View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Working Paper Series

Banking and the Political Support for
Dollarization

WP 00-12

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Huberto M. Ennis
Federal Reserve Bank of Richmond

Edqnlqj dqg wkh Srolwlfdo Vxssruw iru
Groodul}dwlrq
Kxehuwr P1 Hqqlv|
Uhvhdufk Ghsduwphqw
Ihghudo Uhvhuyh Edqn ri Ulfkprqg

Ihghudo Uhvhuyh Edqn ri Ulfkprqg Zrunlqj Sdshu Qr1 33045
Ghfhpehu 5333
MHO Qrv1 H8;/ I63/ J54
Nh|zrugv= groodul}dwlrq/ srolwlfdo htxloleulxp/ edqnlqj edlorxwv

Devwudfw
Lq wklv sdshu zh vwxg| groodul}dwlrq dv d frpplwphqw ghylfh wkdw wkh Fhq0
wudo Edqn frxog xvh wr dyrlg jhwwlqj lqyroyhg lq dq xqghvludeoh edqnlqj0vhfwru
edlorxw1 Zh vkrz krz d srolwlfdo surfhvv frxog lqgxfh dq htxloleulxp rxw0
frph wkdw glhuv iurp wkh rqh wkdw d ehqhyrohqw Fhqwudo Edqn zrxog zdqw wr
lpsohphqw1 Groodul}dwlrq wkhq frxog eh xvhg wr uhvwruh wkh hfrqrp| wr wkh
ehqhyrohqw rxwfrph1 Lq vr grlqj wkrxjk/ srolwlfdo vxssruw iru groodul}dwlrq eh0
frphv hvvhqwldo1 Iru rxu ehqfkpdun fdvh/ groodul}dwlrq grhv qrw kdyh hqrxjk
vxssruw wr eh dfwxdoo| lpsohphqwhg1 Exw zkhq zh vwxg| wkh lqwhudfwlrq dprqj
groodul}dwlrq/ wkh lqwurgxfwlrq ri lqwhuqdwlrqdo edqnv/ dqg wkh srolwlfdo surfhvv/
zh qg wkdw edqn lqwhuqdwlrqdol}dwlrq pd| khos wr dwwdlq wkh qhfhvvdu| srolwlfdo
vxssruw wkdw fdq pdnh groodul}dwlrq d yldeoh srolf|1
 Wkh

uvw gudiw ri wklv sdshu zdv suhsduhg/ zkloh wkh dxwkru zdv dw Fruqhoo Xqlyhuvlw|/ iru
wkh surmhfw Rswlpdo Prqhwdu| Lqvwlwxwlrqv iru Ph{lfr vsrqvruhg e| wkh Lqvwlwxwr Whfqroöjlfr
Dxwöqrpr gh Pì{lfr +LWDP,1 Wkh dxwkru zrxog olnh wr wkdqn Dohmdqgur Khuqäqgh} iru ydoxdeoh
frqyhuvdwlrqv dw wkh hduo| vwdjhv ri wklv vwxg|/ dqg Luhqh Eudpelood dqg Pduwlq Jhuydlv iru frpphqwv
rq d suhylrxv gudiw1 Doo huuruv duh p| rzq1 Wkh ylhzv h{suhvvhg khuh gr qrw qhfhvvdulo| uh hfw wkrvh
ri wkh Ihghudo Uhvhuyh Edqn ri Ulfkprqg ru wkh Ihghudo Uhvhuyh V|vwhp1
| H0pdlo= kxehuwr1hqqlvCulfk1iue1ruj

4

4

Lqwurgxfwlrq

Groodul}dwlrq/ ru wkh r!fldo dgrswlrq e| d iruhljq frxqwu| ri wkh XV groodu dv wkh
ohjdo flufxodwlqj oldelolw|/ lv wkh xowlpdwh h{suhvvlrq ri d {hg h{fkdqjh udwh v|vwhp1
Il{hg h{fkdqjh udwh uhjlphv kdyh ehhq h{whqvlyho| vwxglhg lq wkh olwhudwxuh1 Pxfk
ohvv hruw kdv ehhq ghyrwhg wkrxjk wr wkh vwxg| ri wkh dvshfwv wkdw pdnh groodul}dwlrq
glhuhqw iurp ohvv uljlg {hg h{fkdqjh udwh uhjlphv +vhh Ehuj dqg Eruhqv}whlq +5333,
iru d jhqhudo glvfxvvlrq,1 Wklv sdshu irfxvhv rq dq lpsruwdqw glvwlqfwlrq ehwzhhq d
groodul}hg v|vwhp dqg d fxuuhqf| erdug= groodul}dwlrq fdq eh xvhg dv d pruh fuhgleoh
frpplwphqw ghylvh wr wkzduw wkh xvh ri lq dwlrqdu| wd{ wr qdqfh edqnlqj v|vwhp
edlorxwv1
Lw lv qrw xqfrpprq wr qg fhqwudo edqnv wkdw surylgh gh idfwr ixoo ghsrvlw lqvxu0
dqfh zkhqhyhu wkh edqnlqj v|vwhp h{shulhqfhv jhqhudol}hg qdqfldo glvwuhvv1 Jurss
dqg Yhvdod +5333,/ iru lqvwdqfh/ surylgh vxjjhvwlyh hpslulfdo hylghqfh wr grfxphqw
wklv idfw1 Prvw ri wkh wlph wkrvh uhvfxhv duh qdqfhg zlwk lq dwlrqdu| wd{ +vhh
Ndplqvn| dqg Uhlqkduw +4<<<,,1 Lq sduwlfxodu/ wkh fhqwudo edqn sulqwv prqh| wr
uhlpexuvh ghsrvlwruv iurp edqnv h{shulhqflqj gl!fxowlhv1 Hlwkhu iru srolwlfdo uhdvrqv
ru lvvxhv ri hfrqrplf ihdvlelolw|/ wkh lq dwlrqdu| wd{ lv d wlpho| dydlodeoh wd{ dqg
khqfh ehfrphv wkh fhqwudo edqn*v suhihuuhg vrxufh ri ixqglqj lq wkhvh hphujhqf|
vlwxdwlrqv1 Dgrswlqj d v|vwhp ri groodul}dwlrq doorzv wkh fhqwudo edqn wr h{ dqwh vkxw
grzq vxfk d vrxufh ri hdv| ixqglqj1 Rqh pd| zrqghu wkrxjk zk| d ehqhyrohqw
fhqwudo edqn zrxog zdqw wr uhgxfh wkh qxpehu ri lqvwuxphqwv dydlodeoh wr ghdo zlwk
dq hyhqwxdo djjuhjdwh fulvlv1 D srvvleoh h{sodqdwlrq fdq eh wudfhg wr wkh srolwlfdo
g|qdplfv ri wkh sureohp1 Hyhq lq wkh fdvh zkhq d edlorxw lv qrw wkh ghvluhg srolf|/
wkh jryhuqphqw pd| qrw eh deoh wr ehdu wkh srolwlfdo suhvvxuh eurxjkw rq e| lqwhuhvw
jurxsv wkdw gluhfwo| ehqhw iurp wkh edlorxw1 Lq dgglwlrq/ wkh idfw wkdw wkh fhqwudo
5

edqn pd| jlyh lq wr srolwlfdo suhvvxuhv lq wkh hyhqw ri edqn idloxuhv glvwruwv wkh h{
dqwh ulvn0wdnlqj ehkdylru ri lqglylgxdov +vhh Erowrq dqg Urvhqwkdo +4<<<,,1 Lq wkrvh
vlwxdwlrqv lw pd| zhoo eh wkh fdvh wkdw xvlqj groodul}dwlrq dv d frpplwphqw whfkqrorj|
fdq doorz wkh Fhqwudo Edqn wr uhvlvw wkh diruhphqwlrqhg srolwlfdo ghpdqgv1
Exw wklv udlvhv d qhz txhvwlrq iru wkh fhqwudo edqn/ pdlqo| krz wr uhvsrqg wr
froohfwlyh edqn idloxuhv zkhq wkh hfrqrp| lv groodul}hg1 Rqh srvvlelolw| lv wr wu| wr
dyrlg qdqfldo0edqnlqj fulvhv dowrjhwkhu1 Iru wklv/ lqwhuqdwlrqdo edqnv pd| eh zruwk
frqvlghulqj1 Uhjlrqdo edqnlqj fulvhv xvxdoo| duh dvvrfldwhg zlwk qhjdwlyh ghyhors0
phqwv lq wkh uhdo vhfwruv ri wkh hfrqrp|1 Zkhq wkh h{shfwdwlrqv ri ixwxuh survshulw|
idoo/ wkh sulfh ri uhdo dvvhwv dgmxvwv grzqzdug1 Krzhyhu/ wkh edqnlqj v|vwhp ghew
edodqfhv duh lq qrplqdo whupv1 Lq jhqhudo wklv eulqjv derxw dq deuxsw ghwhulrudwlrq
ri wkh ghew0froodwhudo udwlrv dqg lqgxfhv wkh edqnlqj v|vwhp lqwr d fulvlv1 Iru dq h{0
fhoohqw ghvfulswlrq ri rqh ri wkhvh hslvrghv vhh Ehhuv/ Vdujhqw dqg Zdoodfh +4<;6, +vhh
dovr Fkdqj dqg Yhodvfr +4<<;, dqg Yhodvfr +4<;:, iru d Odwlq Dphulfdq shuvshfwlyh,1
Lq d zd|/ wkhvh nlqg ri qdqfldo fulvhv duh d pdwwhu ri sruwirolr glyhuvlfdwlrq1 Wkh
vkrfn wr wkh uhdo hfrqrp| ri d vshflf uhjlrq lqgxfhv wkh hqwluh sruwirolr ri edqnv
lq wkdw uhjlrq wr ehfrph lqvroyhqw1 Lq wkh fdvh ri lqwhuqdwlrqdo edqnv/ wkh sduw ri
wkh sruwirolrv wkdw lv dvvrfldwhg zlwk dvvhwv lq d sduwlfxodu frxqwu| ru uhjlrq lv lq
jhqhudo uhodwlyho| vpdoo1 Khqfh/ d uhjlrqdo vkrfn fdq jhw srrohg lqwr d odujh vhw ri
rwkhu vkrfnv dqg qrw ehfrph d sureohp iru wkh qdqfldo khdowk ri wkh edqnv +vhh
Fdoyr +5333,/ Vhfwlrq YL,14
Wkh remhfwlyh lq wklv sdshu lv wr vwxg| wkh uhodwlrqvkls ehwzhhq edqnlqj vhfwru
edlorxwv/ srolwlfdo suhvvxuhv/ dqg wkh ghflvlrq wr groodul}h wkh hfrqrp|1 Zh zloo dovr
vwxg| wkh hfrqrplf dqg srolwlfdo frpsohphqwdulwlhv wkdw edqn lqwhuqdwlrqdol}dwlrq
4

Fdoyr +5333, dovr glvfxvv wkh uhfhqw surfhvv ri oldelolw| groodul}dwlrq wkdw kdv ehhq xqghu zd| lq
vrph ri wkh Hphujlqj Pdunhw Hfrqrplhv1 Kh surylghv dq lqvljkwixo uhylhz ri krz wklv skhqrphqrq
fdq dowhu vrph ri wkh g|qdplfv ri wkh qdqfldo fulvhv prwlydwlqj wkh suhvhqw sdshu1

