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1 DISCUSSION PAPER SERIES DP11911 EXPLAINING INTERNATIONAL BUSINESS CYCLE SYNCHRONIZATION: RECURSIVE PREFERENCES AND THE TERMS OF TRADE CHANNEL Rober Kollmann INTERNATIONAL MACROECONOMICS AND FINANCE

2 ISSN EXPLAINING INTERNATIONAL BUSINESS CYCLE SYNCHRONIZATION: RECURSIVE PREFERENCES AND THE TERMS OF TRADE CHANNEL Rober Kollmann Discussion Paper DP11911 Published 17 March 2017 Submied 17 March 2017 Cenre for Economic Policy Research 33 Grea Suon Sree, London EC1V 0DX, UK Tel: +44 (0) This Discussion Paper is issued under he auspices of he Cenre s research programme in INTERNATIONAL MACROECONOMICS AND FINANCE. Any opinions expressed here are hose of he auhor(s) and no hose of he Cenre for Economic Policy Research. Research disseminaed by CEPR may include views on policy, bu he Cenre iself akes no insiuional policy posiions. The Cenre for Economic Policy Research was esablished in 1983 as an educaional chariy, o promoe independen analysis and public discussion of open economies and he relaions among hem. I is pluralis and non-parisan, bringing economic research o bear on he analysis of medium- and long-run policy quesions. These Discussion Papers ofen represen preliminary or incomplee work, circulaed o encourage discussion and commen. Ciaion and use of such a paper should ake accoun of is provisional characer. Copyrigh: Rober Kollmann

3 Powered by TCPDF ( EXPLAINING INTERNATIONAL BUSINESS CYCLE SYNCHRONIZATION: RECURSIVE PREFERENCES AND THE TERMS OF TRADE CHANNEL Absrac The business cycles of advanced economies are synchronized. Sandard macro models fail o explain ha fac. This paper presens a simple model of a wo-counry, wo-raded good, complee-financial-markes world in which counry-specific produciviy shocks generae business cycles ha are highly correlaed inernaionally. The model assumes recursive ineremporal preferences (Epsein-Zin-Weil), and a mued response of labor hours o household wealh changes (due o Greenwood-Hercowiz-Huffman period uiliy and demanddeermined employmen under rigid wages). Recursive ineremporal preferences magnify he erms of rade response o counry-specific shocks. Hence, a produciviy (and GDP) increase in a given counry riggers a srong improvemen of he foreign counry s erms of rade, which raises foreign labor demand. Wih a mued labor wealh effec, foreign labor and GDP rise, i.e. domesic and foreign real aciviy comove posiively. JEL Classificaion: F31, F32, F36, F41, F43 Keywords: inernaional business cycle synchronizaion, recursive preferences, erms of rade, real exchange rae, wealh effec on labor supply Rober Kollmann - rober_kollmann@yahoo.com Universié Libre de Bruxelles and CEPR Acknowledgemens I hank Nelson Mark, Werner Roeger, Gauhier Vermandel, Roland Winkler and workshop paricipans a he Fed Board of Governors, Dallas Fed 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 ).

4 Explaining Inernaional Business Cycle Synchronizaion: Recursive Preferences and he Terms of Trade Channel Rober Kollmann (*) Universié Libre de Bruxelles and CEPR March 15, 2017 The business cycles of advanced economies are synchronized. Sandard macro models fail o explain ha fac. This paper presens a simple model of a wo-counry, wo-radedgood, complee-financial-markes world in which counry-specific produciviy shocks generae business cycles ha are highly correlaed inernaionally. The model assumes recursive ineremporal preferences (Epsein-Zin-Weil), and a mued response of labor hours o household wealh changes (due o Greenwood-Hercowiz-Huffman period uiliy and demand-deermined employmen under rigid wages). Recursive ineremporal preferences magnify he erms of rade response o counry-specific shocks. Hence, a produciviy (and GDP) increase in a given counry riggers a srong improvemen of he foreign counry s erms of rade, which raises foreign labor demand. Wih a mued labor wealh effec, foreign labor and GDP rise, i.e. domesic and foreign real aciviy comove posiively. Key words: inernaional business cycle synchronizaion, recursive preferences, erms of rade, real exchange rae, wealh effec on labor supply. 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 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

