Real Business Cycles in a Small Open Economy with Non-Traded Goods*

Transcription

1 Real Business Cycles in a Small Open Economy wih Non-Traded Goods* Ayele Balsam and Zvi Ecksein * This research was suppored by The Pinhas Sapir Cener for Developmen a Tel Aviv Universiy. We hank Daniel Tssidon, Zvi Hercowiz, Sergiao Rebelo, Marin Eichenbaum, Lars Chrisiano, Marian Baxer, Elhanan Helpman, Benjamin Benal, Ori Levy, Eran Yashiv, Oved Yosha, and all he paricipans in he macroeconomic seminar a Tel-Aviv Universiy, for heir helpful commens. Ayele Balsam, balsam@pos.au.ac.il, Eian Berglas School of Economics, Tel Aviv Universiy. Zvi Ecksein, ecksein@pos.au.ac.il, Eian Berglas School of Economics, Tel Aviv Universiy.

2 . Inroducion The Israeli economy business cycle properies are differen from hose of mos OECD counries in four main dimensions (see, Table ). Firs, aggregae consumpion is weny percen more volaile han oupu. Second, he rade balance is much more volaile han oupu and is procyclical. Third, invesmen is almos five imes more volaile han oupu, and fourh, he auo-correlaion in oupu is low. The goal of his paper is o provide a simple exension of he real business cycle model of small open economy ha can fi hese facs. In paricular, exending he sandard model for wo secors of raded and non-raded goods and using he Israeli daa for he parameer specificaion, we can well fi he above excepional business cycle observaions. Following Tesar (993), our main deviaion from he sandard model is he CES uiliy funcion for raded and non-raded goods, which allows for a wide range of volailiy in consumpion of raded goods. The analysis sars wih a small open economy wih one raded good and endogenous labor supply as in Corria, Neves and Rebelo (995) (CNR). We show ha using his model wih he Israeli economy momen esimaors for he parameers, implies ha consumpion is exremely smooh when uiliy is Cobb-Douglas and is seveny five percen of oupu if he uiliy is as in Greenwood, Huffman and Hercowiz (988) (GHH). 2 Moreover, whenever he model generaes volaile consumpion and invesmen pahs, as observed in he daa, he balance of rade becomes couner-cyclical, which is opposed o he Israeli sylized fac. The one secor open economy model wih free borrowing and lending and a fixed ineres rae, srenghens he ex book claim on consumpion smoohness. Tha is, aggregae consumpion volailiy is lower han oupu volailiy due o he agen's desire o smooh consumpion in response o business flucuaions in oupu. 3 However, he fac ha in counries such as Japan, Unied Kingdom and Ausria consumpion volailiy is higher 2 For an explanaion of he differences in consumpion volailiy due o uiliies funcions specificaions in open small economies, see CNR (995). 3 Fridman s permanen income hypohesis, and Kydland and Presco s (982) classical paper provided he end qualiaive and quaniaive economic foundaions for he observed facs ha he U.S consumpion volailiy is abou seveny five percen of producion 2

3 han oupu volailiy (see Table ) is inconsisen wih he exbook claim. We find ha he Israeli daa shows ha consumpion of raded goods is abou hree imes more volaile han oupu while volailiy of consumpion of non-raded goods is abou wo hirds of he volailiy of oupu. This fac is a odds wih inuiion based on he one secor model of a small open economy. The puzzle ha hese observaions imply is explained in his paper by he resul ha wih he hree parameers of he CES uiliy funcion and he share of non-raded goods in governmen expendiures, one can ge almos any volailiy in consumpion, holding consan he producion side parameers. The hree uiliy funcion parameers are he level of complemenarily beween he raded goods and he non-raded goods, he level of risk aversion and he weigh of aggregae raded goods relaive o non-raded goods. The combinaion of hese parameers drasically affecs he consumer decision on shifing he raded goods consumpion in response o shock in boh secors. The main resul is ha he model fis all he main business cycle properies of he Israeli economy, described above. 4 This resul is based on empirical properies of he Israeli economy. In paricular, he daa shows ha he non-raded goods are a large fracion of aggregae consumpion, raded and non-raded goods are relaively complemen goods in consumer's preferences and he relaive risk aversion parameer is low. The model's assumpions are ha he producion shocks o he wo secors are of sandard firs order auo correlaion process wih he same variance, ha he invesmen cos of adjusmens are fied o he daa (following Baxer and Crucini (993)), and he governmen consumpion of raded and non-raded goods are a consan share of oupu. The remainder of he paper is wrien as follows. In he nex secion we presen he main business cycle facs of he Israeli economy in comparison o oher OECD counries and discuss he main facs on he Israeli aggregae ime series. In secion 3 we presen a model of small open economy wih raded and non-raded goods, and explain how i is solved and esimaed. Then we show ha using he one secor model for he Israeli economy we 4 The main deviaion of he prediced momens from he daa is ha he model predics a high volailiy in he balance of rade series relaive o wha is observed. Ye he direcion of he over predicion is consisen wih he deviaion of he model from he exising sandard models. 3

4 canno fi he main observed business cycle facs. In secion 5 we show how he esimaed model fi he volailiy momen of he Israeli economy. 2. Daa Table below provides business cycle sample momens for he Israeli economy and for seleced OECD counries. The samples range respecively, from 970. hrough and from 972. hrough The daa sources for he Israeli economy are he Bank of Israel and he Cenral Bureau Saisic (CBS). Daa for he OECD counries are from OECD`s Quarerly Naional Accoun and based on Backus, Kehoe and Kydland (995). All series are in logarihms (wih he excepion of he balance of rade (TB)) and derended wih he Hodrick Presco (H-P) filer. Several observaions can be made based on Table.. For mos counries consumpion is less volaile han oupu. For Israel i is mos sriking ha consumpion is more volaile han oupu. The sylized fac is ha consumpion variance is lower han oupu variance as i is for he average of OECD and European counries. Furhermore for all counries, including Israel, consumpion is posiively correlaed wih oupu. 2. Balance-of-rade is less volaile han oupu for all counries excep Israel. Furhermore he balance-of-rade is negaively correlaed wih oupu for all counries excep Israel. 3. For all counries invesmen is abou wo o hree imes more volaile han oupu, while for Israel invesmen i is almos five imes more volaile han oupu. Invesmen is procyclical for all counries including Israel For all economies he oupu is posiively auo-correlaed wih a correlaion coeficien ha ranges beween 0.6 o 0.9 for he OECD counries while for Israel i is much lower and is equal o The differences in relaive volailiy beween Israel and he OECD counries probably reflec differences in he covariance of he aggregae series wihin each economy. 4