6

dqg groodul}dwlrq kdyh lq wklv w|sh ri vlwxdwlrq1
Lq wkh qh{w vhfwlrq/ zh suhvhqw d vlpsoh vw|ol}hg hfrqrp| zkhuh edqnv sod| d uroh
dqg frxqwulhv +uhjlrqv, vxhu vsrudglf djjuhjdwh vkrfnv rq wkh uhwxuq wr lqyhvwphqw1
Lq Vhfwlrq 6 zh xvh wkh prgho wr lghqwli| vrph ri wkh idfwruv wkdw ghwhuplqh zkhq wkh
ghflvlrq wr edlorxw wkh edqnlqj v|vwhp lv dq dssursuldwh uhvsrqvh iru d ehqhyrohqw
prqhwdu|0edqnlqj dxwkrulw|1 Vhfwlrq 7 vkrzv krz wkh srolwlfdo v|vwhp pd| lq xhqfh
wkrvh h{ dqwh ghflvlrqv gulylqj wr xqvdwlvidfwru| h{0srvw rxwfrphv1 Dovr lq wklv
vhfwlrq/ zh lqwurgxfh rxu yhuvlrq ri wkh groodul}dwlrq srolf|1 Edvlfdoo|/ zh dujxh wkdw
lq rxu vlpsoh prgho groodul}dwlrq lv htxlydohqw wr d srolf| e| zklfk wkh Fhqwudo Edqn
h{0dqwh vkxwv grzq wkh vfdo +wd{, vrxufhv ri ixqgv wkdw zrxog eh xvhg lq d edlorxw
ri wkh edqnlqj v|vwhp1 Lq wklv pdqqhu/ wkh prqhwdu|0edqnlqj dxwkrulw| pdqdjhv wr
frpplw wr qr ixwxuh +gh0idfwr, ghsrvlw0lqvxudqfh srolflhv gulyhq e| srolwlfdo suhvvxuhv1
Vhfwlrq 8 vwxglhv krz wkh hfrqrplf dqg srolwlfdo ghflvlrqv ghshqg rq wkh h{lvwhqfh
ri lqwhuqdwlrqdo qdqfldo lqvwlwxwlrqv1 Zh vkrz wkdw hyhq wkrxjk wkh groodul}dwlrq
srolf| pd| qrw rewdlq vx!flhqw vxssruw zkhq lqwurgxfhg dorqh/ zkhq frpelqhg
zlwk d v|vwhp ri lqwhuqdwlrqdo edqnv lw fdq ehfrph srolwlfdoo| yldeoh1 Dqg zh dovr
vkrz wkdw wkh lqwhuqdwlrqdol}dwlrq ri edqnv zrxog qhhg wr eh frpelqhg zlwk +r!fldo,
groodul}dwlrq li lqyhvwruv lq wkh hfrqrp| duh wr fkrrvh wkh lqwhuqdwlrqdo edqnv ryhu
wkh grphvwlf edqnv1 Vhfwlrq 9 suhvhqwv wkh frqfoxvlrqv1

5

D Vlpsoh Prgho

Wkh prgho suhvhqwhg lq wklv vhfwlrq lv dq dgdswdwlrq ri Hqqlv +5333,/ zklfk gudzv
rq Kropvwurp dqg Wluroh +4<<:,1 Frqvlghu dq hfrqrp| +d frxqwu|, srsxodwhg e|
ryhuodsslqj jhqhudwlrqv ri djhqwv1 Hdfk djhqw olyhv iru wzr shulrgv dqg frqvxphv wkh
rqo| jrrg lq wkh hfrqrp|/ wkh qxphudluh1 Wkh| duh doo ulvn qhxwudo dqg glvfrxqw wkh

7

ixwxuh dffruglqj wr wkh glvfrxqw idfwru q 5 Efc  Wkhuh duh wkuhh jurxsv ri djhqwv lq
hdfk jhqhudwlrq= lqyhvwruv/ ghsrvlwruv dqg edqnv1 Wkhuh lv dovr d prqhwdu|0edqnlqj
dxwkrulw| wkdw zh zloo fdoo wkh Fhqwudo Edqn +FE,1
Wkh vl}h ri hdfk jurxs ri djhqwv lv h{rjhqrxvo| jlyhq1 Lw lv qrw kdug wr hqgrjhql}h
wkh vl}h ri wkh jurxsv exw lw zrxog rqo| frpsolfdwh pdwwhuv zlwkrxw dgglqj wr wkh
srlqw wkdw lv ehlqj pdgh1 Ohw E  k eh wkh vl}h ri wkh jurxs ri lqyhvwruv/ k  w wkh
vl}h ri wkh jurxs ri ghsrvlwruv/ dqg w wkh vl}h ri wkh jurxs ri edqnv1 Wkh phdvxuh ri
doo djhqwv lq d jhqhudwlrq lv wkxv htxdo wr rqh1
Djhqwv duh eruq zlwk w|sh0ghshqghqw hqgrzphqwv= lqyhvwruv duh hqgrzhg zlwk
dq lqyhvwphqw surmhfw/ ghsrvlwruv duh hqgrzhg zlwk e xqlwv ri zhdowk +lq whupv ri
wkh qxphudluh,/ dqg edqnv duh hqgrzhg zlwk d prqlwrulqj whfkqrorj| dqg e xqlwv ri
zhdowk1
Lqyhvwphqw surmhfwv duh lqglylvleoh dqg qrq0wudqvihudeoh1 Wkh rzqhu ri wkh surmhfw
qhhgv wr lqyhvw U xqlwv ri wkh qxphudluh wr jhw d uhwxuq - xqlwv +dovr lq whupv ri wkh
qxphudluh,/ zlwk vrph suredelolw|/ li wkh surmhfw vxffhhgv +dqg f rwkhuzlvh,1 Wkh
lqyhvwru fdq h{huw hruw wr lqfuhdvh wkh suredelolw| ri vxffhvv ri wkh surmhfw1 Li vkh
h{huwv hruw wkh surmhfw vxffhhgv zlwk suredelolw| RM czklfk lv dvvxphg wr eh juhdwhu
wkdq wkh suredelolw| Ru rewdlqhg zkhq qr hruw lv h{huwhg1 Krzhyhu/ hruw lv frvwo|
dqg qrq0revhuydeoh e| wklug sduwlhv1 Ohw  eh wkh frvw/ lq xwlolw| whupv/ iru dq
lqyhvwru wr shuirup hruw dqg {R  RM  Ru 
Dvvxpswlrq 41
D41d1 RM -  q U   : f : Ru -  q U
D41e1 -  q U



{R



Dvvxpswlrq D41d lpsolhv wkdw rqo| surmhfwv xqghuwdnhq zlwk kljk hruw kdyh
srvlwlyh qhw suhvhqw ydoxh zkhq wkhuh lv shuihfw lqirupdwlrq1 Dvvxpswlrq D41e lp0
8

solhv wkdw lqyhvwruv duh vxemhfw wr d prudo kd}dug sureohp1 Wkh lpsruwdqfh ri wkhvh
dvvxpswlrqv zloo ehfrph dssduhqw lq wkh qh{w vhfwlrq1
Wkh uhwxuqv ri wkh surmhfwv zlwklq d frxqwu| kdyh d wljkw sdwwhuq ri fruuhodwlrq1
Dw dq| gdwh |c li zh revhuyh wkdw d surmhfw xqghuwdnhq xvlqj hruw kdv idlohg lq
wkdw shulrg/ wkhq zh nqrz wkdw doo wkh rwkhu surmhfwv xqghuwdnhq zlwk hruw dovr
idlohg +wklv kdsshqv E  RM  ri wkh wlphv,1 Vlploduo|/ surmhfwv fduulhg rxw zlwk qr
hruw idlo hyhu| wlph wkh hruw0surmhfwv idlo/ dqg vrph rwkhu wlphv +vr wkdw wkh| idlo
ERu  : ERM  ri wkh wlphv,1 Lq rwkhu zrugv/ wkh hyhqw ri vxffhvv ri dq| sduwlfxodu
surmhfw grhv qrw frqvwlwxwh dq lglrv|qfudwlf vkrfn wr d sduwlfxodu surmhfw/ exw d vkrfn
wr wkh hqwluh frxqwu| +ru uhjlrq, zkhuh wkh surmhfw lv orfdwhg1
Wkh prqlwrulqj whfkqrorj| fdq eh xvhg wr shuihfwo| prqlwru wkh hruw ohyho ri lq0
yhvwruv xqghuwdnlqj surmhfwv1 Wkh dfwlylw| ri prqlwrulqj lv frvwo| dqg qrq0revhuydeoh1
Ohw S ghqrwh wkh shu0surmhfw frvw ri prqlwrulqj1
Wkh FE fdq wd{ wkh |rxqj0jhqhudwlrq phpehuv ri wkh jurxs ri ghsrvlwruv +dqg
rqo| wkhp, lq rughu wr qdqfh d edlorxw ri wkh edqnlqj vhfwru15 Ohw
shu0fdslwd wd{1 Krzhyhu/ zkhq wkh FE udlvhv dq dprxqw

ghqrwh wkh

iurp wd{dwlrq/ rqo| *1

ehfrphv dydlodeoh iru wkh xvh ri wkh FE1 Zh frqvlghu wkh fdvh ri 1  1 Wklv dvvxps0
wlrq lv lqwhqghg wr fdswxuh dq h{wud dgplqlvwudwlyh +dqg srvvleo| wkh ghdg0zhljkw
orvv, frvw ri wd{dwlrq1 Zkhq wkh FE sulqwv prqh| wr qdqfh wkh edqnlqj0v|vwhp
edlorxw/ zh zloo lqwhusuhw

dv wkh sur{| iru wkh lq dwlrqdu| wd{1 Odujh ydoxhv ri

1 fdq eh dvvrfldwhg zlwk vlwxdwlrqv zkhuh wkh h{fhvv ri prqh| fuhdwlrq surpswv d
fxuuhqf| fudvk wkdw eulqjv dorqj d glvuxswlrq lq rwkhu vhfwruv ri wkh hfrqrp|16
5

Wklv lv mxvw d qrupdol}dwlrq1 Zh frxog doorz wkh jryhuqphqw wr wd{ doo djhqwv lq wkh hfrqrp|1
Zkdw uhdoo| pdwwhuv lv wkh qhw wudqvihu wkdw wkh djhqwv jhw iurp wkh lqvxudqfh vfkhph +wkh edlorxw,1
Zh fkrrvh wklv vlpsolfdwlrq ehfdxvh rqo| |rxqj ghsrvlwruv jhw d qhjdwlyh wudqvihu lq hyhu| srvvleoh
fdvh +wkh wd{,1
6
Qrwh wkdw wkhuh lv qr prqh| lq wkh hfrqrp|1 Iru wklv uhdvrq zh pd| vd| wkdw wklv sdshu suhvhqwv
d vfdo wkhru| ri groodul}dwlrq1

9

Dvvxph wkdw ghsrvlwruv dv d jurxs/ diwhu ghsrvlwlqj d wrwdo shu fdslwd dprxqw ( lq
wkh edqnv gxulqj wkh uvw shulrg ri wkhlu olyhv/ hqjdjh lq ryhuodsshg +qrq0frqwlqjhqw,
wudqvdfwlrqv dqg sd|phqw frpplwphqwv dprqj wkhpvhoyhv iru wkh dprxqw (/ zkhuh
 lv wkh jurvv lqwhuhvw udwh17 Ghsrvlwruv zloo qrw eh deoh wr ixooo wkrvh frpplwphqwv lq
wkh vhfrqg shulrg ri wkhlu olyhv li wkh| uhfhlyh +lq shu fdslwd whupv, ohvv wkdq ( iurp
wkh edqnlqj vhfwru1 Dv d frqvhtxhqfh/ wkhuh lv d glvuxswlrq lq hfrqrplf dfwlylwlhv
dqg ghsrvlwruv h{shulhqfh d shu fdslwd xwlolw| orvv D1 Wklv dvvxpswlrq zloo prwlydwh
wkh h{lvwhqfh ri fhqwudo edqn edlorxwv lq wkh prgho18
Ilqdoo|/ qrwh wkdw vlqfh ulvn qhxwudolw| lpsolhv olqhdu xwlolw| ixqfwlrqv/ wkh ohyho
ri ghsrvlwv zloo eh ghwhuplqhg e| wkh ghpdqg vlgh ri wkh pdunhw iru ixqgv1 Ghqh
2
t  qRu {SR dqg f  1q Dq 1
3

