Ramses II - Model Description

Transcription

1 SVERIGES RIKSBANK OCCASIONAL PAPER SERIES Ramses II - Model Descrpon Maln Adolfson, Sefan Laséen, Lawrence Chrsano, Mahas Traband and Karl Walenn February 3

2 OCCASIONAL PAPERS ARE OBTAINABLE FROM Sverges Rksbank Informaon Rksbank SE-3 37 Sockholm Fax nernaonal: Telephone nernaonal: E-mal: nfo@rksbank.se The Occasonal paper seres presens repors on maers n he sphere of acves of he Rksbank ha are consdered o be of neres o a wder publc. The papers are o be regarded as repors on ongong sudes and he auhors wll be pleased o receve commens. The vews expressed n Occasonal Papers are solely he responsbly of he auhors and should no o be nerpreed as reflecng he vews of he Execuve Board of Sverges Rksbank.

3 Ramses II - Model Descrpon Maln Adolfson a Sefan Laséen a Lawrence Chrsano b, Mahas Traband c, Karl Walenn a a Sverges Rksbank b Norhwesern Unversy c Federal Reserve Board February 3 Absrac Ths paper descrbes Ramses II, he dynamc sochasc general equlbrum (DSGE) model currenly n use a he Moneary Polcy Deparmen of Sverges Rksbank. The model s used o produce macroeconomc forecass, alernave scenaros, and for moneary polcy analyss. The model was nally developed by Chrsano, Traband and Walenn (). Ths paper descrbes he verson of he model used for polcy and d ers n some respecs from Chrsano, Traband and Walenn. Compared wh he earler DSGE model a Sverges Rksbank, he Ramses model developed by Adolfson e. al. (8), Ramses II d ers n hree mporan respecs: ) nancal frcons are nroduced n he accumulaon of capal followng Bernanke, Gerler and Glchrs (999), ) he labor marke block ncludes search and machng followng Morensen and Pssardes (994), and ) mpors are allowed o ener expor producon as well as n he aggregae consumpon and nvesmen baskes. Keywords: DSGE, nancal frcons, labor marke frcons, unemploymen, small open economy, Bayesan esmaon. JEL codes: E, E3, F, F4, G, G, J6. The model descrpon draws heavly on Chrsano, Traband, and Walenn (). The vews expressed n hs paper are solely he responsbly of he auhors and should no be nerpreed as re ecng he vews of he Execuve Board of Sverges Rksbank or hose of he Board of Governors of he Federal Reserve Sysem or of any oher person assocaed wh he Federal Reserve Sysem. We are graeful o Ulf Södersröm for commens and suggesons. Correspondng auhor: Sefan Laséen, Sverges Rksbank, Moneary Polcy Deparmen, SE-3 37 Sockholm, Sweden. e-mal: sefan.laseen@rksbank.se.

4 Conens Inroducon Ramses II: A Small Open Economy Model Inermedae npu goods Producon of he Domesc Homogeneous Good Producon of Impored Inermedae Goods Producon of Fnal Consumpon Goods Producon of Fnal Invesmen Goods Producon of Fnal Expor Goods Households Household Consumpon Decson Fnancal Asses and Ineres Rae Pary Capal Accumulaon and Fnancal Frcons Capal Accumulaon and Invesmen Decson The Indvdual Enrepreneur Aggregaon Across Enrepreneurs and he Exernal Fnancng Premum....7 Wage Seng and Employmen Frcons Labor Hours Vacances and he Employmen Agency Problem Worker Value Funcons Barganng Problem Moneary Polcy Fscal Auhores Foregn Varables Resource Consrans Resource Consran for Domesc Homogeneous Oupu Trade Balance Exogenous Shock Processes Esmaon Daa Calbraon Choce of prors Shocks Measuremen errors Measuremen equaons Resuls Poseror parameer values Model Smoohed shock processes Impulse response funcons Varance Decomposon Forecass Level daa on unemploymen Concluson A Tables and Fgures B Appendx B. Scalng of Varables

5 B. Funconal forms B.3 Baselne Model B.3. Frs order condons for domesc homogenous good prce seng B.3. Frs order condons for expor good prce seng B.3.3 Demand for domesc npus n expor producon B.3.4 Demand for Impored Inpus n Expor Producon B.3.5 Frs order condons for mpor good prce seng B.3.6 Household Consumpon and Invesmen Decsons B.3.7 Wage seng condons n he baselne model B.3.8 Oupu and aggregae facors of producon B.3.9 Resrcons across n aon raes B.3. Endogenous Varables of he Baselne Model B.4 Equlbrum Condons for he Fnancal Frcons Model B.4. Dervaon of Aggregaon Across Enrepreneurs B.4. Equlbrum Condons B.5 Equlbrum Condons from he Employmen Frcons Model B.5. Labor Hours B.5. Vacances and he Employmen Agency Problem B.5.3 Agency Separaon Decsons B.5.4 Barganng Problem B.5.5 Fnal equlbrum condons B.5.6 Characerzaon of he Barganng Se B.6 Summary of equlbrum condons for Employmen Frcons n he Baselne Model 99 B.7 Summary of equlbrum condons of he Full Model

6 . Inroducon Ths paper descrbes Ramses II, he dynamc sochasc general equlbrum (DSGE) model currenly n use a he Moneary Polcy Deparmen of Sverges Rksbank. The model s used o produce macroeconomc forecass, o consruc alernave scenaros, and for moneary polcy analyss. The model was nally developed by Chrsano, Traband, and Walenn (), bu he curren verson of he model d ers from CTW n some respecs. Compared wh he earler DSGE model a he Rksbank, he Ramses model developed by Adolfson, Laséen, Lndé and Vllan (8), Ramses II d ers n hree mporan respecs. Frs, nancal frcons are nroduced n he accumulaon of capal, followng Bernanke, Gerler, and Glchrs (999) and Chrsano, Moo, and Rosagno (3; 8). Second, he labor marke block ncludes search and machng frcons followng Gerler, Sala, and Trgar (8). Thrd, mpored goods are used for expors as well as for consumpon and nvesmen. The paper s organzed as follows. In Secon we descrbe he heorecal srucure of Ramses II. Secon 3 descrbes he Bayesan esmaon of he model, and dscusses calbraon and he choce of prors. Ths secon also dsplays how we connec he daa o he model hrough measuremen equaons. Secon 4 conans he esmaon resuls and dscusses model, mpulse responses, varance decomposons and some forecass. Fnally, Secon 5 concludes. The bulk of he dervaons are n varous Appendces.. Ramses II: A Small Open Economy Model The model bulds on Chrsano, Echenbaum and Evans (5) and Adolfson, Laséen, Lndé and Vllan (8) from whch nhers mos of s open economy srucure. The hree nal goods, consumpon, nvesmen and expors, are produced by combnng he domesc homogenous good wh spec c mpored npus for each ype of nal good. Specalzed domesc mporers purchase a homogeneous foregn good, whch hey urn no a specalzed npu and sell o domesc mpor realers. There are hree ypes of mpor realers. One uses he specalzed mpor goods o creae a homogeneous good used as an npu no he producon of specalzed expors. Anoher uses he specalzed mpor goods o creae an npu used n he producon of nvesmen goods. The hrd ype uses specalzed mpors o produce a homogeneous npu used n he producon of consumpon goods. See Fgure A n he Appendx for a graphcal llusraon. Expors nvolve a Dx-Sglz connuum of exporers, each of whch s a monopols ha produces a specalzed expor good. Each monopols produces s expor good usng a homogeneous domescally produced good and a homogeneous good derved from mpors. The specalzed expor goods are sold o foregn, compeve realers whch creae a homogeneous good ha s sold o foregn czens. Below we wll descrbe he producon of all hese goods. 4

7 .. Inermedae npu goods... Producon of he Domesc Homogeneous Good A homogeneous domesc good, Y ; s produced usng Z d Y = Y d ; d ; d < : (.) The domesc good s produced by a compeve, represenave rm whch akes he prce of oupu, P ; and he prce of npus, P ; ; as gven. The h nermedae good producer has he followng producon funcon: Y ; = (z H ; ) K ; z + ; (.) where K ; denoes he capal servces rened by he h nermedae good producer, log (z ) s a echnology shock whose rs d erence has a posve mean, log ( ) s a saonary neural echnology shock and denoes a xed producon cos. In general, he economy has wo sources of growh: a posve drf n log (z ) and a posve drf n log ( ) ; where s he sae of an nvesmen-spec c echnology shock dscussed below. The objec, z + ; n (.) s de ned as: z + = z : In (.), H ; denoes homogeneous labor servces hred by he h nermedae good producer. Frms mus borrow a fracon of he wage bll, so ha one un of labor coss s denoed by W R f ; wh R f = f R + f ; (.3) where W s he aggregae wage rae, R s he nomnal neres rae, and f corresponds o he fracon ha mus be nanced n advance ( f = n hs verson). By combnng he wo rs-order condons wh respec o capal and labor n he rm s cos mnmzaon problem we oban he rm s margnal cos, whch dvded by he prce of he homogeneous good s denoed by mc : mc = d r k w R f ; (.4) where r k s he nomnal renal rae of capal scaled by P, and w = W =(z + =P ): d s a ax-lke shock, whch a ecs margnal cos, bu does no appear n he producon funcon. If here are All he deals regardng he scalng of varables are colleced n secon B. n he Appendx. In general lower-case leers denoe scaled varables hroughou. 5

8 no prce and wage dsorons n he seady sae, d s somorphc o a dsurbance n d,.e., a markup shock. Cos mnmzaon (spec cally he rs order condon for labor) also yelds anoher expresson for margnal cos ha mus be sas ed: mc = d P W R f MP l; where MP l; denoes he margnal produc of labor. = d ; w R f k; (.5) ( ) =H z + ; ; The h rm s a monopols n he producon of he h good and so ses s prce. Prce seng s subjec o Calvo frcons. Wh probably d he nermedae good rm canno reopmze s prce, n whch case he prce s se accordng o he followng ndexaon scheme: P ; = ~ d; P ; ; ~ d; ( ) d ( c ) d { d () { d ; where d ; { d ;are parameers and d ; { d ; d + { d (; ), s he lagged n aon rae, c s he cenral bank s arge n aon rae and s a scalar. Noe ha n he curren verson of he model c = = :5 (.e., he n aon arge s consan a %). 3 Wh probably d he rm can opmze s prce and maxmze dscouned pro s, X E j +j fp ;+j Y ;+j mc +j P +j Y ;+j g; (.6) j= subjec o he ndexaon scheme above and he requremen ha producon equals demand Y ; = P P ; d d Y ; (.7) where s he mulpler on he household s nomnal budge consran. I measures he margnal value o he household of one un of pro s, n erms of currency. The equlbrum condons assocaed wh prce seng problem and her dervaon are repored n secon B.3. n he Appendx. The domesc nermedae oupu good s allocaed among alernave uses as follows: Y = G + C d + I d + X d + D (.8) In Ramses I he combnaon of equaon (.4) and (.5) de nes he renal rae of capal. 3 s a scalar whch allows us o capure, among oher hngs, he case n whch non-opmzng rms eher do no change prce a all (.e., =, { d = ) or ndex only o he seady sae n aon rae (.e., =, { d = ): Noe ha we ge prce dsperson n seady sae f { d > and f s d eren from he seady sae value of. See Yun (996) for a dscusson of seady sae prce dsperson. 6

9 Here, C d denoes nermedae domesc consumpon goods used ogeher wh foregn consumpon goods o produce he nal household consumpon good. Also, I d s he amoun of nermedae domesc goods used n combnaon wh mpored foregn nvesmen goods o produce a homogeneous nvesmen good. X d s domesc resources allocaed o expors, Fnally, D s he coss of he real frcons n he model (nvesmen adjusmen coss, capal ulzaon coss and vacancy posng coss). below. The deermnaon of consumpon, nvesmen and expor demand s dscussed... Producon of Impored Inermedae Goods We now urn o a dscusson of mpors. Foregn rms sell a homogeneous good o domesc mporers. The mporers conver he homogeneous good no a specalzed npu (hey brand name ) and supply ha npu monopolscally o domesc realers. There are hree ypes of mporng rms: () one produces goods used o produce an nermedae good for he producon of consumpon, () one produces goods used o produce an nermedae good for he producon of nvesmen, and () one produces goods used o produce an nermedae good for he producon of expors. All mporers are subjec o Calvo prce seng frcons. Consder () rs. The producon funcon of he domesc realer of mpored consumpon goods s: Z C m = C; m m;c m;c d ; where C; m s he oupu of he h specalzed producer and C m s he nermedae good used n he producon of consumpon goods. Le P m;c denoe he prce ndex of C m and le P m;c ; denoe he prce of he h nermedae npu. The domesc realer s compeve and akes P m;c and P m;c ; as gven. In he usual way, he demand curve for specalzed npus s gven by he domesc realer s rs order condon for pro maxmzaon: C m ; = C m! P m;c m;c m;c P m;c : ; We now urn o he producer of C; m ; who akes he prevous equaon as a demand curve. Ths producer buys he homogeneous foregn good and convers one-for-one no he domesc d erenaed good, C; m : The nermedae good rm mus pay he npus n advance a he begnnng of he perod wh foregn currency, and nance hs abroad. The nermedae good producer s margnal cos s m;c S P R ; ; (.9) where R ; = R + ; (.) 7