5 Table Momens of Macroeconomic Variables Derended wih he Hodrick-Presco filer, OECD Economies and Israel Counry sd(x)/sd(y) Auocorr Corr wih Y C TB I Y C TB I Israel Ausralia Ausria Canada France Germany Ialy Japan Swizeland U.K U.S Europe Noes: Daa are quarerly from OECD`s Quarerly Naional Accoun 972.:990.2 (based on Backus Kehoe and Kydland (995)). The Israeli daa are from Bank of Israel and CBS 970.: All series are in logarihms (wih he excepion of he Ne Expor/GDP) and are derended wih he HP filer. Variables are defined as he following: Y, real oupu; C, real consumpion (nondurable); I real invesmen; TB, raio of ne-expor o oupu-boh in curren prices. The saisics for he Israel economy are based on GMM esimaors as described in Chrisiano and Eichenbaum (992) where he sandard errors wrien in Table 6. An explanaion for hese differences in volailiy of consumpion and invesmen series and he balance-of-rade cyclicaliy is he main subjec of his paper. Our hypohesis is ha he Israeli unique business cycle properies are due o he role of non-raded goods. In order o aggregae he daa for raded and non-raded goods, we follow Sockman and Tesar's (995) caegorizaion of goods secors (based on Kravis ec. (982)). Their classificaion includes agriculure, manufacuring, reail and ransporaion in he raded secor, and elecriciy, consrucion, privae and governmen services in he non-raded 5

6 secor (full deails on decomposiion are provided in Balsam (999)). I urns ou ha in Israel he non-raded secor is relaively large, and amouns o approximaely more han wo hirds of GDP, while under Sockman and Tesar (995) decomposiion he non-raded secor in Canada, France, Germany, Ialy, Japan, Unied Kingdom, Unied Sae is on average one half of oupu 6. Figure in Appendix A depics he raded and non-raded series for he Israeli economy. 7 Final privae consumpion is also consruced as in Sockman and Tesar, where he expenses on services are considered as non-raded goods. The share of he non-raded componen in Israel s oal consumpion equals 0.6 while in he sampled OECD counries he average share is abou 0.5. Table A (Appendix A) summarizes he relaive volailiy of he secoral momens for he Israeli economy from 97. hrough The sriking feaure of Table A is ha he volailiy of consumpion of raded goods is as almos four imes higher as ha of he non-raded goods. Furhermore, he relaive volailiy of non-raded consumpion o non-raded oupu is 0.59 where he counerpar volailiy in he raded secor is These facs show ha for he Israeli economy he opporuniy o rade across borders does no necessiae a smooh pah for he raded consumpion goods and probably oher engines conribue o hese consumpion flucuaions, whereas in his paper we ry o explain his mechanism by inroducing non-raded goods. 9 In order o compare hese facs o he OECD counries, we presen in Table Ab he volailiy of consumpion of raded and non-raded goods as compued in Sockman and Tesar (995). The saisics are based on averages of seleced OECD counries. I is observed ha he relaive volailiy in consumpion of raded and non-raded goods are almos he same, whereas in boh secors he relaive volailiy of consumpion o oupu is less han one. Furhermore, he consumpion pah of he raded goods relaive o oupu of he raded goods seems o be smooher. These facs are differen from he Israeli business cycle properies. 6 This grand value in Israel economy is mainly due o massive public and services secors. 7 The secoral daa on he Israeli ecnonmy is available on annual frequency. In order o derive quarerly series we assume ha he quarerly weigh is he same as he annual weigh. 8 The daa sar from 97 due o availabiliy, as for he classificaion of raded and non-raded goods. 9 I should be noed ha he rade defici in Israel for he examined period is abou 4 percen of oupu, where impor consiss of 39 percen of oupu. 6

7 Table A shows he cyclicle properies of hree differen measures of he real exchange rae, which is defined as he price raio beween raded o non-raded goods. 0 I urns ou ha he alernaive definiions of he real exchange rae produce differen relaive volailiy and conemporaneous correlaions wih oupu. In all cases he price raio is more volaile han oupu. In Table A2 (Appendix A) we display he conemporaneous correlaions of he aggregae series. Mos of he aggregae series exhibi posiive conemporaneous correlaions wih he excepion of he governmen expendiures, which are negaively correlaed wih mos of he oher variables. 3. The Model The economy consiss of wo compeiive firms ha produce raded goods, Y T and non-raded goods, Y NT. Labor, L, is assumed o be consan. There is a represenaive consumer who maximizes her expeced lifeime uiliy from consuming raded goods, and non-raded goods, ha is, financed by a lump sum ransfer, τ. CT C NT and a governmen who consumes non-raded goods, G NT Producion The raded goods and he non-raded goods are produced by Cobb-Douglas producion funcions ha are given by, ξ ξ ( 3. ) Y = ( A L ) K V, 0 < ξ T T T T T < α α ( 3.2) Y = ( A L ) K V 0 < α NT NT NT NT NT < 0 Specifically we compare he model o hree differen measures of he price raio. The firs mehod, which is marked in he Table as A is aken from Helpman and Drazen (987) where he raio is exraced from a general price funcion which is consisen wih he model definiions. The second mehod, which is marked in Table 7 as B is aken from Razin and Cuckerman (976) where he price raio is exraced based on CPI, according o he consumpion's classificaion. The hird mehod which is marked in Table 7 as C is aken from Meridor and Pesach (994) where he raio is calculaed according o he raio of impor prices o oupu prices, C, and he raio of expor prices o oupu prices, C2. The daa availabiliy for mehods B and C are from 98. o 997.4, where he daa availabiliy for mehod A is from 970. o 997.4, which are marked as A, where A2 represens he daa from 98. o