Dvvxpswlrq 51
D51d1 U
D51e1 e :
D51f1 t

k3w
3k



E3k

w

U



e  q1 f 

t
t n k kw f
3

3

Dvvxpswlrq D51d lpsolhv wkdw wkhuh duh hqrxjk ghsrvlwv lq wkh hfrqrp| wr qdqfh
doo surmhfwv1 Dvvxpswlrq D51e lpsolhv wkdw edqn0prqlwruv kdyh hqrxjk rzq ixqgv wr
ghdo zlwk wkhlu prudo kd}dug sureohp1 Ilqdoo|/ dvvxpswlrq D51f olplwv wkh uhodwlyh
vl}h ri wrwdo ghsrvlwv lq wkh v|vwhp1 Zh zloo glvfxvv wkh frqvhtxhqfhv ri dedqgrqlqj
wklv odvw dvvxpswlrq dw wkh hqg ri qh{w vhfwlrq1
Wkh djhqwv hqgrzhg zlwk wkh prqlwrulqj whfkqrorj| zloo sod| wkh uroh ri edqnv lq
wkh prgho1 Edqnv jhw sdlg dq dprxqw  iru wkh vhuylfh ri prqlwrulqj1 Dgglwlrqdoo|
7

Wkurxjkrxw wkh sdshu zh dgrsw wkh iroorzlqj qrwdwlrq= iru dq| yduldeoh {> zh ghqrwh e| { lwv
djjuhjdwh shu fdslwd ydoxh1
8
Vhh Shfn dqg Vkhoo +4<<<, iru d glvfxvvlrq rq dqrwkhu zd| wr prgho wkh sd|phqw vhuylfhv surylghg
e| ghpdqg ghsrvlwv +wkhluv lv dq hqylurqphqw zlwk lqglylvlelolwlhv lq sd|phqwv,1 Lw lv lpsruwdqw wr
qrwlfh wkrxjk wkdw lq wkh vhw0xs ri wkh suhvhqw sdshu wkh ghsrvlwruv* xwlolw| frvw lv gluhfwo| dvvrfldwhg
wr dq djjuhjdwh idloxuh ri wkh qdqfldo vhfwru1 Lw lv qrw d frvw wkdw frxog eh lqglylgxdoo| dyrlghg1

:

wkh FE lpsrvhv d fdslwdo uhtxluhphqw rq edqnv U6 1 Hqwuhsuhqhxuv eruurz U xqlwv
ri ixqgv iurp wkh edqnv dqg sd| edfn U n  li wkh surmhfw vxffhhgv +dqg }hur
rwkhuzlvh,1 Wkh edqn lq wxuq sd|v EU  U6  +shu surmhfw, wr ghsrvlwruv1 Lw zloo eh
frqyhqlhqw wr h{suhvv 7  U6 n  zkhuh  lv wkh htxloleulxp jurvv lqwhuhvw udwh sdlg
rq hqwuhsuhqhxuv* eruurzhg ixqgv dqg  lv wkh edqnv qhw ihh iurp prqlwrulqj1

6

Ehqhyrohqw Htxloleulxp

Iluvw/ zh frqvlghu wkh fdvh zkhuh wkh jryhuqphqw0fhqwudo edqn lv ehqhyrohqw dqg fduhv
htxdoo| derxw ghsrvlwruv dqg surmhfw rzqhuv +|rxqj dqg rog,1 Edqn0prqlwruv dozd|v
rewdlq }hur qhw vxusoxv lq htxloleulxp vr zh fdq devwudfw iurp wkhp lq wkh zhoiduh
frqvlghudwlrqv1
Ghqlwlrq 4 Zh vd| wkdw wkh hfrqrp| lv lq d fulvlv zkhq wkh lqyhvwphqw surmhfwv
grqh h{huwlqj hruw idlo1 Ohw r 5 ifc j eh dq lqglfdwru ri wkh vwdwh ri wkh hfrqrp|=
r '  zkhq hfrqrp| lv lq d fulvlv/ dqg r ' f zkhq lw lv qrw19
Ohw A E(c (c r  f eh wkh FE srolf| ri sd|phqw wr ghsrvlwruv lq wkhlu vhfrqg
shulrg ri olih +frqwlqjhqw rq wkh dprxqw ri wkh djhqw*v ghsrvlwv ( dqg wkh djjuhjdwh
shu fdslwd ohyho ri ghsrvlwv (,1 Vlqfh zh rqo| frqvlghu vwhdg| vwdwhv zh gurs wkh wlph
lqgh{ wr vlpsoli| qrwdwlrq1 Ghsrvlwruv vroyh wkh iroorzlqj sureohp=




pd{lpl}h .dS n q S2  DS2 ( o
vxemhfw wr
S ' e  (  Erc
9

Wkh ghqlwlrq ri d fulvlv lv vshflf wr rxu hqylurqphqw1 Lw lv qrw ri wkh vhoi0ixooolqj w|sh1 Lw
lv lq idfw forvho| dvvrfldwhg wr wkh shuirupdqfh ri wkh uhdo vhfwru ri wkh hfrqrp|1 Iru dq h{fhoohqw
glvfxvvlrq rq pruh jhqhudo ghqlwlrqv ri fulvhv vhh Ndplqvn| dqg Uhlqkduw +4<<<,1 Ndplqvn|
dqg Uhlqkduw dovr surylgh frpshoolqj hylghqfh rq wkh vwurqj olqnv ehwzhhq qdqfldo fulvhv dqg wkh
hyroxwlrq ri wkh uhdo vhfwru +wkh| qg wkdw zhdn rxwsxw lqglfdwruv vljqdo wkh dgyhqw ri ;< shufhqw
ri wkh edqnlqj fulvhv wkh| vwxg|,1

;

+

S2 '

( n A E(c (c f li qr fulvhv/
A E(c (c 
li fulvhv/

zkhuh S2 ( lv dq lqglfdwru ixqfwlrq wkdw wdnhv wkh ydoxh 4 zkhq S2  ( dqg }hur
rwkhuzlvh1 Qrwh wkdw ghsrvlwruv kdyh wr fkrrvh krz pxfk wr vdyh ehiruh nqrzlqj wkh
fxuuhqw uhdol}dwlrq ri

dqg wkdw wkhlu xwlolw| frvw D lv dvvrfldwhg zlwk dq djjuhjdwh

rxwfrph wkdw fdqqrw eh dyrlghg e| fkdqjlqj wkh lqglylgxdo*v ghflvlrq1
Wkh ehqhyrohqw FE pd{lpl}hv wkh iroorzlqj zhoiduh ixqfwlrq=
` EA E# ' Ek  wde  (  RM Ef  E  RM  En




q RM E( n A E(c (c f n E  RM  A E(c (c   DS2 (



on

E  kq ERM E-  U    
vxemhfw wr
A E(c (c r ' Er*1

+4,

Wklv zhoiduh ixqfwlrq lv wkh uhvxow ri vlpso| vxpplqj wkh olihwlph xwlolw| ri doo wkh
djhqwv lq d uhsuhvhqwdwlyh jhqhudwlrq +dv zh zloo vhh/ prqlwruv dozd|v jhw }hur vxusoxv
dv d uhvxow ri wkh frpshwlwlyh dvvxpswlrq,1
Zh zloo fdoo d Ehqhyrohqw Htxloleulxp dq htxloleulxp zkhuh ghsrvlwruv/ hqwuhsuhqhxuv/
dqg prqlwruv pd{lpl}h wkhuh olihwlph xwlolw| vxemhfw wr wkhlu exgjhw frqvwudlqwv/
( ' (c wkh pdunhw iru ixqgv fohduv/ dqg wkh jryhuqphqw0FE fkrrvhv edqnlqj uhjx0
odwlrq srolflhv dqg wudqvihuv wr pd{lpl}h wkh sursrvhg zhoiduh ixqfwlrq ` E vxemhfw
wr wkh edodqfh0exgjhw uhvwulfwlrq +4,1
Sursrvlwlrq 4 Ohw D4 dqg D5 krog1 Wkhq wkhuh h{lvwv d Ehqhyrohqw Htxloleulxp
zkhuh +l, wkh lqwhuhvw udwh lv  ' *q/ +ll, doo surmhfwrzqhuv jhw prqlwruhg e| edqnv
W

wkdw jhw sdlg d ihh  ' S*{R  t *q dqg/ +lll, wkh FE lpsrvhv d fdslwdo uhtxluhphqw
W

rq edqnv U6 ' t dqg d wudqvihuv vfkhgxoh
W

+

A E(c (c r '
W

(
f

li r '  dqg (  (f
rwkhuzlvh
<

zkhuh (f ' f1
Surri1 Wkh surri iroorzv 8 vwhsv1
Vwhs 4= Doo surmhfw0rzqhuv jhwwlqj wkh qhfhvvdu| fuhglw wr xqghuwdnh wkh surmhfw
vkrxog eh prqlwruhg1
Iluvw/ qrwh wkdw li wkh FE surylghv ghsrvlw lqvxudqfh wkhq lw lv lq lwv ehvw lqwhuhvw
wr kdyh doo surmhfwv eh xqghuwdnhq h{huwlqj hruw1 Wr vhh wklv/ vxssrvh surmhfwv duh
fduulhg rxw zlwk qr hruw1 Vlqfh ghsrvlwruv kdyh ghsrvlw lqvxudqfh zh vwloo kdyh wkdw
 ' *q Hqwuhsuhqhxuv rewdlq Ru E-   U iurp wkhlu surmhfwv1 Dovr/ e| D41d zh
W

W

kdyh wkdw
f

RM - 


U 
q

-


Uc
q

zklfk whoov xv wkdw wkh hqwuhsuhqhxuv jhw d srvlwlyh sd|r iurp wkhlu surmhfwv1 Ixu0
wkhupruh/ lw iroorzv iurp D41e wkdw wklv sd|r lv juhdwhu wkdq wkh rqh rewdlqhg zkhq
h{huwlqj hruw1 Krzhyhu/ wkh vlwxdwlrq iru wkh FE lv glhuhqw1 Wkh FE lqwhuqdol}hv
wkh idfw wkdw h{wud wd{hv duh qhhghg wr qdqfh wkh ghsrvlw lqvxudqfh li wkh surmhfwv
duh fduulhg rxw zlwk qr hruw1 Wkh qhw sd|r iru wkh FE fdq eh uhgxfhg wr wkh
iroorzlqj h{suhvvlrq=
E  kqdRu E-  Uo  Ek  wE  Ru  c
zkhuh iurp +4, zh kdyh wkdw

' 1( ' 1E  kU*Ek  w: Lw lv qrw kdug wr

vkrz +diwhu vrph dojheud, wkdw wklv h{suhvvlrq lv qhjdwlyh zkhq  ' *q Khqfh/ wkh
FE zloo zdqw wr lpsohphqw d edqnlqj srolf| wkdw lqgxfhv djhqwv wr xqghuwdnh wkhlu
surmhfw zlwk hruw1
:
Vlqfh wkh qxpehu ri |rxqj ghsrvlwruv ehlqj wd{hg lv wkh vdph dv wkh qxpehu ri rog ghsrvlwruv
ehqhwlqj iurp FE lqvxudqfh/ wkh edodqfhg exgjhw uhvwulfwlrq uhgxfhv wr wkh h{suhvvlrq lq wkh wh{w1

