EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT

Transcription

1 EXCHANGE RATE REGIME AND HOUSEHOLD S CHOICE OF DEBT Summary This papr looks a h impac of h xchang ra rgim and h houshold s choic of db. On of h characrisics of conomic ransiion in asrn Europan counris was an incras in ovrall db holding. Sandard conomic hory assums h rlaionship S=I. In his rlaionship h housholds should us db only for purchass of durabl goods; howvr in som asrn Europan counris hr was a larg incras in consumr loans which ar no rcognizd undr sandard no-ponzi assumpion of conomic modls. This papr aims o invsiga prcisly ha cas: incras in houshold s db which is usd only for living abov hir mans. Th papr hypohsizs and provs a significan impac on h choic of h amoun h db h housholds ar willing o hold is du o h choic of h xchang ra rgim mad by h cnral bank. Th papr invsigas wo main cass: sabl xchang ra rgim (xchang ra rgim wih FX risk) and variabl xchang ra rgim (xchang ra rgim wihou xchang ra risk). Bhavior of h housholds is diffrn undr ach xchang ra rgim can b sn in h modl and in h daa as wll. JEL Classificaion: E51, C61, E58 Ky Words: crdi, xchang ra, dynamic programing. Nvn Vidaković Effcus Businss School Knndy squar Zagrb Croaia 1

2 1. Inroducion Thr ar many basic assumpions which ar applid in conomics. Th wo mos basic ons ar savings qual loans and housholds ar no allowd o borrow in ordr o liv abov hir mans. This papr liminas hs wo assumpions from h conomic modl wih h main objciv o invsiga how housholds bhav undr alrna xchang ra rgims 1. Th sandard approach o conomic modling is o us h wo sad conomic assumpions in a gnral quilibrium modl and hn analyz a paricular bhavior undr crain shock. This papr aks a complly alrna rou. W rmov h wo assumpions and invsiga bhavior of housholds undr diffrn xchang ra rgim. Th main implicaion of h papr lis in h assumpion h bhavior of conomic paricipans is going o chang whr hr is a chang in h xchang ra rgim. Bfor w mov any furhr w hav o mak a clar dfiniion wha is an xchang ra rgim for h purposs of his papr. On of h basic disribuions of h xchang ra rgims was don by IMF and i can b found in Von Hagn and Zhou (2002), Frankl (1999) and Crock (2003). Ths auhors hav hr main xchang ra rgims: fixd, inrmdia and fr floaing rgims. Howvr h dfiniion of hs rgims is basd on h amoun of movmn of h xchang ra, no on h dircion of xchang ra. In his papr w ar going o assum alrna dfiniions of h xchang ra rgim. Sabl xchang ra rgim: is a yp of xchang ra rgim whr h cnral bank kps h xchang ra fixd a on valu or clos o on cnral valu ovr larg priod of im. Ovr im h xchang ra dos no xhibi a clar dircional movmn, h movmn of h xchang ra is similar o a fla lin or man rvring sris. 1 This papr is par of auhor's PHD hsis in Economics a Univrsiy of Maribor which was dfndd in July 2013 undr h mnorship of prof. dr. sc. Dušan Žbašnik o whom I an graly grafull and indbdd. I would also lik o hank prof. dr. sc. Franjo Šiblar, prof. dr. sc. Žan Jan Oplonik and Domagoj Tolić for hlp wih compur programming. 2

3 Variabl xchang ra rgim: h cnral bank acivly affcs h xchang ra and uss monary policy o cra a clar dircional movmn of h xchang ra. Fr floaing rgim: h cnral bank dos no paricipa in h FX mark and h cnral bank is no concrnd wih h movmn of h xchang ra ovr im. Exchang ra is frly allowd o mov up or down and hr is no clar rnd ovr im. Th dfiniions of h xchang ra rgims as w hav prsnd hm in his papr ar basd on h dircion of h xchang ra rgim, no in h volailiy of h xchang ra rgim. This is paricularly imporan for his papr. Wha if a choic of xchang ra rgim as w hav dfind i has an imporan impac on h bhavior of h conomic paricipans? This papr will argu ha i dos. W will invsiga how dos a choic off h xchang ra rgim, fixd vs. sabl impac h bhavior of conomic paricipans. Again h focus is no on h changs in h xchang ra, bu on h acual choic of h xchang ra rgim. Th full scop of h possibl ffcs is larg and i was fully dvlopd in Vidaković (2013), in his papr w ar going o focus on h choic of h amoun of crdi h housholds ar willing o hold undr ach xchang ra rgim. Th acual choic of h xchang ra rgim will a h sam im drmin h bhavior of conomic paricipans. Jus h announcmn of a rgim will pu conomic paricipans ino a crain fram of mind. In ssnc w ar daling wih mulipl modl agns. Th conomic paricipans hav on modl for ach sa of h conomy (choic of h xchang ra rgim). Sinc h modl for ach xchang ra rgim is diffrn, h bhavior of conomic paricipans is going o b diffrn as wll. Th issu of conomic swiching and mulipl modls in h conomy has bn invsigas svral papr, bu i was nvr usd o invsiga how dos h chang in h xchang ra affc h choic of crdi. On of h bs xampls o invsiga conomic swiching in a sandard conomic modl can b found in Farmr, Waggonr, Zha (2007) who invsiga nw-kynsian modls and rgim swiching. Sam auhors also invsiga wha happns whn hr ar forward swiching xpcaions in Farmr, 3

4 Waggonr, Zha (2009). Ohrs invsiga wha happns whn agns hav mulipl modls lik in Cogly and Sargn (2008). Th rs of h papr is sparad in following way. Par wo will dvlop a modl wih wo sas of h sysm: undr sabl and undr variabl xchang ra rgim. Par hr will mahmaically simula h modl and will ry o drmin wha ar h housholds prfrncs in rms of db undr alrna xchang ra rgims. Par four will s h modl on mpirical daa. Par fiv concluds 2. Th modl In his par of h papr w ar going o rprsn h conomic modl whr housholds ar allowd o hav db and incras hir db holding. W ar going o cra wo spara modls for wo sas of h conomy: on modl for variabl xchang ra and on modl for sabl xchang ra. W ar going o us h dfiniions of h xchang ra rgim as providd in h prvious par of h papr Housholds W ar going o assum h housholds hav wo diffrn modls, on for ach of h monary policy rgims. Wha is imporan is h diffrnc bwn h choics mad in alrnaiv modls. W ar going o focus on amoun of crdi h housholds ar willing o hav undr ach xchang ra rgim choic. As mniond hr ar wo basic modls on of ach xchang ra rgim. Th housholds know h sa of h monary policy. Thy do no assum or xpc hr is going o b a swich in h monary policy. Th monary policy is givn xognously o h housholds by h cnral bank and w assum h crdibiliy of h cnral bank Modl of houshold's bhavior undr sabl xchang ra policis 4