8 where L L T and L NT are he raded and non-raded labor inpus, respecively, such ha + L L and L is a consan. The capial sock in he wo secors is denoed by T NT = K T, for raded goods producion and K NT for he non-raded goods producion. The echnology level is given by ha, (.3) A = A = γ 3. NT T A NT, A T and is growing by a consan growh rae, γ such The echnology shocks are given by process such ha, V T and V NT which follow a sochasic AR() ρ T U ( 3.4 ) V = T ρ V e T V T T 0 T ρ NT ρ NT U ( 3.5 ) V = V V e NT NT NT 0 where 0 < ρ i < and i i = U, T, NT NT, are i.i.d. shocks wih zero mean and consan variance. Invesmen The laws of moion for invesmen, which are indusry specific (Sockman and Tesar (995)) are given by, ( 3.6) K T+ = ϑt ( IT / K T ) K T + ( δ) K T ( 3.7) K NT = ϑ NT ( I NT / K NT ) K NT + ( δ) K NT where 0 δ < +, < denoes he depreciaion rae. ( I / K ) ϑ, i = T, NT, are he adjusmen cos funcions following Hayashi (982) and Baxer and Crucini (993). Boh funcions are increasing, concave and wice coninuously differeniable. In order o impose a condiion ha here are no adjusmen coss a he seady sae, i is assumed ha ( γ + δ) = γ + δ and ` ( γ + δ) = ϑ invesmen o capial. i i i ϑ where γ + δ is he seady sae raio of 8

9 Opimizaion Firms choose Li, and i, K +, i = T, NT, o maximize heir presen value profis, where he price of raded goods and he real wage in erms of he raded goods, w, are aken as given sochasic processes and he real ineres rae is a consan ha is equal o r*. As such he opimizaion problem is, (.8) ( K,L,A ) FT T T T wlt IT 3 MAX E ( ( ) ( ) ) 0 = + + δ ϑ 0 r* qt KT KT T IT, / KT, KT, ( 3.9 ) MAX ( K,L,A ) PF NT NT NT NT wlnt INT E ( ( ) ( ) ) 0 = + + δ ϑ 0 r* qnt KNT KNT NT INT, / KNT, KNT, where P PNT / PT is he reciprocal of he real exchange rae. q NT and qt, are he Lagrange mulipliers (Tobin's q). The firs order condiions for he opimizaion problems (3.8) and (3.9) are given by, ( 3.0) I + ϑ` K T T q T = 0 I K NT ( 3.) + ϑ` q = 0 NT F NT T,+ ( 3.2) q ( + r *) = E + ( δ) T K NT, + ( 3.3) P q ( + r *) = E P + ( δ) NT T+ F K NT+ q T+ + q q T+ NT+ I ϑ T K + q T+ T+ NT+ ϑ I ϑt` K NT I K T+ T+ NT+ NT+ I K ϑ T+ T+ NT I ` K NT+ NT+ I K NT+ NT+ ( 3.4) w F = L T, T, ( 3.5) w = P F L NT, NT, 9

10 The Euler equaions (3.0)-(3.) specify he equaliy beween he shadow price of capial and he marginal cos of invesmen. The equaliy beween he shadow price of capial and is expeced marginal gain is given by he Euler equaions (3.2)-(3.3). The labor demand equaions are given by (3.4)-(3.5). Represenaive Consumer The represenaive consumer chooses consumpion, o maximize her expeced lifeime presen value of uiliy from consumpion of raded and non-raded goods, which is, ( 3.6) MAX E U( C,C ) 0 β T NT. =0 E denoes he expecaions condiional on informaion a ime period, and β is he discoun rae. The maximizaion in (3.6) is subjec o he budge consrain, expressed in erms of he raded good, ( 3.7) P C + B = P Y + Y P I I τ + B ( r* ) C T + NT + NT T NT T + where B is a financial asse ha is raded in he inernaional capial markes. The consumer opimizaion problem above can be wrien as he following Lagrangian problem, 0 ( 3.8 ) MAX E β U( C, C ) Λ C T + P C + B P T NT = ( ) 0 Y + P I + I + τ B + r * T NT T NT +, Y NT, where Λ is he lagrangian muliplier. The firs order Euler condiions of (3.8) are, (.9) U ( ) Λ 0 3 CT = (.20) U ( ) Λ P 0 3 CNT = Λ + ( 3.2) + βe ( + r *) 0 = Λ. I is assumed ha he uiliy funcion has he following analyical specificaion, 0

11 / µ ( µ ( )/ µ / µ + ( ) ( µ ) / µ v C v C ) T NT ( 3.22 ) U( CT, C NT ) =, θ where v is he relaive magniude of he raded goods in oal consumpion, θ / θ is he ineremporal rae of subsiuion and he consan relaive risk aversion, and / µ is he elasiciy of inraemporal rae of subsiuion beween he wo goods, such ha θ >, µ > 0, and if µ = hen he uiliy funcion is Cobb-Douglas. Governmen We assume ha he governmen consumes only non-raded goods. As such, each period he governmen budge consrain is given by, ( 3.23) G NT P = τ where, G NT is assumed o be deerminisic. Equilibrium Condiions The clearing markes equilibrium condiions are, ( 3.24 ) C NT + G NT + P I NT = Y NT ( 3.25 ) C T + I T + TB = Y T (.26 ) TB B B ( r *) 3 + = +, where TB is he balance of rade, which is measured as ne expor. + ( ) 0 Finally, we impose he "no-ponzi game condiion", Lim B /( + r *) +, which = rules ou he possibiliy ha he ineres rae paymens are financed wih furher borrowing, and herefore he iniial amouns of deb is never paid back. In secion 5 we relax his assumpion and assume ha he governmen also consumes raded goods.

12 Soluion The model is solved using a numerical approximaion mehod following Kydland and Presco (982) and King, Plosser and Rebelo (988). The soluion for he sochasic equilibrium is based on a log-linearizaion of he model's equaions around is non-sochasic seady sae. Specifically, we log-linearize equaions: (3.),(3.2), (3.6), (3.7), ( ), (3.7), and ( ) where he equilibrium condiions ( ) are subsiued ino he consumer budge consrain, (3.7). The soluion consiss of sochasic processes for he endogenous variables of he model condiional on he parameers and he sochasic specificaion of he echnology shocks. 2 Parameers Table 2 presens he values for he parameers of he model. These values are found by esimaing he parameers using he Israeli aggregae ime series and esimaions of parameers from oher sudies. We assumed ha he discoun rae β is equaled o The relaive risk aversion θ is se o.4 based on he esimaion by Benal and Ecksein (997). This low value is consisen wih resuls from Balsam, Kandel and Levy (998) and Levy (997). The uiliy parameer v is esimaed as 0.4, using he sample mean value of he raio of raded goods o non-raded goods of non-durable privae consumpion. The aggregae labor supply L, which is defined as he oal working ime divided by he oal ime available o he consumer, is se o be equaled o 0.6 as esimaed by Benal and Ecksein (997). The elasiciy of inraemporal subsiuion µ = is esimaed by using he Euler condiion (3.22) a he seady sae given he values of ( θ, β, γ ), and he invesmen oupu raio which is esimaed o be equaled o The growh rae parameer γ = is esimaed by equaing he seady sae growh rae of GDP per capia in he model o quarerly daa of per capia GDP growh rae. The 2 We ake ` INT ( ) ϑ as a parameer. K NT 3 The relevan Euler equaion in seady sae is, ( ) ( µ ) / = β + r* γ µ θ, where r*, which is se o be equal o 0.022, deermines he invesmen oupu raio 2

