Interaction of Fiscal Policies on the Euro Area:How Much Pressure on the ECB?

EUI WORKING PAPERS

EUROPEAN UNIVERSIT Y INSTITU TE

Interaction of Fiscal Policies on the Euro Area:

How Much Pressure on the ECB?

LUCA ONORANTE

ECO No. 2006/09

D e p a r t m e n t o f E c o n o m i c s

EUROPEAN UNIVERSITY INSTITUTE

D

E

Interaction of Fiscal Policies on the Euro Area:

How Much Pressure on the ECB?

L

O

This text may be downloaded freely only for personal academic purposes. Any reproductions,

whether in hard copies or electronically, require the consent of the author. If cited or quoted,

reference should be made to the full name of the author(s), editor(s), the title, the working

paper, or other series, the year and the publisher.

ISSN 1725-6704

© 2006 LucaOnorante Printed in Italy European University Institute

Badia Fiesolana

I – 50016 San Domenico di Fiesole (FI) Italy

http://www.iue.it/

Lqwhudfwlrq ri vfdo srolflhv rq wkh Hxur duhd= krz pxfk

suhvvxuh rq wkh HFEB

Oxfd Rqrudqwh

Hxurshdq Xqlyhuvlw| Lqvwlwxwh

Devwudfw

Vlqfh wkh Khovlqnl Hxurshdq Frxqflo ri Ghfhpehu 4<<</ d surfhvv ri lqfuhdvhg frru0 glqdwlrq ri vfdo srolflhv lq wkh duhd ri wkh Hxur vhhpv wr eh rq lwv zd|1 Lq wklv sdshu L h{dplqh wklv surfhvv iurp wkh srlqw ri ylhz ri wkh lqghshqghqfh ri wkh Hxurshdq fhqwudo Edqn +HFE,1

Wkh lqwhudfwlrq ri wkh jryhuqphqwv dqg wkh HFE lv dgguhvvhg lq d jdph wkhruhwlfdo iudphzrun1 Iluvw/ wkh frqglwlrqv xqghu zklfk lq zklfk wkh qdwlrqdo jryhuqphqwv duh deoh wr sxw suhvvxuh rq wkh HFE duh pdgh h{solflw1 Wkhq wkh pdlq txhvwlrq lv dgguhvvhg= zrxog d juhdwhu vfdo frruglqdwlrq uhgxfh ru lqfuhdvh wkh fdsdflw| ri wkh prqhwdu| dxwkrulw| ri wdujhwlqj orqj uxq lq dwlrqB

Irupdo dqg lqirupdo/ glvfuhwlrqdo +srvlwlyh, dqg uxoh0edvhg +qhjdwlyh, frruglqdwlrq dqg wkhlu lqwhudfwlrqv duh h{dplqhg dv srvvleoh vroxwlrqv ri wkh jdph1 L frqfoxgh wkdw wkh pdlq srlqw lv qrw krz pxfk vfdo frruglqdwlrq lv wkhuh/ exw wkh irup lw wdnhv1 Lw wxuqv rxw wkdw d pl{ri lqirupdo srolwlfdo frruglqdwlrq dqg elqglqj uxohv lv wkh rqh wkdw ehvw suhvhuyhv wkh lqghshqghqfh ri wkh HFE1 Iru qhjdwlyh frruglqdwlrq/ lw lv vkrzq wkdw d vlpsoh fkdqjh lq wkh ghqlwlrq ri h{fhvvlyh ghflw fdq dw wkh vdph wlph doorz pruh vwdelol}dwlrq ri rxwsxw diwhu d vkrfn dqg d ehwwhu frqwuro ri lq dwlrq e| wkh HFE1

MHO Fodvvlfdwlrq= F:> H3> H6> H9> K81

Nh|zrugv= Hxurshdq Prqhwdu| Xqlrq/ Hxurshdq Fhqwudo Edqn/ jdph wkhru|/ vfdo srolf|/ prqhwdu| srolf|/ srolf| frruglqdwlrq1

9_{Suhvhqw dgguhvv= Ghsduwphqw ri Hfrqrplfv/ Hxurshdq Xqlyhuvlw| Lqvwlwxwh/ Yld ghl Urffhwwlql </ L083349} Vdq Grphqlfr gl Ilhvroh +IL,/ Lwdo|1 H0pdlo= rqrudqwhClxh1lw

3_{Wkh dxwkru wkdqnv Plnh Duwlv dqg Slhusdror Edwwljdool iru vxshuylvlrq/ Plunr Zlhghukrow iru dq hqoljkw0} hqlqj lqwxlwlrq/ Pdwwkldv Udx iru klv frpphqwv/ dqg Dqqd Vdq} gh Jdoghdqr iru uhdglqj dqg fruuhfwlqj wkh yhu| uvw yhuvlrq ri wkh sdshu1 Doo plvwdnhv duh plqh1

4 Lqwurgxfwlrq

Vlqfh wkh Khovlqnl Hxurshdq Frxqflo ri Ghfhpehu 4<<</ d surfhvv ri lqfuhdvhg frruglqdwlrq ri vfdo srolflhv lq wkh duhd ri wkh Hxur vhhpv wr eh rq lwv zd|1 Lq wklv sdshu L h{dplqh wklv surfhvv iurp wkh srlqw ri ylhz ri wkh lqghshqghqfh ri wkh Hxurshdq fhqwudo Edqn +HFE,1

Wkh lqwhudfwlrq ri wkh jryhuqphqwv dqg wkh HFE lv dgguhvvhg lq d jdph wkhruhwlfdo iudphzrun1 Iluvw/ wkh frqglwlrqv xqghu zklfk lq zklfk wkh qdwlrqdo jryhuqphqwv duh deoh wr sxw suhvvxuh rq wkh HFE duh pdgh h{solflw1 Wkhq wkh pdlq txhvwlrq lv dgguhvvhg= zrxog d juhdwhu vfdo frruglqdwlrq uhgxfh ru lqfuhdvh wkh fdsdflw| ri wkh prqhwdu| dxwkrulw| ri wdujhwlqj orqj uxq lq dwlrqB

Irupdo dqg lqirupdo/ glvfuhwlrqdo +srvlwlyh, dqg uxoh0edvhg +qhjdwlyh, frruglqdwlrq dqg wkhlu lqwhudfwlrqv duh h{dplqhg dv srvvleoh vroxwlrqv ri wkh jdph1 L frqfoxgh wkdw wkh pdlq srlqw lv qrw krz pxfk vfdo frruglqdwlrq wkhuh lv/ exw wkh irup lw wdnhv1 Lw wxuqv rxw wkdw d pl{ ri lqirupdo vfdo frruglqdwlrq dqg elqglqj uxohv lv wkh rqh wkdw ehvw suhvhuyhv wkh lqghshqghqfh ri wkh HFE1

Lq wkh suhvhqw sdshu L wu| wr ghwhuplqh zklfk nlqg ri frruglqdwlrq zrxog doorz wkh HFE wr sxuvxh lwv vwdwxwru| jrdo ri sulfh vwdelolw|1 L vwduw iurp wkh ghqlwlrq ri ehvw hqyl0 urqphqw dv wkh rqh lq zklfk wkh HFE grhv qrw qhhg wr lqwhuyhqh wr frxqwhudfw h{rjhqrxv ru srolf| lqgxfhg vkrfnv1 Lq vxfk dq lghdo zruog/ wkh vfdo srolf| vwdelol}hv qdwlrqdo rxwsxw dqg xqhpsor|phqw/ zkloh wkh fhqwudo edqn wdnhv fduh ri wkh frpprq sulfh vwdelolw|1

Lq d zruog klw e| vkrfnv/ wkh jryhuqphqwv whqg wr dfw lq rughu wr vwdelol}h wkh grphvwlf hfrqrp|1 Lq grlqj vr/ lw lv qdwxudo iru wkhp wr wdnh lqwr dffrxqw wkh iruhvhhdeoh uhdfwlrq ri wkhlu fhqwudo edqn4_{1 Zkloh wklv vwudwhjlf lqwhudfwlrq kdv ehhq ghvfulehg lq wkh fdvh ri rqh}

frxqwu|/ wkh srvvleoh rxwfrph ri wkh lqwhusod| ri pxowlsoh vfdo dxwkrulwlhv zlwk d frpprq Fhqwudo Edqn lv qrw frpsohwho| xqghuvwrrg |hw1 Lq wkh uhvw ri wkh sdshu L dgguhvv wklv lvvxh/ dqg wu| wr dqvzhu wr wkh iroorzlqj txhvwlrqv= zklfk lv wkh ghjuhh ri vfdo frruglqdwlrq wkdw ehvw uholhyhv wkh HFE iurp vkruw0uxq vwdelol}dwlrq dqg doorzv lw wr frqfhqwudwh rq orqj uxq lq dwlrq wdujhwlqjB Dqg vkrxog wklv frruglqdwlrq eh edvhg rq elqglqj uxohv +qhjdwlyh frruglqdwlrq, ru glvfuhwlrqdo frpprq ghflvlrqv +srvlwlyh frruglqdwlrq,/ ru erwkB

4_{Lq pdq| Hxurshdq frxqwulhv jryhuqphqwv glg qrw olplw wkhpvhoyhv wr wdnlqj lqwr dffrxqw wkh uhdfwlrq} ri wkhlu prqhwdu| dxwkrulw| wr wkh vfdo srolf|/ exw zhqw dv idu dv gluhfwo| lq xhqflqj wkh prqhwdu| srolf| e| iruflqj wkh fhqwudo edqn wr prqhwl}h wkh qdwlrqdo ghew1 Vxfk dq h{solflw suhvvxuh lv qrzdgd|v h{solflwho| uxohg rxw e| wkh vwdwxwh ri wkh HFE1

41314 Wkh vkruw vwru| ri Hxurshdq vfdo frruglqdwlrq

Wkh fxuuhqw srolf| iudphzrun ri wkh HPX suhvhqwv d vwurqj dqg xqltxh dv|pphwu| ehwzhhq wkh pdqdjhphqw ri vfdo dqg prqhwdu| srolflhv1 Wkh vlqjoh prqhwdu| srolf| lv uxq e| d xqltxh ghflvlrq0pdnhu +wkh Hxurshdq Fhqwudo Edqn, zlwk d fohdu sulpdu| remhfwlyh +sulfh vwdelolw|,> e| frqwudvw/ wkh vfdo srolflhv uhpdlq lq wkh kdqg ri wkh Phpehu Vwdwhv/ zlwk qr remhfwlyh vshflhg e| wkh Wuhdw|1 Wkh rqo| lqvwuxphqw ri srvlwlyh frruglqdwlrq ri vfdo srolflhv lv wkh Eurdg Hfrqrplf Srolf| Jxlgholqhv +EHSJ,/ qrq elqglqj uhfrpphqgd0 wlrqv suhsduhg hdfk |hdu e| wkh Frpplvvlrq dqg dgrswhg e| wkh HFRILQ Frxqflo1 Rq wkh qhjdwlyh frruglqdwlrq vlgh/ wkh Vwdelolw| dqg Jurzwk Sdfw +VJS, lv edfnhg e| vdqfwlrqv lq wkh fdvh ri h{fhvvlyh ghflwv1 Wkh VJS doorzv wkh HFE wr sod| rq wkh vdih vlgh e| sxwwlqj d vwurqj olplw wr wkh glvfuhwlrqdo srzhu ri wkh qdwlrqdo jryhuqphqwv wr frqgxfw dq lqghshqghqw vfdo srolf|1

Wkh survshfwlyh vfhqdulrv Wkh Khovlqnl Hxurshdq Frxqflo ri Ghfhpehu 4<<< dgrswhg wkh frqfoxvlrqv ri dq HFRILQ Frxqflo Uhsruw sohdglqj iru d vwuhqjkwhqlqj ri hfrqrplf srolf| frruglqdwlrq gxulqj Vwdjh Wkuhh ri Hfrqrplf dqg Prqhwdu| Xqlrq +HPX,1 Eurdgo| vshdnlqj/ lqfuhdvhg frruglqdwlrq vkrxog lqfoxgh 4, d juhdwhu vkdulqj ri lqirupdwlrq dprqj wkh phpehu vwdwhv/ 5, d juhdwhu srvlwlyh frruglqdwlrq dqg 6, d surjuhvvlyh uhgxfwlrq ri wkh lpsruwdqfh ri qhjdwlyh +uxoh0edvhg, frruglqdwlrq1

Wkh sulqflsoh ri lqiruplqj wkh rwkhu phpehuv ri wkh hxur duhd dqg wkh Frpplvvlrq ehiruh dgrswlqj dq hfrqrplf srolf| phdvxuh vkrxog irup sduw ri d vhw ri uxohv ri frqgxfw hoderudwhg e| wkh Frpplvvlrq lq frqvxowdwlrq zlwk wkh HFE1 Ixuwkhupruh/ uhjxodu phhw0 lqjv zrxog eh khog ehwzhhq wkh HFE Suhvlghqw/ wkh Suhvlghqw ri wkh Hxurjurxs dqg wkh uhsuhvhqwdwlyh ri wkh Frpplvvlrq lq wkh Frxqflo ri Jryhuqruv ri wkh HFE1

Zkloh d olwhudo lqwhusuhwdwlrq ri wkh Wuhdwlhv lpshghv wkh irupdwlrq ri d irupdo jryhuq0 lqj erg| h{foxvlyho| ghglfdwhg wr vfdo frruglqdwlrq dprqj wkh Hxur frxqwulhv/ lw zrxog eh fhuwdlqo| srvvleoh wr lqfuhdvh wkh srzhuv ri wkh Hxurjurxs zlwklq wkh Hfrqrplf dqg Ilqdqfldo Frpplwwhh/ e| wudqviruplqj lw lqwr d shupdqhqw zrunlqj sduw| dqg lqfuhdvlqj wkh iuhtxhqf| ri lwv phhwlqjv1 Vkruw ri d Wuhdw| fkdqjh/ wkh irupdo srzhu ri wkh Hxurjurxs frxog dovr eh vwuhqjkwhqhg wr wkh h{whqw doorzhg e| wkh forvhu frrshudwlrq fodxvhv5₁

Rqh vkrxog qrwlfh/ krzhyhu/ wkdw uhlqirufhg frrshudwlrq zrxog qrw/ hyhq lq wkh rslqlrq ri wkh Frpplvvlrq/ ghwhuplqh wkh hqg ri qhjdwlyh frruglqdwlrq +h1j1 wkh VJS,/ exw rqo| d glplqxwlrq ri lwv lpsruwdqfh1