5 Th houshold ar uiliy maximizing agns, h uiliy coms from consumpion. Th im is discr. Th objc of h housholds is o maximiz consumpion ovr an infini priod of im givn consrains. Th housholds mak hir xpcaions undr h raional xpcaions hypohsis. Th houshold liv in h currn xchang ra rgim and do no assum hr is going o b an xchang ra rgim swich. Th objciv of h housholds is: max 0 u( c ) subjc o consrains (1) Th houshold ris o maximiz h uiliy ovr im, h uiliy coms from consumpion c. Th U(c) funcion is a coninuous, wic diffrniabl funcion, β is a discoun facor. In his modl w ar going follow a novl approach and w ar going o spara savings from crdi. W ar going o look a h flow of funds in ach im priod and w ar going o allow housholds o hav boh crdi and savings a h sam im, his is no h sandard approach in xbook lik Blanchard and Fishr (1989, pag 69) in which usually hav h no ponzzi assumpion. W ar going o invsiga prcisly his opion, whr housholds can paralll sav and incras db sinc i is h opion which has occurrd in ral lif which is o allow housholds o hav crdi. Th crdi is obaind from h bank. I is possibl for h houshold o hav paymns boh for savings and crdi rpaymns in h sam im priod. This rsarch builds furhr on Vidaković (2005). Th inflow of mony for h housholds in any im priod is: I w * S (2) 1 Th inflow of mony I coms from wag w, nw db φ, h porion of savings ha gs liquidad τ; h valus of τ ar 0< τ <1. S is h oal savings h houshold has accumulad up o im priod. Following h inflow quaion w ar also going o hav h xpndiurs quaion in im priod. Th xpndiur quaion is h ouflow for h housholds and w shall dfin in h following way: 5

6 c s (3) * 1 Th houshold xpndiurs or ouflows Ε can b dividd ino consumpion c, savings s and h porion of h xising db paid off in ha im priod. Th porion of h oal db nod as Φ, paid off a im priod is markd wih κ and i has h valu 0<κ<1; s is h nw savings in im priod. Following hs wo quaions w hav givn h housholds h abiliy o borrow, rpay db, liquida hir savings and mak nw savings all in h sam im priod. W hav also allowd h housholds o rpay a porion of h xising db and o obain nw db in h sam im priod. Savings and db accumula ovr im and h accumulaion can b xprssd wih h wo following quaions: 1 0 (1 r wih som maximum valu of Φ* (4) * 1i 1 i ) 1 S s (1 r (5) 0 1i 1 i ) Th db is cosing h housholds h ra r*, his i is h ra h bank is offring o h houshold. W shall assum h inrs ra is h sam for ach houshold, xognous and prfcly inlasic for any lvl of dmand. Th houshold gs savings ra of r also from h bank. In quilibrium h E=I holds, whn w solv h quaions for h c w g h quaion: c w (6) * S 1 s 1 Th quaion (6) rprsns h flow of consumpion in vry im priod for h housholds. As h quaion (6) shows hr is a possibiliy for h housholds o dcras oal savings, hav nw savings, g nw db and rpay old db on on im priod. Th consumpion quaion (6) is h ransiion quaion in our modl. 6

7 Th main characrisic of h modl and h diffrnc bwn his modl and h sandard modl is h combinaion of db and savings a h sam im. Wih h inclusion of nw db φ in h consumpion quaion (2) w hav crad a possibiliy for housholds o hav a dsird lvl of consumpion which is abov hir mans and sav a h sam im. So h choic of db will also dpnd on h lifsyl h houshold wans o liv. Using h modl s up hus far w ar now going o s up h bllman quaion for h housholds undr sabl xchang ra rgim. Th valu funcion for h modl is going o b V A) u( c ) (7) ( 0 Th rminal condiion is going o b ransvrsaliy condiion. Th conrol funcion for h problm is u(c) so h bllman quaion is V 1 c 1 A ) max V ( A c (1 ) ( 1 ) (8) Subjc o h quaion (6) Ou of h rcursion prsnd in h bllman quaion h housholds ar going o obain a policy funcion h(c*,φ*,s*), and hy ar going o plan hir opimal pah of consumpion ovr im. In his modl h only risk for h houshold coms from h wags. And w ar going assum h wag follows a simpl auorgrssiv procss: Whr w is wag, α is h auorgrssiv cofficin and ε is h disurbanc wih disribuion N(0,σ) 7

8 Modl of houshold's bhavior undr variabl xchang ra policis Th modl prsnd in h prvious chapr had uncrainy only in h form of h wags, now w ar going o xpand h risks h housholds fac and inroduc h FX risk. If w hav a variabl xchang ra, h banks will hav o hdg for h currncy risk and h bs way o do ha is o ransfr h risk ovr o h cusomr. Th ransfr of risk can b don asily by lnding in forign currncy or mbdding a forign currncy claus in h loans. Bcaus of his ransfrnc of h FX risk by h banks, undr h variabl xchang ra h housholds ar going o ak on h xchang ra risk vry im hy g a forign currncy loan from h bank. In ordr o hdg hir own posiion, h housholds will hav o sav in forign currncy. This way h incras in loan is going o b somwha offs by h incras in savings. Undr h variabl xchang ra, wih h forign currncy claus mbddd in hir loans h housholds do no know wha hir amoun of db is going o hav in ach priod. Th incom funcion wih FX risk is going o b: I w * S (9) 1 Th amoun of nw db φ is now sochasic sinc whn h houshold obains h loan i knows h xac valu of h loan givn h xchang ra in h im priod. Wha changs in ach priod is h oal valu of savings, sinc h valu of savings will chang will h changs in h xchang ra. Th xpndiur funcion is also going o hav o b augmnd. Th xpndiurs of h housholds ar also no known in advanc. (10) c s * 1 Th consumpion is xpcd and so is h amoun of db h houshold is going o hav in h currn im priod. Th acual amoun of h db rpaymn in local currncy is no fixd sinc h db is dnominad in h forign currncy and h 8