13 producion funcions labor elasiciies parameers are esimaed o equal α = 0.68, and ξ = 0.60 using he raio of nominal wage expendiure o nominal oupu in each secor (see, Balsam (2000)). The parameer VNT V T is normalized o be equal o one and is esimaed by he raio of consumpion of non-raded goods o raded goods, following Rebelo and Vegh (995). The depreciaion rae is se o δ = following Dahan and Hercowiz (998). The governmen expendiure of non-raded goods, Gn=0.24 is esimaed by he raio of he governmen expendiure on non-raded goods and oupu 4. The parameer, b, which demonsraes he foreigner deb level in seady sae, is esimaed such ha he raio of consumpion o oupu is 0.64 (see, Rebelo and Vegh'(995)). As in Baxer and Crunici (993) we se he parameer csi, (he elasiciy of he adjusmen cos funcion) o be equal o /5. Since he invesmen pah generaed by he model depends heavily on his value, In secion 6 we examine differen parameerizaion values for csi. We follow Kydland and Presco (982) and se he sochasic processes of shock o producion, ρ 2 2 NT = ρt = 0.55, σnt = σt = as observed in he daa..002, such ha he oupu persisence and is volailiy is 3

14 Parameers Table 2: Parameers Values Relaive risk aversion ( θ).4 Momenary uiliy ( v ).4 Labor supply ( L) 0.6 Growh rae ( γ).0055 Labor share, non-raded secor( α) 0.68 Labor share, raded secor ( ξ) 0.6 Level parameer, non-raded secor ( VNT ).36 Level parameer, raded secor ( VT ) Foreign deb ( b) 9 5 Depreciaion ( δ) 0.02 Governmen expendiure on non-raded goods( Gn) Elasiciy of inraemporal subsiuion ( µ ) 0.54 Time preference coefficien ( β) Adjusmen cos elasiciy ( csi) /5 Shock's Persisence ( NT,ρ T ) Shock's variance ( ) σ 2 T,σ NT 4 This raio is compued afer subracing he raded governmen expendiures from oupu and ne impor. In secion 6 we consider an elaborae environmen in which he model includes governmen expendiure on raded goods. 5 This value generaes a long run raio of foreign deb o oupu which equals o 2.4. "ד 6 This value generaes a long run raion of governmen expendiure on non-raded goods o oupu which equal o

15 4. The One Secor Model As explained in he inroducion, he one secor neo-classical model of a small open economy canno replicae he Israeli business cycle daa. Corria, Neves and Rebelo (995) (CNR) show ha using a Coub-Douglas uiliy funcion implies a miniscule relaive volailiy in consumpion pah in conjuncion wih procyclicaliy in he balance of rade series. While adoping a GHH (Greenwood, Huffman and Hercowiz (988)) uiliy funcion, which has he unique propery ha hours worked are deermined solely by wage, can generae higher volailiy in he consumpion and couner-cyclicaliy in he balance-of-rade, as i is observed in mos OECD conries. This uiliy funcion implies a differen link beween labor supply movemens and consumpion movemens, which produces higher variance in consumpion where he higher volailiy in consumpion has an impac on he balance of rade dynamics. These properies of he neo-classical open economy model are no consisen wih he business cycle properies of he Israel economy ha we presened above. Specifically, for he Israel economy he variabiliy in consumpion has o be larger han oupu and he balance of rade has o be pro-cyclical raher han couner-cyclical. In his secion, we follow CNR model and ry o find wheher i is possible, using he Israeli esimaed momens o specify a version of he model sochasic processes in order o fi he unique Israeli observed facs. As such, we modify he model presened in secion 3, o be consisen wih CNR. Boh he uiliy and he producion funcions include only one raded good and we assume ha he represenaive consumer derives uiliy from leisure such ha he labor supply is endogenous. The model's parameers are esimaed o fi he Israeli daa (see, Appendix B for deails), and Table 2 below summarizes our simulaion resuls for his one secor model. In case we assume a Cobb-Douglas uiliy funcion, where he shocks o producion sochasic process parameers are esimaed using he Solow residual (see Appendix B). In his case consumpion is exremely smooh, as a resul of he borrowing and lending opporuniies in he inernaional marke a a consan real ineres rae. Therefore, he rade balance volailiy becomes almos five imes larger han he volailiy of GDP and 5

16 he correlaion of he balance of rade wih GDP is almos one. Obviously his resul is inconsisen wih he Israeli facs, bu i is similar o he resul repored by CNR. In case 2 we assume a GHH uiliy funcion. Using his uiliy funcion wih he relevan esimaors of parameers (see Appendix B) we ge ha consumpion is more volaile and he balance of rade is couner-cyclical as repored by CNR. Furhermore, we ge low variabiliy in he balance of rade. 7 In case 3, we follow Kydland and Presco (982) and se he sochasic process of he shock o producion( ρ =. 55and σ = 0.04), such ha he oupu persisence and is volailiy is as observed in he daa. I is shown ha pro-cyclicaliy of he balance of rade can be achieved under he GHH preference assumpion. However, he invesmen pah exhibis a counerfacual smoohness. This smoohness is a direc resul of he low shock persisence, which follows he low auo-correlaion observed in oupu daa. In case 4 we follow he shock's specificaion as assumed in case 3 and se he adjusmen cos parameer (csi) in a way ha guaranees a replicaion of he relaive volailiy in he invesmen dynamics. 8 As expeced his high volailiy in he invesmen pah leads o a "pro-invesmen" dominance, which causes a couner cyclicaliy in he balance of rade and an excess volailiy in is pah. Furhermore, consumpion volailiy is lower han ha of oupu. To sum up, he above-menioned examples show he failure of he sandard small open economy model o replicae business cycle properies which exhibi high variance in consumpion and invesmen series in conjuncion wih procyclicaliy in he balance of rade. In Balsam (2000) i is shown ha his model performance canno be improved by considering a more elaborae environmen, which conains sochasic shocks o governmen expendiures or o foreign ransfers 9. These experimens provide he moivaion for deviaing from he sandard one-secor framework. 7 CNR (pages ) provide a very deailed explanaion for he funcions. 8 Specifically, we choose values for he sochasic process and he elasiciy of adjusmen cos (csi) ( ρ= 0.485, σ= 0.04 and csi= / 200) ha are consisen wih boh volailiy in oupu and in invesmen as well as wih he observed auo-correlaion of oupu. 9 As shown in CNR, in his framework governmen and foreign ransfer shocks have he same influence on he decision rules hrough he income effec. 6