10 R s he foregn nomnal neres rae, and S he exchange rae (domesc currency per un foregn currency). There s no rsk o hs rm, because all shocks are realzed a he begnnng of he perod, and so here s no uncerany whn he duraon of he cash n advance loan abou he realzaon of prces and exchanges raes. Also, m;c s a ax-lke shock, whch a ecs margnal cos bu does no appear n he producon funcon. If here are no prce and wage dsorons n he seady sae, d s somorphc o a markup shock. Now consder (). The producon funcon for he domesc realer of mpored nvesmen goods, I m ; s: Z I m = I m ; m; m; d : The realer of mpored nvesmen goods s compeve and akes oupu prces, P m; ; and npu prces, P m; ; ; as gven. The producer of he h nermedae mpored nvesmen npu buys he homogeneous foregn good and convers one-for-one no he d erenaed good, I m ; : The margnal cos of Im ; s m; S P R ; : Noe ha hs mples he mporng nvesmen rm s cos s P (before borrowng coss and exchange rae converson), whch s he same cos for he specalzed npus used o produce C m : Ths may seem nconssen wh he propery ha domescally produced consumpon and nvesmen goods have d eren relave prces. Below, we suppose ha he e cency of mpored nvesmen goods grows over me, n a way ha makes our assumpons abou he relave coss of consumpon and nvesmen, wheher mpored or domescally produced. Now consder (). The producon funcon of he domesc realer of mpored goods used n he producon of an npu, X m ; for he producon of expor goods s: Z X m = X m ; m;x m;x d : The mpored good realer s compeve, and akes oupu prces, P m;x ; and npu prces, P m;x ; ; as gven. The producer of he specalzed npu, X; m ; has margnal cos m;c S P R ; : Each of he above hree ypes of nermedae good rms s subjec o Calvo prce-seng frcons. Wh probably m;j ses prce accordng o: P m;j m;j ; he j h ype of rm can reopmze s prce and wh probably ; = ~ m;j ~ m;j P m;j ; ; m;j m;j ( c ) m;j { m;j { m;j : (.) 8

11 for j = c; ; x, and m;j ; { m;j ; m;j + { m;j (; ). Noe also ha n he curren verson of he model c = = :5. The equlbrum condons assocaed wh prce seng by mporers are analogous o he ones derved for domesc nermedae good producers and are repored n secon B.3.5 n he Appendx. The real margnal cos s for j = c; ; x: = m;j S P mc m;j = m;j = m;j P m;j R ; (.) S P P c P P cp m;j R ; P q p c p m;j R ;.. Producon of Fnal Consumpon Goods Fnal consumpon goods are purchased by households. These goods are produced by a represenave compeve rm wh he followng lnear homogeneous echnology: C = " (! c ) c C d # c ( c ) c +! c c (C m ) ( c ) c c ; (.3) usng wo npus. The rs, C d ; s a one-for-one ransformaon of he homogeneous domesc good and herefore has prce, P : The second npu, C m ; s he homogeneous compose of specalzed consumpon mpor goods dscussed n he nex subsecon. The prce of C m s P m;c. The represenave rm akes he npu prces, P and P m;c, as well as he oupu prce of he nal consumpon good, P c, as gven. Pro maxmzaon leads o he followng demand for he nermedae npus (n scaled form): where p c = P c =P and p m;c c d = (! c ) (p c ) c c ; p c m c c =! c p m;c c : (.4) = P m;c =P. The prce of C s relaed o he prce of npus by: p c = The rae of n aon of he consumpon good s: c = P c P c h (! c ) +! c (p m;c ) c c : (.5) " # (! c ) +! c (p m;c ) c c = (! c ) +! c p m;c c : (.6) 9

12 .3. Producon of Fnal Invesmen Goods Invesmen goods are produced by a represenave compeve rm usng he followng echnology: I + a (u ) K = " (! ) I d # +! (I m ) ; where we de ne nvesmen o be he sum of nvesmen goods, I ; used n he accumulaon of physcal capal, plus nvesmen goods used n capal manenance, a (u ) K ; where K s he physcal capal sock and secon B. n he Appendx de nes he funconal form of a (u ). Capal manenance are expenses ha arse from varyng he ulzaon of capal, dscussed n secon.5 below. The ulzaon rae of capal, u, s de ned from K = u K : To accommodae he observaon ha he prce of nvesmen goods relave o he prce of consumpon goods s declnng over me, we assume ha s a un roo process wh posve drf. The deals of he law of moon of hs process s dscussed below. (In he curren verson of Ramses II hs s no sochasc). As n he consumpon good secor he represenave nvesmen goods producers akes all relevan prces as gven. demand for he nermedae npus n scaled form: d = p k + a (u )! m p =! p m; + a (u ) Pro maxmzaon leads o he followng ; z + ; where p = P =P and p m; = P m; =P. The prce of I s relaed o he prce of he npus by: p = (! ) +! p m; (! ) (.7) k ; z + ; (.8) : (.9) The rae of n aon of he nvesmen good s: = ; 6 (! ) +! 4 (! ) +! p m; p m; : (.).4. Producon of Fnal Expor Goods Toal foregn demand for domesc expors s: P x X = P f Y :

13 In scaled form, hs s x = (p x ) f y : (.) Here, Y s foregn GDP and P s he foregn currency prce of foregn homogeneous goods. P x s an ndex of expor prces, whose deermnaon s dscussed below. The goods, X ; are produced by a represenave, compeve foregn realer rm usng specalzed npus as follows: Z x x X = X; d : (.) where X ; ; (; ) ; are expors of specalzed goods. The realer ha produces X akes s oupu prce, P x ; and s npu prces, P; x ; as gven. Opmzaon leads o he followng demand for specalzed expors: P x x ; x X ; = X : (.3) Combnng (.) and (.3), we oban: P x Z P x = P; x x x d : The h expor monopols produces s d erenaed expor good usng he followng CES producon echnology: X ; = "! x x X; m x x + (! x ) x X; d x x # x x ; where X m ; and Xd ; are he h exporer s use of he mpored and domescally produced goods, respecvely. We derve he margnal cos from he mulpler assocaed wh he Lagrangan represenaon of he cos mnmzaon problem: 8 " h < mn x P m;x R x X; m + P R x X; d + : X ;! x x X; m x x + (! x ) x X; d # x x x x where P m;x s he prce of he homogeneous mpor good and P s he prce of he homogeneous domesc good. I s assumed ha he exporers mus nance a fracon of her producon coss n advance mplyng ha R x eners he npu cos. Usng he rs order condons of hs problem we derve he real margnal cos, mc x : mc x = S P x = x R x h q p c! x (p m;x px ) x + (! x ) x ; (.4) where lower case leers denoe scaled varables and 9 = ; ; R x = x R + x ; (.5)

14 where x = n he curren verson, and where we have used S P x P = S P P c P c P P x P = q p c p x : (.6) From he soluon o he same problem we also ge he demand for domesc npus for expor producon: x X; d = x Rx P X; (! x ) (.7) The aggregae expor demand for he domesc homogeneous npu good s X d = Z X d ;d = h x! x (p m;x ) x + (! x ) x (! x ) (p x ) x; x; (p x ) f Y ; (.8) where p x s a measure of he prce dsperson, whch s no acve n hs verson of he model and hence equal o one (see also secon B.3.3 n he Appendx). The aggregae expor demand for he mpored npu good s: X m B =! h! x (p m;x ) x + (! x ) x p m;x C A x (p x ) x x (p x ) f Y (.9) The h expor rm akes (.3) as s demand curve, and ses he prce subjec o Calvo frcons. Wh probably x he h expor good rm canno reopmze s prce, n whch case updae s prce as: P x ; = ~ x P x ; ; ~ x = x x ( x ) x {x () {x ; (.3) where x ; { x ; x + { x (; ) :Noe also ha n he curren verson of he model x = = :5: The equlbrum condons assocaed wh prce seng by exporers ha do ge o reopmze her prces are analogous o he ones derved for domesc nermedae good producers and are repored n secon B.3. n he Appendx..5. Households Household preferences are gven by: " X NX c ln(c bc ) h A L E j = =!# (& ; ) + L l ; (.3) + L where c s a shock o consumpon preferences, h s labor supply shock, & ; s hours worked per employee and l s he number of workers n cohor f; :::N g (see Secon.7). The household owns he sock of ne foregn asses and deermnes s rae of accumulaon.

15 .5.. Household Consumpon Decson The rs order condon for consumpon s: where c c + be z c bc c z + + z + ;+ bc + ;p c ( + c ) = : (.3) ; z + ; = P z + s he margnal value of one un of he homogenous domesc good a me..5.. Fnancal Asses and Ineres Rae Pary The household does he economy s savng. Perod savng occurs by he acquson of ne foregn asses, A + ; and a domesc asse. The domesc asse s used o nance he workng capal requremens of rms. Ths asse pays a nomnally non-sae conngen reurn from o + ; R : The rs order condon assocaed wh hs asse s: z z + ; + E + ;+ R b (R + ) = ; (.33) z + ;+ where b s he ax rae on he real neres rae on bond ncome (for addonal dscusson of b, see secon.9.) A consequence of our reamen of he axaon on domesc bonds s ha he + seady sae real afer ax reurn on bonds s nvaran o : In he model he ax reamen of domesc agens earnngs on foregn bonds s he same as he ax reamen of agens earnngs on foregn bonds. The scaled dae rs order condon assocaed wh A + ha pays R n erms of foregn currency s: S = E + S + R b S + R S P + : (.34) P Recall ha S s he domesc currency prce of a un of foregn currency. On he lef sde of hs expresson, we have he cos of acqurng a un of foregn asses. The currency cos s S and hs s convered no uly erms by mulplyng by he Lagrange mulpler on he household s budge consran, : The erm n square brackes s he afer ax payo of he foregn asse, n domesc currency uns. The rs erm s he perod + pre-ax neres payo on A +, whch s S +R : Here, R s he foregn nomnal rae of neres, whch s rsk free n foregn currency uns. The erm, represens a rsk adjusmen, so ha a un of he foregn asse acqured n pays o R uns of foregn currency n + : The deermnaon of s dscussed below. The remanng erm perans o he mpac of axaon on he reurn on foregn asses. If we gnore he erm afer he mnus sgn whn he se of parenheses, we see ha axaon s appled o he whole nomnal payo on he bond, ncludng prncple. The erm afer he mnus sgn s desgned o ensure ha he prncpal s deduced from axes. The prncpal s expressed n nomnal erms and s se so ha 3

16 he real value a + concdes wh he real value of he currency used o purchase he asse n perod : In parcular, recall ha S s he perod domesc currency cos of a un (n erms of foregn currency) of foregn asses. So, he perod real cos of he asse s S =P : The domesc currency value n perod + of hs real quany s P + S =P : where We scale he rs order condon, eq. (.34), by mulplyng boh sdes by P z + =S : z + ;+ z + ; = E [s + R b (s + R + )]; (.35) + z + ;+ s = S S : The rsk adjusmen erm has he followng form: where, recall, = a ; E s + s ; ~ = exp ~a (a a) s ~ E s + s s + ~ ; (.36) a = S A + P z + ; and ~ s a mean zero shock whose law of moon s dscussed below. In addon, ~ a ; ~ s ; a are posve parameers. In he seady sae dscusson n he Appendx, we derve he equlbrum oucomes ha a concdes wh a and = n non-sochasc seady sae. The dependence of on a ensures, n he usual way, ha here s a unque seady sae value of a ha s ndependen of he nal ne foregn asses and capal of he economy. The dependence of on he ancpaed growh rae of he exchange rae s desgned o allow he model o reproduce wo ypes of observaons. The rs concerns observaons relaed uncovered neres pary. The second concerns he hump-shaped response of oupu o a moneary polcy shock. A log lnear approxmaon of he model (n whch corresponds o he log devaon of abou s seady sae value of uny) mples he followng represenaon of he uncovered neres pary condon: R R = E log S + log S + ; = E log S + log S s ~ E log S + s ~ log S a ~ (a a) + ~ ; = s ~ E log S + s ~ log S a ~ (a a) + ~ ; where s he d erence operaor and denoes he rsk premum on domesc asses. 4 Consder rs he case n whch (and ~ s = ): In hs case, a fall n R relave o R produces an ancpaed apprecaon of he currency. Ths drop n E log S + log S s accomplshed n par by an nsananeous deprecaon n log S : The dea behnd hs s ha asse holders respond o 4 Noe ha he rsk premum has an endogenous par, namely ~ s E log S + ~ s log S ~ a (a a) as well as an exogenous par, namely ~ whch we refer o as he rsk premum shock below. 4

