Inflation Targeting and Variability of Money Market Interest Rates Under a Zero Lower Bound*

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1 JEL Classificaion: E43, E44 Kywords: mony mar inrs ras, volailiy, inflaion arging, zro lowr bound, Baysian VAR, Hisorical dcomposiion Inflaion Targing and Variabiliy of Mony Mar Inrs Ras Undr a Zro Lowr Bound Karl BRUNA - Univrsiy of Economics, Pragu, Dparmn of Monary Thory and Policy, Pragu, Czch Rpublic (bruna@vs.cz) corrsponding auhor Quang VAN TRAN - Univrsiy of Economics, Pragu, Dparmn of Monary Thory and Policy, Pragu, Czch Rpublic (ran@vs.cz) Absrac Th papr prsns a formal framwor of mony mar inrs ras variabiliy undr a zro lowr bound in a monary policy sragy of inflaion arging. Th ponial facors influncing h variabiliy of mony mar inrs ras ar considrd wihin a nar zro lvl of main policy ra variabiliy. A h sam im, modl opimal main policy ra shows significan volailiy du o changs in h srucural characrisics of conomy facing dp conomic and financial shocs, changing prcpion of inflaion riss, cnral ban s wand crdibiliy and uncrainy abou h fficin ransmission of monary masurs. Th mony mar inrs ras ar modld in h framwor of VAR modl wih xognous variabls using h xampl of h Czch conomy for a priod Th modl is simad by Baysian mhod and is srucural form is obaind hrough sign rsricion. Th rpo ra and mony mar inrs ras ar dcomposd ino a sris of cumulaiv srucural shocs of ach ndognous componn in h modl. Th rsuls show ha global financial crisis and h xchang ra alrnaiv monary policy masurs ar wo main sourcs of ndognous variabls shocs for inrs ras which confirm high imporanc of n xpor, baning loans and invsmn for h dynamics of an opn conomy. 1. Inroducion In a framwor of inflaion arging, h main policy ra and mony mar inrs ras ar ypically considrd as y signaling and ransmission variabls ha iniia furhr adapaions in clin inrs ras, xchang ras, xpcaions and lnding/spnding aciviy consisn wih inflaion arg. I is assumd ha boh h lvl and variabiliy of main policy ra and mony mar inrs ras ar a nonzro lvl o provid adqua lvl of ral inrs ras and opimal simulus o conomic sysm ha could b considrd as a sris of nominal and ral financial and conomic shocs. In a shor hisory of inflaion arging in h Czch Rpublic, cnral ban dvlopd diffrn sags of h prdicion modls ha rflc h fac of nonzro characr of h lvl and variabiliy of main policy ra and mony mar inrs This papr is suppord by h Gran Agncy of h Czch Rpublic no S and by h Univrsiy of Economics, Pragu as a par of Insiuional Rsarch Suppor no. IP Th auhors han anonymous rfrs for hir hlpful suggsions and commns. Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no

2 ras as a naural mchanism for sablishing inrnal pric quilibrium in a mar conomy. I is challnging for all cnral bans ha adopd policy of inflaion arging o corrcly rflc and analyz h raliy of dp financial and conomic crisis ha causd a dclin in monary policy inrs ras and mony mar inrs ras clos o zro lvl and in som cass vn slighly blow zro. Consqunly, alrnaiv monary policy masurs wr bing applid in many counris o ovrcom rsriciv characr of xpcd dflaion, high crdi ris and db dlvraging rsuling in high xpcd ral inrs ras, high ris prmiums and high db burdn. Th papr prsns formal framwor of mony mar inrs ras variabiliy undr a zro lowr bound in a monary policy sragy of inflaion arging. Th goal of h rsarch is o s a gnral lin bwn alrnaiv monary policy masurs in a modl of inflaion arging and h facors influncing h variabiliy of mony mar inrs ras in cas of a zro variabiliy of main policy ra whn modl opimal main policy ra shows high variabiliy du o changing srucur of ndognous and xognous shocs in conomic sysm. To quanify h variabiliy of mony mar ra, w us a Vcor Auo Rgrssiv (VAR) modl wih xognous variabls simad by Baysian chniqu for is rducd form. Th corrsponding srucural form is hn rcovrd by sign rsricion mhod. Th obaind cofficins ar usd o dcompos rsiduals ino h corrsponding srucural shocs which allows us o xprss mony mar inrs ra as a funcion of individual ndognous srucural shocs, hnc o masur how ach of hm conribus o oal variabiliy of mony mar inrs ra. For simaion purpos, w us quarrly daa from h Czch mony mar and h Czch conomy for a priod 000q1 o 016q4.. Mony Mar Yild Curv Variabiliy and Inflaion Targing undr a Zro Lowr Bound Mony Mar Inrs Ra and Tradiional Framwor of Inflaion Targing A concp of prfrrd habia hory assums ha agns in h mony mar compar acual n-day inrs ra wih h xpcd fuur dvlopmn of O/N inrs ras avrag lvl in n-day horizon. Th prfrncs of h agns also ma hm rqus incrasing rm prmium rflcing highr mauriy includd ris prmium as a pric for crdi and liquidiy riss. Thrfor, h mony mar quilibrium can b in gnral xprssd as a posiion of a ris avrs spculaor who (basd on availabl informaion (Ω )) quos h acual n-day inrs ra ( IR ) as h sum of h xpcd avrag of O/N ras in h priod of o + and rm/ris prmium ( ): n n IR n 1 n 1 = n = 0 IR O / N, + + n (1) In a framwor of inflaion arging, i is assumd ha cnral ban uss posiiv s-day argd inrs ra ( IR CB,, s ) as a pric of main policy masurs whil h mauriy of his ra maximally quals h mauriy of ulra-shor mony mar ras. Cnral ban s policy insrumns ar ypically usd o manag h liquidiy of 50 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

