WP/15/227 acrofnancal nalyss n he World Economy: Panel Dynamc Sochasc General Equlbrum pproach by Francs Vek IF Workng Papers descrbe research n progress by he auhor(s) and are publshed o elc commens and o encourage debae. The vews expressed n IF Workng Papers are hose of he auhor(s) and do no necessarly represen he vews of he IF s Execuve oard or IF managemen.
215 Inernaonal oneary Fund WP/15/227 IF Workng Paper oneary and apal arkes Deparmen acrofnancal nalyss n he World Economy: Panel Dynamc Sochasc General Equlbrum pproach Prepared by Francs Vek 1 uhorzed for dsrbuon by Ulrc Erckson von llmen Ocober 215 IF Workng Papers descrbe research n progress by he auhor(s) and are publshed o elc commens and o encourage debae. The vews expressed n IF Workng Papers are hose of he auhor(s) and do no necessarly represen he vews of he IF s Execuve oard or IF managemen. bsrac Ths paper develops a srucural macroeconomerc model of he world economy dsaggregaed no fory naonal economes. Ths panel dynamc sochasc general equlbrum model feaures a range of nomnal and real rgdes exensve macrofnancal lnkages and dverse spllover ransmsson channels. varey of moneary polcy analyss fscal polcy analyss macroprudenal polcy analyss spllover analyss and forecasng applcaons of he esmaed model are demonsraed. These nclude quanfyng he moneary fscal and macroprudenal ransmsson mechansms accounng for busness cycle flucuaons and generang relavely accurae forecass of nflaon and oupu growh. JEL lassfcaon Numbers: 11; 33; 51; E3; E44; E52; E62; F41; G21; G28 Keywords: oneary polcy analyss; Fscal polcy analyss; acroprudenal polcy analyss; Spllover analyss; Forecasng; World economy; ayesan economercs uhor s E-al ddress: FVek@mf.org 1 The auhor graefully acknowledges advce provded by Tamm ayoum and Peer Daels as well as commens and suggesons receved from semnar parcpans a he ank of anada and he IF.
2 onens Page I. Inroducon... 5 II. The Theorecal Framework... 6. The Household Secor... 7 onsumpon and Savng... 7 ank Inermedaed Households... 11 apal arke Inermedaed Households... 11 red onsraned Households... 13 Labor Supply... 13. The Producon Secor... 15 Oupu Demand... 15 Labor Demand and Invesmen... 16 Oupu Supply... 19. The ankng Secor... 2 red Demand... 2 Fundng Demand and Provsonng... 22 red Supply... 24 D. The Trade Secor... 25 The Expor Secor... 25 The Impor Secor... 26 Impor Demand... 27 Impor Supply... 28 E. oneary Fscal and acroprudenal Polcy... 3 The oneary uhory... 3 The Fscal uhory... 3 The acroprudenal uhory... 32 F. arke learng ondons... 33 III. The Emprcal Framework... 34. Endogenous Varables... 35. Exogenous Varables... 45 IV. Esmaon... 46. Transformaon of he Daa Se... 47. Pror and Poseror Parameer Dsrbuons... 47 V. Polcy nalyss... 48. Impulse Response Funcons... 49. Hsorcal Decomposons... 52 VI. Spllover nalyss... 53. Smulaed ondonal eas... 53. Impulse Response Funcons... 54 VII. Forecasng... 56 VIII. oncluson... 57 ppendx. Descrpon of he Daa Se... 58
3 ppendx. Tables and Fgures... 6 Table 1. Parameer Esmaon Resuls... 6 Fgure 1. IRFs of acro Varables o a Domesc Producvy Shock... 61 Fgure 2. IRFs of Fnancal Varables o a Domesc Producvy Shock... 62 Fgure 3. IRFs of acro Varables o a Domesc Labor Supply Shock... 63 Fgure 4. IRFs of Fnancal Varables o a Domesc Labor Supply Shock... 64 Fgure 5. IRFs of acro Varables o a Domesc onsumpon Demand Shock... 65 Fgure 6. IRFs of Fnancal Varables o a Domesc onsumpon Demand Shock... 66 Fgure 7. IRFs of acro Varables o a Domesc Invesmen Demand Shock... 67 Fgure 8. IRFs of Fnancal Varables o a Domesc Invesmen Demand Shock... 68 Fgure 9. IRFs of acro Varables o a Domesc oneary Polcy Shock... 69 Fgure 1. IRFs of Fnancal Varables o a Domesc oneary Polcy Shock... 7 Fgure 11. IRFs of acro Varables o a Domesc red Rsk Premum Shock... 71 Fgure 12. IRFs of Fnancal Varables o a Domesc red Rsk Premum Shock... 72 Fgure 13. IRFs of acro Varables o a Domesc Duraon Rsk Premum Shock... 73 Fgure 14. IRFs of Fnancal Varables o a Domesc Duraon Rsk Premum Shock... 74 Fgure 15. IRFs of acro Varables o a Domesc Equy Rsk Premum Shock... 75 Fgure 16. IRFs of Fnancal Varables o a Domesc Equy Rsk Premum Shock... 76 Fgure 17. IRFs of acro Varables o a Domesc Fscal Expendure Shock... 77 Fgure 18. IRFs of Fnancal Varables o a Domesc Fscal Expendure Shock... 78 Fgure 19. IRFs of acro Varables o a Domesc Fscal Revenue Shock... 79 Fgure 2. IRFs of Fnancal Varables o a Domesc Fscal Revenue Shock... 8 Fgure 21. IRFs of acro Varables o a Domesc Lendng Rae arkup Shock... 81 Fgure 22. IRFs of Fnancal Varables o a Domesc Lendng Rae arkup Shock... 82 Fgure 23. IRFs of acro Varables o a Domesc apal Requremen Shock... 83 Fgure 24. IRFs of Fnancal Varables o a Domesc apal Requremen Shock... 84 Fgure 25. IRFs of acro Varables o a Domesc Loan Defaul Shock... 85 Fgure 26. IRFs of Fnancal Varables o a Domesc Loan Defaul Shock... 86 Fgure 27. IRFs of acro Varables o an Energy ommody Prce arkup Shock... 87 Fgure 28. IRFs of Fnancal Varables o an Energy ommody Prce arkup Shock... 88 Fgure 29. IRFs of acro Varables o a Nonenergy ommody Prce arkup Shock... 89 Fgure 3. IRFs of Fnancal Varables o a Nonenergy ommody Prce arkup Shock... 9 Fgure 31. Hsorcal Decomposons of onsumpon Prce Inflaon... 91 Fgure 32. Hsorcal Decomposons of Oupu Growh... 92 Fgure 33. Smulaed ondonal eas of Oupu... 93 Fgure 34. Peak IRFs o Foregn Producvy Shocks... 94 Fgure 35. Peak IRFs o Foregn Labor Supply Shocks... 95 Fgure 36. Peak IRFs o Foregn onsumpon Demand Shocks... 96 Fgure 37. Peak IRFs o Foregn Invesmen Demand Shocks... 97 Fgure 38. Peak IRFs o Foregn oneary Polcy Shocks... 98 Fgure 39. Peak IRFs o Foregn red Rsk Premum Shocks... 99 Fgure 4. Peak IRFs o Foregn Duraon Rsk Premum Shocks... 1 Fgure 41. Peak IRFs o Foregn Equy Rsk Premum Shocks... 11 Fgure 42. Peak IRFs o Foregn Fscal Expendure Shocks... 12 Fgure 43. Peak IRFs o Foregn Fscal Revenue Shocks... 13 Fgure 44. Peak IRFs o Foregn Lendng Rae arkup Shocks... 14