5 1. Inroducion Cyclical flucuaions of GDP, labor and invesmen are highly posiively correlaed across advanced economies. Sandard macroeconomic models fail o explain ha key fac--in hose models, shocks originaing in one counry have a weak effec on foreign real aciviy, and prediced cross-counry business cycle correlaions 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. (1992, 1994)). 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 inernaionally synchronized business cycles. A wo-counry world wih wo raded goods is considered. The specificaion of producion and marke srucures follows sandard Inernaional Real Business Cycle (RBC) models; see, e.g., Backus e al. (1994). 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 here is a spending bias owards he domesic raded good. Financial markes are complee, so ha consumpion risk is efficienly shared across counries. Economic flucuaions are driven by persisen exogenous produciviy shocks. The model differs from sandard open economy macro models by assuming recursive ineremporal preferences (Epsein and Zin (1989), Weil (1989, 1990)), whereas convenional inernaional macro models assume ime-separable preferences. Recursive preferences magnify he erms of rade response o counry-specific shocks. Hence, a produciviy (and GDP) increase in a given counry can rigger a srong improvemen of he foreign counry s erms of rade, which raises foreign labor demand. Wih a mued labor wealh effec, foreign labor and GDP rise, i.e. domesic and foreign real aciviy comove posiively. I show ha he srucure wih recursive preferences and a mued labor wealh effec can generae sizable cross-counry business cycle correlaions. The model can reproduce he empirical fac ha cross-counry correlaions of GDP, oal hours worked and invesmen growh raes are markedly higher han he cross-counry 1 Oher relaed Inernaional RBC models include Dellas (1986), Canor and Mark (1988), Crucini (1989), Devereux e al. (1992), Kollmann (1991,1996), and Heahcoe and Perri (2002). 2

6 correlaion of oal facor produciviy growh. The model also generaes higher, more realisic, real exchange rae volailiy han convenional macro models. To highligh he role of he labor wealh effec for cross-counry shock ransmission, I consider a period uiliy funcion à la Greenwood, Hercowiz and Huffman (1988) [GHH] ha enails a zero wealh effec on desired labor supply. By conras, he more widely used King, Plosser and Rebelo (1989) [KPR] period uiliy funcion implies a negaive response of desired labor supply o a wealh increase. I also sudy a seing in which he wage rae expressed in aggregae consumpion unis (he consumpion wage rae ) is rigid in he shor-run, and hours worked are deermined by firms labor demand, while workers can be off heir desired labor supply schedule; his also mues he (negaive) labor wealh effec, and i induces especially powerful crosscounry shock ransmission, in conjuncion wih recursive preferences. Consider he effec of a persisen exogenous produciviy increase in one of he wo counries, named Home. Tha posiive aggregae supply shock induces a persisen rise in Home GDP, hours worked, consumpion and invesmen; i lowers he relaive price of he Home oupu good (compared o he Foreign oupu good), i.e. he Home erms of rade deeriorae. Thus, he oher counry s ( Foreign ) erms of rade improve. This raises he value marginal produc of labor in he Foreign counry, relaive o he price of Foreign aggregae consumpion; hence, Foreign firms labor demand rises (a any consumpion wage rae). Under wage flexibiliy, he equilibrium Foreign consumpion wage rae increases, hus. Wih sandard period uiliy, his induces opposing subsiuion and wealh effecs on Foreign labor supply, wih he former increasing, and he laer decreasing he Foreign household s desired hours worked. The presen paper discusses models in which he couneracing labor wealh effec is mued. I show ha a se-up wih a weak labor wealh effec can generae a sizable rise in Foreign hours worked and GDP (in response o a Home produciviy increase), if he Foreign erms of rade improve srongly (as his powerfully booss Foreign labor demand). Wih complee financial markes, he (gross) rae of appreciaion of he Home real exchange rae is equaed, in equilibrium, o he raio of he Home ineremporal marginal rae of subsiuion in consumpion (IMRS) o he Foreign IMRS. Under ime separable ineremporal preferences, he real exchange rae (and erms of rade) response o a 3