17 Table 3: Simulaion Resuls, Basic Neo-Classic Model Case sd(x)/sd(y) Corr wih Y.067 C TB I C,Y TB,Y I,Y (0) 2.75 (0) 3.75 (0) 4.74 (0) 4.77 (.0).22 (.0075).3 (.005) 5.24 (.5).9 (.005).00 (.005).64 (.002) 4.78 (.4).97 (.005).99 (0).99 (0) (0).99 (0) -.7 (.06).97 (.004) -.84 (.03).97 (.007).98 (0.002).99 (.00).89 (.02) Noes: C is defined as Consumpion; TB is defined as he Balance of Trade measured as Ne-Expor; I is defined as Invesmen; Y is defined as Oupu. Case shows he simulaion resuls for he Coubb-Douglas uiliy funcion. Case 2 shows he simulaion resuls for he GHH uiliy funcion. Case 3 shows he simulaion resuls for he GHH uiliy funcion where ρ =. 55 insead of ρ =. 67 as in he previous case. This low value generaes he persisence and volailiy in he oupu series as observed in he daa. In case 4 we pine down he adjusmen cos parameer so ha invesmen volailiy is replicaed. The percen relaive sandard deviaions and correlaion wih oupu are sample means of saisics compued for each 000 simulaions. Each simulaion is 2 periods which is he same number of periods compued in he daa. The sample sandard deviaions of hese saisics are in he parenheses. Each simulaion is logged and derended as done in he daa. 5. The Two Secors Model In his secion we presen he resuls of simulaing for he wo secors model of secion 3, using he esimaed parameers presened in secion 4. I should be emphasized ha here we use he CES preferences for raded and non-raded goods where labor supply is exogenous. Table 4 presens he simulaion resuls, where he role of he non-raded goods in generaing consumpion variance is emphasized. The main resul from Table 4 is ha for he benchmark parameers of a wo-secor economy model implies ha consumpion volailiy is higher han oupu volailiy and rade balance is posiively correlaed wih oupu. Hence, he main puzzle of he Israeli excess volailiy in consumpion can be 7

18 easily explained by a wo secors model where labor supply is exogenous and he uiliy is sandard. Two parameers characerize he size of he non-raded secor in he model. One is v, which deermines he relaive imporance of he raded goods in he uiliy funcion, and he second is Gn, which is he level of governmen expendiures on non-raded goods. I can be seen from Table 4 ha he smaller is v and he bigger is Gn he consumpion pah becomes more volaile. Furhermore, under all parameerizaions he balance of rade is posiively correlaed wih oupu. 20 Noe ha he uiliy funcion becomes he same as he one-secor model when v is equal o. As v converges o (case 4 in Table 4), he business cycle momens become he same as in he one secor neo-classical model In Table 6 we show ha his procyclicaliy propery shows sensiiviy o he sochasic process specificaions and o he adjusmen cos parameers. 2 Tha is also a es for he correcness of he model's soluion. 8

19 Table 4: Basic Business Cycle Properies Case Relaive volailiy Sd (C)/Sd(Y). V=.4, Gn=.77 Bench.36 (.) 2. V=.3.52 (.07) 3. V=.5.2 (.2) 4. V= (.003) 5. Gn=0.83 (.07) 6. Gn=..03 (.09) 7. Gn=.2.52 (.3) Corr (Y,TB).94 (.0).92 (.0).98 (.003).88 (.02).73 (.05).85 (.03).96 (.008) Noes: C is defined as consumpion; TB is defined as he balance-of- rade measured as ne-expor; Cases -4 show he simulaion resuls for he role of he relaive magniude of raded goods in he uiliy funcion. Cases 5-7 show he simulaion resuls for he role of he non-raded in he public secor. The relaive sandard deviaions and correlaion wih oupu are sample means of saisics compued for each 000 simulaions. Each simulaion is 2 periods which is he same number of periods compued in he daa. The sample sandard deviaions of hese saisics are in parenheses. Each simulaion is logged and derended as done in he daa. The preference parameers are known o have an imporan role in generaing he consumpion pah. In Table 5 we examine he effecs of hese parameers on consumpion and balance-of-rade co-movemens wih oupu. As presened in Tesar (993) he bigger he elasiciy of inraemporal subsiuion beween he wo goods (measured by µ ) relaive o elasiciy of ineremporal subsiuion (measured by becomes more sensiive o changes in he iming of consumpion. / θ ), he consumer As such, he consumer is willing o change he composie of he consumpion bundle in order o spread he marginal uiliy of consumpion. In oher words, he consumpion pah becomes smooher. I urns ou ha hese parameers do have a role in shaping he dynamics, where he lower is he elasiciy of inraemporal (ineremporal) subsiuion he bigger (smaller) is he volailiy consumpion. However, in all he experimens under 9

20 any convenional parameer specificaions se, he relaive volailiy in consumpion remains relaively high. 22 Table 5: Sensiive Analysis on he Preferences Parameers Case Relaive volailiy Sd(C)/Ss(Y). µ =. 50, θ = (.0) 2. µ =. 50, θ = 2.0 (.09) 3. µ =. 50, θ = 5.53 (.04) 4. θ =.5, µ = (.0) 5. θ =.5, µ =.08 (.08) 6. θ =.5, µ = 2.8 (.05) Corr (Y,TB).94 (.0).99 (.00).97 (.006).94 (.0).97 (.006).98 (.002) Noes: C is defined as Consumpion; TB is defined as he Balance-of-Trade measured as Ne-Expor; θ, is he consan relaive risk averse (CRRA) while ( / θ ) is elasiciy of ineremporal subsiuion; µ, is elasiciy of inraemporal subsiuion. The relaive sandard deviaions and correlaion wih oupu are sample means of saisics compued for each 000 simulaions. Each simulaion is 2 periods which is he same number of periods compued in he daa. The sample sandard deviaions of hese saisics are in he parenheses. Each simulaion is logged and derended as done in he daa. In Table 6 (Appendix C) we sudy he model performance and sensiiviy for addiional momens including he relaive volailiy of invesmen and balance-of-rade, as well as he co-movemens beween oupu and consumpion, oupu and invesmen. We focus here on he sensiiviy of he momens changing he parameers for sochasic processes and he adjusmen coss. Case considers he benchmark parameerizaion and shows ha he co-movemens beween he differen aggregae variables and oupu have he same signs and relaive level as ha of he daa. However, here are wo ousanding caveas. Firs, he conemporaneous correlaions are higher han he daa. Second, he relaive volailiy of 22 Tha is he case where all oher parameers are as in benchmark. In general i is possible o find µ and θ as well as oher parameers o ge low variabiliy in consumpion. 20