4 Fgure 45. Peak IRFs o Foregn apal Requremen Shocks... 15 Fgure 46. Peak IRFs o Foregn Loan Defaul Shocks... 16 Fgure 47. Forecas Performance Evaluaon Sascs... 17 Fgure 48. Sequenal Uncondonal Forecass of onsumpon Prce Inflaon... 18 Fgure 49. Sequenal Uncondonal Forecass of Oupu Growh... 19 References... 11
5 I. INTRODUTION Esmaed dynamc sochasc general equlbrum models are wdely used by moneary and fscal auhores for polcy analyss and forecasng purposes. Ths class of srucural macroeconomerc models has many varans ncorporang a range of nomnal and real rgdes and ncreasngly ofen macrofnancal lnkages. Is unfyng feaure s he dervaon of approxmae lnear equlbrum condons from consraned opmzaon problems facng households and frms whch nerac wh governmens n an unceran envronmen o deermne equlbrum prces and quanes under raonal expecaons. Developng and esmang a dynamc sochasc general equlbrum model of he world economy dsaggregaed no a large number of naonal economes presens unque challenges. dequaely accounng for nernaonal busness cycle comovemen requres suffcen spllover ransmsson channels n parcular nernaonal fnancal lnkages. opng wh he curse of dmensonaly whch manfess hrough explosons of he numbers of varables and parameers as he number of economes ncreases requres argeed parameer resrcons. Ths paper develops a srucural macroeconomerc model of he world economy dsaggregaed no fory naonal economes. Ths panel dynamc sochasc general equlbrum model feaures a range of nomnal and real rgdes exensve macrofnancal lnkages and dverse spllover ransmsson channels. Followng Smes and Wouers (23) he model feaures shor run nomnal prce and wage rgdes generaed by monopolsc compeon saggered reopmzaon and paral ndexaon n he oupu and labor markes. Followng hrsano Echenbaum and Evans (25) he resulan nera n nflaon and perssence n oupu s enhanced wh oher feaures such as hab perssence n consumpon adjusmen coss n nvesmen and varable capal ulzaon. Followng Galí (211) he model ncorporaes nvolunary unemploymen hough a renerpreaon of he labor marke. Households are dfferenaed accordng o wheher hey are bank nermedaed capal marke nermedaed or cred consraned. ank nermedaed households have access o domesc banks where hey accumulae deposs whereas capal marke nermedaed households have access o domesc and foregn capal markes where hey rade fnancal asses. Followng Vek (213) hese capal marke nermedaed households solve a porfolo balance problem allocang her fnancal wealh across domesc and foregn money bond and sock marke secures whch are mperfec subsues. To cope wh he curse of dmensonaly argeed parameer resrcons are mposed on he opmaly condons deermnng he soluon o hs porfolo balance problem avodng he need o rack he evoluon of blaeral asse allocaons. Frms are grouped no dfferenaed ndusres. Followng Vek (213) he commody ndusres produce nernaonally homogeneous goods under decreasng reurns o scale whle all oher ndusres produce nernaonally heerogeneous goods under consan reurns o scale. anks perform global fnancal nermedaon subjec o fnancal frcons and a regulaory consran. uldng on Hülsewg ayer and Wollmershäuser (29) hey ssue rsky domesc currency denomnaed loans o domesc and foregn frms a nfrequenly adjused predeermned lendng raes. lso buldng on Geral Ner Sessa and Sgnore (21) hey oban fundng from
6 domesc bank nermedaed households va deposs and from he domesc money marke va loans and accumulae bank capal ou of reaned earnngs gven cred losses o sasfy a regulaory capal requremen. ovaed by Kyoak and oore (1997) he model ncorporaes a fnancal acceleraor mechansm lnked o collaeralzed borrowng. Fnally followng onacell (25) he model accouns for shor run ncomplee exchange rae pass hrough wh shor run nomnal prce rgdes generaed by monopolsc compeon saggered reopmzaon and paral ndexaon n he mpor markes. n approxmae lnear sae space represenaon of he model s esmaed by ayesan maxmum lkelhood condonal on pror nformaon concernng he generally common values of srucural parameers across economes. varey of moneary polcy analyss fscal polcy analyss macroprudenal polcy analyss spllover analyss and forecasng applcaons of hs esmaed panel dynamc sochasc general equlbrum model of he world economy are demonsraed. These nclude quanfyng he moneary fscal and macroprudenal ransmsson mechansms accounng for busness cycle flucuaons and generang forecass of nflaon and oupu growh. The moneary fscal and macroprudenal ransmsson mechansms as quanfed wh esmaed mpulse response funcons are broadly n lne wh he emprcal leraure as are he drvers of busness cycle flucuaons as accouned for wh esmaed hsorcal decomposons. Sequenal uncondonal forecass of nflaon and oupu growh domnae a random walk n erms of predcve accuracy by wde margns on average across economes and horzons. Ths paper s he sequel o Vek (214) whch also develops a srucural macroeconomerc model of he world economy dsaggregaed no fory naonal economes o faclae mullaerally conssen polcy analyss spllover analyss and forecasng. These closely relaed panel dynamc sochasc general equlbrum models dffer prmarly wh respec o he exsence of a global bankng nework. Ths exenson sgnfcanly enhances he macrofnancal lnkages embedded n he presen model whle renderng applcable o macroprudenal polcy analyss. The organzaon of hs paper s as follows. The nex secon develops a panel dynamc sochasc general equlbrum model of he world economy whle he followng secon descrbes an approxmae mulvarae lnear raonal expecaons represenaon of. Esmaon of he model based on an approxmae lnear sae space represenaon of s he subjec of secon four. Polcy analyss whn he framework of he esmaed model s conduced n secon fve whle spllover analyss s underaken n secon sx and forecasng n secon seven. Fnally secon egh offers conclusons and recommendaons for furher research. II. THE THEORETIL FREWORK onsder a fne se of srucurally somorphc naonal economes ndexed by {1 N} whch consues he world economy. Each of hese economes consss of households frms banks and a governmen. The governmen n urn consss of a moneary auhory a fscal auhory and a macroprudenal auhory. Households frms and banks opmze