17 he unfavorable domesc rae of reurn by aempng o sell domesc asses and acqure foregn exchange for he purpose of acqurng foregn asses. Ths sellng pressure pushes log S up, unl he ancpaed apprecaon precsely compensaes raders n nernaonal nancal asses holdng domesc asses. There s evdence ha he precedng scenaro does no hold n he daa. Vecor auoregresson evdence on he response of nancal varables o an expansonary domesc moneary polcy shock suggess ha E log S + log S acually rses for a perod of me (see, e.g., Echenbaum and Evans (995)). One nerpreaon of hese resuls s ha when he domesc neres rae s reduced, say by a moneary polcy shock, hen rsk n he domesc economy falls and ha alone makes raders happer o hold domesc nancal asses n spe of her lower nomnal reurn and he losses hey expec o make n he foregn exchange marke. Our funconal form for s desgned o capure hs dea when 6= (and ~ s 6= )..6. Capal Accumulaon and Fnancal Frcons We assume ha only he accumulaon and managemen of capal nvolves frcons, bu ha workng capal loans are frconless. Our sraegy of nroducng frcons n he accumulaon and managemen of capal follows he varan of he Bernanke, Gerler and Glchrs (999) (henceforh BGG) model mplemened n Chrsano, Moo and Rosagno (3). The dscusson here borrows heavly from he dervaon n Chrsano, Moo and Rosagno (8) (henceforh CMR). The nancal frcons we nroduce re ec fundamenally ha borrowers and lenders are dfferen people, and ha hey have d eren nformaon. Thus, we nroduce enrepreneurs. These are agens who have a specal skll n he operaon and managemen of capal. Alhough hese agens have her own nancal resources, her skll n operang capal s such ha s opmal for hem o operae more capal han her own resources can suppor, by borrowng addonal funds. There s a nancal frcon because he managemen of capal s rsky. Indvdual enrepreneurs are subjec o dosyncrac shocks whch are observed only by hem. The agens ha hey borrow from, banks, can only observe he dosyncrac shocks by payng a monorng cos. Ths ype of asymmerc nformaon mples ha s mpraccal o have an arrangemen n whch banks and enrepreneurs smply dvde up he proceeds of enrepreneural acvy, because enrepreneurs have an ncenve o undersae her earnngs. An alernave arrangemen ha s more e cen s one n whch banks exend enrepreneurs a sandard deb conrac, whch spec es a loan amoun and a gven neres paymen. Enrepreneurs who su er an especally bad dosyncrac ncome shock and who herefore canno a ord o pay he requred neres, are bankrup. Banks pay he cos of monorng hese enrepreneurs and ake all of her ne worh n paral compensaon for he neres ha hey are owed. For a graphcal llusraon of he nancng problem n he capal marke, see Fgure B. The amoun ha banks are wllng o lend o an enrepreneur under he sandard deb conrac 5

18 s a funcon of he enrepreneur s ne worh. Ths s how balance shee consrans ener he model. When a shock occurs ha reduces he value of he enrepreneur s asses, hs cus no her ably o borrow. As a resul, hey acqure less capal and hs ranslaes no a reducon n nvesmen and ulmaely no a slowdown n he economy. The ulmae source of funds for lendng o enrepreneurs s he household. The sandard deb conracs exended by banks o enrepreneurs are nanced by ssung lables o households. Alhough ndvdual enrepreneurs are rsky, banks hemselves are no. We suppose ha banks lend o a su cenly dverse group of enrepreneurs ha he uncerany ha exss n ndvdual enrepreneural loans washes ou across all loans. Exensons of he model ha nroduce rsk no bankng have been developed, bu s no clear ha he added complexy s jus ed. In he model, he neres rae ha households receve s nomnally non sae-conngen. Ths gves rse o poenally neresng wealh e ecs of he sor emphaszed by Irvng Fsher (933). For example, when a shock occurs whch drves he prce level down, households receve a wealh ransfer. Because hs ransfer s aken from enrepreneurs, her ne worh s reduced. Wh he ghenng n her balance shees, her ably o nves s reduced. 5 As we shall see, enrepreneurs all have d eren hsores, as hey experence d eren dosyncrac shocks. Thus, n general, solvng for he aggregae varables would requre also solvng for he dsrbuon of enrepreneurs accordng o her characerscs and for he law of moon for ha dsrbuon. However, as emphaszed n BGG, he rgh funconal form assumpons have been made n he model, whch guaranee he resul ha he aggregae varables assocaed wh enrepreneurs are no a funcon of dsrbuons. The loan conrac spec es ha all enrepreneurs, regardless of her ne worh, receve he same neres rae. Also, he loan amoun receved by an enrepreneur s proporonal o hs level of ne worh. These are enough o guaranee he aggregaon resul. 5 Wh hs model, s ypcally he pracce o compare he ne worh of enrepreneurs wh a sock marke quany (ndex), and we follow hs roue. Wheher hs s really approprae s unceran. A case can be made ha he bank loans of enrepreneurs n he model correspond well wh acual bank loans plus acual equy. I s well known ha dvdend paymens on equy are very smooh. Frms work hard o accomplsh hs. For example, durng he US Grea Depresson some rms were wllng o sell her own physcal capal n order o avod cung dvdends. Tha hs s so s perhaps no surprsng. The asymmerc nformaon problems wh acual equy are surely as severe as hey are for he banks n our model. Under hese crcumsances one mgh expec equy holders o demand a paymen ha s no conngen on he realzaon of uncerany whn he rm (paymens could be conngen upon publcly observed varables). Under hs vson, he ne worh n he model would correspond no o a measure of he aggregae sock marke, bu o he ownershp sake of he managers and ohers who exer mos drec conrol over he rm. The bank loans n hs model would, under hs vew of hngs, correspond o he acual loans of rms (.e., bank loans and oher loans such as commercal paper) plus he ousandng equy. Whle hs s perhaps oo exreme, hese observaons hghlgh ha here s subsanal uncerany over exacly wha varable should be compared wh ne worh n he model. I s mporan o emphasze, however, ha whaever he rgh nerpreaon s of ne worh, he model poenally capures balance shee problems very ncely. 6

19 .6.. Capal Accumulaon and Invesmen Decson The sock of physcal capal s owned by he enrepreneur, who deermnes he rae a whch he capal sock s accumulaed and s ulzaon rae. The law of moon of he physcal sock of capal s subjec o nvesmen adjusmen coss as nroduced by Chrsano, Echenbaum and Evans (5): K + = ( ) K + S ~ I I ; I where s a saonary nvesmen-spec c echnology shock ha a ecs he e cency of ransformng nvesmens no capal. In scaled erms he law of moon of capal can be wren 6 k + = z k + S ~ + ; ; : (.38) z + ; ; The rs order condon wh respec o I (derved from he Lagrangan represenaon of he nvesmen purchase and he law of moon for capal) s n scaled erms: z + ;p z + z + ;p k ; S ~ + ; ; ~S z + ; ; + z + ;+p k ;+ + ~ S.6.. The Indvdual Enrepreneur z + ;+ ;+ + z + ; ; + ;+ z +;+ = : (.39) A he end of perod each enrepreneur has a level of ne worh, N + : The enrepreneur s ne worh, N + ; consues hs sae a hs me, and nohng else abou hs hsory s relevan. We magne ha here are many enrepreneurs for each level of ne worh and ha for each level of ne worh, here s a compeve bank wh free enry ha o ers a loan conrac. The conrac s de ned by a loan amoun and by an neres rae, boh of whch are derved as he soluon o a parcular opmzaon problem. Consder a ype of enrepreneur wh a parcular level of ne worh, N + : The enrepreneur combnes hs ne worh wh a bank loan, B + ; o purchase new, nsalled physcal capal, K+ ; from capal producers. The loan he enrepreneur requres for hs s: B + = P P k ; K + N + : (.4) The enrepreneur s requred o pay a gross neres rae, Z + ; on he bank loan a he end of perod +; f s feasble o do so. Afer purchasng capal he enrepreneur experences an dosyncrac 6 See subsecon B. n he Appendx for he funconal form of he nvesmen adjusmen coss, S. ~ Noe ha he rs order condon for capal n he baselne model (.e. he model whou nancal frcons and he labour marke block) mples: z + ; = E z + ;+ R k + + z + ;+ : (.37) 7

20 producvy shock whch convers he purchased capal, K+ ; no K +!: Here,! s a un mean, lognormally and ndependenly dsrbued random varable across enrepreneurs. The varance of log! s : The subscrp ndcaes ha s self he realzaon of a random varable. Ths allows us o consder he e ecs of an ncrease n he rskness of ndvdual enrepreneurs. We denoe he cumulave dsrbuon funcon of! by F (!; ): and s paral dervaves as e.g. F! (!; ), F (!; ) Afer observng he perod + shocks, he enrepreneur ses he ulzaon rae, u + ; of capal and rens capal ou n compeve markes a nomnal renal rae, P + r+ k. In choosng he capal ulzaon rae, he enrepreneur akes no accoun ha operang one un of physcal capal a rae u + requres a(u + ) of domescally produced nvesmen goods for manenance expendures, where a s de ned n (B.4). The rs order condon assocaed wh capal ulzaon s, n scaled erms: r k = p a (u ) ; (.4) r k = r k s he scaled real renal rae of capal. 7 The enrepreneur hen sells he undeprecaed par of physcal capal o capal producers. Per un of physcal capal purchased, he enrepreneur who draws dosyncrac shock! earns a reurn (afer axes), of R+ k!, where Rk + s he rae of reurn on a perod nvesmen n a un of physcal capal: where R k + = h ( k ) u + r + k p + a(u +) P ( )P + P k ;+ + k P P k ; ; (.4) P P k ; p P = P ; s he dae prce of he homogeneous nvesmen good. Here, P k ; denoes he prce of a un of newly nsalled physcal capal, whch operaes n perod + : Ths prce s expressed n uns of he homogeneous good, so ha P P k ; s he domesc currency prce of physcal capal. The numeraor n he expresson for R+ k represens he perod + payo from a un of addonal physcal capal. The mng of he capal ax rae re ecs he assumpon ha he relevan ax rae s known a he me he nvesmen decson s made. The expresson n square brackes capures he dea ha manenance expenses assocaed wh he operaon of capal are deducble from axes. The las expresson n he numeraor expresses he dea ha physcal deprecaon s deducble a hsorcal cos. reurn across all enrepreneurs s R k + :8 Because he mean of! across enrepreneurs s uny, he average 7 The ax rae on capal ncome does no ener here because manenance coss are assumed o be deducble from axes. 8 I s convenen o express R k n scaled erms: R k + = + ;+ ( k ) u +r k + p +a(u +) + ( )p k ;+ + k ;+ p k ; + p k ; : (.43) 8

21 Afer enrepreneurs sell her capal, hey sele her bank loans. A hs pon, he resources avalable o an enrepreneur who has purchased K + uns of physcal capal n perod and who experences an dosyncrac producvy shock! are P P k ;R+ k! K + : There s a cuo value of!;! + ; such ha he enrepreneur has jus enough resources o pay neres:! + R+P k P k ;K + = Z + B + : (.44) Enrepreneurs wh! <! + are bankrup and urn over all her resources, R k +!P P k ; K + ; whch s less han Z + B + ; o he bank: In hs case, he bank monors he enrepreneur, a cos R k +!P P k ; K + ; where s a parameer. Banks oban he funds loaned n perod o enrepreneurs by ssung deposs o households a gross nomnal rae of neres, R. The subscrp on R ndcaes ha he payo o households n + s no conngen on he perod + uncerany. Ths feaure of he relaonshp beween households and banks s smply assumed. There s no rsk n household bank deposs, and he household Euler equaon assocaed wh deposs s exacly he same as (.33). We suppose ha here s compeon and free enry among banks, and ha banks parcpae n no nancal arrangemens oher han he lables ssued o households and he loans ssued o enrepreneurs. 9 I follows ha he bank s cash ow n each sae of perod + s zero, for each loan amoun. For loans n he amoun, B + ; he bank receves gross neres, Z + B + ; from he F (! + ; ) enrepreneurs who are no bankrup. The bank akes all he resources possessed by bankrup enrepreneurs, ne of monorng coss. Thus, he sae-by-sae zero pro condon s: Z!+ [ F (! + ; )] Z + B + + ( )!df (!; ) R+P k P k ;K + = R B + ; or, afer makng use of (.44) and rearrangng, [ (! + ; ) G(! + ; )] Rk + R % = % (.45) where p k ; = P k ;: 9 If banks also had access o sae conngen secures, hen free enry and compeon would mply ha banks earn zero pro s n an ex ane expeced sense from he pon of vew of perod : Absence of sae conngen secures markes guaranee ha cash ow s non-negave. Free enry guaranees ha ex ane pro s are zero. Gven ha each sae of naure receves posve probably, he wo assumpons mply he sae by sae zero pro condon quoed n he ex. 9

