CSAE WPS/2006-04
Ulglqj wkh Zdyh= Prqhwdu| Uhvsrqvhv wr Dlg
Vxujhv lq Orz0Lqfrph Frxqwulhv
Hgzdug Ex!h
Xqlyhuvlw| ri Lqgldqd
Fkulvwrskhu DgdpW
Xqlyhuvlw| ri R{irug dqg FVDH
Vwhskhq R*Frqqhoo
Vzduwkpruh Froohjh/ SD dqg FVDH
Fdwkhulqh Sdwwloor
Lqwhuqdwlrqdo Prqhwdu| Ixqg dqg FVDH
Mdqxdu| 5339
Devwudfw
Zh irfxv rq wkh pdqdjhphqw ri kljko| shuvlvwhqw vkrfnv wr dlg rzv/
lqfoxglqj KLSF ru PGJ0uhodwhg lqfuhdvhv lq qhw rzv/ lq wkh suhvhqfh ri
fxuuhqf| vxevwlwxwlrq e| wkh grphvwlf sulydwh vhfwru1 Vxfk vkrfnv kdyh
ehqhfhqw orqj0uxq hhfwv/ exw zkhq fxuuhqf| vxevwlwxwlrq lv kljk wkh|
fdq surgxfh gudpdwlf pdfurhfrqrplf pdqdjhphqw sureohpv lq wkh vkruw
uxq1 Zkdw lv wkh dssursuldwh pl{ ri prqh| dqg h{fkdqjh udwh wdujhwlqj lq
vxfk fdvhv/ dqg wkh uroh ri whpsrudu| vwhulol}dwlrqB Zh dqdo|}h wkhvh dqg
uhodwhg lvvxhv lq dq lqwhuwhpsrudo rswlpl}lqj prgho wkdw doorzv d sruwlrq
ri dlg wr eh ghyrwhg wr uhgxflqj wkh jryhuqphqw*v vhljqlrudjh uhtxluhphqw1
Rxu uhvxowv dujxh wkdw d pdqdjhg rdw/ zlwk olwwoh ru qr vwhulol}dwlrq ri
lqfuhdvhv lq wkh prqhwdu| edvh/ lv wkh prvw dwwudfwlyh dssurdfk1
MHO Frghv= R45/ R56/ I74/ F941
Nh|zrugv Dlg/ Vwhulol}dwlrq/ Fxuuhqf| Vxevwlwxwlrq/ Vhljqlrudjh/ Diulfd1
W Fruuhvsrqglqj
dxwkru ^fkulvwrskhu1dgdpChfrqrplfv1r{1df1xn`
4
4
Lqwurgxfwlrq
Vlqfh wkh hduo| 4<<3v/ Diulfdq fhqwudo edqnv kdyh vwuxjjohg wr qg wkh dssur0
suldwh pl{ ri prqh| dqg h{fkdqjh udwh wdujhwlqj zkhq idfhg zlwk kljko| shu0
vlvwhqw vkrfnv wr dlg lq rzv +lqfoxglqj SUVS0 dqg KLSF0uhodwhg lqfuhdvhv lq
qhw rzv,14 Lq pdq| hslvrghv/ kljkhu dlg rzv kdyh dwwudfwhg htxdoo| odujh lq0
rzv ri sulydwh fdslwdo15 Wkh frpelqhg vxujh ri r!fldo dqg sulydwh fdslwdo rzv
lv ehqhfldo lq wkh orqj uxq exw frqiurqwv srolf| pdnhuv zlwk gudpdwlf prq0
hwdu| pdqdjhphqw sureohpv lq wkh vkruw uxq1 Wkxv ihdu ri rdwlqj +Fdoyr
dqg Uhlqkduw/ 5333, lqlwldoo| vsxuv wkh fhqwudo edqn wr lqwhuyhqh lq wkh iruhljq
h{fkdqjh pdunhw1 Exw uhvhuyh dffxpxodwlrq wkhq h{sdqgv wkh prqhwdu| edvh/
jhqhudwlqj ihduv ri lq dwlrq dqg ryhukhdwlqj1 Erqg vdohv pd| eh xvhg wr vwhu0
lol}h wkh oltxlglw| lqmhfwlrq/ exw wklv ohdgv wr odujh lqfuhdvhv lq uhdo lqwhuhvw udwhv1
Lq wkh hqg/ srolf| pdnhuv kdyh wr pdnh d gl!fxow ghflvlrq= zkdw frpelqdwlrq
ri fkdqjhv lq lq dwlrq/ qrplqdo dqg uhdo h{fkdqjh udwhv/ dqg uhdo lqwhuhvw udwhv
vkrxog eh xvhg wr devrue wkh dlg vkrfn1 Uhfhqw prphqwxp iru d elj dlg sxvk
wr phhw wkh Ploohqlxp Ghyhorsphqw Jrdov vxjjhvwv wkdw wkhvh srolf| fkdoohqjhv
pd| eh hyhq pruh lpsruwdqw lq wkh qh{w ghfdgh1
Wkh qdwxudo sodfh wr orrn iru dqvzhuv lv lq wkh ydvw olwhudwxuh rq fdslwdo rzv
wr hphujlqj pdunhw hfrqrplhv/ zklfk kdv zuhvwohg zlwk pdq| ri wkh sureohpv
wkdw frqfhuq Diulfd*v fhqwudo edqnv1 Exw zkloh wkh fdslwdo lq rzv olwhudwxuh lv
odujh/ lw frqwdlqv olwwoh lq wkh zd| ri fohdq/ suhflvh uhvxowv1 Wklv lv qrw vxusulv0
lqj1 D ixoo dqg uljrurxv wuhdwphqw ri wkh lvvxhv dvvrfldwhg zlwk fdslwdo lq rzv
uhtxluhv wkh dqdo|vlv ri pxowlsoh vfhqdulrv lq pxowlsoh prghov +{hg yv1 h{leoh
h{fkdqjh udwhv dqg sdvvlyh yv1 dfwlyh prqhwdu| srolf|/ iru d vwduw,1 Uhvhdufkhuv
lq wkh hog kdyh vwhhuhg zhoo fohdu ri wklv wdvn/ uho|lqj lqvwhdg rq jhqhudo wkhr0
uhwlfdo sulqflsohv wr hydoxdwh wkh olnho| hhfwv ri fdslwdo lq rzv dqg dowhuqdwlyh
srolf| uhphglhv1
Frqmhfwxuh lqiruphg e| wkhru| fdq jhqhudwh xvhixo lqvljkwv1 Wkhuh lv d olplw/
krzhyhu/ wr zkdw lw fdq dfklhyh1 Ghvslwh doo wkdw kdv ehhq zulwwhq/ wkh h{lvwlqj
olwhudwxuh kdv qrw pryhg eh|rqg d fkhfn olvw ri wklqjv wr wklqn derxw1 Frqwur0
yhuv| shuvlvwv wkhuhiruh uhjduglqj wkh h!fdf| ri erqg vwhulol}dwlrq/ wkh dsshdo ri
dowhuqdwlyh dssurdfkhv wr devruelqj grphvwlf oltxlglw|/ dqg wkh uhohydqfh ri xq0
ghuo|lqj frqfhuqv derxw ryhukhdwlqj17 Wkh odfn ri up frqfoxvlrqv kdv lqwhu
dold suhyhqwhg wkh olwhudwxuh iurp vhwwolqj rq d frkhuhqw erwwrp olqh iru srolf|1
Fdoyr/ Ohlghupdq/ dqg Uhlqkduw +4<<7,/ iru h{dpsoh/ uhfrpphqg frxqwhulqj
wkh xqghvluhdeoh hhfwv ri fdslwdo lq rzv wkurxjk d frpelqdwlrq ri vwhulol}dwlrq/
vfdo dgmxvwphqw/ juhdwhu h{fkdqjh udwh h{lelolw|/ dqg +shukdsv, kljkhu uhvhuyh
uhtxluhphqwv1 Wklv pd| eh wkh uljkw srolf| uhvsrqvh/ exw lw lv kdug wr hvfdsh
wkh lpsuhvvlrq wkdw lw lv d frqfhvvlrq wr ljqrudqfh/ wkdw wkh xqvsrnhq udwlrqdoh
lv pruh ru ohvv= Zh grq*w kdyh d jrrg kdqgoh rq wkh uhshufxvvlrqv ri glhuhqw
srolf| phdvxuhv/ vr gr d elw ri hyhu|wklqj dqg krsh iru wkh ehvw1
Wkh phvvdjh zh wdnh dzd| iurp wklv fulwltxh lv wkdw lw lv wlph wr jhw rq
zlwk wkh mre ri dqdo|}lqj fdslwdo lq rzv zlwk wkh dlg ri ixoo| duwlfxodwhg pdfur0
prghov1 Dffruglqjo|/ wkh suhvhqw sdshu vroyhv d g|qdplf jhqhudo htxloleulxp
prgho iru dq duud| ri srolf| vfhqdulrv wkdw gholqhdwh wkh wudghrv dvvrfldwhg