7 neremporally neracng wh governmens n an unceran envronmen o deermne equlbrum prces and quanes under raonal expecaons n globally negraed oupu and fnancal markes. Economy * ssues he quoaon currency for ransacons n he foregn exchange marke.. The Household Secor There exss a connuum of households ndexed by h [1]. Households are dfferenaed accordng o wheher hey are cred consraned and accordng o how hey save f hey are cred unconsraned bu are oherwse dencal. red unconsraned households of ype Z and measure have access o domesc banks where hey accumulae deposs and are endowed wh one share of each domesc frm where 1. In conras cred unconsraned households of ype Z and measure have access o domesc and foregn capal markes where hey rade fnancal asses where 1. Fnally cred consraned households of ype Z and measure do no have access o banks or capal markes and are endowed only wh one share of each domesc frm where 1 and 1. In a renerpreaon of he labor marke n he model of nomnal wage rgdy proposed by Erceg Henderson and Levn (2) o ncorporae nvolunary unemploymen along he lnes of Galí (211) each household consss of a connuum of members represened by he un square and ndexed by ( f g) [1] [1]. There s full rsk sharng among household members who supply ndvsble dfferenaed nermedae labor servces ndexed by f [1] ncurrng dsuly from work deermned by g [1] f hey are employed and zero oherwse. Trade specfc nermedae labor servces suppled by bank nermedaed capal marke nermedaed and cred consraned households are perfec subsues. onsumpon and Savng The represenave nfnely lved household has preferences defned over consumpon hs 1 labor supply { Lh f s} real bank balances D H H f hs 1 / Ps and real porfolo balances hs 1 / P represened by neremporal uly funcon DH H s 1 h s 1 h s1 Uh E u hs { Lh f s} f s Ps P (1) s where E denoes he expecaons operaor condonal on nformaon avalable n perod and 1. The nraemporal uly funcon s addvely separable and represens exernal hab formaon preferences n consumpon s
8 DH H Z 1 hs 1 1 1 hs s 1 u hs { Lh f s} f s hs Z Ps P s 11/ 11/ 1 L h f s D D H H L 1/ s hs 1 s hs 1 s g dgdf 1 1/ P s 11/ P s 11/ 11/ L D where 1. Endogenous preference shfers s s and s depend on aggregae consumpon and employmen accordng o nraemporal subuly funcons Z Z 1/ L L s s 1 1/ s s ( Ls ) Z Z Z Z 1/ D D s s 1 1/ s ( s ) Z Z (2) (3) (4) Z Z 1/ s s 1 1/ s ( s ) Z Z where. The nraemporal uly funcon s srcly ncreasng wh respec o consumpon f and only f serally correlaed consumpon demand shock s sasfes s. Gven hs parameer resrcon hs nraemporal uly funcon s srcly decreasng wh respec o L L labor supply f and only f serally correlaed labor supply shock s sasfes s s srcly D ncreasng wh respec o real bank balances f and only f and s srcly ncreasng wh respec o real porfolo balances f and only f. Gven hese parameer resrcons hs nraemporal uly funcon s srcly concave f and. In seady sae equlbrum equaes he margnal rae of subsuon beween real porfolo balances and consumpon o one. The represenave household has capals spr moves for holdng real bank and porfolo balances ndependen of fnancng deferred consumpon movaed by Weber (195). I also has a dversfcaon move over he allocaon of real porfolo balances across alernave fnancal asses whch are mperfec subsues movaed by Tobn (1969). The se of fnancal asses under consderaon consss of nernaonally raded and local currency denomnaed shor erm bonds long erm bonds and socks. Shor erm bonds are dscoun bonds whle long erm bonds are perpeual bonds. Preferences over he real values of nernaonally dversfed SH L H H shor erm bond hs 1 / Ps long erm bond hs 1 / Ps and sock Shs 1 / Ps porfolos are represened by consan elascy of subsuon nraemporal subuly funcon (5) 1 1 1 1 1 1 1 H SH LH H hs 1 hs 1 hs 1 S hs 1 s S s P s P s P s P s S ( ) ( ) ( ) (6)
9 where nernaonally and serally correlaed duraon rsk premum shock s sasfes s S S and nernaonally and serally correlaed equy rsk premum shock s sasfes s whle 1 1 S 1 S 1 and. Preferences over he real SH N values of economy specfc shor erm bond { j sh j s1 / P s} j1 long erm bond L H N { j sh j s1 / P s} j1and sock { H 1 / } N j ssh j s P s j1 porfolos are n urn represened by consan elascy of subsuon nraemporal subuly funcons SH N 1 SH 1 j s hs h j s1 j j s P s j1 Ps 1 1 ( ) LH N 1 LH 1 j s hs h j s1 j j s P s j1 Ps 1 1 ( ) (7) (8) S H N 1 H 1 j ss hs S h j s1 j j s P s j1 Ps 1 1 ( ) where serally correlaed currency rsk premum shocks j s sasfy js whle j 1 N S N S 1 1 j j j 1 and 1 1 j j. Fnally preferences over he real values of economy and vnage specfc long erm bonds {{ L H 1 / } s 1} N j svj k sh j k s P s k j1and economy ndusry and 1 frm specfc shares {{{ S H 1 / } } 1} N j svj k l ssh j k l s P s l k j1are represened by consan elascy of subsuon nraemporal subuly funcons (9) LH s 1 LH j sh j s1 j svj k s h j k s1 j k s P s k 1 Ps 1 1 ( ) (1) 1 1 H 1 1 S H j ssh j s1 j svj k l ss S h j k l s1 ( j k) dl P s k 1 P (11) s s S S where j k s 1 1 1 k j k s j k 1 and 1 1 k j k. In he lm as D here s no capals spr move for holdng real bank balances and n he lm as here s no capals spr move for holdng real porfolo balances. In he lm as here s no dversfcaon move over he allocaon of real porfolo balances across alernave fnancal asses whch n hs case are perfec subsues.