22 where G(! + ; ) = Z!+!dF (!; ): (! + ; ) =! + [ F (! + ; )] + G(! + ; ); % = P P k ; K + N + : The expresson, (! + ; ) G(! + ; ) s he share of revenues earned by enrepreneurs ha borrow B + ; whch goes o banks. Noe ha!(! + ; ) = F (! + ; ) > and G! (! + ; ) =! + F! (! + ; ) > : I s hus no surprsng ha he share of enrepreneural revenues accrung o banks s non-monoone wh respec o! + : BGG argue ha he expresson on he lef of (.45) has an nvered U shape, achevng a maxmum value a! + =! ; say. The expresson s ncreasng for! + <! and decreasng for! + >! : Thus, for any gven value of he leverage rao, % ; and R k + =R ; genercally here are eher no values of! + or wo ha sasfy (.45). The value of! + realzed n equlbrum mus be he one on he lef sde of he nvered U shape. Ths s because, accordng o (.44), he lower value of! + corresponds o a lower neres rae for enrepreneurs whch yelds hem hgher welfare. As dscussed below, he equlbrum conrac s one ha maxmzes enrepreneural welfare subjec o he zero pro condon on banks. Ths reasonng leads o he concluson ha! + falls wh a perod + shock ha drves R k + up. The fracon of enrepreneurs ha experence bankrupcy s F (! + ; ) ; so follows ha a shock whch drves up R+ k has a negave conemporaneous mpac on he bankrupcy rae. Accordng o (B.8), shocks ha drve R+ k up nclude anyhng whch rases he value of physcal capal and/or he renal rae of capal. As jus noed, we suppose ha he equlbrum deb conrac maxmzes enrepreneural welfare, subjec o he zero pro condon on banks and he spec ed requred reurn on household bank lables. The dae deb conrac spec es a level of deb, B + and a sae + conngen rae of neres, Z + : We suppose ha enrepreneural welfare corresponds o he enrepreneur s expeced wealh a he end of he conrac. I s convenen o express welfare as a rao o he amoun he enrepreneur could receve by deposng hs ne worh n a bank: E R! + R k +!P P k ; K + Z + B + df (!; ) afer makng use of (.4), (.44) and = R N + = E R! [!! + +] df (!; )R+ k P P k ;K + R N ( + ) = E [ (! + ; )] Rk + % R ; Z!dF (!; ) = Z! +!df (!; ) + G(! + ; ):

23 We can equvalenly characerze he conrac by a sae- + conngen se of values for! + and a value of % : The equlbrum conrac s he one nvolvng! + and % whch maxmzes enrepreneural welfare (relave o R N + ), subjec o he bank zero pro s condon. The Lagrangan represenaon of hs problem s: ( max % ;f! + g E [ (! + ; )] Rk + R % + + [ (! + ; ) G(! + ; )] Rk + R % % + where + s he Lagrange mulpler whch s de ned for each perod + sae of naure. The rs order condons for hs problem are: (!) E [ (! + ; )] Rk [ (! + ; ) G(! + ; )] Rk + R R =!(! + ; ) Rk + R + + [!(! + ; ) G! (! + ; )] Rk + R = [ (! + ; ) G(! + ; )] Rk + R % % + = ; where he absence of + from he complemenary slackness condon re ecs ha we assume + > n each perod + sae of naure. Subsung ou for + from he second equaon no he rs, he rs order condons reduce o: 8 >< [ (! + ; )] Rk +!(! R + + ; ) E >: [ (! + ; ) G(! + ; )] Rk + R for = ; ; ; ::: and for =!(! + ; ) G!(! + ; ) 9 >= >;!) = ; (.46) [ (! + ; ) G(! + ; )] Rk + R % % + = ; (.47) ; ; ; ; ::: respecvely. Snce N + does no appear n he las wo equaons, we conclude ha % and! + are he same for all enrepreneurs, regardless of her ne worh. The resuls for % mples ha B + N + = % ;.e. ha an enrepreneur s loan amoun s proporonal o hs ne worh. Rewrng (.4) and (.44) we see ha he rae of neres pad by he enrepreneur s ; Z + =! +R+ k N + P P k ; K+ =! + R k + % ; (.48) whch s he same for all enrepreneurs, regardless of her ne worh Aggregaon Across Enrepreneurs and he Exernal Fnancng Premum The law of moon for he ne worh of an ndvdual enrepreneur s

24 V = R k P P k ; K (! ; )R k P P k ; K ; (.49) Each enrepreneur faces an dencal and ndependen probably of beng seleced o ex he economy. Wh he complemenary probably, ; each enrepreneur remans. Because he selecon s random, he ne worh of he enrepreneurs who survve s smply V : A fracon, ; of new enrepreneurs arrve. Enrepreneurs who survve or who are new arrvals receve a ransfer, W e : Ths ensures ha all enrepreneurs, wheher new arrvals or survvors ha experenced bankrupcy, have su cen funds o oban a leas some amoun of loans. The average ne worh across all enrepreneurs afer he W e s N + = V + W e ; or, N + = fr k P P k ; K " +W e ; R ransfers have been made and exs and enry have occurred, + R!!dF (!; )R k P P k ; K # P P k ; K N (P P k ; K N )g where upper bar over a varable denoes s aggregae average value. aggregaon across enrepreneurs see Appendx B.4.. For a dervaon of he We now urn o he exernal nancng premum for enrepreneurs. The cos o he enrepreneur of nernal funds (.e., hs own ne worh) s he neres rae, R ; whch he loses by applyng o capal raher han jus deposng n he bank. The average paymen by all enrepreneurs o he bank s he enre objec n square brackes n equaon (.5). So, he erm nvolvng represens he excess of exernal funds over he nernal cos of funds. As a resul, hs s one measure of he rsk premum n he model. Anoher s he excess of he neres rae pad by enrepreneurs who are no bankrup, over R : accordng o (.48). Z + R =! +R+ k n + R ; p k ;k+.7. Wage Seng and Employmen Frcons The labor marke s modeled hrough he search and machng framework of Morensen and Pssardes (994) and, more recenly, Hall (5a,b,c) and Shmer (5 and ) - followng he GST sraegy mplemened n Chrsano, Ilu, Moo, and Rosagno (7). Ths framework allows for varaon n boh he exensve (employmen) and nensve (hours per worker) margn, whch s an mporan emprcal observaon. Mos of he varaon n hours worked n Sweden appears o be generaed by he exensve margn. A smple daa analyss on Swedsh daa 995q-9q, followng he mehod of Hansen (985), usng he decomposon (.5)

25 In he model, labor servces are suppled o he homogeneous labor marke by employmen agences (see Fgure B for a graphcal llusraon). Ths leaves he equlbrum condons assocaed wh he producon of he homogeneous good una eced. Key labor marke acves - vacancy posngs, layo s, labor barganng, seng he nensy of labor e or - are all carred ou nsde he employmen agences. Each household s composed of many workers, each of whch s n he labor force. A worker begns he perod eher unemployed or employed wh a parcular employmen agency. Unemployed workers do undreced search. They nd a job wh a parcular agency wh a probably ha s proporonal o he e ors made by he agency o arac workers. Workers are separaed from employmen agences eher exogenously, or because hey are acvely cu. Workers pass back and forh beween unemploymen and employmen wh an agency. There are no agency o agency ransons. The evens durng he perod n an employmen agency are dsplayed n Fgure C. Each employmen agency begns a perod wh a sock of workers. Tha sock s mmedaely reduced by exogenous separaons and s ncreased by new arrvals ha re ec he agency s recrung e ors n he prevous perod. Then, he economy s aggregae shocks are realzed. A hs pon, each agency s wage s se. The agences are allocaed permanenly no N equalszed cohors and each perod =N agences esablsh a new wage by Nash barganng. When a new wage s se, evolves over he subsequen N perods accordng o: W j;+ = ~ w;+ W j; (.5) ~ w;+ = ( c ) w c ( w { w) + () { w ( z +) #w ; (.5) where w ; { w ; # w ; w + { w (; ) : The wage updang facor, ~ w;+ ; s su cenly exble ha we can adop a varey of neresng schemes. The wage negoaed n a gven perod covers all workers employed a an agency for each of he subsequen N perods, even hose ha wll no arrve unl laer. The barganng arrangemen s unonzed, so ha a unon represenng he average worker bargans wh he employmen agency. Nex, f we allow for endogenous layo s, each worker draws an dosyncrac producvy shock. A cuo level of producvy s deermned, and workers wh lower producvy are lad o. From a var (H ) = var (& ) + var (L ) + covar (& ; L ) ; where H denoes oal hours worked, & hours per worker and L number of people employed. H and L are n per capa erms (of he adul populaon) and all seres are HP- lered wh = 6, ndcaes ha roughly 4/5h of he varaon n oal hours worked comes from varaon n employmen and /5h from varaon n hours per worker. The covarance erm s close o, whch s n lne wh prevous Swedsh evdence and nsuonal facors ha dscourage over-me work. An alernave, perhaps more naural, formulaon would be for he nermedae good rms o do her own employmen search. We nsead separae he ask of ndng workers from producon of nermedae goods n order o avod addng a sae varable o he nermedae good rm, whch would complcae he soluon of her prce-seng problem. 3

26 echncal pon of vew hs modellng s symmerc o he modelng of enrepreneural dosyncrac rsk and bankrupcy. We consder wo mechansms by whch he cuo s deermned. One s based on he oal surplus of a gven worker and he oher s based purely on he employmen agency s neres. 3 Afer hs endogenous layo decson, he employmen agency poss vacances and he nensy of work e or s chosen e cenly,.e. so ha he value of labor servces o he employmen agency s equaed o he cos of provdng by he household. A hs pon he employmen agency supples labor o he labor marke. We now descrbe hese varous labor marke acves n greaer deal. We begn wh he decsons a he end of he perod and work backwards o he barganng problem. Ths s a convenen way o develop he model because he barganng problem nernalzes everyhng ha comes afer. The acual equlbrum condons are dsplayed n he Appendx..7.. Labor Hours Labor nensy s chosen o equae he value of labor servces o he employmen agency wh he cos of provdng by he household. To explan he laer, we agan dsplay he uly funcon of he household: X E l f c +l ln(c +l bc +l ) h +l A L l= Here, f; :::; N " N X = (& ;+l ) + L + L F a +l l +l # g; (.53) g ndexes he cohor o whch he employmen agency belongs. The ndex, = corresponds o he cohor whose employmen agency renegoaes he wage n he curren perod, = corresponds o he cohor ha renegoaed n he prevous perod, and so on. The objec, l denoes he number of workers n cohor ; afer exogenous separaons and new arrvals from unemploymen have occurred. F a l (.54) denoes he number of workers wh an employmen agency n he h cohor who survve he endogenous layo s. 4 I should be noed ha he curren verson of Ramses II does no allow for endogenous layo s, so F = for all j and, n he subsequen equaons. Le & ; denoe he number of hours suppled by a worker n he h cohor. The absence of he ndex, a; on & ; re ecs our assumpon ha each worker who survves endogenous layo s n 3 In he curren verson of Ramses II we do no consder endogenous layo s, where each worker draws an dosyncrac producvy shock, a cuo level of producvy s deermned, and workers wh lower producvy are lad o. There are wo mechansms by whch he cuo can be deermned. One s based on he oal surplus of a gven worker and he oher s based purely on he employmen agency s neres. 4 Le a denoe an dosyncrac producvy shock drawn by a worker n cohor : Then, a, denoes he endogenously-deermned cuo such ha all workers wh a < a are lad o from he rm. Also, le h F a = P a < a denoe he cumulave dsrbuon funcon of he dosyncrac producvy shock. (In pracce, we assume ha F s lognormal wh Ea = and sandard devaon of log (a) equal o a:) 4

27 cohor works he same number of hours, regardless of he realzaon of her dosyncrac level of producvy. The dsuly experenced by a worker ha works & ; hours s: h A L (& ; ) + L + L : The uly funcon n (.53) sums he dsuly experenced by he workers n each cohor. Alhough he ndvdual worker s labor marke experence - wheher employed or unemployed - s deermned by dosyncrac shocks, each household has su cenly many workers ha he oal fracon of workers employed, L = NX = F a l ; as well as he fracons allocaed among he d eren cohors, F a l ; = ; :::; N ; are he same for each household. We suppose ha all he household s workers are suppled nelascally o he labor marke (.e., labor force parcpaon s consan). The household s currency receps arsng from he labor marke are: N ( y ) ( L X ) P b u z + + = W F a l & ; y + w where W s he nomnal wage rae earned by workers n cohor = ; :::; N he erm nvolvng b u ndcaes he assumpon ha unemployed workers, paymen of b u z + (.55) : The presence of L ; receve a pre-ax nal consumpon goods. These unemploymen bene s are nanced by lump sum axes. As n our baselne model, here s a labor ncome ax y and a payroll ax w afer-ax wage. ha a ec he Le W denoe he prce receved by employmen agences for supplyng one un of labor servce. I represens he margnal gan o he employmen agency ha occurs when an ndvdual worker ncreases me spen workng by one un. Because he employmen agency s compeve n he supply of labor servces, akes W as gven. We rea W as an unobserved varable n he daa. In pracce, s he shadow value of an exra worker suppled by he human resources deparmen o a rm. Followng GST, we assume ha labor hours are chosen o equae he worker s margnal cos of workng wh he agency s margnal bene : W G = h A L & L ; y + w (.56) for = ; :::; N separaon: : Here, G denoes expeced producvy of workers who survve endogenous E G = F ; (.57) 5