zlwk dowhuqdwlyh vwudwhjlhv iru pdqdjlqj odujh fdslwdo lq rzv1 Vlqfh zh kdyh wkh
Diulfdq frqwh{w lq plqg/ wkh lqlwldwlqj lq rzv duh r!fldo udwkhu wkdq sulydwh>
wkh r!fldoo| surqrxqfhg qrplqdo dqfkru lv prqh| udwkhu wkdq wkh h{fkdqjh
udwh> dqg wkh hfrqrplhv lq txhvwlrq duh orz0lqfrph udwkhu wkdq hphujlqj0pdunhw
5
hfrqrplhv/ zlwk fruuhvsrqglqjo| ohvv ghyhorshg qdqfldo pdunhwv1 Wkhvh ihd0
wxuhv jlyh wkh dqdo|vlv dq Diulfdq wzlvw/ exw wkh fhqwudo lvvxhv duh wkh vdph dv
lq wkh fdslwdo lq rzv olwhudwxuh1
Wkh uhvw ri wkh sdshu lv rujdql}hg lqwr vhyhq vhfwlrqv1 Iroorzlqj Ex!h
+5336,/ vhfwlrq 5 ghyhorsv wkh fruh vwuxfwxuh ri dq rswlpl}lqj wzr0vhfwru fxuuhqf|
vxevwlwxwlrq prgho lq zklfk dlg dffuxhv gluhfwo| wr wkh sxeolf vhfwru1 Wkh
jryhuqphqw vshqgv prvw exw qrw doo ri wkh dlg> frqvlvwhqw zlwk wkh gdwd iru
Vxe0Vdkdudq Diulfd/ zh dvvxph wkdw 58( ri wkh h{wud dlg lv ghyrwhg wr uhgxflqj
wkh jryhuqphqw*v vhljqlrudjh uhtxluhphqw1 Khqfh lq dwlrq ghfuhdvhv lq wkh orqj
uxq1
Lq vhfwlrqv 6 dqg 7 zh vroyh wkh prgho iru wkh srodu fdvhv ri d sxuh rdw dqg d
fudzolqj shj1 Zh doorz sulfhv wr eh h{leoh ru vwlfn| dqg fdoleudwh wkh prgho+v,
wr wkh gdwd iru Jkdqd/ d kljk0lq dwlrq hfrqrp| vodwhg wr uhfhlyh vxevwdqwldo ghew
uholhi lq wkh qh{w wkuhh |hduv18 Lw wxuqv rxw wkdw qhlwkhu ri wkh srodu h{fkdqjh udwh
uhjlphv gholyhuv vdwlvidfwru| uhvxowv1 D sxuh rdw nhhsv vkruw0uxq lq dwlrqdu|
suhvvxuhv lq fkhfn dw wkh frvw ri h{wuhph lqvwdelolw| lq wkh uhdo h{fkdqjh udwh
dqg vhyhuh frqwudfwlrq lq wkh qrqwudgdeohv vhfwru +dvvxplqj sulfhv duh qrw kljko|
h{leoh lq wkh grzqzdug gluhfwlrq,1 Xqghu d fudzolqj shj/ rq wkh rwkhu kdqg/
wkh sdwk ri wkh uhdo h{fkdqjh udwh lv vwdeoh exw qrw wkh sulfh ohyho kljkhu
dlg vshqglqj dqg sulydwh fdslwdo rzv wuljjhu d wuhphqgrxv xsiurqw vslnh lq wkh
FSL1 Wkxv srolf| pdnhuv kdyh wr fkrrvh wkhlu srlvrq> d frpplwphqw wr { ru
rdw hqwdlov wkh vdfulfh ri dw ohdvw rqh lpsruwdqw pdfurhfrqrplf wdujhw1
Vhhnlqj d ehwwhu phqx ri fkrlfhv/ zh h{dplqh wzr dowhuqdwlyh vwudwhjlhv lq
vhfwlrq 8= +l, whpsrudu| vwhulol}dwlrq ri fdslwdo lq rzv lq d fudzolqj shj dqg +ll,
d pdqdjhg rdw wkdw wdujhwv wkh orqj0uxq htxloleulxp uhdo h{fkdqjh udwh1 Lq
wkh Jkdqdldq hfrqrp|/ vwhulol}dwlrq kdv olplwhg dsshdo1 Whpsrudu|/ yhu| odujh
erqg vdohv fdq uhgxfh wkh lqlwldo sulfho ohyho vslnh e| 730:3(> exw wkh vslnh wkdw
uhpdlqv lv odujh lq devroxwh whupv +S mxpsv 408(,/ dqg wkh uhdo lqwhuhvw udwh pd|
lqfuhdvh 43053 shufhqwdjh srlqwv lq wkh vkruw uxq1 E| frqwudvw/ d pdqdjhg rdw
doorzv odujh r!fldo dqg sulydwh fdslwdo lq rzv wr eh devruehg zlwkrxw dgyhuvh
vlgh hhfwv rq lq dwlrq/ vwdelolw| ri wkh uhdo h{fkdqjh udwh/ wkh uhdo lqwhuhvw udwh
ru uhdo rxwsxw1 Lq sudfwlfh/ lw pd| qrw eh hdv| wr txdqwli| wkh srolf| uxoh wkdw
jxlghv wkh shuihfw pdqdjhg rdw1 Exw wklv lv qrw d vhulrxv sureohp1 Rxu uhvxowv
lqglfdwh wkdw iru d zlgh udqjh ri sdudphwhu ydoxhv wkh fhqwudo edqn vkrxog ohdq
khdylo| djdlqvw qrplqdo dssuhfldwlrq= urxjko| vshdnlqj/ wkh uljkw pdqdjhg rdw
lv 930;3( ri wkh zd| wrzdug wkh fudzolqj shj hqg ri wkh frqwlqxxp1
Vhfwlrq 9 lqyhvwljdwhv wkh urexvwqhvv ri wkh uhvxowv wr wkh wlph suroh ri dlg
rzv +judgxdo yv1 vxgghq lqfuhdvhv, dqg d glhuhqw vshflfdwlrq ri vwlfn| sulfhv
+rqh wkdw uh hfwv lqhuwldo lq dwlrq,1 Wkh qdo vhfwlrq uhfdslwxodwhv dqg glvfxvvhv
surplvlqj gluhfwlrqv iru ixwxuh uhvhdufk1
5
Wkh Fruh Vwuxfwxuh ri wkh Prgho
Zh zrun zlwk d vlpsoh fxuuhqf| vxevwlwxwlrq prgho ri d vpdoo rshq hfrqrp|
wkdw surgxfhv d qrqwudghg jrrg dqg d frpsrvlwh wudghg jrrg1 Uhdo rxwsxw lv
{hg lq erwk vhfwruv dqg wkh zruog sulfh ri wkh wudghg jrrg htxdov xqlw|1 Wkh
sulydwh vhfwru glylghv lwv zhdowk ehwzhhq grphvwlf fxuuhqf|/ iruhljq fxuuhqf|/
dqg jryhuqphqw erqgv1 Qrwdwlrqdo frqyhqwlrqv duh dv iroorzv= Sq dqg ghqrwh
wkh uhodwlyh sulfh ri wkh qrqwudghg jrrg dqg lwv vkduh lq djjuhjdwh frqvxpswlrq>
6
Tl lv rxwsxw lq vhfwru l> e lv wkh qrplqdo vwrfn ri erqgv gh dwhg e| wkh sulfh
ohyho> dqg p> I> dqg H duh uhdo prqh| edodqfhv/ wkh vwrfn ri iruhljq fxuuhqf|/
dqg djjuhjdwh uhdo h{shqglwxuh phdvxuhg lq grooduv +l1h1/ xqlwv ri wkh wudghg
jrrg,1
Sulfhv
Sq dgmxvwv wr fohdu wkh jrrgv pdunhw lq wkh qrqwudgdeohv vhfwru1 Wklv uh0
txluhv
+4,
Gq +Sq > H, @ Tq >
zkhuh G+, lv wkh Pduvkdooldq ghpdqg ixqfwlrq iru wkh qrqwudghg jrrg1
Wkh ryhudoo sulfh ohyho S lv d jhrphwulf zhljkwhg dyhudjh ri wkh sulfhv ri
wkh wudghg dqg qrqwudghg jrrgv1 Vlqfh wkh qrplqdo h{fkdqjh udwh h vhwv wkh
grphvwlf sulfh ri wkh wudghg jrrg/9
S @ hSq =
+5,
Wkh Sulydwh Djhqw*v Rswlpl}dwlrq Sureohp
Doo hfrqrplf ghflvlrqv lq wkh sulydwh vhfwru duh frqwuroohg e| d uhsuhvhqwdwlyh
djhqw zkr srvvhvvhv dq lqvwdqwdqhrxv xwlolw| ixqfwlrq ri wkh irup Y +Sq > H, .