1 The represenave household eners perod s n possesson of prevously accumulaed bank D H D balances hs whch bear neres a depos rae and porfolo balances H s 1 hs whch yeld H reurn hs. These porfolo balances are dsrbued across he values of nernaonally SH L H H dversfed shor erm bond hs long erm bond hs and sock S hs porfolos whch yeld SH L H H H SH S H SH reurns hs hs and hs respecvely. I follows ha (1 hs ) hs (1 hs ) hs LH H L H S H (1 hs ) hs (1 hs ) Shs. The values of hese nernaonally dversfed shor erm bond long erm bond and sock porfolos are n urn dsrbued across he domesc currency SH N denomnaed values of economy specfc shor erm bond { j sh j s} j1 long erm bond L H N H N { j sh j s} j1 and sock { j ssh j s} j1 porfolos where nomnal blaeral exchange rae j s measures he prce of foregn currency n erms of domesc currency. I follows ha S H S H N S S H S (1 hs ) hs 1 js (1 js 1 ) j h js where j s 1 denoes he economy specfc yeld o LH N LH L H L H L H maury on shor erm bonds (1 h s) h s 1 j s(1 h j s) j h j s where h js denoes he H H S H N S H economy specfc reurn on long erm bonds and (1 hs ) Shs 1 js (1 h js ) S j h js where H S h js denoes he economy specfc reurn on socks. The local currency denomnaed values of L H N economy specfc long erm bond porfolos { h js } j 1 are n urn dsrbued across he values L H s1 N of economy and vnage specfc long erm bonds {{ Vj ks h jks } k 1} where j 1 V j ks denoes he local currency denomnaed prce per long erm bond wh V jkk 1. I follows ha LH L H s1 L H (1 h js ) h js ( 1 jks Vjks ) k h jks where L j ks jk Vjkk denoes he local currency L denomnaed coupon paymen per long erm bond and j k denoes he economy and vnage specfc yeld o maury on long erm bonds a ssuance. In parallel he local currency denomnaed values of economy specfc sock porfolos { H N Sh js } j 1 are dsrbued across he S H 1 N values of economy ndusry and frm specfc shares {{{ Vj kls Sh jkls } l } k 1} where S j 1 V j kls H S H denoes he local currency denomnaed prce per share. I follows ha (1 h js ) S 1 h js ( S S ) H S 1 jkls Vjkls S k h jkls dl where j kls denoes he local currency denomnaed dvdend paymen per share. Durng perod s he represenave household supples 1 dfferenaed nermedae labor servces { Lh f s} f earnng labor ncome a rade specfc 1 nomnal wages { W f s}. The governmen leves a ax on labor ncome a rae f s and rems Z household ype specfc lump sum ransfer paymen T. These sources of wealh are summed n household dynamc budge consran: 1 H DH H D DH H Z hs 1 hs 1 s 1 hs hs hs s f s h f s s hs (1 ) (1 ) (1 ) W L df T P. (12) ccordng o hs dynamc budge consran a he end of perod s he represenave D H H household holds bank balances hs 1 and porfolo balances hs 1. I allocaes hese porfolo SH balances across he values of nernaonally dversfed shor erm bond hs 1 long erm bond LH H hs 1 and sock porfolos S ha s H SH LH H hs 1 hs 1 hs 1 hs 1 Shs 1. The values of hese nernaonally dversfed shor erm bond long erm bond and sock porfolos are n urn allocaed across he domesc currency denomnaed values of economy specfc shor erm bond SH N L H N H N { j sh j s1} j1 long erm bond { j sh j s1} j1 and sock { j ssh j s1} j1 porfolos subjec o SH N SH LH N LH H N H hs 1 j 1 js h js 1 hs 1 j 1 js h js 1 and S hs 1 j 1 js S h js 1 respecvely. The local currency denomnaed values of economy specfc long erm bond porfolos L H N { h js 1} j 1 are n urn allocaed across he local currency denomnaed values of economy and L H s N vnage specfc long erm bonds {{ V } } subjec o LH s LH V. j ks h jks 1 k 1 j 1 h js 1 k1 jks h jks 1
11 In parallel he local currency denomnaed values of economy specfc sock porfolos H N { Sh js 1} j 1 are allocaed across he local currency denomnaed values of economy ndusry and S H 1 N frm specfc shares {{{ Vj kls Sh jkls 1} l } k 1} subjec o 1 H S H j 1 Sh js 1 V 1 jkls S k h jkls 1dl. Fnally he represenave household purchases fnal prvae consumpon good hs a prce P s. ank Inermedaed Households In perod he represenave bank nermedaed household chooses sae conngen sequences for consumpon { hs } labor force parcpaon 1 s {{ N h f s } f } s and bank balances DH { hs 1} s o maxmze neremporal uly funcon (1) subjec o dynamc budge consran (12) he applcable resrcons on fnancal asse holdngs and ermnal nonnegavy consran DH ht 1 for T. In equlbrum absracng from he capals spr move for holdng real bank balances he soluons o hs uly maxmzaon problem sasfy neremporal opmaly condon u ( h 1) D E (1 ) 1 u( h ) P 1 P (13) whch equaes he expeced presen value of he gross real depos rae o one. These soluons also sasfy nraemporal opmaly condon ul ( h f ) W f f (1 ) (14) u ( h ) P whch equaes he margnal rae of subsuon beween lesure and consumpon for he margnal rade specfc labor force parcpan o he correspondng afer ax real wage. Provded ha he neremporal uly funcon s bounded and srcly concave ogeher wh oher opmaly condons and a ransversaly condon derved from he necessary complemenary slackness condon assocaed wh he ermnal nonnegavy consran hese opmaly condons are suffcen for he unque uly maxmzng sae conngen sequence of bank nermedaed household allocaons. apal arke Inermedaed Households In perod he represenave capal marke nermedaed household chooses sae conngen sequences for consumpon { hs } labor force parcpaon 1 s {{ N h f s } f } porfolo s H balances { hs 1} shor erm bond holdngs SH N s {{ h js 1} j 1} s long erm bond holdngs LH N {{{ h jks 1} k 1} j 1} and sock holdngs H 1 N s {{{{ S h jkls 1} l } k 1} j 1} s o maxmze neremporal uly funcon (1) subjec o dynamc budge consran (12) he applcable resrcons on SH fnancal asse holdngs and ermnal nonnegavy consrans h jt 1 LH h jkt 1 and H for T. In equlbrum absracng from he capals spr move for holdng Sh jklt 1