3 h baning sysm wihin a minimum rsrvs mainnanc priod. I is assumd ha h duraion of mainnanc priod r is longr/maximally quals h mauriy of main policy ra (s r) whil i holds good ha r is usually h whol mulipl of s. Th nd of h mainnanc priod would hn b idnical wih h mauriy of a ndr for liquidiy supply/wihdrawal a s-day ffciv main policy ra. Th main policy ra is considrd as an insrumnal variabl ha minimiss h valus of fuur dviaions of h variabls ha ar h objcs of cnral ban s inrs from argd valus in rlaion o rsricions givn by h xising srucur of an conomy. Thus h loss funcion (L ) of cnral ban is usually h sum of h prsn valus of quadraic dviaions of xpcd inflaion ( i +i growh ( y + ) from inflaion arg ( ) and ponial oupu ( 1999): i= 0 i L = (1 )( ) + ( y y ) + i + i + i + i ) and xpcd conomic + i y + i ) (Srour, () whr δ sand for h discoun facor (0 δ 1), α and (1-α) ar h rlaiv wighs of quadraic dviaions of inflaion and conomic growh from argd valus and i is a im shif indicaing forward looing characr of monary policy and h xisnc of im lags of h ffcs wihin ransmission mchanism. To s h main policy ra, h prsn conomic srucur implis rsricions for achivmn of monary args. Wih rgard o h cnral ban s loss funcion and modl of conomic srucur, h main inrs ra ha minimiss cnral ban s loss funcion for h acual inflaion forcas applid for h modl of conomic srucur in h horizon of fficin ransmission ( priod) is considrd as opimal. Formally OPTIM h opimal lvl of h main inrs ra ( IR, ) is dfind by h racion funcion of cnral ban of h Taylor s yp: OPTIM EQ CB CB IR CB, = IR + ( + + ) + ( y + y+ ) (3) EQ whr IR CB is h main policy ra corrsponding o long-rm conomic quilibrium, paramrs β and/or γ xprss h innsiy by which h cnral ban racs o h ovrshooing (undrshooing) of inflaion arg and/or posiiv (ngaiv) oupu gap. As sad by Svnsson (000) and Favro and Rovlli (000), im variabl paramrs β and γ ar h convoluion of paramrs dscribing cnral ban s prfrncs o h inflaion and conomic cycl and srucural characrisics of conomy. Sac (1998) and Rudbusch (001) poin ou ha hr xiss a disproporion bwn h modl opimum lvl of h main policy ra and h argd main policy ra ( IR, ) which is lss volail and srongly posiivly corrlad wih is laggd CB valus (Clarida, Gali and Grlr 1998) o avoid impairmn of cnral ban s crdibiliy ha could b conncd wih high variabiliy of h main policy ra (Goodhar 1998). Thrfor, h variabiliy of h argd main policy ra ofn bcoms a par of h cnral ban s objciv funcion whil opimal main policy ra is basd o Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6 51