43

Qrz/ uhfdoo wkdw vlqfh wkh surmhfw rzqhuv kdyh qr zhdowk/ wkh| qhhg d fuhglw ri U
xqlwv wr eh deoh wr fduu| rxw wkh surmhfw1 E| D41e zh kdyh wkdw
-  U    -  U


c
{R

dqg khqfh
Ru E-  U   : RM E-  U    c
zklfk phdqv wkdw wkh lqfhqwlyh frpsdwlelolw| frqvwudlqw wkdw zrxog lqgxfh hqwuhsuhqhxuv
wr h{huw hruw lv qrw vdwlvhg dqg wkdw wkh rqo| zd| wr lqgxfh hruw lv wkurxjk edqn
prqlwrulqj1
Vwhs 5= Wkh FE lpsrvhv d fdslwdo uhtxluhphqw U6 rq edqnv dqg edqnv jhw sdlg d
W

ihh  
W

Dvvxph wkdw edqnv gr qrw jhw ghsrvlw lqvxudqfh rq wkhlu ghsrvlw1; Wzr lqfhq0
wlyh frqglwlrqv rq wkh ehkdylru ri edqnv qhhg wr eh frqvlghuhg1 Rq rqh kdqg/ wkh
sduwlflsdwlrq frqvwudlqw lv jlyhq e|
q ERM 7  S  U6 c

+5,

zklfk vd|v wkdw +srwhqwldo, prqlwruv fdq fkrrvh ehwzhhq ehfrplqj d edqn +lq zklfk
fdvh/ wkh| frpplw U6 xqlwv ri ixqgv shu surmhfw prqlwruhg dqg jhw sdlg 7 zlwk vrph
suredelolw| lq wkh ixwxuh,/ ru vlpso| frqvxplqj wkhlu hqgrzphqw gxulqj wkhlu uvw
shulrg ri olih1 Qrwh wkdw vlqfh edqnv gr qrw jhw ghsrvlw lqvxudqfh dqg qRM U6 
U6 / zh fdq frqfoxgh wkdw wkh| zloo qrw pdnh gluhfw ghsrvlwv lq wkh v|vwhp dw wkh
htxloleulxp lqwhuhvw udwh  Rq wkh rwkhu kdqg/ lqfhqwlyh frpsdwlelolw| uhtxluhv wkdw
wkh iroorzlqj frqglwlrq krogv=
RM 7  S  Ru 7
;

+6,

Wklv lv pdlqo| iru frqyhqlhqfh1 Wkh dqdo|vlv fdq eh fduulhg rxw zlwk ghsrvlw lqvxudqfh ryhu
edqn0ghsrvlwv zlwk rqo| plqru fkdqjhv1

44

Wkh FE vhwv d uhvhuyh uhtxluhphqw U6 wkdw plqlpl}hv wkh htxloleulxp edqn ihh   Lq
W

idfw/ xvlqj frqvwudlqwv +5, dqg +6, zh fdq vhh wkdw li wkh FE vhwv U6 ' tc frpshwlwlrq
dprqj edqnv zloo gulyh  wr lwv plqlpxp ihdvleoh ydoxh +vhh Iljxuh 4,1
W

Vwhs 6= Li A E(c (c r

( wkhq A E(c (c r ' f Dqg A E(c (c f ' f

W

W

W

Uhfdoo wkdw lq htxloleulxp ( ' ( Xvlqj wkh uhvxowv iurp Vwhs 5/ zh fdq uhzulwh
` EA E# dv
f̀ ' Ek  wde  (  R Ef  E  R  Eon
M
M
#
#

Ef
n E  RM 
nqRM Ek  w( n Ek  wq RM
1
#

E
 DS2 (
1

$

$$

n

S
nE  kq RM E- 
    qRM E  kEU  U6 
{R

+7,

E| D51d wkh pdunhw fohdulqj frqglwlrq iru ixqgv lv jlyhq e|
E  kEU  U6  ' Ek  w(
E| vxevwlwxwlqj wklv frqglwlrq lq f̀ lw lv hdv| wr vhh wkdw wkh vhfrqg dqg odvw whup
rq wkh uljkw kdqg vlgh ri htxdwlrq +7, fdqfho rxw1 Wkhq/ zh rewdlq
+

#

$

,

f̀ ' Ek  w e  (    q dR Ef n E  R  Eo 
M
M
1
#

$

S
Ek  wqE  RM DS2 ( n E  kq RM E- 
 
{R
Vlqfh q*1 lv ohvv wkdq rqh/ lw ehfrphv dssduhqw iurp wklv h{suhvvlrq wkdw wkh FE
vkrxog vhw Ef ' f dqg E ' f zkhqhyhu E lv qrw vx!flhqw wr ixoo| lqvxuh wrwdo
ghsrvlwv ( soxv lqwhuhvw sd|phqwv1 Khqfh/ wkh fodlp lq Vwhs 6 iroorzv1
Vwhs 7= Wkh htxloleulxp lqwhuhvw udwh xqghu srolf| A E(c (c r lv  ' *q
W

E| D51f zh kdyh wkdw (

W

(f  Hqwuhsuhqhxuv qhhg ixqgv1 Khqfh ( kdv wr

eh srvlwlyh lq htxloleulxp1 Iurp wkh ghsrvlwruv* sureohp/ wklv lpsolhv wkdw   *q
W

E| dvvxpswlrq D51d zh jhw wkdw   *q ru rwkhuzlvh wkhuh zrxog eh dq h{fhvv
W

vxsso| ri ghsrvlwhg ixqgv1
45

Vwhs 8= Wkh FE vhwv wudqvihuv wr A E(c (c r
W

E| Vwhs 6 zh rqo| qhhg wr frpsduh wkh ydoxh ri f̀ zkhq wkh FE vhwv E htxdo
wr }hur zlwk wkh fdvh zkhq E ' 1( Khqfh/ wkh FE vkrxog vhw E ' 1( rqo|
zkhq wkh iroorzlqj lqhtxdolw| krogv
+

#

$

,

#

$

q
S
E  RM 1( n E  kq RM E- 
 :
Ek  w e  (   
1
{R
#

$

S
Ek  wde  (  qE  RM Do n E  kq RM E- 
 c
{R
zklfk lq wxuq uhgxfhv wr wkh vlpsohu h{suhvvlrq
qD

E1  q(

+8,

Khqfh/ zkhq wkh htxloleulxp lqwhuhvw udwh  ' *q +dv vkrzq lq Vwhs 7,/ zh kdyh
W

wkdw wkh FE zloo lpsohphqw ixoo ghsrvlw lqvxudqfh zkhqhyhu (

(f  q 2 D*E1 

q Ilqdoo|/ vxssrvh wkdw
E1  q( : qDc
zkhq  ' *q Li wkh FE vhwv A E( ' f/ wkh htxloleulxp lqwhuhvw udwh zloo eh  '


*RM q Iurp h{suhvvlrqv +5, dqg +6, zh nqrz wkdw U6 lv lqghshqghqw ri  +dqg vr lv
(c vhh Iljxuh 4,1 Wkhuhiruh/ wkh iroorzlqj lqhtxdolw| krogv
E1  q




( : E1  q ( : qDc
RM q
q

zklfk yhulhv wkdw A E( ' f lv lq idfw wkh srolf| wkdw d ehqhyrohqw FE zrxog olnh wr
sxuvxh1 Wklv/ wrjhwkhu zlwk Vwhs 6/ suryhv wkh fodlp lq Vwhs 81
Zkhwkhu wkh FE zlvkhv wr lpsohphqw d v|vwhp ri ghsrvlw lqvxudqfh ghshqgv rq
vhyhudo idfwruv lq wkh prgho +vhh h{suhvvlrq +8,,1 Lw lv xvhixo wr pdnh d vshfldo phqwlrq
ri wkuhh ri wkhp khuh dv wkh| duh dozd|v ri pdmru lpsruwdqfh iru wkh glvfxvvlrq ri wkh
jhqhudo sureohp1 Iluvw/ qrwh wkdw wkh kljkhu wkh frvw D wr ghsrvlwruv dvvrfldwhg zlwk
46

wkh hfrqrplf wxuprlo fdxvhg e| wkh fulvlv/ wkh pruh olnho| lw lv wkdw wkh FE zloo fkrrvh
wr kdyh d ghsrvlw lqvxudqfh v|vwhp1 Vhfrqg/ wkh kljkhu wkh dgplqlvwudwlyh dqg glv0
wruwlrqdu| frvwv ri wd{dwlrq +kljkhu 1c wkh ohvv dwwudfwlyh zloo eh wkh lpsohphqwdwlrq
ri d jhqhudol}hg ghsrvlw lqvxudqfh1 Ilqdoo|/ wkh vl}h ri wkh qdqfldo v|vwhp +phdvxuh
khuh e| wkh vl}h ri (, lv lpsruwdqw iru wkh hydoxdwlrq ri wkh frvwv ri lpsohphqwlqj
d ghsrvlw lqvxudqfh v|vwhp1 Wklv odvw idfw dsshduv lq wkh prgho dv d frqvhtxhqfh ri
wkh sxuh wudqvihu ri uhvrxufhv dprqj ghsrvlwruv +iurp |rxqj wr rog, wkdw lv lqyroyhg
lq wkh qdqflqj ri wkh ghsrvlw lqvxudqfh vfkhph1 Pruh jhqhudoo|/ wkh prgho vxjjhvwv
wkdw lw lv lpsruwdqw wr ghwhuplqh wkh vl}h ri wkh uhdoorfdwlrq ri ixqgv lqgxfhg e| wkh
ghsrvlw lqvxudqfh v|vwhp zkhq ghflglqj derxw lwv lpsohphqwdwlrq1
Frqvlghu wkh iroorzlqj dowhuqdwlyh dvvxpswlrq wr D51f=
+D51f, 1 U : t n k kw f


3

3

Wklv lv mxvw vd|lqj wkdw wkh htxloleulxp vl}h ri wkh edqnlqj v|vwhp phdvxuhg e|
wrwdo ghsrvlwv lv uhodwlyho| odujh1 Zh zloo fdoo Dvvxpswlrq D5 wr wkh vdph vhw ri


lqhtxdolwlhv dv lq dvvxpswlrq D5 exw zlwk lqhtxdolw| +D51f, uhsodflqj lqhtxdolw|


D51f1 Xqghu wklv qhz dvvxpswlrq +l1h1/ zkhq D51f grhv qrw krog,/ wkh ehqhyrohqw
htxloleulxp kdv  ' *RM qc Er ' f iru doo r dqg qr ghsrvlw lqvxudqfh1 Lw lv qrw kdug
W

wr vkrz wkdw hyhq zkhq wkh FE grhv qrw vhw d pdqgdwru| fdslwdo uhtxluhphqw/ frp0
shwlwlrq dprqj edqnv dqg wkh qhfhvvlw| ri hqwuhsuhqhxuv wr dwwudfw h{whuqdo ixqglqj
zloo gulyh wkh prqlwrulqj ihh wr lwv plqlpxp ohyho  ' S*RM 1 Wklv v|vwhp uhvhp0
W

eohv d fhuwlfdwlrq pdunhw iru surmhfwv zkhuh wkh ixqfwlrq ri edqn0prqlwruv lv rqo|
wr fhuwli| wkdw wkh lqyhvwruv duh hhfwlyho| h{huwlqj wkh uhtxluhg ohyho ri hruw +vhh
Kropvwurp dqg Wluroh +4<<:, iru ghwdlov,1