12 real porfolo balances he soluons o hs uly maxmzaon problem sasfy neremporal opmaly condon u ( 1) H h E (1 h 1) 1 u( h ) P 1 P (15) whch equaes he expeced presen value of he gross real porfolo reurn o one. In addon hese soluons sasfy nraemporal opmaly condon ul ( h f ) W f f (1 ) (16) u ( h ) P whch equaes he margnal rae of subsuon beween lesure and consumpon for he margnal rade specfc labor force parcpan o he correspondng afer ax real wage. bsracng from rsk premum shocks he expeced presen value of he gross real porfolo reurn sasfes nraemporal opmaly condon N ( 1) ( ) H u h u h S j 1 j1e (1 h 1 ) (1 j ) j1 u( h ) u( h ) P 1 j P N L u( h 1) u( h ) H jk jk 1 j 1 j jk 1E (1 1) h j1 k1 u( h ) u( h ) P 1 Vjk j P 1 V 1 (17) P N 1 S S ( 1) ( ) H S S u h u h jkl 1 jkl 1 j 1 S j jk 1 E (1 h 1) S j1 k1 u( h ) u( h ) P 1 V jkl j V 1 dl 1 whch relaes o he expeced presen values of he gross real reurns on domesc and foregn shor erm bonds long erm bonds and socks. Furhermore absracng from he porfolo dversfcaon move hese soluons sasfy nraemporal opmaly condon u( h 1) P S S j 1 u( h ) E (1 ) (1 j ) ( j ) (18) u() h P 1 j u() h whch equaes he expeced presen values of he gross real rsk adjused reurns on domesc and foregn shor erm bonds. In addon absracng from he porfolo dversfcaon move hese soluons sasfy nraemporal opmaly condon L u( h 1) P S k V k 1 u( h ) E (1 ) (1 ) (19) u( h ) P 1 V k u( h ) whch equaes he expeced presen values of he gross real rsk adjused reurns on domesc shor and long erm bonds. Fnally absracng from he porfolo dversfcaon move hese soluons sasfy nraemporal opmaly condon S S u ( h 1) P S kl 1 V kl 1 u( h ) S E (1 ) (1 ) S (2) u( h ) P 1 V k l u( h )
13 whch equaes he expeced presen values of he gross real rsk adjused reurns on domesc shor erm bonds and socks. Provded ha he neremporal uly funcon s bounded and srcly concave ogeher wh oher opmaly condons and ransversaly condons derved from necessary complemenary slackness condons assocaed wh he ermnal nonnegavy consrans hese opmaly condons are suffcen for he unque uly maxmzng sae conngen sequence of capal marke nermedaed household allocaons. red onsraned Households In perod he represenave cred consraned household chooses sae conngen sequences for consumpon { hs } and labor force parcpaon 1 s {{ N h f s } f } s o maxmze neremporal uly funcon (1) subjec o dynamc budge consran (12) and he applcable resrcons on fnancal asse holdngs. In equlbrum he soluons o hs uly maxmzaon problem sasfy household sac budge consran 1 S h f h f P (1 ) W L df (21) whch equaes consumpon expendures o he sum of prof and dsposable labor ncome. These soluons also sasfy nraemporal opmaly condon ul ( h f ) W f f (1 ) (22) u ( h ) P whch equaes he margnal rae of subsuon beween lesure and consumpon for he margnal rade specfc labor force parcpan o he correspondng afer ax real wage. Provded ha he neremporal uly funcon s bounded and srcly concave hese opmaly condons are suffcen for he unque uly maxmzng sae conngen sequence of cred consraned household allocaons. Labor Supply L The unemploymen rae u measures he share of he labor force N n unemploymen U L U ha s u where unemploymen equals he labor force less employmen L N ha s 1 U N L. The labor force sasfes N N df. f There exs a large number of perfecly compeve frms whch combne dfferenaed nermedae labor servces L f suppled by rade unons of workers o produce fnal labor servce L accordng o consan elascy of subsuon producon funcon L L 1 L 1 L 1 L ( Lf ) df (23)
14 L L L L where serally uncorrelaed wage markup shock sasfes 1 wh. The represenave fnal labor servce frm maxmzes profs derved from producon of he fnal labor servce wh respec o npus of nermedae labor servces mplyng demand funcons: L L W f f L W. Snce he producon funcon exhbs consan reurns o scale n equlbrum he represenave fnal labor servce frm generaes zero prof mplyng aggregae wage ndex: 1 1 L L 1 1 f W ( W ) df. (25) L s he wage elascy of demand for nermedae labor servces ncreases hey become closer subsues and ndvdual rade unons have less marke power. In an exenson of he model of nomnal wage rgdy proposed by Erceg Henderson and Levn (2) along he lnes of Smes and Wouers (23) each perod a randomly seleced L L fracon 1 of rade unons adjus her wage opmally where 1. The remanng L fracon of rade unons adjus her wage o accoun for pas consumpon prce nflaon and producvy growh accordng o paral ndexaon rule W L L 1 P 1 1 P 1 1 f W f 1 P 2 2 P 2 2 L where 1. Under hs specfcaon alhough rade unons adjus her wage every perod hey nfrequenly do so opmally and he nerval beween opmal wage adjusmens s a random varable. If he represenave rade unon can adjus s wage opmally n perod hen does so o maxmze neremporal uly funcon (1) subjec o dynamc budge consran (12) nermedae labor servce demand funcon (24) and he assumed form of nomnal wage rgdy. Snce all rade unons ha adjus her wage opmally n perod solve an dencal * uly maxmzaon problem n equlbrum hey all choose a common wage W gven by necessary frs order condon: W W L L L s L 1 * s ( ) u ( ) s L h f s L s u h s L P f 1 1 P 1 1 W s W E ( ) s Lhs * s u( h ) u( h s) Ps 1 s 1 Ps 1 s 1 W W L L L s 1 L 1 * s s L s ( ) 1 1 1 1 E ( ) ( L W u h s 1)(1 ) s P P W s W s s Lhs s u( h ) P s P s1 s1 P s1 s1 W W Ths necessary frs order condon equaes he expeced presen value of he margnal uly of consumpon ganed from labor supply o he expeced presen value of he margnal uly cos ncurred from lesure foregone. ggregae wage ndex (25) equals an average of he wage se by. (24) (26) (27)
15 L he fracon 1 of rade unons ha adjus her wage opmally n perod and he average L of he wages se by he remanng fracon of rade unons ha adjus her wage accordng o paral ndexaon rule (26): 1 L 1 L L L 1 1 L L * 1 L P 1 1 P 1 1 1 P 2 2 P 2 2 W (1 )( W ) W. Snce hose rade unons able o adjus her wage opmally n perod are seleced randomly from among all rade unons he average wage se by he remanng rade unons equals he value of he aggregae wage ndex ha prevaled durng perod 1 rescaled o accoun for pas consumpon prce nflaon and producvy growh. (28). The Producon Secor The producon secor consss of a fne se of ndusres ndexed by k{1 } of whch he frs * produce nonrenewable commodes. In parcular he energy commody ndusry labeled k 1 and he nonenergy commody ndusry labeled k 2 produce nernaonally homogeneous goods for foregn absorpon under decreasng reurns o scale represenng he exsence of a fxed facor whle all oher ndusres produce nernaonally heerogeneous goods for domesc and foregn absorpon under consan reurns o scale. Labor s perfecly moble across ndusres. Oupu Demand There exs a large number of perfecly compeve frms whch combne ndusry specfc fnal oupu goods { } o produce fnal oupu good k k 1 accordng o fxed proporons producon funcon k mn k k 1 where k 1 and 1 1 k k. The represenave fnal oupu good frm maxmzes profs derved from producon of he fnal oupu good wh respec o npus of ndusry specfc fnal oupu goods mplyng demand funcons:. k k (3) Snce he producon funcon exhbs consan reurns o scale n equlbrum he represenave fnal oupu good frm generaes zero prof mplyng aggregae oupu prce ndex: k Pk k1 P. (31) (29)
