Dynamic Small Open Economy Model. with Involuntary Unemployment

Transcription

1 Dynamic Small Open Economy Model wih Involunary Unemploymen Zuzana Janko San Francisco Sae Universiy June, 2010 Absrac I is well known ha real business cycle small open economy models rely on Greenwood, Hercowiz and Huffman (1988) preferences o mach he counercyclical rade balance observed in open economies, as well as oher second momens. In conras, sandard preferences a la King, Plosser and Rebelo (1988) are abandoned in his lieraure and are commonly labeled as ineffecive due o heir inabiliy o yield a counercyclical rade balance. In his paper, I re-examined sandard preferences in a small open economy (SOE) model calibraed o Canada. Conrary o prior claims I show ha a SOE model wih sandard preferences and involunary unemploymen wih efficien risk sharing obains a counercyclical rade balance and well maches main empirical regulariies ha emerge in open economies. JEL Classificaion: F41, E32. Keywords: small open economy, indivisible labor, rade balance, preferences. Deparmen of Economics, 1600 Holloway Ave., San Francisco, CA, USA 94132, (415) , E- mail: zjanko@sfsu.edu. I am graeful o commens by and discussions wih Jang-Ting Guo, Francisco Gonzalez, Marc-Andre Leendre, John Boyce, Gary Hansen, seminar paricipans a McMaser Universiy, he Co-Edior a CJE and wo anonymous referees. All errors and opinions are mine.

2 1. INTRODUCTION In a seminal paper, Mendoza (1991) builds a real business cycle small open economy (SOE) model ha is consisen wih main empirical business cycle regulariies of Canada. In paricular, he model correcly predics a counercyclical rade balance and a posiive correlaion beween savings and invesmen. 1 However, a number of anomalies arise, such as a low sandard deviaion of oal hours and a perfec posiive correlaion beween hours and oupu. These irregulariies emerge due o a Greenwood, Hercowiz and Huffman (1988) momenary uiliy specificaion, where he elasiciy of ineremporal subsiuion associaed wih leisure is zero. 2 Subsequenly, Correia, Neves and Rebelo (1995) and Schmi-Grohe and Uribe (2003) naurally consider he sandard preferences of King, Plosser and Rebelo (1988) o overcome he above-menioned anomalies, however hey find hese preferences o produce adverse resuls. 3 Firs, in conras o empirical open economy observaions, he correlaion beween oupu and he rade balance is srongly posiive insead of negaive. 4 Furhermore, he model undersaes volailiies of a number of real variables, including consumpion and oal hours. In ligh of hese findings, i is a common pracice in he SOE lieraure o label sandard 1 Backus e al. (1992) find ha he relaionship beween rade balance and oupu is negaive when looking a quarerly daa for 12 developed (OECD) counries. Similar resuls obain in Backus and Kehoe (1992), who look a a hundred years of annual daa for 10 developed counries, and in he empirical work of Krugman and Baldwin (1987). 2 Henceforh referred o as GHH preferences. 3 Schmi-Grohe and Uribe (2003) calibrae he model o Canadian daa, while Correia, Neven and Rebelo (1995) use daa for Porugal. 4 In he small open economy model he response of he rade balance o a posiive echnology shock depends on wo opposing effecs, a pro-invesmen effec and a pro-borrowing effec. The pro-invesmen effec implies ha individuals increase invesmen abroad due o he spread of he rise in income over fuure periods, while he pro-borrowing effec induces individuals o increase foreign borrowing o increase domesic capial sock and ake advanage of he rise in produciviy. In he GHH framework, he laer effec dominaes, leading o a counercyclical rade balance, while in he sandard preference framework, consumpion is very smooh, and hence he pro-invesmen effec dominaes, which yields a posiive correlaion beween oupu and he rade balance. 1

3 preferences as inep in maching business cycle flucuaions and o rely on GHH preferences insead. Recenly, a number of modificaions have been added o he model of Mendoza (1991). Leendre (2004) finds ha inroducing endogenous capial uilizaion improves he sandard deviaions of oupu and hours, while adding habi in consumpion improves he dynamic properies of consumpion and he rade balance. 5 Leendre and Luo (2007) show he impac of combining produciviy shocks and invesmen specific shocks. They find ha business cycle dynamics improve wih respec o oupu and he rade balance dynamics, bu a he expense of consumpion and oal hours flucuaions. Guo and Janko (2008) inroduce ineremporally non-separable labor supply and endogenous capial uilizaion and find ha he model accouns for key business cycle properies of Canadian daa. 6 However, common o all hree papers is he necessary use of GHH preferences. To dae, lile aemp has been made o model non-ghh preferences in a echnology driven SOE model. 7 In his paper, I re-examine sandard preferences of King, Plosser and Rebello (1988, henceforh KPR) in a SOE model, preferences ha incorporae a posiive wealh effec. The model is modified o include indivisible labor, following Rogerson and Wrigh (1988) and is calibraed o Canadian daa. Given his specificaion, i is shown 5 In conras o Mendoza (1991) who uses annual daa, Leendre (2004) calibraes he model o quarerly Canadian daa. In addiion, Mendoza calibraes he AR(1) echnology process by maching he volailiy of oupu in he model o he one observed in he daa, while Leendre (2004) esimaes he AR(1) process using Canadian daa. Given his parameerizaion, he finds ha a base model wihou endogenous capial uilizaion and habi in consumpion leads o a low volailiy in oupu and hours. 6 Theirs is he only model ha obains a correlaion beween oupu and hours ha closely maches he daa. All oher papers have a correlaion of 1. 7 In a recen paper Jaimovich and Rebelo (2008) consider a specificaion of preferences ha allow for a varying wealh effec in a SOE model, preferences ha nes sandard preferences of King e al. (1988) and he GHH preferences as special cases. However, he objecive of heir work is o analyze he impac of unanicipaed news abou fuure oal facor produciviy. 2