4 achiv monary-policy objcivs undr h lows possibl variabiliy of h main inrs ra. Th dynamics of argd main inrs ra may show dviaions from monary rul (3) du o applicaion of monary policy sragis following ohr han inflaion args ha ar prsnd as a corrlaion of random shocs w (Rudbusch 00): OPTIM IRCB, = ( 1 1 ) IR CB, + 1IRCB, 1 + w (4) w = q n= 0 r z 1 1, n + DU, n DmU m, n (5) n= 0 n= 0 D U whr ρ 1 is h wigh of h laggd argd main policy ra, bing h masur of cnral ban s aggrssivnss in h sabilisaion of inflaion and oupu gap, ρ is h wigh of alrnaiv cnral ban s args, D 1, D,, D m ar h vcors of paramrs, U 1,-n, U,-n,, U m,-n ar h acual and laggd valus of variabls considrd by h cnral ban for sing h main inrs ra. Variabiliy of Main Policy Ra Undr a Zro Lowr Bound I is normally assumd ha opimal main policy ra is posiiv and ponionally high volail inrs ra ha sabilizs inflaion and oupu gap o (nar) zro lvls considring a modl framwor of an conomy and rflcing xognous and ndognous shocs simulaing h dynamics of h whol conomic sysm. In cas of xpcd dp dflaion, conomic rcssion and financial insabiliy i sms o b opimal o s h main policy ra o dp ngaiv lvl and o say blow zro for a long priod o nabl h ral and financial scor o rcovr. Whn opimal main policy ra gos o ngaiv, inflaion arging policy facs up is limiaion as argd main policy ra is rarly usd o cross is zro lowr bound (Brnan 000). A s of alrnaiv monary policis (ourigh purchass of asss, hom currncy dprciaion, mony-financd aggrga dmand xpansion) ar ypically suggsd o ovrcom a rsriciv characr of nar zro lvl argd main policy ras. Using hs alrnaiv monary policy masurs, argd main policy ra is manim fixd o (nar) zro lvl for a long im which rducs is variabiliy and rspciv covariancs o zro in h sam priod as wll. This fac dals wih an implici chang in monary policy mchanism of inflaion arging wihin which unconvnional monary policy insrumns a ovr a posiion of main policy ra in h racion funcion. Thrfor, variabiliy of argd main policy ra is considrd as posiiv if and only if cnral ban blivs ha racion funcion could b ffcivly applid o rach monary policy args in h cnral ban s loss funcion. For h cas of high rsriciv impac of (nar) zro argd main policy ra whn OPTIM IR < 0, i holds good: CB, 5 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

5 var IR CB, = (1 ) var IR + (1 ) cov( IR + cov( IR CB, 1 OPTIM CB, + OPTIM CB,, w ) = 0 1 var IR, IR CB, 1 CB, 1 ) + (1 ) cov( IR 1 + var w + OPTIM CB,, w ) + (6) Zro variabiliy of argd main policy ra rflcs h cas whn corrlad shocs ha sm from alrnaiv monary policy masurs offs opimal main policy ra (high ngaiv covarianc bwn hs variabls is mainaind) and wigh ρ is opimizd according i: var w OPTIM OPTIM 1 ) var IR CB, + (1 1 ) cov( IR CB,, w ) (1 = (7) Alhough argd main policy ra rmains a a zro lvl which is ypically mainaind by ovrall xcss of baning sysm liquidiy providd by cnral ban hrough alrnaiv monary policy insrumns, h dynamics of conomic fundamnals bhind mony mar inrs ras could b a sourc of hir significan nominal and ral variabiliy. Alhough h variabiliy of argd main policy ra is a a zro lvl, h variabiliy of conomic fundamnals is sill rflcd in h variabiliy of opimal main policy ra, which using Goodman s bradown of h produc of random variabls (Goodman 1960) could b wrin in h following form: var IR OPTIM CB, = var( + cov + var( y + ( y ( + y + y ) cov + ) + ( y y 1 + var ) + ( + + y + ) cov ) var + ( y ) var + ( + var ( + ) cov ( y y ) + cov ( ), ( y y ) y ) + y cov ) cov y (8) whr and/or is h man valu of paramr β and/or γ, h rm ( + + ) and/or ( y + y + ) is h man valu of h dviaion of xpcd inflaion from h inflaion arg and/or xpcd oupu gap, cov ij is i + cov ( ), ( ( + )), j y ij i j cov is cov ( ), ( (y y )) + +, h symbol Δ xprsss h dviaion of h rspciv variabl from is man valu (.g. = ). Thr ar a fw main lmns of variabiliy of opimal main policy ra undr a zro lowr bound. Firs, i rflcs insabiliy of xpcd inflaion and oupu gap, which rprsn h applicaion of acual prdicion of inflaion facors in h form of inflaion forcas o h modl of an conomic srucur. Espcially long-lasing dflaion prssur and/or conomic rcssion oghr wih dp dlvraging of financial Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6 53