28 where Z E E a ; a; adf (a; a; ) (.58) a Z F = F a a ; a; = df (a; a; ) : (.59) To undersand he expresson on he rgh of (.56), noe ha he margnal cos, n uly erms, o an ndvdual worker who ncreases labor nensy by one un s h A L & L ; : Ths s convered o currency uns by dvdng by he mulpler, ; on he household s nomnal budge consran, and by he ax wedge ( y ) = ( + w ). The lef sde of (.56) represens he ncrease n revenues o he employmen agency from ncreasng hours worked by one un (recall, all workers who survve endogenous layo s work he same number of hours.) Dvson by ha he expecaon s relave o he dsrbuon of a condonal on a a j : F s requred n (.57) so Labor nensy s he same n all cohors snce Ramses II does no allow for endogenous layo s..7.. Vacances and he Employmen Agency Problem The employmen agency n he h cohor deermnes how many employees wll have n perod + by choosng vacances, v : The vacancy posng coss assocaed wh v are: z + Q v F a l! F a l ; uns of he domesc homogeneous good. The parameer deermnes he curvaure of he cos funcon and n pracce we se =. Also, z + = s a cos parameer whch s assumed o grow a he same rae as he overall economc growh rae and, as noed above, F a l denoes he number of employees n he h cohor afer endogenous separaons have occurred. Also, Q s he probably ha a posed vacancy s lled, a quany ha s exogenous o an ndvdual employmen agency. The funconal form of our cos funcon reduces o he funcon used n GT and GST when = : Wh hs parameerzaon, coss are a funcon of he number of people hred, no he number of vacances per se. We nerpre hs as re ecng ha he GT and GST spec caons emphasze nernal coss (such as ranng and oher) of adjusng he work force, and no search coss. In models used n he search leraure (see, e.g., Shmer (5a)), vacancy posng coss are ndependen of Q ;.e., hey se = : To undersand he mplcaons for our ype of emprcal analyss, consder a shock ha rggers an economc expanson and also produces a fall n he probably of llng a vacancy, Q : We expec he expanson o be smaller n a verson of he model ha emphaszes search coss (.e., = ) han n a verson ha emphaszes nernal coss (.e., = ). To furher descrbe he vacancy decsons of he employmen agences, we requre her objecve funcon. We begn by consderng F l ;! ; he value funcon of he represenave employmen 6

29 agency n he cohor, = ; ha negoaes s wage n he curren perod. The argumens of F are he agency s workforce afer begnnng-of-perod exogenous separaons and new arrvals, l ; and an arbrary value for he nomnal wage rae,! : Tha s, we consder he value of he rm s problem afer he wage rae has been se. We suppose ha he rm chooses a parcular monoone ransform of vacancy posngs, whch we denoe by ~v : where F j ~v Q v ; F j l denoes he fracon of he begnnng-of-perod workforce n cohor j whch survves endogenous separaons. The agency s hrng rae, ; s relaed o ~v by: To consruc F = Q ~v : (.6) l ;! ; we mus derve he law of moon of he rm s work force, durng he perod of he wage conrac. If l s he perod work force jus afer exogenous separaons and new arrvals, hen (.54) s he sze of he workforce afer endogenous separaons. The me + workforce of he represenave agency n he h cohor a me s denoed l+ + : Tha workforce re ecs he endogenous separaons n perod as well as he exogenous separaons and new arrvals a he sar of perod + : Le denoe he probably ha an ndvdual worker aached o an employmen agency a he sar of a perod survves he exogenous separaon. Then, gven he hrng rae, ; we have for j = ; ; :::; N as j =. l j+ + = j + F j l j ; (.6) ; wh he undersandng here and hroughou ha j = N s o be nerpreed Expresson (.6) s deermnsc, re ecng he assumpon ha he represenave employmen agency n cohor j employs a large number of workers. The value funcon of he rm s: N F l X ;! = j= j E +j P +j z + +j + N E +N F Z max (~v j +j ;aj +j) [ (W +j a ;j! ) & j;+j df (a) (.6) a j +j F j +j ]l j +j l+n; W ~ +N ; ~v j +j where l j evolves accordng o (.6), & j; sas es (.56) and ~w;+j ~ ;j = w;+ ; j > j = : (.63) Here, ~ w; s de ned n (.5). The erm, ;j! ; represens he wage rae n perod + j; gven he wage rae was! a me and here have been no wage negoaons n perods + ; + ; up o 7

30 and ncludng perod + j: In (.6); ~ W+N denoes he Nash barganng wage ha s negoaed n perod + N; whch s when he nex round of barganng occurs. A me, he agency akes he sae + N conngen funcon, ~ W+N ; as gven. The vacancy decson of employmen agences solve he maxmzaon problem n (.6). I s easly ver ed usng (.6) ha F l ;! s lnear n l : F l ;! = J (! ) l ; (.64) where J (! ) s no a funcon of l : The funcon, J (! ) ; s he surplus ha a rm barganng n he curren perod enjoys from a mach wh an ndvdual worker, when he curren wage s! : Alhough laer n he perod workers become heerogeneous when hey draw an dosyncrac shock o producvy, he fac ha ha draw s..d. over me means ha workers are all dencal a he me ha (.64) s evaluaed Worker Value Funcons Le V denoe he perod value of beng a worker n an agency n cohor ; afer ha worker has survved ha perod s endogenous separaon: V = ; W ~ y & ; + w + +E F + + A L h & + L ; (.65) ( + L ) V F + + U+ ; for = ; ; :::; N : In (.65), ~ W denoes he wage negoaed perods n he pas, and ; ~ W represens he wage receved n perod by workers n cohor : The wo erms afer he equaly n (.65) represen a worker s perod ow uly, convered no uns of currency. 5 The erms n square brackes n (.65) correspond o uly n he wo possble perod + saes of he world. Wh probably F+ + he worker survves he exogenous and endogenous separaons n perod +; n whch case s value funcon n + s V+ + : Wh he complemenary probably, + F+ +, he worker separaes no unemploymen n perod + ; and enjoys uly, U + : The currency value of beng unemployed n perod s: U = P z + bu ( y ) + E + [f V+ x + ( f ) U + ]; (.66) where f s he probably ha an unemployed worker wll land a job n perod +. Also, V+ x s he perod + value funcon of a worker who knows ha he has mached wh an employmen agency a he sar of +, bu does no know whch one. In parcular, NX V+ x = = F l m ~ V + + : (.67) 5 Noe he dvson of he dsuly of work n (.65) by, he mulpler on he budge consran of he household opmzaon problem. 8

31 Here, oal new maches a he sar of perod + ; m ; s gven by: m = NX j= j F j l j : (.68) In (.67), F l m s he probably of ndng a job n + n an agency belongng o cohor n perod : Noe ha hs s a proper probably dsrbuon because s posve for each and sums o uny by (.68). In (.67), V ~ s he analog of V+ ; excep ha he former s de ned before he worker knows f he survves he endogenous producvy cu, whle he laer s de ned afer survval. The superscrp + appears on V ~ + + because he probables n (.67) refer o acves n a parcular agency cohor n perod ; whle n perod + he ndex of ha cohor s ncremened by uny: We complee he de non of U n (.66) by gvng he formal de non of ~ V j ~V j = F j U + F j V j : (.69) Tha s, a he sar of he perod, he worker has probably F j of reurnng o unemploymen, and he complemenary probably of survvng n he rm o work and receve a wage n perod :.7.4. Barganng Problem We assume ha barganng occurs beween a unon represenng he average worker and he employmen agency, and ha gnores he mpac of he wage bargan on decsons lke vacances and separaons, aken by he rm. The Nash barganng problem ha deermnes he wage rae s a combnaon of he worker surplus and rm surplus max! ~V U J (! ) ( ) ; where represens he barganng power of he workers, V ~ U s he worker surplus (where U s he ousde opon of unemploymen), and J (! ) s he rm surplus, whch re ecs ha he ousde opon of he rm n he barganng problem s zero. We denoe he wage ha solves hs problem by ~ W : The rs order condon of hs problem can be found n he appendx. The rs dervave : 9

32 of he surplus wh respec o he wage rae, J w;, s. &; J w; = F + + [ ;& ;+ F + F ] + + [ ;& ;+ ] F + F + F +::: + + N +N [ ;N & N ;+N ] N F N +N where should be noed ha here are no endogenous layo s so ha F j = for all j and :A rse n he wage reduces J only n fuure saes of he world n whch he worker survves boh exogenous ( ) and endogenous separaon ( F j ). If we absrac from axes s easy o verfy ha J w; = V ~ w; : Tha s, a conemplaed ncrease n he wage smply reallocaes resources beween he rm and he worker..8. Moneary Polcy We model moneary polcy accordng o an nsrumen rule of he followng form: ln R R = R ln +r y ln R R h h c + ( R ) [ln c c ] + r ln c + r ln + r y ln c c h h + " R; ; F ; (.7) where he polcy parameers are esmaed o capure he hsorcal behavor of he Rksbank beween 995 and 8. Noce ha we use hours worked nsead of oupu as a measure of he ulzaon of resources. The wo reasons for hs s ha, ) lered hours worked s an observed varable (where he ler s an HP-rend or a KAMEL-rend 6 ) whch enable judgmens of hs measure of resource ulzaon o drecly n uence moneary polcy (whch s only mplcly he case wh he (unobserved) model oupu gap), and ) hs spec caon had a slgh emprcal advanage..9. Fscal Auhores Governmen consumpon expendures are modeled as G = g z + ; where g s an exogenous sochasc process, orhogonal o he oher shocks n he model. suppose ha ln g = g ln g + g ln g + " g ; We 6 KAMEL s a model developed by he Naonal Insue of Economc Research for demographc descrpon of labor marke varables. 3

33 where g = g Y: We se g = :3, he sample average of governmen consumpon as a fracon of GDP. The ax raes n our model are: k ; b ; y ; c ; w : We se he ax rae on capal ncome, k = :5; he payroll ax rae, w = :35; he value-added ax on consumpon, c = :5; and he personal ncome ax rae ha apples o labor, y = :3. We se he ax raes on bonds o zero, b = ; o be able o mach he pre-ax real rae on bonds of.5% n he daa. Seng b = s requred o ge he neres rae on bonds o be hs low, gven he hgh GDP growh rae, log uly of consumpon and no oo close o. All he ax raes are held consan n he model, mplyng ha here are no sochasc ax shocks... Foregn Varables Our represenaon of he sochasc processes drvng he foregn varables akes no accoun ha foregn oupu, Y ; s a eced by dsurbances o z + our model of Y s: ; jus as domesc varables are. In parcular, ln Y = ln y + ln z + = ln y + ln z + ln ; where log (y ) s assumed o be a saonary process. We assume: y ln 3 y y a a a 3 ln y a a a a 3 a 4 4 R R a = a 3 a 3 a 33 a R R z; 6 7 z; B C z 4 A z 5 B C z A ; ln ; ln 3 y " y ; c c c 4 4 " ; + c 6 c 3 c 3 R c B " R ; C 4 z " z ; A ; " ; (.7) where he " s are mean zero, un varance,..d. processes uncorrelaed wh each oher. In marx form, X = AX + C" ; n obvous noaon. Noe ha he marx C has elemens, so ha he order condon for den caon s sas ed, snce CC represens 5 ndependen equaons. We now bre y dscuss he nuon underlyng he zero resrcons n A and C: Frs, we assume ha he shock, " y ;; a ecs he rs hree varables n X ; whle " ; only a ecs he second wo and 3

34 " R ; only a ecs he hrd. The assumpon abou " R ; corresponds o one sraegy for denfyng a moneary polcy shock, n whch s assumed ha n aon and oupu are predeermned relave o he moneary polcy shock. Under hs nerpreaon of " R ;; our reamen of he foregn moneary polcy shock and he domesc one are nconssen because n our model domesc prces are no predeermned n he perod of a moneary polcy shock. Second, noe from he zeros n he las wo columns of he rs row n A and C, ha he echnology shocks do no a ec y : Ths re ecs our assumpon ha he mpac of echnology shocks on Y s compleely aken no accoun by z + ; whle all oher shocks o Y are orhogonal o z + and hey a ec Y va y : Thrd, he A and C marces capure he noon ha nnovaons o echnology a ec foregn n aon and he neres rae va her mpac on z + : Fourh, our assumpons on A and C mply ha ln ; and z; ln are unvarae rs order auoregressve processes drven by " ; and " z ;; respecvely. z Ths s a sandard assumpon made on echnology shocks n DSGE models... Resource Consrans... Resource Consran for Domesc Homogeneous Oupu Resources expressed from he producon sde de nes domesc homogeneous good, Y, n erms of aggregae facors of producon. The scaled verson of he producon funcon (.) yelds real, scaled GDP: y = ; z + ; k (H ) : (.7) where should be noed ha n he curren verson of Ramses II here s no prce dsperson (p = ). I s convenen o also have an expresson ha exhbs he uses of domesc homogeneous oupu. Usng (.8) and (.8), h x z + y = G + C d + I d +! x (p m;x ) x + (! x ) x (! x ) (p x ) or, afer scalng by z + and usng (.4) and (.7): y = g + (! c ) (p c ) c c + p + a (u ) k ; z + ; h x +! x (p m;x ) x + (! x ) x (! x ) (p x x; ) x; (p x ) f y : x; x; (p x ) f Y ; (! ) (.73) where should be noed ha n he curren verson of Ramses II here s no prce dsperson (p = ). When we mach GDP o he daa we use subrac capal ulzaon coss, recrumen coss 3