!+pSq > I Sq ,1 Y +, lv d vwdqgdug lqgluhfw xwlolw| ixqfwlrq wkdw phdvxuhv
xwlolw| iurp jrrgv frqvxpswlrq/ zkloh !+, uh hfwv oltxlglw| vhuylfhv jhqhudwhg
e| kroglqjv ri grphvwlf dqg iruhljq fxuuhqf|1 Wkh sulydwh djhqw fkrrvhv p> e> I>
dqg H wr pd{lpl}h
] 4
^Y +Sq > H, . !+pSq > I Sq ,`hw gw>
+6,
X@
3
vxemhfw wr wkh zhdowk frqvwudlqw
D @ p . Sq e . I
+7,
Db @ Sq Tq . TW . Sq j . uSq e . + ",Sq e "p H>
+8,
dqg wkh exgjhw frqvwudlqw
zkhuh lv wkh wlph suhihuhqfh udwh> j lv uhdo oxps0vxp wudqvihuv> " @ h@h
b lv wkh
udwh ri fxuuhqf| ghsuhfldwlrq> u lv wkh uhdo lqwhuhvw udwh> dqg @ Sb @S lv wkh
lq dwlrq udwh1 Sq @ S@h pxowlsolhv j dqg e ehfdxvh zhdowk lv phdvxuhg lq grooduv
exw wudqvihuv dqg erqgv duh lqgh{hg wr wkh sulfh ohyho1 Iru wkh vdph uhdvrq/ wkh
duwlfldo fdslwdo jdlqv whup + ",Sq e dsshduv lq wkh exgjhw frqvwudlqw +8,1
Ohw $ eh wkh pxowlsolhu dwwdfkhg wr wkh frqvwudlqw lq +8,1 Wkh qhfhvvdu|
frqglwlrqv iru dq rswlpxp wkhq frqvlvw ri
YH
!4 @$Sq
!5 @$Sq
@ $>
@ u . >
@ u . ">
+9,
+:,
+;,
dqg wkh fr0vwdwh htxdwlrq
$b @ $+ . " u ,=
+<,
Htxdwlrqv +9,0+;, vwdwh wkdw wkh pdujlqdo xwlolw| ri frqvxpswlrq htxdov wkh
vkdgrz sulfh ri zhdowk dqg wkdw wkh pdujlqdo udwh ri vxevwlwxwlrq ehwzhhq frq0
vxpswlrq dqg p ru I htxdov wkh lqfrph iruhjrqh iurp kroglqj wkdw w|sh ri
7
prqh|1 Wkh fr0vwdwh htxdwlrq +<, pd| orrn ohvv idploldu/ exw lw lv qrwklqj pruh
wkdq d vwdqgdug Hxohu htxdwlrq1 Glhuhqwldwh +9, zlwk uhvshfw wr wlph dqg
vxevwlwxwh iru $1
b Xqghu wkh dvvxpswlrq ri krprwkhwlf suhihuhqfhv/ wklv jlyhv:
+ . ,
Hb
@
+u ,>
H
+43,
zkhuh @ YH @YHH H lv wkh lqwhuwhpsrudo hodvwlflw| ri vxevwlwxwlrq dqg lv
wkh frpshqvdwhg rzq0sulfh hodvwlflw| ri ghpdqg iru wkh qrqwudghg jrrg1
Suhihuhqfhv
Zh zrun zlwk d h{leoh/ idluo| jhqhudo xwlolw| ixqfwlrq1 Wkh lqgluhfw xwlo0
lw| ixqfwlrq Y +Sq > H, lv ghulyhg e| pd{lpl}lqj ryhu d FHV0FUUD ixqfwlrq ri
wudgdeohv dqg qrqwudgdeohv frqvxpswlrq1 Wkh oltxlglw| vhuylfhv ixqfwlrq !+, lv
dovr d qhvwhg FHV0FUUD ixqfwlrq1 Wkdw lv
+44@ ,@+4,
H 44@ nr . n4 Sq4
>
Y +Sq > H, @
4 4@
q
@+4, r44@
n6 p
@+4 . n7 I +4,@
>
!+p>
I , @ n5
4 4@
zkhuh p
pSq dqg I I Sq > nr n7 duh frqvwdqwv> lv wkh hodvwlflw| ri
vxevwlwxwlrq ehwzhhq wudghg dqg qrqwudghg frqvxphu jrrgv> lv wkh hodvwlflw|
ri vxevwlwxwlrq ehwzhhq grphvwlf dqg iruhljq fxuuhqf|> dqg / wr uhshdw/ lv wkh
lqwhuwhpsrudo hodvwlflw| ri vxevwlwxwlrq1
Wkh Sxeolf Vhfwru Exgjhw Frqvwudlqw
Prqh| lv lqmhfwhg lqwr wkh hfrqrp| zkhqhyhu wkh fhqwudo edqn dffxpxodwhv
iruhljq h{fkdqjh uhvhuyhv ] ru uxqv wkh sulqwlqj suhvv wr qdqfh wkh vfdo ghflw
ri wkh fhqwudo jryhuqphqw1 Iru qrz/ zh ljqruh erqg vdohv dqg rshq pdunhw
rshudwlrqv1 Wkh frqvrolgdwhg sxeolf vhfwru exgjhw frqvwudlqw lv wkxv
p
b @ Sq +j . ue, . ]b [ "p>
+44,
zkhuh [ lv vdoh ri dlg grooduv qhw ri jryhuqphqw lpsruwv dqg lqwhuhvw sd|phqwv
rq wkh sxeolf vhfwru iruhljq ghew qhw1; Vhyhqw|0yh shufhqw ri qhz dlg sd|v
iru wudqvihuv wr wkh srru +l1h1/ wkh uhsuhvhqwdwlyh djhqw,> wkh uhvw lv xvhg iru
jhqhudo exgjhw vxssruw1
Qhw Iruhljq Dvvhw Dffxpxodwlrq dqg wkh Edodqfh ri Sd|phqwv
Rqh odvw htxdwlrq frpsohwhv wkh fruh vwuxfwxuh ri wkh prgho1 Vxpplqj wkh
sulydwh dqg sxeolf vhfwru exgjhw frqvwudlqwv surgxfhv wkh dffrxqwlqj lghqwlw|
wkdw iruhljq dvvhw dffxpxodwlrq htxdov qdwlrqdo vdylqj ru wkh fxuuhqw dffrxqw
vxusoxv=
+45,
Ib . ]b @ Sq Tq . TW . [ H=
Wklv hqgv wkh irupdo qrwdwlrq0lqwhqvlyh sduw ri wkh sdshu1 Prvw ri wkh vsdfh
lq wkh qh{w yh vhfwlrqv lv ghyrwhg wr lqwxlwlyh/ qrq0whfkqlfdo h{sodqdwlrqv ri krz
dlg dhfwv wkh hfrqrp|*v htxloleulxp sdwk1 Dgglwlrqdo htxdwlrqv dsshdu rqo|
lqvridu dv wkh| duh qhhghg wr vwdwh lpsruwdqw uhvxowv ru ghvfuleh h{whqvlrqv ri wkh
8
fruh prgho1 Doo ri wkh dojheud lqyroyhg lq vroylqj iru wkh vwhdg|0vwdwh rxwfrph/
ghulylqj nh| frqglwlrqv/ dqg fkdudfwhul}lqj wkh g|qdplf v|vwhpv dvvrfldwhg zlwk
glhuhqw srolf| uhjlphv pd| eh irxqg lq wkh dsshqgl{1
514
Wkh Vwhdg|0Vwdwh Rxwfrph
Wkh orqj0uxq htxloleulxp lv lqghshqghqw ri wkh h{fkdqjh udwh uhjlph1 Lw lv qrw