9 changs in h xchang ra ar going o caus changs in h amoun of h db h houshold has. Now h valu funcion of h housholds is going o chang and w ar going o hav: n i V( A) maxe u( ci ) (11) 0 By quaing h I and E w g h following funcion for consumpion c w * S 1 s * 1 (12) Whr h conrol funcion is dfind as f (, s, ) (13) So h bllman quaion is going o b n i V (, s, ) max f (, s, ) E u( ci ) c, n (14) From his rcursion h housholds is going o form h policy funcion: h ( *, s*, *) (15) Th quaion (15) shows h policy funcion in rms of h flow variabls, bu h policy funcion can also b shown in h balanc variabls as h ( S*, *) (16) Th quaion (16) shows h policy funcion as how much savings and db h houshold is willing o hold a any poin in im. Whr S* and Φ* rprsn h 9

10 opimal lvls of db and savings h housholds is willing o hav in ach im priod. Undr variabl xchang ra h housholds is no choosing how much nw db is going o obain, bu rahr h houshold is choosing h oal amoun of db i is willing o hold. So why was his so imporan for h modl? For sarrs w hav o look a h diffrn policy funcions. In h modl wih h fixd xchang ra rgim h housholds did no car abou h lvl of db bcaus hir consumpion was no affcd by h changs in h xchang ra. Thy jus card abou h consumpion, whil in h modl wih h variabl xchang ra rgim h housholds ar aking ino concrn h oal amoun of db hy hav sinc siz of h db and rpaymns of h db ar sochasic. This is dircly imposd by h forign xchang ra risk crad by h variabl xchang ra rgim chosn by h cnral bank. W could look a h whol rgim choic from a diffrn prspciv as wll. Using h logic prsnd in Sanini (2007) and Vidaković (2008) w could look a h choic of h monary policy as a budg consrain. Undr h sabl xchang ra rgim h housholds hav a sof budg consrain bcaus hy can borrow as much as h banks ar willing o lnd hm. Undr h variabl xchang ra rgim h housholds hav a hard budg consrain. If h housholds wan o hav mor db h housholds hav o ak on h xchang risk. From h modl i is clar h xchang ra can b an imporan policy ool o conrol h lvl of db h housholds ar willing h hold hus making h xchang ra a ool for conrol of h crdi policy in h conomy. W hav dircly sn in h modl how h choic of h monary policy affcs h bhavior of h housholds. Th sabl xchang ra rgim in ssnc givs h houshold s fr hands whn i coms o db. In ha cas h only drminan of h lvl of db h housholds ar going o hav is h housholds im prfrnc of consumpion and h db limi imposd by h bank. In cas h housholds wan o hav prfrnc owards prsn consumpion, hy ar going o obain as much db as possibl and consum as much as hy can in h nar fuur. If h individual houshold prfrnc is owards h fuur hn h housholds will incras hir savings ra and sav in ordr o b abl o consum mor in h fuur. 10

11 Givn h modl w hav prsnd hr i is no hard o undrsand h srong incras in houshold db in x-socialis counris ovr h las wo dcads. If h housholds hav srong consumpion prfrncs owards prsn and hr ar no rsricions for h banks o m h incras in dmand for loans, hr is going o b an xplosion in houshold db. This yp of bhavior was prsnd in Kraf and Jankov (2004). Undr h variabl xchang ra h choic of h xchang ra rgim is h on which srvs as sopping ool for h incras in houshold s db. Th variabl xchang ra wih h xchang ra risk ransfr srvs as drrn for h housholds o g db jus o incras hir consumpion. Undr h variabl xchang ra policy whn h houshold g a loan in forign currncy and h forign currncy claus h houshold is going o hav o compar hir xpcaions of wag growh wih hir xpcaions of h chang in h xchang ra. If h xchang ra is dprciaing mor han h houshold s wag is growing, by choosing o hav db h houshold will hav o dcras consumpion as a rsul of h changs in h nominal xchang ra sinc hir paymn annuiis ar going o go up. Th diffrnc bwn h hard and sof budgary consrains is h main sourc of imbalancs in h conomy. If h housholds hav hard budg consrains hy will hav o liv wihin hir own mans. If h housholds do no hav hard budg consrain, bu can borrow from h banks as much as hy wan, h whol dynamics of h conomic sysm of h small opn conomy changs, as obsrvd in Zbašnik (2008). Wih h abiliy o borrow frly h housholds can saia hir consumpion as much as hy wan. So h policy choic of fixd xchang ra dircly changs h bhavior of h housholds. Howvr h alrna bhavior of housholds will chang hir rlaionship wih ohr conomic paricipans as wll. Sinc w hav concludd h sabl xchang ra rgim is going o incras h dmand for loans h banks hav o find ways o fund incras in dmand for loans. If h banks canno g funding from primary sourcs h bank will hav o go ousid of h counry o obain funding. This in urn will incras forign db. Howvr hr is on major problm: h housholds canno liv abov hir sandard for infini priod of im. A on poin in im h lvl of db rachs h lvl whr 11

12 h banks ar no longr willing o giv loans o h houshold. A h poin of maximum db h houshold s consumpion can b prsnd wih h following quaion: I w (17) * S 1 * * 1 Now h incom of h housholds is h wag, plus liquidad savings minus h rpaymn of db. Th db is Φ* and i indicas h housholds has rachd h uppr limi of db. Naurally h paradox hr is ha if h houshold dos no hav any savings or i dos no wan o liquida accumulad savings h availabl incom for h housholds is going o b blow h wag. This hard landing will dcras h consumpion of h housholds and hir sandard will fall. Evn if h houshold dcids o kp h unnaurally high lvl of consumpion by liquidaing h savings his also has a limi sinc h savings h housholds hav accumulad ar no infini. Th sop in lnding and h consquncs of ha sop hav bn dscribd in Vidaković (2005a). Th choic of h variabl xchang ra rgim lads o complly diffrn oucom hn h choic of h sabl xchang ra rgim. Th variabl xchang ra rgim immdialy srvs as a hard budg consrain of for h housholds and a drrn agains living abov hir mans Exchang ra rgim swichs In his par w ar going o discuss h implicaions of h xchang ra rgim chang. W ar going o modl h swich in h monary xchang ra rgim and is implicaions. Th focus will b whn h xchang ra rgim changs from fixd o a variabl xchang ra rgim. Th swich from sabl o variabl xchang ra rgim is mor srssful for h housholds sinc h housholds hav o larn h ru modl h cnral banks is using o chang h xchang ra. Bcaus of inroducion of h xchang ra risk h housholds will hav o adjus hir db holdings. Incras in xchang ra implis dcras in consumpion sinc h dprciaion causs db annuiy o go up. Also hr will b adjusmn in obain nw db o financ consumpion. 12

