Explaining International Business Cycle Synchronization

Transcription

1 Explaining Inernaional Business Cycle Synchronizaion Rober Kollmann (*) Universié Libre de Bruxelles and CEPR February The business cycles of major advanced economies are synchronized. Sandard macro models fail o explain ha fac. This paper presens a simple wo-counry wo-good complee-markes dynamic general equilibrium model in which counry-specific produciviy shocks generae highly correlaed business cycles. The srucure here differs from sandard open economy macro models by assuming recursive ineremporal preferences and a weak wealh effec on labor supply. Recursive preferences magnify he erms of rade response o shocks. In he model here a persisen produciviy (and GDP) increase in a given counry riggers a srong improvemen of he foreign counry s erms of rade. When he wealh effec on labor supply is weak his induces a rise in foreign hours worked and GDP i.e. domesic and foreign real aciviy comove posiively. Key words: inernaional business cycles erms of rade real exchange rae wealh effec on labor supply GHH preferences wage rigidiy. JEL codes: F31 F32 F36 F41 F43. (*) Conac address: European Cenre for Advanced Research in Economics and Saisics (ECARES) Universié Libre de Bruxelles 50 Av. Franklin Roosevel 1050 Brussels Belgium; rober_kollmann@yahoo.com I hank Nelson Mark Werner Roeger Gauhier Vermandel Roland Winkler and workshop paricipans a he Fed Board of Governors Dallas Fed American Economic Associaion meeing and a he IMAC3-Rennes conference for useful discussions. The research leading o hese resuls has received funding from he European Communiy s Sevenh Framework Programme (FP7/ ) under gran agreemen no Projec MACFINROBODS ( Inegraed Macro-Financial Modelling for Robus Policy Design ). 1

2 1. Inroducion GDP employmen and invesmen are highly posiively correlaed across advanced economies. Sandard macro models fail o explain ha key fac--in hose models shocks ha originae in one counry have a weak effec on foreign GDP and prediced crosscounry correlaions of real aciviy are markedly smaller han empirical correlaions. Explaining inernaional business cycle synchronizaion is hus one of he main challenges for macroeconomics (e.g. Backus e al. ( )). The presen paper provides a possible resoluion of he inernaional correlaion puzzle. I develops a simple dynamic general equilibrium model in which counry-specific produciviy shocks induce flucuaions of real aciviy ha are highly correlaed across counries. A wo-counry world wih wo raded goods is considered. The specificaion of echnologies and markes follows sandard Inernaional Real Business Cycle models. 1 Each counry is inhabied by a represenaive household who produces one raded good using domesic capial and labor. Households use domesic and impored raded goods for consumpion and physical invesmen bu each household has a spending bias owards he domesic good. The global financial marke is complee. Economic flucuaions are driven by persisen produciviy shocks. The model differs from sandard open economy macro models by making wo key assumpions we show ha hese assumpions joinly allow o generae high crosscounry business cycle correlaions: (i) Recursive ineremporal preferences (Epsein and Zin (1989) Weil ( )) are considered here while sandard open economy models assume ime-separable preferences. (ii) A mued effec of wealh changes on labor supply is assumed. I consider a period uiliy funcion of he Greenwood Hercowiz and Huffman (1988) [GHH] ype ha enails a zero wealh effec on desired labor supply. By conras sandard open economy macro models mosly assume he King Plosser and Rebelo (1989) [KPR] period uiliy funcion ha implies a srong negaive response of desired labor supply o a wealh increase. I also consider a seing in which he real (consumpion) wage rae is rigid in he shor-run and hours worked are deermined by 1 E.g. Dellas (1986) Canor and Mark (1988) Crucini (1989) Backus e al. (1994) Kollmann ( ) Devereux (1992) Heahcoe and Perri (2002). 2

3 firms labor demand (workers can be off heir labor supply schedule); his mechanism also eliminaes he effec of wealh shocks on labor. Consider he effec of a persisen exogenous produciviy increase in one of he counries named Home. Tha supply shock induces a persisen rise in Home GDP employmen consumpion invesmen and welfare; i lowers he relaive price of he Home oupu good (compared o he Foreign oupu good) and hus he Home erms of rade deeriorae. Due o consumpion home bias he relaive price of he Home consumpion baske falls i.e. he Home (consumpion-based) real exchange rae depreciaes. Conversely he oher counry s ( Foreign ) erms of rade improve. This raises he Foreign marginal produc of labor expressed in unis of Foreign consumpion which increases Foreign firms labor demand. The effec of he shock on he Foreign labor supply depends on opposing subsiuion and wealh effecs of he Foreign erms of rade improvemen wih he former increasing and he laer reducing he Foreign labor supply. In he shor run he Home produciviy increase raises Foreign oupu if Foreign hours worked rise. In sandard macro models he erms of rade (and real exchange rae) response o a produciviy shock is weak and he subsiuion and wealh effecs of erms of rade changes on labor supply largely offse each oher. As a resul sandard models predic a mued response of Foreign oupu o a Home produciviy increase. Recursive preferences (considered here) magnify he erms of rade responses o persisen shocks. Under hese preferences he coefficien of risk aversion CRA can differ from he inverse of he ineremporal elasiciy of subsiuion IES (sandard imeseparable preferences imply ha CRA=1/IES). When CRA1/IES hen a household s ineremporal marginal rae of subsiuion (IMRS) depends on her (fuure) lifeime uiliy. Under he common assumpion ha he coefficien of risk aversion exceeds he inverse of he ineremporal elasiciy of subsiuion (CRA>1/IES) a rise in fuure lifeime uiliy reduces he IMRS. 2 Financial marke compleeness implies ha in equilibrium he raio of he Home IMRS o he Foreign IMRS is equaed o he (gross) rae of appreciaion of he Home real exchange rae. Wih recursive preferences a persisen rise in Home produciviy (ha increases Home life-ime uiliy and hus 2 CRA>1/IES implies a preference for he early resoluion of uncerainy over fuure consumpion (Weil 1990). 3