|hw qhfhvvdu| wkhuhiruh wr vshfli| zkhwkhu wkh fhqwudo edqn rshudwhv d fudzolqj
shj/ d fohdq rdw/ ru vrph w|sh ri pdqdjhg rdw1
Dfurvv vwhdg| vwdwhv/ p
b @ Ib @ ]b @ Hb @ 3 dqg u @ 1 Lpsrvlqj wkhvh frq0
glwlrqv surgxfhv wkh htxloleulxp ghslfwhg lq Iljxuh 4d1 Wkh U dqg I vfkhgxohv
lq wkh uvw dqg irxuwk txdgudqwv vkrz krz vhljqlrudjh +U p, dqg kroglqjv
ri iruhljq fxuuhqf| ydu| zlwk lq dwlrq1 Wkh vorshv ri wkhvh wzr vfkhgxohv duh
gU@g
gI@g
@ p+4 ,>
@ + ,p I@l>
zkhuh l @ . lv wkh qrplqdo lqwhuhvw udwh> m lv wkh vkduh ri oltxlglw| vhuylfhv
surylghg e| fxuuhqf| m> dqg @ + p . i ,@l lv wkh hodvwlflw| ri prqh|
ghpdqg zlwk uhvshfw wr lq dwlrq1 Lq wkh hqvxlqj dqdo|vlv zh dvvxph ? 4
dqg A 1 Qhlwkhu dvvxpswlrq lv sduwlfxoduo| uhvwulfwlyh1 Wkh uvw nhhsv wkh
hfrqrp| dzd| iurp wkh volsshu|/ grzqzdug0vorslqj sruwlrq ri wkh vhljqlrudjh
Odhu fxuyh1 +Zkhq A 4/ orqj0uxq frpsdudwlyh vwdwlfv uhvxowv duh shuyhuvh dqg
wkh htxloleulxp sdwk lv lqghwhuplqdwh1, Wkh vhfrqg lpsolhv wkdw orzhu lq dwlrq
uhgxfhv wkh ghpdqg iru iruhljq fxuuhqf|1 Dowkrxjk wkhru| grhv qrw jxdudqwhh
wklv uhvxow/ wkhuh lv qrw pxfk grxew wkdw lw lv hdvlhu wr vxevwlwxwh ehwzhhq wkh
wzr fxuuhqflhv wkdq wr vxevwlwxwh lqwhuwhpsrudoo| lq frqvxpswlrq> khqfh vrph
ljkw fdslwdo frphv krph zkhq lq dwlrq ghfolqhv1
Wkh G vfkhgxoh lq wkh vhfrqg txdgudqw vxppdul}hv wkh jhqhudo htxloleulxp
uhodwlrqvkls ehwzhhq dlg dqg wkh vfdo ghflw diwhu judqwv1 +Khuhdiwhu zh xvh
wkh vkruwhu whup vfdo ghflw dqg rplw diwhu judqwv1, Zkhq pruh dlg rzv
lq/ [ ulvhv dqg wkh jryhuqphqw lqfuhdvhv uhdo wudqvihuv wr wkh sulydwh vhfwru e|
g+Sq j, @ #g[1 Lq nhhslqj zlwk srolf| pdnhuv* lqwhqwlrqv/ wkh gluhfw hhfw rq
wkh ghflw ^+# 4,g[` lv idyrudeoh1 Exw dlg dovr gulyhv xs wkh uhodwlyh sulfh ri
wkh qrqwudghg jrrg e| wkh dprxqw gSq @Sq @ g[@H/ zklfk lqfuhdvhv wkh vl}h
ri wkh lqwhuqdo ghew phdvxuhg lq grooduv1 Wkh ryhudoo lpsdfw rq wkh vfdo ghflw
G lv wkxv
gG @ +# 4 . v@,g[ B 3>
zkhuh v Sq e@H1
Lq wkh orqj uxq/ lv slqqhg grzq e| wkh uhtxluhphqw wkdw uhyhqxh iurp wkh
lq dwlrq wd{ fryhu wkh vfdo ghflw1 Pxfk ghshqgv wkhuhiruh rq wkh vorsh ri
wkh G vfkhgxoh1 Zh dvvxph # ? 4 v@ vr wkdw wkh vhljqlrudjh uhtxluhphqw
grhv/ lq idfw/ ghfolqh1 Wklv hqvxuhv wkdw lq dwlrq idoov dqg wkdw wkh uhdo prqh|
vxsso| lqfuhdvhv1 Sulydwh fdslwdo rzv frxog jr hlwkhu zd| vlqfh orzhu lq dwlrq
dqg kljkhu frqvxpswlrq vshqglqj h{huw frq lfwlqj hhfwv rq wkh ghpdqg iru
iruhljq fxuuhqf|1 Qrupdoo|/ krzhyhu/ wkh fxuuhqf| vxevwlwxwlrq hhfw grplqdwhv
wkh rxwfrph> srlqw K olhv wr wkh qruwk ri srlqw J surylghg lv qrw xqxvxdoo|
vpdoo +vhh wkh dsshqgl{,1
9
515
Uhpdunv rq wkh Vshflfdwlrq ri wkh Prgho
Irxu dvshfwv ri wkh prgho phulw frpphqw1 Iluvw/ wkh dvvxpswlrq wkdw wkh
iruhljq dvvhw grhv qrw hduq lqwhuhvw lv lqqrfrxv1 Zkdw lv fulwlfdo/ hvshfldoo| lq
wkh frqwh{w ri vwhulol}dwlrq/ lv wkdw wkh iruhljq dvvhw dqg grphwlf erqgv duh qrw
shuihfw vxevwlwxwhv> khqfh wkh grphvwlf lqwhuhvw udwh lv qrw wlhg grzq e| wkh
lqwhuhvw sdulw| frqglwlrq1 Vhfrqg/ zkhq dlg vshqglqj vkliwv rxw wkh ghpdqg
fxuyh lq wkh qrqwudgdeohv vhfwru/ wkh uhdo h{fkdqjh udwh zrxog dssuhfldwh ohvv li
wkh vxsso| fxuyh zhuh qrw yhuwlfdo1 Wklv grhv qrw vxevwdqwlyho| dowhu wkh uhvxowv1
Wkh rqo| fkdqjh lq wkh vroxwlrqv lv wkdw wkh frpshqvdwhg hodvwlflw| ri ghpdqg/
zkhqhyhu lw dsshduv/ lv uhsodfhg e| wkh vxp ri wkh ghpdqg hodvwlflw| dqg wkh
jhqhudo htxloleulxp hodvwlflw| ri qrqwudgdeohv vxsso|1 Wklug/ li dlg qdqfhg
jryhuqphqw sxufkdvhv ri qrqwudghg jrrgv lqvwhdg ri oxps0vxp wudqvihuv wr wkh
sulydwh vhfwru/ wkh rxwzdug vkliw ri wkh ghpdqg fxuyh dqg wkh lqfuhdvh lq wkh
uhodwlyh sulfh ri wkh qrqwudghg jrrg zrxog eh wzlfh dv odujh1 Lw lv qrw qhfhvvdu|
wr lqwurgxfh d qhz srolf| yduldeoh lq rughu wr dqdo|}h wklv vfhqdulr= zh fdq
plplfn wkh hhfwv lq wkh suhvhqw prgho hlwkhu e| kdoylqj wkh frpshqvdwhg
hodvwlflw| ri ghpdqg iru wkh qrqwudghg jrrg ru e| grxeolqj wkh vl}h ri wkh dlg
lq rz1< Ilqdoo|/ lv lw fruuhfw wr dvvxph wkdw sduw ri wkh dlg lq rz lv hdupdunhg iru
exgjh vxssruwB Wklv pd| vhhp duwlfldo jlyhq wkdw r!fldoo| doo dlg lv vshqw1 Exw
