wason (22). 4 Working Paper Series No. 39 Sepember 24

16 capial uilisaion as, for example, argued in King and Rebelo (2). In boh cases, he produciviy process is esimaed o be very persisen and close o a uni roo, in paricular over he longer sample period. The linear rend in produciviy is esimaed o be someha higher in he US economy (.6 annualised) han in he euro area (.88). Finally, he variances of he oher shocks, in paricular he cospush shocks and he labour supply shock, do no appear o be significanly differen. I is also orh noing ha he innovaions in he non-saionary inflaion objecive shock have a small, hough significan sandard error. When comparing hose esimaes ih hose in he more recen sample, one sriking difference is he fall in he variance and he persisence of he labour supply shocks in he US. Turning o he behavioural parameers he overall picure of similariy beeen boh economies is confirmed. A rough measure of his similariy is ha in almos all cases he median esimae of a parameer in one region falls in he esimaed confidence band for he same parameer of he oher region. There are only o excepions. Someha surprisingly, he Calvo parameer for age sickiness appears o be signficanly larger in he US han in he euro area, hen esimaed over he hole sample period. Similarly, he indexaion parameer of prices, hich capures he degree of inflaion persisence, is esimaed o be higher in he Unied Saes han in he euro area. To he exen ha in paricular he former parameer is hough o capure srucural rigidiies in labour markes, his finding does no conform o he common isdom ha labour markes are more flexible in he Unied Saes. The average lengh of age conracs is esimaed o be around 5 quarers in he US, hile i is close o hree quarers in he euro area. Consisen ih our previous findings for he euro area (Smes and Wouers, 23a,b), e find ha he Calvo parameer for price sickiness is relaively high in boh he euro area and he US. This is in conras o he resuls repored by Chrisiano, Eichenbaum and Evans (2) and ACEL (22), finding ha he esimaed degree of price sickiness in he US is relaively small and economically unimporan. Our resuls are more in line ih he findings of Gali and Gerler (999) and Gali, Gerler and Lopez-Salido (2). The finding ha in boh areas he average conrac lengh is higher in he goods marke han in he labour marke is a firs sigh surprising. Hoever, as discussed in Smes and Wouers (23b) his is parly he resul of our assumpion ha he marginal cos curve ha firms face in he goods marke is fla, hile i is upard-sloping in he labour marke. As discussed in Woodford (23), he laer assumpion creaes a sraegic complemenariy beeen age seers, hich ill end o reduce he sensiiviy of ages o is fundamenal deerminans for a given Calvo parameer. This sraegic complemenariy is absen in he price seing conex because i is assumed ha producion facors move freely beeen individual firms so ha all firms produce ih he same capial/labour echnology and all firms face he same marginal cos independen of he producion level. As a resul, a similar Calvo sickiness parameers in he age seing process compared o he price seing problem implies a much sloer response of ages o he fundamenal driving forces as i is he case for prices. Comparing he esimaes of hose parameers ih hose for he shorer sample, a sriking finding is ha he degree of nominal age sickiness increases quie dramaically boh in erms of he Calvo parameer (around.9 in boh areas) and in erms of he indexaion parameer. As a resul real ages become very sicky in he mos recen period. One explanaion may be ha because of he more sable moneary environmen since he mid eighies Our conjecure is ha he finding of limied price rigidiy is parly a resul of he differen mehodology used in CEE (2). Working Paper Series No. 39 Sepember 24 5

17 nominal age conracs are se for longer periods. This inerpreaion is consisen ih he fac ha he esimaed sickiness moves in he o economies in he same direcion. Overall, given he simple srucure of he labour marke model, hese resuls should be aken ih a grain of sal. Regarding he oher behavioural parameers, he esimaes are in he same ballpark as our previous esimaes (Smes and Wouers, 23a,b) and broadly conform o he findings in he lieraure. The invesmen adjusmen cos parameer is esimaed beeen 5 and 7, hich implies a gradual and persisen response of invesmen o he differen shocks. The inverse of he ineremporal subsiuion parameer in he uiliy funcion is esimaed around.5 and 2 for boh counries. The habi parameer (.59 for he euro area and.69 for he US) is esimaed o be relaively on he lo side compared o, for example, he esimaes provided in Fuhrer (2). The labour supply parameer in he uiliy funcions is beeen 2 and 2.8, he share of fixed coss around.5 and he capial uilisaion cos parameer is esimaed around.3. Overall, hese resuls appear o be robus in he shorer esimaion period. Finally, he esimaed policy rules are also very similar in boh economies. The