35 and monorng/bankrupcy coss from y : See secon 3.6 for deals. gdp = y p k a (u ) (! ) NX j=... Trade Balance ; z + ; h ~v j F j l j p Z!!dF (!; )R k P P k ; K We begn by developng he lnk beween ne expors and he curren accoun. Expenses on mpors and new purchases of ne foregn asses, A + ; mus equal ncome from expors and neres from prevously purchased ne foregn asses: S A + + expenses on mpors = receps from expors + R S A ; where s he rsk premum de ned n (.36). Expenses on mpors correspond o he purchases of he specalzed mporers n he consumpon, nvesmen and expor secors, so ha he curren accoun can be wren as ) m;c S A + + S P R ; C m (p m;c m;c + I m p m; m; m; + X m (p m;x! ) m;x m;x = S P x X + R S A ; where p m;c = p m; = p m;x =. Wh prce dsorons among he mpored nermedae goods, he expenses of he homogeneous mpor goods would be hgher for any gven value of C m : Wrng he curren accoun n scaled form and dvdng by P z + ; we oban usng (.6) ) m;c a + q p c R ; c m (p m;c m;c + m where a = S A + =(P z + ): p m; m; m; + x m (p m;x! ) m;x m;x = q p c p x x + R a s ; z + ; (.74).. Exogenous Shock Processes The srucural shock processes n he model are gven by he unvarae represenaon d ^& = &^& + " & ; " & N ; & (.75) where & = f z, ; j ; c ; h ; ; ~ ; " R ; ; " g ; " y ; " ; " R g, j = fd; x; mc; m; mxg ; z = z =z,and a ha denoes he devaon of a log-lnearzed varable from a seady-sae level (^v dv =v for any varable v, where v s he seady-sae level). j," R; " g ; " y ; " ; " R are all assumed o be whe nose (ha s, j = ; "R = ; ec.). 33

36 3. Esmaon We esmae he model usng Bayesan echnques. The equlbrum condons of he model are summarzed n Appendx B Daa We esmae he model usng quarerly Swedsh daa for he perod 995Q 8Q. We do no a hs sage wan o nclude he exraordnary nancal crss afer he collapse of Lehman Brohers why we have cu he sample shor. Compared o ALLV s 5 macro varables, hree addonal varables are ncluded among he observed varables: unemploymen, he spread beween he rskfree rae (.e., he neres rae on governmen bonds wh a maury of 6 monhs o mach he duraon of he corporae deb) and he loan rae enrepreneurs face (.e, he neres rae on all ousandng loans o non- nancal corporaons). The vecor of 8 observed varables are herefore ~Y = [ R daa ^H daa ln(w =P ) daa c;daa ln Y daa ln q daa daa ln C daa ln Unemprae daa ;daa ln I daa ;daa ln X daa R ;daa ln M daa ln spread daa ln G daa ln Y ;daa where he rs seven varables are mached n levels; he repo rae, CPI n aon, GDP de aor, nvesmen de aor, foregn n aon, foregn neres rae, and he hours gap (hours devaon from an hp-rend). The n aon and neres raes are measured as annualzed quarerly raes. The res of he varables are mached n growh raes measured as quarer-o-quarer log-d erences; GDP, consumpon, nvesmen, expors, mpors, real wage, real exchange rae, unemploymen rae, neres rae spread, governmen consumpon, and foregn oupu. All real quanes (excep hours and foregn oupu) are n per capa erms. All varables are seasonally adjused bu no oher pre- lerng of he daa s done (such as demeanng) excep for expors, mpors and governmen consumpon. Snce expors, mpors and governmen consumpon grow a subsanally d eren raes compared o oupu we adjus he mean growh raes of hese hree seres so ha hey are growng a he same pace as oupu (.e., we ake ou he excess rends n expors and mpors and add an exra rend o governmen consumpon). We also exrac an obvous ouler n 997 from he governmen consumpon seres. The daa are aken from Sascs Sweden and Sverges Rksbank (.e., repo rae, neres rae spread, foregn varables). The foregn varables on oupu, he neres rae and n aon are weghed ogeher across Sweden s larges radng parners n 99 usng weghs from he IMF. The hck black lne n Fgure D n he Appendx plos he daa used n he esmaon. ] ; (3.) 34

37 3.. Calbraon We choose o calbrae he parameers relaed o he seady-sae values of he observable quanes, for example he grea raos (.e., C=Y, I=Y and G=Y ). Table shows he calbraed parameers. The dscoun facor and he ax rae on bonds b are calbraed o yeld a real neres of rae equal o :4 percen annually. We calbrae he capal share o :35 whch yelds a capaloupu rao slghly below on an annual bass. The capal share s se hgher han mos of he leraure o compensae for he e ec of a posve exernal nance premum. Sample averages are used when avalable, e.g. for he varous mpor shares! ;! c ;! x (obaned from npu-oupu ables), he remanng ax raes, he governmen consumpon share of GDP, g, growh raes of echnology (usng nvesmen prces o dsenangle neural from nvesmen-spec c echnology) and several oher parameers. To calbrae he seady value of he n aon arge we smply use he n aon arge saed by Sverges Rksbank. We le he markup of expor good producers x be low so as o avod double markng up of hese goods. All oher prce markups are se o :, followng a wde leraure. We requre full workng capal nancng n all approprae secors. The ndexaon parameers { j ; j = d; x; mc; m; mx; w are se so ha here s no ndexaon o he n aon arge, bu nsead o whch s se equal o he seady sae n aon. Ths mples ha we do no allow for paral ndexaon n hs esmaon, whch would resul n seady sae prce and wage dsperson. The curvaure parameer deermnng he cos of varyng he capacy ulzaon, a, s calbraed o : o allow for a varyng degree of ulzaon of he capal sock. Bayesan poseror odds ndcae ha daa are srongly agans havng a xed capacy ulzaon ( a = 6 ) when we compared wo calbraed values. We dd no nclude hs parameer n he esmaon because n ALLV (7) a urned ou o generae convergence problems n he Meropols chan. For he nancal block of he model we se F (!) equal o he sample average bankrupcy rae accordng o mcrodaa from he leadng Swedsh cred regsry, called UC AB. W e =y has no oher noceable e ec han jonly wh deermnng he n=(p k k) and s se o yeld a he pror mean: For he labor block, he seady sae unemploymen rae s o 7% whch s :3% below he sample average (995Q 8Q) bu more or less equal o he average over a longer horzon (986Q 8Q). The lengh of a wage conrac N s se o an annual negoaon frequency, = o yeld quadrac recrumen coss, and s se so ha akes an unemployed person on average 3 quarers o nd a job (.e. f = =3), n lne wh he evdence presened n Forslund and Johansson (7) for compleed unemploymen spells. Holmlund (6) presen evdence of unemploymen duraon for all unemploymen spells beng slghly hgher, around 4 quarers. The machng funcon parameer s se o :5 so ha number of unemployed and vacances have equal facor shares n he producon of maches. m s calbraed o mach he probably Q = :9 of 35

38 llng a vacancy whn a quarer, alhough hs s merely a normalzaon. We assume hrng coss, and no search coss by seng = and hereby follow GST. We are renforced n hs calbraon by he lmed mporance of search coss ha has been documened usng Swedsh mcrodaa by Carlsson, Erksson and Gofres (6). Parameer Value Descrpon :35 Capal share n producon :9999 Dscoun facor! :43 Impor share n nvesmen goods! c :5 Impor share n consumpon goods! x :35 Impor share n expor goods g :3 Governmen consumpon share of GDP k :5 Capal ax rae w :35 Payroll ax rae c :5 Consumpon ax rae y :3 Labor ncome ax rae b Bond ax rae z :5 Seady sae growh rae of neural echnology :4 Seady sae growh rae of nvesmen echnology ; :5 Seady sae gross n aon arge x :5 Expor prce markup j : Prce markups, j = d; mc; m; mx ; x ; f Workng capal shares a : Capacy ulzaon (curvaure) e a : Rsk premum dependence on ne foregn asses # w ; w Wage ndexaon o real growh rend and lagged n aon { j j Indexaon o n aon arge for j = d; x; mc; m; mx; w F (!) :63 Seady sae bankrupcy rae W e =y : Transfers o enrepreneurs L :7 Seady sae fracon of employmen N 4 Number of agency cohors/lengh of wage conracs Curvaure of recrumen coss :976 Exogenous survval rae of a mach :5 Unemploymen share n machng echnology m :5559 Level parameer n machng funcon Employmen adj. coss dependence on ghness Table. Calbraed parameers. Throughou he esmaon, four observable raos are chosen o be exacly mached n our seady-sae soluon and accordngly four correspondng seady-sae parameers are recalbraed for each (esmaed) parameer draw. We se he deprecaon rae o mach he rao of nvesmen over oupu, p =y, he enrepreneural survval rae o mach he ne worh o asses rao 7, 7 We used mcro daa o calculae he average equy/oal asses durng he sample perod boh for all Swedsh rms and for only he sock marke lsed rms. In he rs case book values where used, and n he second case marke value of equy was used. Boh raos where close o.5. 36

39 n=(p k k);he seady sae real exchange rae ~ o mach he expor share P x X=(P Y ) n he daa, and nally we se he dsuly of labor scalng parameer A L o x he fracon of her me ha ndvduals spend workng. The values of hese four calbraed parameers (evaluaed a he poseror mode) are presened n Table. Parameer descrpon Calbraed value Momen Momen value Deprecaon rae of capal : p =y.7 Enrepreneural survval rae :969 n=(p k k).5 ~ Real exchange rae :87 P x X=(P Y ).44 A L Scalng of dsuly of work 46:9 L&.7 Table. Mached momens and correspondng parameers (evaluaed a he poseror mode) Choce of prors In oal we esmae 64 parameers, of whch 6 are VAR parameers for he foregn economy, 8 are AR-coe cens and 7 are sandard devaons of he shocks. The prors are dsplayed n Tables A and A. Compared o he old model (Ramses) he pror dsrbuon s smlar for many of he parameers. For example, he Calvo prce sckness parameers are esmaed wh a bea dsrbuon wh mean :75 and sandard devaon :75, correspondng o an adjusmen of prces once a year based on he mcro evdence n Apel, Frberg and Hallsen (5). As n Ramses, bu n conras o CTW, we le he ndexaon parameers o pas n aon n he prce seng, j j(d; mc; m; mx), be he same n all secors and esmae wh a relavely d use bea pror cenered a :5. There are also some noable excepons compared o Ramses as well as o CTW: The nverse of he Frsch elascy of labor supply, L ; whch, n conras o Ramses, s now esmaed. We use a gamma dsrbuon wh pror mode and sandard devaon.5. The pror mode follows Smes and Wouers (3) and falls beween he calbraed value of n Ramses as well as n Chrsano, Echenbaum and Evans (5) and CTW:s pror mode of 7:5. Mcro evdence end o nd lower Frsch elasces (.e., / L ) han normally used n DSGE models. Typcally mcro esmaes of he Frsch elascy le n he range of :5-:3, see e.g. MaCurdy (986) who repors a Frsch elascy of :5 for U.S. men. 8 However, Flodén and Domej (6) show ha esmaes of he labor supply elascy s based downward f borrowng consrans are gnored. They repor an elascy of :36 for U.S. marred men when hey ake hs no accoun, mplyng a value of :7 for L : There are wo new parameers relaed o he labor model compared o Ramses ha are beng esmaed. For he fracon of GDP spen on vacancy coss, recshare, we use a pror wh a mode 8 See Mullgan (998) for an alernave vew on he small mcro esmaes and Rogerson and Wallenus (9) on he relaon beween mcro and macro esmaes. 37

40 of :% correspondng o = :3. 9 Ths s slghly below he value of :4% used by Galí (). We se he mode for he replacemen rae for unemployed workers, bshare, o :75 whch s slghly above he average sauory replacemen rao afer ax for hs me perod whch s :7. The reason o pu he pror above he sauory rae s ha he laer gnores he uly value of lesure and any prvae unemploymen nsurance, whch s reasonably common. Regardng he nancal model here are wo new parameers beng esmaed. The pror mode for s se o :33 o yeld a :6% annual exernal nance premum, as hs s he sample average. We choose a d use pror so as o le daa deermne he elascy of he nance premum n erms of bass pons, as hs s wha a ecs he dynamcs of he economy. For he shock o enrepreneurs dosyncrac producvy (.e., he survval rae of he enrepreneur) we use an unnformave nverse gamma dsrbuon wh pror mode :5. The pror mode of he correspondng perssence parameer s :85. In Ramses he nsrumen rule responded o oupu, whereas n Ramses II responds o hours worked. We se he pror mode of he response coe cens o he resource ulzaon o almos he same values, however. We use a normal dsrbuon wh pror mode :5 for r y, and a gamma dsrbuon wh pror mode :5 for r y Shocks In oal, here are 3 exogenous sochasc varables n he model. of hese evolve accordng o AR() processes: ; ; c ; c ; h ; ~ ; ; ; g; ; m ; a Furher, we have 6 shock processes ha are..d.: d ; x ; m ; mc ; mx ; " R : Fnally, he las 5 shock processes are assumed o follow a VAR(): y ; ; R ; z ; : In he esmaon we only allow for 7 shocks. Accordngly we do no allow sx shocks presen n he heorecal model: he n aon arge shock c, he shock o barganng power ; he shock o machng echnology m ; he shock o he sandard devaon of dosyncrac producvy of workers a ; he un roo shock o nvesmen-spec c echnology enrepreneur rsk shock. Indeed for our sample, Formally he seady sae recrumen share s de ned as recrushare = N ~v l y and he dosyncrac 8, he de jure n aon arge has In hs way we are no consraned by he assumpon for he funconal form of he dosyncrac rsk. 38