7 supply shock is weak, as he shock has a mued effec on he relaive Home/Foreign IMRS (e.g., Backus e al. (1994)), and cross-counry shock ransmission is likewise weak. Recursive ineremporal preferences magnify he real exchange rae (and erms of rade) response o a counry-specific produciviy shock; wih recursive preferences, he shock can hus induce srong posiive cross-counry comovemen of real aciviy, if he labor wealh effec is mued. Under recursive ineremporal preferences, he coefficien of risk aversion (CRA) may differ from he inverse of he ineremporal elasiciy of subsiuion (IES). (By conras, CRA=1/IES holds under sandard ime-separable preferences.) Crucially, when CRA1/IES, hen a household s IMRS depends on her (fuure) lifeime uiliy. Under he common assumpion ha CRA>1/IES (e.g. Swanson (2014)), he IMRS is decreasing in (fuure) life-ime uiliy. 2 A persisen rise in Home produciviy increases Home life-ime uiliy, which lowers he Home IMRS, when CRA>1/IES. 3 This implies ha, in response o a Home produciviy increase, he Home real exchange rae depreciaes more srongly under recursive preferences han under ime-separable preferences. Efficien risk sharing under recursive preferences wih high risk aversion (CRA>1/IES) implies ha he Home household (whose relaive IMRS has dropped) makes a sizable wealh ransfer o he Foreign household (he Home ne foreign asse posiion falls, on impac). Tha risk sharing ransfer (riggered by he Home produciviy increase) booss demand for he Foreign raded good (and lowers demand for he Home raded good), which amplifies he deerioraion of he Home erms of rade and he depreciaion of he Home real exchange rae; he wealh ransfer hereby aligns he relaive Home/Foreign IMRS and he real exchange rae change. Imporanly, recursive preferences (generaing a srong erms of rade response) and a mued labor wealh effec (due o GHH period uiliy and/or consumpion wage rigidiy) are joinly needed for cross-counry business synchronizaion. In a flex-wage seing wih KPR period uiliy (negaive labor wealh effec), he assumpion of recursive preferences lowers he prediced cross-counry correlaion of labor hours and oupu (compared o ime-separable preferences), i.e. he inernaional correlaion puzzle 2 CRA>1/IES implies a preference for he early resoluion of uncerainy over fuure consumpion (Weil, 1990). 3 In response o he Home produciviy increase, Foreign life-ime uiliy rises oo, bu less han Home lifeime uiliy (due i.a. o he local spending bias); hus, he relaive Home/Foreign IMRS falls. 4

8 worsens. Inuiively, he wealh ransfer from Home o Foreign ha is riggered, under recursive preferences, by a Home produciviy increase, dampens he expansion of Foreign hours worked and oupu, when he labor wealh effec is negaive. The asse pricing lieraure has for long used models wih recursive preferences, as he separaion beween he CRA and IES parameers helps o capure he join behavior of financial reurns and consumpion (e.g., Rudebusch and Swanson (2012)). By conras, he inernaional macro lieraure has only recenly begun o sudy models wih recursive preferences. Mos open economy models wih recursive preferences assume endowmen economies; see, e.g., Kollmann (2009, 2015, 2016), Colacio and Croce (2011, 2013), Küçük (2011), Gourio e al. (2013), Caporale e al. (2014), Dou and Verdelhan (2015), Lewis and Liu (2015), Lusig and Verdelhan (2015), and Sauze (2015). Endowmen models canno endogenously explain he cross-counry correlaion of real aciviy, he focus of he presen paper. Open economy models wih recursive preferences and endogenous producion have been analyzed by Kollmann (2010), Benigno e al. (2012), Colacio e al. (2014), Mumaz and Theodoridis (2015), Backus e al. (2016) and Trevoll (2016), bu he focus of hese papers is differen. 4 Among oher differences, hose models do no feaure he posiive inernaional ransmission channel induced by a mued labor wealh effec (due especially o wage rigidiy), ha he presen paper idenifies and highlighs; hose previous models fail o generae simulaneously high cross-counry correlaions of oupu, of oal hours worked and of invesmen. The paper here is also relaed o several sudies ha have explored open economy models wih GHH period uiliy, bu wihou considering recursive ineremporal preferences or analyzing he role of he mued labor wealh effec for he cross-counry correlaion of real aciviy; e.g., Devereux e al. (1992), Correia and Rebelo (1995), Jaimovich and Rebelo (2008) and Raffo (2010). 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. 4 Kollmann (2010) and Trevoll (2016) analyze he deerminans of real exchange rae variabiliy. Benigno e al. (2012), Mumaz and Theodoridis (2015) and Backus e al. (2016) sudy he effec of volailiy shocks. Colacio e al. (2014) explore differenial effecs of permanen and ransiory produciviy shocks on inernaional capial flows. 5