dlg lv uhdglo| ixqjleoh zlwk rwkhu uhyhqxh vrxufhv143 Wkh uhodwlrqvkls ehwzhhq dlg
dqg wkh vfdo ghflw lv wkxv d pdwwhu iru hpslulfdo lqyhvwljdwlrq1 Lq rxu zrunlqj
sdshu +Ex!h hw do1/ 5336,/ zh xvhg gdwd iru 4<<405333 iurp Jxswd hw do1*v +5335,
vdpsoh ri 6< orz0lqfrph frxqwulhv wr hydoxdwh wkh lpsdfw ri dlg rq wkh vfdo
ghflw dqg wkh grphvwlf qdqflqj uhtxluhphqw1 Lw wxuqv rxw wkdw lq Vxe0Vdkdudq
Diulfd 54 fhqwv ri wkh dlg groodu vxevwlwxwhv/ rq dyhudjh/ iru grphvwlf qdqflqj1
+Wkh qxpehu ulvhv wr 63( lq wkh vhfrqg kdoi ri wkh qlqhwlhv1, Wkh lqwhuhvwlqj
lvvxh lv zkhwkhu wklv iudfwlrq lv odujh hqrxjk wr frpsolfdwh pdfurhfrqrplf olih
e| dwwudfwlqj vxevwdqwldo sulydwh fdslwdo lq rzv1 Rxu dqvzhu lv dq hpskdwlf |hv1
6
Srodu H{fkdqjh Udwh Uhjlphv
Rq sdshu/ h{leoh h{fkdqjh udwhv dqg vwulfw wdujhwlqj ri wkh prqh| vxsso|
duh wkh qrup lq VVD1 Exw wkh frpplwphqw wr prqh|0edvhg vwdelol}dwlrq dqg
pdunhw0ghwhuplqhg h{fkdqjh udwhv lv idu iurp devroxwh/ hvshfldoo| lq shulrgv ri
dgmxvwphqw wr odujh h{whuqdo vkrfnv1 Pdq| frxqwulhv kdyh uhvsrqghg wr odujh
dlg lq rzv e| vkliwlqj wr pdqdjhg rdwv dqg sduwo| dffrprgdwlqj prqhwdu|
srolf|1
Wkh ghflvlrq derxw krz pxfk wr pdqdjh wkh h{fkdqjh udwh lv d ghflvlrq
derxw krz pxfk wr pryh lq wkh gluhfwlrq ri d {hg h{fkdqjh udwh1 Prvw ri
wkh lqirupdwlrq uhohydqw wr wklv ghflvlrq lv frqwdlqhg lq wkh rxwfrphv dw wkh
hqgsrlqwv ri wkh srolf| vshfwuxp1 Dffruglqjo|/ zh vwduw e| lqyhvwljdwlqj wkh
wudqvlwlrq sdwk dvvrfldwhg zlwk d sxuh rdw1 Vhfwlrq 615 dqdo|}hv wkh srodu
rssrvlwh fdvh ri d fudzolqj shj1
:
614
Ioh{leoh H{fkdqjh Udwhv
Lq d sxuh rdw wkh fhqwudo edqn qhyhu lqwhuyhqhv lq wkh iruhljq h{fkdqjh pdunhw1
Zlwk ]b @ 3/ wkh Hxohu htxdwlrq
+ . ,
Hb @
H+u ,>
+43,
p
b @ Sq +j . ue, [ "p
Ib @ Sq Tq . TW . [ H
+443 ,
+453 ,
dqg
frpsulvh d 6{6 g|qdplf v|vwhp lq zklfk I lv suhghwhuplqhg dqg p dqg H duh
mxps yduldeohv1 Wklv v|vwhp lv ghslfwhg lq Iljxuh 51 Vlqfh Sq ghshqgv rqo| rq H
dqg dlg lv frqvwdqw diwhu lwv lqlwldo mxps/ wkh Ib @ 3 vfkhgxoh lv krul}rqwdo dw wkh
vwhdg|0vwdwh ohyho ri h{shqglwxuh H 1 Dw srlqwv deryh wkh vfkhgxoh/ h{shqglwxuh
h{fhhgv lqfrph/ wkh fxuuhqw dffrxqw vkrzv d ghflw/ dqg wkh vwrfn ri iruhljq
fxuuhqf| lv ghfuhdvlqj1 Frqyhuvho|/ zkhq H ? H / wkh fxuuhqw dffrxqw uhjlvwhuv
d vxusoxv dqg I lv lqfuhdvlqj1 Wkh NN dqg PP vfkhgxohv vkrz krz H dqg p
ydu| zlwk I rq wkh frqyhujhqw vdggoh sdwk ^vhh htxdwlrqv +D4;, dqg +D4<, lq
wkh dsshqgl{`/ zkloh QQ wudfnv wkh sdwk ri Sq 1 NN vorshv xszdug dv vdylqj
ghshqgv srvlwlyho| rq wkh jds ehwzhhq I dqg lwv ghvluhg ohyho1 Wkh vorsh ri
PP lv lqghwhuplqdwh/ exw iru wkh udqjh ri ydoxhv frqyhuhg e| wkh qxphulfdo
vlpxodwlrqv wkh vfkhgxoh lv srvlwlyho| vorshg dv lq Iljxuh 51
Diwhu dlg lqfuhdvhv/ wkh vwdwlrqdu| htxloleulxp vkliwv iurp DEF wr JKM1 Dq0
wlflsdwlqj orzhu lq dwlrq/ wkh sulydwh djhqw wulhv wr h{fkdqjh iruhljq iru grphvwlf
fxuuhqf| dw w @ 31 Lq d rdwlqj udwh v|vwhp/ krzhyhu/ wkh sulydwh vhfwru fdqqrw
uhgxfh lwv froohfwlyh kroglqjv ri iruhljq fxuuhqf| e| wudglqj grooduv iru grphv0
wlf fxuuhqf| lq wkh iruhljq h{fkdqjh pdunhw1 Wkh ghvluh wr krog ohvv iruhljq
fxuuhqf| ohdgv lqvwhdg wr dssuhfldwlrq ri wkh qrplqdo h{fkdqjh udwh/ d zlqgidoo
jdlq lq zhdowk +p % rq lpsdfw,/ dqg orzhu vdylqj1 Wklv slqv grzq vhyhudo uh0
vxowv= dw w @ 3 h{shqglwxuh lqfuhdvhv pruh wkdq dlg +H+3, A H ,/ wkh fxuuhqw
dffrxqw zruvhqv/ dqg wkh uhdo h{fkdqjh udwh +4@Sq , ryhuvkrrwv lwv vwhdg|0vwdwh
b Ib ? 3/ ;w/ wkh uhdo lqwhuhvw udwh lv
ohyho ^Sq +3, A Sq `1 Ixuwkhupruh/ vlqfh H>
orzhu +u ? e| wkh Hxohu htxdwlrq, dqg fxuuhqw dffrxqw +FD, ghflwv shuvlvw
wkurxjkrxw wkh dgmxvwphqw surfhvv1
Wkh vshqglqj errp wkdw dffrpsdqlhv dlg pljkw vhhp wr eh d vrxufh ri
wurxeoh iru wkh sulfh ohyho lq wkh vkruw uxq1 Exw wklv lv qrw wkh fdvh1 Zkhq wkh
sulydwh vhfwru dwwhpswv wr vhoo iruhljq fxuuhqf| dw w @ 3 wkh qrplqdo h{fkdqjh
udwh dssuhfldwhv hqrxjk wr ixoo| qhxwudol}h wkh lq dwlrqdu| suhvvxuhv ri kljkhu
frqvxpswlrq vshqglqj1 Lq wkh dsshqgl{ zh ghprqvwudwh wkdw wkh sulfh ohyho