long-run response o inflaion is esimaed around.5, hile he long-run response o he oupu gap is someha smaller han suggesed by Taylor (993). The ineres rae persisence is higher in he euro area, hereas he shor-run response o changes in inflaion and oupu is greaer in he US. From Table, here does no appear o be any srong evidence ha he Fed has become more reacive o inflaion and oupu developmens in he more recen period. This finding is in conras o resuls in he lieraure hich poin o insabiliy in he moneary policy rule before and afer he lae sevenies (e.g. Clarida, Gali and Gerler, 999). Our specificaion deviaes, hoever, from mos oher sudies in ha e allo for o ypes of moneary policy shocks: a emporary ineres rae shock and a permanen inflaion objecive shock. As discussed belo, he inflaion objecive shock akes up mos of he long-erm rend behaviour in inflaion. Our resuls sugges ha around his non-saionary inflaion objecive, he shor run dynamics of moneary policy does no seem o have changed much over ime. Overall, he main conclusions from he resuls presened in Table are ofold. Firs, here is no srong evidence ha he srucure of he US and euro area economies are significanly differen. Second, here is no srong evidence ha his srucure has significanly changed over ime. If anyhing, he variances of he sochasic processes (in paricular of he demand shocks) have fallen in he mos recen period. 4. Comparing sources of business cycle flucuaions in he US and he euro area The analysis of he previous Secion suggess ha he sources of business cycle movemens ill be broadly similar in boh areas. Graphs o 4 confirm his finding based on a comparison of he variance decomposiion of he main macro-economic variables in boh areas. Each of he graphs repor he Anoher possibiliy is ha in he shorer sample, i becomes harder o disinguish beeen persisen labour supply shocks ih a relaively lo degree of age sickiness and emporary age mark-up shocks ih a relaively high degree of age sickiness. Tha some of his migh be going on is suggesed by he fac ha in he laer period he variance of he labour supply shocks falls dramaically in favour of he emporary age mark-up shocks. 6 Working Paper Series No. 39 Sepember 24

18 variance decomposiion of he forecas errors of oupu, inflaion, ages and he shor-erm ineres rae for, 4, and 3 quarers ahead. 2 Focusing firs on he sources of oupu flucuaions, i is clear ha in he shor run (up o one year) oupu developmens are mainly driven by demand shocks, in paricular he governmen spending and preference shocks, and o a lesser exen by he moneary policy shock. In agreemen ih he larger variances of hose shocks in he US compared o he euro area, hose shocks are relaively more imporan in driving shor-erm developmens in he US han in he euro area. A he one-year horizon hose hree shocks sill accoun for around 45% of oupu flucuaions in he US, hile hey accoun for 28% in he euro area. Hoever, over he medium o long run, he conribuion of he hree supply shocks (i.e. he produciviy, labour supply and he invesmen-specific echnology shock) o oupu developmens increases quie dramaically, hile he conribuion of he oher shocks falls. A he quarer horizon, he produciviy and labour supply shocks accoun for 7% and 52% of oupu flucuaions in he euro area and he US respecively. This rises o 87 and 74% respecively a he 8-year horizon. Boh shocks are abou equally imporan. In conras o a recen VAR analysis by Fischer (22), he invesmen-specific echnology shock accouns for a significan, bu much less imporan fracion of oupu developmens a he medium o long run horizon. Overall, he relaive conribuion of produciviy and labour supply shocks does conform o he analysis of Shapiro and Wason (989), ho use an idenified VAR mehodology for he US. In he medium o long run, he conribuion of he oher shocks (including moneary policy shocks) is raher limied. The produciviy shock is also one of he main medium o long run deerminans of real ages and consumpion and invesmen. In his respec, he labour supply shock conribues relaively less o long-run movemens in invesmen as capial is subsiued for labour, hereas he invesmen-specific echnology shock explains relaively more of long-erm movemens in invesmen (in paricular in he US). Turning o price and age developmens (Graph 2 and 3), i is clear ha he price and age mark-up shocks are by far he mos imporan driving forces behind shor o medium-erm flucuaions in boh areas. Hoever, in he long run he nominal rends in prices and ineres raes are mainly driven by he inflaion objecive shock. I is quie sriking ha neiher of hese shocks conribues o he oupu developmens. The limied oupu cos of changes in he inflaion objecive shock is a resul of he assumpion ha disinflaions are assumed o be perfecly perceived by he agens in he economy. A more realisic assumpion ould be o assume asymmeric informaion regarding he inflaion objecive as, for example, in Erceg and Levin (2). Finally, urning o he deerminans of ineres rae flucuaions (Graph 4), i is clear ha in he shor o medium run hose are mosly driven by he demand shocks, in paricular he preference shock, and he emporary moneary policy shock. As menioned before, in he longer run also he inflaion objecive shock becomes an imporance source of flucuaions. A he quarer horizon, abou 65% of ineres rae 2 The variance decomposiions depiced in he graphs are calculaed for he esimaed mode of he parameers for he longer sample period. The degree of uncerainy around his variance decomposiion is illusraed by 5 and 95 perceniles of he poserior disribuion of he forecas error variance decomposiion shon under each graph. Working Paper Series No. 39 Sepember 24 7