9 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 he domesic firms. Labor and capial are immobile inernaionally. 0 is exogenous sochasic labor augmening produciviy in counry i. 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 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 ( P ) equals is marginal cos: 1 Pi, ( p ) ( p j, ), j where p j, is he price of inermediae good j. Inpu demands are: i j yi, (1 ) Pi, Z / pi,, y 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 i 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 6

10 RER 12 ( qi, ) ; due o home bias (1-2α>0), an improvemen of a counry s erms of rade is accompanied by an appreciaion of is real exchange rae. 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 (1989, 1990): 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 i 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 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 / i u u X and u i is he seady sae value of u ; X, 0 is a weighed geomeric 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) 7

11 wih 5 Noe ha when = and b=0 is assumed, hen 1 1 ( b/ i, ) [( Ui, / i, ) 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 Ui, 1. When >, hen an unexpeced rise in Ui, 1induces 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 Home real exchange rae (Kollmann (1991, 1995), Backus and Smih (1993)): / RER / RER. (5) H, 1 F, 1 H, 1 H, The marke value of counry i s ne foreign asses a he end of period (expressed in unis of aggregae consumpion), NFAi, 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 ) are ne k1 vk,, 1. expors a dae and i k v i, v Opimal counry i capial invesmen decisions are described by he Euler equaion MPK (1 ) Y / K where E {( p / P ) MPK 1 }, is he dae +1 physical marginal produc of capial. Le w i, denoe he wage rae, in aggregae consumpion unis (he consumpion wage rae ). Inermediae good producing firms equae he marginal produc of labor, in aggregae consumpion unis, o he consumpion wage rae: ( p / P ) MPL w, (6) where MPLi, Y / Li, is he physical marginal produc of labor. The relaive price beween counry i s oupu and aggregae consumpion is an increasing funcion of he counry s erms of rade (and hence also of is real exchange rae): pi, / Pi, ( qi, ). Thus, an (expeced) improvemen in he fuure erms of rade raises he fuure marginal produc of capial, in aggregae consumpion unis, ( pi, 1 / Pi, 1 ) MPK 1, which increases he demand 5 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. 8

12 for capial (invesmen). Similarly, a erms of rade improvemen raises he marginal produc of labor, expressed in consumpion unis, ( pi, / Pi, ) MPLi,. This increases labor demand in counry a any given consumpion wage rae w. As shown below, a posiive shock o Home produciviy improves he Foreign erms of rade. This booss Foreign labor demand. Thus, he Foreign consumpion wage rae increases, under flexibiliy of he consumpion wage rae. Wih sandard period uiliy funcions, his induces opposing subsiuion and wealh effecs on Foreign labor supply, wih he former increasing and he laer decreasing he Foreign household s desired hours worked. To highligh he role of he labor wealh effec 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]. Under KPR period uiliy, a wealh increase riggers a fall in desired labor supply. By conras, he wealh effec on labor supply is zero under GHH period uiliy. KPR period uiliy obains when ( Ci,, Li, ) C ( Li, ), wih 0, ' 0 (see (2)). 6 The model varians wih GHH period uiliy assume ( Ci,, Li, ) C X ( Li, ), wih ν>0 and, <0; X 0 is he weighed geomeric 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 period uiliy, mrs C '( Li, )/ ( Li, ) where i i 6 2 Concaviy of he KPR period uiliy funcion requires '' (2 1/ )( ') /. 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 household home producion (e.g., Rudebusch and Swanson (2012)). KPR period uiliy is consisen wih balanced growh and saionary hours when he disuiliy of work is no scaled by produciviy. 9