41 been n place he enre perod and has been consan. also seems super uous as we already have he sandard labor supply shock - he labor preference shock h. We excluded as dd no conrbue subsanally o explanng any varable n prelmnary esmaons. For he reason for excluson was he hgh correlaon wh he oher nancal shock, Measuremen errors Snce Swedsh macro daa s measured wh subsanal nose, we allow for measuremen errors n all varables excep for he nomnal neres raes n Sweden and abroad. The varance of he measuremen errors s calbraed so ha corresponds o % of he varance n each daa seres Measuremen equaons Below we repor how he model s lnked o he observable daa hrough he 8 measuremen equaons. The daa s measured n percenages so he model varables are accordngly mulpled by. Furhermore he daa seres for n aon and neres raes are annualzed, so hese model varables are mulpled by 4. R daa = 4(R ) # 4(R ) R ;daa = 4(R ) # 4(R ) daa = 4 ln # 4 ln + " me ; c;daa = 4 ln c # 4 ln c + " me c ; ;daa = 4 ln # 4 ln + " me ; ;daa = 4 ln # 4 ln + " me ;; 39

42 ln Y daa = (ln z + ; + ln(y p a (u ) NX j= h ~v j F j l j # (ln z +) + " me y; k ; z + ; ln Y ;daa = (ln z + ; + ln y ) # (ln z +) + " me y ; ln C daa = (ln z + ; + ln c ) # (ln z +) + " me c; ln X daa = (ln z + ; + ln x ) # (ln z +) + " me x; ln q daa = ln q + " me q; ln H daa = ln H meas + " me H; Z!!dF (!; )R k P P k ; K ) ln M daa = (ln z + ; + ln Impors ) # (ln z +) + " me 3 = 6 4 ln z + ; + ln c m + m (p m;c p m; +x m (p m;x ln I daa = ln z + ; + ln ; + ln ) m;c m;c m; m; ) m;x m;x ln G daa = (ln z + ; + ln g ) # (ln z +) + " me g; M; C7 A5 # (ln z +) + " me # (ln z + + ln ) + " me I; M; ln(w =P ) daa W = ln ~ z + P = (ln z + ; + ln w avg ) # (ln z +) + " me W=P; ln Spread daa = ln(z + R ) = +R+ k ln Unemp daa = ln( L ) + " me Unemp;: n + p k ; k+ R A + " me Spread; where " me ; denoe he measuremen error for he respecve varable. In addon, we nroduce he parameers # f; g and # f; g whch allows us o handle demeaned and non-demeaned daa. However, n hs verson of he model we are only workng wh non-demeaned daa; # = ; # =. Noe ha neher measured GDP nor measured nvesmen nclude nvesmen goods used for capal manenance. The reason s ha he documenaon for calculaon of he Swedsh Naonal Accouns (SOU ()) ndcae ha hese are no ncluded n he nvesmen de non (and he naonal accouns are prmarly based on he expendure sde). To calculae measured GDP we also exclude monorng coss and recrumen coss. Fnally, de ne he measuremen equaon for real wages we have used he employmen-weghed 4

43 average Nash barganng wage n he model: w avg = L NX j= l j G j;jw j w j 4. Resuls 4.. Poseror parameer values In Tables A and A he poseror mode esmaes of he parameers are shown. All Calvo prce rgdy parameers have a poseror mode of roughly around :8, see Table A. Compared o he old model (Ramses), he prce sckness n he domesc secor s a lo larger; :84 compared o :7. Ths means ha he domesc Phllps curve wll be much aer n Ramses II. In conras, he prces n he mpor and expor secors are subsanally more exble n Ramses II han n he old model. Now mpor and expor prces are re-se opmally a leas once a year compared o every second or even every fourh year as for he mpored nvesmen goods n he old model. There are several reasons for hs ndng. In Ramses II a subsanal par of mpors ener drecly no expors, so a lo of he varaon n he real seres can be accouned for whou creang a enson n machng also he consumpon seres, for nsance. Ths also apples when he exchange rae ucuaes. Varaon n mpors due o exchange rae movemens does no lead o he same exen of expendure swchng no he domesc good. The e ec of exchange rae ucuaons are hus smaller n Ramses II, and prces need no be as rgd o avod large movemens n n aon. Alogeher hs splls over o he prce seng and hus he degree of prce sckness. The nvesmen adjusmen cos, S ; s esmaed o be a lo lower compared o he leraure as well as compared o Ramses. The parameer, S ; s esmaed o be :9 n Ramses II, whch s abou four mes smaller han n he old model. However, he nancal frcons appled o he enrepreneur nduce a gradual response of nvesmen, whch means ha he nvesmen adjusmen coss ake on a more super ous role n he new model. Also he frcon peranng o consumpon, he hab perssence b, urn ou o be a lo lower han expeced. The poseror mode for b equals :53 n Ramses II. Agan should be noed ha a possble explanaon for hs s ha par of he mpors are used for expors. Wh lower expendure swchng e ecs boh he subsuon elascy beween domesc and mpored goods, c ; and he hab perssence can be lower whou generang large ucuaons n he consumpon seres. c s now beng esmaed o :4 nsead of beng calbraed o 5 n he old model. The poseror mode of he perssence n he nsrumen rule, R s esmaed o :83, whch makes he polcy rule a lle b less perssen n he new model. However, snce he nsrumen rule s spec ed n erms of hours worked nsead of oupu as n he old model, and here s no exchange rae response, also he response coe cens on he real varables changes somewha. The poseror mode esmae of he coe cen on he hours gap s r h = :5: 4

44 ~ s deermnes how much he forward premum puzzle s allowed o a ec he rsk premum n he neres rae pary condon, and hereby he hump shape of he exchange rae o a moneary polcy shock. The poseror mode esmae s :3 n Ramses II whch s slghly lower han n he old model (:48). Ths mples devaons from UIP, bu as we shall see below, he hump shape of he real exchange rae s no as pronounced as n he old model. We now urn o he new parameers n Ramses II. The degree of nancal frcons n he model s deermned by, whch capures he bank s monorng coss and hereby he sze of he spread beween he rsk free rae and he neres rae pad by he enrepreneurs. The poseror mode esmae of s :47, whch mples a spread of :3% durng he sample perod. Regardng he new parameers n he labor marke block, he replacemen rae for unemployed workers, bshare, s esmaed o be :97, whch s subsanally hgher han he replacemen rae n he publc Swedsh unemploymen nsurance. The model needs bshare o be hgh n order for he household o be relavely nd eren beween workng and sayng n unemploymen n order o be able o explan varaons n unemploymen. The recrumen coss as a fracon of GDP, recshare, s esmaed o be :9 percen. I should be noed ha he Frsch elascy of labor supply, = L, s hard o denfy and hghly dependen on whch pror we choose. Wh a pror mean of :; we oban an esmae of L = :53. Ths mples ha a larger par of ucuaons n hours worked are arbued o he nensve margn nsead of unemploymen compared o he case wh a larger pror on L, whch would have generaed more dsuly for he household n changng he workng nensy. As menoned n Secon 3.3 hs s a conroversal parameer snce he mcro and macro evdence are so dspersed. We have aken a conservave vew here and reled more on pror macro evdence and he resuls of Flodén and Domej (6) when hey ake ncomplee markes no accoun. We noe from he poseror sandard devaons n Table A ha daa seem nformave abou mos of he esmaed parameers and ha he poseror dsrbuon s more concenraed han he pror dsrbuon. 4.. Model Fgure D shows he daa (hck lne) used n he esmaon and he one-sded Kalman- lered onesep-ahead predcons from he model (hn lne) compued a he poseror mode. We see ha he model capures he low-frequency ucuaons n he daa relavely well for mos of he observed varables bu msses ou on many of he hgh-frequency movemens, especally n he four n aon seres as well as n expors and mpors. In addon, he real wage grows oo slowly n he model compared wh he daa, hroughou he sample. One explanaon o hs s ha he real wage s compued usng he GDP de aor whch s an exremely volale seres. Much of he varance n he daa should hus no be arbued o he srucural model. For he hree new varables (compared o Ramses I), he model can explan he growh rae n unemploymen reasonably well 4

45 bu makes a bad job n explanng governmen consumpon and he spread. However, scal polcy s only rudmenary modeled so hs s perhaps no so surprsng. I s more cumbersome ha he of he spread s no sasfacory. Table A3 presens he rs and second momens n he daa and n he model (calculaed a he poseror mode), as well as he mporance of he measuremen errors. We see ha here s an excess rend n expors and mpors ha can no be mached by he model, where all real varables grow a he same pace. Governmen consumpon on he oher hand grows oo slowly n he daa compared wh he model why we have adjused hs seres oo. As can be seen from he able here s also a clear downward rend n unemploymen ha can no be explaned whn he model. We have, however, no pre- lered hs seres. The same apples o he nvesmen seres, whch grows much faser n he daa compared o he model. Regardng he volaly n he model and he daa we see ha he second momens seems o be capured sasfacory. The las column shows how much of he varance n he daa ha can be accouned for by he srucural shocks n he model. We see ha he measuremen error n he wage equaon s obvously oo large snce hs accouns for almos 3% of he varaon of he real wage growh n he daa. As already menoned above, hs s a problemac seres. For he oher varables, he srucural shocks accoun for abou 95% or more of he varance n he daa, wh he excepon of mpor and expor growh whch have a slghly lower rao of srucural explanaon (84% and 9%, respecvely). All n all, we herefore beleve he sze of measuremen errors are approprae. An addonal, perhaps more ndrec, way o evaluae he way he addon of nancal frcons o he baselne model s he daa s o compare daa whch was no used n he esmaon of he model, such as bankrupcy daa, wh he smoohed, wo-sded Kalman lered, esmaes of he bankrupcy rae n he model. Fgure H shows he smoohed, wo-sded Kalman lered, esmaes of he bankrupcy rae compued a he poseror mode and bankrupcy daa aken from UC AB. We see ha he model capures he low-frequency ucuaons n he bankrupcy daa relavely well Smoohed shock processes Fgure E shows he smoohed, wo-sded Kalman lered, esmaes of he shock processes (devaons from seady sae). The un-roo echnology shock, z, appears o have a clear rend. The reason for hs s he way he shock s den ed hrough he foregn VAR and he measuremen equaons for he domesc and foregn real varables. Because he echnology shock has a drec mpac on he foregn neres raes n he VAR (see eq. (.7) where a 34 6= and c 34 6= ), permanen echnology shocks jonly explan boh foregn neres raes as well as he real varables domescally and abroad. Snce he foregn neres rae conans a downward rend n our sample, daa forces he poseror mode esmae of he perssence n he echnology process up o 43

46 z = :93, o be able o explan hs movemen n he neres rae and he smoohed esmae of z urns ou rendng. Ths s also he reason for why he un-roo echnology shock comes ou so mporan n he varance decomposon for he hree foregn varables. In conras, f he drec e ec of he permanen echnology on he foregn neres rae s urned o, a 34 = and c 34 =, z s only den ed hrough he measuremen equaons (whch s more lke he seng n Ramses). Ths would mply a lower esmae of he perssence, z, snce echnology s no longer forced o drecly explan he neres rae, and he smoohed esmae of z would no longer be rendng.impulse response funcons 4.4. Impulse response funcons We plo mpulse response funcons a he poseror mode for all 7 shocks. The rs gure for each shock shows he observed varables n levels (.e., percenage devaons from seady-sae for all shocks excep he un-roo echnology shock for whch we plo he rue level n percen). As an example, unemploymen rases.% o a posve moneary polcy shock whch means ha unemploymen ncreases from 7% o 7:%. The second gure for each shock shows he mpulse response funcons for some key varables of neres rae relaed o he labor marke and he capal marke, such as for nsance nensy, wages, value funcons for he worker and he employer, and nancal varables such as he spread, ne worh, bankrupcy rae as well as he real raes domescally and abroad. The mpulse response funcons o a moneary polcy shock s relavely smlar n Ramses II and Ramses, wh a reasonable ransmsson mechansm. A emporary hke n he nomnal neres rae wh 5 bass pons, lowers CPIF n aon wh abou.%. The response n Ramses s smlar bu a lle b more hump-shaped. The same perans o he real exchange rae whch have a hump ha s a lo more pronounced. The reason for hs s he smaller esmae of s, whch deermnes he degree o whch he UIP-condon n he model s mod ed. As saed above hs parameer s :48 n Ramses whle :3 n Ramses II. Ths mples less mpac on he rsk premum from exchange rae changes and hence he response s more lke a spke. CTW uses anoher spec caon of he rsk premum and appears no o oban much of hump-shape. The e ecs of he posve moneary polcy shock s ampl ed by he nancal frcons. Enrepreneural ne worh s reduced boh because of he fallng prce of capal and because of he surprse dsn aon ha ncreases he real value of he nomnal deb. Accordngly he neres rae rsk spread ncrease by abou 5 bass pons (annualzed). Ths has mpac foremos on he response of nvesmen. We see ha he nvesmens decreases by almos % n Ramses II and by more han.5% n CTW compared o he modes response of.5% n Ramses. One should however remember ha he moneary polcy shocks explan relavely lle of he varaon n nvesemen (see Table A4). The oupu response do no change much beween RamsesII and Ramses whch s probably due o he fac he resources n Ramses II are used up because monorng ncreases followng he shock. I s also worh nong 44