4 lowers he Home IMRS) riggers hus a sharper depreciaion of he Home real exchange rae (compared o he depreciaion prediced by a model wih ime-separable uiliy in which he IMRS does no depend on life-ime uiliy); his implies a sronger deerioraion of he Home erms of rade and a sronger improvemen of he Foreign erms of rade. When he wealh effec on labor supply is weak he sronger Foreign rade improvemen induces a noiceable rise in Foreign hours worked. This explains why in he model here counry-specific produciviy shocks can generae highly correlaed flucuaions of Home and Foreign GDP. Imporanly recursive preferences and a weak wealh effecs on labor are boh needed for his resul. Thus GHH uiliy or a rigid real wage rae are crucial ingrediens of he mechanism described here (in flex-wage model varians wih KPR uiliy he prediced cross-counry oupu correlaions are lower under recursive preferences han under ime-separable preferences i.e. he correlaion puzzle worsens). The srucure here also maches oher key business cycle facs beer han convenional open economy models. In paricular he seup here generaes a more volaile real exchange rae. The asse pricing lieraure has for many years sudied models wih recursive preferences as he flexibiliy afforded by he separaion beween he IES and CRA parameers helps o capure he join dynamics of consumpion and asse reurns (e.g. Rudebusch and Swanson (2012)). By conras he inernaional macroeconomics lieraure has only recenly begun o consider models wih recursive preferences. See e.g. Colacio and Croce ( ) Benigno e al. (2012) Gourio e al. (2013) Caporale e al. (2014) Kollmann ( ) Lewis and Liu (2015) and Sauze (2015). These sudies show ha models wih recursive preferences can generae higher real exchange rae volailiy han sandard models (wih ime-separable preferences). However hese papers consider endowmen economies and hus hey canno explain why oupu employmen and invesmen are synchronized across counries he focus of he paper here. The presen paper updaes and exends Kollmann (2009) he firs analysis of a wo-counry producion economy wih recursive preferences. Benigno e al. (2012) Colacio e al. (2014) Mumaz and Theodoridis (2015) Backus e al. (2016) and Trevoll (2016) also sudy open economy producion economies wih recursive preferences bu 4

5 he focus of hose papers is differen; he quaniaive models in hese papers do no explain he high empirical cross-counry correlaions of oupu employmen and invesmen. 3 Secion 2 describes he baseline wo-counry model wih producion and recursive preferences. Secion 3 discusses sylized facs abou inernaional business cycles. Secion 4 presens simulaion resuls and Secion 5 concludes. 2. A wo-counry model 2.1. Preferences echnologies shock process risk sharing A world wih wo symmeric counries Home (H) and Foreign (F) is assumed. Each counry is inhabied by a represenaive infiniely-lived household. A dae perfecly compeiive firms in counry i produce Y unis of a perishable radable inermediae good using he echnology Y L K 1 ( ) ( ) 1 where L and K are hours worked and capial respecively. The counry i capial sock is owned by he local household and rened o compeiive domesic firms. Labor and capial are immobile inernaionally. 0 is exogenous sochasic labor augmening produciviy. Produciviy is non-saionary (see below). The counry i household combines local and impored inermediaes ino a nonradable final good : Z ( y /(1 )) ( y / ) j (1) i 1 j j where y is he amoun of inermediae good j used by counry i. There is a bias owards using he local inpu: The final good is used for consumpion C and gross i 3 Those models do no feaure he mued wealh effec on labor assumed in he presen paper he key condiion for inernaional synchronizaion highlighed here. Benigno e al. (2012) and Mumaz and Theodoridis (2015) use wo-counry New Keynesian model o sudy he effec of volailiy shocks. Colacio e al. (2014) explore differenial effecs of permanen and ransiory produciviy shocks on inernaional capial flows. Backus e al. (2016) analyze he dynamics of Pareo weighs in a wo-counry world wih volailiy shocks. Trevoll (2016) focuses on real exchange rae variabiliy. 5

6 invesmen I : Z Ci I. The law of moion of he capial sock is K 1 (1 ) K I where 0 1 is he capial depreciaion rae. A dae he price of counry i s final good equals is marginal cos: 1 Pi ( pi ) ( p j ) j where p j is he price of inermediae good j. Inpu demands are: i j yi (1 ) Pi Z / pi yi Pi Z / p j for j i. Marke clearing for radable goods i i requires yh yf Yi for i H F. Counry i s erms of rade and real exchange rae are defined as qi pi / pj and RER Pi / Pj wih ij respecively. Thus increases in qi and RER represen an improvemen in he counry i erms of rade and an appreciaion of is real exchange rae respecively. Noe ha RER 12 ( qi ) ; due o home bias an improvemen of a counry s erms of rade induces an appreciaion of is real exchange rae as 1-2α>0 (he logged real exchange rae and erms of rade are perfecly posiively correlaed). The counry i household has a concave period uiliy funcion ha is increasing in consumpion and decreasing in hours worked: u C L C L 0 0 (2) 1 1 ( ) 1 [ i i i ( )] where ( C Li ) 0 is an affine funcion of C (see below). Ineremporal household preferences are described by a recursive life-ime uiliy funcion inspired by Epsein and Zin (1989) and Weil ( ): U {(1 ) [ ( C L )] [ EU ] } 1 1 (1 )/(1 ) 1/(1 ) 1 where U 0 is counry i life-ime uiliy a dae. (Epsein Zin and Weil assume ha uiliy only depends on consumpion. The specificaion of recursive preferences used here ha also depends on labor follows Rudebusch and Swanson (2012).) 0 i 1 is i s subjecive discoun facor beween periods and +1 1/ is he ineremporal elasiciy of subsiuion (IES). γ indexes he household s aversion agains uncerainy in fuure life-ime uiliy. Sandard ime-separable preferences obain when γ= i.e. when γ=1/ies. Epsein Zin and Weil assume ha he subjecive discoun facor is consan. To 6