6 scor producs inflaion and conomic aciviy forcas blow inflaion arg and ponial oupu and rquirs a downward rnd of h cnral ban s opimal main policy ra. Scond, ralizd conomic and financial shoc ypically mas srucural characrisics of conomy and consqunly h cnral ban s prfrncs o h inflaion and/or conomic cycl unsabl which is rflcd in h variabiliy of paramrs and. In cas of sabiliy of srucural characrisics, larg and rlaivly closd conomis supposd o hav low inrs ra lasiciy of inflaion and conomic growh du o h limid innsiy of ransmission bwn xrnal quilibrium and inrnal quilibrium ha produc high variabiliy of h main policy ra for h achivmn of monary objcivs. In small opn conomis, on can xpc highr sabiliy of h main policy ra as a rsul of ngaiv corrlaion of h ral monary rsricion and xchang ra and is dirc and quic impac on fficin ransmission of monary masurs. This is also on of h main rasons why larg and rlaivly closd conomis follow (undr a zro lowr bound) alrnaiv monary masurs basd on quaniaiv asing whil small opn conomis prfr a policy of hom currncy dprciaion. Consqunly, undr a zro lowr bound, dclining snsiiviy of h argd conomic fundamnals o convnional inrs ra policy (and prdicabiliy of is ransmission) oghr wih a swich of cnral bans prfrncs o conomic growh and financial sabiliy args (cnral ban s policy dynamic inconsisncy) could b xpcd, which gnras a sris of corrlad shocs w arising from applicaion of alrnaiv monary masurs and mas paramrs and mor volail. Covarianc cov and cov also shows ha h variabiliy of paramrs β βπ ij γy ij and γ and hrfor h insabiliy of h cnral ban s opimum main policy ra is influncd by h pro-cyclic characr of monary rsricion innsiy ( cov and cov > 0). y ij Third, variabiliy of h opimal main policy ra undr a zro lowr bound rflcs ponial asynchronizaion of h inflaion cycl, conomic cycl and ra of monary rsricion which sms from nominal and/or ral dmand and supply sid shocs o ral conomy undr financial crisis and pos-crisis priod (s sign and xn of cov ( + + ), (y + y+ ) ). Conrary o pur dmand facors of inflaion cycl producing h posiiv covarianc of conomic cycl and ra of monary policy rsricion, h unsabl mix of dmand and supply sourcs of inflaion wih much lowr covarianc of inflaion and conomic cycl and ra of monary rsricion ar xpcd o bcom dominan. On h ohr hand, in ransiion conomis suddn dprciaion of hom currncy following ouflow of forign capial undr a financial crisis can ponially incras h inflaionary prssur in cas of dp conomic downurn ha would rquir highr main policy ra racion comparing wih ohr supply sid shocs. Variabiliy of Main Policy Ra Undr a Zro Lowr Bound Undr a zro lowr bound, h variabiliy of n-monh mony mar inrs ra is limid by ngaiv covarianc bwn xpcd opimal main policy ra and h sris of shocs producd by alrnaiv monary policy masurs. Thrfor, h βπ ij 54 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

7 variabiliy of mony mar inrs ras rflcs spcially h variabiliy of ris and rm prmium whil monary impulss ar mporally wa unil h xi sragy is bing applid: var IR n = 1 n [ n=1 (1 ρ 1 ρ ) OPTIM, var IR CB,+j + (1 ρ 1 ρ )ρ cov( IR CB,+j + ρ varφ n + n=1 n=1 + ρ var w +j OPTIM, + n cov {[(1 ρ OPTIM, 1 ρ ) IR CB,+j n=1 + ρ 1 IR, CB,+j 1 + n=1 n=1 + ρ w +j n=1, w +j ], φ n } ) + ] (9) n 1 OPTIM, var IR CB,+j = n 1,+j = var β +j (π ++j n 1,+j + var γ +j (y ++j n 1,+j + cov( β +j (π ++j n 1 π ++j ) y ++j ) π,+j ++j ), γ +j (y ++j ) y ++j ) (10) As for a long-nd of mony mar yild curv h xpcd dynamics of inflaion and conomic growh rachs h horizon of fficin ransmission of monary policy, variabiliy of mony mar inrs ras may rflc h anicipad macroconomic ffcs of monary policy, which mas i possibl o achiv whn a zro lowr bound will nd soon and xi sragy is plannd or a las xpcd by mar - high variabiliy of longr inrs ras in h siuaion of mporarily low variabiliy of shor-rm inrs ras. Thrfor, sabl xpcaions of agns ar crucial for low variabiliy of long-rm mony mar inrs ras in a priod wihin which fuur variabiliy of opimal main policy ra will b offs by alrnaiv policy masurs which sm from xpcd rcovry of conomic fundamns, changs in h cnral Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6 55