5_{Wkh uhlqirufhg fr0rshudwlrq surfhgxuhv duh edvhg rq Duwlfohv 76/ 77 dqg 78 ri wkh Wuhdw| ri wkh Xqlrq} dqg Duwlfoh 44 ri wkh HF Wuhdw|1

Wkh whupv ri wkh ghedwh Olnh dq| rwkhu Fhqwudo edqn/ wkh HFE idfhv wkh frq lfwlqj remhfwlyhv ri orqj0uxq sulfh vwdelolw| dqg vkruw0uxq vwdelol}dwlrq ri wkh hfrqrp| lq wkh suhvhqfh ri vkrfnv1 Xqolnh dq| rwkhu Fhqwudo Edqn/ wkh HFE grhv qrw idfh d vlqjoh vfdo dxwkrulw|/ exw 45 glhuhqw rqhv1 Lq vxfk xqsuhfhghqwhg iudphzrun wkh frqvhtxhqfhv lq whupv ri suhvvxuh rq wkh HFE duh gl!fxow wr dvvhvv/ dqg wkhuh lv qr xqdqlplw| ri rslqlrqv1 Lw lv wkhq qrw vxusulvlqj wkdw wkh Khovlqnl Frxqflo kdv uhylyhg wkh h{lvwlqj ghedwh derxw frruglqdwlrq ri vfdo srolflhv/ dqg wkdw qr djuhhphqw h{lvw1

Wkh uvw vxssruwhu ri vwurqj vfdo frruglqdwlrq lv wkh Hxurshdq Frpplvvlrq1 Wkh dgydqwdjh ri frruglqdwlrq zrxog eh wkdw dfwlyh vfdo srolf| lv uhfryhuhg iru vwdelol}dwlrq1 Dovr/ lw lv shufhlyhg e| vrph wkdw wkhuh lv d qhhg iru vfdo frruglqdwlrq wr hqvxuh fuhglelolw| ri orqj0whup frpplwphqwv wr pdfurhfrqrplf vwdelolw|1

Rq wkh rwkhu kdqg/ d frqvlvwhqw sduw ri wkh hfrqrplf surihvvlrq whqgv wr eh vnhswlfdo derxw wkh qhhg iru vxfk d pryh1 Pdq| hfrqrplvwv wklqn wkdw frruglqdwhg vfdo srolflhv zrxog sodfh d juhdwhu exughq rq wkh prqhwdu| dxwkrulw|1 D pruh lqwhqvh frruglqdwlrq frxog ohdg wr cNh|qhvldq vw|oh* qh0wxqlqj ri vfdo srolflhv dfurvv wkh phpehu vwdwhv/ dqg wklv zrxog irufh wkh HFE wr lqwhuyhqh lq wkh srolf| pl{ dqg wr sd| wrr pxfk dwwhqwlrq wr f|folfdo vwdelol}dwlrq/ qhjohfwlqj wkh remhfwlyh ri orqj uxq sulfh vwdelol}dwlrq1

Wkh uhsruwhg ghfodudwlrqv e| phpehuv ri wkh Erdug ri Gluhfwruv ri wkh Hxurshdq Fhqwudo Edqn +HFE, vhhp wr surfhhg dorqj erwk olqhv ri uhdvrqlqj= rq wkh rqh kdqg/ d vwurqjhu frruglqdwlrq ehwzhhq hxur frxqwulhv frxog eh d srwhqwldo wkuhdw wr wkh lqghshqghqfh ri wkh HFE> rq wkh rwkhu/ lw frxog uhgxfh wkh ohyho ri srolwlfdo xqfhuwdlqw| uhvxowlqj iurp d vlwxdwlrq zkhuh hfrqrplf srolflhv duh sxuvxhg lqghshqghqwo| e| d odujh qxpehu ri lqvwlwxwlrqv1 Rq wklv srlqw hyhq wkh HFE grhv qrw vhhp wr glvolnh wkh lghd ri d fuhgleoh lqwhuorfxwru1

Lw lw wkh rslqlrq ri wklv sdshu wkdw wklv txhvwlrq fdq eh dgguhvvhg rqo| e| dqdo|}lqj wkh vwudwhjlf lqwhudfwlrq ri wkh ydulrxv srolf|pdnhuv1 Wkh sdshu lv vwuxfwxuhg dv iroorzv= vhfwlrq 5 ghvfulehv wkh prgho dqg fodulhv wkh k|srwkhvhv wkdw xqghuolqh wkh lghd ri vfdo srolflhv sxwwlqj suhvvxuh rq wkh HFE> lw qdoo| surylghv d forvhg irup vroxwlrq iru wkh prgho1 Vhfwlrq 6 h{dplqhv wkh frqvhtxhqfhv ri glhuhqw ohyhov ri srvlwlyh dqg qhjdwlyh frruglqdwlrq dqg wkhlu lqwhudfwlrqv1 Wkh uhvxowv duh dovr looxvwudwhg yld d vlpxodwlrq ri d prqhwdu| xqlrq ri 45 frxqwulhv zkrvh zhljkwv duh htxdo wr wkrvh lqwr wkh HPX1 Wkh frqfoxvlrqv iroorz1 Wkh pdwkhpdwlfdo dsshqgl{ surylghv d pruh frpsohwh fkdudfwhul}dwlrq ri wkh uhvxowv ri wkh sdshu1

Vrph olwhudwxuh Wkh lvvxh ri frruglqdwlrq lq d prqhwdu| xqlrq lv h{solflwo| dgguhvvhg lq Gl{lw dqg Odpehuwlql +5333,/ Ervfd dqg Ruwv +4<<4,/ Ydq Dduoh dqg Kxduw +4<<:,/ Ehhwvpd dqg Eryhqehuj +4<<8, dqg lq d jdph wkhru| iudphzrun e| Gld}0Urogdq +5333,1

Jdwwl dqg Ydq Zlmqehujhq +5335, h{dplqh wkh frqglwlrqv iru vfdo uhvwudlqw wr hphujh dv Qdvk htxloleulxp lq wkh jdph ehwzhhq vfdo dxwkrulwlhv lq d prqhwdu| xqlrq1 Ed|rxpl dqg Hlfkhqjuhhq +4<<6, dqg wkh wh{wv ri wkh Rswlpxp Fxuuhqf| Duhdv lq wkhlu eleolrjudsk| duh d jrrg vwduwlqj srlqw iru wkh dqdo|vlv ri wkh vkrfnv wkdw pd| klw d prqhwdu| xqlrq1 Wkh frqfoxvlrqv ri wklv sdshu derxw wkh uljlglw| ri wkh VJS duh vlplodu wr wkrvh lq Hlfkhqjuhhq +4<<9,1 Wkh ohjdo iudphzrun lq zklfk frruglqdwlrq pxvw dulvh lv lq wkh Wuhdw| ri Pddvwulfkw/ glvfxvvhg lq Exwhu/ Fruvhwwl dqg Urxelql +4<<6,/ Yrq Kdjhq dqg Hlfkhqjuhhq +4<<9,/ dqg ri frxuvh lq Hxurshdq Frpplvvlrq +4<<4,1 Iru vfdo ihghudolvp rqh fdq orrn dw Rdwhv +4<:5,/ Wdq}l +4<<9,/ Zdovk +4<<5, dqg Slvdql0Ihuu| +4<<4,1

5 Wkh prgho

Lq d vlpsoh prqhwdu| xqlrq klw e| h{rjhqrxv vkrfnv/ wkh vlqjoh fhqwudo edqn dqg Q qdwlrqdo vfdo dxwkrulwlhv lqwhudfw wr dfklhyh orz lq dwlrq dqg ixoo hpsor|phqw1 Wkh lqwhudfwlrq ehwzhhq wkh djhqwv lv prghohg zlwk d jdph wkhru| prgho vroydeoh e| edfnzdug lqgxfwlrq/ lq zklfk wkh qdwlrqdo jryhuqphqwv duh deoh wr sxw suhvvxuh rq wkh HFE e| uxqqlqj wkhlu vfdo srolflhv diwhu dq hfrqrplf vkrfn1 Wkh irfxv lv rq vwdelol}dwlrq diwhu d vkrfn/ qrw rq uhsxwdwlrqdo lvvxhv ri wkh sod|huv/ wkhuhiruh wkh jdph lv vwdwlf1

Wkh suhihuhqfhv ri qdwlrqdo jryhuqphqwv glhu iurp wkrvh ri wkh fhqwudo edqn ehfdxvh ri wkh juhdwhu zhljkw sxw rq vprrwklqj xqhpsor|phqw6_{1 Wkh jryhuqphqwv lq doo sduwlflsdwlqj}

frxqwulhv kdyh lghqwlfdo suhihuhqfhv1 Wkh prgho lv rqh ri vkruw krul}rq/ wkhuhiruh wkh hhfw ri vfdo dqg prqhwdu| srolf| rq lq dwlrq dqg xqhpsor|phqw lv ghvfulehg e| wzr vlpsoh ghpdqg htxdwlrqv zlwk {hg h{shfwdwlrqv ri wkh sxeolf1

Wr nhhs qrwdwlrq vlpsoh/ rqo| wzr jryhuqphqwv duh h{solflwo| uhsuhvhqwhg1 Jryhuq0 phqw m fdq eh vhhq dv wkh zhljkwhg dyhudjh ri doo rwkhu sduwlflsdwlqj frxqwulhv dv vhhq e| jryhuqphqw l1 Wklv vlpsolfdwlrq grhv qrw dowhu wkh v|pphwulf htxloleulxp ri wkh prgho1

Lq wkh uvw vhfwlrq wkh jdph lv ghvfulehg dqg vroyhg iru wkh jhqhudo fdvh1 Wkh htxloleulxp frqglwlrqv duh wkhq xvhg lq wkh vhfrqg sduw wr dqdo|}h vrph glhuhqw vfhqdulrv1

Wkh uvw0ehvw prqhwdu| srolf| Wkh HFE kdv wzr/ frq lfwlqj remhfwlyhv= orqj0uxq lq dwlrq wdujhwlqj +sulpdu| remhfwlyh, dqg vkruw0uxq vwdelol}dwlrq ri wkh Hxur duhd1 Wkh pruh wkh HFE fdq qhjohfw vwdelol}dwlrq/ wkh ehwwhu lw fdq frqfhqwudwh rq wkh rwkhu jrdo1 Iru wklv uhdvrq lw lv hqrxjk wr prgho h{solflwo| wkh vkruw0uxq suhihuhqfhv iru vwdelol}dwlrq1 Wkhvh suhihuhqfhv vkrxog eh lqwhusuhwhg dv wkh wudgh0r ehwzhhq lq dwlrq dqg xqhpsor|phqw wkdw

6_{Jlyhq wkh vkruw whup fkdudfwhulvwlfv ri wkh prgho d juhdwhu zhljkw rq xqhpsor|phqw fdq dovr eh} lqwhusuhwhg dv d juhdwhu LIDDC ri ghvluhg dgmxvwphqw1

wkh HFE frqvlghuv frqvlvwhqw zlwk orqj0uxq sulfh vwdelolw|1 Wkh rswlpdo zrunlqj hqylurq0 phqw iru wkh HFE lv wkhq wkh rqh lq zklfk lw grhv qrw kdyh wr lqwhuyhqh wr fruuhfw zkdw duh/ lq whupv ri lwv suhihuhqfhv/ huuruv ri wkh qdwlrqdo jryhuqphqwv1 Pruh vshflfdoo|=

 lw grhv qrw qhhg wr lqwhuyhqh wr rvhw wkh lq dwlrqdu| hhfwv ri dq h{fhvvlyh h{shq0 glwxuh ri wkh jryhuqphqwv/ zkhuh h{fhvvlyh h{shqglwxuh lv wkh h{shqglwxuh wkdw lpsolhv pruh lq dwlrq wkdq wkh HFE zrxog olnh jlyhq wkh h{rjhqrxv vkrfn1

 lw grhv qrw qhhg wr lqwhuyhqh ehfdxvh ri wkh odfn ri dfwlrq ri wkh qdwlrqdo jryhuqphqwv1 Wklv pd| vhhp xqolnho| lq wkh prgho/ ehfdxvh wkh suhihuhqfhv ri wkh qdwlrqdo vfdo dxwkrulwlhv duh uhodwlyho| pruh frqfhuqhg derxw xqhpsor|phqw/ exw wklv hyhqwxdolw| pd| dulvh lq suhvhqfh ri lq h{leoh frqvwudlqwv wr vfdo srolf| vxfk dv wkh rqhv lpsoh0 phqwhg lq wkh VJS1 Lw zloo eh vkrzq wkdw xqghu vrph flufxpvwdqfhv wkhvh frqvwudlqwv fdq suhyhqw wkh phpehu vwdwhv iurp frslqj zlwk dv|pphwulf vkrfnv7 _{dqg sxw wkh}

exughq ri wkh lqwhuyhqwlrq rq wkh HFE1

Wkh phdqlqjri suhvvxuh rq wkh HFE Wkh jhqhulf zruu| wkdw wkh jryhuqphqwv fdq lq xhqfh wkh HFE klghv pdq| rwkhu dvvxpswlrq/ wkdw lv lpsruwdqw wr pdnh h{solflw lq rughu wr fkhfn wkhlu olnholkrrg1 L vkdoo eulh | rxwolqh wkhvh k|srwkhvhv khuh1

41 Edfnzdug lqgxfwlrq= wkh jryhuqphqwv pxvw eh deoh wr irup h{shfwdwlrqv derxw wkh uhdfwlrq ri wkh HFE dqg wdnh wkhp lqwr dffrxqw zkhq irupxodwlqj vfdo srolf|1 Lq wkh mdujrq ri jdph wkhru|/ wkh jryhuqphqwv pryh uvw1

51 Wkh HFE fdq kdyh suhihuhqfhv wkdw duh txlwh frqvhuydwlyh/ exw wkh| pxvw dovr wr vrph h{whqw lqfoxgh xqhpsor|phqw1 Zkhq wkh HFE lv frpplwwhg wr wkh h{foxvlyh wdujhwlqj ri sulfhv8 _{wkhuh lv qr vfrsh iru sxwwlqj suhvvxuh rq lw ehfdxvh wkhuh lv qr}

wudgh r ehwzhhq sulfhv dqg xqhpsor|phqw lq lwv ehvw uhvsrqvh1 Wkh wzr uvw |hduv ri HPX kdyh fohduo| vkrzq wkdw hpsor|phqw lv d uhohydqw yduldeoh lq wkh HFE srolf| ghflvlrqv9₁