4 ha he model overcomes he claim common o he SOE lieraure ha GHH preferences are necessary for he model o be consisen wih main business cycle regulariies of open economies and ouperforms he GHH model specificaion along several dimensions. The model in his paper differs from he non-ghh model considered in Correia, Neves and Rebelo (1995) and Schmi-Grohe and Uribe (2003) in ha i assumes ha labor is indivisible. Hence, agens eiher work a fixed number of hours or hey do no work a all. This non-convexiy in preferences is eliminaed using employmen loeries as in Rogerson and Wrigh (1988). Individual agens ener a loery ha wih some posiive probabiliy deermines wheher hey work or remain unemployed. 8 Moreover, efficien risk sharing implies ha he consumpion levels of he employed and unemployed differ, ha is he employed consume more. 9 Consequenly, when he economy is hi wih a posiive echnology shock, he number of employed rises and so does heir individual consumpion level. Hence, he rise in consumpion for hose ha become employed causes a jump in aggregae consumpion. Moreover, he value of he risk aversion parameer plays an imporan role, since risk sharing implies ha he higher he value of risk aversion he greaer he consumpion of hose ha are employed. Consequenly, while individual agens smooh consumpion, aggregae consumpion is much more volaile wih involunary unemploymen. The high jump in consumpion in he presence of a posiive echnology shock ulimaely gives rise o a negaive response of he rade balance for a sufficienly high risk aversion parameer. 8 Individuals ener ino a conrac ha allows for random layoffs and he loery iself deermines wheher one is employed or is unemployed. 9 Hansen (1985) shows ha wih he use of log-log uiliy he consumpion of employed and unemployed agens is idenical. Here, he log-log uiliy case is no considered. Hence, in our model consumpion is higher for employed as compared o unemployed, which implies ha unemployed are worse off. Rogerson and Wrigh (1988) is labeled refer o he unemploymen in his model as involunary unemploymen 3

5 I is imporan o noe ha indivisible labor alone is no enough o obain a counercyclical rade balance in a SOE wih an operaing wealh effec. A sensiiviy analysis reveals ha he value of he risk aversion parameer has o be above 3 in order o obain a negaive correlaion beween oupu and he rade balance. However, even wih a lower risk aversion value, he model improves upon he divisible labor model, alhough he correlaion is sill posiive. Specifically, in he involunary unemploymen model, wih a risk aversion coefficien of 2 he correlaion beween oupu and he rade balance is 0.37, while he sandard KPR model yields a correlaion of Alhough, his is an improvemen, i does no mach he daa (= 0.29), nor is he correlaion negaive as in he basic GHH model (= 0.89). 10 However, increasing he risk aversion parameer o for example 3(4) yields a negaive correlaion of 0.20( 0.36). Thus, he indivisible labor KPR model can yield a counercyclical rade balance given reasonable parameerizaion. 11 Wih respec o oher momens, he involunary unemploymen model yields higher oupu, consumpion and labor volailiies, which rise in he risk aversion parameer. Overall, he KPR model wih indivisible labor can well mach a number of empirical regulariies ha emerge in open economies. However, as he GHH model, i fails o accoun for he correlaion of hours and consumpion wih oupu. The paper is organized as follows. The model is presened in secion 2. In secion 3 he equilibrium, he soluion mehod and he calibraion are discussed. Secion 10 These findings are based on a basic SOE model in ha i does no incorporae habi formaion, variable capial uilizaion or ineremporally non-separable labor supply. Moreover, he comparisons are made given a risk aversion parameer of 2 in all models. 11 Noe ha considering higher values of he risk aversion parameer in he sandard KPR model does no yield a negaive correlaion beween oupu and he rade balance, in fac he correlaion remains posiive and high. 4

6 4 presens quaniaive resuls ha include a sensiiviy analysis o he relaive risk aversion parameer. Secion 5 concludes he paper. 2. THE ECONOMY The economy consiss of a uni measure of idenical, infiniely-lived individuals who maximize expeced discouned lifeime uiliy E β U(c, l ) = 0, (1) where β (0,1), c is consumpion, and l is leisure. The funcional form of he momenary uiliy funcion exploied here follows King, Plosser and Rebelo (1998) and is he one considered by Correia, Neven and Rebelo (1995) and Schmi-Grohe and Uribe (2003). I is given by ω 1 ω 1 σ c l 1 U(c, l ) =, 0 < ω < 1,σ > 0, (2) 1 σ where σ is he relaive risk aversion parameer. In conras, ypical preferences uilized in he SOE lieraure are of GHH form and are given by ( l ) U c, ω 1 σ ( 1 l ) c 1 ω = 1 σ I is easy o show ha he wealh effec in (3) is zero. 12, ω > 1, σ > 0. (3) The uiliy funcion in (2) is nonseparable in consumpion and leisure, concave and wice coninuously differeniable. Agens in he economy are endowed wih one uni 12 Alhough I provide resuls for a model wih GHH preferences in secion 4 o faciliae comparisons, he reader is referred o Mendoza (1991), Correia e al. (1995), ec. for a deailed exposiion of hese preferences. 5