13 Onc hr is a chang from variabl o sabl xchang ra rgim h housholds swich hir modl as wll. Th chang in h modl is insananous and hr is no nd for h housholds o adap in any way. Wih h chang in h modl, coms h chang in h bhavior. Th housholds hav o larn h modl which h cnral bank is using. Th modls which us larning chniqus and siuaions whr xpcaions ar no prfcly raional can b found in Hansn, Sargn, Turmuhambova, Williams (2006), Marc and Sargn (1989), Parlman and Sargn (2005), Woodford (2006). Sinc w ar dvloping modl on paricipan a h im now w ar going o dvlop a gnral larning principl which will volv ovr im and w ar going o dvlop i on only on variabl: nominal xchang ra. Th sam principl can b usd on ohr variabls as wll. Th modl which w ar going o prsn hr closly follows Evans, Honkapohja, Williams, Sargn (2012). Raional xpcaions modl for h movmn of h xchang ra is E * z (18) 1 1 Whr is h nominal xchang ra, E* -1 dnos xpcaions of nominal xchang ra on availabl informaion a -1. Th variabl z is an xognous obsrvabl variabl following saionary AR(1) procss which w will dfin as z z w (19) 1 Whr w ~ iid (0, σ 2 ) and η is an unobsrvabl whi nois shock wih Eη 2 = σ 2 η. Th valu of h inrcp µ will b pu o 0 for simpliciy. Wha his paricular s up givs us is h abiliy o look a h monary policy from wo spara prspcivs. Firs prspciv is h xpcaions E* which do no hav o b ru raional xpcaions, bu can b basd on subjciv disribuions of houshold of fuur changs in h xchang ra. Th xpcaions E* migh b somhing which is dply rood in houshold's mnaliy lik far of inflaion or far of dvaluaion as dscribd in Grgurk and Vidaković (2008). Th main poin is ha in h sabl raional xpcaions quilibrium h E* which is subjciv should bcom ral raional xpcaions E* which is qual o h modl h cnral bank has undr h raional 13

14 xpcaions assumpions of h on modl. Th monary policy of h cnral bank is givn by h xognous shocks z. Th variabl z in our cons ar monary inrvnions of h cnral bank which chang h valu of h nominal xchang ra. Th houshold (or any ohr paricipan) dos no know wha h cnral bank will do, so hy hav o larn how h cnral bank works. For h quaions (18) and (19) h raional xpcaions soluion is 1 (1 ) z 1 (20) For simpliciy w will s β = (1-α) -1 δ. Wha paricipans ry o do is o larn h changs of β ovr im and o b abl o do ha hy will hav o mploy Baysian chniqus. Using simplifid noaion w can now g h paricipans blifs and how hy volv ovr im. 1 (21) z Whr w will assum η z -1 and η ~ N (0, σ 2 η). Th quaion (4.118) is h foundaion for h law of moion of h variabl β. As ims gos by h xognous shocks z will chang h valu of h variabl β bcaus h housholds will larn h cnral bank's modl. So now w ar going o s h law of moion as b 1 z (22) 1 Whr b -1 is h -1 sima of β. For mahmaical purposs w ar going o assum hr is som prior disribuion of β, which mans h xchang ra rgim swich did no occur in im priod -1 bu som im bfor and h houshold is abl o alrady hav som prior valus of β which ar going o b disribud as β ~ N(b 0,V 0 ), his prior disribuion implis a posrior disribuion of f(β y -1 ) whr y is qual o y = (y, y -1, y -2,...) and y' = (p, z ) of h form N(b,V ). In ordr o upda h paramrs w s up sandard Kalman filr: 14

15 b V b c V V z V 1z 1 z V ( b z ) V 1z 1 ( b z 1) (23) (24) In Evans, Honkapohja, Williams, Sargn (2012) hr is formal prof h modl convrgs wih probabiliy 1 if α < 1 and hy also g ha V 2 /( 1) S z 2 0 (25) Wih probabiliy 1 for all σ 2 η rgardlss of whhr σ 2 η is corrc or no. Th modl prsnd hr lls us how h housholds (any ohr conomic paricipans) larn ovr im and how vnually h raional xpcaions modl prvails: h cnral bank and h conomic paricipans nd up having h sam modl. W ar now going o implmn h larning procss in our modl and w ar going o connc h houshold consumpion choic wih h larning modl. In our cas h housholds ar going o larn h cnral bank s ru modl afr h swich from sabl o variabl xchang ra rgim. W can dfin h variabl xchang ra rgim as n f ( ) (1 ) x (26) 0 0 Whr δ is h chang in h xchang ra givn h acions prformd by h cnral bank. Th paramr δ is sochasic. Whn h xchang ra rgim changs h housholds ar awar hy hav o modify hir modl for h xchang ra risk. Thr ar wo possibiliis: h ra of chang of h xchang ra is known o h housholds and ra of chang of h xchang ra is no known o h housholds. Cas 1: h ra of chang is known. In his cas h xpcaions ar mad raionally and h bllman quaion has h sam form as bfor: 15

16 RE RE V, s, ) max f ( u( c), ) E V (, s,, ) (27) ( c Whr RE now shows ha h xpcaions ar mad raionally undr h raional xpcaions hypohsis. Cas 2: h ra of chang of h xchang ra is no known o h housholds. Whn h xchang ra rgim swich is announcd h houshold dos no know wha h avrag ra of dprciaion going o b is and h houshold has o mak xpcaions and h only way o mak xpcaions is o hav som probabiliy disribuion. This is h sam probabiliy disribuion usd in quaion (21). Th houshold assums h chang of h xchang ra is going o hav disribuion N(µ,σ). This disribuion is no corrc and dos no mach h policy funcion disribuion h cnral bank has. Hr w ar going o follow similar approach from Cogly and Sargn (2008). Sinc h disribuion h housholds hav is wrong, hus h xpcaions crad basd on ha disribuion ar wrong as wll. Th only way for housholds o improv hir disribuion is o obain h corrc disribuion and h only way for h houshold o obain h corrc disribuion is hrough sampling. So vry im whn h priod nds hr is going o b anohr im addd o h sampl as shown hrough Kalman filr in quaions (23) and (24). In ha cas h ransiion quaion w hav bn using bfor is now going o b changd, c g(, s,, ) (28) 1 Whr θ rprsns h xpcd valu of disribuion of xchangs ra of h hus far collcd obsrvaions of h changs in h nominal xchang ra. Th paramr θ is obaind from h Kalman filr hrough larning procss dscribd in h quaions (23) and (24). Givn his knowldg w can chang h bllman quaion o b V B ( c B B, s,, ) max f ( u( c), ) E V ( A,, ) (29) 16