47 ha we oban a more scky or slow response of hours n Ramses II han n Ramses. Changes n hours, for hs parcular shock, are due o varaons n unemploymen (raher han nensy). Snce unemploymen s predeermned (recall agan ha we only have exogenous layo s), hours wll also be rgd. Ths sems well wh he fac he labor marke lags producon n he daa. The mpulse responses o a saonary echnology shock are prncpally smlar (qualavely) n Ramses and Ramses II alhough he dscrepances are somewha larger han for he moneary polcy shock. I s manly he responses o n aon ha are somewha smaller n Ramses II. The e ecs of d erences n producvy ares maller because of he rgdes n he labor marke (hours). However, for hs shock boh hours per employee (nensy) and employmen changes. An ncrease n producvy leads o drop n hours worked. Snce here s a posve correlaon n he daa beween employmen and oupu we have rgged he model so ha unemploymen decreases o hs shock. However, hs mples ha hours per employee drops subsanally o make hours work decrease. We see he oppose response n CTW; unemploymen ncreases afer a posve echnology shock. If one nerpres he saonary echnology shock as posve busness cycle chock, hs would square well wh he ncrease n employmen n Ramses II. Noce also ha he nsrumen rule n Ramses II responds o he gap and growh rae n hours worked, whereas Ramses rule responds o oupu. Ths means ha moneary polcy do no ry o counerac echnolgy shocks n Ramses II (hey are accomodaed by a decrease n neres raes), whereas moneary polcy res o balance he ncrease n he oupu gap n Ramses (where poenal oupu by de non s no a eced by saonary echnology shocks so ha he oupu gap ncreases.) Comparng he mpulse response funcons o a rsk premum shock, we see ha he exchange rae channel s weaker n Ramses II han n Ramses. Ths s due o several reasons. Frs, we allow for a par of mpors o ener expors drecly. Ths mples less of a enson n he model when machng boh consumpon (small volaly) and aggregae mpors (large volaly). Par of he volaly can be dreced no expors whch yelds a smaller esmae of he subsuon elascy n he consumpon baske ( c ) and hereby smaller expendure swchng e ecs han n Ramses. Second, he rsk premum shock s esmaed o be smaller and less perssen. Thrd, and mos mporan s, however, ha he nsrumen rule d ers n Ramses II and Ramses. We do no allow for a drec response o he real exchange rae n Ramses II. Ths mplcly yelds lower n aon and lower volaly n oupu due o more emphass on hese varables. The enrepreneural wealh shock drves up CPIF n aon, consumpon, nvesmen and oupu. The responses o oupu s very perssen. The key d erence versus he nvesmen-spec c shock s ha he wealh shock mples an ncrease n ne worh (he sock marke) Varance Decomposon Table A4a and A4b presens he varance decomposon a, 4, 8 and 4 quarers ahead compued a he poseror mode. The rs hng o noe s ha n he shor run, quarer ahead, moneary 45

48 polcy shocks explan he larges par (55%) of he varaons n he neres rae, domesc and mpored markup shocks explan almos 8% of he varaon n CPIF n aon, and saonary echnology shocks are he man deermnan (3%) behnd varaons n oupu growh. However, markup shocks, especally mpors-for-expors markup shocks are also mporan (5%) for he shor-run varaon n oupu growh. A longer horzons, 8 and 4 quarers, he pcure s more dspersed and echnology shocks, boh un-roo and saonary shocks have a larger mpac on all varables (nomnal as well as real). Unemploymen s predeermned (snce we only allow for exogenous layo s), so he measuremen error explans % of he varaon one-sep ahead. A longer horzons, he labor preference shock explans slghly below % of changes n he unemploymen seres, bu echnology shocks as well as markup shocks are also man facors explanng he developmen n he labor marke. For hours worked also consumpon preference shocks play an mporan role. Noe ha markup shocks can be mporan also a longer horzons even f hey are..d. The shock relaed spec cally o he nancal block, ha s he enrepreneural wealh shock, explans 35-45% of he varaon n nvesmen growh and abou 45% of he varaon n he spread d erence a he d eren horzons, bu only abou 3% of he varaon n oupu growh. Noce, however, ha he enrepreneural wealh shock has a larger mpac on he level of oupu, where explans abou % of he varance (no shown). As a sde noe; also durng he nancal crses, followng he collapse of Lehman Brohers, shocks n he nancal secor play only a mnor role n explanng he large fall n oupu. The model nsead explans hs wh a combnaon of foregn dsurbances, expor markup shocks, rsk premum shocks and o a small exen, he enrepreneural wealh shock. The nvesmen spec c echnology shock s sll mporan n explanng ucuaons n nvesmen growh as well as changes n he spread. I accouns for abou 3-4% of he varaon n nvesmen and 5% of he varaon n he spread. CTW repors ha he nvesmen echnology shock s crowded ou by he enrepreneural shock, whch holds rue for he level of nvesmen bu no he growh rae. I should be noed ha he un-roo echnology shock sands ou as very mporan for he foregn varables, n parcular he foregn neres rae. The permanen echnology shock accouns for 55% of he varaon n he foregn neres rae a 8 quarers horzon and he foregn oupu shock explans almos all of he res (4%). The foregn neres rae s, hence, predomnanly drven by movemens n foregn oupu raher han he foregn polcy shock Forecass In Fgure F, he recursve model forecass wh daa up o and ncludng 3Q4 8Q are ploed agans acual daa. I should be noed ha he model s no reesmaed and ha he projecons are n-of-sample forecass - quarers ahead based on he same poseror mode vecor 46

49 (see Tables A and A). The model forecass capure oupu growh, CPIF n aon, and n parcular nvesmen growh relavely well. The model also seems o capure he man movemens n unemploymen well. On he oher hand, he model ends o overesmae he nomnal neres rae. Ths s, however, no spec c o Ramses II bu was also he case for he old model (Ramses). If one compares he (n-of-sample) forecas accuracy of Ramses II and Ramses, he roo mean square error for he neres rae s n fac smaller for Ramses II (see Fgure I). In erms of hours and CPIF n aon, Ramses II also does beer for all horzons. The models have more or less he same accuracy for GDP growh, whereas Ramses II forecass for he real exchange rae are slghly worse, a leas for he very shor horzons ( o 4 quarers ahead) Level daa on unemploymen The model s esmaed machng changes n unemploymen ( rs d erenced daa). However, snce he sample mean n he daa s hgher han our seady-sae calbraon (8:3% agans 7%), hs mples ha he model Kalman- lers ou an esmae of he unemploymen level ha s roughly % lower han he acual unemploymen level n he daa. Ths also has consequences for many oher unobserved levels, such as capal, nvesmen, consumpon, oupu ec., n he model. In he recen polcy rounds he model has, n conras o he sraegy durng esmaon, been fed wh he unemploymen level as an observable varable Snce he (observed) hours gap s he same n boh cases, equaon (B.94) mples ha hours per employee (.e., he nensy) mus move around o compensae for he change n (un)employmen. A d eren esmae of nensy, n urn, a ecs he consumpon euler equaon and we ge, for example, anoher esmae of he consumpon level n he model. To llusrae hs, Fgure G shows he wo-sded (smoohed) Kalman lered esmaes of some of he sae varables n he model when we use he unemploymen growh or he unemploymen level as an observable varable. Noce ha many of he level seres are no cenered around zero for he level code, whch should be aken no accoun when analyzng he curren sae of he economy. 5. Concluson Ths paper descrbes Ramses II, he dynamc sochasc general equlbrum (DSGE) model currenly n use a he Moneary Polcy Deparmen of Sverges Rksbank. The model s used o produce macroeconomc forecass, o consruc alernave scenaros, and for moneary polcy analyss. The model was nally developed by Chrsano, Traband, and Walenn (), bu he curren verson of he model d ers from CTW n some respecs. Compared wh he earler DSGE model a he Rksbank, he Ramses model developed by Adolfson, Laséen, Lndé and Vllan (8), Ramses II d ers n hree mporan respecs. Frs, The daa used n hs exercse s from Moneary Polcy Repor :. 47

50 nancal frcons are nroduced n he accumulaon of capal, followng Bernanke, Gerler, and Glchrs (999) and Chrsano, Moo, and Rosagno (3; 8). Second, he labor marke block ncludes search and machng frcons followng Gerler, Sala, and Trgar (8). Thrd, mpored goods are used for expors as well as for consumpon and nvesmen. 48

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55 A. Tables and Fgures Pror Poseror Dsr. Mean S.d. Mode S.d. d x mc m mx w L b S R r N r N r y N r y N x c f ~ s recshare; % bshare z " c h ~ g a N a N a33 N a N a3 N a N a3 N a4 N a3 N..5.. a3 N a34 N c N c3 N c3 N c4 N c34 N Table A. Esmaon resuls. Parameers. 53

56 Pror Poseror Dsr. Mean S.d. Mode S.d. z Inv-.5 Inf.78.9 " Inv-.5 Inf Inv-.5 Inf.74.6 c Inv-.5 Inf.4.9 h Inv-.5 Inf ~ Inv-.5 Inf "R Inv-.5 Inf.75. g Inv-.5 Inf d Inv-.5 Inf x Inv-.5 Inf mc Inv-.5 Inf..64 m Inv-.5 Inf..3 mx Inv-.5 Inf Inv-.5 Inf..3 y Inv-.5 Inf.68.4 Inv-.5 Inf.8. R Inv-.5 Inf.9.4 Table A. Esmaon resuls. Sandard devaon of shocks. Mean Sandard dev. Srucural explanaon Daa Model Daa Model var(measure error) - var(daa) CPIF n aon Domesc n aon Inves. n aon Nom. nres rae GDP growh Real wage growh Consumpon growh Invesmen growh Gov. cons growh Impor growh Expor growh Toal hours Real exchange rae growh Spread growh Unemploymen growh Foregn GDP growh Foregn n aon Foregn neres rae The rend above(under) he growh rae n oupu (.59) s aken ou before esmaon. Table A3: Frs and second momens n he daa and n he model (n percen), and mporance of measuremen errors 54

57 55 Table A4a: Varance decomposon (a and 4 quarers horzon)

58 56 Table A4b: Varance decomposon (a 8 and 4 quarers horzon)

59 Fgure A. Graphcal llusraon of he goods producon par of he model. Fgure B. Graphcal llusraon of he labor and capal markes of he model. 57

60 Fgure C. Tmelne for labor marke n employmen frcon model. 58

61 Oupu growh Consumpon growh Hours worked Foregn oupu growh Ineres rae Invesmen growh Real wage growh Foregn nflaon CPIF nflaon Expor growh Real exch. rae dff Foregn neres rae Domesc nflaon Impor growh Unemploymen growh Invesmen nflaon Governmen cons growh Spread dff Daa Model (one sded predcons) Fgure D. Daa (hck black) and one-sded Kalman- lered predcons (hn red). 59

62 x Un roo 3 ech Moneary polcy Expor markup y* Saonary ech Domesc markup Rsk premum x 3 p* Inves spec ech Impor cons markup x 3 Enrepreneural wealh x 3 R* Cons pref Impor nves markup g Labor supply Impor for expor markup Fgure E. Smoohed (wo-sded Kalman lered) esmaes of he shocks (devaons from seady-sae) 6

63 .5.5 Oupu growh Consumpon growh Hours gap Foregn oupu growh Nomnal neres rae Invesmen growh Real wage growh Foregn nflaon CPIF nflaon 5 8 Expor growh Real exch rae dff Foregn neres rae Domesc nflaon 5 8 Impor growh Unemploymen dff Daa Model Invesmen nflaon 5 8 Gov. consumpon growh 5 8 Spread dff 5 8 Fgure F. Acual daa (hck lne) and (n-of-sample) model forecass (hn lne) wh daa up o 3Q4-8Q 6

64 lunempraeu 5 lvxzplusu 5 lyu 5 lrkbaru lnensyu 5 ljzplusu 5 lcu 5 lku lhu 5 lvu 5 lu 5 lepslonu Unemploymen dff Unemploymen level 4 6 lwbaru 5 lfu 5 lxu 5 x 3 lmuzu lavg N ashu 5 lgu 5 limporu 5 lzeahu 5 Fgure G. Two-sded (smoohed) Kalman lered esmaes of some key sae varables when eher unemploymen growh or unemploymen s used as observable. 6

65 Fgure H. Smoohed (wo-sded Kalman lered) esmae of he bankrupcy rae n Ramses II and acual bankrupcy daa (black lne) from UC AB - Sweden s larges busness and cred nformaon agency. 63