8 ban s prfrncs bac o inflaion arg and insabiliy of h conomic srucur. Variabiliy of mony mar inrs ras is hn a rsul of a conflic bwn h cnral ban s official inflaion forcas and analogical forcas of h financial mar ha could b significanly influncd by cnral ban s crdibiliy in a pos crisis priod and consisncy of prcding monary masurs. Bcaus h variabiliy of inrs ras in quaions (9) and (10) is influncd by variabiliy of h avrag xpcd valus of h paricular facors ovr h obsrvd priod, h shocs affcing variabiliy of inrs ras ar assumd o b of a long-rm characr. 3. Th Analysis of Endognous and Exognous Shocs and Variabiliy of Mony Mar Inrs Ra Modl of Hisorical Dcomposiion wih Exognous Variabls As sad bfor, h variabiliy of mony mar inrs ra is causd by shocs in ndognous and xognous variabls includd in h modl. To masur hir impac, w us h hisorical dcomposiion chniqu for a VAR modl wih xognous variabls in h following srucural form: p DY = c + A i Y i + BX + U, (11) i=1 whr Y is a vcor of ndognous variabls, X is a vcor of xognous variabl, U is a vcor of srucural shocs, C is vcor of consans, D, A i and B ar marics of cofficins, and p is h lngh of lags of a VAR modl. By muliplying wih marix D 1, quaion (11) can b ransformd ino h following rducd form: p Y = + P i Y i + QX + E, (1) i=1 whr = D 1 c, P i = D 1 A i, Q = D 1 B, and E = D 1 U is h rducd form rrors. Having all cofficins marics and marix D, w can dcompos ach ndognous sris ino sris of individual srucural shocs using hisorical dcomposiion chniqu. Th principl of his chniqu coms from h fac ha h rducd form of a VAR modl in (1) can b xprssd by is corrsponding moving avrag rprsnaion wih rcursiv subsiuions as follows (for p = in our cas): Y = μ + Φ i E i + Ψ i X i, (13) i=1 whr Y 1 = K 1 + P 1 Y 0 + P Y 1 + QX 1 + E 1. As E = D 1 U, quaion (13) can b rwrin as: i=1 For ohr rms Φ i is a funcion of P 1 and P, Ψ i is a funcion of P 1, P and Q. 56 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