19 flucuaions in he US and 43% of ineres rae flucuaions in he euro area are driven by fundamenal shocks, he res being he resuls of unsysemaic moneary policy. 5. Propagaion of shocks in he euro area and he US Ye anoher ay of comparing he esimaion resuls for he euro area and he US is o look a he impulse response funcions. Graph 5 focuses on one example of each of he four ypes of shocks considered: a supply shock (produciviy), a demand shock (preference), a cos-push shock (price mark-up) and a moneary policy shock (emporary ineres rae shock). Overall, he similariy of he findings in boh areas is again sriking. As discussed in Smes and Wouers (23a,b), he qualiaive feaures of he responses o a produciviy shock and a moneary policy shock are very much in line ih hose obained using differen mehodologies such as idenified VARs (see, for example, Gali (999), Francis and Ramey (22) and ACEL (22) for a produciviy shock and CEE (2) and Peersman and Smes (22) for a moneary policy shock). A robus feaure of he response o a posiive produciviy shock in boh areas is ha employmen falls. As in Francis and Ramey (22), his is mosly due o he sluggish response of he demand componens due o habi formaion and invesmen adjusmen coss. The deflaionary effec of a posiive produciviy shock appears someha larger in he US compared o he euro area. Turning o he preference shock, i is clear ha in boh regions a posiive preference shock on consumpion and oupu leads o some inflaionary pressures and a parial croding ou of invesmen. This croding ou is, hoever, much less imporan in he US and his in spie of a larger shor-erm ineres rae response and a higher invesmen ineres rae elasiciy. One of he facors explaining his may be he much higher persisence of he ineres rae response in he euro area. In line ih he larger esimaed age sickiness in he US, real ages respond more sluggishly o he various shocks in he US han in he euro area. This is also refleced in a more persisen response of inflaion o mos of he shocks. For example, hile, folloing a moneary policy shock, inflaion reaches is rough afer 4 quarers in he euro area he rough is reached only afer 6 quarers in he US. The higher price and age sickiness in he US also explains hy he oupu cos of a emporary mark-up shock is significanly larger in he US compared o he euro area. 6. Hisorical decomposiion of he business cycles Overall, our main finding is ha he sources of he shocks, he fricions and he policy reacion funcions appear o be very similar in he o economies. Hoever, he acual macro-economic developmens ere a imes quie differen. This can parially be explained by he differen iming of he shocks in he o counries. One indicaion of his asynchroniciy is he lo correlaion beeen he srucural shocks in he euro area and he US as shon in Table 3. In general, he correlaion is close o zero. To excepions are he preference shocks and he moneary policy shocks. 8 Working Paper Series No. 39 Sepember 24

20 In order o ge a beer idea of ha has driven paricular business cycle developmens, Table 2 summarises some of he informaion by focusing on he conribuions of he various shocks o he hree main boom and recession periods in boh areas. 3 A firs ineresing exercise is o compare he deerminans of he oupu boom in he second half of he 99s and he subsequen slodon (las se of columns in Table 2). In he US, here does no seem o be any paricular shock ha has driven mos of he oupu boom in ha period. Posiive conribuions of abou he same size came from he hree supply shocks, he preference shock, relaively loose moneary policy and a posiive age mark-up shock. This analysis herefore suggess ha a combinaion of facors as responsible for he good groh performance in he second half of he 99s, no only favourable produciviy groh. In conras, in he euro area mos of he oupu boom can be explained by a posiive labour supply shock. Also preference, produciviy and moneary policy shocks had a posiive, hough much more limied conribuion, bu he invesmen shock had a significan negaive effec. Turning o he subsequen donurn, i appears ha in he US he donurn is mosly driven by a negaive preference and invesmen shock, hile produciviy developmens coninued o provide a posiive conribuion. In conras in he