7 ensure ha he model has a unique deerminisic seady sae and an equilibrium in which he consumpion/gdp raio is saionary I posi ha he subjecive discoun facor of household i is a decreasing funcion of is period uiliy normalized by produciviy: b ln( u / u ) for <1 and bln( u / u ) for >1 wih b>0. Here 1 u u X i / and u i is he seady sae value of u ; X 0 is a geomeric moving average of pas produciviy: X i ( X ) ( ) wih 0 1. (3) Counry i s ineremporal marginal rae of subsiuion (IMRS) beween aggregae consumpion a daes and +1 is: u / C U /(1 ) ui / Ci ( EU 1) (4) wih 4 Noe ha when = and b=0 is assumed hen 1 1 ( b/ i ) [( Ui / ) 1]. ( u / C )/( u / C ) i.e. he IMRS only depends on consumpion and hours a and +1. When hen he IMRS depends also on life-ime uiliy U 1. When > hen an unexpeced rise in U 1 induces a fall in he IMRS. The model assumes complee inernaional financial markes. In equilibrium he Home/Foreign IMRS raio is hus equaed o he growh facor of he real exchange rae (Kollmann ( ) Backus and Smih (1993)): / RER / RER. (5) H 1 F 1 1 The marke value of counry i s ne foreign asses a he end of period NFA 1 equals he presen value of i s fuure ne impors: NFAi 1 E i k( Pi / Pi k) ( NX k) where NX p Y P C I k 1 vk k v1 i v. ( ) are ne expors a dae and Opimal counry i capial invesmen decisions are described by he Euler equaion 1 E {( p / P ) MPK 1 } In he numerical simulaions b is se a a very small value which implies ha he erm i 1 / in (4) makes a negligible conribuion o high-frequency flucuaions of i 1. 7

8 MPK (1 ) Y / K where is he dae +1 physical marginal produc of capial in he counry; ( p 1 / Pi 1 ) MPK 1 is he marginal produc of capial expressed in unis of counry i consumpion. Le w denoe he wage rae in final consumpion unis. Inermediae good producing firms equae he marginal produc of labor in consumpion unis o he wage rae: ( p / P ) MPL w (6) where MPLi 1 Y / Li is he physical marginal produc of labor. Noe ha /(1 2 ) pi / Pi ( qi ) ( RERi ) ; hus an improvemen of he counry i erms of rade q (and an appreciaion of is real exchange rae) raise he marginal producs of capial and of labor in consumpion unis. This increases he demand for capial (invesmen) and labor in counry i. As shown below a posiive shock o Home produciviy improves he Foreign erms of rade. Under sandard period uiliy funcions his induces opposing subsiuion and wealh effecs on Foreign hours worked wih he former increasing and he laer decreasing Foreign labor supply. To highligh he role of he wealh effec on labor supply for inernaional shock ransmission I compare model varians wih he King Plosser and Rebelo (1989) [KPR] period uiliy funcion ha is widely used in he inernaional macro lieraure (e.g. Backus e al. (1994)) o model varians wih period uiliy à la Greenwood Hercowiz and Huffman (1988) [GHH]. 5 Under KPR uiliy a wealh increase reduces desired labor supply. By conras he wealh effec on labor supply is zero under GHH uiliy. KPR uiliy obains when C ( Li ) wih ' 0 (see (2)). 6 The model varians wih GHH uiliy below assume ( Ci Li ) C X ( Li ) wih <0 5 Some sudies ha have explored open economy models wih GHH period uiliy bu wihou considering recursive ineremporal preferences and wihou discussing implicaions for cross-counry real aciviy correlaions; e.g. Devereux e al. (1992) Correia and Rebelo (1995) Jaimovich and Rebelo (2008) and Raffo (2010). 6 2 Concaviy of he KPR period uiliy funcion requires '' (2 1/ )( ') /. 8

9 where X is he moving average of pas produciviy defined in (3). 7 The simulaions below use hese funcional forms of labor disuiliy: 1 11/ 11/ ( L ) 1 ( L ) wih ( L ) {( L ) L } (7) where L denoes seady sae hours. 11/ The household deermines her desired labor supply by equaing he marginal rae of subsiuion beween consumpion and leisure o he consumpion wage: mrs w mrs ( / L )/( / C ). Under KPR uiliy mrsi C '( Li )/ ( Li ) holds; where hus a rise in consumpion increases he marginal rae of subsiuion which raises he household s asking wage. The effec of a wage increase ha also raises consumpion on desired labor supply is ambiguous under KPR uiliy: he posiive subsiuion effec of he wage increase is couneraced by a negaive wealh effec. 8 Under GHH uiliy by conras mrsi X '( Li ) i.e. he marginal rae of subsiuion does no depend on consumpion: given he exogenous quaniy X a wage increase raises labor supply unambiguously (zero wealh effec). I compare model varians wih a flexible consumpion wage rae in which firm labor demand equals household labor supply ( pi MPLi 1 / Pi 1 wi mrsi ) o model varians wih wage rigidiy in which he real consumpion wage rae is se one period in advance a he expeced fuure marginal rae of subsiuion beween consumpion and leisure: w E 1 mrs. Under a predeermined wage rae labor hours are deermined by i i firms labor demand (6); 9 hus households can (emporarily) be off heir labor supply schedule ( wi mrsi ) which mues he wealh effec on hours. i i 7 Under GHH uiliy he disuiliy of labor is scaled by X o permi balanced growh and o ensure ha equilibrium hours worked are saionary; he X erm can be raionalized by assuming ha here is home producion by households (e.g. Rudebusch and Swanson (2012)). KPR uiliy is consisen wih balanced growh and saionary hours when he disuiliy of work is no scaled by produciviy. 8 Toal differeniaion of he KPR labor supply condiion gives w C L wih x dx/ x and ( '' L/ ' ' L/ ). The Frisch labor supply elasiciy (compued a consan consumpion) LSE is: LSE=1/Ξ. A a given wage rae a rise in consumpion reduces hours worked when LSE>0. 9 Rigid-wage models usually assume ha hours are demand-deermined (e.g. Blanchard and Gali (2007) Kollmann e al. (2016)). 9