ghfuhdvhv rq lpsdfw dqg wkdw lq dwlrq lv frqwlqrxvo| orzhu rq wkh wudqvlwlrq
sdwk wr wkh qhz vwhdg| vwdwh1
61414
Qxphulfdo Uhvxowv= Krz Elj Duh wkh HhfwvB
Wr fdoleudwh wkh prgho zh fkrvh xqlwv vr wkdw Sqr @ Hr @ 4 dqg vhw
pr
@ =43>
@ =83>
er @ =53> r @ =58> r @ =83> [r @ =43>
@ =:8 6> @ =3;> @ =58 =83> Ir @ =48=
;
Wkh qxpehuv dvvljqhg wr pr / r / er / r / dqg [r duh urxjk dyhudjhv ri wkh ydoxhv
revhuyhg lq Jkdqd lq wkh shulrg 5333053361 Zlwk uhvshfw wr wkh rwkhu fkrlfhv=
Hodvwlflw| ri vxevwlwxwlrq lq frqvxpswlrq ehwzhhq wudghg dqg qrqwudghg
frqvxphu jrrgv +,1 Il{lqj dw 183 lpsolhv wkdw wkh frpshqvdwhg hodv0
wlflw| ri ghpdqg iru wkh qrqwudghg jrrg lv 158 lqlwldoo|1 Wklv djuhhv zlwk
wkh qglqj lq hpslulfdo vwxglhv wkdw frpshqvdwhg hodvwlflwlhv ri ghpdqg
whqg wr eh vpdoo dw kljk ohyhov ri djjuhjdwlrq144
Hodvwlflw| ri vxevwlwxwlrq ehwzhhq grphvwlf dqg iruhljq fxuuhqf| +,1 Wkhuh
duh qr uholdeoh hvwlpdwhv ri iru Jkdqd ru dq| rwkhu frxqwu| lq Diulfd1
Iru Odwlq Dphulfd wkh qxpehuv udqjh iurp 418 wr : +Udpluh}0Urmdv/ 4<;8>
Pdutxh}/ 4<;:> Jlrydqqlql dqg Wxuwoherrp/ 4<<7> Ndplq dqg Hulffvrq/
4<<6,1 Qrw wuxvwlqj wkh kljk0hqg hvwlpdwhv +:BB,/ zh ghflghg wr ohw ydu|
iurp 1:8 wr 61
Wlph suhihuhqfh udwh +,1 Dfurvv vwhdg| vwdwhv/ wkh uhdo lqwhuhvw udwh lv
{hg e| wkh wlph suhihuhqfh udwh1 Wkh ydoxh dvvljqhg wr +;(, lv voljkwo|
ohvv wkdq wkh dyhudjh uhdo udwh sdlg e| vkruw0whup wuhdvxu| eloov vlqfh 4<<5
+;158( dffruglqj wr LPI 5336/ s199,1
Hodvwlflw| ri lqwhuwhpsrudo vxevwlwxwlrq + ,1 Prvw hvwlpdwhv iru OGFv sodfh
ehwzhhq 153 dqg 1831 +Vhh Djhqru dqg Prqwlho/ 4<<</ Wdeoh 45141, Zh
vhwwohg wkhuhiruh rq 158 dqg 183 dv wkh orz dqg kljk ydoxhv iru wkh lqwhuwhp0
srudo hodvwlflw| ri vxevwlwxwlrq145 Rffdvlrqdoo|/ zh dovr uhsruw uhvxowv iru
wkh lqwhuphgldwh fdvh ri @ =681
Udwlr ri iruhljq fxuuhqf| wr qdwlrqdo lqfrph +Ir ,1 Iruhljq fxuuhqf| gh0
srvlwv lq wkh grphvwlf edqnlqj vhfwru duh 93( ri uhvhuyh prqh| lq Jkdqd1
Wklv vxjjhvwv Ir @ =39/ exw wkh wuxh ydoxh lv kljkhu ehfdxvh d jrrg ghdo
ri iruhljq fxuuhqf| lv khog rxwvlgh ri wkh grphvwlf edqnlqj v|vwhp1 Zh
duelwudulo| vhw Ir dw 1481 Wklv lv lq olqh zlwk groodul}dwlrq udwlrv lq rwkhu
sduwv ri wkh Wklug Zruog146
Vkduh ri dlg lq rz vhw dvlgh iru ghflw uhgxfwlrq + #,1 D ydoxh ri 1:8 iru
# lv frqvlvwhqw zlwk Diulfdq gdwd iru wkh 4<<3v dqg zlwk wkh wkh vwdwhg
lqwhqw ri wkh Jkdqldq jryhuqphqw wr xvh sduw ri wkh vdylqj lq ghew vhuylfh
lq xsfrplqj |hduv wr uhgxfh wkh vfdo ghflw147
Doo ri wkh vlpxodwlrqv dvvxph wkdw dlg lq rzv lqfuhdvh e| 6( ri qdwlrqdo
lqfrph +wkh surmhfwhg lqfuhdvh iru 533505339,1 Vlqfh wkh dlg vkrfn lv odujh/
olqhdul}dwlrq huuru lv d srwhqwldo sureohp1 Wr dgguhvv wklv frqfhuq/ zh vroyhg
iru wkh wudqvlwlrq sdwk xvlqj d yduldqw ri wkh surfhgxuh uhfrpphqghg e| Qrydohv
hw do1+4<<<,148
Vwhdg|0Vwdwh Rxwfrph
Sdqho D ri Wdeoh 4 uhsruwv wkh uhvxowv iru yh glhuhqw uxqv1 Lq hyhu| fdvh/
wkh orqj0uxq hhfwv ri wkh dlg vkrfn duh vljqlfdqw1 Wkh ydoxh iru # lpsolhv
wkdw wkh vfdo ghflw ghfuhdvhv e| 1:8( ri JGS1 Wklv uhgxfhv wkh vwhdg|0vwdwh
lq dwlrq udwh iurp 58( wr 44048(1 Fxpxodwlyh sulydwh fdslwdo lq rzv udqjh
iurp 14( wr 43( ri qdwlrqdo lqfrph/ zkloh wkh uhdo h{fkdqjh udwh dssuhfldwhv
44(1
<
Wkh Wudqvlwlrq Sdwk
Zkdw kdsshqv rq wkh zd| wr wkh orqj0uxq htxloleulxp ghshqgv pdlqo| rq
wkh fxuuhqf| vxevwlwxwlrq sdudphwhu 1 Iru @ =:8 sulydwh fdslwdo lq rzv duh
vpdoo dqg wkh hfrqrp| pryhv txlfno| wr wkh ylflqlw| ri wkh qhz vwhdg| vwdwh1
Exw zkhq @ 5 6 wkh ulgh lv d elw zlog1 Frqvxpswlrq vshqglqj vwurqjo|
ryhuvkrrwv lwv vwhdg|0vwdwh ohyho> dv d uhvxow/ wkh uhdo h{fkdqjh udwh dssuhfldwhv
53057( lq wkh vkruw uxq dqg wkh fxuuhqw dffrxqw ghflw/ lqfoxvlyh ri dlg/ mxpsv
wr 516061:( ri qdwlrqdo lqfrph1 Wkhuh duh dovr surqrxqfhg xfwxdwlrqv lq dqg u lq wkh uxqv zkhuh @ =581 Wkh uhdo lqwhuhvw udwh ghfuhdvhv 418 shufhqwdjh
srlqwv lq wkh uvw |hdu> lw ulvhv vwhdglo| wkhuhdiwhu exw lv vwloo 40415 shufhqwdjh
srlqwv orzhu dw w @ 61 Ehfdxvh ri wkh whpsrudu| ghfuhdvh lq wkh uhdo lqwhuhvw