7_{D uhohydqw sureohp lv zkhq wkh vkrfnv frph iurp rxwvlgh ru lqvlgh wkh prqhwdu| xqlrq1 Lw lv dvvxphg} khuh wkdw wkhuh lv frqvhqvxv dprqj wkh sod|huv rq wkh uhohydqw yduldeohv wr zdwfk/ dqg wkh suhihuhqfhv ri wkh sod|huv duh h{suhvvhg lq whupv ri wkhvh yduldeohv1 Wklv lv qrw dq hvvhqwldo ihdwxuh ri wkh prgho dqg wklv dvshfw lv wkhuhiruh dvvxphg dzd|/ irfxvlqj wkh dwwhqwlrq rqo| rq wkh lqwhudfwlrq ri wkh sod|huv1

8_{Rwkhu vroxwlrqv pd| h{lvw1 Iru lqvwdqfh/ wkh Uhvhuyh Edqn ri Qhz ]hdodqg h{foxghv iurp wkh wdujhwhg} lq dwlrq wkh hhfw ri jryhuqphqw vdohv wd{hv1 Wklv fdq eh vhhq dv dq dwwhpsw wr olplw wkh lq xhqfh ri wkh jryhuqphqw1

9_{Hpsor|phqw frxog eh lqfoxghg dv d suhglfwru ri ixwxuh lq dwlrq1 Lq wklv fdvh lw zrxog dsshdu dv li wkh} HFE zdv frqfhuqhg e| hpsor|phqw1

61 Wkh qdwlrqdo vfdo dxwkrulwlhv duh uhodwlyho| pruh frqfhuqhg derxw lqfuhdvhv lq xqhp0 sor|phqw wkdq wkh HFE1 Lq devhqfh ri wklv lq dwlrq eldv wkh sureohp ri suhvvxuh rq wkh HFE grhv qrw h{lvw1 Lw kdv ehhq fruuhfwo| vwdwhg wkdw wkh fdvh iru vfdo frrugl0 qdwlrq +dqg pruh lq jhqhudo iru pdfurhfrqrplf frruglqdwlrq, lv zhdn zkhq wkh HFE dqg wkh vfdo dxwkrulwlhv nhhs wkh krxvh lq rughu dfwlqj rq wkhlu rzq1 Dw d forvhu orrn/ wkh devhqfh ri lq dwlrq eldv lv qrw uhdolvwlf1 Wkh h{suhvvlrq nhhs wkhlu krxvhv lq rughu grhv qrw rqo| lpso| wkdw wkh vfdo dxwkrulwlhv gr qrw ghyldwh iurp suxghqw ehkdylru ehfdxvh ri vkruw uxq srolwlfdo lqfhqwlyhv1 Lw dovr dprxqwv wr dvvxplqj wkdw wkh qdwlrqdo jryhuqphqwv vkrz wkh vdph olwwoh frqfhuq derxw xqhpsor|phqw wkdq d frqvhuydwlyh fhqwudo edqn1 Wklv dvvxpswlrq grhv qrw vhhp wr eh revhuyhg lq sudfwlfh lq wkh HX frxqwulhv:_{1 Lq wkh uhvw ri wkh sdshu/ wkh jryhuqphqwv kdyh dq lq dwlrq eldv1}

71 Prqhwdu| srolf| lv dvvxphg wr eh uhodwlyho| pruh h!flhqw rq sulfhv wkdq vfdo srol0 flhv;_{1 Wklv vlpso| phdqv wkdw wkh lqvwlwxwlrq uhodwlyho| pruh frqfhuqhg derxw sulfhv}

+wkh HFE, kdv ehhq dvvljqhg wkh lqvwuxphqw wkdw ehvw frqwurov lq dwlrq1 D vlwxdwlrq ri plvdoorfdwlrq ri lqvwuxphqwv zrxog ohdg wr wkh devhqfh ri htxloleulxp1

Rwkhu k|srwkhvhv ri wkh prgho duh wkhuh vlpso| wr lpsuryh fodulw| dqg wudfwdelolw|1 Wkh jdph dlpv dw ghvfulelqj wkh lqwhudfwlrq dprqj sxeolf djhqwv lq uhvsrqglqj wr vkrfnv1 Hdfk hfrqrp| lv wkhq ghvfulehg e| wkh vdph wzr vlpsoh htxdwlrqv ri sulfhv dqg xqhpsor|phqw1 Wkh lqwhuhvwlqj wlph krul}rq ehlqj wkh yhu| vkruw shulrg/ wkh h{shfwdwlrqv ri wkh sxeolf duh nhsw {hg1 Ilqdoo|/ L zdqw wr frqfhqwudwh rq wkh hhfwv ri prqhwdu| srolf| dqg prqhwdu| h{whuqdolwlhv/ wkhuhiruh L qhjohfw wkh gluhfw vfdo h{whuqdolwlhv dqg dvvxph wkdw wkh glhuhqw frxqwulhv duh olqnhg rqo| e| wkh frpprq prqhwdu| srolf|= lq rwkhu zrugv/ hdfk qdwlrqdo vfdo srolf| kdv gluhfw hhfwv lq wkh grphvwlf pdunhw rqo|/ dqg lqgluhfw hhfwv deurdg wkurxjk prqhwdu| srolf|1 Wkh plqlpl}dwlrq ri wkhvh lqgluhfw hhfwv lv dw wkh fhqwhu ri wkh dwwhqwlrq ri wkh suhvhqw zrun1

Wkh vhtxhqfh ri pryhv Dw wkh ehjlqqlqj ri wkh jdph wkh pdunhw lv lq htxloleulxp/ zkhuh htxloleulxp lv ghqhg dv wkh vlwxdwlrq zkhuh doo djhqwv +HFE dqg Jv, duh sod|lqj wkhlu ehvw uhvsrqvhv/ wkh frpprq wdujhw ydoxhv iru sulfhv dqg xqhpsor|phqw duh phw dqg

:_{Rqh vkrxog qrwlfh wkdw d eljjhu frqfhuq iru xqhpsor|phqw ri wkh vfdo dxwkrulwlhv grhv qrw qhhg wr} dulvh iurp fruuxswlrq ru srolwlfdo f|fohv> zkloh wkh HFE kdv d pdqgdwh rulhqwhg wrzdugv sulfh vwdelolw|/ qdwlrqdo jryhuqphqwv duh hohfwhg dqg wkhlu suhihuhqfhv vkrxog uh hfw wkrvh ri wkh srsxodwlrq1

;_{Lq uhdolw| lw lv hqrxjk wkdw wkh jryhuqphqwv eholhyh wklv zkhq wkh| pryh/ exw wklv zrxog frpsolfdwh wkh} ghvfulswlrq ri wkh jdph1 Zkloh k|srwkhvlv 7 lv glhuhqw iurp wkh pruh frpprqo| xvhg Skloolsv fxuyh/ rqh fdq hdvlo| vkrz wkdw wkh odwwhu zrxog qrw jlyh dq| lqfhqwlyh wr wkh vfdo dxwkrulwlhv wr sxw suhvvxuh rq wkh HFE1 Zkloh wklv fdvh lv shuihfwo| srvvleoh/ prvw hfrqrplvwv vhhp wr eholhyh wkdw wklv suhvvxuh lv d uhdo ulvn1

wkhuh lv qr vkrfn1 Wkh pryhv duh dv iroorzv= uvw/ wkh qdwlrqdo pdunhw duh klw e| lqghshqghqw vkrfnv wr sulfhv dqg2ru wr hpsor|phqw> vhfrqg/ wkh qdwlrqdo jryhuqphqwv xvh wkh vfdo ohyhu/ dqg qdoo| wkh fhqwudo edqn vhwv wkh prqhwdu| srolf|1 Wkh vwuxfwxuh ri suhihuhqfhv ri wkh djhqwv lv frpprq nqrzohgjh/ wkhuhiruh wkh jdph doorzv iru edfnzdug lqgxfwlrq/ l1h1 wkh qdwlrqdo jryhuqphqwv wdnh lqwr dffrxqw wkh iruhvhhdeoh uhdfwlrq ri wkh fhqwudo edqn zkloh vhwwlqj wkhlu rswlpdo srolflhv1

The order of the moves

Outcome (P1,U1) Nature ε,η GovG1 Outcome (P2,U2) Gov 0 ECB M Nature 0,0

Wkh rughu ri wkh sod|huv kdv ehhq fkrvhq wr uh hfw erwk wkh fdsdflw| ri lq xhqflqj hdfk rwkhu wkdw lv revhuyhg lq uhdo zruog dqg +dv dujxhg lq wkh suhylrxv vhfwlrq, wkh rqo| lqwhuhvwlqj fdvh1 Lq wkh uvw wzr |hduv ri HPX/ wkh srolf| ri wkh HFE kdv ehhq dwwhqwlyh wr erwk lq dwlrq dqg xqhpsor|phqw ohyhov/ zkloh wkh lq xhqfh ri wkh HFE rq phpehu vwdwhv zdv olplwhg wr vshhfkhv/ zlwk wkh VJS dv wkh rqo| elqglqj lqvwlwxwlrq1 Li wkh HFE lv qrw xqltxho| frpplwwhg wr sulfh vwdelolw| lw lv uhdvrqdeoh wr dvvxph wkdw/ dv orqj dv wkh jryhuqphqwv kdyh vrph iuhhgrp lq wkh xvh ri vfdo srolf|/ wkh| fdq wdnh lqwr dffrxqw d srvvleoh uhdfwlrq ri wkh HFE<_{1 Wkh rughu ri sod| wkhq uh hfwv wkh uhodwlrqv ri srzhu}

dprqj djhqwv1 D vhfrqg lqwhusuhwdwlrq frxog eh wkdw wkh HFE lv idvwhu wr uhdfw/ lq wkh vhqvh wkdw lw fdq fkdqjh srolf| pxfk pruh iuhtxhqwo| wkdq wkh qdwlrqdo jryhuqphqwv> wklv juhdwhu h{lelolw| doorzv wkh HFE wr iroorz dq| fkdqjh lq vfdo srolflhv zlwk dq dssursuldwh uhvsrqvh1 Xqghu wklv lqwhusuhwdwlrq/ wkh rughu ri sod|huv uh hfwv d vhtxhqfh lq wlph1

514 Wkh qdwlrqdo pdunhwv

Doo qdwlrqdo pdunhwv duh lghqwlfdo lq vwuxfwxuh/ exw pd| kdyh glhuhqw lq dwlrq dqg xq0 hpsor|phqw ohyhov dqg glhuhqw vl}hv1 Hdfk ri wkhp lv dhfwhg e| sxeolf srolflhv lq wkh iroorzlqj vw|ol}hg zd|43₌

<_{Wkh VJS lv d +yhu| lpsuhflvh, zd| wr wdnh dzd| vxfk iuhhgrp iurp wkh jryhuqphqwv1} 43_{Lw lv lpsruwdqw wr qrwlfh wkdw qr vlqjoh lq dwlrq ohyho dfurvv wkh xqlrq lv lpsrvhg1}

S @ s6P . s}J . % +4,

X @ x6P  x}J .  +5,

zkhuh S> X> P> J lqglfdwh wkh ghyldwlrqv ri sulfhv/ xqhpsor|phqw/ prqh| vxsso|/ vfdo h{shqglwxuh iurp wdujhw ydoxhv/ dqg % dqg  duh L1L1G1 vkrfnv wr sulfhv dqg wr xqhpsor|phqw1 Wkh wdujhw ydoxhv duh frpprq wr wkh HFE dq wkh qdwlrqdo jryhuqphqwv/ exw wkh iruphu lv ohvv lqfolqhg wr vkruw0uxq rxwsxw vwdelol}dwlrq +k|srwkhvlv 6,1 Doo rwkhu ohwwhuv duh srvlwlyh sdudphwhuv1 K|srwkhvlv 7 lpsolhv= s6 x6 A s} x}

Wklv frqglwlrq vlpso| vwdwhv wkdw prqhwdu| srolf| kdv d frpsdudwlyh dgydqwdjh lq frqwuroolqj sulfhv/ dqg vfdo dqg prqhwdu| lqvwuxphqwv kdyh fruuhfwo| ehhq doorfdwhg1

515 Wkh HFE

Lq prghov vroydeoh e| edfnzdug lqgxfwlrq lw lv riwhq frqyhqlhqw wr vwduw iurp wkh sod|hu zkr pryhv odvw/ lq wklv fdvh wkh fhqwudo edqn +HFE,1 Wkh uhdvrq lv wkdw wkh vwudwhj| ri wkh HFE lv wdnhq lqwr dffrxqw e| wkh jryhuqphqwv +J,/ zkloh wkh sod| ri J lv douhdg| nqrzq wr wkh HFE zkhq lw pryhv1

Wkh HFE uxqv wkh prqhwdu| srolf| iru wkh zkroh xqlrq1 Wkh prqhwdu| srolf| lv frpprq dqg kdv v|pphwulfdo hhfwv lq doo frxqwulhv +jlyhq wkdw wkh| kdyh lghqwlfdo vwuxfwxuhv,1

Wkh suhihuhqfhv ri wkh HFE duh ghqhg ryhu xqlrq djjuhjdwhv=

O.+P> J> %> , @ ^S +P> J> %,`2.  ^X+P> J> ,`2 +6,

zkhuh wkh yduldeohv zlwkrxw d vxevfulsw duh wkh zhljkwhg dyhudjh ri wkh Q sduwlflsdwlqj frxqwulhv= P @S_'P J @S_'J % @S_'%  @S_' zlwkS_' @ 4

Wkh sdudphwhu  h{suhvvhv wkh uhodwlyh dyhuvlrq ri wkh HFE wr lq dwlrq dqg xqhpsor|0 phqw1

Preferences and Best Response of CB

U

P

BR_ECB

Wkh Ehvw uhvsrqvh ri wkh HFE fdq eh h{suhvvhg dv iroorzv +vhh dsshqgl{,=

P +J> %> , @ } # _ [ ' J $  e # _ [ ' % $ .  # _ [ '  $ Ru lq d frqghqvhg uhsuhvhqwdwlrq= P+J> %> , @ }J  e% .  zlwk } @  k  R6nq6 l +x6x} s}s6, e@  k  R6nq6 l +s6,  @ . k  R6nq6 l x6 doo srvlwlyh1

Wkh ehvw vwudwhj| ri wkh HFE lv wr gh dwh lq uhvsrqvh wr dq lqfuhdvh ri h{shqglwxuh e| wkh jryhuqphqwv +J, dqg wr dq h{rjhqrxv lqfuhdvh ri sulfhv %/ dqg wr vxssruw hpsor|phqw zkhq d qhjdwlyh vkrfn  klwv lw1