7 of ime ha hey allocae beween leisure and labor. In addiion, following Hansen (1985), individuals are assumed o eiher work h0 > 0 fixed hours or no a all. This indivisibiliy of labor inroduces non-convexiies in preferences. Here, employmen loeries are uilized o convexify he choice se as in Hansen (1985), Rogerson (1988) Rogerson and Wrigh (1988) and Hansen and Sargen (1988). 13 A he beginning of period individuals ener a loery ha, wih probabiliy p deermines wheher hey work and wih probabiliy 1- p remain unemployed. The loery provides a mechanism for dividing he coninuum of agens ino wo subses, one where each individual is employed (and receives an income ha allows him o consume c 1 ) and anoher where each agen is unemployed (receiving an income ha allows for he consumpion of c 2 ). 14 Agens herefore rade conracs wih he firm, a conrac ha allows for random layoffs. Prior o he draw of he loery he expeced uiliy for an individual is p u(c,1 h ) + (1 p )u(c,1) (4) Toal consumpion allocaion across boh ypes of individuals mus saisfy he feasibiliy condiion p c + (1 p )c = c. (5) 1 2 Maximizing (4) subjec o he consrain in (5) yields he risk-sharing condiion ( 1 ω)( 1 σ) 1 h0 1 ω( 1 σ) c1 = c 2, 1 (6) 13 Convexifying he se via loeries allows agens o be beer off ex ane and hus is welfare improving. Rogerson and Wrigh (1988) provide a horough welfare analysis in economies wih involunary unemploymen via indivisibiliies in labor. 14 Following Hansen (1985), one can hink of each agen drawing a realizaion of a random variable z from a uniform disribuion on [0,1]. Each individual i is hen idenified as x(i,z) according o he following rule: x (i,z) i+z if i+z 1 and x (i,z) i+z 1 if i+z > 1. If x (i,z) 1-p hen he agen is unemployed, and if x (i,z) > 1-p hen he agen is employed. 15 Subscrip 1 is used for employed workers and subscrip 2 for unemployed workers. 6

8 which saes ha employed agens consume more han unemployed agens as long as σ > Now when he economy is hi wih a posiive echnology shock, he number of employed rises and so does heir individual consumpion level, a jump from c 1 o c 2. Hence, as consumpion for hose ha become employed rises, so does aggregae consumpion. Furhermore, wih a higher value of σ a given rise in employed causes he rise in heir consumpion o be higher, hus furher increasing aggregae consumpion. In addiion, equaion (6) implies ha for σ > 1aggregae consumpion smoohing is no as prominen as individual consumpion smoohing. Consequenly, he volailiy of consumpion in he indivisible labor economy wih σ > 1 is greaer, as compared o he divisible economies of Correia, Neves, and Rebelo (1995) and Schmi-Grohe and Uribe (2003). 17 Using Eq. (6) and (5) in (4) yields, afer some algebra, he uiliy funcion of a represenaive consumer: u(c, ) γ γ { c Φ( l ) 1 } 1 1 l = (7) 1 σ 16 Wih log-log preferences as in Hansen (1985), he risk sharing condiion ogeher wih he feasibiliy condiion implies c 1 =c 2 =c, hus all agens consume he same level of consumpion. This laer specificaion is known o only slighly increase aggregae consumpion and is only considered in he sensiiviy analysis secion of his paper. See Greenwood and Huffman (1988) and Rogerson and Wrigh (1988) for a discussion of he σ > 1 case. 17 As in he sandard real business cycle lieraure, a posiive echnology shock in his model is followed by an immediae rise in oal hours worked (due here o he exensive margin). A large lieraure quesions his predicion. In paricular he work by Gali (1999), Shea (1998), Kiley (1998) and Francis and Ramey (2005), among ohers argue ha his predicion is inconsisen wih he empirical evidence, which hey argue shows echnology shocks o lead o an immediae fall in oal hours followed by a rise. Neverheless, his line of hough has come under criique as well Chrisiano e al. (2004) argue ha wha deermines wheher a posiive echnology shock has an immediae posiive or negaive impac on hours is how lowfrequency componen of hours worked is reaed; hey argue he response i posiive. Moreover, in heir (2003) paper hey show ha Canadian hours worked increase following a posiive echnology shock. Chang and Hong (2003) use disaggregaed daa and find he resuls o be mixed. Uhlig (2003) argues ha he iniial response is zero, followed by a posiive response. In ligh of he inconsisen findings I consider he proposiion of a posiive response of hours o a posiive echnology shock o be reasonable. Furhermore, relying on his proposiion allows for a comparison o oher papers in he SOE lieraure. 7