47

7

Srolwlfdo Htxloleulxp

Lqvwhdg ri ohwwlqj wkh ehqhyrohqw fhqwudo edqn ghflgh zkhwkhu wr uxq dq +lpsolflw,
ghsrvlw lqvxudqfh srolf|/ zh qrz frqvlghu d vfhqdulr lq zklfk wklv ghflvlrq lv wkh
rxwfrph ri d srolwlfdo surfhvv1< Dvvxph wkdw rqo| ghsrvlwruv dqg hqwuhsuhqhxuv yrwh
dqg wkdw wkh| yrwh dffruglqj wr wkhlu uhvshfwlyh sd|rv rewdlqhg xqghu wkh glhuhqw
v|vwhpv +edqn0prqlwruv duh lqglhuhqw ehwzhhq v|vwhpv dv frpshwlwlrq dozd|v gulyhv
wkhlu sd|r grzq wr wkh sduwlflsdwlrq frqvwudlqw,1 Lq rwkhu zrugv/ hdfk djhqw ghflghv
khu yrwh zlwk wkh eholhi wkdw vkh zloo eh ghflvlyh1 Djhqwv wkdw duh lqglhuhqw ehwzhhq
v|vwhpv gr qrw yrwh143 Wkh wlplqj ri hyhqwv lv dv iroorzv= dw wkh ehjlqqlqj ri hdfk
shulrg/ djhqwv yrwh iru d v|vwhp1 Wkhq/ wkh v|vwhp zlwk pruh wkdq 83( ri wkh yrwhv
jhwv lpsohphqwhg dqg djhqwv pdnh wkh uhvw ri wkhlu hfrqrplf ghflvlrqv1 Ilqdoo|/
xqfhuwdlqw| derxw wkh uhwxuq ri wkh surmhfwv lq wkh uhjlrq jhwv uhdol}hg dqg djhqwv
rewdlq wkhlu shulrg0sd|rv1 Wkh fkrlfh ri wkh wlplqj lv lpsruwdqw khuh1 Zh frxog
dowhuqdwlyho| kdyh dvvxphg wkdw hdfk shulrg*v yrwlqj wdnhv sodfh diwhu wkh xqfhuwdlqw|
lv uhvroyhg1 Rqh frxog dujxh wkdw wklv pruh gluhfwo| dgguhvvhv wkh h{0dqwh2h{0srvw
fkrlfh0ri0srolf| frq lfw +wlph lqfrqvlvwhqf|, idfhg e| yrwhuv1 Krzhyhu/ lq rxu fxuuhqw
vlpsolhg vhw0xs wklv dowhuqdwlyh wlplqj ri hyhqwv uhqghuv wkh yrwlqj ghflvlrqv ghyrlg
ri dq| lqwhuhvwlqj frqwhqw1 Pruhryhu/ zh pd| vd| wkdw vxfk wlplqj lv qrw qhfhvvdulo|
wkh ehvw zd| wr uhsuhvhqw uhdo0zruog vlwxdwlrqv iru zklfk wkh ghhsqhvv ri wkh fulvlv
dqg wkh wlplqj ri edlorxwv duh qrw vr fohdu0fxw1
Diwhu wkh srolwlfdo surfhvv wdnhv sodfh/ li d ghsrvlw lqvxudqfh vfkhph lv lpsoh0
<

Srolwlfdo lqvwlwxwlrqv duh wdnhq dv jlyhq lq wklv sdshu1 Erowrq dqg Urvhqwkdo +4<<<, vwxg|
dq hfrqrp| zkhuh wkh srolwlfdo duudqjhphqwv wkdw ghwhuplqh dq h{0srvw edlorxw srolf| fdq eh lq0
whusuhwhg dv dulvlqj hqgrjhqrxvo| wr uhphg| frqwudfwxdo lqfrpsohwhqhvv1 Krzhyhu/ wkhlu vhwxs lv
vxevwdqwldoo| glhuhqw iurp rxuv lq wkdw wkh| frqvlghu h{0srvw khwhurjhqhrxv lqyhvwruv dqg yrwlqj
ghflvlrqv wkdw wdnh sodfh diwhu w|shv jhw sulydwho| uhyhdohg1
43
Iru dq h{fhoohqw glvfxvvlrq ri srolwlfr0hfrqrplf htxloleulxp vhh Nuxvhoo/ Txdgulql dqg Ulrv0Uxoo
+4<<:,1

48

phqwhg zh dvvxph wkdw wkh FE iroorzv wkh rswlpdo wudqvihuv dqg fdslwdo0uhtxluhphqw
srolflhv ghvfulehg lq wkh suhylrxv vhfwlrq +vhh wkh surri ri Sursrvlwlrq 4,144 Hv0
vhqwldoo| wkh yrwhu qhhgv wr fkrrvh ehwzhhq ehlqj lq dq htxloleulxp zlwk dq rswlpdo
ghsrvlw lqvxudqfh olnh wkh rqh lq Sursrvlwlrq 4 ru zlwk qr ghsrvlw lqvxudqfh dw doo1
Ohw  5 i c 2 j eh d vwdwh yduldeoh wkdw lqglfdwhv wkh uhvxow ri wkh edoorw1 Li
wkh ghsrvlw lqvxudqfh sursrvdo jhwv wkh pdmrulw| ri wkh yrwhv/  wdnhv wkh ydoxh  /
rwkhuzlvh  ' 2 1 Jlyhq wkh wlplqj ri hyhqwv/ lw vhhpv qdwxudo wr frqvlghu wkdw wkh
lqwhuhvw udwh  iru wkh fxuuhqw shulrg zloo eh frqwlqjhqw rq wkh ydoxh ri  lq wkh
iroorzlqj shulrg1 Ilqdoo|/ zh zloo fdoo A  E(c ( wkh wudqvihuv ixqfwlrq xqghu v|vwhp
/ l1h1/ A  E(c ( ' E( dqg A 2 E(c ( ' f Zlwk wkh hohphqwv mxvw ghvfulehg/
zh fdq ghqh d Srolwlfdo Htxloleulxp lq wkh reylrxv zd|1 Wkh iroorzlqj sursrvlwlrq
vkrzv wkdw hyhq zkhq d ehqhyrohqw fhqwudo edqn fkrrvhv qrw wr vhw xs d ghsrvlw
lqvxudqfh v|vwhp/ wkh srolwlfdo surfhvv pd| dssuryh rqh1
Sursrvlwlrq 5 Ohw D4 dqg D5



krog1 Wkhq wkhuh h{lvwv d Srolwlfdo Htxloleulxp

zkhuh +l, wkh lqwhuhvw udwh lv  ' *qc dqg +ll, wkh ghsrvlw lqvxudqfh v|vwhp lv
W

lpsohphqwhg1
Surri1 Iluvw qrwh wkdw E  ' *q dqg E2  ' *RM q dv djhqwv lq wkh prgho
kdyh shuihfw iruhvljkw derxw wkh srolwlfdo rxwfrphv1 Zh kdyh dvvxphg wkdw djhqwv
eholhyh wkh| duh ghflvlyh zkhq wkh| ghflgh wkhlu yrwhv1 Li d ghsrvlwru eholhyhv wkdw wkh
ghsrvlw0lqvxudqfh sursrvdo zloo qrw eh dffhswhg qh{w shulrg/ wkhq vkh zloo rqo| djuhh
wr ghsrvlw khu ixqgv dw dq lqwhuhvw udwh ri dw ohdvw *RM q1 Dovr/ e| dvvxpswlrq D51d
wkh pdunhw fohdulqj lqwhuhvw udwh fdqqrw eh juhdwhu wkdq *RM q1 Lw iroorzv wkhq wkdw
E2  ' *RM q Vlploduo|/ frqglwlrqdo rq  wkh pdunhw fohdulqj lqwhuhvw udwh zloo eh
jlyhq e| *qc l1 h1/ E  ' *q1
44

Wklv uxohv rxw fdvhv zkhuh wkh +lpsolflw, edlorxw lqgxfhv h{fhvvlyh ulvn0wdnlqj ehkdylru e| eru0
urzhuv1

49

Frqvlghu qrz wkh yrwlqj ghflvlrqv ri wkh uhohydqw djhqwv=
+l, Rog ghsrvlwruv* h{shfwhg sd|r dw wkh yrwlqj wlph lv jlyhq e|
RM E( n E  RM dA  E(c (  DA  E(c( ( o
Qrz/ li  '  wkhq wkhlu sd|r lv E ( dqg li  ' 2 wkhq wkhlu sd|r lv
RM E2 (  E  RM D1 Vlqfh
E ( '



( : (  E  RM D ' RM E2 (  E  RM D
q
q

zh kdyh wkdw rog ghsrvlwruv zloo yrwh lq idyru ri wkh ghsrvlw lqvxudqfh v|vwhp>
+ll, \rxqj ghsrvlwruv* h{shfwhg sd|r lv




RM Ee  ( n E  RM de  (  Eo n qdRM  ( n E  RM  A E(c (  DA E(c(  ( o








zkhuh A lv wdnhq dv jlyhq e| wkhvh djhqwv +lw zloo eh ghflghg qh{w shulrg, exw htxl0


oleulxp frqvlvwhqf| uhtxluhv wkdw A eh wkh zlqqlqj srolf| lq wkh qh{w shulrg edoorw1


Reylrxvo| zlwkrxw d ghsrvlw lqvxudqfh v|vwhp lq sodfh |rxqj ghsrvlwruv dyrlg wd{0
dwlrq gxulqj wkh fulvlv dqg rewdlq kljkhu h{shfwhg sd|rv1 Khqfh |rxqj ghsrvlwruv
zloo yrwh djdlqvw ghsrvlw lqvxudqfh>
+lll, \rxqj hqwuhsuhqhxuv* sd|r grhv qrw ghshqg rq wkh yrwlqj ghflvlrqv ri wkh
fxuuhqw shulrg1 Dv d uhvxow/ wkh| gr qrw yrwh>
+ly, Rog hqwuhsuhqhxuv kdyh dq h{shfwhg sd|r jlyhq e|
%

#

$

&

S
 
q RM -  EEU  U6  
{R
Vlqfh E 

E2  dqg U  U6 : f/ zh kdyh wkdw rog hqwuhsuhqhxuv zloo yrwh iru wkh

ghsrvlw lqvxudqfh1
Lq vxppdu|/ wkh rog jhqhudwlrq yrwhv iru wkh ghsrvlw lqvxudqfh v|vwhp exw rqo|
wkh ghsrvlwruv ri wkh |rxqj jhqhudwlrq yrwh djdlqvw lw1 Khqfh wkh ghsrvlw lqvxudqfh
4:

sursrvdo zloo zlq lq d srolwlfdo frqwhvw wkdw uhshdwv lwvhoi hyhu| shulrg1 Wkh lqwhuhvw
udwh lq wkh srolwlfdo htxloleulxp lv wkhq  ' E  ' *q
W