Wkh whup lq vtxduhg eudfnhwv lv wkh uhflsurfdo ri wkh uhvsrqvlyhqhvv ri wkh wdujhw ydul0 deohv wr d srolf| fkdqjh dqg ghwhuplqhv wkh vl}h ri wkh lqwhuyhqwlrq1 Wkh HFE lqwhuyhqhv dffruglqj wr wkh vorsh ri lwv Skloolsv fxuyh +x6@s6, dqg wr wkh suhihuhqfhv 1 Revhuyh

wkdw zkhq rqo| rqh ru vrph frxqwulhv ri zhljkw  duh klw e| d vkrfn ru dgrsw d srolf|

fkdqjh/ wkh HFE zloo pryh sursruwlrqdoo| iurp wkh shufhlyhg vlwxdwlrq wr lwv EU olqh1 Wklv lpsolhv wkdw hdfk jryhuqphqwv idfhv d edfnzdug0lqgxfwlrq exgjhw frqvwudlqw wkdw grhv qrw frlqflgh zlwk wkh EU ri HFE xqohvv  @ 41 Dv dq h{dpsoh/ wkh orfxv ri htxloleuld

fkrvhq e| d edfnzdug lqgxfwlqj jryhuqphqw lv slfwxuhg ehorz iru  @ i3> 4@5> 4j1

λ=1/2

U

P

BR_ECB

Size and possible equilibria

λ=0 λ=1 0 1 2a 2c 2b L_G

516 Wkh jryhuqphqwv

Lq wklv vhfwlrq wkh ehvw uhvsrqvh ixqfwlrq ri wkh qdwlrqdo jryhuqphqwv lv fdofxodwhg lq wkh prvw jhqhudo iudphzrun1 Wklv zloo ohdg wr vrph fxpehuvrph qrwdwlrq/ exw lw kdv wkh dgydqwdjh ri hqfrpsdvvlqj doo wkh rwkhu vlwxdwlrqv dv vshfldo fdvhv1

Lq wkh jhqhudo vlwxdwlrq +v|pphwulf lqirupdwlrq, hdfk jryhuqphqw lv qrw frqvwudlqhg lq wkh fkrlfh ri lwv vfdo vwdqfh dqg lv dzduh ri wkh vwuxfwxuh ri wkh prgho dqg ri wkh pryhv ri qdwxuh +wkh vkrfnv lq doo sduwlflsdwlqj frxqwulhv,1 Wkxv/ hdfk jryhuqphqw lv deoh wr irup h{shfwdwlrqv derxw wkh pryhv ri lwv shhuv dqg +e| edfnzdug lqgxfwlrq, derxw wkh pryh ri wkh HFE44_{/ dqg dfwv dffruglqjo|1}

Wkh orvv ixqfwlrq ri hdfk jryhuqphqw l lv

OC+P> J> %> , @ ^S+P> J> %,`2.  ^X+P> J> ,`2 +7,

dqg +k|srwkhvlv 6, wkh jryhuqphqw fduhv derxw xqhpsor|phqw pruh wkdq wkh HFE/ wkhuh0 iruh  A 1

44_{Wkh pryh ri HFE lv wkh rqo| yduldeoh ri lqwhuhvw iru wkh jryhuqphqw ehfdxvh lw dhfwv wkh sd|r ri lwv} vwudwhj|/ zkloh wkh vfdo srolflhv ri wkh rwkhu frxqwulhv gr qrw kdyh gluhfw grphvwlf hhfwv exw rqo| lqgluhfw h{whuqdolwlhv frplqj iurp wkh uhdfwlrq ri wkh HFE1

Preferences and Best Response of the Governments

U

P BRG

Vroylqj wkh IRF iru J +lq dsshqgl{,/ rqh rewdlqv wkh EU ixqfwlrq ri jryhuqphqw l=

J> > %> %> J@ @  ; A A A A A A A ? A A A A A A A = .+s6,s6}. s} x6} x}+4  x6, .+s6,s6}. s} x6} x}+x6, +4  s6e,s6}. s} x6} x}+x6e,% +s6e,s6}. s} x6} x}+x6e,% .s6} s6}. s}. x6} x} x6}J < A A A A A A A @ A A A A A A A > zlwk @ % 4  x6} x}2 .s6}. s}2 &

Iruwxqdwho| wklv zloo eh wkh prvw frpsolfdwhg h{suhvvlrq lq wkh sdshu1 Lq rughu wr judvs wkh lqwxlwlrq rqh kdv wr wdnh lqwr dffrxqw wkdw wkh uhdfwlrq ri wkh HFE lv dxwrpdwlfdoo| wdnhq lqwr dffrxqw lq wkh h{suhvvlrq deryh/ zkloh wkrvh ri wkh rwkhu sod|huv duh qrw +dqg wkh| h{solflwo| dsshdu dv dujxphqwv,1 Wklv glhuhqfh lq wuhdwphqw lv gxh wr wkh idfw wkdw wkh jryhuqphqwv pryh vlpxowdqhrxvo|1

Rqh h{wuhph fdvh + @ 3, lv uxohg rxw e| k|srwkhvhv 5 dqg 6/ exw lw lv xvhixo wr frqvlghu lw iru wkh sxusrvh ri h{srvlwlrq1 Li J fduhv rqo| derxw lq dwlrq +wkdw lv/ li lw lv hyhq

pruh frqvhuydwlyh wkdq wkh HFE, d vfdo uhvwulfwlrq zloo iroorz d vkrfn wr grphvwlf ru iruhljq xqhpsor|phqw ehfdxvh wkh frpsdudwlyho| zhdn HFE lv jrlqj wr doorz vrph pruh lq dwlrq1 Wkh vdph lv wuxh diwhu d grphvwlf sulfh vkrfn rqo| sduwldoo| rvhw e| wkh HFE1

D vfdo h{sdqvlrq iroorzv d iruhljq sulfh vkrfn vlpso| ehfdxvh wkh HFE uhvwulfwlrq lv qrw zhofrph1

D jryhuqphqw xqltxho| frqfhuqhg derxw wkh lqwhuqdo ohyho ri hpsor|phqw + $ 4, dozd|v lqfuhdvhv vshqglqj diwhu d vkrfn wr xqhpsor|phqw1 Wklv uhdfwlrq lv vrphkrz vprrwkhg ehfdxvh wkh jryhuqphqw nqrzv wkdw wkh HFE zloo wdnh sduw ri wkh exughq ri wkh lqwhuyhqwlrq +4  x6,1 Li wkh vkrfn dulvhv lq dqrwkhu frxqwu|/ wkh h{shfwhg prq0

hwdu| h{sdqvlrq ri wkh HFE +x6, ohdgv wr vfdo frqvrolgdwlrq1 Wkh vdph lv wuxh

+zlwk glhuhqw vljqv/ ehfdxvh wkh h{shfwhg uhdfwlrq ri wkh HFE jrhv lq wkh rwkhu gluhfwlrq, iru d vkrfn wr sulfhv> wkh HFE zloo uhvwulfw wkh txdqwlw| ri prqh|/ dqg wklv fdoov iru vfdo h{sdqvlrq1

Wklv frh!flhqw } lv wkh lqgluhfw h{whuqdolw| uhdfwlrq wr wkh vfdo h{sdqvlrq ri rwkhu

phpehuv1 Lq dsshqgl{ lw lv vkrzq wkdw k|srwkhvlv 7 lpsolhv wkdw wklv sdudphwhu fdq wdnh ydoxhv ehwzhhq 3 dqg 4 +qrw lqfoxghg,45_{1 Wklv frqglwlrqv hqvxuhv wkh h{lvwhqfh ri wkh}

Vxejdph Shuihfw Htxloleulxp46₁

Ilqdoo|/ d vkruwhu qrwdwlrq lv lqwurgxfhg iru wkh frpsoh{ h{shqglwxuh ixqfwlrq ri wkh jhqhulf jryhuqphqw l= wklv ixqfwlrq uhsuhvhqwv wkh EU ri d jryhuqphqw iuhh wr pryh/ dzduh ri wkh idfw wkdw wkh HFE zloo pryh qh{w dqg lqiruphg derxw wkh vkrfnv lq doo sduwlflsdwlqj frxqwulhv1 J@ +e%. , .  se%. s_  . }J +8, Zlwk _e? 3> _A 3> se A 3> s_ ? 3 dqg 3 ? }? 4 xqghu wkh k|srwkhvhv ri wkh prgho1 Wkh vljq ri wkh frh!flhqwv lv ghulyhg dqdo|wlfdoo| lq dsshqgl{1

6 Ilyh srvvleoh vfhqdulrv

Wkh sursrvdov iru frruglqdwlrq duh ri wzr nlqgv= srvlwlyh frruglqdwlrq dqg qhjdwlyh frru0 glqdwlrq1 Srvlwlyh frruglqdwlrq frqvlvwv ri uhjxodu phhwlqjv lq zklfk wkh srolf| uhvsrqvhv duh frruglqdwhg rq d fdvh0e|0fdvh edvlv/ qhjdwlyh frruglqdwlrq frqvlvwv ri uxohv odlg grzq dw wkh ehjlqqlqj dqg wkhq iroorzhg wkurxjkrxw1 E| dsso|lqj uhvwulfwlrqv wr wkh jhqhudo prgho vroyhg lq vhfwlrq 5/ zh fdq dqdo|}h wkh iroorzlqj vfhqdulrv/ udqnhg iurp plqlpdo wr pd{lpdo srvlwlyh frruglqdwlrq dqg frqwudvwhg zlwk qhjdwlyh frruglqdwlrq=

45_{Lq wkh jdph wkh frh!flhqw }

} uhsuhvhqwv wkh +qhjdwlyh, uhdfwlrq ri C wr wkh +qhjdwlyh, uhdfwlrq ri . wr wkh yduldwlrq lq C1 Wklv lv vrphwlphv uhihuuhg wr dv grplqr hhfw ri vfdo srolflhv1

46_{Whfkqlfdoo|/ rqh kdv d Qdvk Htxlolelxp ri d uhgxfhg irup jdph ehwzhhq jryhuqphqwv/ zlwk wkh uhdf0} wlrq ixqfwlrq ri wkh HFEidfwruhg lq wkhlu remhfwlyh ixqfwlrq1 Wklv fruuhvsrqgv wr wkh Vxejdph Shuihfw Htxloleulxp ri wkh ruljlqdo jdph1

 qr frruglqdwlrq dqg dxwrqrprxv vfdo srolflhv1 Wkh vfdo dxwkrulwlhv lq wkh glhu0 hqw frxqwulhv duh iuhh wr w wkhlu srolflhv wr wkhlu frxqwu|*v vshflf qhhgv/ dqg qr lqwhudfwlrq +qhlwkhu lqirupdo qru irupdo, lv uhohydqw>

 srvlwlyh frruglqdwlrq yld vkdulqj ri lqirupdwlrq +lqirupdo frrshudwlrq,1 D orrvh irup ri frrshudwlrq dprqj vfdo dxwkrulwlhv frxog wdnh wkh irup ri shulrglfdo lqirupdo phhwlqjv1 Vxfk phhwlqjv zrxog irvwhu lqirupdwlrq h{fkdqjh/ zlwkrxw frpplwwlqj dq| ri wkh sduwlflsdqwv wr vshflf srolflhv1 Wkh Hxur045 jurxs vhhpv wr eh d jrrg h{dpsoh ri vxfk dq lqvwlwxwlrq>

 srvlwlyh frruglqdwlrq wkurxjk irupdo phfkdqlvpv1 Lq wkh frqwh{w ri dq lqfuhdvhg frrshudwlrq/ iru h{dpsoh zlwklq d uhlqirufhg yhuvlrq ri wkh EHSJ +Eurdg Hfrqrplf Srolf| Jxlgholqhv,/ rqh frxog kdyh irupdo phhwlqjv lq zklfk wkh vfdo vwdqfh ri wkh sduwlflsdwlqj frxqwulhv zrxog eh ghflghg1 Wkh ghflvlrqv wdnhq lq wkhvh phhwlqjv zrxog wkhq eh elqglqj iru doo Hxur phpehuv>

 qhjdwlyh frruglqdwlrq= VJS>

 qhjdwlyh frruglqdwlrq= dq HFE0edvhg/ dowhuqdwlyh VJS1 Li wkh HFE kdv wr eh iuhh iurp suhvvxuh/ lw pxvw eh deoh wr lpsrvh lwv suhihuhqfhv rq wkh qdwlrqdo phpehu vwdwhv1 Wkh sursrvdo lv wkdw wkh dowhuqdwlyh VJS vkrxog eh edvhg rq wkh ghfoduhg suhihuhqfhv ri wkh Fhqwudo Edqn/ dqg wkh phpehu vwdwhv vkrxog frpso| zlwk wkrvh uhtxluhphqwv dv wkh| gr zlwk wkh fxuuhqw VJS1 Vxfk dq duudqjhphqw zrxog eulqj wkh HFE rxw ri lwv uroh ri Vwdfnhoehuj iroorzhu dqg doorz lw wr qhjohfw prvw ri wkh vwdelol}dwlrq lvvxh1

Wkh fxuuhqw iudphzrunri wkh HPX lqfoxghv wkh VJS dqg srvlwlyh lqirupdo frrshudwlrq1

614 Qr frruglqdwlrq

Zkhq qr frruglqdwlrq lv srvvleoh dqg wkh h{fkdqjh ri lqirupdwlrq lv vfdufh/ rqh jryhuqphqw lv qrw deoh wr iruhfdvw wkh srolflhv ri wkh rwkhuv1

Lq rxu prgho wklv lpsolhv wkdw hdfk jryhuqphqw wdnhv wkh d sulrul h{shfwhg ydoxh ri wkh vkrfnv iru wkh rwkhuv/ wkdw lv }hur1 Dovr/ zkhq wkh vkrfnv duh qrw nqrzq deurdg/ doo wkh sduwlflsdwlqj jryhuqphqwv fdq rqo| dvvxph wkdw wkh rwkhuv zloo eh lqdfwlyh1 Wklv ohdgv wr d yhu| vlpsoh ehkdylru= hdfk jryhuqphqw uhdfwv dv li lw zdv wkh rqo| rqh klw e| d vkrfn1

λ=1/2 U P BR_ECB No coordination λ=0 λ=1 0 1 L_G

Dq dv|pphwulf vkrfn zlwk qr frruglqdwlrq Wkh rxwfrph ri d vkrfnlq frxqwu| l zkhq wkhuh lv qr frruglqdwlrq ru h{fkdqjh ri lqirupdwlrq lv

J@ +e%. , S@ s6P +J> %> , . s}J. % @s}. s6 s6}.4 . s} s6e s6}% X@ x6P +J> %> ,  x}J.  @ @x6}. 4  x6 x}.x6}e x}e. x6e% J @ 3 S @ s6P +J> %> , @ @s6}. s6.s6}e s6e% X @ x6P +J> %> , @ @x6} x6.x6}e. x6e% PJ_{@ P +} J> %> , @ @}. .}e e%