9 Y = μ + Φ i D 1 U i + Ψ i Z i = μ + Γ i U i + Ψ i Z i, (14) i=1 i=1 whr Γ i = Φ i D 1. Clarly in quaion (14) ach ndognous variabl in h modl is xprssd as a sum of srucural shocs up o im. Collcing h conribuion of ach shoc sparaly, w obain h dcomposiion of a sris in ach priod from h bginning o h nd. Daa and Thir Pr-Procssing This rsarch is prformd using h publicly availabl daa for h Czch Rpublic. Th main sourcs of daa ar h daabass of h Czch Saisical Offic and h Czch Naional Ban. Th ral GDP sris of Grmany is providd by Dsais daabas, h hisorical sris on oil pric (Europ Brn Spo Pric FOB) by US Enrgy Informaion Adminisraion daabas and h sris on EURIBOR 1 monhs by Europan Mony Mars Insiu, and finally sris on CPI in Euro Ara 19 and uni labor coss sris for Czch Rpublic ar from h OECD daabas. All sris ar quarrly daa from 000Q1 o 016Q4. Each of hm consiss of 68 obsrvaions. All sris ar lisd in Tabl 1. Tabl 1 Lis of Primary Daa Usd for Economric Analysis Noaion Full nam Uni 1 REPO Monary policy Rpo ra % YD Disposabl incom Mil. CZK 3 CPI Consumr Pric Indx Indx 4 CONS Housholds consumpion Mil CZK 5 INV Invsmns Mil. CZK 6 UNE Unmploymn ra % 7 NX N xpor Mil. CZK 8 CRE Clin loans Mil. CZK 9 PRIBOR Inrban pribor on yar ra % 10 EURER Avrag EURCZK xchang ra CZK 11 ULC Uni labor coss,yar-o-yar chang % 1 PROGINF Inflaion Prognoss % 13 GDPGE Grman GDP indx 14 EURIBOR Inrban uribor on yar ra % 15 OILP Avrag oil pric Crud Brn Europ USD 16 USDER Avrag USDCZK xchang ra CZK 17 CPIEA19 Consumr Pric Indx in Euro Ara 19 indx Nos: () dnos ral variabls. i=1 i=1 For modl simaion sris rpo ra REPO, unmploymn ra UNE, uni labor coss ULC, and inrban inrs ras PRIBOR and EURIBOR ar p unchangd. On h ohr hand, h oil pric sris in USD is convrd ino sris in CZK using xchang ra USD/CZK, nominal clin loans and xchang ra EUR/CZK ar ransformd ino ral quaniis using pric indx CPI and pric indics CPI and CPIEA19 rspcivly. Afr ha hs sris and h rs ar convrd ino corrsponding yar-o-yar prcnag changs sris. All sris hus hav h sam masur and h numbr of obsrvaion is rducd o 64. In Tabl w show som dscripiv saisics of h original daa s w us for our analysis. Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6 57

10 Afr ha sris on Disposabl incom, CPI, Consumpion, Invsmn, N Expor, EURCZK xchang ra, Oil pric, Grman GDP, ar convrd o yar on yar chang sris (in pr cns). Wih rspc o sris on clin loans volum, firs w convr i ino a sris of ral valus and hn w ransform i ino a sris of yar on yar chang ras. Th numbr of obsrvaions of our daas is hn rducd o 6. Th lngh of unransformd sris is adjusd accordingly. Th dscripiv saisics of ransformd sris ar shown in Tabl 3. In our analysis h ndognous variabls ar hos variabls from h Czch conomy (hy ar n) and h xognous variabls ar h GDP of Grmany, Oil pric, Inflaion prognosis, Uni labor coss and Euribor ra. Tabl Dscripiv Saisics of Original Daa Usd for Analysis Man Mdian Maximum Minimum Sd. Dv. Swnss Kurosis Man Mdian Maximum Minimum Sd. Dv. Swnss Kurosis CONS 447, ,540 50,90 344,55 46, CPI CRE 707, , ,663 45, , EURER EURIBOR GDPGE INV 49,114 49,076 33, ,900 35, UNE NX 4,39,88 91, , OILP ULC PROGINF PRIBOR1Y REPO Tabl 3 Dscripiv Saisics of Transformd Daa Usd for Analysis Man Mdian Maximum Minimum Sd. Dv. Swnss Kurosis CONS CRE EURER GDPGE INV NX OIL PI YD Empirical Economric Analysis W choos h Baysian mhod o sima h modl paramrs (s Lupohl (005) and Canova (007) for mor informaion on his mhod). This mhod allows us o ignor h possibl issu wih saionariy in sris includd in our modl. 58 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

11 Wih rspc o h numbr of obsrvaions in our daas as wll as h rsul of informaion criria, h lngh of lags of our VAR modl p =. Whn simaing paramrs of our modl by Baysian mhod, w us h so calld Mnssoa prior (s Lupohl (005) for priors). In ordr o rcovr h srucural form in (11) from h rducd from (1), w nd o idnify marix D from covarianc marix Σ E = E E. For his purpos, w us h sign rsricion approach which has bn usd in svral sudis in h pas (Faus (1998), Canova and D Nicolo (00), Uhlig (005)). Our focus is placd on h rspons of h ohr ndognous variabls o a shoc in rpo ra and ra PRIBOR and h xpcd signs of h rsponss o a posiiv chang of an ndognous variabl ar summarizd in Tabl 4. All ncssary calculaions hav bn don in Malab wih our own programming. Tabl 4 Th Supposd Sign of Rsponss wih Rspc o a Posiiv Chang of a Variabl REPO YD PI CONS UNE INV NX CRE PRIB1Y REPO PRIB1Y EU- RER In Figurs 1 and w compar h simad rpo ra and on yar pribor ra wih hir acual counrpars. In boh cass, hr is a high closnss bwn hm indicaing ha our modl is corrcly spcifid. Figur 1 confirms ha sinc h nd of 01 rpo ra and consqunly also 1Y pribor ra droppd o nar zro lvl which is mainaind by h nd of 016 wih a zro volailiy of boh ras. Du o long-lasing undrshooing of inflaion arg, CNB dcidd o apply a sragy of hom currncy dprciaion and s a floor a a war lvl of EUR/CZK xchang ra o boos h whol conomy and ovrcom dflaionary xpcaions. Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6 59