16 Ths aggregae oupu prce ndex equals he mnmum cos of producng one un of he fnal oupu good gven he prces of ndusry specfc fnal oupu goods. There exs a large number of perfecly compeve frms whch combne ndusry specfc dfferenaed nermedae oupu goods kl suppled by ndusry specfc nermedae oupu good frms o produce ndusry specfc fnal oupu good k accordng o consan elascy of subsuon producon funcon k 1 k k 1 k 1 k ( kl ) dl (32) where serally uncorrelaed oupu prce markup shock k sasfes k 1 wh k whle k k for 1 k * and k oherwse. The represenave ndusry specfc fnal oupu good frm maxmzes profs derved from producon of he ndusry specfc fnal oupu good wh respec o npus of ndusry specfc nermedae oupu goods mplyng demand funcons: k P kl kl k Pk. Snce he producon funcon exhbs consan reurns o scale n equlbrum he represenave ndusry specfc fnal oupu good frm generaes zero prof mplyng ndusry specfc aggregae oupu prce ndex: 1 1 1 k 1 k k kl P ( P ) dl. (34) s he prce elascy of demand for ndusry specfc nermedae oupu goods k ncreases hey become closer subsues and ndvdual ndusry specfc nermedae oupu good frms have less marke power. (33) Labor Demand and Invesmen There exs connuums of monopolscally compeve ndusry specfc nermedae oupu good frms ndexed by l [1]. Inermedae oupu good frms supply ndusry specfc dfferenaed nermedae oupu goods bu are oherwse dencal. We rule ou enry no and ex ou of he monopolscally compeve ndusry specfc nermedae oupu good secors. The represenave ndusry specfc nermedae oupu good frm sells shares o domesc and S foregn capal marke nermedaed households a prce V kl. cng n he neress of s shareholders maxmzes s pre-dvdend sock marke value whch absracng from he capals spr move for holdng real porfolo balances equals he expeced presen value of curren and fuure dvdend paymens
17 E (35) s S S s S kl Vkl kls s where s denoes he Lagrange mulpler assocaed wh he perod s capal marke nermedaed household dynamc budge consran. The dervaon of hs resul mposes a ransversaly condon whch rules ou self-fulfllng speculave asse prce bubbles. S Shares enle households o dvdend paymens equal o ne profs kls defned as he sum of afer ax earnngs and ne borrowng less nvesmen expendures (1 )( P W L ) ( (1 )(1 ) ) P I (36) S I kls s kls kls s kls kls kls 1 s s kls s kls K where kls ukls Kkls s Lkls ( ). Earnngs are defned as revenues derved from sales of ndusry specfc dfferenaed nermedae oupu good kls a prce P kls less expendures on fnal labor servce L kls and oher varable coss kls. The governmen leves a ax on earnngs a rae s. ovaed by he collaeralzed borrowng varan of he fnancal acceleraor mechansm due o Kyoak and oore (1997) he fnancal polcy of he represenave ndusry specfc nermedae oupu good frm s o manan deb equal o a fxed fracon of he value of he capal sock P K F kls 1 I s kls 1 (37) F where 1. Ne borrowng s defned as he ncrease n loans kls 1from domesc and foregn banks ne of wredowns a loan defaul rae s where s 1 and neres paymens E a corporae loan rae s. Ths loan defaul rae apples unformly o all loans receved from domesc and foregn banks. The represenave ndusry specfc nermedae oupu good frm ulzes capal K kls a rae K u kls and rens fnal labor servce L kls o produce ndusry specfc dfferenaed nermedae oupu good kls accordng o producon funcon K K K k kls kls s kls kls kls s kls k ( u K L ) ( u K ) ( L ) (38) where serally correlaed producvy shock s sasfes s whle K (1 F ) K k k and L F L K L F F (1 ) wh 1 and for 1 k * and oherwse. k k k L In ulzng capal o produce oupu he represenave ndusry specfc nermedae oupu K good frm ncurs a cos ( ukls Kkls ) denomnaed n erms of capal I K P ( u K ) F (39) kls s kls kls ks where ndusry specfc fxed cos F ks ensures ha ks. Followng hrsano Echenbaum and Evans (25) hs capal ulzaon cos s ncreasng n he capal ulzaon rae a an ncreasng rae k
18 K K K K ( u 1) ( ) kls ukls Kkls e 1 Kkls (4) K K where and. In seady sae equlbrum he capal ulzaon rae equals one and he cos of ulzng capal equals zero. The represenave ndusry specfc nermedae oupu good frm eners perod s n possesson of prevously accumulaed capal sock K kls whch subsequenly evolves accordng o accumulaon funcon K (1 ) K ( I I ) (41) kls 1 kls kls kls 1 where 1. Followng hrsano Echenbaum and Evans (25) effecve nvesmen funcon ( Ikls Ikls 1) ncorporaes convex adjusmen coss 2 I I k l s ( Ikls Ikls 1 ) s 1 1 Ikls 2 I (42) kls 1 I I where serally correlaed nvesmen demand shock s sasfes s whle. In seady sae equlbrum hese adjusmen coss equal zero and effecve nvesmen equals acual nvesmen. In perod he represenave ndusry specfc nermedae oupu good frm chooses sae conngen sequences for employmen { L kls } he capal ulzaon rae K s { u kls } s nvesmen { I kls } and he capal sock s { K kls 1} s o maxmze pre-dvdend sock marke value (35) subjec o producon funcon (38) capal accumulaon funcon (41) and ermnal nonnegavy consran KklT 1 for T. In equlbrum demand for he fnal labor servce sasfes necessary frs order condon K W L( ukl Kkl Lkl ) kl (1 ) (43) P k where Pks kls denoes he Lagrange mulpler assocaed wh he perod s producon echnology consran. Ths necessary frs order condon equaes real margnal cos kl o he rao of he afer ax ndusry specfc real wage o he margnal produc of labor. In equlbrum he capal ulzaon rae sasfes necessary frs order condon P ( u K ) (44) K K k k l K u kl kl K ( ukl Kkl Lkl ) (1 ) u K I P Kkl whch equaes he margnal revenue produc of ulzed capal o s margnal cos. In equlbrum demand for he fnal nvesmen good sasfes necessary frs order condon Q ( I I ) E Q ( I I ) P (45) kl 1 kl kl 1 1 I kl 1 2 kl 1 kl
19 whch equaes he expeced presen value of an addonal un of nvesmen o s prce where Q kls denoes he Lagrange mulpler assocaed wh he perod s capal accumulaon funcon. In equlbrum hs shadow prce of capal sasfes necessary frs order condon 1 I K K Pk 1 kl 1 Qkl E 1 1 ( 1 1 1 1) P ukl K u u K kl Kkl Lkl I P 1 (46) I K P E (1 1 ) K( ukl 1 Kkl 1 ) (1 1 )(1 1) I (1 ) kl 1 Q P 1 1 whch equaes o he expeced presen value of he sum of he fuure margnal revenue produc of capal ne of s margnal ulzaon cos and he fuure shadow prce of capal ne of deprecaon less he produc of he loan o value rao wh he spread beween he effecve cos of bank and capal marke fundng. Provded ha he pre-dvdend sock marke value s bounded and srcly concave ogeher wh oher necessary frs order condons and a ransversaly condon derved from he necessary complemenary slackness condon assocaed wh he ermnal nonnegavy consran hese necessary frs order condons are suffcen for he unque value maxmzng sae conngen sequence of ndusry specfc nermedae oupu good frm allocaons. Oupu Supply In an exenson of he model of nomnal oupu prce rgdy proposed by alvo (1983) along he lnes of Smes and Wouers (23) each perod a randomly seleced fracon 1 k of ndusry specfc nermedae oupu good frms adjus her prce opmally where k 1 wh k for k *. The remanng fracon k of nermedae oupu good frms adjus her prce o accoun for pas ndusry specfc oupu prce nflaon accordng o paral ndexaon rule k 1 k P k 1 P k 1 kl P kl 1 P k 2 P k 2 P where k 1 wh k for 1 k * and k oherwse. Under hs specfcaon opmal prce adjusmen opporunes arrve randomly and he nerval beween opmal prce adjusmens s a random varable. If he represenave ndusry specfc nermedae oupu good frm can adjus s prce opmally n perod hen does so o maxmze pre-dvdend sock marke value (35) subjec o producon funcon (38) ndusry specfc nermedae oupu good demand funcon (33) and he assumed form of nomnal oupu prce rgdy. We consder a symmerc equlbrum under whch all ndusry and frm specfc endogenous sae varables are resrced o equal her ndusry specfc aggregae counerpars. I follows ha all nermedae oupu good frms ha (47)