Sulfhv dqg xqhpsor|phqw rxwfrphv iru wkh xqlrq duh wkh zhljkwhg dyhudjh ri qdwlrqdo ydoxhv zlwk zhljkwv  dqg @ +4  ,1

Lq fdvh ri dq dv|pphwulf vkrfnlq frxqwu| l/ erwk sulfhv ru xqhpsor|phqw udlvh diwhu lqwhuyhqwlrq ri wkh sod|huv47_{> wkh vroxwlrq iru erwk % A 3> }

 A 3 lv/ iru hyhu|  5 +3> 4,48/ 47_{Wkh sulfhv duh wrwdoo| vprrwkhg li b}

' c zklfk fdq eh lqwhusuhwhg dv wkh rqh frxqwu| fdvh ru d wrwdoo| frpprq vkrfn1 Zkhq b' f wkh uhvxow lv +wulyldoo|, }hur dv zhoo1

48_{Rqfh djdlq b}

'  dqg b' f lpso| wkdw wkh vkrfnv kdyh qr hhfw rq sulfhv dqg xqhpsor|phqw1

+S A 3> SA 3> S ? 3> X A 3> X A 3> PJ ? 3,1 Rqh vkrxog uhpdunwkdw wkh vljq lv qrw

xqltxho| ghwhuplqhg iru X1 Wklv lv qrw vxusulvlqj= wkh slfwxuh deryh vkrzv wkdw X fdq eh

hlwkhu srvlwlyh ru qhjdwlyh ghshqglqj rq wkh ydoxh ri 1 Rxu frpsxwhu vlpxodwlrqv vkrz/

krzhyhu/ wkdw iru uhdolvwlf ydoxhv ri wkh sdudphwhuv lw wdnhv d ydoxh ri  yhu| forvh wr 4 wr

kdyh qhjdwlyh ydoxhv49₁

615 Srvlwlyh frruglqdwlrq

Lq lwv vwulfwhvw ghqlwlrq/ srvlwlyh frruglqdwlrq lpsolhv wkh lpsohphqwdwlrq ri d vfdo srolf| iru wkh HX dv d zkroh e| d froohjldo ghflvlrq0pdnlqj erg|/ zkrvh ghflvlrqv zrxog eh elqglqj iru doo1 Wklv lv wkh w|slfdo prgh ri rshudwlrq ri wkh frpprq prqhwdu| srolf| lq wkh HFE Frxqflo/ dqg lw kdv ehhq vxjjhvwhg dv d orqj0whup remhfwlyh iru frruglqdwlrq lq wkh iudphzrunri wkh forvhu frrshudwlrq fodxvhv1

Dv vwdwhg ehiruh/ wkh olnho| vfhqdulr iru wkh yhu| vkruw whup vhhpv wr eh olplwhg wr d juhdwhu vkdulqj ri lqirupdwlrq lq vhdufk iru ghflvlrqv edvhg rq frqvhqvxv1 Wklv lv wkh zhdnhvw irup ri srvlwlyh frruglqdwlrq/ dqg lv dqdo|}hg uvw1

61514 Lqirupdo frrshudwlrq

Lw kdv ehhq sursrvhg wkdw frrshudwlrq frxog eh lqirupdo/ lq wkh uhvshfw ri wkh h{lvwlqj wuhdwlhv wkdw lpshgh irupdo frruglqdwlrq dprqj d vxejurxs ri HX phpehuv1 Wklv lqirupdo frrshudwlrq frxog iru h{dpsoh lqfuhdvh wkh vkdulqj ri lqirupdwlrq derxw wkh vlwxdwlrq lq wkh glhuhqw frxqwulhv/ zlwkrxw uhdfklqj wkh srlqw ri frqfhuwdwlrq ri srolflhv4:_{1 Lq wklv vhfwlrq}

lw zloo eh fohdu wkdw/ hyhq wkrxjk wkh vkdulqj ri lqirupdwlrq lv jhqhudoo| shufhlyhg wr eh d srvlwlyh idfwru dprqj hfrqrplvwv/ wklv qhhg qrw eh wkh fdvh lq d vwudwhjlf hqylurqphqw1 D vkrfn zlwk lqirupdo frrshudwlrq Wkh qhz htxloleulxp iroorzlqj d vkrfnzloo eh wkh Qdvk htxloleulxp ri wkh uhgxfhg irup jdph/ zkhuh wkh EUv ri wkh wzr jryhuqphqwv lqwhuvhfw1 Wkh frpsohwh h{suhvvlrq ri wkh Qdvk htxloleulxp lv uhsruwhg lq dsshqgl{1 Diwhu

49_{Lq frpsxwhu vlpxodwlrqv zlwk R}

6' 2c R} ' } ' 6' c k ' 2Dc q ' f.D lw wdnhv d ydoxh dv elj dv b' fHD wr kdyh d qhjdwlyh Ldv frqvhtxhqfh ri d vkrfn lq hlwkhu #ru 0 Wkh eljjhvw frxqwu| lq Hxursh lv Jhupdq|/ zkrvh vkduh lq wkh HX JGS lv rqo| voljkwo| deryh 63(1

4:_{Wkh pdfurhfrqrplf gdwd duh xvxdoo| froohfwhg e| lqghshqghqw vwdwlvwlfdo djhqflhv/ dqg ehfrph nqrzq} wr wkh sxeolf dw d odwhu vwdjh +h{ srvw fkhfn,1 Lw lv wkhuhiruh dvvxphg wkdw wkh gdwd duh wuxwkixoo| uhyhdohg wr wkh sduwqhuv1

dv dv|pphwulf vkrfnlq frxqwu| l/ wkh rxwfrph lv iru frxqwu| l J @ +e%. , . }  se%. s_  4  2_} S @ 3 Cs6. s}  . }s   s6} k . s_  .s_.   } l 4  2 } 4 D . . 3 C4  s6e. s}  e. }se   s6} k e. se  .e. se  } l 4  2 } 4 D % X @ 3 Cx6e. x6} k e. se  .e. se  _}l x}  _e. _}se  4  2 } 4 D % 3 C4  x6. x6} k . s_  .s_.   } l  x}  . }s  4  2 } 4 D _ dqg iru frxqwu| m J @  se%. s  . }+e%. , 4  2_} S @ 3 Cs}  se . }e   s6} k e. se  .e. se  } l 4  2 }  s6e 4 D %. 3 Cs6. s}  s_. _}_ s6} k . s_  .s_.   _}l 4  2 } 4 D _ X @ 3 Cx6} k e. se  .e. se  } l  x}  se . }e  4  2 } . x6e 4 D % . 3 Cx6} k . s_  .s_.   } l  x}  s_. }  4  2_}  x6 4 D _ dqg iru wkh frpprq prqhwdu| srolf|=

P _{@ P +} J. J> %> , @ @   4 4  2 }  s_.   _}. . s_  _}. _  _ .  _{4  }4 ₂ }  e. se  }. e. se  } e  %

Wklv uhvxow fdq eh frpsduhg zlwk wkh rqh ri qr frrshudwlrq1 Lq wkh suhylrxv fdvh/ wkh lqlwldo uhvsrqvh wr wkh vkrfn +e% . , zdv dovr wkh qdo rxwfrph1 Khuh/ wkh lqlwldo

vkrfnvsuhdgv durxqg wkurxjk prqhwdu| h{whuqdolwlhv1 Iluvw/ hdfk jryhuqphqw lv lqiruphg derxw wkh vkrfnv rffxuulqj deurdg/ dqg nhhsv wkhp lqwr dffrxqwse%. s



> wkhq/ wkh uhdfwlrq ri wkh sduwqhuv lv dovr frqvlghuhg +vtxduh eudfnhwv,1 Ilqdoo|/ wkh zkroh qxphudwru lv pxowlsolhg e| 4@4  2

}ehfdxvh ri wkh lqwhudfwlrq ri sod|huv1

Wkh HFE lqwhuyhqwlrq fdq dovr eh frpsduhg zlwk wkh rqh ri wkh suhfhghqw fdvh +qr h{fkdqjh ri lqirupdwlrq,1 Iru h{dpsoh/ lq fdvh ri dq dv|pphwulf xqhpsor|phqw vkrfnlq l wkh glhuhqfh lq lqwhuyhqwlrq lv P_{ P}J _{@ } 4 4  2 }}  s_.   }. 2}. s_  

zklfk fdq eh vkrzq wr eh srvlwlyh iru  5 +3> 4, e| vxevwlwxwlqj lq wkh ghqlwlrqv1 D

vlplodu frqfoxvlrq dssolhv wr dq lq dwlrq vkrfnlq l1 Zkhq wkh glhuhqw jryhuqphqwv duh dzduh ri hdfk rwkhu*v pryhv exw wkh| fdqqrw frruglqdwh/ wkh HFE lv irufhg wr vkrz pruh dfwlylvp1

Wkh vljqv ri wkh yduldeohv lq htxloleulxp duh qrw xqltxh dv lq wkh uvw fdvh/ dqg ghshqg rq 1 Vxevwlwxwlrq lq wkh ghqlwlrq ohdgv wr wkh iroorzlqj vljqv= iru  5 +3> 4, zh kdyh



SA 3> S ? 3> X A 3> P ? PJ? 31 Li wkh frxqwu| lv wkh vpdoohu rqh/  5 +3> 4@5,/

wkhq +S A 3> X A 3> XA 3,/ iru eljjhu ydoxhv ri  lw lv wuxh wkdw +S ? 3> X ? 3,1 Dv lq

wkh suhylrxv fdvh/ X uhpdlqv lqghwhuplqdwh dowkrxjk jhqhudoo| srvlwlyh1

D judsklf frpsdulvrq Wkh h{dpsoh ri dq dv|pphwulf vkrfnlq frxqwu| l lv vkrzq lq wkh jxuh ehorz1 Wkh glhuhqfh lq ryhudoo vfdo h{sdqvlrq fdq eh vhhq rq d judsk +J> J,

e| wudflqj d gldjrqdo olqh wkdw uhsruwv wkh wrwdo h{sdqvlrq rq wkh J d{lv= wkh glvwdqfh

ehwzhhq wkh txdqwlwlhv +R, dqg wkh srlqw +Q,lv wkh lqfuhdvh lq h{shqglwxuh deryh wkh qrq frrshudwlrq fdvh/ zklfk zrxog eh uhdol}hg li wkh lqwhudfwlrq whupv +_}/se dqg s_, zhuh }hur1

Wkh lqwhudfwlrq ehwzhhq wkh wzr Jv lv gxh wr wkh idfw wkdw frxqwu| m revhuyhv wkh vkrfn lq l dqg dqwlflsdwhv wkh HFE uhvwulfwlrq wr wkh vfdo h{sdqvlrq lq l/ wkhuhiruh m h{sdqgv lq rughu wr rvhw lw1 Wklv lq wxuq lv dqwlflsdwhg e| l/ dqg wkh vfdo h{sdqvlrq lv dpsolhg/ dqg vr rq1 Wkh uhvxow lv dq lqfuhdvh lq h{shqglwxuh erwk lq wkh fdvh ri dq h{rjhqrxv lqfuhdvh lq sulfhv ru xqhpsor|phqw1

Exchange of information Gi G_j BRGj BRGi N O T N 61515 Irupdo frruglqdwlrq

Lq wkh frqwh{w ri irupdo vfdo frruglqdwlrq/ wkh vfdo dxwkrulwlhv dfw dv li wkh| zhuh rqh/ revhuyh wkh dyhudjh vkrfnv wr wkh zkroh xqlrq dqg frpsxwh wkh rswlpdo srolf| uhvsrqvh dv li wkh| zhuh d vlqjoh jryhuqphqw4;_{1 Wrwdo frruglqdwlrq ohdgv h{dfwo| wr wkh vdph rxwfrph}

dv wkh rqh frxqwu| fdvh/ zkhuh wkh vkrfnv duh frpsohwho| vprrwkhg dw wkh xqlrq ohyho1 Dv xvxdo/ wkh frpsohwh fkdudfwhul}dwlrq ri wkh vroxwlrq lv lq wkh dsshqgl{1 Wkh rxwfrph ri dq dv|pphwulf vkrfnlq frxqwu| l lv= JA _{@ } +e%. , S @ s6P . s}J . % @ 3 X @ x6P  x}J .  @ 3 J @ JA S @ s}+e%. , . % X @ x}+e%. , .  J @ JA S @ s}2 +e%. ,  % X @ x}2 +e%. ,   PA _@ _ }. .}e e%

zkhuh e>  duh wkh forvhg0hfrqrp| htxlydohqwv ri e dqg 4<1

4;_{Wkh zhljkwv xvhg wr fdofxodwh wkh djjuhjdwh vkrfnv duh dvvxphg wr eh wkh vdph wkh HFExvhv zkhq lw} kdv wr frpsxwh lwv srolf| uhvsrqvh> wklv dvvxpswlrq lv qrw xquhdolvwlf +wkh zhljkwv frxog eh wkh qdwlrqdo JGSv iru h{dpsoh, dqg doorzv iru d fohduhu h{srvlwlrq/ exw lw lv lq qr zd| hvvhqwldo1

4<_{Wkh forvhg hfrqrp| htxlydohqwv fdq eh fdofxodwhg e| vhwwlqj b}

wr xqlw|1 Wkhlu dqdo|wlfdo h{suhvvlrq lv

Erwk lq fdvh ri d v|pphwulf vkrfnru dq dv|pphwulf vkrfnlq frxqwu| l/ sulfhv ru xqhp0 sor|phqw uhpdlq xqdowhuhg dw wkh djjuhjdwh ohyho1 Diwhu d sulfh vkrfn +%A 3, >iru hyhu|  5

+3> 4,/ wkhqS @ 3> S A 3> S ? 3> X @ X @ X @ 3> PA ? 31 Diwhu dq lqfuhdvh lq xqhp0

sor|phqw + A 3, >iru hyhu|  5 +3> 4,/ wkhqS @ S @ S @ 3> X @ 3> X A 3> X ? 3> PA ? 31

Lq erwk fdvhv/ wkh vkrfnlv sduwldoo| wudqvodwhg wr wkh rwkhu frxqwu|/ zkloh wkh frqvhtxhqfhv rq wkh rwkhu yduldeoh duh }hur1