10 Empirical flucuaions of produciviy and of relaive (domesic/foreign) produciviy are highly persisen. The model assumes ha log produciviy has a uni roo and ha log produciviy is co-inegraed across counries: ln( ) ln( ) [ln( ) ln( )] wih 0 for i=hf and j (8) 1 j 1 where 1 is a Gaussian whie noise Numerical soluion mehod As produciviy is assumed non-saionary bu coinegraed across counries I reformulae he model by normalizing counry i GDP consumpion invesmen ne expors and uiliy by i s produciviy. The model has a saionary equilibrium in erms of he normalized variables. I solve he reformulaed model wih he Dynare oolbox (Adjemian e al. (2014)) using a hird-order approximaion around he symmeric deerminisic seady sae Calibraion Preference and echnology parameers One period represens one quarer. The seady sae subjecive discoun facor and he slope parameer of he endogenous discoun facor are se a 0.99 and b=0.001 respecively. 10 The ineremporal elasiciy of subsiuion (IES) 1/ is se a 1.5 in line wih sandard values used in he macro lieraure. Following he macro-finance lieraure (e.g. Swanson (2014)) I consider high risk aversion coefficiens: γ=10 and γ=50 bu I also discuss a case wih γ=1/ies=0.66 (sandard ime-separable preferences). The Frisch labor supply elasiciy in se a 2 a sandard value used in macro models; ha elasiciy generaes hours volailiy broadly in line wih he daa. 11 The model will be evaluaed by comparing model-prediced business cycle saisics o empirical saisics of quarerly daa for he US and for an 10 The small value of b implies ha shor erm model dynamics are similar o hose generaed by a (nonsaionary) model varian wih a consan subjecive discoun facor (b=0). 11 Under KPR uiliy he Frisch labor supply elasiciy LSE a he seady sae is LSE=1/(1/η+ω/s C ) where η is he curvaure of labor disuiliy (see (7)) and s C is he seady sae consumpion/gdp raio. s C depends solely on δ and. Under GHH uiliy LSE=η. 10

11 aggregae of 13 oher OECD economies (hereafer named res of he world ROW) for which quarerly aggregae hours worked series were consruced by Ohanian and Raffo ( ). 12 Long hisorical quarerly imes on hours worked are only available for hese 13 counries and for he US (he US hours daa used here is he BLS series hours of wage and salary worked on nonfarm payrolls ). The choice of 13 ROW counries is hus dicaed by he availabiliy of quarerly hours daa (ha are needed for esimaing quarerly produciviy series he driving force of economic flucuaions in he model). The labor share is calibraed a ω=0.65 consisen wih US and ROW daa. 13 The depreciaion rae of capial is se a δ=0.025 as in sandard quarerly macro models. In he mean US rade share (0.5*(expors+impors)/GDP) was 10%. Hence he impor share parameer in he model is se a α=0.10 (see (1)) Exogenous process I esimae he parameers of he produciviy process (8) using quarerly US and ROW produciviy series ( ). Empirical log labor augmening produciviy for counry i is consruced as ln( ) (ln( GDPi ) iln( Li ) (1 i)ln( K )) / i where i is he sample average of counry i s wage share. Quarerly capial series are obained by cubic spline inerpolaion of annual capial socks from he Penn World Table. Aggregae ROW produciviy is a GDP-weighed index of produciviy in he 13 individual ROW counries. 14 The sandard deviaions of firs differenced quarerly US and (aggregae) ROW log produciviy are 0.88% and 0.68% respecively i.e. he average sandard deviaion (across he wo regions) is 0.78%. The empirical correlaion beween US and ROW produciviy growh is In he calibraed model I hus se he sandard 12 The 13 ROW counries are: Ausralia Ausria Canada Finland France Germany Ireland Ialy Japan Korea Norway Sweden UK. The Ohanian-Raffo quarerly hours daa (available unil 2013) are esimaed from ime series on employmen and hours worked per employee (ILO OECD). 13 In he model he share of GDP going o labor equals ω; he sample average of he labor share (compensaion of employees/(gdp ne of indirec axes)) is 0.64 (0.66) in he US (ROW). 14 ROW aggregaes of produciviy are Törnqvis indices and so are he ROW aggregaes for GDP C I and L discussed in Sec. 3 below. For variable X he ROW aggregae X ROW obeys 13 ln X s lnx ROW j1 j j where X j is he counry j observaion and s j he weigh of counry j a dae wih s j 1. Weighs j equal counries smoohed nominal GDP shares in aggregae ROW nominal US$ GDP a curren exchange raes; o reduce he effec of nominal exchange rae volailiy exponenial ime rends are fied o raw GDP shares and fied rend shares are used as weighs. 11

12 deviaion of ln( i ) a 0.78% (for i=hf); he correlaion beween ln( H ) and ln( F ) is se a An Augmened Dickey-Fuller es fails o rejec he hypohesis ha relaive US/ROW produciviy has a uni roo. To ensure saionariy of he normalized model he produciviy error correcion parameer (see (8)) is se a a small posiive value κ= The parial adjusmen parameer of he preference shifer X (see (3)) is se a η=0.001 which ensures ha a produciviy shock has a negligible shor-run effec on preferences. 3. Sylized facs abou inernaional business cycles Table 1 repors hisorical business cycle saisics ( ) for US and ROW quarerly GDP consumpion gross invesmen hours worked ne expors (NX) and he US real effecive exchange rae (CPI-based). The empirical consumpion measure is he sum of privae and governmen consumpion. Ne expors are normalized by domesic GDP. 15 The saisics shown in Table 1 perain o firs differenced quarerly daa. GDP consumpion invesmen hours and he real exchange rae are logged before firs differencing. The hisorical sandard deviaion of GDP growh is 0.81% in he US and 0.59% in he ROW; hus US GDP is more volaile han ROW GDP. The Table repors relaive sandard deviaions of oher variables i.e. sandard deviaions divided by he sandard deviaion of GDP. Relaive sandard deviaions are broadly similar across he US and he ROW. Consumpion ne expors and hours worked are less volaile han GDP while invesmen and he real exchange rae are 3-4 imes more volaile han GDP. Consumpion invesmen and hours worked are posiively correlaed wih domesic GDP. US ne expors are negaively correlaed wih domesic GDP; he real exchange rae is weakly counercyclical. This paper is mainly moivaed by he fac ha cross-counry (US-ROW) correlaions of GDP and hours worked are sizable (abou 0.45). Cross-counry correlaions of consumpion and invesmen oo are posiive (abou 0.35) bu slighly lower. Imporanly he cross-counry correlaions of GDP consumpion invesmen and hours are noiceably higher han he cross-counry correlaion of produciviy (0.13). 15 The NX/GDP series for he ROW is a GDP-weighed average of individual counries NX/GDP. 12