13 holds. Thus, under KPR uiliy, a rise in consumpion increases he marginal rae of subsiuion, which raises he household s asking wage. A shock ha raises he wage w and consumpion, hus has an ambiguous effec on desired labor supply, under KPR period uiliy. 8 Under GHH period uiliy, by conras, mrsi, X '( Li, ), i.e. he marginal rae of subsiuion does no depend on consumpion (zero labor wealh effec); given he exogenous quaniy X, an increase in he consumpion wage rae raises desired labor supply unambiguously. I compare model varians wih a flexible consumpion wage rae, in which labor demand equals he household s desired labor supply ( pi, MPLi, / Pi, wi, mrs ), o model varians wih wage rigidiy, in which he real consumpion wage rae is assumed o be se one period in advance, a he expeced fuure marginal rae of subsiuion beween consumpion and leisure: w, E 1 mrs,. Under a predeermined consumpion wage rae, i i labor hours are deermined by firms labor demand (6); hus, households can (emporarily) be off heir desired labor supply schedule ( wi, mrsi, ), which mues he (negaive) wealh effec on hours worked. 9 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: 1 ln( ) ln( ) [ln( ) ln( )], wih 0, for i=h,f 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 (labor augmening) produciviy. The model has a saionary equilibrium, in erms of he normalized variables. I solve he reformulaed model wih he 8 Holding consumpion consan, a rise in he wage rae w induces an increase in desired labor supply, as -ζ / ζ is increasing in hours worked; for a given wage rae w, a rise in consumpion lowers desired hours worked (negaive wealh effec), under KPR period uiliy. 9 Rigid-wage models usually assume ha hours are demand-deermined (e.g., Blanchard and Gali (2007), Kollmann e al. (2016)). 10

14 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 (recursive preferences); however, I also discuss a case wih γ=1/ies=0.66 (ime-separable preferences). The Frisch labor supply elasiciy is 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 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 (2012, 2014). 12 Long hisorical quarerly imes on oal 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 workers 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). 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 period uiliy, he Frisch labor supply elasiciy (LSE), evaluaed 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. 12 The 13 ROW counries are: Ausralia, Ausria, Canada, Finland, France, Germany, Ireland, Ialy, Japan, Korea, Norway, Sweden, UK. The Ohanian-Raffo quarerly labor hours daa (available unil 2013) are esimaed from ime series on employmen and hours worked per employee (ILO, OECD). 11

15 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 calibrae he parameers of he produciviy process (8) o quarerly US and ROW labor augmening produciviy series ( ). As an empirical measure of ROW aggregae produciviy, I use a GDP-weighed index of produciviy in he 13 individual ROW counries. 14 The hisorical 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 deviaion of ln( i, ) a 0.78% (for i=h,f); 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 quarerly US and ROW GDP, consumpion, gross invesmen, oal hours worked and ne expors (NX), and for he US real effecive exchange rae (CPI-based). The empirical consumpion 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 I consruc empirical log produciviy (labor augmening) for counry i as ln( ) (ln( GDP ) ln( L ) (1 ) ln( K ))/, where i is he sample average of i s wage share. The labor inpu i, i i, i i measure is oal hours worked; quarerly capial series are cubic spline inerpolaes of annual capial socks from he Penn World Table. A Törnqvis index is used o consruc aggregae ROW produciviy ( ROW, ) : 13 ln ROW, s 1 j, ln j j, where s j, is he weigh of counry j a dae, wih s j, 1. The weighs are j 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). 12