Wkh lqyroyhphqw ri wkh HFE lq wkh vwdelol}dwlrq lv ri wkh vdph rughu ri pdjqlwxgh ri lqirupdo frrshudwlrq1 Wkh wrwdo vprrwklqj ri glvwxuedqfhv lv gxh wr wkh idfw wkdw qrz wkh uhvsrqvh ri wkh HFE lv frpsohwho| lqwhuqdol}hg/ dqg wkhuhiruh wkh mrlqw vfdo dxwkrulw| fdq ghflgh rq zklfk srlqw ri wkh HFE Ehvw Uhvsrqvh lw zdqwv wr eh srvlwlrqhg1 Wkh iroorzlqj slfwxuh vkrzv wkdw wkh rqo| srlqw lq zklfk wkh EU ri J dqg HFE lqwhuvhfw lv wkh ruljlq1

U P BR_ECB Formal coordination λ=1 0 ₁ 2 L_G BR_G

Vxejdph Shuihfw Htxloleulxp dqg Qdvk Htxloleulxp Rqh reylrxv remhfwlrq zrxog eh wkdw wkh edfnzdug lqgxfwlrq vwru| lv qrw uhdoo| fuhgleoh lq wklv fdvh/ ehfdxvh d uhlqirufhg Hxurjurxs zrxog hyroyh lq vrphwklqj vlplodu wr d htxdo lqwhuorfxwru wr wkh HFE1 Dv d pdwwhu ri idfw/ zkhq wkh ghflvlrq derxw vfdo srolf| lv wdnhq dv li wkhuh zdv d vlqjoh dxwkrulw|/ wkh edfnzdug lqgxfwlrq vroxwlrq dozd|v frlqflghv zlwk wkh Qdvk Htxloleulxp +QH, ehwzhhq Jv dqg HFE1 Lq wklv vlpsoh jdph lw grhv qrw pdnh d glhuhqfh zkhwkhu wkh HFE pryhv odvw +Vxejdph Shuihfw Htxloleulxp, ru dw wkh vdph wlph +Qdvk Htxloleulxp,/ ehfdxvh lq erwk fdvhv wkh qdo rxwfrph lv wrwdo vprrwklqj ri vkrfnv/ lq wkh rqo| sodfh zkhuh wkh wzr EU lqwhuvhfw1 Iru wkh rqh frxqwu| fdvh +ru wkh Hxurjurxs fdvh, wkh rughu ri wkh pryhv lv luuhohydqw1 e' d#!Rjo jknR#jc ' kj # jknR#j 53

616 Qhjdwlyh frruglqdwlrq

Qhjdwlyh frruglqdwlrq ghqrwhv frpprqo| djuhhg uxohv wr suhyhqw vfdo srolf| iurp ryhu0 exughqlqj wkh prqhwdu| srolf|1 Fxuuhqwo|/ wkh Vwdelolw| dqg Jurzwk Sdfw suhyhqwv wkh hphujhqfh ri odujh sxeolf ghflwv dqg wkh uhvxowlqj wkuhdw wr sulfh vwdelolw|1 Lq wkh iroorz0 lqj vhfwlrq wkh lpsohphqwhg VJS zloo eh frpsduhg zlwk d glhuhqw rqh wr vkrz wkdw lw lv idu iurp ehlqj rswlpdo/ erwk iurp wkh srlqw ri ylhz ri vwdelol}dwlrq dqg iurp wkh srlqw ri ylhz ri wkh HFE1

61614 Wkh Vwdelolw| dqg Jurzwk Sdfw +VJS,

Wkh VJS lpsolhv wkdw wkh ohyho ri vfdo h{sdqvlrq lv erxqghg deryh e| d {hg ohyho/ vd| e| J iru wkh zkroh xqlrq1 Zkhq wkh frqvwudlqw lv qrw elqglqj wkh vroxwlrq lv rqh ri wkrvh ghvfulehg deryh1 Jlyhq wkdw wkh jryhuqphqwv duh uhodwlyho| pruh frqfhuqhg derxw xqhpsor|phqw wkdq wkh HFE/ wkh uhvxow ri ohwwlqj wkhp dfw iuhho| zrxog dozd|v eh d uhvwulfwlyh srolf| e| HFE1 Wkh udwlrqdoh ri wkh VJS lv wr olplw wkh srwhqwldo lqyroyhphqw ri HFE lq vkruw uxq vprrwklqj e| sxwwlqj d fds rq wkh vfdo h{sdqvlrq wkdw jryhuqphqwv duh doorzhg wr gr1 Lq wkh fdvh ri qr frrshudwlrq53_/

J @ plq+e%. , > J

J @ plqe%. > J

P7 _{@ }

}+J. J,  e+%. %, . . 

 _}J   _e+%. %, . . 

Wkh iroorzlqj slfwxuh vkrzv wkh udwlrqdoh iru wkh VJS1 Diwhu d vkrfnlq l wkdw ohdgv wr R/ wkh lqwhudfwlrq dprqj jryhuqphqwv zrxog surgxfh Q dv qdo rxwfrph1 Li wkh VJS olplwv wkh h{sdqvlrq ri hdfk ri wkhp/ wkh wrwdo vfdo h{sdqvlrq lv olplwhg wr V? +wkh pd{lpxp

shuplwwhg e| wkh Sdfw iru frxqwu| l/ wkh EU wr l iru frxqwu| m,1

53_{Wkh fdvh ri lqirupdo frrshudwlrq lv qrw dqdo|wlfdoo| h{srvhg ehfdxvh wkh dujxphqw iroorzv h{dfwo| wkh} vdph olqh1 Wkh rqo| glhuhqfh lv wkdw wkh fds rq wkh ghflw lv pruh xvhixo ehfdxvh lw kdv wkh dgglwlrqdo hhfw ri olplwlqj wkh vwudwhjlf hvfdodwlrq ri ghflwv w|slfdo ri wkh QH1

Rationale for the SGP G_i G_j BR_Gj BR_Gi N O N Sn SGP BOX Sn T

Lqwhudfwlrq zlwk srvlwlyh frruglqdwlrq Dq lpsruwdqw srlqw wr vwuhvv lv wkdw qhjdwlyh frruglqdwlrq +xsshu erxqgv wr vfdo h{sdqvlrq/ olnh lq wkh VJS, ehfrphv ohvv hhfwlyh li frxsohg zlwk irupdo srvlwlyh frruglqdwlrq1 Wklv phdqv wkdw wkh VJS frxog eh irupdoo| pdlqwdlqhg exw zrxog orrvh vrph ri lwv srwhqwldo vkrxog wkh phpehu vwdwhv pryh wr d irupdol}hg surfhvv ri vfdo frruglqdwlrq1

Wkh h{shfwhg ydoxh ri wkh uhvwulfwlrq ri wkh VJS lv d phdvxuh ri wkh srwhqwldo surwhfwlrq wkdw wkh HFE fdq uhfhlyh iurp wkh frqvwudlqwv ri wkh Sdfw1 Lq dsshqgl{ lw lv suryhg wkdw wklv ydoxh lv orzhu zkhq irupdo frruglqdwlrq lv sxw lqwr sodfh1 Wkh uhdvrq lv wkdw/ lq devhqfh ri irupdo frrshudwlrq/ wkh olplw elqgv hyhu| frxqwu| vhsdudwho|/ zkloh lq irupdo frruglqdwlrq wkh sdfw rqo| frqwurov wkh ryhudoo txdqwlw| JA_{1 Zkhq wkh srolflhv duh frpprqo| uxq/ doo}

wkh frxqwulhv uxq wkh vdph +shufhqwdjh, ghflw/ qr pdwwhu zkdw wkhlu sulydwh vkrfnfdq eh/ dqg doo klw wkh frqvwudlqw dw wkh vdph wlph ru qrw dw doo1 Lq rwkhu zrugv/ wkh vfdo dxwkrulwlhv eruurz iurp hdfk rwkhu wkh xqxvhg pdujlqv ri iuhhgrp1

SGP and Formal Cooperation

Gi Gj Sn BR_Gj SGP BOX Sn Sc Sc

Wkhvh uhvxowv duh vkrzq dqdo|wlfdoo| lq dsshqgl{1 Khuh lw lv lpsruwdqw wr qrwlfh wkdw 55

wkh uhvxow lv h{wuhpho| jhqhudo= wkh srzhu ri d qhjdwlyh frqvwudlqw olnh wkh VJS lv dozd|v dqg frqvlghudeo| zhdnhqhg zkhq wkh vfdo dxwkrulwlhv fdq dfw wrjhwkhu +VSA V? dozd|v,1

Srvlwlyh irupdo frruglqdwlrq zhdnhqv gh idfwr wkh h{lvwlqj qhjdwlyh frruglqdwlrq1

Shuyhuvh hhfwv ri wkh VJS Wkh VJS frxog +vxusulvlqjo|, dovr ohdg wr d juhdwhu df0 wlylvp ri wkh HFE= lq wkh fdvh ri d elj xqhpsor|phqw vkrfn/ wkh HFE frxog kdyh lqfhqwlyhv wr lqfuhdvh wkh txdqwlw| ri prqh| lq suhvhqfh ri lqvx!flhqw vfdo uhdfwlrq1 Wkh jxuh ehorz vkrzv wkdw lq suhvhqfh ri d vwurqj glvwxuedqfh lq xqhpsor|phqw wkh HFE frxog ghflgh wr lqfuhdvh wkh txdqwlw| ri prqh| +5e $ 6e, ehfdxvh wkh VJS frqvwudlqv wkh qdwlrqdo jry0 huqphqwv1 Wkh slfwxuh dovr vkrzv wkdw wkh {hg fds wr vfdo h{shqglwxuh lpsohphqwhg lq wkh VJS idyruv wkrvh frxqwulhv zklfk kdyh ehhq klw e| d oljkw glvwxuedqfh ryhu wkrvh zkr uhdoo| zrxog qhhg wr xvh wkh vfdo ohyhu hyhq dffruglqj wr wkh frqvhuydwlyh mxgjhphqw ri wkh HFE1 Zkloh wkh pruh oxfn| frxqwulhv klw e| d vpdoo vkrfn duh doorzhg wr suryrnh xqqhfhvvdu| lq dwlrq +5d,/ wkrvh lq uhdo qhhg duh irufhg wr zdlw lq +5e, iru dq lqwhuyhqwlrq +5e $ 6e, ri wkh HFE1 Vxfk lqwhuyhqwlrq fdqqrw eh jlyhq iru judqwhg/ ehfdxvh lw ghshqgv rq wkh ryhudoo vlwxdwlrq lq wkh xqlrq> ixuwkhupruh/ lw zrxog eh frvwo| ehfdxvh wkh prqhwdu| vwdqfh kdv pruh hhfw rq sulfhv wkdq rq xqhpsor|phqw1 Srlqw +6e, kdv pruh lq dwlrq dqg pruh xqhpsor|phqw wkdq +6e9_,1

Is the SGP too rigid?

U P BR_ECB 0 _1a SGP 1b 2a 2b 3b 3b*

Jlyhq wkh h{shulhqfh ri wkh qdwlrqdo jryhuqphqwv ehiruh Pddvwulfkw ehfdph elqglqj/ lw lv fhuwdlq wkdw wkh vfdo glvflsolqh lpsrvhg e| wkh VJS frqwulexwhv wr olplw wkh h{whqw ri vkruw uxq lqwhuyhqwlrqv ri wkh HFE1 Vwloo/ lw dsshduv wr eh dq h{wuhpho| uljlg ghylfh/ uvw ehfdxvh lw lpsrvhv duelwudu| olplwv/ dqg wkhq ehfdxvh lw kdv wkh xqsohdvdqw frqvhtxhqfh ri doorzlqj xqqhfhvvdu| h{sdqvlrq e| vrph zkloh lpshglqj wkh qhfhvvdu| lqwhuyhqwlrq zkhuh wklv zrxog eh qhfhvvdu|1

61615 Frpsdulqj wkh VJS zlwk d Ioh{leoh VJS

Wkh VJS fdq eh frpsduhg zlwk d vlplodu rqh edvhg rq glhuhqw fulwhuld1 Vxssrvh wkdw wkh HFE frppxqlfdwhv lwv suhihuhqfhv lq whupv ri pd{lpxp lq dwlrq doorzhg iru hdfk yduldwlrq lq xqhpsor|phqw +,1 Hyhu| phpehu vwdwh lv wkhq frqvwudlqhg wr dgrsw d vfdo srolf| wkdw/ dffruglqj wr wkh frpprqo| djuhhg prgho/ nhhsv wkh wdujhw yduldeohv zlwklq wkh olplwv dqqrxqfhg e| wkh Fhqwudo Edqn1 Lq rwkhu zrugv/ wkh olplw J @ J rq vfdo

h{sdqvlrqv lv uhsodfhg e| a

J v=w= ^S+J> %> , @   X+J> %> ,` ;l

Wkh h{fhvvlyh ghflw surfhgxuh fdq eh dssolhg wr qrq frpso|lqj vwdwhv h{dfwo| dv lq wkh fxuuhqw VJS1

Wkh uhvxowlqj srolflhv iroorz gluhfwo| iurp wkh vhwxs dqg gr qrw qhhg fdofxodwlrqv1 Wdnh dv dq h{dpsoh d vkrfnwkdw lqfuhdvhv sulfhv ru xqhpsor|phqw1 Wkh qdwlrqdo jryhuqphqwv/ ehlqj pruh surqh wr dffrpprgdwh vkrfnv/ dozd|v xvh wkh zkroh glvfuhwlrqdu| pdujlq do0 orzhg e| wkh Sdfw1 E| grlqj wklv/ wkh| shuihfwo| vxevwlwxwh wkh HFE lq wkh vkruw0uxq vwdelol}dwlrq ixqfwlrq1 Wkh HFE wkhq grhv qrw qhhg wr uhdfw wr lq dwlrqdu| suhvvxuhv dqg lv deoh wr frqfhqwudwh rq wkh orqj uxq vwdelolw| ri sulfhv1

Iurp wkh srlqw ri ylhz ri htxlw|/ wklv fulwhulrq kdv dovr wkh dgydqwdjh ri doorzlqj wkrvh frxqwulhv wkdw duh klw e| eljjhu vkrfnv d odujhu pdujlq ri lqwhuyhqwlrq1 Rq wkh rwkhu kdqg/ wkhuh lv qr prqhwdu| vslooryhu wkdw fdq srvvleo| dpsoli| wkh hhfwv ri wkh ruljlqdo vkrfn dqg wkh uhvsrqvhv ri wkh jryhuqphqwv> wkh sursdjdwlrq ri vkrfnv ri wkh Qdvk Htxloleulxp lv vwrsshg dw wkh uvw vwdjh1 SGP Another SGP? U P BR_ECB 0 _{1a 1b} 2a 2b 57