21 invesmen (balance-of-rade) is relaively low (high) han he daa. Two parameers influence he invesmen dynamic, he shock's persisence, ρ, and he adjusmen cos parameers, csi. In cases 2 o 5 and 6 o 8 we explore, respecively, he sensiiviy of he resuls o hese wo parameers. We find ha he smaller (bigger) he adjusmen cos parameer (shock persisence) he more volaile he invesmen pah. As a resul, he lower is he covariance of he balance-of-rade and income (due o "pro invesmen effec" dominance). Furhermore, we find a posiive monoonic impac of he shock's persisence on he consumpion dynamics, and ha he volailiy in he balance of rade pah remains high in all cases. In case 5 we explore he effec of a posiive diffusion beween he wo shocks, which urns ou o preserve he basic characerisics of he benchmark case. In case 8 we adap he adjusmen cos parameer and he shock's persisence in a way ha guaranees ha volailiy of invesmen and oupu as well as oupu persisence prediced by he model maches he momens observed in he daa 23. I urns ou ha his specificaion increases he volailiy of consumpion and of he balance of rade, bu improves he correlaion of hese variables wih oupu as well as he correlaion of invesmen wih oupu. However, he co-movemens of invesmen and consumpion wih oupu are sill oo high, and moreover, he volailiy in he balance of rade is exaggeraed. 24 In cases 9, and 0, we use he value of he adjusmen cos parameer as in case 8 and explore he sensiiviy of he model o he variance of he shock o producion. We find ha he bigger he variance of he shock in he non-raded (raded), he larger (smaller) he volailiy of consumpion and he larger (smaller) is he procyclicaliy of he balance of rade, while he opposie occurs o he invesmen volailiy. In case we assume ha he wo shocks are posiively correlaed. This leads o a lower volailiy in consumpion, and a lower level of procyclicaliy in he balance of rade. The above cases show ha he consumpion pah is more volaile han wha is observed in he daa. This over volailiy is due o our benchmark parameerizaion in which we 23 2 In paricularly, ρ i =.475, σi = I should be noed ha hese properies also exis in he one secor model. 2

22 assume ha governmen expendiures consis of only non-raded goods. In case 2 we add he level of governmen expendiure on raded goods and fi he momens of he model. 25 I urns ou ha his case improves he closeness of he second momens prediced by he model o he daa second momens. In Table 7 we exend he analysis o he dynamics of each secor separaely as well as he dynamic of real exchange rae exraced from he price raio beween raded and non-raded goods. We compare he momens of hese variables o he momen from he Israeli daa, using he parameers of case 2 in Table 6 (Appendix C) as a benchmark. In general, we find ha he model is consisen wih he observaions ha raded goods oupu and consumpion are more volaile han non-raded oupu and consumpion. However, he relaive volailiy of raded o non-raded oupu is exaggeraed. We also find consisency wih mos signs of he conemporaneous correlaions wih wo excepions, he correlaion of raded oupu o non-raded oupu, and oupu correlaion wih he price raio. 26 I is well known ha he sandard business cycle model fails o rack he cyclicaliies of he real wage and he ineres rae. This propery exiss as well in a model of non-raded goods of Sockman and Tesar (995) and also in a wo secor model in Baxer (992). Chari, Kehoe and McGraan (998) have shown ha a model ha includes sicky prices wih cerain assumpions on preferences and moneary shocks can accoun for he persisence, volailiy and he co-movemen of he real exchange rae and oupu. However heir "preferred" model parameerizaion fails o rack he oher aggregae momens such as he conemporaneous co-movemens beween he balance of rade and oupu. 25 In his case µ = 0. 35, such ha he invesmen oupu raio is replicaed. 22

23 Table 7: Saisical Momens, Traded and Non-Traded Secors Variable Israel Daa Model Sd(P)/Sd(Y) 5.25 (4.83, 5.67) 2.89 (2.60,3.8) Sd(CT)/Sd(Y) 2.77 (2.44, 3.0) 2.36 (2.2,2.60) Sd(CNT)/Sd(Y) 0.68(.6,.74) 0.48 (.44,..52) Sd(CT)/Sd(CNT) 3.95 (3.57, 4.33) 4.88 (4.88,4.88) Sd(YT)/Sd(YNT).4 (.06,.2) 6.23 (6.3, 6.33) Corr (P,Y) 0. (.0,.2) (-.39, -.55) Corr(CNT,Y) 0.8 (.0,.27) 0.55 (.48,.62) Corr(CT,Y) 0.30 (.23,.37) 0.49 (.4,.57) Corr(CNT,CT) 0.59 (.53,.65) 0.99 (.99,.99) Corr(YNT,YT) 0.57 (.5,.63) -0.8 (-.08,.-28) AR(P) 0.75 (.7,.79) 0.25 (.6,.34) Noes: CNT and CT are defined as Consumpion of Non- Traded and Traded good respecively; P is defined as price raio beween non-raded and raded good (reciprocal of real exchange rae) which is calculaed in accordance o Drazen and Helpman (987); YNT and YT are defined as Oupu of Non-raded and Traded good respecively; Y is defined as Oupu. Numbers in daa's parenheses are GMM sandard errors, calculaed as described in Chrisiano and Eichenbaum (992). The relaive sandard deviaions and correlaions derived from he model are sample means of saisics compued for each 000 simulaions. Each simulaion is 2 periods which is he same number of periods compued in he daa. Each simulaion is logged and derended as done in he daa. 6. Concluding Remarks The main resul of his paper is ha he observed phenomenon ha volailiy of consumpion is weny percen higher han he volailiy of oupu is compaible wih a simple specificaion of a wo-secor model of a small open economy. Furhermore, using parameers ha fi he seady sae firs momens of he Israeli daa, he main second momens from he daa are close o he corresponding momens prediced by he model. We also show ha he prediced second momens are very sensiive o changes in several parameers ha are wihin he range used in he lieraure. The higher volailiy of aggregae consumpion relaive o aggregae oupu is due o he volailiy of raded consumpion bu no ha of he non-raded consumpion. This 26 The price raio is compued according o Drazen and Helpman (987). 23