13 Thus he model here will only produce realisic cross-counry correlaions if i generaes synchronized responses o counry-specific produciviy shocks. 4. Model predicions Table 2 repors prediced sandard deviaions and cross-correlaions of key variables generaed by differen model varians. Prediced momens of GDP consumpion invesmen hours worked and he real exchange rae perain o log firs differenced variables while momens for ne expors perain o he firs differenced ne expors/gdp raio. The Table also repors he Hansen-Jagannahan (1991) bound [ HJ bound ] generaed by he model i.e. he raio of he sandard deviaion of he ineremporal marginal rae of subsiuion (IMRS) divided by he mean IMRS. Tha saisic allows o evaluae wheher he model has he poenial o generae realisic risk premia on financial asses. In equilibrium he Sharpe raio of any raded risky asse is bounded above by he HJ bound. The hisorical quarerly Sharpe raio of US equiy reurns was 0.22 in Thus a model-generaed HJ bound below 0.22 indicaes ha he model canno generae a realisic equiy premium. Cols. (1)-(6) of Table 2 repor prediced momens generaed by model varians wih a flexible consumpion wage rae ( flex-wage ) while Cols. (7)-(12) show momens for predeermined-wage model varians. For each of hese model varians I repor prediced momens generaed under KPR uiliy and under GHH uiliy and ha for hree values of he risk aversion coefficien: γ=1/ies γ=10 and γ=50. Hisorical US momens (from Table 1) are shown in Col. (13) of Table 2. Table 3 repor dynamic effecs of a one-sandard deviaion (0.78%) posiive innovaion o Home produciviy for he flex-wage model varian (Panel (a)) and for he predeermined-wage model varian (Panel (b)) Flex-wage model varians (Table 2 Cols. (1)-(6); Table 3 Panel (a)) Consider firs he prediced momens generaed by he flex-wage model varian. Tha varian maches well he hisorical volailiy of US GDP; i also capure he fac ha 16 Tha Sharpe raio is based on reurns daa from Ken French s web page. The Sharpe raio of an asse is he raio of he mean of is excess reurn (relaive o a risk-free asse) divided by is sandard deviaion. 13

14 invesmen is much more volaile han GDP while consumpion hours and ne expors are less volaile han GDP. Under all model specificaions (KPR/GHH ime separable/recursive) invesmen and hours worked are pro-cyclical (posiively correlaed wih domesic oupu) and he real exchange rae is counercyclical. Consumpion is procyclical in all model varians wih GHH uiliy. 17 The following discussion focuses on model predicions for he real exchange rae and for inernaional correlaions. Flex-wage model varians wih ime-separable preferences (γ=1/ies) show wellknown shorcomings of sandard inernaional macro models (e.g. Backus e al. (1994)); in paricular he prediced cross-counry correlaions of GDP invesmen and hours worked are smaller han empirical cross-counry correlaions; his is he case under boh KPR and GHH period uiliy (see Cols. (1) and (4)). The prediced cross-counry GDP correlaions wih γ=1/ies is 0.23 (0.14) under KPR (GHH) uiliy while he empirical correlaion is Furhermore he prediced relaive sandard deviaion of he real exchange rae (0.37 [0.16] under KPR [GHH] uiliy) is much smaller han he empirical relaive sandard deviaion (3.03). In addiion he HJ bounds generaed by he model varians wih =1/IES are close o zero i.e. hose varians canno generae a realisic equiy premium. The flex-wage model varians wih recursive preferences (γ=10 and γ=50; see Cols. (2)-(3) and (5)-(6)) generae greaer real exchange rae volailiy and greaer HJ bounds (i.e. higher IMRS volailiy) han he flex-wage model varians wih imeseparable preferences (=1/IES). Persisen produciviy shocks have a sizable effec on life-ime uiliy; wih recursive preferences (1/IES) he IMRS is affeced by flucuaions in life-ime uiliy which riggers srong real exchange rae responses under efficien risk sharing (see (4)(5)). The greaer he risk aversion coefficien he greaer he prediced volailiy of he IMRS and of he real exchange rae. The KPR and GHH flex-wage model varians wih γ=10 (γ=50) generae HJ bounds of abou 0.05 (0.24) respecively and a relaive sandard deviaion for he real exchange rae of abou 1.2 (1.5). Hence recursive preferences wih subsanial risk aversion are needed o generae a realisic HJ bound and a volaile real exchange rae. 17 Consumpion is counercyclical in KPR model varians wih recursive preferences. 14

15 Recursive preferences have an effec on prediced cross-counry correlaions; ha effec depends on he period uiliy funcion. In he flex-wage model wih KPR period uiliy he assumpion of recursive preferences lowers he prediced cross-counry correlaions (compared o ime-separable preferences) i.e. he correlaion puzzle worsens. By conras under GHH uiliy recursive preferences produce higher crosscounry correlaions. When γ=50 he prediced cross-counry correlaions of GDP consumpion invesmen and hours are and 0.15 respecively under KPR uiliy (in he flex-wage srucure); see Col. (3). The corresponding prediced correlaions under GHH uiliy are and 0.62 respecively (Col. (6)). In he flex-wage GHH model varian wih high risk aversion (γ=50) he prediced crosscounry correlaion of GDP remains hus below he empirical correlaion (0.45) bu he prediced cross-counry correlaions of consumpion invesmen and hours exceed he empirical correlaions. The dynamic responses o a one-sandard Home produciviy innovaion (0.78%) repored in Table 3 (Panel (a)) help o undersand hese properies if he flex-wage model. The Home produciviy shock riggers a persisen rise in Home GDP consumpion and invesmen; i also deerioraes he Home erms of rade and depreciaes he Home real exchange rae. Under ime-separable preferences (γ=1/ies) he erms of rade (and real exchange rae) response is modes and Home ne expors fall persisenly (see Cols. (9) and (10) of Panels (a1) and (a3)). Home ne foreign asses (he presen value of Home ne impors) increase hus on impac and remain persisenly above heir unshocked pah (Col. (11)). Under ime-separable preferences he Home counry receives hus a wealh ransfer from he Foreign counry in response o he posiive Home produciviy shock. Home hours worked rise he rise is more persisen under GHH uiliy han under KPR uiliy. Under ime-separable preferences (KPR and GHH) Foreign consumpion falls iniially because of he appreciaion of he Foreign real exchange rae; Foreign hours and GDP rise very slighly which reflecs he modes improvemen in he Foreign erms of rade. 18 Tha mued Foreign response explains he low prediced cross-counry correlaions generaed by he flex-wage model varians wih ime-separable preferences. 18 The Home produciviy increase raises Home hours. Under KPR uiliy (wih <1) a rise in hours reduces he marginal (period) uiliy of consumpion while he opposie is he case under GHH. This helps o 15