2 adjus her prce opmally n perod solve an dencal value maxmzaon problem whch * mples ha hey all choose a common prce P gven by necessary frs order condon: k ks k 1k * k s s s s P k 1 P k 1 P ks P k E ( k ) k s k l s Pks ks * s Pks 1 Pks 1 Pk Pk k ks 1 k k 1k * k s s s s P k 1 P k 1 P ks P k E ( k ) ( ks 1)(1 s ) P ks ks s Pks 1 Pks 1 Pk Pk P P (48). Ths necessary frs order condon equaes he expeced presen value of he afer ax margnal revenue ganed from oupu supply o he expeced presen value of he margnal cos ncurred from producon. ggregae oupu prce ndex (34) equals an average of he prce se by he fracon 1 k of nermedae oupu good frms ha adjus her prce opmally n perod and he average of he prces se by he remanng fracon k of nermedae oupu good frms ha adjus her prce accordng o paral ndexaon rule (47): 1 1 k 1 1 k k k * 1 k P k 1 P k 1 k k k k k 1 P k 2 P k 2 P (1 )( P ) P. Snce hose nermedae oupu good frms able o adjus her prce opmally n perod are seleced randomly from among all nermedae oupu good frms he average prce se by he remanng nermedae oupu good frms equals he value of he ndusry specfc aggregae oupu prce ndex ha prevaled durng perod 1 rescaled o accoun for pas ndusry specfc oupu prce nflaon. (49). The ankng Secor The bankng secor performs global fnancal nermedaon subjec o fnancal frcons and a regulaory consran. In parcular banks ssue rsky domesc currency denomnaed loans o domesc and foregn frms a nfrequenly adjused predeermned lendng raes oban fundng from domesc bank nermedaed households va deposs and from he domesc money marke va loans and accumulae bank capal ou of reaned earnngs gven cred losses o sasfy a regulaory capal requremen. red Demand There exs a large number of perfecly compeve banks whch combne local currency F N denomnaed fnal loans { j } o produce domesc currency denomnaed fnal loan j 1 accordng o fxed proporons porfolo aggregaor F
21 F F j 1 j mn F j N N j1 F F where j 1 and 1 1 j j. The represenave nernaonal fnal bank maxmzes profs derved from nermedaon of he domesc currency denomnaed fnal loan wh respec o npus of local currency denomnaed fnal loans mplyng demand funcons: F F F j j j 1. Snce he porfolo aggregaor exhbs consan reurns o scale n equlbrum he represenave nernaonal fnal bank generaes zero prof mplyng aggregae gross corporae loan rae ndex: N E F j 1 j(1 j 1). j1 j 1 Ths aggregae gross corporae loan rae ndex equals he mnmum cos of producng one un of he domesc currency denomnaed fnal loan gven he raes on local currency denomnaed fnal loans. There exs a large number of perfecly compeve banks whch combne dfferenaed nermedae loans m 1suppled by nermedae banks o produce fnal loan 1 accordng o consan elascy of subsuon porfolo aggregaor 1 1 1 11 1 1 1 ( m 1) dm (53) where serally uncorrelaed lendng rae markup shock 1sasfes 1 1 wh. The represenave domesc fnal bank maxmzes profs derved from nermedaon of he fnal loan wh respec o npus of nermedae loans mplyng demand funcons: 1 1 m m 1 1 1. Snce he porfolo aggregaor exhbs consan reurns o scale n equlbrum he represenave domesc fnal bank generaes zero prof mplyng aggregae gross lendng rae ndex: 1 1 1 1 1 1 m 1 (1 ) dm. (55) s he rae elascy of demand for nermedae loans 1ncreases hey become closer subsues and ndvdual nermedae banks have less marke power. (5) (51) (52) (54)
22 Fundng Demand and Provsonng There exss a connuum of monopolscally compeve nermedae banks ndexed by m [1]. Inermedae banks supply dfferenaed nermedae loans bu are oherwse dencal. We rule ou enry no and ex ou of he monopolscally compeve nermedae bankng secor. The represenave nermedae bank sells shares o domesc bank nermedaed households a prce V m. cng n he neress of s shareholders maxmzes s pre-dvdend sock marke value whch absracng from he capals spr move for holdng real porfolo balances equals he expeced presen value of curren and fuure dvdend paymens E (56) s s m Vm ms s where s denoes he Lagrange mulpler assocaed wh he perod s bank nermedaed household dynamc budge consran. The dervaon of hs resul mposes a ransversaly condon whch rules ou self-fulfllng speculave asse prce bubbles. Shares enle households o dvdend paymens ms defned as profs derved from provdng fnancal nermedaon servces less reaned earnngs I ms : ( (1 ) ) ( (1 ) ) ( (1 )(1 ) ) I.(57) D D D S S S ms ms 1 s 1 ms ms 1 s 1 ms ms 1 s ms 1 ms ms ms D Profs are defned as he sum of he ncrease n deposs ms 1from households ne of neres S paymens a he depos rae and he ncrease n loans ms 1from he money marke ne of neres paymens a he yeld o maury on shor erm bonds less he ncrease n dfferenaed E nermedae loans ms 1o frms ne of wredowns a cred loss rae s and neres receps a lendng rae less a cos of sasfyng he regulaory capal requremen ms 1 ms. The represenave nermedae bank ransforms depos and money marke fundng no rsky dfferenaed nermedae loans accordng o balance shee deny: K (58) D S. ms 1 ms 1 ms 1 ms 1 S S D S The money sock s 1 measures aggregae bank fundng ha s s 1 s 1 s 1 whle he Ks 1 bank capal rao s 1 equals he rao of aggregae bank capal o asses ha s. s 1 In ransformng depos and money marke fundng no rsky loans he represenave nermedae bank ncurs a cos of sasfyng he regulaory capal requremen ( K ) F (59) ms ms ms s where fxed cos F s ensures ha s. ovaed by Geral Ner Sessa and Sgnore (21) hs regulaon cos s decreasng n he rao of bank capal o asses a a decreasng rae s 1