9 1 l 1 l Φ ( l ) = 1 h h h 0 0 γ γ ( ) ( ) γ γ where l =1-p h 0, γ 1 = ( 1 ω)( 1 σ ) and 2 1 ( 1 ) γ2 γ 1 γ = ω σ. Toal hours (=h ) in he economy are given by p h 0 and flucuae wih movemens in he employmen rae, p. 18 The budge consrain of he represenaive consumer is given by c + i + (1 + r )d + ψ(d d) = y + d, ψ > 0, (8) where i is invesmen and r -1 is he inernaional real ineres rae on foreign deb d. Agens are assumed o incur posiive porfolio adjusmen coss whenever foreign deb differs from is long run level d. 19 This assumpion is made for purely echnical reasons, as wihou porfolio adjusmen coss he equilibrium is nonsaionary. 20 Oupu in his economy is produced using a consan reurns o scale Cobb- Douglas producion funcion: y 1 = z k θ h θ (9) where k is capial and z represens he echnology shock. The producion funcion is increasing in boh is argumens and is wice coninuously differeniable. The echnology shock is assumed o evolve according o z z 1 = ρ + ε, (10) where he random variable ε is i.i.d. wih mean zero and a sandard deviaion of σ z. Capial sock in he economy evolves according o he following law of moion 18 Ex-pos he loery, he represenaive consumer chooses h. 19 The assumpion ha ψ>0 guaranees ha lim E d = d. j + j 20 Schmi-Grohe and Uribe (2003) consider alernaive saionariy-inducing mechanisms, such as he endogeneous discoun facor uilized by Mendoza (1991) and show he quaniaive resuls along business cycle frequencies o be insensiive o oher saionariy-inducing echniques. 8

10 ( ) 2 k = (1 δ )k + i φ k k, φ > 0, (11) where δ (0,1) represens he capial depreciaion rae. The las erm in (11) gives he capial adjusmen coss of ne invesmen. 21 The firs-order condiions of he represenaive household wih respec o h, c, k +1, and d, and he associaed ransversaliy condiions (TVC) are 1 γ 1 σ γ ( ) 1 γ λ = Φ 1 1 c : c 1 h (12) ( 1 h ) y γ1 γ γ 1 Φ : λ = c Φ( 1 h ) h 1 σ h l (13) [ ] { z θ 1 1 θ } k : λ 1+ 2 φ(k k ) = βe λ θ e k h + 1 δ + 2 φ(k k ), (14) ( ) d : λ 1 2 ψ(d d) = β 1+ r E λ, (15) + 1 TVC : lim E θ λ k 0, (16) 1 + j + j + 1+ j j where λ is he marginal uiliy of consumpion given in (12). Equaion (13) is he inraemporal condiion ha equaes he real value of he marginal produc of labor o he represenaive consumer s marginal rae of subsiuion beween consumpion and leisure and equaion (14) gives he Euler equaion for ineremporal consumpion choices. The represenaive consumer s ineremporal choices of foreign bonds are governed by (15), where he lef hand side is he benefi in uiliy erms of increasing deb by one uni, hus increasing consumpion by one uni minus he cos of adjusing deb, and he righ hand side is he cos in oday s uiliy erms of aking on his deb plus he ineres on he deb. 21 Mendoza (1991) finds ha wihou capial adjusmen coss he volailiy of invesmen is much oo high, due o he household s abiliy o borrow from abroad o finance domesic invesmen in he presence of a posiive echnology shock. 9

11 3. EQUILIBRIUM, SOLUTION METHOD AND CALIBRATION The compeiive equilibrium is a se of sochasic processes { c, h, k, y,d, } 1 + λ ha saisfy equaions (8)-(9), he law of moion for capial (11), he firs-order condiions (12) -(15) ogeher wih he produciviy disurbance (10), he iniial condiions z 0, k 0, and d -1, and he ransversaliy condiion in (16). The world ineres rae is assumed o be consan and equal o r. Finally, he model is solved using he mehod of undeermined coefficien (Campbell, 1994). The parameer values are calibraed for Canada. Following Mendoza (1991), he discoun facor β is se a and he capial s share in oal income θ is se a The depreciaion rae δ is se equal o 0.02 corresponding o an 8% annual depreciaing rae. The value of ω is se o 0.22 as in Schmi-Grohe and Uribe (2003) so ha he seady sae oal hours equal 0.2 when labor is divisible. In he involunary unemploymen model, h 0 and p are chosen, ensuring ha he seady sae level of oal hours h is again equal o 0.2, and ω is lef a The porfolio adjusmen coss parameer ψ is se o mach he volailiy of he curren accoun o oupu raio in he daa (=0.29) and he seady sae of he rade balance o oupu raio is se a The capial adjusmen coss parameer φ is se o ensure ha he volailiy of invesmen o he volailiy of oupu in he model maches he one in he daa (=2.97). Finally, he values of ρ and respecively. σ z are obained from Leendre (2004) and are se equal o and 22 The common pracice is o mach he curren accoun o oupu raio when pinning down ψ. However, in he sandard KPR model i is no possible o mach his raio, and hence he rade balance o oupu raio is mached insead. 10