16 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, labor 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. 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 procyclical (posiively correlaed wih domesic GDP). US ne expors are counercyclical; he US real exchange rae is weakly counercyclical. Cross-counry (US-ROW) correlaions of GDP and hours worked are sizable (abou 0.45). Cross-counry correlaions of consumpion and invesmen (abou 0.35) are somewha lower. Imporanly, he cross-counry correlaions of (growh raes of) GDP, consumpion, invesmen and hours are noiceably higher han he cross-counry correlaion of produciviy growh raes (0.13). To explain he fac ha endogenous variables are more srongly correlaed across counries han he driving process, he model will have o generae posiive inernaional shock ransmission (synchronized domesic and foreign 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 firs differenced logged 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 15 ROW aggregaes for GDP, C, I and L (hours worked) are Törnqvis indices (GDP-weighed) of individual counries series. The ROW NX/GDP series is a GDP-weighed average of individual counries NX/GDP. 13

17 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 (hereafer referred o as flex-wage varians), while Cols. (7)-(12) show prediced momens generaed by model varians wih a predeermined consumpion wage rae. For each of hese model varians, I repor prediced momens generaed under KPR period uiliy (Cols. (1)-(3) and (7)-(9)) and under GHH period uiliy (Cols. (4)-(6) and (10)-(12)), and ha for hree values of he risk aversion coefficien: γ=1/ies (ime-separable preferences); γ=10 and γ=50 (recursive preferences). Hisorical US momens (from Table 1) are shown in Col. (13) of Table 2. Table 3 repor dynamic effecs of a one-sandard deviaion innovaion o Home produciviy, for flex-wage model varians (Panel (a)), and for model varians wih a predeermined consumpion wage rae (Panel (b)) Flex-wage model varians (Table 2, Cols. (1)-(6); Table 3, Panel (a)) Prediced momens Consider firs he prediced momens generaed by he flex-wage model varians. Those varians mach well he hisorical volailiy of US GDP; hey also capure he fac ha invesmen is 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 procyclical, and he real exchange rae is counercyclical. Consumpion is pro-cyclical in all model varians wih GHH period uiliy. 17 The following discussion focuses on model-prediced real exchange rae behavior and inernaional correlaions. The flex-wage model varians wih ime-separable preferences, γ=1/ies, (Table 2, Cols. (1) and (4)) show well-known shorcomings of sandard inernaional macro models (e.g., Backus e al. (1994)); in paricular, he prediced cross-counry correlaions of GDP, 16 Based on reurns daa from Ken French s daa base. 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. 17 Consumpion is counercyclical in model varians wih KPR period uiliy and recursive ineremporal preferences (see discussion below). 14

18 invesmen and hours worked are smaller han empirical cross-counry correlaions; his is he case under boh KPR and GHH period uiliy. The prediced cross-counry GDP correlaion wih γ=1/ies is 0.23 (0.14) under KPR (GHH) period uiliy, while he empirical correlaion is Furhermore, he prediced relaive sandard deviaion of he real exchange rae (0.37 [0.16] under KPR [GHH] period uiliy) is much smaller han he empirical relaive sandard deviaion (3.03). In addiion, he HJ bounds generaed by he model varians wih ime-separable preferences (=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, (Table 2, 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). The explanaion for his is ha persisen counryspecific produciviy shocks have a srong effec on (relaive) life-ime uiliy. Wih recursive preferences (1/IES), he IMRS is affeced by unexpeced changes in life-ime uiliy. This riggers srong real exchange rae responses, as he (gross) rae of appreciaion of he Home real exchange rae is equaed, in equilibrium, o he raio of he Home IMRS o he Foreign IMRS (see equaions (4),(5)). The greaer he risk aversion coefficien, he greaer he 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. In he flex-wage seing, he effec of recursive ineremporal preferences on prediced cross-counry correlaions hinges on he funcional form of period uiliy. Wih KPR period uiliy, he assumpion of recursive preferences lowers he prediced crosscounry correlaions of labor hours and oupu (compared o he correlaions under imeseparable preferences), i.e. he inernaional correlaion puzzle worsens. By conras, under GHH period uiliy, he assumpion of recursive preferences increases he prediced cross-counry correlaions (compared o he correlaions under ime-separable preferences). In he flex-wage model varian wih KPR period uiliy and recursive preferences (γ=50), he prediced cross-counry correlaions of GDP, consumpion, 15