23 1 K ms (2 ) 1 R s ms ( ms Kms ) e 1 Kms (6) R R where regulaory capal requremen s sasfes s 1 whle and. In seady sae equlbrum he bank capal rao equals s requred value and he cos of regulaon s consan. The fnancal polcy of he represenave nermedae bank s o smooh reaned earnngs neremporally gven cred losses. I eners perod s n possesson of prevously accumulaed bank capal sock K ms whch subsequenly evolves accordng o accumulaon funcon K (1 ) K ( I I ) (61) ms 1 s ms ms ms 1 E where bank capal desrucon rae s sasfes s s wh. Effecve reaned earnngs funcon ( I I 1) ncorporaes convex adjusmen coss ms ms 2 I m s Ims Ims 1 I ms 2 I ms 1 ( ) 1 1 (62) where. In seady sae equlbrum hese adjusmen coss equal zero and effecve reaned earnngs equals acual reaned earnngs. In perod he represenave nermedae bank chooses sae conngen sequences for depos D fundng { ms 1} money marke fundng S s { ms 1} reaned earnngs s { I ms } s and he bank capal sock { K ms 1} s o maxmze pre-dvdend sock marke value (56) subjec o balance shee deny (58) bank capal accumulaon funcon (61) and ermnal nonnegavy D consrans mt 1 S mt 1 and KmT 1 for T. In equlbrum he soluons o hs value maxmzaon problem sasfy necessary frs order condon 1 1 (63) D S whch equaes he depos rae o he yeld o maury on shor erm bonds. In equlbrum reaned earnngs sasfes necessary frs order condon Q ( I I ) E Q ( I I ) 1 (64) 1 m 1 m m 1 m 1 2 m 1 m whch equaes he expeced presen value of an addonal un of reaned earnngs o s margnal cos where Q kls denoes he Lagrange mulpler assocaed wh he perod s bank capal accumulaon funcon. In equlbrum hs shadow prce of bank capal sasfes necessary frs order condon 1 S Qm E (1 1 ) Qm 1 K( m 1 Km 1 ) (1 ) (65) 1
24 whch equaes o he expeced presen value of he fuure shadow prce of bank capal ne of desrucon less he sum of he margnal ulzaon cos of bank capal and he spread beween he cos of depos and money marke fundng. Provded ha he pre-dvdend sock marke value s bounded and srcly concave ogeher wh oher necessary frs order condons and ransversaly condons derved from he necessary complemenary slackness condons assocaed wh he ermnal nonnegavy consrans hese necessary frs order condons are suffcen for he unque value maxmzng sae conngen sequence of nermedae bank allocaons. red Supply In an adapaon of he model of nomnal oupu prce rgdy proposed by alvo (1983) o he bankng secor along he lnes of Hülsewg ayer and Wollmershäuser (29) each perod a randomly seleced fracon 1 of nermedae banks adjus her gross lendng rae opmally where 1. The remanng fracon of nermedae banks do no adjus her lendng rae: 1m 1 m 1. (66) Under hs fnancal frcon nermedae banks nfrequenly adjus her lendng rae mmckng he effec of maury ransformaon on he spread beween he lendng and depos raes. If he represenave nermedae bank can adjus s gross lendng rae n perod hen does so o maxmze pre-dvdend sock marke value (56) subjec o balance shee deny (58) nermedae loan demand funcon (54) and he assumed fnancal frcon. We consder a symmerc equlbrum under whch all bank specfc endogenous sae varables are resrced o equal her aggregae counerpars. I follows ha all nermedae banks ha adjus her lendng rae n perod solve an dencal value maxmzaon problem whch mples ha hey all * choose a common lendng rae gven by necessary frs order condon: * s * s s S s s (1 s 1 ) ( ms K ) ms 1 s 1 1 s s 1 s s 1s 1 1 1 s s 1 * s s s E 1 s 1 1 E ( ) ( s 1)(1 s ) (1 s 1 ) s s 1 1 E ( ) (1 ) 1 1 Ths necessary frs order condon equaes he expeced presen value of he margnal revenue ganed from loan supply o he expeced presen value of he margnal cos ncurred from nermedaon. ggregae gross lendng rae ndex (55) equals an average of he gross lendng rae se by he fracon 1 of nermedae banks ha adjus her lendng rae n perod and he average of he gross lendng raes se by he remanng fracon of nermedae banks ha do no adjus her lendng rae: 1 * 1 1 1 1 1 1 1 1 (1 )(1 ) (1 ).. (67) (68)
25 Snce hose nermedae banks able o adjus her lendng rae n perod are seleced randomly from among all nermedae banks he average gross lendng rae se by he remanng nermedae banks equals he value of he aggregae gross lendng rae ndex ha prevaled durng perod 1. D. The Trade Secor The nomnal effecve exchange rae measures he rade weghed average prce of foregn currency n erms of domesc currency whle he real effecve exchange rae measures he rade weghed average prce of foregn oupu n erms of domesc oupu N N T T w j w j j j j1 j1 ( ) ( ) (69) j j T where he real blaeral exchange rae j sasfes j and blaeral rade wegh w P T T N T sasfes w w j 1 and w 1 j 1. Furhermore he erms of rade j equals he rao of he nernal erms of rade o he exernal erms of rade P P X X X P P X where he nernal erms of rade measures he relave prce of expors and he exernal erms of rade measures he relave prce of mpors whle P denoes he prce of he fnal noncommody oupu good. Fnally under he law of one prce * Pk Pk for 1 k * whch mples ha N k * k 1 P w P (71) where P k denoes he quoaon currency denomnaed prce of energy or nonenergy N commodes and world oupu wegh w sasfes w 1 and w 1. P 1 j (7) The Expor Secor There exs a large number of perfecly compeve frms whch combne ndusry specfc fnal oupu goods { X } o produce fnal expor good k k 1 X accordng o fxed proporons producon funcon X X k mn X k k 1 X X where Xk k for 1 k * whle k 1 and 1 1 k k. The represenave fnal expor good frm maxmzes profs derved from producon of he fnal expor good wh respec o npus of ndusry specfc fnal oupu goods mplyng demand funcons: (72)
26 X (73) X. k k X Snce he producon funcon exhbs consan reurns o scale n equlbrum he represenave fnal expor good frm generaes zero prof mplyng aggregae expor prce ndex: X X k Pk k1 P. (74) Ths aggregae expor prce ndex equals he mnmum cos of producng one un of he fnal expor good gven he prces of ndusry specfc fnal oupu goods. The Impor Secor There exs a large number of perfecly compeve frms whch combne he fnal h h h h f f f f noncommody oupu good Z { I G } wh he fnal mpor good Z { I G } o produce fnal prvae consumpon prvae nvesmen or publc consumpon good Z { I G } accordng o consan elascy of subsuon producon funcon 1 1 1 1 1 D h D f Z Z Z ( ) ( ) ( ) ( ) D where serally correlaed mpor demand shock sasfes whle 1 D D D 1 1 and. The represenave fnal absorpon good frm maxmzes profs derved from producon of he fnal prvae consumpon prvae nvesmen or publc consumpon good wh respec o npus of he fnal noncommody oupu and mpor goods mplyng demand funcons: h D P f D 1 P Z Z Z P P Z Z Z. Snce he producon funcon exhbs consan reurns o scale n equlbrum he represenave fnal absorpon good frm generaes zero prof mplyng aggregae prvae consumpon prvae nvesmen or publc consumpon prce ndex: Z D 1 D P P 1 1 1 P ( ). ombnaon of hs aggregae prvae consumpon prvae nvesmen or publc consumpon prce ndex wh fnal noncommody oupu and mpor good demand funcons (76) yelds: (75) (76) (77) 1 1 1 1 h D D D f D D D Z Z Z Z. (78)