12 Lasly he value of σ is chosen. The empirical lieraure esimaing he relaive risk aversion parameer yields a wide range of parameer values. For example, Hansen and Singleon (1982) argue ha σ is beween 0.35 and 1, Consaninides (1990) obains values in he range of [10,15], and Lucas (1994) finds he values o be in he midrange of [2,3], as do Consaninides, Donaldson and Mehra (2002) who obain esimaes in he range of [2,5]. 23 In addiion, in recen sudies Meyer and Meyer (2005, 2006) asser ha differences across esimaes sem from differences in oucome variable and ha he range in he esimaes is no as large as i may a firs appear. Specifically, hey consider four previous sudies and obain a comparable esimae of he relaive risk aversion for wealh, which hey find o be in beween 0.8 and In ligh of hese findings, pining down a specific value for σ is difficul. Hence, he saring poin in his paper is o follow he SOE lieraure and se he coefficien of relaive risk aversion o 2 in all models. 25 This is hen followed by a sensiiviy analysis, where-in he values in he range of [1,5] are considered QUANTITATIVE RESULTS Tables 1-3 repor second momens obained from Canadian daa, he GHH model, he sandard KPR-divisible labor model, and he KPR-indivisible labor model; all 23 Oher lieraure ha argues for a low value (less han 1) for σ includes he work of Blake (1996) who obains a value of 0.23 and Szpizo (1986) who obains values in he range of [ ]. Sudies ha yield double-digi esimaes include Obsfeld (1994) who obains he value of 18 and Kandel and Sambaugh (1991) wih 30. Lasly, for esimaes in he midrange, see also Barsky, Juser, Kimball and Shapiro (1997) who find he range of [4,8] and Zeldes (1989) who obains esimaes beween 2 and Moreover, heir findings sugges ha for consumpion, relaive risk aversion is abou 5 imes as high as he relaive risk aversion for wealh. 25 This is he value used in he work of Mendoza (1991), Leendre (2004), Guo and Janko (2009), ec. 26 This range akes ino accoun a reasonable se of values and shows he impac on he saisical momens as σ rises. 11

13 models use he value of σ=2. 27 The models are simulaed for 84 periods, he same number as in he Canadian sample, , where all series are passed hrough he Hodrick-Presco filer. 28 Saisics ha display he superscrip * and ** indicae ha a momen is no saisically differen from is simulaed counerpar a he 5% and 1% level of significance, respecively. 29 Tables 4-6 give he sensiiviy analysis resuls. Tables 1 and 4 shows he sandard deviaions, Tables 2 and 5 show he auocorrelaions, and Tables 3 and 6 give he correlaions wih oupu. Lasly, Figures 1 and 2 show he quarerly impulse response funcions of oupu, hours, consumpion, invesmen, and he rade balance o oupu raio in % erms o a 1% deviaion in he echnology shock Simulaion findings I sar by confirming he findings of Correia e al. (1995) and Schmi-Grohe and Uribe (2003), repored in column hree. Wih sandard preferences, he KPR-divisible model yields a low volailiy of consumpion as agens excessively smooh consumpion over ime. Furhermore, he volailiy of oupu and oal hours is undersaed, and he correlaion beween oupu and he rade balance is highly procyclical (=0.99). I is for hese reasons ha sandard preferences of King, Plosser and Rebelo (1988) are in general 27 Noe ha alhough he GHH model is idenical o ha of Mendoza (1991), here quarerly daa are used as compared o he annual daa used by Mendoza. 28 The daa are colleced following Leendre (2004) from he Canadian Socio-economic Informaion and Managemen (CANSIM) daa base. Oupu is he real gross domesic produc (D100126); consumpion is he personal expendiure on non-durable goods and services (D100107); invesmen includes invesmen in machinery and equipmen, non-residenial srucures, and residenial srucures (D100114). The Curren Accoun is obained by using he nominal curren accoun balance (D59832) and deflaing by he GDP deflaor (raio of nominal (D14816) o real GDP), and he rade balance is calculaed using expors (D100119) and impors for goods and services (D100122). Lasly, employmen of age 15 and above (D980595) is used o obain employmen. 29 Under he null hypohesis ha our heoreical model is rue, we examine wheher he hisorical sample saisics obained from he daa lie wihin he 95% or 99% confidence inerval based on he disribuion of 1,000 realizaions of simulaed momens. All repored momens are averages of he 1,000 realizaions. This mehod was proposed by Gregory and Smih (1991) and uilized in Leendre (2004), Leendre and Luo (2007), and Guo and Janko (2009). 30 Figure 1 repors he resuls for all hree models given σ=2 and Figure 2 gives impulse responses for σ=2,3,4 and 5. 12

14 deemed unsuiable in he SOE lieraure and abandoned in favor of he GHH preferences, which fairly well mach main empirical regulariies for Canada (see column 2). The effec of adding involunary unemploymen o he model of Correia e al. (1995) and Schmi-Grohe and Uribe (2003) is repored in he las column (KPRindivisible) of Table 1 hrough 3. When labor is indivisible, he level of employed workers increases in response o a posiive echnology shock. Specifically, Figure 1 shows ha he response of oal hours is wice as high in a model wih involunary unemploymen as compared o he model wih sandard KPR preferences. This is consisen wih he findings of Hansen (1985) and Hansen and Wrigh (1985), who find involunary unemploymen o increase he elasiciy of labor supply. Overall, he impac is a sandard deviaion in hours of 1.24% when labor is indivisible, as compared o 0.58% when i is divisible, hus leading o a beer mach he 1.25% volailiy found in he daa (see Table 1). 31 The greaer response in employmen ranslaes o a greaer response in oupu. Specifically, he volailiy of oupu in he KPR-indivisible model is 1.60%, which closely maches 1.72% found in he daa, in conras o 1.14% obained in he KPR-divisible model. 32 In addiion, Figure 1 shows he response of oupu in he involunary unemploymen economy o be qualiaively similar o ha of hours, where he persisence of boh hours and oupu are higher han in he KPR-divisible model. The impac on consumpion is similar, in ha again he volailiy rises, now from 0.43% o 0.54% when indivisible labor is added, however his rise is no enough o mach he volailiy found in he daa (=0.93%). Hence, along his dimension he GHH model does 31 Here, he KPR-indivisible model is he only model ha yields a momen ha is no saisically differen from he value found in he daa a he 5% level of significance. 32 Noe ha he value of 1.60% is no saisically differen from he 1.72% found in he daa a he 5% level. 13