Dw wkh hqg ri wkh suhylrxv vhfwlrq zh vkrzhg wkdw zkhq Dvvxpswlrqv D4 dqg D5



krog wkh Ehqhyrohqw Htxloleulxp zloo kdyh qr ghsrvlw lqvxudqfh lq sodfh1 Krzhyhu/
Sursrvlwlrq 5 vkrzv wkdw li wkh jryhuqphqw lv vxemhfw wr srolwlfdo suhvvxuh dqg lwv
ghflvlrqv duh ghwhuplqhg sulpdulo| e| wklv suhvvxuh/ wkhq lw pd| eh wkdw lq htxloleulxp
+Srolwlfdo Htxloleulxp, wkh ghsrvlw lqvxudqfh v|vwhp dfwxdoo| pdnhv lwv zd| lqwr wkh
prqhwdu|0edqnlqj duudqjhphqwv ri wkh hfrqrp|1 Lq wklv fdvh/ wkh jryhuqphqw pd|
ehqhw iurp d srolf| wkdw vkxwv grzq h{0dqwh wkh vrxufhv ri ixqgv wkdw duh xvhg wr
qdqfh wkh lqvxudqfh v|vwhp1 Wklv eulqjv xv wr rxu irupdo ghqlwlrq ri groodul}dwlrq
lq wklv hqylurqphqw1
Ghqlwlrq 5 D Shulrg0|_ Groodul}dwlrq lv wkh FE srolf| wkdw vhwv Erc c |  f iru
doo |  |_ 
Wklv lv zk| zh fdoo rxu vwxg| d vfdo wkhru| ri groodul}dwlrq145 Wkhuh lv qr prqh|
lq rxu prgho1 Dv zh dujxh lq wkh lqwurgxfwlrq/ wkh lq dwlrqdu| wd{ lv jhqhudoo| xvhg lq
edlorxwv ri wkh edqnlqj vhfwru1 Lw sod|v wkh uroh ri dq hphujhqf| wd{1 Groodul}dwlrq
lv wkhq d zd| wr eorfn wklv vrxufh ri ixqgv1 Zh frqvlghu wkdw rxu vshflfdwlrq zhoo
fdswxuhv wklv hvvhqwldo ihdwxuh ri wkh sureohp1 Qrwh wkdw wkh suhylrxv ghqlwlrq
ghvfulehv groodul}dwlrq dv dq luuhyhuvleoh srolf|1 Vfkplww0Jurkì dqg Xuleh +5333, fdvw
vrph grxewv rq wkh dssursuldwhqhvv ri wklv vwulfw ghqlwlrq1 Wkh| surylgh h{dpsohv
ri uhjlrqdo hfrqrplhv wkdw kdyh ehhq deoh wr +uh0, lqwurgxfh d orfdo fxuuhqf| lqwr wkh
v|vwhp gxulqj shulrgv ri qdqfldo glvwuhvv1 Yhogh dqg Yhudflhuwr +5333, dovr glvfxvv
wklv srlqw dqg wkh| surylgh vrph vshflf duudqjhphqwv wkdw d jryhuqphqw frxog xvh
lq rughu wr dgrsw d fuhgleo| luuhyhuvleoh groodul}dwlrq srolf|1
45

Iru d vlplodu shuvshfwlyh rq wkh vfdo glvflsolqlqj uroh ri groodul}dwlrq vhh Exuqvlgh/ Hlfkhqedxp
dqg Uhehor +5333,1

4;

Ohw xv fdoo Ehqhyrohqw Rxwfrph wkh rxwfrph ri d Ehqhyrohqw Htxloleulxp dv gh0
vfulehg lq Sursrvlwlrq 41 Wkhq/ wkh iroorzlqj sursrvlwlrq gluhfwo| iroorzv1
Sursrvlwlrq 6 Ohw D4 dqg D5 krog1 Wkh FE fdq lpsohphqw wkh Ehqhyrohqw Rxw0


frph e| groodul}lqj dw wkh ehjlqqlqj ri wlph/ l1h1/ zlwk |_ ' 1
Zh fdq wkhq vd| wkdw lq wklv hqylurqphqw wkh groodul}dwlrq srolf| doorzv wkh FE
wr frpplw wr d srolf| ri qr gh0idfwr ghsrvlw lqvxudqfh1 Lq d vhqvh/ e| dgrswlqj
groodul}dwlrq wkh jryhuqphqw0FE lv deoh wr uhvlvw wkh srolwlfdo suhvvxuhv wr edlorxw
wkh edqnlqj v|vwhp xqghujrlqj d shulrg ri fulvlv1 Krzhyhu/ wklv vroxwlrq ohdyhv xv
zlwk wkh qh{w qdwxudo txhvwlrq= krz grhv wkh jryhuqphqw0FE qg srolwlfdo vxssruw
iru groodul}dwlrqB Wkh qh{w sursrvlwlrq vkrzv wkdw groodul}dwlrq zloo qrw qg wkh
vxssruw ri d pdmrulw| ri yrwhuv dw dq| jlyhq shulrg |1
Sursrvlwlrq 7 Ohw D4 dqg D5



krog1 Wkhq/ d Shulrg0| Groodul}dwlrq lv qrw d

Srolwlfdo Htxloleulxp ri wkh hfrqrp| iru dq| |  1
Surri1 Wkh surri iroorzv wkh vdph orjlf dv wkdw ri Sursrvlwlrq 51 Qhyhuwkhohvv/
wkh yrwlqj ghflvlrqv duh qrz fkdqjhg gxh wr wkh shupdqhqw qdwxuh +luuhyhuvlelolw|, ri
groodul}dwlrq1 Ohw xv xvh wkh yduldeoh _ 5 i_ c _2 j wr lqglfdwh zkhwkhu wkh v|vwhp lv
groodul}hg +_  ru qrw groodul}hg +_2 ,1 Iurp Sursrvlwlrq 5 zh nqrz wkdw
 E_2  ' E c _2  '
W


c
q

dqg wkdw A E(c (( _2  ' A  E(c (1 Lw lv dovr vwudljkwiruzdug wr vhh wkdw
W

 E_  ' Ec _  '
W


RM q



Frqvlghu qrz wkh yrwlqj ghflvlrqv iru wkh glhuhqw djhqwv lq wkh hfrqrp|=

4<

+l, Rog ghsrvlwruv* sd|r lv jlyhq e|
k

l

RM  E_( n E  RM  A E(c (( _  DA E(c((_ ( 
W

W

W

Li _ ' _ wkhq wkhlu sd|r lv jlyhq e| E*q(  E  RM Dc dqg li _ ' _2 lw lv jlyhq
e| E*q( Khqfh/ rog ghsrvlwruv yrwh djdlqvw wkh groodul}dwlrq sursrvdo1
+ll, \rxqj ghsrvlwruv* sd|r lv jlyhq e|
e  (  E  RM 
zkhuh

W

W

k

l

n q RM  E_( n E  RM EA E(c (( _  DA E(c((_ (  c
W

W

W

' 1A E(c (( _ Qrwh wkdw zkhq yrwlqj rq groodul}dwlrq wkh |rxqj djhqwv
W

pd| dfwxdoo| eh deoh wr lq xhqfh wkhlu rog0djh sd|r1 Wklv lv qrw wuxh zlwk wkh yrwlqj
ri ghsrvlw lqvxudqfh hyhu| shulrg dv lq Sursrvlwlrq 51 Qrz/ li _ ' _ wkhlu sd|r lv
e  ( n qdE*q(  E  RM Do dqg li _ ' _2 wkhlu sd|r lv e  (  E  RM E1*q( n
qE*q( Khqfh/ |rxqj ghsrvlwruv zloo yrwh lq idyru ri groodul}dwlrq zkhqhyhu wkh
iroorzlqj lqhtxdolw| krogv
qD

1
(
q

+9,

Exw e| Dvvxpswlrq +D51f, zh nqrz wkdw ( ' ( : (f lq htxloleulxp zklfk


lpsolhv wkdw lqhtxdolw| +9, dozd|v krogv1 Wkdw lv/ |rxqj ghsrvlwruv zloo idyru groodu0
l}dwlrq lq htxloleulxp1
+lll, Erwk |rxqj dqg rog hqwuhsuhqhxuv fdq qrz ghwhuplqh e| yrwlqj +ru dw ohdvw
wkh| eholhyh vr, zklfk lv wkh lqwhuhvw udwh rq ordqv wkh| zloo dfwxdoo| idfh1 Vlqfh
 E_  :  E_2 c wkh| yrwh djdlqvw groodul}dwlrq146
W

W

Dv d uhvxow/ wkh groodul}dwlrq sursrvdo grhv qrw jhw vx!flhqw vxssruw dqg lv qrw d
Srolwlfdo Htxloleulxp ri wkh prgho1
46

Hqwuhsuhqhxuv sd|r lv vwloo jlyhq e|
 


f
 sK U  +g,+L  Lp , 
E
s

dqg Lp lv lqghshqghqw ri g +vhh Iljxuh 4,1

53

Rqh pd| wklqn wkdw Sursrvlwlrq 7 lv dq duwlfldo frqvhtxhqfh ri wkh jhqhudwlrqdo
vwuxfwxuh ri rxu prgho1 Krzhyhu/ dq lqwhuhvwlqj jhqhudo lqvljkw frphv rxw iurp wklv
vshflf uhvxow1 Wkh sursrvlwlrq vxjjhvwv wkdw hyhq zkhq groodul}dwlrq lv frqvlghuhg
wkh ehvw srolf| iru vrflhw| ryhudoo/ wkh FE pd| kdyh wr zdlw iru dq dssursuldwh
wlph wr odxqfk wkh sursrvdo1 Zkhq srolwlfdo frqvlghudwlrqv ehfrph lpsruwdqw/ lw
vhhpv hvvhqwldo iru wkh vxffhvv ri wkh groodul}dwlrq sodq wr qg d wlph shulrg lq zklfk
wkhuh lv d uhodwlyho| vpdoo jurxs ri ghsrvlwruv jhwwlqj srvlwlyh qhw wudqvihuv iurp d
frqwlqjhqw edlorxw ri wkh edqnlqj vhfwru +rog ghsrvlwruv lq wkh prgho duh wkh qhw0
wudqvihuv uhflslhqwv,1

8

Wkh Edqnlqj V|vwhp

Dv zh vdz lq wkh suhylrxv vhfwlrq/ groodul}dwlrq pd| eh d xvhixo srolf| iru wkh FE wr
frpplw lwvhoi dqg qrw jhw lqyroyhg lq edqnlqj0vhfwru edlorxwv wkdw duh ghwulphqwdo iru
vrflhw| ryhudoo1 Krzhyhu/ zh dovr vkrzhg wkdw lq wkhvh vlwxdwlrqv lw lv vrphwlphv gli0
fxow wr rewdlq wkh srolwlfdo vxssruw qhfhvvdu| wr lpsohphqw wkh groodul}dwlrq srolf|1
Exw hyhq li wkh FE fdq jdlq wkh yrwhuv dgyrfdf| iru wkh sursrvdo/ dqrwkhu lpsruwdqw
txhvwlrq vwloo dulvhv= Zkdw vkrxog wkh FE gr zkhq d fulvlv frphvB Rqh srvvlelolw|
frxog eh wr wu| wr dyrlg wkhvh edqnlqj fulvhv dowrjhwkhu +hyhq dw wkh frvw ri pdmru hfr0
qrplf uhvwuxfwxulqj,1 Iru wklv/ lqwhuqdwlrqdo edqnv rxjkw wr eh vhulrxvo| frqvlghuhg
+vhh Fdoyr +5333,,1
Vxssrvh wkdw wkh grphvwlf hfrqrp| frqvlghuhg lq wkh suhylrxv wzr vhfwlrqv lv
lq idfw sduw ri d odujh jurxs ri lqghshqghqw hfrqrplhv +frxqwulhv, wkdw irup wkh
zruog1 Dovr dvvxph wkdw wkh hyhqw ri surmhfw0vxffhvv lq hdfk ri wkh glhuhqw frxqwulhv
lv xqfruuhodwhg1 Khqfh/ dq lqwhuqdwlrqdo edqn frxog ixoo| glyhuvli| lwv sruwirolr ri
surmhfwv dqg dozd|v jhw d sursruwlrq RM ri vxffhvv shu shulrg +vhh Hqqlv/ 5333,1