16 The effec of he Home produciviy increase on Foreign real aciviy changes when recursive preferences (γ>1/ies) are assumed. The produciviy shock raises Home lifeime uiliy. When γ>1/ies his lowers he Home counry s IMRS (beween he period preceding he shock and he dae of he shock); see (4). Foreign life-ime uiliy rises less because of consumpion home bias and hence he relaive Home/Foreign IMRS falls. Efficien risk sharing wih recursive preferences hen implies ha Home consumpion rises less han under ime-separable preferences while Foreign consumpion rises more. 19 Also he Home real exchange rae depreciaes more srongly and hus he Home erms of rade deeriorae more sharply. (Recall ha he gross rae of appreciaion of he Home real exchange rae is equaed in equilibrium o he relaive Home/Foreign IMRS; see (5)). For example under GHH uiliy he Home real exchange rae depreciaes by 0.99% on impac wih recursive preferences (γ=50) compared o a 0.010% depreciaion wih ime-separable preferences (he corresponding changes of he Home erms of rade are -1.23% and % respecively). The greaer deerioraion of he Home erms of rade (wih recursive preferences) dampens he rise in Home invesmen induced by he Home produciviy shock and i srenghens he rise in Foreign invesmen. The more mued rise in Home consumpion and invesmen under recursive preferences implies ha Home ne expors rise persisenly in response o he Home produciviy increase. Thus Home ne foreign asses fall on impac. This shows ha efficien risk sharing wih recursive preferences implies ha he Home household makes a wealh ransfer o he Foreign household. This ransfer conribues o he sronger depreciaion of he Home real exchange rae. The sronger rise in Foreign consumpion under recursive preferences explains why in he flex-wage srucure Foreign hours worked rise less when households have KPR period uiliy (negaive wealh effec on labor supply). This is why in a flex-wage world wih KPR uiliy he assumpion of recursive preferences lowers he prediced cross-counry correlaions of hours and oupu (as discussed above). By conras under undersand why Home consumpion rises less and he Home real exchange rae depreciaes more wih KPR uiliy han wih GHH uiliy. 19 Wih recursive preferences and KPR period uiliy Home consumpion acually falls on impac and hus consumpion is counercyclical as menioned above (wih GHH uiliy Home consumpion rises on impac). 16

17 GHH uiliy (zero wealh effec on labor supply) Foreign hours and GDP rise more srongly when recursive preferences are assumed (compared o ime-separable preferences)--he sronger improvemen in he Foreign erms of rade under recursive preferences implies a sronger rise in Foreign hours due o a sronger posiive subsiuion effec on labor supply as well as a sronger rise in Foreign labor demand. This highlighs ha recursive preferences and a weak wealh effecs on labor are joinly needed for generaing synchronized responses of Home and Foreign real aciviy o counry-specific produciviy shocks Predeermined-wage model varians (Table 2 Cols. (7)-(12); Table 3 Panel (b)) When he consumpion wage rae is se one period in advance hen a posiive innovaion o Home produciviy induces on impac a sronger rise in Home labor hours GDP and invesmen han in he flex-wage model. This holds for all preferences specificaions and is due o he fac ha in he period of he shock workers are off heir labor supply schedule and hours worked are solely demand-deermined. However afer one period workers are again on heir labor supply schedule and responses o he shock are similar o he ones prediced by he flex-wage model. 20 The impac effec of a produciviy shock on he real exchange rae remain similar o he effec in he flex-wage world; hus he Home real exchange rae (and erms of rade) depreciaion is again much sronger under recursive preferences han under ime-separable preferences (see Table 3 Panel (b)). Imporanly he recursive-preferences model varians wih a predeermined wage rae predics ha he Home produciviy shock riggers a srong iniial rise in Foreign hours worked and GDP (see Table 3 Panels (b2)(b4)). Wih risk aversion γ=50 a one-sandard deviaion innovaion o Home produciviy raises Home and Foreign GDP by abou 1.2% and 0.2% respecively on impac under boh KPR and GHH period uiliy. Inuiively he sizable Foreign erms of rade improvemen under recursive preferences booss Foreign firms labor demand which raises Foreign hours worked and GDP on impac 20 The sronger shor-run rise in Home GDP explains why he prediced sandard deviaion of oupu (abou 1.4%) is higher han in he flex-wage srucures. Also he prediced relaive sandard deviaion of hours worked is now slighly larger han he empirical relaive sandard deviaion (by conras he flex-wage model varians yields a relaive volailiy of hours ha is slighly below he empirical relaive volailiy). 17