24 phenomenon exiss boh in he daa and in he model (Table 7). This resul migh be a odds wih inuiion based on a one secor model version of a small open economy and hence can be viewed as surprising. Since for ha model he raded consumpion has a very low volailiy relaive o oupu. We show ha when he wo-secors economy converges o he one secor economy he volailiy in consumpion become a small fracion of oupu volailiy whereas oher parameers say he same. The puzzle ha his observaion implied is explained by he resul ha wih he hree parameers of he CES uiliy funcion and he share of non-raded goods in governmen expendiures, one can ge almos any volailiy in consumpion holding consan he producion side parameers. The join imporance of raded goods complemenarily o non-raded goods, he level of risk aversion and he relaive imporance of oal raded goods which affec he agen's decision on shifing he raded goods consumpion in response o shock in boh secors. The openness of he economy enables he represenaive consumer o reac in differen ways o shocks in raded and non-raded goods, depending on her preferences. By lending and borrowing, consumers can change drasically or moderaely heir consumpion of raded goods while non-raded goods consumpion can a mos be smoohed in response o shock in non-raded oupu. We show ha here exiss a configuraion of parameers of he model ha is compaible wih cerain facs of he Israeli economy and generae he resul ha he opimal pah for raded consumpion is almos wo and half imes more volaile han aggregae oupu as also observed in he daa. 27 Ineresingly, mos of he oher implicaions of he model wih he same parameers are also consisen wih he observed second momens of he economy. 27 The main deviaion of he prediced momens from he daa is ha he model predic a high volailiy in he balance of rade series relaive o wha observed. Ye he direcion of he over predicion is consisen wih he deviaion of he model from he exising sandard models. 24

25 7. References Backus, D., K and P.J. Kehoe and F. Kydland Inernaional Business Cycle: Theory and Evidence. In: Fronier of Business Cycle Research, Edied by Thomas F. Cooley, pp Princeon: Princeon Universiy Press. Balsam., A "The Role of he Non-Traded Goods in Affecing Business Cycle Properies of Small Open Economy". Ph.D. Disseraion Tel-Aviv Universiy. Balsam, A, S. Kandel, and O. Levy, 998. "Ex-ane Real Ineres Raes and he Non-parameric Pricing Kernel: An Applicaion o Risk Premia and Marke Expecaions", mimeo. Baxer, M, 992. "Are Consumer Durables Imporan For Business Cycles?" Rocheser Cener for Economic Research., Working Paper Series No Baxer, M., and M.Crunici. 993 Explaining Saving/Invesmen Correlaions. A.E.R 83: Benal, B., and Z. Ecksein On a Fi of a Neoclassical Model in High Inflaion: Israel Journal of Money Credi and Banking 29 (4): Chari, V.P., J. Kehoe and E. R. McGraan 996. "Sicky Price Models of he Business Cycle: Can he Conrac Muliplier Solve he Persisence Problem?". NBER Working Paper No Chrisiano, L. J. and M. Eichenbaum Curren Real Business Cycle Theory and Aggregae Labor Marke Flucuaions. A.E.R 82: Corria E., J.C. Neves., and S. Rebelo Business Cycle in a Small Open Economy. European Economic Review 39:

26 Cukerman A., and A., Razin. 976 "Inernaional Transacions - Measuremen and Policy, he Inerdependence Beween Exchange Rae Policy and Impors and Expors. Dahan., M., and Z. Herkowiz "Fiscal Policy and Saving Under Disorionary Taxaion". Journal of Moneary Economics, 42, Drazen A., and E. Helpman Sabilizaion wih Exchange Rae Managemen. Q.J.E 02: Greenwood, J., Z. Herkowiz, and G. Huffman " Invesmen, Capaciy Uilizaion and he Business Cycle". American Economic Review, Hayashi F., 982. "Tobin's Marginal q and Average q: A Neoclassical Inerpreaion". Economerica, 50. Hodrick, R. and E. Presco., 980. "Pos-war Business Cycles: An Empirical Invesigaion". Working Paper, Carnegie-Mellon Universiy. King R. G., C. I. Plosser., and S.T. Rebelo 988a. Producion Growh and Business Cycle: Technical Appendix. Working Paper, Universiy of Rocheser. King R. G., C. I. Plosser., and S.T. Rebelo 988b. Producion Growh and Business Cycle New Direcions. Journal of Moneary Economics 2: Kydland F. E., and E. C. Presco 982, Time o Build And Aggregae Flucuaion, Economerica, 50, 6 November: Levy, O., 998. "The Equiy Premium: A Puzzle? The Case of a Volaile Economy", mimeo. 26

27 Mendoza, E. G., 99. "Real Business Cycles in a Small Open Economy". American Economic Review, 8, 4, Meridor., L., S., Pesah " Real Exchange Rae in Israel Over Three Decades". Bank of Israel Research Deparmen Discussion Paper No Rebelo. S., and C.A. V`egh Real Effecs of Exchange-Rae Based Sabilizaion: An Analysis of Compeing Theories. NBER, Annual Obsfeld M., and K. Rogoff Foundaions of Inernaional Macroeconomics Ch. 2, 4. M.I.T Press. Sockman A.C., and L.L Tesar Tases and Technology in a Two Counry Model of he Business Cycle: Explaining Inernaional Comovemen. A.E.R 85: Tesar. L. L.993. "Saving, Invesmen and Inernaional Capial Flow." Journal of Inernaional Economics"