17 As w can s h bllman quaion has now changd and svral nw propris hav bn addd. Th firs propry is ha h bllman quaion is now crad wih h Baysian xpcaions bcaus hr is a suprscrip B. Th addiion of h Baysian xpcaions changs h whol procss of h rcursion. Undr h raional xpcaions onc h quaion is obaind h housholds solv h dynamic programming problm and h soluion is valid for vry im priod. Wih h Baysian xpcaions ha is no h cas. Sinc h man of h disribuion of h xchang ra changs vry priod, h Baysian housholds obains h bllman quaion vry priod and hn solvs h dynamic programming in ach im priod and no jus onc and for all lik undr h raional xpcaions. From his procss coms h avrsion owards high lvl of db. Ovr im h housholds is going o obain h corrc disribuion of h changs in h nominal xchang ra and h housholds and h cnral bank ar going o hav h sam disribuion lading o h raional xpcaions quilibrium Banks Onc h monary policy is chosn h banks ar pu ino a framwork hy will follow in ordr o gain maximum profis undr h circumsancs. Th banks ar jus lik ohr conomic paricipans in rms of how hy ar going o b modld, howvr hy ar of gra imporanc for ohr conomic paricipans and how hy bhav givn h xchang ra rgim. Th issu of banks in ransiion counris has bn a snsiiv on. For xampl Ribnikar (1995, 2004b) saw banks as dsirabl o b privaizs, bu imporan nough for h conomy no o b privaizd fas. On h ohr hand Kraf (2002, 2003) and Kraf, Faulnd, Tpuš (1998) s privaizaion of banks and sal of bank o forignrs as somhing vry bnficial. Th cnral bank imposs h monary policy ono banks. Onc h banks know h monary policy hy ry o minimiz h cos of rgulaion and maximiz hir profis. Th profi maximizaion is an opimizaion problm. To us h imporan o undrsand wha is h porfolio choic of h banks undr diffrn xchang ra rgims and is hr a diffrnc. 17

18 Modling banks as uiliy maximizing conomic agns W ar going o modl banks as uiliy maximizing conomic agns. Th banks bhav in h sam way as h housholds do xcp h objc of h maximizaion is no consumpion, bu profis. In banking businss h profi coms from buying mony (ging dposis from primary and/or scondary sourcs of funds) a som pric and slling i (giving ou loans or paricipaing in rading aciviis) a a highr pric. Th diffrnc bwn cos of funds and h pric of funds "sold" givs bank's n inrs incom and consqunly profi. Th pursui of profi aks plac whil h banks ar rying o solv h problm of minimizing h businss risks and maximizing h profis. Th assumpion of maximizing profis, whil minimizing h risk is h horical basis for using h uiliy funcion. W ar going o assum h uiliy funcion has following sandard propris u'( )>0 and u''( )<0, uiliy funcion is coninuous and as las wic diffrniabl. Th incras in profis is ncssarily id wih incras in risks akn. Th bank wans mor profis and gs mor plasur from arning mor mony (h firs drivaiv of h uiliy funcion is grar han 0). Howvr incras in profis is followd by incras in risk xposur, making h plasur of ach nw dollar arnd undr highr risk lss and lss plasurabl (h scond drivaiv of h uiliy funcion is lss han 0). Th bank has opion o invs in as many invsmns as i can g funding for. Th invsmns hav a ra of rurn. W will us CRRA class of uiliy funcion so h bank has rlaiv risk pr uni of xposur. Th bank has a fixd prcnag of risk accpancs for ach invsmn. This givs h bank flxibiliy in is invsmns, bu a h sam im h bank has a fixd risk olranc. Th profi is an accouning variabl, no conomic variabl. In accouning rms h profi is h diffrnc bwn h incom and h cos. Sinc profi is an accouning variabl i is impossibl for a bank, or any ohr firm o us h profi as a conrol variabl. Th bank can influnc ihr h incom or h coss and hn s h rsuls in h profis. Th profi can b influncd only indircly. In ordr o hav profi in h 18

19 uiliy funcion w hav o driv h conncion bwn h incom, xpndiur and hn us ha conncion as h conrol variabl. Th formula for profi will b: ra L (30) Whr π is profi, A is a marix for asss and L is h marix for liabiliis 2, r is h vcor of h inrs ras on asss and δ is h vcor of h inrs ras on liabiliis. Asss hav o qual liabiliis bcaus of funding w g h following quaion for banks profis. ra A A( r ) A (31) Whr τ is h vcor of h n ffciv inrs ra h bank gs or h inrs ra sprad bwn h asss and liabiliis. W ar assuming all ohr coss ar covrd from all ohr incom. Alhough his is no chnically corrc w ar mor focusd on h dcisions h banks mak, no on h acual valu of h profis. Th uiliy funcion w ar going o us is 1 u ( ) (32) 1 Whr π is profi and γ is lasiciy of subsiuion wih h valu 0<γ<1. Th imporanc of h choic of h uiliy funcion can bs b found in Kimball (1993) whr i is srssd ha h foundaion of mos conomic modls is h uiliy funcion and h choic of h uiliy funcion can dica h whol modl. Th valu of h choic of h uiliy funcion lis in h sandard risk avrsion masur which is proposd by Kimball (1993): u' ' (33) u' 2 W ar only going o look a h inrs baring asss and inrs baring liabiliis plus capial. W ar no going o look a ohr ims of h bank's balanc sh. So whn w ar rfrring o asss or liabiliis w ar rfrring o h inrs baring pars of h balanc sh plus capial. 19