18 a he predeermined consumpion wage rae. 21 The KPR and GHH predeermined-wage model varians wih recursive preferences and high risk aversion (γ=50) mach closely he empirical cross-counry GDP correlaions (0.45). These model varians also generae sizable prediced cross-counry correlaions of consumpion invesmen and hours worked (in he range ). By conras under ime-separable preferences he assumpion of a predeermined wage rae does no raise he cross-counry GDP correlaion (compared o he flex-wages srucure) as he erms of rade response o produciviy shocks remains mued. This confirms ha recursive preferences and a weak wealh effecs on labor are joinly necessary for inernaional business cycle synchronizaion in response o produciviy shocks. 5. Conclusion This paper has shown ha a simple wo-counry business cycle model can generae sizable cross-counry correlaions of real aciviy if wo key assumpions are made: (i) households have recursive preferences; (ii) he wealh effec on labor supply is mued. Wih recursive preferences a persisen produciviy (and GDP) increase in a given counry riggers a srong improvemen of he foreign counry s erms of rade. This induces a rise in foreign hours worked and GDP when he wealh effec on he foreign labor supply is weak. In he model here counry-specific produciviy shocks can hus generae highly correlaed domesic and foreign business cycles and a volaile real exchange rae. 21 Wih wage flexibiliy he rise in Foreign labor demand increases he Foreign wage rae which dampens he rise in hours worked. When he wage rae is predeermined he labor inpu rises more srongly as he wage rae does no increase immediaely. 18

19 References Adjemian Séphane Houan Basan Frédéric Karamé Michel Juillard Junior Maih Ferha Mihoub George Perendia Johannes Pfeifer Marco Rao and Sébasien Villemo Dynare: Reference Manual Version CEPREMAP Paris. Backus David Parick Kehoe and Finn Kydland Inernaional Real Business Cycles. Journal of Poliical Economy Backus David and Gregor Smih Consumpion and Real Exchange Raes in Dynamic Economies wih Non-raded Goods. Journal of Inernaional Economics Backus David Parick Kehoe and Finn Kydland Dynamics of he Trade Balance and he Terms of Trade: The J-Curve? American Economic Review Backus David Chase Coleman Axelle Ferriere and Spencer Lyon Risk and Risksharing in Two-Counry Models. Journal of Economic Dynamics and Conrol 72. Benigno Gianluca Pierpaolo Benigno and Salvaore Nisicò Risk Moneary Policy and he Exchange Rae. NBER Macroeconomics Annual Volume Blanchard Olivier and Jordi Gal Real Wage Rigidiies and he New Keynesian Model. Journal of Money Credi and Banking 39(S1) Canor Richard and Nelson Mark The Inernaional Transmission of Real Business Cycles. Inernaional Economic Review Caporale Guglielmo Maria Michael Donadelli and Alessia Varan Inernaional Capial Markes Srucure Preferences and Puzzles: The US-China Case. CESifo Working Paper Colacio Riccardo and Mariano Croce Risks for he Long Run and he Real Exchange Rae. Journal of Poliical Economy Colacio Riccardo and Mariano Croce Inernaional Asse Pricing wih Recursive Preferences. Journal of Finance Colacio Riccardo Mariano Croce Seven Ho and Philip Howard BKK he EZ Way. Working Paper Universiy of Norh Carolina. Correia Isabel and Sergio Rebelo Business Cycles in Small Open Economies. European Economic Review

20 Crucin M A wo-counry real business cycle model. Working Paper Universiy of Rocheser. Dellas Harris A Real Model of he World Business Cycle. Journal of Inernaional Money and Finance Devereux Michael B. Alan Gregory and Gregor Smih Realisic Cross-Counry Consumpion Correlaions in a Two-Counry Equilibrium Business Cycle Model. Journal of Inernaional Money and Finance Epsein Larry and Sanley Zin Subsiuion Risk Aversion and he Temporal Behavior of Consumpion and Asse Reurns: A Theoreical Framework. Economerica Gourio François Michael Siemer and Adrien Verdelhan Inernaional Risk Cycles. Journal of Inernaional Economics Greenwood Jeffrey Zvi Hercowiz and Gregory Huffman Invesmen Capaciy Uilizaion and he Real Business Cycle Hansen Lars Peer and Ravi Jagannahan Implicaions of Securiy Marke Daa for Models of Dynamic Economies. Journal of Poliical Economy Heahcoe Jonahan and Fabrizio Perr Financial Globalizaion and Real Regionalizaion. Journal of Economic Theory Jaimovich Nir and Sergio Rebelo News and Business Cycles in Open Economies. Journal of Money Credi and Banking King Rober Charles Plosser and Sergio Rebelo Producion Growh and Business Cycles: I. The Basic Neoclassical Model. Journal of Moneary Economics Kollmann Rober Essays on Inernaional Business Cycles. PhD Disseraion Economics Deparmen Universiy of Chicago. Kollmann Rober Consumpion Real Exchange Raes and he Srucure of Inernaional Asse Markes. Journal of Inernaional Money and Finance Kollmann Rober Incomplee Asse Markes and he Cross-Counry Consumpion Correlaion Puzzle. Journal of Economic Dynamics and Conrol Kollmann Rober EZW in a World Economy. Working Paper ECARES Universié Libre de Bruxelles. 20

21 Kollmann Rober Exchange Rae Dynamics wih Long-Run Risk and Recursive Preferences. Open Economies Review Kollmann Rober Inernaional Business Cycles and Risk Sharing wih Uncerainy Shocks and Recursive Preferences. Journal of Economic Dynamics and Conrol Kollmann Rober wih Bearice Paaracchia Rafal Raciborsk Marco Rao Werner Roeger and Lukas Vogel The Pos-Crisis Slump in he Euro Area and he US: Evidence from an Esimaed Three-Region DSGE Model. European Economic Review Lewis Karen and Edih Liu Evaluaing Inernaional Consumpion Risk Sharing Gains: An Asse Reurn View. Journal of Moneary Economics Mumaz Haroon and Konsaninos Theodoridis Common and Counry Specific Economic Uncerainy. Working Paper 752 Queen Mary College London. Ohanian Lee and Andrea Raffo Aggregae Hours Worked in OECD Counries: New Measuremen and Implicaions for Business Cycles. Journal of Moneary Economics Ohanian Lee and Andrea Raffo Updaed daase ( ) on Aggregae Hours Worked in OECD Counries (posed on A. Raffo s web page). Raffo Andrea Technology Shocks: Novel Implicaions for Inernaional Business Cycles. Federal Reserve Board Inernaional Finance Discussion Paper 992. Rudebusch Glenn and Eric Swanson The Bond Premium in a DSGE Model wih Long-Run Real and Nominal Risks. American Economic Journal: Macroeconomics Sauze Maxime Grea Rerenchmen Financial Conagion and Inernaional Risk- Sharing. Working Paper Sciences Po Paris. Swanson Eric A Macroeconomic Model of Equiies and Real Nominal and Defaulable Deb. Working Paper UC Irvine. Trevoll Håkon Real Exchange Rae Variabiliy in a Two-Counry Business Cycle Model. Working Paper BI Norwegian Business School. Weil Philippe The Equiy Premium Puzzle and he Risk-Free Rae Puzzle. Journal of Moneary Economics