15 beer, wih a sandard deviaion of 0.92%. However, in ligh of equaion (6), higher values of σ will yield higher consumpion volailiy, as shown in he sensiiviy analysis below. Nex, adding indivisible labor o he sandard KPR model drasically decreases he correlaion beween oupu and he rade balance (see Table 3). While he correlaion is sill posiive (=0.37), i is much lower han wha is found in he KPR-divisible model (=0.99). Since consumpion is no longer excessively smoohed ou wih involunary unemploymen, he response of he rade balance is sronger when he economy is subjec o a posiive produciviy shock. Specifically, Figure 1 shows ha he qualiaive response of he rade balance in he KPR-indivisible labor model more closely resembles ha in he GHH model, boh exhibiing a hump-shape response, while he response in he KPR-divisible model is minimal. Alhough overall, he correlaion is posiive given σ=2, he nex secion shows ha a slighly higher σ resuls in a counercyclical rade balance. There are a number of dimensions along which he indivisible KPR model does poorly. Firs, he correlaion beween oupu and hours remains high, as does he correlaion of consumpion and invesmen wih oupu as repored in Table 3. Second, Table 2 shows ha he auocorrelaion of he rade balance is oo high. Lasly, he auocorrelaions of oupu, hours and invesmen are oo low. Similar drawbacks persis in he GHH model as well. 4.2 Sensiiviy Analysis The effecs of alering he relaive risk aversion parameer in he KPR-indivisible model are repored in Tables 4 hrough 6 and shown in Figure 2. Wih indivisible labor, as σ rises, he volailiy of hours, oupu and consumpion rises (see Table 4). When σ=4.5 for 14

16 example, he volailiy of oupu is mached o ha found in he daa (=1.72%), he volailiy of hours is oo high (=1.42% vs. 1.25%) and he volailiy of consumpion is only slighly lower (=0.85% vs. 0.93%). Neverheless, all values of σ considered in Table 2, give rise o sandard deviaions of oupu and hours ha are no saisically differen from heir empirical counerpars a he 5% level of significance. This is an improvemen over he GHH model, where his holds only for oupu. Figure 2 shows ha he impulse responses of oupu and hours are only slighly quaniaively differen as σ rises, however he difference beween he GHH model and he KPR-indivisible model is sriking, wih hours being more responsive in he iniial period. In he case of consumpion, Figure 2 shows ha consumpion is more volaile as σ rises, wih he volailiy in he daa being mached a he 5% level of significance for value of σ greaer han 2.5. As σ rises, he raio of c 1 o c 2 increases, hence consumpion of employed increases more han ha of unemployed, hus increasing aggregae consumpion. The impac on he rade balance o oupu raio from a rise in σ is shown in he las panel of Figure 2. For a risk aversion parameer greaer han 2, he iniial response of he rade balance is negaive, as i is in he GHH model. In subsequen periods, he rade balance rises, reaching a peak in approximaely quarers, and hen falls back o zero. Noice ha he response of invesmen is very limied, hus i is he rade balance ha moves in he opposie direcion as consumpion rises. Hence, in he SOE model, separaion beween he saving-invesmen decision causes consumpion-smoohing via he rade-balance. 33 Moreover, as agens become more risk averse hey rely more on he 33 This poin is emphasized in Mendoza (1991, pp.807). The lack of a wealh effec reinforces his mechanism, as he pro-borrowing effec dominaes he pro-lending effec. However, when sandard 15

17 foreign asse, which acs as an insurance agains consumpion volailiy. However, when preferences are sandard, and consumpion smoohing operaes via he wealh effec, less consumpion-smoohing occurs via he rade balance. 34 Consequenly, as shown in Table 6, for σ = 3.5 and above he rade balance is counercyclical, wih he correlaions no being saisically differen from heir empirical counerpar a he 5% level of significance. Hence, he KPR-indivisible model can yield a counercyclical rade balance given reasonable σ parameerizaion. Lasly, a rising σ does yield a lower auocorrelaion of he rade balance, however he impac of changing σ is minimal wih respec o he auocorrelaions of oupu, consumpion, invesmen and oal hours (see Table 5). In addiion, increasing σ does no improve upon he correlaions of consumpion, invesmen, and hours wih oupu (Table 6). Clearly, while he model is able o improve upon cerain momens, he KPRindivisible model has an inabiliy o mach he daa along some dimensions, especially wih respec o he auocorrelaions and he correlaion of oupu and hours remain problemaic. 5. CONCLUSION In his paper, a small open economy model wih sandard King, Plosser and Rebello (1988) preferences is re-examined. The model is modified by incorporaing indivisible labor, specifically focusing on involunary unemploymen, in which case employed agens consume higher levels of consumpion from unemployed agens. The model is preferences of KPR are considered, he wealh effec implies he pro-lending effec dominaes and hence consumers do no make use of he rade balance for consumpion-smoohing. 34 The correlaion in he sandard KPR coninues o be high and posiive for high values of he risk aversion parameer, such as σ =