20 Using h CRRA funcion w hav h rlaiv risk as a consan. Th bank is always willing o risk γ pr loan, a rlaiv amoun Bank s dynamic programming problm Th banks fac wo spara opimizaion problms. Th firs problm is how o maximiz h profis from h crdi porfolio, which is drivd from h funds collcd in liabiliis and hn allocad in asss. Th scond opimizaion problm is how o minimiz h cos of rgulaion. Th asss of h bank ar going o b sparad in wo vcors, shown in h marix form hy ar x A q (34) Whr A is asss a im, x is h inrs baring asss and q is h par of asss allocad spcifically as dmandd by h rgulaion. Sinc w ar no inrsd in h inrplay bwn h cnral bank and h bank w ar only going o focus on h x par of h balanc sh. Th problm will b sochasic sinc h banks fac risk in hir businss and hav o cra xpcaion abou fuur. Basic s up of h problm can b also found in Coopr and Adda (2003). Th bank ris o maximiz prsn valu of xpcd uiliy from profis ovr im. maxe 0 u( ) (35) Th profi is nod as π, discound ovr by h ra β in ordr o g h prsn valu of profi, E sands for h xpcaions opraor, and bfor w s up h Bllman quaion w nd h valu funcion. Th valu funcion aks h form: 20

21 V x ) maxe u( ) (36) 0 ( Subjc o x 0 0, x 0 is fr; x 0 for all im priods. Whr x is h par of h bank's balanc sh ha is inrs baring and is n of rgulaion imposd by h cnral bank. W ar assuming ha x has som iniial valu of; valu x is a par of h bank's balanc sh whn h bank sars h conrol problm, h nd valu is fr, so w do no impos a growh limi on banks. W ar also assuming ha hrough im h valu of x is grar han 0, sinc i would b impossibl for h bank o hav no inrs baring asss in his par of h balanc sh. Th ransiion quaion for inrs baring par of h balanc sh is: x ( ) (37) x 1 In ach priod h bank has n inrs baring asss x -1 from h prvious priod and h currn priod changs in h valus of inrs baring asss. Whr Λ rprsns h incoming funds ino h bank, λ ar h ougoing funds in ach im priod. Sinc w ar invsigaing do banks alr hir lnding undr alrna xchang ra rgims w ar going o giv banks wo possibiliis: o lnd o lnd o housholds and o lnd o all ohr paricipans in h conomy. Th formula for profi in ach im priod will b: wih 0 ω 1 x ( ) * r z 1 1 (38) In quaion (38) w s wo ras of rurn and wo classs of asss. Th firs ra of rurn is r, which is h avrag ra of rurn on all ohr asss in h balanc sh and i is porion of ω of h inrs baring asss. Th scond group is h loans o housholds, hos loans hav h 1-ω porion of h risk baring asss and h xpcd ra of rurn is z. As w can s boh ras hav subscrip, which dnos im priod and suprscrip which dnos xpcaions abou h risk baring ra of rurn for h banks. 21

22 To obain of h soluion for h maximizaion problm in quaion (36) w nd a rcursiv soluion of h problm. To obain ha rcursiv soluion w will us Bllman principl of opimaliy as dscribd in Adda and Coopr (2003 pag 14). Now w can s up h bllman quaion: 1 V ( x ) max u( ) E V 1( x 1) (39) Th E in bllman quaion indicas xpcaions sinc h bank has risk baring asss whr h ra is no known wih crainy, bu i has o b obaind hrough xpcaions. Equaion (39) is lling how h bank is going o bhav. By solving h bllman quaion w can find h opimal pah for h bank in ordr o achiv h maximizaion of profis. Firs ordr condiions ar for π 1 r 1 z 1 1 u ( ) E V ' ( x (40) ' 1 1) For ω E V ( x )( r z ) 0 ' 1 1 (41) 1 In h quaion (41) w hav usd h fac ha (1 ) ( x ) is known a im. Using quaion (39) and h nvlop horm dscribd in Blanchard and Fishr (1989 pag 280) w can g: 1 1 r 1 z 1 V ' ( x ) u'( ) V '( x ) E 1 1 (42) Now w can conclud ha marginal uiliy of profi has o b qual o h marginal incras in x, h inrs baring par of h balanc sh. Using his rlaionship w can limina V'(x+1) from h firs ordr condiions and g quaions in (40) and (42). u ( 1 ) E 1 r 1 z 1 u '( (43) ' 1) E r u'( ) Eu '( ) z (44) 22

23 W can now subsiu (44) ino (43) h wo firs ordr condiions bcom: 1 r Eu '( 1 Eu '( ) 1 z 1 u ( ) (45) ' 1) u ( ) (46) ' 1 As w can s h bank is rying o solv a dynamic problm of how o opimiz invsmns of h funds i has collcd. 3. Modl simulaion W ar going o s h modl in wo spara ways. Firs w ar going o prform a Malab simulaion of h modl and in h nx par of h papr w ar going o prform a ral lif daa s of h modl. Th paramrs usd for h modl ar givn in h appndix. Going back o h main hsis of h papr w should s diffrn amouns of crdi h housholds ar willing o hold undr diffrn xchang ra rgims. Undr variabl xchang ra rgim w should s smallr amouns of crdi bcaus h housholds do no prfr larg db holding bcaus of forign xchang db. On h ohr hand undr sabl xchang ra w should s highr db holdings. In h modl w sar wih ω=1, so hr is no houshold db. Picur 1 shows wha happns undr sabl xchang ra rgim and Picur 2 shows wha happns undr variabl xchang ra rgim. Picur 1. : ω undr sabl xchang ra rgim 23

24 Undr boh xchang ra rgims w s incras in valu of ω, so h housholds db sars o appar and from h iniial poin whn h banks do no lnd o housholds hy sar o lnd a h sar of h simulaion. In boh cass w s hr is an incras in h lnding o housholds and afr im h housholds sar o incras in h oal balanc. Picur 2. : ω undr variabl xchang ra rgim Howvr hr is on main diffrnc bwn sabl and variabl xchang ra rgims. Undr variabl xchang ra rgims lnding o housholds sars o dcras, pks a around 30% of oal lnding and hn sabilizs is porion in h balanc sh. On h ohr hand lnding o housholds undr sabl xchang ra rgim sadily incrass ovr im and as w can s clos o h nd of h simulaion aks ovr as h majoriy of bank s lnding. From h simulaion w can s ovr im h lnding o housholds complly crowds ou lnding o ohr paricipans in h conomy. 4. Ral lif xampl Th ral lif xampl will b prformd on Croaia, Hungary, Lavia and Slovakia. Firs w hav o dfin h xchang ra rgims. As i is obvious from h daa in Picur 3, hr is no nd for conomric sing for Hungary and Slovakia sinc from h daa w can s h xchang ra is variabl and hn i swichs o sabl xchang ra rgim. Thrfor h conomric sing will b form only on Croaia and Lavia. W hav prformd conomric ss for boh counris and hav found hr was an xchang ra rgim swich. Th dails ar in appndix 1. 24