12 Figur 1 Th Modld Rpo Ra Compard o h Acual Rpo Ra (in %) Figur Th Modld 1y Pribor Ra Compard o h Acual 1y Pribor Ra (in %) W disassmbl wo sris: rpo ra and 1 monhs pribor ra (Figurs 3 and 4) as a cumulaiv sum of individual srucural shocs. Th siz of ach shoc in ach quarr is xprssd by a bar of a crain color whos magniud is scald according o h lf-hand-sid y-axis. On can obsrv ha h magniud as wll as h sign of ach shoc may chang from a quarr o a quarr and in ach quarr h shocs diffr in hir signs, hnc h aggrga impac of all shocs nds o b much lowr. W display h aggrga rsuls for a quarr in h sam figurs as a blac lin wih h magniud corrsponding o h scal on h righ-hand-sid y-axis. As a h bginning h impac of Y 0 and Y 1 is sill vry srong and i dis ou afr a dozn of priods, w show hm for priods from 004Q1 o h nd. W procd similarly whn w calcula h impac of ach individual shocs on rpo ra and 1y pribor ra in h acual priods (Figurs 5 and 6). Finally, w valua h impac of xognous variabls on rpo ra and 1y pribor ra (Figur 7 and 8). 530 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

13 Figur 3 Th Cumulaiv Effc of Shocs on Rpo Ra Figur 4 Th Cumulaiv Effc of Shocs on 1y Pribor Ra Figur 5 Th Effc of Shocs on Currn Priod Rpo Ra Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no

14 Figur 6 Th Effc of Shocs on Currn Priod 1y Pribor Ra As far as h impac of ndognous variabls includd in h modl is concrnd, in Figurs 3 and 4 w can s wo groups of facors which affc h mony mar inrs ra in boh dircions. Th srucur of ach group is no consan ovr im and so dos h impac of ach ndognous variabl in h modl. On h ohr hand, long-lasing characr of conribuion of spcific variabl o rpo ra and mony mar inrs ra dynamics confirms sris corrlaion of hs shocs ha is in lin wih our xplanaion of dynamics of inrs ras as a rnd drivn macroconomic variabls. Th srucur and h xn of h shocs also slighly diffrs for boh h rpo ra and 1y pribor ra which is mor volail bu in gnral boh ras could b xplaind via h sam sory. Th posiiv impac of ndognous variabls on rpo ra and mony mar ras ar shown in cas of h dynamics of ban loans, consumpion and unmploymn bfor firs ngaiv ffcs of criss cam in 008 and 009. Ngaiv shocs in pr-crisis priod ar rprsnd by h invsmns, n xpor and disposabl incom. Th global financial crisis producd high xrnal shoc, dp dclin in inflaion wih limid dflaion xpcaions and pssimisic invsmns xpcaions ha say bhind ngaiv impac of invsmns, ban loans, and inflaion on mony mar inrs ras. Sinc 011 invsmns and baning loans sar o rcovr bu unmploymn and consumpion rmain wa. Th applicaion of xchang ra commimn in 013 iniiad posiiv impac of ral xchang ra, unmploymn and consumpion (mainaining posiiv ffcs of n xpor). 53 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

15 Figur 7 Th Impac of Exognous Variabls on Rpo Ra Figur 8 Th Impac of Exognous Variabls on 1y Pribor Ra Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no