54

Lq wkdw fdvh/ wkh djhqf| sureohp dw wkh prqlwru*v ohyho glvdsshduv dqg qr fdslwdo
uhtxluhphqwv duh qhfhvvdu| iru lqwhuqdwlrqdo edqnv1 Dvvxph krzhyhu wkdw wkhuh h{lvwv
dq h{wud rshudwlrqdo frvw ri kdylqj d ixoo| glyhuvlhg zlghvsuhdg lqvwlwxwlrq1 Ohw wkdw
frvw eh sursruwlrqdo wr wkh vl}h ri wkh edqn dqg ghqrwhg e| Bc wkh shu0ghsrvlwru frvw1
Iru prvw ri wkh uhvxowv lq wkh vhfwlrq zh zloo vhw B ' f
Ohw xv fdoo   wkh dprxqw sdlg wr wkh lqwhuqdwlrqdo edqn e| d vxffhvvixo hq0
wuhsuhqhxu zlwk d fuhglw ri U xqlwv1 Lw lv qrw kdug wr vhh wkdw
 '


U n  
RM

Qrwh wkdw wkh lqwhuhvw udwh ryhu wkh ordq lv kljkhu wkdq wkh lqwhuhvw udwh ryhu ghsrvlwv1
Wklv vsuhdg lv gxh wr wkh idfw wkdw wklv v|vwhp uhpryhv wkh vxevlg| ryhu ordqv lpsolflw
lq wkh ghsrvlw lqvxudqfh vfkhph1
Vlqfh dq|rqh rzqlqj d prqlwrulqj whfkqrorj| fdq vhw xs dq lqwhuqdwlrqdo edqn/
wkh iroorzlqj }hur0surw frqglwlrq zloo krog lq htxloleulxp/
RM   ' U n S n B
Wklv lpsolhv wkdw lqwhuqdwlrqdo edqnv fkdujh d ihh  jlyhq e|
 '

SnB

RM

Ohw  eh wkh dprxqw sdlg wr edqnv e| hqwuhsuhqhxuv zlwk d ordq ri U xqlwv xqghu
W

wkh gh0idfwr ghsrvlw0lqvxudqfh v|vwhp1 Iurp wkh suhylrxv vhfwlrq zh kdyh wkdw
 ' U n c
W

W

W

zkhuh  ' *q dqg  ' E  Ru S*{R Zkhq B ' f zh kdyh wkdw  :   Krzhyhu/
W

W

W

lw pd| vwloo zhoo eh wkdw   :  vlqfh wkh lqwhuhvw udwh rq ordqv lv kljkhu xqghu
W

wkh lqwhuqdwlrqdo0edqnv v|vwhp1 Wklv lv lpsruwdqw ehfdxvh zkhq   :  wkh lqwhu0
W

qdwlrqdo edqnv zloo qrw eh xvhg e| wkh hqwuhsuhqhxuv ri dq hfrqrp| zlwk +lpsolflw,
55

ghsrvlw lqvxudqfh1 Zh fdq qrz frpsduh wkh ydoxh ri wkh ehqhyrohqw0FE remhfwlyh
ixqfwlrq xqghu wkh dowhuqdwlyh v|vwhpv= wkh ghsrvlw lqvxudqfh v|vwhp +` E(, dqg/
wkh lqwhuqdwlrqdo0edqnv v|vwhp +`  ,1 Vlpsoh dojheud jlyh xv wkh iroorzlqj h{suhvvlrq/
` E(  `  ' E  kqRM E      Ek  wE  RM  Ec
W

zklfk fohduo| vkrzv wkdw hyhq zkhq lqwhuqdwlrqdo edqnv duh qrw xvhg lq htxloleulxp
+l1h1/   :   lw frxog eh wkh fdvh wkdw lw zrxog eh ehvw iru wkh hfrqrp| ryhudoo wr
W

kdyh wkhp ixqfwlrqlqj +l1h1 ` E(  `

f,1

Vr idu zh kdyh frqvlghuhg wkh gh0idfwr ghsrvlw0lqvxudqfh v|vwhp wr eh wkh ghidxow
v|vwhp1 Wklv pdnhv vhqvh vlqfh zh kdyh suryhg lq wkh suhylrxv vhfwlrqv wkdw lw lv wkh
v|vwhp wkdw wkh Srolwlfdo Htxloleulxp zloo vhohfw1 Exw iru uhdvrqv wkdw zloo ehfrph
fohdu ehorz/ lw lv dovr lqwhuhvwlqj wr frqvlghu wkh hhfwv ri lqwhuqdwlrqdo edqnlqj xqghu
d groodul}dwlrq srolf|1 Dv ehiruh/ ohw xv fdoo  _ wkh vxp wkdw hqwuhsuhqhxuv zlwk U
xqlwv ri fuhglw sd| wr edqnv1 Iurp wkh suhylrxv vhfwlrq zh nqrz wkdw
 _ '  _ U n _ '


RM q

Un

S
c
RM

zkhuh zh kdyh ghqhg  _   E_  wr vlpso| wkh qrwdwlrq ri Vhfwlrq 71 Qrwh wkdw  _ '
W

   Khqfh/ hqwuhsuhqhxuv zloo eh lqglhuhqw ehwzhhq wdnlqj d fuhglw iurp d orfdo edqn
ru dq lqwhuqdwlrqdo edqn1 Krzhyhu/ vlqfh orfdo edqnv idlo zlwk suredelolw| E  RM 
dqg ghsrvlwruv vxhu d orvv D zkhq wklv kdsshqv/ lqwhuqdwlrqdo edqnv zloo fdswxuh
ghsrvlwv dqg fdq suhydlo ryhu orfdo edqnv lq htxloleulxp147 Wklv uhvxow lv lpsruwdqw1
Frqvlghu wkh vlwxdwlrq zkhuh wkh FE suhihuv wkh lqwhuqdwlrqdo0edqnv v|vwhp ryhu wkh
ghsrvlw0lqvxudqfh v|vwhp/ wkdw lv zkhq ` E(
47

`  1 Li wkh FE fdq lpsohphqw d

Wkhuh lv d frruglqdwlrq lvvxh khuh wkdw zh fkrvh wr sxw dvlgh1 Zkhq doo exw rqh ghsrvlwru gr
exvlqhvv zlwk orfdo edqnv/ wkh rqh lqglylgxdo uhpdlqlqj zloo eh lqglhuhqw ehwzhhq ghsrvlwlqj lq wkh
lqwhuqdwlrqdo edqnv ru lq wkh grphvwlf edqnv1 Wklv lv ehfdxvh hlwkhu zd|/ xqghu wkh fulvlv vlwxdwlrq/
vkh zloo h{shulhqfh wkh xwlolw| frvw  gxh wr wudqvdfwlrqv0sd|phqwv glvuxswlrq1 Qrwh wkdw zh duh
dvvxplqj khuh wkdw doo ghsrvlwruv fkrrvh wkh lqwhuqdwlrqdo edqn hyhq lq wklv vlwxdwlrq1

56

groodul}dwlrq0soxv0lqwhuqdwlrqdo0edqnv v|vwhp wkhq lw zloo eh deoh wr rewdlq wkh ghvluhg
` 1
Lq vxppdu|/ zh kdyh vhhq wkdw zkhq d +shukdsv lpsolflw, ghsrvlw lqvxudqfh v|vwhp
lv lq sodfh/ lqwhuqdwlrqdo edqnv zloo qrw eh xvhg hyhq zkhq wkh| duh ehqhfldo iru wkh
vrflhw| dv d zkroh1 Krzhyhu/ zkhq wkh hfrqrp| lv groodul}hg/ lqwhuqdwlrqdo edqnv zloo
eh h{whqvlyho| xvhg lq htxloleulxp1 Groodul}dwlrq dqg lqwhuqdwlrqdo edqnlqj duh lq d
vhqvh jrrg frpsohphqwv1
Dq lpsruwdqw txhvwlrq vwloo uhpdlqv= zrxog wkh lqwhuqdwlrqdo edqnlqj soxv groodu0
l}dwlrq srolf| rewdlq vx!flhqw srolwlfdo vxssruw wr eh lpsohphqwdeohB Wkh iroorzlqj
sursrvlwlrq vxjjhvwv d srvvleoh dqvzhu1
Sursrvlwlrq 8 Ohw D4 dqg D5 krog1 Li 2E  k

Ek  w wkhq wkh groodul}dwlrq



0soxv0lqwhuqdwlrqdo0edqnv srolf| frqvwlwxwhv d Srolwlfdo Htxloleulxp1
Surri1 Zkhq yrwlqj/ djhqwv zloo frpsduh wkhlu sd|r lq wkh +lpsolflw, ghsrvlw
lqvxudqfh v|vwhp zlwk wkhlu sd|r lq d groodul}dwlrq0soxv0lqwhuqdwlrqdo0edqnv v|vwhp1
Wklv lv ehfdxvh wkh srolwlfdo htxloleulxp zlwkrxw groodul}dwlrq kdv ghsrvlw lqvxudqfh
dv wkh rxwfrph1 Frqvlghu uvw wkh yrwlqj ghflvlrq ri ghsrvlwruv1 Rog ghsrvlwruv jhw
E*q( lq hlwkhu v|vwhp dqg khqfh wkh| gr qrw yrwh1 \rxqj ghsrvlwruv jhw
e  (  E  RM  n q (
W

W

lq wkh ghsrvlw0lqvxudqfh v|vwhp dqg e(q  ( lq wkh groodul}dwlrq0soxv0lqwhuqdwlrqdo0
edqnv v|vwhp1 Vlqfh   '  ' *q/ |rxqj ghsrvlwruv zloo yrwh lq idyru ri groodul}d0
W

wlrq1 Ilqdoo|/ wkh sd|r iru erwk |rxqj dqg rog hqwuhsuhqhxuv lv jlyhq e|
q dRM E-     o 
Wzr srvvleoh fdvhv qhhg wr eh frqvlghuhg khuh1 Iluvw/ zkhq  



W

lw lv fohdu

wkdw hqwuhsuhqhxuv zloo yrwh iru groodul}dwlrq1 Wkhq/ groodul}dwlrq zlqv wkh edoorw
57

e| xqdqlplw|1 Vhfrqg/ zkhq   :  hqwuhsuhqhxuv yrwh iru wkh vwdwxv txr/ wkdw
W

lv/ wkh lpsolflw ghsrvlw0lqvxudqfh v|vwhp1 Krzhyhu/ vlqfh 2E  k

Ek  w krogv/

groodul}dwlrq vwloo grplqdwhv wkh yrwhv dqg khqfh lw zloo jhw lpsohphqwhg1
Qrwh wkdw rqfh lqwhuqdwlrqdo edqnv duh lqwurgxfhg/ zkhwkhu wkh hfrqrp| lv gro0
odul}hg ru qrw grhv qrw lq xhqfh wkh htxloleulxp rxwfrph1 Krzhyhu/ groodul}dwlrq
lv lpsruwdqw wr hqvxuh wkdw lqyhvwruv dqg ghsrvlwruv rshudwh zlwk wkh lqwhuqdwlrqdo
edqnv lq htxloleulxp1 Lq wkh groodul}hg hfrqrp| wkh grphvwlf edqnlqj v|vwhp sur0
ylghv qr ghsrvlw lqvxudqfh dqg khqfh lqwhuqdwlrqdo edqnv fdq suhydlo1
Wkh dvvxpswlrq wkdw 2E  k