25 From Picur 3 w can clarly s h daa confirmaion of h modl. In Hungary h daa follows h modl prfcly. Th houshold loans sar wih almos 40% a h sar of h daa and w can clarly s h dcras of h amoun of houshold loans in h amoun of oal long. Thn in 2001 Hungary sabilizs h currncy and h loans o housholds sar growing and h amoun of loans o housholds a porion of oal loans mor han doubls. Wih h sar of h financial crisis in 2008 h Hungarian Forin sars o dprcia and h porion of loans sabilizs and from 2009 o 2011 i is almos unchangd. Also a h sam im priod h currncy dprcias 15% so porion of growh of loans can also b conribud o h dprciaion of h xchang ra, no o acual growh of loans. nd of yar Picur 1. : ω undr variabl xchang ra rgim Croaia Hungary Lavia Slovakia Croaian kuna 1-ω Hungarian forin 1-ω Lavian Las 1-ω Slovčka Krona 1-ω 1990 : 83,77 39,7% : 1991 : 101,40 27,8% : 1992 : 101,68 29,2% 1, : 9,4% 112,35 30,1% 0,67 37,04 7,3% ,96 12,7% 136,73 26,1% 0,67 38,48 6,5% ,96 14,5% 183,30 21,3% 0,71 38,86 5,4% ,94 19,6% 206,91 14,9% 0,70 39,95 5,0% ,96 26,3% 224,71 16,1% 0,66 2,4% 38,43 6,1% ,29 29,7% 252,39 14,1% 0,66 5,2% 43,21 7,6% ,68 34,7% 254,70 15,0% 0,59 13,3% 42,40 10,1% ,58 38,6% 265,00 16,8% 0,58 17,3% 43,93 12,1% ,37 40,5% 245,18 21,9% 0,56 21,8% 42,78 18,3% ,48 44,8% 236,29 28,9% 0,61 26,7% 30,13 21,3% ,65 49,8% 262,50 36,1% 0,67 36,0% 30,13 25,5% ,67 51,9% 245,97 40,5% 0,70 42,4% 30,13 35,1% ,37 53,3% 252,87 42,2% 0,70 50,0% 30,13 40,9% ,35 52,9% 251,77 42,3% 0,70 59,1% 30,13 42,0% ,33 54,5% 253,73 43,8% 0,70 61,1% 30,13 42,9% ,32 54,7% 266,70 46,1% 0,71 61,4% 30,13 44,9% ,31 53,5% 270,42 48,1% 0,71 62,0% 1,00 48,3% ,39 52,3% 277,95 50,8% 0,71 61,9% 1,00 50,8% ,53 50,0% 311,13 50,2% 0,70 60,2% 1,00 51,5% Similar parn can b sn in Slovakia as wll. Th raio of loans in h bank s balanc sh was low as long as h currncy was dprciaing. Thn in 1998 h currncy sabilizs and h loans o housholds sar o grow as h porion of oal loans. Th incras is vn fasr as h Slovakia sabilizs h currncy bcaus of h joining of h EMU. Wha is mos sarling cass w can s hr is h crowding ou ffc h loans o housholds hav on ohr loans. Jus lik h cas of our hypohical modl w s h loans o housholds ovr im ak ovr as h majoriy of loans in h balanc sh. Jus lik in h modl ovr im h loans o housholds crowd ou ohr loans and hy bcom h dominan balanc in h balanc sh. Modl is consisn for Lavia as wll. Th raio of houshold s loans is incrasing, which w s in h modl, bu i ruly xplods onc h xchang ra sabilizs. 25

26 5. Conclusion This papr ss forh o invsiga h ffcs of h xchang ra rgim choic on banks and housholds. Th main faur of h modl prsnd in his papr is h abiliy of housholds o hold boh db and savings a h sam im. In his propry h modl significanly diffrs from ohr modls whr savings qual loans. In his modl savings can qual o crdi and h crdi can b usd o incras consumpion. Furhr h modl assums h FX risk plays a significan rol in h acual dcision procss of h housholds. If h xchang ra is sabl h propnsiy of housholds owards db is grar. On h ohr hand if h xchang ra rgim is variabl, h vry xisnc of h FX risk will srv as a drn owards h housholds and db holding. Th modl is sd in boh laboraory and ral lif sing. W can s from h ss wo main facs: h choic of h xchang ra rgim plays a significan rol in rms of h db holdings of h housholds and savings quals loans assumpion nds o b rvisd whn modling asrn Europan ransiion conomis. Apar from h confirmaion of h modl in h daa h mor implicaion of h modl is h imporanc of h xchang ra rgim on h bank s crdi policy. This papr has shown ha jus h choic of h xchang ra rgim has significan impac on h conomy. Appndix 1: xchang ra rgim swich in Croaia In rms of h xchang ra rgim swich hr ar hr counris whr i is immdialy clar from h daa hr was an xchang ra rgim swich. In cas of Croaia his is no xacly clar so w ar going o us Chow s. Th basic prmis of h Chow s (Chow 1960) is o invsiga was hr a srucural brak in h daa, somhing which has alrd h conomic parn of h daa craion. Chow s dos no hav h abiliy o ll us wha is h rason hr was a srucural brak in h daa. This suis jus fin, sinc w ar assuming h rason for h srucural brak in h daa was h chang in h xchang ra rgim in h counry. 26

27 Th mchanisms of h Chow s ar rahr simpl. Th acual s is don in h following way. Th indpndn variabl and indpndn variabls ar drmind hn a rgrssion is run using h whol daa s. Thn h daa s is spli ino wo pars, bfor and afr h suspcd srucural brak. Thn again wo rgrssions ar run; on using h daa bfor h srucural brak and on rgrssion is ran using h daa afr h srucural brak. In h nd F-s is prformd using h sum of squars from all hr rgrssions. L us assum w hav a rgrssion wih wo indpndn variabls and n+m= im priods. W ar going o assum ha n is h im bfor h srucural brak and m is h im afr h srucural brak. Th n and m do no hav o b h sam. Th rgrssion using h im priods is going o b y 2 1 x z (A.1) W ar going o run wo mor rgrssions which ar going o b: n y (A.2) n n 1 x1 2 z1 m y x (A.3) m m z2 Suprscrips indica cofficins obaind using im priods. Th null hypohsis for h chow s is: n m n m m m ; ; (A.4) In ordr o s his hypohsis h following F-s is prformd F ~ S S S 1 1 S k S 2 2 N M 2k (A.5) 27