18 found o yield higher volailiy of oupu, hours, and consumpion, as well as a counercyclical rade balance given reasonable parameer values. Of course, I do find he resuls o depend on he calibraion of he risk aversion parameer. While he GHH model considered in his paper followed Mendoza (1991), a number of modificaions have been made recenly o he SOE model o improve upon his findings. Specifically, Leendre (2004) incorporaes consumpion habi and variable capial uilizaion, and Guo and Janko (2008) inroduce ineremporal labor supply ino a SOE model wih variable capial uilizaion. The impac of variable capial uilizaion in he wo papers, is a rise in volailiy of hours, oupu and consumpion. I added variable capial uilizaion (using he parameerizaion used by Guo and Janko) ino he KPRindivisible model and found i o have similar resuls. The volailiy of hours, oupu, invesmen, and consumpion increased beyond he levels found in he Canadian daa, his being due o he addiional amplificaion mechanism ha variable capial uilizaion provides. Moreover, he value of he risk aversion parameer slighly increased o 5.5 in order o obain a counercyclical rade balance as found in he daa. Again, in ligh of he findings of Leendre (2004) and Guo and Janko (2008), i is likely ha consumpion habi would reduce he volailiy of consumpion in he KPR-indivisible model, and similarly leisure habi (or labor adjusmen coss) would likely reduce he volailiy of hours and oupu. However, a deailed analysis of he role of hese addiional mechanisms is no conduced here, as he objecive of he paper is no o obain a model wih bes performing second momens relaive o he daa, bu o show ha sandard preferences can o some exen mach imporan business cycle regulariies of open economies conrary o claims made o dae. The simpliciy of he SOE model considered in his 17

19 paper allows for a clear exposiion of his finding, and hence shows ha sandard preferences may have been premaurely abandoned in he lieraure. 18

20 References Backus, D. and Kehoe, P. (1992) Inernaional evidence on he hisorical properies of business cycles American Economic Review 82, Backus, D., Kehoe, P. and Kydland, F. (1992) Inernaional real business cycles Journal of Poliical Economy 100, Barsky, R.B., Juser, F.T., Kimball, S. and Shapiro, M.D. (1997) Preference parameers and behavioral heerogeneiy: An experimenal approach in he healh and reiremen sudy, The Quarerly Journal of Economics 112, Blake, D. (1996) Efficiency, risk aversion and porfolio insurance: An analysis of financial asse porfolios held by invesors in he Unied Kingdom, Economic Journal 106, Cambell, J.Y. (1994) Inspecing he mechanism, An analyical approach o he sochasic growh model Journal of Moneary Economics 33, Chang, Y. and Hong, J.H. (2003) On he employmen effec of echnology: Evidence from U.S. manufacuring for , Richmond Fed, working paper Chrisiano, L.J., Eichenbaum, M. and Vigfusson, R. (2003) How do Canadian hours worked respond o a echnology shock? working paper. Chrisiano, L.J., Eichenbaum, M. and Vigfusson, R. (2004) Wha happens afer a echnology shock? working paper. Consaninides, G.M. (1990) Habi formaion: A resoluion of he equiy premium puzzle, Journal of Poliical Economy 98, Consaninides, G.M., Donadson, J.B. and Mehra, R. (2002) Junion can borrow: A new perspecive on he equiy premium puzzle, Quarerly Journal of Economics 117, Correia, I., Neves, J.C. and Rebelo S.T (1995) Business cycles in a small open economy European Economic Review 39, Francis, N. and Ramey, V.A Is he echnology-driven real business cycle hypohesis dead? Shocks and aggregae flucuaions revisied, Journal of Moneary Economics 52, Gali, J. (1999) Technology, employmen, and he business cycle: Do echnology shocks explain aggregae flucuaions? American Economic Review 89, Greenwood, J., Hercowiz, Z. and Huffman, G.W. (1988) Invesmen, capaciy uilizaion, and he real business cycle American Economic Review 78,

21 Greenwood, J. and Huffman, G.W. (1988) On modeling he naural rae of unemploymen wih indivisible labour Canadian Journal of Economics 21, Gregory, A.W. and Smih, G.W. (1991) Calibraion as esing: Inference in simulaing macroeconomic models Journal of Business and Economic Saisics 9, Guo, J-T. and Janko, Z. (2008) Reexaminaion of real business cycles in a small open economy manuscrip. Hansen, G.D. (1985) Indivisible labor and he business cycle Journal of Moneary Economics 16, Hansen, G.D. and Sargen T.J. (1988) Sraigh ime and overime in equilibrium Journal of Moneary Economics 21, Hansen, L.P. and Singleon, K. (1982) Generalized insrumenal variables esimaion of nonlinear raional expecaion models, Economerica 50, Jaimovich, N. and Rebelo, S. (2008) News and business cycles in open economies, Journal of Money, Credi and Banking 40, Kandel, S. and Sambaugh, R.F. (1991) Asse reurns and ineremporal preferences, Journal of Moneary Economics 27, Kiley, M. (1998) Labor produciviy in U.S. manufacuring: Does secoral conmovemen reflec echnology shocks? Mimeo, Federal Reserve Board. King, R.G., Plosser, C.I. and Rebelo, S.T. (1988) Producion, growh, and business cycles I: The basic neoclassical model Journal of Moneary Economics 21, Krugman, P. and Baldwin, R. (1987) The persisence of he U.S. rade defici Brooking Papers Economic Aciviy, Leendre, M-A. (2004) Capial uilizaion and habi formaion in a small open economy model Canadian Journal of Economics 37, Leendre, M-A. and Luo, D. (2007) Invesmen-specific shocks and exernal balances in a small open economy model Canadian Journal of Economics 40, Lucas, D. (1994) Asse pricing wih undiversifiable risk and shor sales consrains: Deepening he equiy premium puzzle, Journal of Moneary Economics 34, Mendoza, E.G. (1991) Real business cycles in a small open economy American Economic Review 81,