19 invesmen and hours are 0.14, -0.02, 0.34 and 0.15, respecively (Table 2, Col. (3)). The corresponding prediced correlaions wih GHH period uiliy and recursive preferences (γ=50) are 0.35, 0.65, 0.64 and 0.62 (Table 2, Col. (6)). In he flex-wage model varian wih GHH period uiliy and recursive preferences, he prediced cross-counry correlaion of GDP remains hus below he empirical correlaion (0.45), bu he prediced cross-counry correlaions of consumpion, invesmen and hours exceed he corresponding empirical correlaions. Impulse responses The dynamic responses o a posiive one-sandard deviaion (0.78%) Home produciviy innovaion repored in Table 3 (Panel (a)) help o undersand hese properies of he flexwage model varians. The Home produciviy shock riggers a persisen rise in Home GDP, consumpion and invesmen; i deerioraes he Home erms of rade, and depreciaes he Home real exchange rae. Home hours worked rise (he rise is more persisen under GHH period uiliy han under KPR period uiliy). Under ime-separable preferences (γ=1/ies), he real exchange rae (and erms of rade) response is modes. Wih boh KPR and GHH period uiliy, Foreign labor hours, GDP and invesmen rise slighly, consisen wih he modes improvemen in he Foreign erms of rade (Table 3, Panels (a1) and (a3), Cols. (2),(8) and (9)). Tha mued response of Foreign real aciviy explains he low prediced cross-counry business cycle correlaions generaed by he flex-wage model varians wih ime-separable preferences (see above). Recursive preferences (γ>1/ies) magnify he real exchange rae response o he Home produciviy increase (see Table 3, Panels (a2) and (a4), Col. (9)). A posiive Home 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 equaion (4). (Foreign life-ime uiliy rises less, because of consumpion home bias.) Hence he Home real exchange rae depreciaes much more under recursive ineremporal preferences (wih high risk aversion) han under ime-separable preferences (in response o he Home produciviy increase). This implies ha he Home erms of rade oo deeriorae much more sharply, under recursive preferences. For example, in he flexwage srucure wih GHH period uiliy, he Home real exchange rae depreciaes by 16

20 0.99% on impac, under recursive preferences (γ=50), compared o a 0.010% depreciaion under ime-separable preferences (he corresponding changes of he Home erms of rade are -1.24% and %, respecively). Under recursive preferences, Home consumpion rises markedly less han under ime-separable preferences, while Foreign consumpion rises more han under imeseparable preferences (in response o he Home produciviy increase). 18 The greaer deerioraion of he Home erms of rade (wih recursive preferences) dampens he rise in Home invesmen, and i booss he rise in Foreign invesmen. The weakened rise in Home absorpion, under recursive preferences, implies ha Home ne expors rise persisenly, in response o he Home produciviy increase. Thus, Home ne foreign asses (he presen value of Home ne impors) fall, on impac (by abou 7% of quarerly GDP) Efficien risk sharing wih recursive preferences implies hence ha he Home household (whose relaive IMRS has dropped) makes a wealh ransfer o he Foreign household. Tha risk sharing ransfer booss demand for he Foreign raded good (and lowers demand for he Home raded good), which amplifies he depreciaion of he Home real exchange rae; he wealh ransfer hereby aligns he relaive Home/Foreign IMRS and he real exchange rae change. In a flex-wage seing wih KPR period uiliy, Foreign hours worked rise less under recursive preferences (>1/IES) han under ime-separable preferences, and may even fall (in response o he Home produciviy increase). Inuiively, he sizable wealh ransfer from Home o Foreign, ha occurs under recursive preferences, dampens he expansion of he Foreign labor supply and oupu, when he labor wealh effec is negaive. This explains why, in a flex-wage seing wih KPR period uiliy, he assumpion of recursive preferences lowers he prediced cross-counry correlaions of labor hours and oupu (compared o he correlaions under ime-separable preferences), as discussed above. By conras, in a flex-wage seing wih GHH period uiliy (zero labor wealh effec), Foreign hours and GDP rise more srongly (in response o he Home produciviy increase), when recursive preferences are assumed (compared o imeseparable preferences); his reflecs he sronger rise in Foreign labor demand (wihou 18 Wih recursive preferences and KPR period uiliy, Home consumpion acually falls on impac. This explains why consumpion is counercyclical, in ha model configuraion, as menioned above. 17