22 Weil Philippe Nonexpeced Uiliy in Macroeconomics Quarerly Journal of Economics

23 Table 1. Hisorical saisics ( ) US ROW Sandard deviaions (in %) GDP Sandard deviaions relaive o GDP Consumpion Invesmen Hours worked Ne expors/gdp Real exchange rae 3.03 n.a. Correlaions wih domesic GDP Consumpion Invesmen Hours worked Ne expors/gdp Real exchange rae n.a. Cross-counry correlaions GDP 0.45 Consumpion 0.35 Invesmen 0.34 Hours worked 0.43 Noe: Empirical saisics (1973q1-2013q4) are shown for quarerly macroeconomic variables in he US and in an aggregae of 13 oher OECD economies ( ROW ); see ex for lis of counries. The saisics perain o firs differenced quarerly daa. Consumpion is he sum of privae and governmen consumpion. Invesmen is gross invesmen (privae and public). GDP consumpion invesmen hours worked and he real exchange rae are logged before firs differencing. ROW aggregaes of GDP consumpion invesmen and hours worked are GDP-weighed Törnqvis indices of variables in individual ROW counries. ROW ne expors/gdp is a GDP-weighed average of NX/GDP in individual counries. The GDP weighs (used for he consrucion of ROW aggregaes) are smoohed GDP shares in aggregae ROW GDP (see main ex). The real exchange rae is he US (rade weighed) real effecive exchange rae (CPI based). A rise in RER represens an appreciaion. Due o limied daa availabiliy saisics for he real effecive exchange rae are only shown for he US. Daa sources Hours worked: US Bureau of Labor Saisics; Ohanian and Raffo ( ). All oher daa are from he OECD saisics daabase. 23

24 Table 2. Prediced momens: role of flexible & predeermined wage KPR & GHH uiliy risk aversion coefficien (γ). Flexible wage raes Predeermined wage raes KPR uiliy GHH uiliy KPR uiliy GHH uiliy γ=1/ies γ=10 γ=50 γ=1/ies γ=10 γ=50 γ=1/ies γ=10 γ=50 γ=1/ies γ=10 γ=50 Daa (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) Sandard deviaions (in %) Y Sandard deviaions relaive o GDP C I L NX RER Correlaions wih domesic GDP C I L NX RER Cross-counry correlaions Y C I L Hansen-Jagannahan bound Noe: This Table repors prediced momens generaed by model varians wih flexible wage raes (Cols. (1)- (6)) and by model varians wih predeermined consumpion wage rae (Cols. (7)-(12)). Cols. (1)-(3) and (7)- (9) assume a period uiliy funcion of he King Plosser and Rebelo (1988) [KPR] ype while Cols. (4)-(6) and (10)-(12) assume a period uiliy funcion of he Greenwood Hercowiz and Huffman (1988) [GHH] ype. Cols. (1)(4)(7)(10) assume risk aversion of =1/IES(=0.66); Cols. (2)(5)(8)(11) assume risk aversion =10; Cols. (3)(6)(9)(12) assume risk aversion =50. Col. (13) shows empirical saisics for he US (from Table 1). Variables are lised in he lef-mos column. Saisics for GDP (Y) consumpion (C) invesmen (I) hours worked (L) and he real exchange rae (RER) perain o log growh raes of hese variables. Saisics for ne expors (NX) perain o he firs difference of he ne expors/gdp raio. A rise in RER represens an appreciaion. The Hansen-Jagannahan bound is defined as he raio of he uncondiional sandard deviaion of he ineremporal marginal rae of subsiuion (IMRS) divided by he uncondiional mean of he IMRS. The Table repors simulaed momens. For each model varian a simulaion run of periods was generaed (iniialized a he deerminisic seady sae); he firs 5000 periods were discarded (o reduce influence of iniial condiions); repored momens were compued using he remaining periods. Averaging momens across repeaed shorer simulaion runs (e.g. of lengh 164 periods he number of periods in he hisorical sample) produces resuls close o he figures repored in he Table. 24

25 Table 3. Dynamic responses o a Home counry produciviy innovaion (1 sandard dev.) Horizon Y H Y F C H C F I H I F L H L F RER H NX H NFA H (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (a) Flexible wage rae (a1) KPR uiliy; risk aversion =1/IES (a2) KPR uiliy; risk aversion = (a3) GHH uiliy; risk aversion =1/IES (a4) GHH uiliy; risk aversion = (b) Predeermined wage rae (b1) KPR uiliy; risk aversion =1/IES (b2) KPR uiliy; risk aversion = (b3) GHH uiliy; risk aversion =1/IES (b4) GHH uiliy; risk aversion = Noe: The Table shows effec of an exogenous one-ime innovaion (1 sd 0.78%) o Home produciviy on seleced variables afer 0 4 and 50 quarers (see lef-mos Column labeled Horizon ). Cols. (1)-(8) show responses of Home and Foreign GDP (Y) consumpion (C) invesmen (I) hours worked (L). Cols. (9)-(11) show responses of he Home real exchange rae (RER) ne expors (NX) and ne foreign asses (NFA). A rise in RER is an appreciaion. Ne expors and ne foreign asses are normalized by quarerly Home GDP. Responses of GDP consumpion invesmen and hours are expressed as % deviaions from unshocked pahs. Responses of ne expors and ne foreign asses (normalized by GDP) are expressed as percenage poin differences from unshocked pahs. All predeermined sae variables are se a heir uncondiional mean in he period of he shock (=0). 25