udwh/ wkh vfdo ghflw dqg lq dwlrq dovr ryhuvkrrw wkhlu vwhdg|0vwdwh ohyhov1
Fdyhdw
Xqiruwxqdwho|/ wkh uhvxowv lq Sdqho D suhvxph idu wrr pxfk h{lelolw| ri
qrplqdo sulfhv1 Frqvlghu krz wkh hfrqrp| dgmxvwv lq wkh vkruw uxq1 Dffruglqj
wr rxu prgho/ wkh qrplqdo h{fkdqjh udwh dssuhfldwhv 5507;( dw w @ 3 wr iruhvwdoo
lqflslhqw fdslwdo lq rzv +I lv suhghwhuplqhg,1 Vlqfh wkh uhdo h{fkdqjh udwh
dssuhfldwhv rqo| 45057(/ wkh qrplqdo sulfh lq wkh qrqwudgdeohv vhfwru kdv wr
lpphgldwho| idoo 44068( wr nhhs ghpdqg htxdo wr vxsso|1 Wklv vwudlqv eholhi wr
vd| wkh ohdvw1 Exw li qrplqdo sulfh dgmxvwphqw lv lqfrpsohwh wkh hfrqrp| volghv
lqwr d uhfhvvlrq suredeo| d ghhs uhfhvvlrq jlyhq wkh pdjqlwxgh ri qrplqdo
dssuhfldwlrq dw w @ 31 Zh uhwxuq wr wklv srlqw odwhu lq vhfwlrq 91
615
D Fudzolqj Shj
Xqghu d fudzolqj shj/ wkh prqh| vxsso| dgmxvwv hqgrjhqrxvo| wkurxjk wkh
fdslwdo dffrxqw wr vdwlvi| prqh| ghpdqg1 Exw zkloh grphvwlf fxuuhqf| fdq
eh vzdsshg iru iruhljq fxuuhqf| dw wkh fhqwudo edqn/ wkh wrwdo groodu ydoxh ri
fxuuhqf| kroglqjv lv suhghwhuplqhg1 Wkxv M p . I lv wkh vwdwh yduldeoh lq
wkh g|qdplf v|vwhp ghqhg e| +43,0+45,1 Wr eulqj M lqwr ylhz/ dgg +44, dqg
+45,1 Wklv jlyhv
Mb @ Sq +j . ue, . Sq Tq . TW H "p=
+46,
Zh dvvxph wkh jryhuqphqw orzhuv wkh udwh ri fxuuhqf| ghsuhfldwlrq " wr lwv
qhz vwhdg|0vwdwh ohyho lpphgldwho| dw w @ 31 Wkh hfrqrp|*v g|qdplfv duh wkhq
jryhuqhg e| +46, dqg wkh Hxohu htxdwlrq +43,1 Wkh VV vfkhgxohv lq wkh uvw
txdgudqw ri Iljxuh 6 duh srwhqwldo vdggoh sdwkv iru wklv v|vwhp1 Wr wkh ohiw/ lq
wkh vhfrqg txdgudqw/ wkh QQ vfkhgxoh djdlq wudfnv wkh sdwk ri Sq 1
Iljxuh 6 orrnv pxfk olnh Iljxuh 5/ h{fhsw M uhsodfhv I rq wkh krul}rqwdo d{lv1
Wklv glhuhqfh lv fulwlfdo1 Lq wkh fdvh ri d sxuh rdw zh nqrz wkdw I ? Ir dqg
khqfh wkdw uhdo vshqglqj ryhuvkrrwv lwv vwhdg|0vwdwh ohyho1 Xqghu d fudzolqj shj
wkh wudqvlwlrq sdwk lv ohvv zhoo ghqhg ehfdxvh M pd| eh hlwkhu odujhu ru vpdoohu
wkdq Mr 1 Wkh vwhdg|0vwdwh vroxwlrqv iru p dqg I |lhog +vhh wkh dsshqgl{,
M ? Mr
l A +4 . @i , .
l+4 ,+ . ,
M
> +47,
i ^+ . , v . +4 #,` H
~}
Srvlwlyh iru #?4v@
zkhuh p@H dqg i lv wkh vkduh ri oltxlglw| vhuylfhv surylghg e| iruhljq fxu0
uhqf| kroglqjv1 Dowkrxjk wklv frqglwlrq lv frpsolfdwhg/ lw dgplwv ri d vwudljkw0
43
iruzdug lqwxlwlyh h{sodqdwlrq1 Vshqglqj lv kljkhu dqg lq dwlrq orzhu dw wkh qhz
vwhdg| vwdwh1 Erwk idfwruv lqfuhdvh wkh sulydwh djhqw*v ghpdqg iru oltxlglw| vhu0
ylfhv1 Dq lqfuhdvh lq oltxlglw| vhuylfhv/ krzhyhu/ grhv qrw qhfhvvdulo| uhtxluh dq
lqfuhdvh lq wrwdo fxuuhqf| kroglqjv1 Qrwh iurp wkh uvw0rughu frqglwlrqv +:, dqg
+;, wkdw d vwudljkw vzds ri iruhljq iru grphvwlf fxuuhqf| lqfuhdvhv wkh vxsso| ri
oltxlglw| vhuylfhv +!, e| =49
4 g! @ !4 !5 @ =
YH gp gM@3
Frqvhtxhqwo|/ zkhq lq dwlrq lv kljk dqg fxuuhqf| vxevwlwxwlrq hdv| + odujh,/
wkh sulydwh djhqw pd| uhvsrqg dv lq Iljxuh 7/ lqfuhdvlqj frqvxpswlrq ri oltxlglw|
vhuylfhv e| kroglqj pxfk pruh grphvwlf fxuuhqf| exw ohvv wrwdo prqh|1 Wkh
suhflvh frqglwlrq iru wklv wr kdsshq lv vwdwhg lq htxdwlrq +47,1 Li vdwlvhv wkh
lqhtxdolw|/ wkhq fxuuhqf| vxevwlwxwlrq doorzv wkh sulydwh djhqw wr hqmr| pruh
oltxlglw| vhuylfhv zkloh vshqglqj grzq sduw ri klv zhdowk1 Wkh vwhdg|0vwdwh
htxloleulxp vkliwv iurp D wr F dqg wkh sdwkv iru h{shqglwxuh/ wkh uhdo h{fkdqjh
udwh/ wkh fxuuhqw dffrxqw/ dqg wkh uhdo lqwhuhvw udwh duh txdolwdwlyho| wkh vdph
dv wkh sdwkv lq d sxuh rdw1 Wkh lwhp plvvlqj iurp wkh olvw lv wkh lpsdfw hhfw
rq wkh sulfh ohyho1 Vlqfh wkh qrplqdo h{fkdqjh udwh lv suhghwhuplqhg/ wkh elj
lqfuhdvh lq vshqglqj dw w @ 3 wuljjhuv odujh mxpsv lq wkh qrplqdo sulfh ri wkh
qrqwudghg jrrg dqg wkh FSL1
Wkh g|qdplfv duh txlwh glhuhqw zkhq wkh frqglwlrq lq +47, grhv qrw krog=
rq sdwk DJK/ h{shqglwxuh dqg wkh uhdo h{fkdqjh udwh xqghuvkrrw wkhlu vwhdg|0
vwdwh ohyhov/ wkh uhdo lqwhuhvw udwh ulvhv/ dqg wkh fxuuhqw dffrxqw uhjlvwhuv vxu0
soxvhv lqvwhdg ri ghflwv1 Pruhryhu/ h{shqglwxuh pd| ghfuhdvh lqlwldoo| +sdwk
DNO,/ fdxvlqj wkh uhdo h{fkdqjh udwh wr ghsuhfldwh dqg wkh sulfh ohyho wr mxps