617Wkh lqwhudfwlrq ri srvlwlyh dqg qhjdwlyh frruglqdwlrq

Lq wkh iroorzlqj vhfwlrq d vlpxodwlrq looxvwudwhv krz hohphqwv ri srvlwlyh dqg qhjdwlyh frruglqdwlrq lqwhudfw1

D prqhwdu| xqlrq ri 45 frxqwulhv lv vlpxodwhg1 Wkh frxqwulhv kdyh zhljkwv wkdw fruuh0 vsrqgv wr wkh JGSv ri wkh frxqwulhv wkdw sduwlflsdwh lq wkh HPX1 Dv lq wkh wkhruhwlfdo sduw/ L irfxv rq wkh prqhwdu| h{whuqdolwlhv/ wkhuhiruh doo wkh frxqwulhv kdyh wkh vdph vwuxfwxuh +s6 @ 5> s} @ x} @ x6 @ 4, wkdw uhvshfwv wkh uhtxluhg k|srwkhvlv ri doorfdwlrq ri lqvwux0

phqwv1

Iru hdfk frxqwu| dqg hdfk shulrg L fuhdwh d vkrfnwr sulfhv dqg rqh wr hpsor|phqw1 Doo wkh vkrfnv duh gudzq iurp vwdqgdugl}hg qrupdo glvwulexwlrq dqg wkh| duh L1L1G1 D vhulhv ri Prqwh Fduor h{shulphqwv lv wkhq uxq lq rughu wr vhh zklfk iudphzrunlpsrvhv wr wkh HFE wkh eljjhu txdqwlw| ri vkruw whup vwdelol}lqj lqwhuyhqwlrqv1 Wkh uhvxowv duh vxppdul}hg lq wkh wdeoh ehorz zkhuh wkh glhuhqw ohyhov ri srvlwlyh frruglqdwlrq +urzv, lqwhudfw zlwk pruh ru ohvv elqglqj VJS {hg olplwv1 Iru hyhu| frpelqdwlrq wkh phdq dqg yduldqfh ri wkh vfdo dfwlylvp ri d frxqwu| zlwk zhljkw 314: +olnh Lwdo|, duh uhsruwhg1 Lq wkh iroorzlqj urz wkh dfwlylvp ri wkh HFE lv ghvfulehg1 Ilqdoo|/ zkhuh dssolfdeoh L uhsruwhg wkh shufhqwdjh ri fdvhv lq zklfk wkh VJS dfwxdoo| frqvwudlqhg wkh vfdo srolf| ri wkh frxqwu|1

Qr VJS VJS 5 VJS 4 Frruglqdwlrq H{s Ydu H{s Ydu H{s Ydu Qrqh Ilvfdo 135 183 0134 183 013; 17: Prqhwdu| 3 3 3 3 134 3 ( fxw 0 317( 91:( Qdvk Ilvfdo 3 4198 0143 416; 0164 1<9 Prqhwdu| 3 183 13: 16< 154 157 ( fxw 0 618( 58( Irupdo Ilvfdo 0134 1;: 3 1<: 013< 1:7 Prqhwdu| 3 167 3 16: 139 164 ( fxw 0 615( 4819(

Wkh pdlq sureohp lv zkhq wkh HFE ihhov lw kdv wr lqwhuyhqh +wr dedqgrq lwv orqj uxq srolf|, wr frqwudvw zkdw lw shufhlyhv wr eh dq h{fhvvlyh lq dwlrq ri wkh Xqlrq1 D pruh ghwdlohg uhsruw +rq uhvwulfwlyh prqhwdu| srolf| rqo|, lv suhvhqwhg lq wkh wdeoh ehorz1 Wkh vdph wdeoh +lq judsklfdo irup, dovr dsshduv lq wkh frqfoxvlrqv1

Vl}h ri qhjdwlyh lqwhyhqwlrqv Qr VJS VJS5 VJS4 Qrqh 4< 54 48 Qdvk 5;< 564 <9 Irupdo 584 573 543

Wkh ryhudoo vl}h ri wkh HFE uhvwulfwlrqv lq 4333 wuldov

Wkh uvw revhuydwlrq lv wkdw wkh wkhruhwlfdo fdvh ri qr0frrshudwlrq qr0lqirupdwlrq sur0 gxfhv yhu| vpdoo vfdo uhvsrqvhv frpsduhg wr wkh rwkhuv1 Lq wklv fdvh wkh VJS grhv qrw kdyh d uroh/ dqg rqh fdq vhh wkdw vhwwlqj wkh fhlolqj J wr 5 dqg wkhq wr 4 fkdqjhv yhu| olwwoh wkh rxwfrph1

Wkh vlpxodwlrq looxvwudwhv wkh wkhruhwlfdo suhglfwlrqv> lq devhqfh ri VJS/ wkh vfdo h{sdqvlrqv lpsolhv dq lqyroyhphqw ri wkh HFE lq vkruw0uxq vwdelol}dwlrq wkdw lv qrw rqo| rqh rughu ri pdjqlwxgh eljjhu wkdq wkh qr0frrshudwlrq fdvh/ exw dovr eljjhu wkdq wkh fdvh ri irupdo frruglqdwlrq1 Rq wkh rwkhu kdqg/ wkh VJS hhfwlyho| frqvwudlqv wkh ghflw ri wkh phpehu frxqwulhv lq d zd| wkdw olplwv wkh lqyroyhphqw ri wkh fhqwudo edqn+iurp 5;< wr <9 lq wkh uljkw wdeoh,1

Wkh VJS ehfrphv doprvw luuhohydqw zkhq wkh frxqwulhv fdq dfw dv lw wkh| zhuh rqh> wkh fhlolqj J olplwv wkh lqyroyhphqw ri wkh HFE iurp 584 wr 543 dqg fdqqrw gr ehwwhu/ ehfdxvh wkh vfdo dxwkrulwlhv duh qrz deoh wr frruglqdwh lq d zd| wkdw doorzv wkhp wr wdnh ixoo dgydqwdjh ri wkh iuhhgrp wr vshqg ohiw e| wkh Sdfw1

7Frqfoxvlrqv

Lq wkh suhvhqw sdshu wkh txhvwlrq ri zklfk irup ri vfdo frruglqdwlrq zrxog lpso| wkh ohdvw vwdelol}lqj hruw e| wkh HFE kdv ehhq dgguhvvhg1 Iurp wkh dqdo|wlfdo ghyhorsphqw ri wkh jdph/ lw dsshduv wkdw wzr pdlq irufhv hqwhu lqwr sod|=

 rq wkh rqh kdqg/ wkh dzduhqhvv ri wkh lqwhusod| ri vfdo srolflhv dqg prqhwdu| srolflhv e| wkh sod|huv fdq vwduw txlwh frpsoh{ lqwhudfwlrqv/ wkdw ohdg wr wkh pxowlsolfdwlrq ri wkh lqlwldo glvwxuedqfhv dqg wr wkhlu sursdjdwlrq wr wkh zkroh xqlrq wkurxjk prqhwdu| h{whuqdolwlhv1 Lqirupdwlrq zlwkrxw frruglqdwlrq ohdgv wr srolf| lqgxfhg lqvwdelolw|1  rq wkh rwkhu kdqg/ d frpsohwh frruglqdwlrq zrxog lqwhuqdol}h vxfk hhfwv dqg dyrlg

sursdjdwlrqv/ zkloh jlylqj edfnwr wkh vfdo dxwkrulwlhv dw ohdvw rqh ghjuhh ri iuhhgrp lq vfdo srolf| wr frxqwhudfw frpprq glvwxuedqfhv1 Wkh jdph rxwolqhg wkh ulvnwkdw frpsohwh frruglqdwlrq pd| zhdnhq wkh VJS1

 Lq wkh fdvh ri irupdo frruglqdwlrq/ erwk wkh VJS dqg wkh QH lpso| suhvvxuh rq wkh HFE dqg wkh frpsohwh vprrwklqj ri vkrfnv1 Wklv uhvxow frqwudglfwv wkh frpprq zlvgrp dffruglqj wr zklfk srolf| frruglqdwlrq frpsulvlqj erwk vfdo dqg prqhwdu| dxwkrulwlhv zrxog lpso| d orw ri suhvvxuh rq wkh HFE/ zkloh irupdo vfdo frruglqdwlrq dorqh zrxog qrw1

Qhjdwlyh frruglqdwlrq lv vrphzkdw vlpsohu/ dqg wkh uxohv ri wkh jdph duh ghflghg rqfh dqg iru doo/ wkhuhiruh lw lv hdvlhu wr dsso|1 Iru wkhvh uhdvrq lw kdv suredeo| ehhq fkrvhq wr hqvxuh olplwhg oldelolw| ri wkh HFE lq d vwudwhjlf frqwh{w zklfk zdv qrw +dqg suredeo| vwloo lvq*w, frpsohwho| xqghuvwrrg1 Wkh vlpxodwlrqv xqghuolqh erwk wkh lpsruwdqfh ri qhjdwlyh frruglqdwlrq dqg wkh gdqjhu wkdw dq h{fhvvlyh srvlwlyh frruglqdwlrq frxog pdnh lw lqhhfwlyh> dv rq fdq revhuyh/ wkh VJS lv hhfwlyh lq uhgxflqj wkh lqyroyhphqw ri wkh HFE/ xqohvv wkh vfdo ghflvlrqv duh irupdoo| frruglqdwhg1

Wkh suhvhqw olplwv vwdwhg lq wkh VJS vhhp vrphzkdw lq h{leoh> wr wkh h{whqw wkdw wkh VJS lv ghvljqhg wr olplw wkh oldelolw| ri wkh HFE/ lw vkrxog eh dovr ghvljqhg dffruglqj wr wkh suhihuhqfhv ri wkh HFE lwvhoi1 D vlpsoh h{dpsoh vkrzhg wkdw pruh h{lelolw| fdq eh judqwhg lq vxfk d zd| wr rewdlq dw wkh vdph wlph pruh vwdelol}dwlrq dqg pruh lqghshqghqfh ri wkh Fhqwudo Edqn1

714 Srvvleoh h{whqvlrqv

Wkh jrdo ri wkh sdshu zdv wr rxwolqh d yhu| vshflf phfkdqlvp wkdw pd| ghwhuplqh dq xqiruhvhhq ohyho ri suhvvxuh rq wkh HFE/ dorqj zlwk d odujhu xvh ri vfdo srolf|/ vkrxog vwurqjhu vfdo frruglqdwlrq eh lpsohphqwhg lq wkh HPX1 Pdq| h{whqvlrqv ri wkh prgho duh srvvleoh lq rughu wr pdnh lw pruh uhdolvwlf1 Wkh uvw/ reylrxv rqh/ zrxog eh wr doorz iru glhuhqw suhihuhqfhv qrw rqo| rq vprrwklqj/ exw dovr rq wkh wdujhw ohyho ri xqhpsor|phqw1 Gluhfw h{whuqdolwlhv ri vfdo srolf| frxog eh dovr lpsohphqwhg/ dqg wkhlu hhfw zrxog vprrwk wkh vnhswlfdo frqfoxvlrqv derxw srvlwlyh frruglqdwlrq1 Zh qhjohfwhg wkhp khuh iru fodulw| ri h{srvlwlrq dqg ehfdxvh wkhlu hhfw vrphkrz dggv xs wr wkh rqh ghvfulehg/ zlwkrxw d vwurqj lqwhudfwlrq ehwzhhq wkh wzr1

Vwuxfwxudo glhuhqfhv lq wkh qdwlrqdo pdunhwv lv suredeo| wkh prvw lqwhuhvwlqj h{whqvlrq1 Wklv zloo eh wkh remhfw ri d iruwkfrplqj sdshu/ lq zklfk wkhvh glhuhqfhv duh exlow0lq lq wkh irup ri d wklug fdwhjru| ri sod|huv/ zrunhu*v xqlrqv1

Pdq| rwkhu h{whqvlrqv kdyh ehhq vxjjhvwhg/ exw wkh| duh suredeo| ehwwhu ghdow zlwk lq d vhsdudwh sdshu1

8 DSSHQGL[

81314 Iluvw rughu frqglwlrq iru wkh HFE

E| wrwdo glhuhqwldwlrq ri wkh IRF ghulyhg iurp +6,/ wkh orfxv ri wkh rswlpdo uhvsrqvh ri wkh HFE lv ghvfulehg e|=

# _ [ ' S $ @ Y6Y YR Y6 # _ [ ' X $ +9, Jlyhq wkdw wkh HFE lv wkh odvw sod|hu/ Y

Y6@Y6YR lv vlpso| !R661

81315 Iluvw rughu frqglwlrq iru jryhuqphqw J

Wkh glhuhqwldwlrq ri wkh uvw rughu frqglwlrq 

.s} s6}^s6P +J> %> , . s}J. %` @

@ x6} x}+x6P +J> %> ,  x}J. ,

iru hdfk ri wkh jryhuqphqwv ohdgv wr=

S@  Y Y} YR Y} X +:, 5;

Iurp wkh ghqlwlrqv ri S> X dqg P+,/ dqg xvlqj edfnzdug lqgxfwlrq= Cs Cj @ C Cj +s6P +J> %> , . s}J. %, @ .s} s6} Cx Cj @ C Cj +x6P +J> %> ,  x}J. , @ x6} x} 81316 Wkh v|pphwulf Qdvk htxloleulxp J @ +_e%. , .  se%. s_  . _}k_e%. .  se%. s_ l 4  2 } J @  e%. .  se%. s  . } k +e%. , .  se% . s l 4  2_} P @ PJ. J> %. %> . @ @  _{4  }4 ₂ }  . s_  _}. s_.   _}. _  _ .  _{4  }4 ₂ }  s_.   }. . s_  }.    .  _{4  }4 ₂ }  e. se  }. e. se  } e  % .  _{4  }4 ₂ }  e. se  }. e. se  } e  % 81317 Irupdo frruglqdwlrq JA @ e+%. %, . .  PA @ }.  . e. }e+%. %, S @ s6P . s}J . +%. %, @ 3 X @ x6P  x}J .. @ 3 J @ JA S @ s}e+%. %, . . . % +%. %, X @ x}e+%. %, . . . .  J @ JA S @ s}e+%. %, . . . % +%. %, X @ x}e+%. %, . . . . 