28 Appendix A Figure : The Raio of Non-Traded Oupu o Traded Oupu, Israel 97:

29 Table A: Relaive Volailiy Israeli Daa Variable Israel Daa Sd(CT)/Sd(YT) 2.45 (2.24,2.66) Sd(CT)/Sd(Y) 2.77 (2.44, 3.0) Sd(CNT)/Sd(YNT) 0.59 (.53,0.65) Sd(CNT)/Sd(Y) 0.68 (.6,.74) Sd(CT)/Sd(CNT) 3.95 (3.57, 4.33) Sd(YT)/Sd(YNT).4 (.07,.2) Sd(P)/Sd(Y). A Sd(P)/Sd(Y). A2 Sd(P)/Sd(Y). B Sd(P)/Sd(Y). C Sd(P)/Sd(Y). C2 Corr (P,Y). A Corr (P,Y). A2 Corr (P,Y). B Corr (P,Y). C Corr (P,Y). C (4.83, 5.67) 3.94 (3.53, 4.35).79 (.56, 2.02) 4.70 (4.6, 5.24) 3.0 (2.68,3.52) 0. (.0,.2) 0.44 (.36,.52) (-.098,.082) -0.9 (-.3,-.05) -0.2 (-.34,.08) Noes: CNT and CT are defined as Consumpion of Non- Traded and Traded good respecively; P is defined as price raio beween non-raded and raded good (reciprocal of real exchange rae) which is calculaed in hree differen ways (see noe 7 in secion 2); YNT and YT are defined as Oupu of Non-raded and Traded good respecively; Y is defined as Oupu. Numbers in daa's parenheses are GMM sandard errors, calculaed as described in Chrisiano and Eichenbaum (992). 29

30 Table Ab: Volailiy in Seleced OECD Counries Based on Sockman and Tesar (995) Variable Daa Sd(CT).77 (0.99, 2.54) Sd(YT) 3.45 (2.38, 4.52) Sd(CNT).78 (0.85, 2.7) Sd(YNT) 2.02 (.48, 2.56) Sd(Y) 2.53 (2.00, 3.06) The numbers are aken from Sockman and Tesar (995), where he figures in he "Daa" column are cross-counry averages of he momens. The figures in parenheses are he wo sandard deviaions range around he cross counry average; oupu sandard deviaion by secor are five counries averages (Canada, Germany, Ialy, Japan, Unied Sae), where he sample range from 970 o he las available observaion, which varies from 984 o 986 depending on he counry and he secor; consumpion sandard deviaion by secor are six counries averages which conains France o all he five menioned above. 30

31 Table A2: Conemporaneous Correlaions for he Israeli Economy CNT CT C Y G I YNT YT TB CNT CT C Y G I YNT YT TB Noes: CNT and CT are defined as Consumpion of Non- Traded and Traded good respecively where C defined as oal consumpion; YNT and YT are defined as Oupu of Non-raded and Traded good respecively; Y is defined as Oupu; G is defined as governmen expendiures ; I is defined as invesmen; TB is defined as balance of rade measure as ne-expor. The daa are from , due o daa availabiliy as for he raded and non-raded oupu series (noe ha he daa shown in secion are from ). All series are in logarihms (wih he excepion of he Ne Expor/GDP) and are derended wih he HP filer. 3

32

33 Appendix B This appendix summarizes he assumpions ha we impose on he wo secors model of secion 3 in order o be consisen wih he one secor framework of CNR (995). The economy is assumed o consis of a represenaive firm ha produces raded goods, Y T. There is a represenaive consumer who maximizes her expeced lifeime uiliy from consuming raded goods, C T and leisure L. There is a governmen who consumes raded goods, G T ha is financed by a lump sum ransfer, τ. Producion The raded goods is produced by a Cob-Douglas producion funcion ha is given by, ξ ξ ( A ) Y = ( A N ) K V 0 < ξ < T T T T where N T is labor inpu, and K T is capial sock. The echnology level is given bya T and is growing by a consan growh rae, γ such ha, ( 2 ) A = γ A. T The echnology shock is given by ha, V T which follows a sochasic AR() process such ρ ρ U ( A3 ) V = V e V 0 where 0 < ρ < <, and U is i.i.d. wih zero mean and consan variance. Invesmen The laws of moion for invesmen, is given by, ( A4) K T+ = ϑt ( IT / K T ) K T + ( δ) K T where he definiions for he parameers are as in secion 3. 33

34 Opimizaion The firm chooses N T andk T, ha maximize is presen value profi, where he opimizaion problem is, ( A5) MAX ( K, L, A ) FT T T T wnt IT E ( ( ) ( ) ) 0 = + + δ ϑ 0 r* qt KT KT T IT, / KT, KT Represenaive Consumer The represenaive consumer chooses consumpion, and leisure which maximize her expeced life ime presen value of uiliy which is, ( A6) MAX E U( C, L ) 0 β T. =0 E denoes he expecaions condiional on informaion a ime period, and β is he discoun rae. The maximizaion in A6 is subjec o he budge consrain, ( ) B = Y I τ + B ( r* ) A7, C T + + T T + where B is a financial asse ha raded in he inernaional capial markes. As in CNR we assume ha he uiliy funcion has wo of he following analyical specificaions, ( A8) Coub Douglas : U( C,! ) where N T = v v [ C ( N ) ] T θ θ 0 < v < N T = L, and v describes he relaive magniude of he consumpion goods in uiliy, and θ expresses he relaive risk aversion. θ > v ( A9) GHH: U( C, N ) = [ C ψa N ] v >, ψ 0 where A expresses he growh rae, which is added in order o guaranee a sable seady sae. Here, he parameer v defines he elasiciy of labor supply. Governmen 34

35 A each period he governmen budge consrain is given by, ( A0) τ G T =, where G T is assumed o be deerminisic. 28 Equilibrium Condiions The clearing markes equilibrium condiions are, ( A ) C T + I T + G T + TB = Y T ( A2 ) TB B B ( r *) = +, + where TB is he balance of rade, which is measured as ne expor. Soluion The model is solved using a numerical approximaion mehod following Kydland and Presco (982) and King, Plosser and Rebelo (988) as explained in secion 3. Parameerizaion The values of he following parameers, relaive risk aversion, () θ, growh rae ( γ ), depreciaion () δ, level parameer ( V T ) adjusmen cos elasiciy ( csi ), are calculaed as in secion 4. The labor share ( ξ ) is compued, as presened in secion 4, hough is value in a one-secor producion funcion equals o All oher parameers are esimaed according o he model's seady sae soluion and he decision rules coefficiens. As such, he aggregae macroeconomic basic raios are esimaed. Namely, we se S c, which is he raio of consumpion o oupu, o be equal o 0.55 as observed in he daa, and se S g, which is he raio of governmen expendiure o oupu o equal o be 0.4. Since he raio of invesmen o oupu is deermined by he model parameers, we se he discoun facor 28 We have made he necessary adapaions o he governmen expendiure specificaions according o he uiliy funcions as explained in CNR. 35