Ek  w lv d vwdwhphqw derxw wkh uhodwlyh vl}h

glvwulexwlrq ri qhw ghewruv dqg fuhglwruv lq wkh yrwlqj srsxodwlrq1 Lw vd|v wkdw wkh
qxpehu ri qhw fuhglwruv shu jhqhudwlrq lv dw ohdvw wzlfh wkh qxpehu ri qhw ghewruv1
Zh duh lqfolqhg wr eholhyh wkdw wklv lv d uhdolvwlf dvvxpswlrq/ exw rxu dqdo|vlv fdq
fhuwdlqo| eh grqh zlwkrxw vxfk d uhvwulfwlrq1 Groodul}dwlrq0soxv0lqwhuqdwlrqdo0edqnv
zloo qrw dozd|v eh d srolwlfdo htxloleulxp lq wkdw fdvh wkrxjk1

9

Frqfoxvlrqv

Wkhuh duh dw ohdvw wzr srvvleoh zd|v wr wklqn derxw wkh uroh ri groodul}dwlrq gxulqj d
qdqfldo fulvlv1 Rq wkh rqh kdqg/ rqh frxog wklqn wkdw groodul}dwlrq whqgv wr uhgxfh
wkh fkdqfhv ri dq h{shfwdwlrqv0gulyhq fxuuhqf| froodsvh +vhh Yhogh dqg Yhudflhuwr
+5333, dqg Exuqvlgh/ Hlfkhqedxp dqg Uhehor/ 5333,1 Rq wkh rwkhu kdqg/ lw frxog
eh wkdw groodul}dwlrq lv d vxlwdeoh phfkdqlvp wr dyrlg wkh dpsolfdwlrq ri d grphvwlf
edqnlqj fulvlv lqwr d pruh jhqhudo ryhudoo frxqwu| ghidxow1 Wkh ylhzv h{suhvvhg lq
wkh suhvhqw sdshu duh forvhu lq vslulw wr wklv vhfrqg olqh ri lqwhusuhwdwlrq +vhh Fkdqj
dqg Yhodvfr +4<<;, dqg Ndplqvn| dqg Uhlqkduw +4<<<, iru d ghwdlohg glvfxvvlrq rq
wkh qdwxuh ri qdqfldo fulvhv xqghu wklv ylhz,1

58

Rxu vhw0xs lv kljko| vw|ol}hg1 Zh gr qrw lqwhqg wr eh ghvfulswlyh lq dq| zd|1
Lqvwhdg/ wkh remhfwlyh ri wkh sdshu lv wr looxvwudwh wkh lqwhudfwlrq ehwzhhq wkh uhodwlyh
shuirupdqfh ri wkh edqnlqj vhfwru dqg wkrvh jryhuqphqw srolflhv rulhqwhg wr frsh
zlwk lwv vsrudglf pdmru euhdngrzqv1 Zh vwuhvv wkh uroh wkdw wkh srolwlfdo surfhvv
pd| sod| lq wkh ghwhuplqdwlrq ri vshflf srolflhv/ dqg lq sduwlfxodu lq wkh ghflvlrq ri
zkhwkhu ru qrw wr groodul}h wkh hfrqrp|1 Zh vkrz wkdw lw pd| eh rswlpdo iru vrflhw|
dv d zkroh wr dgrsw d groodul}dwlrq v|vwhp wr klqghu wkh srolwlfdo suhvvxuhv wkdw idyru
d edqnlqj vhfwru edlorxw gxulqj d fulvlv1 Exw/ zh dovr vkrz wkdw zkhq lqwurgxfhg
dorqh groodul}dwlrq idfhv vxevwdqwldo srolwlfdo rssrvlwlrq/ uhgxflqj lwv fkdqfhv ri df0
wxdo lpsohphqwdwlrq1 Wkh uhdvrqv iru wklv uhvxow duh vrphzkdw glvwlqfw1 Rxu prgho
suhvhqwv d sduwldo wkhru| ri groodul}dwlrq wkdw vwuhvvhv lwv uroh dv d fulvlv srolf|1 Zh
ylhz groodul}dwlrq dv dq lqvwuxphqw wkdw wkh Fhqwudo Edqn fdq xvh wr frpplw qrw wr
jhw lqyroyhg lq shuqlflrxv wudqvihu vfkhphv gxulqj shulrgv ri qdqfldo glvwuhvv1 Wkhuh
lv qr dqqxdo vhljqrudjh orvv dvvrfldwhg zlwk groodul}dwlrq lq rxu prgho +vhh Ehuj
dqg Eruhqv}whlq +5333, dqg dovr Frroh| dqg Txdgulql +4<<<, dqg Vfkplww0Jurkì
dqg Xuleh +5333, iru vrph txdqwlwdwlyh dvvhvvphqwv ri wkh srvvleoh orvvhv dvvrfldwhg
zlwk groodul}dwlrq,1 Krzhyhu/ xqghu d qrq0groodul}hg v|vwhp wkhuh lv dozd|v d odwhqw
pdvv0wudqvihu ri uhvrxufhv yld edlorxwv uhdg| wr eh wuljjhuhg e| wkh vxujh ri pdmru
edqnlqj0vhfwru wxuprlo1 Zkhq wkh wudqvihu jrhv iurp d vpdoo jurxs +ohvv srolwlfdoo|
srzhuixo, wr d odujh jurxs +pruh srolwlfdoo| srzhuixo,/ lw fdq xqghuplqh wkh srolwlfdo
vxssruw iru groodul}dwlrq/ hyhq lq fdvhv zkhuh groodul}dwlrq lv dq rwkhuzlvh vrfldoo|
ehqhfldo srolf|1 Wklv dffrxqw pd| vhhp shvvlplvwlf xs wr wklv srlqw1 Exw zh kdyh
dovr vkrzq wkdw wkhuh h{lvwv dq dowhuqdwlyh srolf| wkdw fdq dfklhyh wkh ghvluhg qr0
edlorxwv rxwfrph= wkh lqwurgxfwlrq0surprwlrq ri lqwhuqdwlrqdo edqnv1 Wklv lqghhg
fdq vx!flhqwo| lqfuhdvh wkh srolwlfdo vxssruw iru groodul}dwlrq1 Dqg vlpxowdqhrxvo|/
groodul}dwlrq lv dq hvvhqwldo frpsrqhqw iru wkh surprwlrq ri lqwhuqdwlrqdo edqnv dv
59

lw fxuwdlov wkh lpsolflw vxevlg| dwwdfkhg wr wkh xvh ri grphvwlf qdqfldo lqvwlwxwlrqv1
Khqfh/ wkh frpelqdwlrq ri groodul}dwlrq dqg edqn lqwhuqdwlrqdol}dwlrq fdq vroyh wkh
sureohp ri kdylqj wudqvihu vfkhphv +lpsolflw edqnlqj edlorxwv, wkdw duh ghwulphqwdo
iru vrflhw| dv d zkroh1

5:

Uhihuhqfhv
^4` Ehhuv/ G1/ W1 Vdujhqw dqg Q1 Zdoodfh +4<;6,/ Vshfxodwlrqv Derxw wkh Vshfxodwlrq
Djdlqvw wkh Krqj Nrqj Groodu/ Ihghudo Uhvhuyh Edqn ri Plqqhdsrolv Txduwhuo|
Uhylhz :/ Idoo1
^5` Ehuj/ D1 dqg H1 Eruhqv}whlq +5333,/ Wkh Surv dqg Frqv ri Ixoo Groodul}dwlrq/
LPI Zrunlqj Sdshu 33283/ Pdufk1
^6` Erowrq/ S1 dqg K1 Urvhqwkdo +4<<<,/ Srolwlfdo Lqwhuyhqwlrq lq Ghew Frqwudfwv=
Prudwruld dqg Edlorxwv/ plphr/ Sulqfhwrq Xqlyhuvlw|1
^7` Exuqvlgh F1/ E1 Hlfkhqedxp dqg V1 Uhehor +5333,/ Rq wkh Ixqgdphqwdov ri
Vhoi0Ixooolqj Vshfxodwlyh Dwwdfnv/ QEHU Zrunlqj Sdshu &:887/ Iheuxdu|1
^8` Fdoyr/ J1 +5333,/ Fdslwdo Pdunhwv dqg wkh H{fkdqjh Udwh/ plphr/ Xqlyhuvlw|
ri Pdu|odqg1
^9` Fkdqj/ U1 dqg D1 Yhodvfr +4<<;,/ Wkh Dvldq Oltxlglw| Fulvlv/ Ihghudo Uhvhuyh
Edqn ri Dwodqwd Zrunlqj Sdshu <;0441
^:` Frroh|/ W1 dqg Y1 Txdgulql +4<<<,/ Wkh Frvwv ri Orvlqj Prqhwdu| Lqghshqghqfh=
Wkh Fdvh ri Ph{lfr/ iruwkfrplqj lq Mrxuqdo ri Prqh|/ Fuhglw dqg Edqnlqj1
^;` Hqqlv/ K1 +5333,/ Ordqdeoh Ixqgv/ Prqlwrulqj dqg Edqnlqj/ iruwkfrplqj lq
Hxurshdq Ilqdqfh Uhylhz1
^<` Jurss/ U1 dqg M1 Yhvdod +5333,/ Fkduwhu Ydoxh dqg Ghsrvlw Lqvxudqfh dv Ghwhu0
plqdqwv ri Ulvn Wdnlqj lq HX Edqnlqj/ plphr/ Hxurshdq Fhqwudo Edqn1
^43` Kropvwurp/ E1 dqg M1 Wluroh +4<<:,/ Ilqdqfldo Lqwhuphgldwlrq/ Ordqdeoh Ixqgv/
dqg Wkh Uhdo Vhfwru/ Txduwhuo| Mrxuqdo ri Hfrqrplfv 95/ 99609<41
5;

^44` Ndplqvn|/ J1 dqg F1 Uhlqkduw +4<<<,/ Wkh Wzlq Fulvhv= Wkh Fdxvhv ri Edqnlqj
dqg Edodqfh0ri0Sd|phqwv Sureohpv/ Dphulfdq Hfrqrplf Uhylhz ;</ 7:608331
^45` Nuxvhoo/ S1/ Y1 Txdgulql dqg M1 Ulrv0Uxoo +4<<:,/ Srolwlfr0Hfrqrplf Htxloleulxp
dqg Hfrqrplf Jurzwk/ Mrxuqdo ri Hfrqrplf G|qdplfv dqg Frqwuro 54/ 57605:51
^46` Shfn/ M1 dqg N1 Vkhoo +4<<<,/ Edqn Sruwirolr Uhvwulfwlrqv dqg Htxloleulxp Edqn
Uxqv/ FDH Zrunlqj Sdshu &<<03:/ Fruqhoo Xqlyhuvlw|1
^47` Vfkplww0Jurkì/ V1 dqg P1 Xuleh +5333,/ Vwdelol}dwlrq Srolf| dqg wkh Frvwv ri
Groodul}dwlrq/ iruwkfrplqj lq Mrxuqdo ri Prqh|/ Fuhglw dqg Edqnlqj1
^48` Yhod}fr/ D1 +4<;:,/ Ilqdqfldo Fulvhv dqg Edodqfh ri Sd|phqwv Fulvhv/ Mrxuqdo ri
Ghyhorsphqw Hfrqrplfv 5:/ 59605;61
^49` Yhogh/ I1 dqg P1 Yhudflhuwr +5333,/ Groodul}dwlrq lq Dujhqwlqd/ Ihghudo Uhvhuyh
Edqn ri Fklfdjr Hfrqrplf Shuvshfwlyhv/ Iluvw Txduwhu1

5<

Iljxuh 4=


63