814 Fdofxodwlrq ri vrph vljqv

Wkhvh vljqv duh lpsruwdqw lq wkdw wkh| doorz pruh frpsoh{ fdofxodwlrqv odwhu1 5<

Vrph edvlf lghqwlwlhv Wkh uvw htxdwlrq lv mxvw d glhuhqw yhuvlrq ri wkh k|srwkhvlv

R6 6 A

R}

}> zkhq } @ 3 wkh uhodwlrq krogv zlwk htxdolw|/ zkhq } lv srvlwlyh wkh k|srwkhvlv lv

wuxh zlwk vwulfw lqhtxdolw|1 Wkh rwkhu lghqwlwlhv duh wkh vdph vhhq ehiruh1 s6 @ +4 . }, x6_R}_} } @  k  R2_6nq2₆ l +x6x} s}s6, e@  k  R2_6nq2₆ l +s6,  @ . k  R2_6nq2₆ l x6  @ 4   Hhfw ri h{shqglwxuh rq sulfhv Vljqs6}. s}@ vljq s}b 2 }qnbR2}n2bR2}5nb5q2}nbR2}52!R2}!2R}25!R2}52!q2} R2_}n2R2_}5nR2_}52_nq2_} = Wkh qxphudwru ri wkh iudfwlrq lv x2 }. s2}. 5s2}} . }x}2. s2}}2+ 4, dozd|v qhj0

dwlyh1 Wkhuhiruh wkh frh!flhqw lv dozd|v srvlwlyh1

Hhfw ri h{shqglwxuh rq xqhpsor|phqw Vljqx6} x}@ vljq x}!b 2 }q!bR2}!bR2}5nR2}n2R2}5nR2}52nq2} R2 }n2R2}5nR2}52nq2} =

Wkh qxphudwru lv htxdo wr +4,x2} . s2}. s}2}.s2}} .s2}}2 dozd|v srvlwlyh1 Wkhuh0

iruh wkh frh!flhqw lv qhjdwlyh

D vkrfn wr xqhpsor|phqw ohvv wkh lqwhuyhqwlrq ri wkh HFE Vljq +4  x6, @

+4  ,x2}. s2}. 5s2}} . s2}}2 lv dozd|v srvlwlyh1

D vkrfn wr sulfhv ohvv wkh lqwhuyhqwlrq ri wkh HFE Vljq +4  s6e, @

vljq !R2}!2R2}5!R2}52!q2}nbR2}n2bR2}5nbR2}52 R2_}n2R2_}5nR2_}52_nq2_} =

Wkh qxphudwru ri wkh iudfwlrq lv s2

}. 5s2}} . s2}}2+ 4,  x2} dozd|v qhjdwlyh1

Wkhuhiruh wkh frh!flhqw lv dozd|v srvlwlyh1

815 Frh!flhqwv ri jryhuqphqw uhdfwlrq ixqfwlrq zkhq wkh doorfdwlrq ri

lqvwuxphqwv lv lqglhuhqw

Vljq ri wkh frh!flhqw ri  = wkh sdudphwhu lv dozd|v srvlwlyh

Vljq +s6,s6}. s} x6} x}+4  x6,

@ vljq s2} . s2}  x2} . x2}+4 . ,_R2} }nq2}

Nqrzlqj wkdw



s2} . s2}  x2} . x2}@ +4  , x2}.s2}+  , A 3 lv wuxh/ wkh zkroh

sdudphwhu lv srvlwlyh1

Vljq ri wkh frh!flhqw ri  = wkh sdudphwhu lv dozd|v qhjdwlyh

+s6,s6}. s} x6} x}+x6, @

 s2

}. x2}+ 4, x}_R}2_nqb 2_} ? 3 dozd|v1

Vljq ri wkh frh!flhqw ri %= wkh vljq ri wkh frh!flhqw ri %ghshqgv rq wkh vl}h ri wkh

h{shfwhg uhdfwlrq ri wkh HFE wr wkh vkrfn %/ wkdw lv rq 1 Zkhq wkh vl}h ri wkh frxqwu|

lv vpdoo hqrxjk wkh vljq lv qhjdwlyh1 Vljq +4  s6e,s6}. s} x6} x}+x6e,@ vljq s2 } x2}. s2}. x}2+4 . ,_R2_}nqR} 2_} @ vljq s2 } x2}. s}2. x2}@s2}. x2}s2}. x2}

qhjdwlyh zkhq  lv vpdoo hqrxjk +xqohvv  lv yhu| forvh wr rqh,1

Vljq ri wkh frh!flhqw ri %= wkh sdudphwhu lv dozd|v srvlwlyh

+s6e,s6}. s} x6} x}+x6e,@

@ s2

}. x2}+ 4, s}_R}2_nqb 2_} A 3 dozd|v srvlwlyh1

Vljq ri wkh frh!flhqw ri J= wkh sdudphwhu lv dozd|v srvlwlyh

Vljq .s6} s6}. s}. x6} x} x6}@

@ s2

}. x2}+ 4,  A 3 dozd|v srvlwlyh

Wkh frh!flhqw ri J lv ohvv wkdq rqh li } A 31 Wkh frh!flhqw ri J lv ohvv wkdq rqh

li dqg rqo| li wkh h{suhvvlrq ehorz lv qhjdwlyh= 

s6} s6}. s}. x6} x} x6}

x6} x}2 .s6}. s}2



Wkh odpegdv vxp xs wr rqh/ vr wkh h{suhvvlrq fdq eh uhzulwwhq dv  x6} x} x6} x} .s6}. s} s6} s} ru  x2}. s2}. }s2} s}2 5}s2} }2s2} x2}}s2}+4 . }, k 2 }nR2} +R2_}n25R2_}n52_R2_}nq2_},2

Zkhq wkh }hwd lv }hur +wkh frqglwlrq rq lqvwuxphqwv krogv rqo| zlwk htxdolw|, wkh zkroh h{suhvvlrq lv }hur dqg wkh frh!flhqw lv h{dfwo| rqh1 Qr QH h{lvwv1

Zkhq }hwd lv srvlwlyh/ wkhq wkh uhohydqw whup iru wkh vljq lv 

x2}. s2}. }s2} s2} 5}s2} }2s2} x2}@

}2_s2

}.5s2}. s2}} .x2}. s2}+ 4,

wklv sduw kdv qhjdwlyh vljq1 Wkhuhiruh wkh frh!flhqw lv vwulfwo| ohvv wkdq rqh/ dqg wkh QH h{lvwv lq wkh fdvh ri srvlwlyh lqirupdo frrshudwlrq1

816 Srvlwlyh irupdo frruglqdwlrq zhdnhqv wkh VJS

Wklv dsshqgl{ vkrzv wkdw qhjdwlyh frruglqdwlrq +xsshu erxqgv wr vfdo h{sdqvlrq/ olnh lq wkh VJS, ehfrphv ohvv hhfwlyh li frxsohg zlwk irupdo srvlwlyh frruglqdwlrq1

Vxssrvh wkh xqlrq0zlgh olplw wr wkh ghflw lv J> dqg fdoo wkh dfwxdo ghflwv J dqg

J1Wkh ghqvlw| ixqfwlrq ri +J> J, lv i +J> J,1

Lq devhqfh ri irupdo frrshudwlrq +qr frrshudwlrq ru vlpsoh h{fkdqjh ri lqirupdwlrq, wkh olplw elqgv hyhu| frxqwu| vhsdudwho|/ wkhuhiruh wkh qdwlrqdo fdsv duh J>  J1 Wkh

uhvwulfwlrq lpsxwdeoh wr wkh rshudwlrq ri wkh VJS lv 

J Jli J A J



J  Jli J A J

Zkhq wkhuh lv irupdo frruglqdwlrq/ wkh sdfw rqo| frqwurov wkh ryhudoo txdqwlw| JA_{1 Wklv}

fdq eh vhhq e| revhuylqj wkdw lq irupdo frruglqdwlrq J @ JA dqg J @ JA dozd|v/

wkhuhiruh zkhq JA _{ J lw lv dovr yhulhg wkdw J}

  J dqg J   J1

Wkh uhvwulfwlrq lpsxwdeoh wr wkh rshudwlrq ri wkh VJS lv wkhq 

J. J  Jli J. J  J1

Wkh h{shfwhg ydoxh ri wkh uhvwulfwlrq ri wkh VJS lv d phdvxuh ri wkh srwhqwldo surwhfwlrq wkdw wkh HFE fdq uhfhlyh iurp wkh frqvwudlqwv ri wkh Sdfw1 Wklv ydoxh lv orzhu zkhq irupdo frruglqdwlrq lv sxw lqwr sodfh1 Wr vkrz wklv/ wkh vsdfh +J> J, lv sduwlwlrqhg lq F @+J> J, = J. J  J> D @+J> J, = JA J> E @+J> J, = J A J G @ D q F H @ F q E I @ D ^ E J @ F q D K @ E q F 65

Wkhq wkh h{shfwhg ydoxh ri wkh uhvwulfwlrq lpsrvhg e| wkh Sdfw lv HJJ. J J @ ] (.8  J J i+,gJgJ . ] 8 CM  J J i+,gJgJ H8 Jo6@,J. J J @ ] .8 C  J. J J i+,gJgJ @ ] .8 C  J J.J J i+,gJgJ HJ H8 Jo6@, @ ] (  J J i+,gJgJ. ] M  J J i+,gJgJ ] .  J J i+,gJgJ  ] C  J J i+,gJgJ

Doo lqwhjudov lq wkh odvw h{suhvvlrq duh srvlwlyh/ h{fhswhg wkrvh ghqhg ryhu H dqg J dqg wkh rqh ghqhg ryhu I zklfk lv }hur1 Wkhq wkh vxp lv dozd|v srvlwlyh1

817UHIHUHQFHV

Ed|rxpl/ W1 dqg Hlfkhqjuhhq/ E1 +4<<6,/ Vkrfnlqj dvshfwv ri Hxurshdq prqhwdu| xqlrq/ lq I1 Wruuhv dqg I1 Jldyd}}l/ Dgmxvwphqw dqg jurzwk lq wkh Hxurshdq Prqhwdu| Xqlrq/ Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ ss1 4<6055<1

Ydq Dduoh E1 dqg Kxduw/ I1 +4<<:,/ Prqhwdu| dqg vfdo xqlfdwlrq lq wkh HX= d vw|ol}hg dqdo|vlv/ Z1S1 47</ Fhqwhu iru Hfrqrplf Vwxglhv/ Xqlyhuvlw| ri Pxqlfk/ Pxqlfk1

Ehhwvpd/ U1 dqg Eryhqehuj/ O1 +4<<8,/ Prqhwdu| xqlrq zlwk vfdo frruglqdwlrq pd| glvflsolqh srolf|pdnhuv/ Glvfxvvlrq Sdshu/ Fhqwhu iru Hfrqrplf Uhvhdufk/ Wlooexuj Xqlyhu0 vlw|1

Ervfd/ M1H1 dqg Ruwv/ Y1 +4<<4,/ Od frruglqdflrq gh srolwlfdv vfdohv hq ho pdufr gh xqd Xqlrq Hfrqrplfd | Prqhwduld/ ZS0HF <30391 Lqvwlwxwr Ydohqfldqr gh Lqyhvwljdflrqhv hfrqrplfdv/ Ydohqfld1

Exlwhu/ Zloohp/ Jldqfduor Fruvhwwl dqg Qrxulho Urxelql +4<<6,/ H{fhvvlyh Ghflwv= Vhqvh dqg Qrqvhqvh lq wkh Wuhdw| ri Pddvwulfkw/ Hfrqrplf Srolf| 49/ ss18:04331

Frpplvvlrq ri wkh Hxurshdq Frppxqlwlhv +4<<4,/ Wkh Hfrqrplfv ri HPX/ Hxurshdq Hfrqrp|/ Vshfldo Lvvxh Qr1 41

Gld}0Urogdq/ F1 +5333,/ Frruglqdwlrq ri vfdo srolflhv lq d prqhwdu| xqlrq/ Z1S1 5333236/ Ghsduwphqw ri hfrqrplfv/ Xqlyhuvlgdg Sxeolfd gh Qdyduud/ Sdpsorqd1

Gl{lw/ D1 dqg O1 Odpehuwlql +5333,/ Ilvfdo glvfuhwlrq ghvwur|v prqhwdu| frpplwphqw/ XFOD zrunlqj sdshu1

Hlfkhqjuhhq/ E1 +4<<:,/ Vdylqj Hxursh*v dxwrpdwlf vwdelol}huv/ Qdwlrqdo Lqvwlwxwh Hfr0 qrplf Uhylhz/Mdqxdu| 4<<:1

Jdwwl/ G1 dqg Ydq Zlmqehujhq/ F1 +5335,/ Fr0ruglqdwlqj Ilvfdo Dxwkrulwlhv lq wkh Hxur0 }rqh1 D Nh| Uroh iru wkh HFE/ R{irug Hfrqrplf Sdshuv 87/Mdqxdu| 53351

Pddvwulfkw Wuhdw| +4<<4,/ Wuhdw| rq Hfrqrplf dqg Prqhwdu| Xqlrq/ Ox{hperxuj= R!fh iru R!fldo Sxeolfdwlrqv ri wkh Hxurshdq Frppxqlwlhv1

Rdwhv/ Zdoodfh +4<:5,1 Ilvfdo Ihghudolvp1 Qhz \run= Kdufrxuw/ Eudfh/ Mrydqrylfk1 Slvdql0Ihuu|/ M1 +4<<4,1 Pdlqwdlqlqj d Frkhuhqw Pdfur0hfrqrplf Srolf| lq d Kljko| Gh0 fhqwudol}hg Ihghudo Vwdwh= Wkh H{shulhqfh ri wkh HF1 RHFG Vhplqdu rq Ilvfdo Ihghudolvp lq Hfrqrplhv lq Wudqvlwlrq/ Dsulo 506/ 4<<41

Wdq}l/ Ylwr +4<<9,1 Ilvfdo Ihghudolvp dqg Ghfhqwudol}dwlrq= D Uhylhz ri Vrph Hi0 flhqf| dqg pdfurhfrqrplf Dvshfwv1 Dqqxdo Zruog EdqnFrqihuhqfh rq Ghyhorsphqw Hfrqrplfv/ 4<<81 Zruog Edqn/ Zdvklqjwrq/ GF/ 5<806491

yrq Kdjhq/ Mÿujhq dqg Eduu| Hlfkhqjuhhq +4<<9,/ Ilvfdo Uhvwudlqwv/ Ihghudolvp dqg Hxurshdq Prqhwdu| Xqlrq= Lv wkh H{fhvvlyh Ghflw Surfhgxuh FrxqwhusurgxfwlyhB Dphu0 lfdq Hfrqrplf Uhylhz ;9 +Pd|,/ ss1467046;1

Zdovk/ Fol +4<<5,1 Ilvfdo Ihghudolvp= Dq Ryhuylhz ri Lvvxhv dqg d Glvfxvvlrq ri Wkhlu Uhohydqfh wr wkh Hxurshdq Frppxqlw|1 Ihghudolvp Uhvhdufk Fhqwuh Glvfxvvlrq Sdshu Qr1 45/ DQX1