16 Figur 5 and 6 shows individual shocs and hir conribuion o on priod dynamics of h rpo ra and 1y pribor ra. Th rsuls confirm lowr magniud of h shocs in cas 1y pribor ra comparing wih h rpo ra and much volail quarr by quarr adapaions of boh ras. Cnral bans long-rm horizon forcasing ypically smoohs hs shor-rm flucuaions o ovrcom h uncrainy abou rnd rvrsals which sabilizs h rpo ra and consqunly h 1y pribor ra bu also rducs h abiliy of CNB o adap is policy if suddn chang is ndd. Too long cumulaion of h shocs is hn followd by laggd bu quaniaivly fas racion of main policy ra which mas 1y pribor ra changs lss prdicabl. In Figur 7 and 8 w can obsrv a posiiv, bu dclining impac of xognous variabls on h rpo ra and h mony mar inrs ra xcp h priod I rflcs a pr-crisis boom in forign dmand for h gross xpor oghr wih high growh of oil pric followd by hir dclining rnd afr 008. In h las svral yars hir influnc is almos ngligibl du o ovrall sabilizaion of hs facors. As h rpo ra and h mony mar inrs ras rachd hir (nar) zro lvls wih (nar) zro volailiy and hrfor sragy of hom currncy dprciaion was adopd, h ffcs of xognous variabls mus b absorbd in ndognous ons which could b a sourc of nw shocs whn conomic rcovry will com and xi sragy will follow hn. 4. Conclusion Bfor h xi from unconvnional monary policy sragis, main policy ra as wll as mony mar inrs ras variabiliy could b found in h proximiy of h zro lowr bound. I raiss a poin on h ponial facors which p hm ha low as wll as wha may influnc hir apparn involailiy. Whil mony mar inrs ras ar clos o a nar zro lvl, h opimal main policy ras may xhibi significan volailiy as h conomy facs dp conomic and/or financial shocs and uncrainis of various inds. Thrfor, w prsnd h modl whr main aspcs of nar zro variabiliy oghr wih inhrn high variabiliy of main policy ra could b xplaind applying a sris of shocs ha com from alrnaiv monary policy masurs. Th anion is paid on variabiliy of modl opimal main policy ra du o shocs in h srucural characrisics of conomy, cnral ban s prcpion of inflaion riss, is wand crdibiliy and uncrainy abou h fficin ransmission of alrnaiv monary masurs. Variabiliy of mony mar inrs ras is drivn by monary forcs spcially whn h xi from zro lowr bound sragy is xpcd by mar. Th mony mar inrs ras in h Czch conomy ar modld in h framwor of VAR modl wih xognous variabls. Th modl is simad by Baysian mhod and is srucural form is obaind hrough sign rsricion. Th modl s paramrs ar hn usd o dcompos mony mar inrs ra sris ino a sris of cumulaiv srucural shocs of ach ndognous componn in h modl. Th rsuls show ha global financial crisis and h xchang ra commimn ar wo main sourcs of ndognous variabls shocs on mony mar inrs ras. Ths ndognous variabls shocs confirm high imporanc of baning loans, unmploymn, consumpion and invsmn as xrmly snsiiv conomic variabls for h dynamics of an opn conomy as wll as raching h inflaion arg. Exognous sourcs of 534 Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no. 6

17 inrs ra dynamics sply dclind afr h impac of a pr-crisis boom in forign dmand for h gross xpor oghr wih high growh of oil pric diminishd and xchang ra inrvnions wr bing applid by cnral ban o boos h whol conomy and ovrcom dflaionary xpcaions. Policy implicaions ha sm from h rsarch ar hs ons. Th firs, o undrsand corrcly h problm of variabiliy of main policy ra and mony mar inrs ras h variabls chosn for h simaion of h modl should b dircly lind o h characr of h conomy ha nabl o corrcly rflc ndognous and xognous shocs ha h conomy facs up. In cas of small opn conomy, i assums o mploy boh h dynamics of forign dmand and rlaiv pric compiivnss of h conomy ha is ssnial for h dynamics of all ohr variabls wihin h modl and consqunly main policy ra and mony mar inrs ras. Th scond, high volailiy of quarr by quarr shocs of individual variabl confirmd an imporanc of a rflcion of conomy s sory which suppor smoohing in sing h main policy ra and sabiliz variabiliy of mony mar inrs ras whn h cnral ban s policy is crdibl. Th hird, whn zro lowr bound is m, in ordr o consisnly follow h concp of inflaion arging i rquirs o adop som unconvnional monary policy sragy o offs a cumulaion of ngaiv shocs for h main policy ra and o simula conomic aciviy. Las bu no las xpcd xi from unconvnional policy rgim sms o b h main sourc of ponially highr mony mar inrs ras variabiliy whn ping h main policy ra unchangd bfor xi s ral applicaion. Financ a úvěr-czch Journal of Economics and Financ, 68, 018, no

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