22 Meyer, D. and Meyer, J. (2005) Relaive Risk Aversion: Wha do we know?, The Journal of Risk and Uncerainy 31, Obsfeld, M. (1994) Risk aking, global diversificaion, and growh, American Economic Review 84, Rogerson, R. (1988) Indivisible labour, loeries and equilibrium Journal of Moneary Economics 21, Rogerson, R. and Wrigh, R. (1988) Involunary unemploymen in economies wih efficien risk sharing Journal of Moneary Economic 22, Schmi-Grohe, S. and Uribe, M. (2003) Small open economy models Journal of Inernaional Economics 61, Shea, J. (1998) Wha do echnology shocks do? NBER working paper Szpiro, George G. (1986) Measuring risk aversion: An alernaive approach Review of Economics and Saisics 68, Uhlig, H. (2003) Do echnology shocks lead o a fall in oal hours worked? Journal of he European Economic Associaion 2, Zeldes, S.P. (1989) Consumpion and liquidiy consrains: An empirical invesigaion, Journal of Poliical Economy 97,

23 FIGURE 1. Impulse Response Funcions Oupu Hours GHH KPR - Divisible KPR - Indivisible GHH KPR - Divisible KPR - Indivisible Consumpion Invesmen GHH KPR - Divisible KRP - Indivisible 4 3 GHH KPR - Divisible KPR - Indivisible Trade Balance o Oupu Raio GHH KPR - Divisible KPR - Indivisible

24 FIGURE 2. Impulse Reseponse Funcions: Sensiiviy Analysis Oupu GHH Sigma 2 Sigma 3 Sigma 4 Sigma Hours GHH Sigma 2 Sigma 3 Sigma 4 Sigma Consumpion Invesmen GHH Sigma 2 Sigma 3 Sigma 4 Sigma GHH Sigma 2 Sigma 3 Sigma 4 Sigma Trade Balance o Oupu Raio GHH Sigma 2 Sigma 3 Sigma 4 Sigma

25 TABLE 1. Sandard Deviaions Daa GHH KPR-divisible KPR-indivisible Oupu 1.72(0.19) 1.26* ** Consumpion 0.93(0.12) 0.92** relaive volailiy Invesmen 5.13(0.49) * Toal Hours 1.25( ** relaive volailiy TBY 0.87(0.09) * 0.28 CAY 0.28(0.03) 0.28* * TABLE 2. Auocorrelaions Daa GHH KPR-divisible KPR-indivisible Oupu 0.91(0.21) Consumpion 0.83(0.24) 0.69* 0.70* 0.69* Invesmen 0.88(0.18) Toal Hours 0.92(0.24) TBY 0.67(0.17) 0.68** 0.69** 0.95 CAY 0.68(0.18) 0.68** 0.69** 0.95 TABLE 3. Correlaions wih Oupu Daa GHH KPR-divisible KPR-indivisible Consumpion 0.80(0.23) Invesmen 0.77(0.21) Toal Hours 0.91(0.24) TBY -0.29(0.21) CAY -0.26(0.21) Noes for all ables: Numbers in parenheses are he Newey-Wes heeroskedasiciy and auocorrelaion consisen sandard errors of he momens. In columns 2-4, he superscrips ** and * show ha a daa momen is no saisically differen from is simulaed counerpar a he 5% and 1% level of significans, respecively. 24

26 TABLE 4. Sensiiviy Analysis - Sandard Deviaions Daa σ=1 σ=1.5 σ=2 σ=2.5 σ=3 σ=3.5 σ=4 σ=4.5 σ=5 Oupu ** 1.60** 1.60** 1.65** 1.67** 1.69** 1.70** 1.72** 1.75** Consumpion relaive volailiy Invesmen * 4.76* 4.77* 4.92** 4.99** 5.04** 5.07** 5.13** 5.22** Toal Hours ** 1.22** 1.24** 1.30** 1.34** 1.37** 1.38** 1.42** 1.45** relaive volailiy TBY CAY TABLE 5. Sensiiviy Analysis - Auocorrelaions Daa σ=1 σ=1.5 σ=2 σ=2.5 σ=3 σ=3.5 σ=4 σ=4.5 σ=5 Oupu Consumpion * 0.69* 0.69* 0.70* 0.70* 0.70* 0.70* 0.70* 0.71* Invesmen Toal Hours TBY CAY * 0.84* 0.82* TABLE 6. Sensiiviy Analysis - Correlai0ns wih Oupu Daa σ=1 σ=1.5 σ=2 σ=2.5 σ=3 σ=3.5 σ=4 σ=4.5 σ=5 Consumpion Invesmen Toal Hours TBY * -0.08** -0.20** -0.28** 0.36 CAY * -0.12** -0.23** -0.32** -0.39**