euro area, produciviy fell significanly only o be couneraced by a rise in he labour supply. The srong groh expansion in he second half of he 98s seem o have been mainly suppored by a rise in he labour supply in boh areas. In he euro area, his as backed up by posiive developmens in produciviy and invesmen, hile he opposie occurred in he US. In boh areas he subsequen recession as mainly due o negaive preference and invesmen shocks, very much like in he curren donurn. The role of moneary policy shocks in driving oupu booms and buss is quie limied. One excepion is he recession of he early 98s. In boh areas, he moneary policy shocks ere he mos imporan source of he donurn in oupu in his period. Turning o he behaviour of inflaion during hose boom and recession periods, i is clear from he loer ro in Table 2 ha in each recession period inflaion falls. Consisenly, ih he analysis of oupu developmens in hose periods, negaive preference and invesmen shocks are imporan conribuors. In he euro area, here as also a major disinflaion in he boom periods of and This disinflaion is compleely explained by a fall in he inflaion objecive. 7. Conclusions In his paper e have esimaed a DSGE model ih many ypes of shocks and real and nominal fricions for boh he US and he euro area economy over a common sample period (974-22). The srucural esimaion mehodology allos us o invesigae heher differences in business cycle behaviour in he o economic areas are due o differences in he ype of shocks ha affec he o economies, differences in he propagaion mechanism of hose shocks or differences in he ay he cenral bank responds o hose 3 Hisorical decomposiions ere performed using he mode of he poserior disribuion. Working Paper Series No. 39 Sepember 24 9

21 economic developmens. Our main conclusion is ha each of hose characerisics is remarkably similar across boh currency areas. Moreover, he idenified sources of business cycle flucuaions and he esimaed effecs of he various shocks on he o economies conform o he empirical resuls obained using idenified VARs. Of course, he comparison using empirical DSGE models performed in his paper is only a saring poin. There are a leas o ineresing avenues for fuure research, hich ill also serve o examine he robusness of our resuls. Firs, e need o look a alernaive models ih differen and richer goods, labour and financial marke srucures. Imposing a relaively simple, idenical srucure in each of he o economies may bias he resuls agains finding significan differences. Second, e have reaed each of he o economies as o separae closed economies. Given he limied imporance of bilaeral rade beeen he o areas, his may be a reasonable firs approximaion. Recen experience has, hoever, suggesed ha he linkages beeen he o blocs are sronger han may have been expeced on he basis of rade links only. Linking he o economies in a ell-specified o-counry model ill allo us o examine hose ransmission channels and heir effecs on he esimaed parameers of he model. Daa appendix For he US, consumpion, invesmen and GDP are aken from he US Deparmen of Commerce - Bureau of Economic Analysis daabank. Real Gross Domesic Produc is expressed in billions of chained 996 dollars. Nominal Personal Consumpion Expendiures and Fixed Privae Domesic Invesmen are deflaed ih he GDP-deflaor. 4 Inflaion is he firs difference of he log Implici Price Deflaor of he GDP series. Hours and ages are aken from he Bureau of Labour Saisics (hours and hourly compensaion for he NFB secor for all persons). Hourly compensaion is divided by he GDP price deflaor o ge he real age variable. Hours are adjused o ake ino accoun he limied coverage of he NFB secor compared o GDP. The index of average hours for he NFB secor is muliplied ih civilian employmen (6 years and over). The aggregae real variables are expressed per capia by dividing ih he populaion over 6. All series are seasonally adjused. The ineres rae is he Federal Funds Rae. For he euro area, all daa are aken from he AWM daabase from he (see Fagan e al, 2). Invesmen includes boh privae and public invesmen expendiures. Real variables are deflaed ih heir on deflaor. Inflaion is calculaed as he firs difference of he log GDP deflaor. In he absence of 4 We follo Alig, Chrisiano, Eichenbaum and Linde (22) here. This approach avoids he posiive rend in he invesmen share of oupu ha resuls from he decline in he relaive invesmen expendiures deflaor. A fully specified model ould sar from a o-secor model alloing for a separae rend in echnological progress in he invesmen good secor. In such a o-secor model, he relaive price of invesmen and consumpion goods can be used o idenify he invesmen specific echnological progress. In our one secor model, i as difficul o idenify a separae deerminisic rend in invesmen specific echnology. Hoever, here are significan shor run shocks around his rend ha influence invesmen in he shor and medium run. 2 Working Paper Series No. 39 Sepember 24