28 Whr S is h sum of squars rsidual from ach of h hr rgrssions, n and m and h numbrs of obsrvaion and h k is h dgrs of frdom. Using h appropria F disribuion abl h null hypohsis is sd and ihr accpd or rjcd. W ar rying o drmin was hr a srucural brak in h xchang ra rgim. In cas of Croaia w ar going o us h ARMA rgrssion. Using h monhly im sris for h xchang ra w ar going o hav h following rgrssion: EX 1EX EXMA (A.6) Whr h EX is h xchang ra and h EXAM 12 is h 12 monh moving avrag of h xchang ra. Th wo im priods w ar going o spli h daa ino ar going o b and for Croaia, for Croaia h F s is 0, F ~ , (A.8) *3 Using h F disribuion abl for k=3 and 158 w g ha h p valu is 4,8%, which is jus blow a 5% significanc lvl. In his paricular cas w ar going o rjc h null hypohsis and sa ha in Croaia hr was also a rgim swich. Appndix 2: h daa In ordr o calibra h modl for malab simulaion w usd o following daa and paramrizaion. Th wags wr akn from Croaia in priod For h variabls xchang ra h Slovnian xchang ra was usd from priod Savings was s as 20% of wags. This assumpion is mpirically consisn wih Croaia. W could hav usd various paramrs for savings, bu ha is no h objc of h rsarch. Iniially h banks balanc sh was s a 0 loans o housholds. Inrs ras on loans and dposis was usd from Croaian cnral bank s wb si. For our rsarch i is 28

29 no imporan wha was h acual ra, bu hough h sampl h ra on asss is grar han h ra on loans. For uiliy funcions paramrs γ and θ whr pu a 2. Discoun facor β is 4% pr yar. All hs facors ar consis wih h paramrs usd in Bokan, Grguric, Krznar and Lang (2009). Rfrncs Adda, J, Coopr, R. (2003) Dynamic Programming: Thory and Macroconomic Applicaions, MIT Prss, 296 pags Blanchard, O., Fichr, S (1989). Lcurs on Macroconomics, MIT Prss 650 sr. Bokan, N, Grgurić, L, Krznar, I, Lang, M (2009) Th Impac of h Financial Crisis and Policy Rsponss in Croaia, CNB working paprs W - 22 Dcmbr Chow, G. (1960) Tss of Equaliy Bwn Ss of Cofficins in Two Linar Rgrssions Economrica vol 28, issu 3, pags Cogly, T, Sargn, T (2008) Anicipad Uiliy And Raional Expcaions As Approximaions Of Baysian Dcision Making, Inrnaional Economic Rviw vol 49, issu 1, pags Crock, A. (2003) Exchang Ra Rgims in Thory and Pracic, in Monary Hisory, Exchang Ras and Financial Marks. Essays in Honour of Charks Goodhar, Edward Elgar, p. 281 d Mizn P. Evans, G, Honkapohja, S, Sargn T, Williams, N (2012) Baysian Modl Avraging, Larning and Modl Slcion working papr hps://fils.nyu.du/s43/public/nw_paprs.hml Farmr, R, Waggonr, D, Zha T. (2007) Undrsanding h Nw-Kynsian Modl Whn Monary Policy Swichs Rgims, Fbruary hp://hom.arhlink.n/~zha01/workingpaprs/wp.hml Farmr, R, Waggonr, D, Zha T. (2009) Indrminacy in a Forward Looking Rgim Swiching Modl Inrnaional Journal of Economic Thory vol 5, pags Frankl, J, (1993). On Exchang Ras, Th MIT Prss. 29

30 Grgurk, M, Vidakovic, N. (2007) Th paradox of kuna savings: Why do Croaians sav in forign currncy Libras Businss School paprs Ivo Andrijanić d. pags Hansn, L. P, Sargn T. Turmuhambova G, Williams, N. (2006) Robus Conrol and Modl Misspcificaion Journal of Economic Thory vol 128. pags Kraf, E. (2002) Forign Banks in Croaia: Anohr Look Croaian Naional Bank Working Paprs W-10 Kraf, E. (2003) Monary Policy Undr Dollarizaion: h Cas of Croaia Comparaiv Economic Sudis 45 (3) Kraf, E, Jankov, Lj. (2005) Dos Spd Kill? Lnding Booms and Thir Consquncs in Croaia Journal of Banking and Financ, vol. 29, issu 1, pags Kraf, E, Faulnd M, Tpus, M. M. (1998) Rpor on h Crdi Policis of Croaian Banks, Naional Bank of Croaia Working Papr 9 Marc, A, Sargn, T, (1989) Las Squars Larning and h Dynamics of Hyprinflaion Economic Complxiy: Chaos, Sunspos, and Nonlinariy Barn, W., Gwk, J. and Shll, K ds. Cambridg Univrsiy Prss. Parlman J, Sargn T. (2005) Knowing h Forcass of Ohrs. Rviw of Economic Dynamics Ribnikar, I (1995) Th monary sysm of a small currncy ara: h cas of Slovnia. Dvlopmn and inrnaional coopraion 11 (20/21) Sanini, G (2007) Iluzija i svarnos hrvaskoga gospodarsva, Rifin, Zagrb. Vidaković, N. (2005). Thory of Raional Expcaions and Microconomics of Db Ekonomija/Economics 12 (4) Vidaković, N. (2007a) Comparison of Ral Exchang Ra in Croaia and Slovnia (2007) Naš Gospodarsvo/Our Economy 1-2, Vidaković, N. (2007b) Th impac of h choic of h monary policy on housholds Monngrin journal of conomics 3(6) Vidaković, N. (2008) Economic policy, sof budg rsrains and h craion of forign db in Croaia Ekonomija/Economics vol 14 issu 2 Vidaković, N. (2013) Exchang ra rgim and bhavior of conomic paricipans, PHD hsis Univrsiy of Maribor. 30

31 Von Hagn, J, Zhou, J. (2002). Th Choic of Exchang Ra Rgims: An Empirical Analysis for Transiion Economis Working Papr, B 03, Znrum für Europäisch Ingraionsforschung 23. Woodford, M. (2006). An Exampl of Robusly Opimal Monary Policy wih Nar- Raional Expcaions. Journal of h Europan Economic Associaion 4(2-3) Zbašnik, D. (2008a) Dva dficia i dug 520 Ekonomija/Economics, vol. 14, issu 2, pags