21 couneracing negaive labor supply wealh effec), due o he sronger improvemen of he Foreign erms of rade, under recursive preferences. These resuls highligh ha recursive preferences and a mued labor wealh effec are joinly needed for generaing cross-counry business cycle synchronizaion Predeermined-wage model varians (Table 2, Cols. (7)-(12); Table 3, Panel (b)) A posiive innovaion o Home produciviy induces, on impac, a sronger rise in Home labor hours, GDP and invesmen, when he consumpion wage rae is se one period in advance, han when he consumpion wage rae is flexible. This holds for all preference specificaions considered here, and is due o he fac ha hours worked are demanddeermined, in he predeermined-wage model. On impac, workers are pushed off heir desired labor supply schedule. However, one period afer he shock, workers are again on heir desired labor supply schedule; hus, shock responses afer he impac period are similar o he ones prediced by he flex-wage model. 19 Wih a predeermined consumpion wage rae, he effec of he Home produciviy increase on he real exchange rae remains similar o he effec in a flex-wage seing; hus he Home real exchange rae (and erms of rade) depreciaion riggered by he shock is again much sronger under recursive preferences (>1/IES) han under ime-separable preferences (Table 3, Panel (b), Col. (9)). Imporanly, he recursive-preferences model varians wih a predeermined consumpion wage rae predic ha a Home produciviy increase riggers a srong iniial rise in Foreign hours worked and GDP (Table 3, Panels (b2),(b4), Cols. (2) and (8)). Wih high 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 labor demand more srongly when he consumpion wage rae canno adjus, on impac. (By conras, wih wage 19 The sronger iniial rise in Home GDP, under a predeermined consumpion wage rae, explains why he prediced sandard deviaion of oupu (abou 1.4%) is higher han in a flex-wage srucure. Also, he prediced relaive sandard deviaion of hours worked is now larger han he empirical relaive sandard deviaion. By conras, he flex-wage model varians yield a relaive volailiy of hours worked ha is below empirical relaive hours volailiy. 18

22 flexibiliy, a rise in Foreign labor demand increases he Foreign consumpion wage rae, which dampens he rise in hours worked.) Under boh KPR and GHH period uiliy, he predeermined-wage model varian wih recursive preferences and high risk aversion γ=50 generae a cross-counry oupu correlaion of abou 0.5 (see Table 2, Cols. (9), (12)), which is close o he empirical cross-counry GDP correlaion, Tha model varian also generaes 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 consumpion wage rae does no raise he cross-counry GDP correlaion (compared o he flex-wage srucure), due o he mued response of he real exchange rae (and he erms of rade) o produciviy shocks, in ha seing (Table 3, Panels (b1) and (b3), Col. (9)). These findings confirm ha recursive preferences and a weak labor wealh effec are joinly needed for inernaional business cycle synchronizaion. Consumpion wage rigidiy induces especially powerful cross-counry shock ransmission, in conjuncion wih recursive preferences. 5. Conclusion This paper has presened a simple model of a world wih wo counries, wo raded goods, complee financial markes, exogenous produciviy shocks, and recursive ineremporal preferences. Recursive preferences magnify he erms of rade response o counryspecific produciviy shocks, which srenghens posiive cross-counry shock ransmission, if a mued response of labor hours o household wealh changes is assumed. The recursive-preferences model wih a mued labor wealh effec generaes crosscounry correlaions of GDP, hours worked and invesmen growh raes ha are markedly higher han he cross-counry correlaion of produciviy growh. 19

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