grzqzdug dw w @ 31 Wkh uhvxow lv rgg exw lw fdqqrw eh uxohg rxw e| sodxvleoh
sdudphwhu ydoxhv1
61514
Qxphulfdo Uhvxowv dqg Frpsdulvrqv zlwk d Sxuh Iordw
Krz grhv vzlwfklqj iurp d sxuh rdw wr d fudzolqj shj dhfw wkh sdwkv ri nh|
pdfurhfrqrplf yduldeohvB Zh vkrxog eh deoh wr vd| d orw derxw wklv zlwkrxw
wdnlqj d vwdqg rq wkh frqglwlrq lq +47,1 Lq d sxuh rdw/ vsrw dssuhfldwlrq ri wkh
qrplqdo h{fkdqjh udwh dw w @ 3 frqihuv d odujh zhdowk jdlq rq wkh sulydwh vhfwru
+p . I % rq lpsdfw, zkloh dovr h{huwlqj vwurqj grzqzdug suhvvxuh rq wkh sulfh
ohyho1 Qr vlplodu hhfwv rshudwh lq d fudzolqj shj1 Wkxv lqwxlwlrq dujxhv wkdw lq
frpsdulvrqv ri wkh wzr v|vwhpv d fudzolqj shj ex|v juhdwhu vwdelolw| ri wkh uhdo
h{fkdqjh udwh dqg vpdoohu fxuuhqw dffrxqw ghflwv +ru srvvleo| fxuuhqw dffrxqw
vxusoxvhv, dw wkh sulfh ri kljkhu lq dwlrq dqg kljkhu uhdo lqwhuhvw udwhv1
Wkh frqglwlrq lq +47, grhv qrw krog iru wkh wzr uxqv zkhuh @ =:8 ru wkh
uxq zkhuh @ =83 dqg @ 5 +vhh Sdqho E ri Wdeoh 4,1 Lq wkhvh uxqv/ wkh
uhdo lqwhuhvw udwh ulvhv/ wkh fxuuhqw dffrxqw lpsuryhv/ dqg lq dwlrq dqg wkh uhdo
h{fkdqjh udwh xqghuvkrrw/ dssurdfklqj wkhlu vwhdg|0vwdwh ohyhov iurp deryh1 Lq
wkh rwkhu wzr fdvhv/ wkh txdolwdwlyh surshuwlhv ri wkh wudqvlwlrq sdwk duh wkh
vdph +dsduw iurp wkh lqlwldo mxps lq wkh sulfh ohyho, dv lq d rdw1 Xqghu d
fudzolqj shj/ krzhyhu/ lq dwlrq dqg wkh uhdo lqwhuhvw udwh ghfuhdvh ohvv/ wkh uhdo
h{fkdqjh udwh dssuhfldwhv ohvv/ dqg wkh fxuuhqw dffrxqw ghflw lv vpdoohu1
44
Wzr rwkhu uhvxowv vkrxog eh phqwlrqhg1 Iluvw/ wkh lqfuhdvh lq wkh uhdo lqwhuhvw
udwh lv vpdoo1 Iru @ =:8/ wkh udwh mxpsv lqlwldoo| wr <170<19(/ exw e| wkh hqg ri
wkh uvw |hdu u idoov edfn ehorz <(1 Vhfrqg/ lq dwlrqdu| suhvvxuhv duh frqqhg
wr wkh vslnh lq wkh sulfh ohyho dw w @ 31 Dowkrxjk wkh vslnh lv odujh +S mxpsv
60<(,/4: wkh sdwk ri wkh FSL gursv ehorz wkh suh0dlg sdwk zlwklq 70: prqwkv
dqg wkh lq dwlrq udwh iru wkh uvw |hdu ghfuhdvhv iurp 58( wr 49053(1 +Wkh
qxpehu lq sduhqwkhvhv lq wkh fhoo iru w @ 4 lv wkh fxpxodwlyh shufhqwdjh lqfuhdvh
lq wkh sulfh ohyho ryhu wkh uvw |hdu wkh uhdo zruog ghqlwlrq ri lq dwlrq1,4;
7
Vwlfn| Sulfhv
Wkhuh lv vrph xqqlvkhg exvlqhvv frqqhfwhg zlwk wkh dqdo|vlv ri dlg lq d sxuh
rdw1 Wxuq edfn wr Sdqho D ri Wdeoh 41 Wkh qxpehuv orrn qlfh exw wkh| uho|
rq h{wuhph grzqzdug sulfh h{lelolw| wr suhvhuyh ixoo hpsor|phqw zkhq wkh
qrplqdo h{fkdqjh udwh dssuhfldwhv 5507;( lq wkh vkruw uxq1 Zh frqmhfwxuhg
wkdw uhdo rxwsxw zrxog ghfuhdvh vkduso| li/ lqvwhdg/ qrplqdo sulfhv zhuh vwlfn|
grzqzdug1 Wklv qhhgv wr eh frquphg ehiruh gudzlqj dq| frqfoxvlrqv derxw
wkh h!fdf| ri pdqdjlqj dlg rzv lq h{leoh yv1 {hg h{fkdqjh udwh v|vwhpv1
Zh lqwurgxfh vwlfn| sulfhv ã od Fdoyr dqg Yhjk +4<<6,1 Wkh sulfh ri wkh
wudghg jrrg lv vhw e| wkh h{fkdqjh udwh exw upv lq wkh qrqwudgdeohv vhfwru
dgmxvw sulfhv rqo| zkhq wkh| uhfhlyh d udqgrp sulfh0fkdqjh vljqdo1 Ilupv wkdw
uhfhlyh d vljqdo fkrrvh d qhz sulfh e| iruhfdvwlqj wkh ixwxuh sdwkv ri wkh sulfh
ohyho dqg h{fhvv ghpdqg14< Sulfh dgmxvwphqw lv wkxv iruzdug0orrnlqj1 Fdoyr
+4<;6, vkrzv wkdw zkhq wkh sulfh0fkdqjh vljqdo reh|v d Srlvvrq surfhvv
Sb q
b q
@ +q ",Sq
q `>
@ ^Gq +Sq > H, T
A 3>
+48,
+49,
q ghqrwhv qrwlrqdo rxwsxw +l1h1/ wkh ohyho ri rxwsxw dvvrfldwhg zlwk d
zkhuh T
qrupdo fdsdflw| xwlol}dwlrq udwh,1 Htxdwlrq +48, iroorzv iurp wkh idfw wkdw/ dw
dq| jlyhq srlqw lq wlph/ wkh qrplqdo sulfh ri wkh qrqwudghg jrrg lv {hg e|
sdvw sulfh txrwdwlrqv1 +Pruh suhflvho|/ dw dq| wlph w wkh vhw ri upv wkdw dgmxvw
wkhlu sulfhv lv ri phdvxuh }hur1, Htxdwlrq +49, lv d kljkhu0rughu Skloolsv Fxuyh1
Lw vd|v wkdw wkh fkdqjh lq q / wkh lq dwlrq udwh lq wkh qrqwudgdeoh vhfwru/ lv d
ghfuhdvlqj ixqfwlrq ri h{fhvv ghpdqg1 Wkh sdudphwhu lv odujhu wkh vkruwhu wkh
ohqjwk ri wkh dyhudjh sulfh txrwh1
Vwlfn| sulfhv dgg wzr yduldeohv wr wkh g|qdplf v|vwhpv dqdo|}hg hduolhu1 Lq
d sxuh rdw/ erwk q dqg Sq duh mxps yduldeohv153 Xqghu d fudzolqj shj/ q
lv d mxps yduldeoh exw Sq lv suhghwhuplqhg1 Qrqwudgdeohv rxwsxw lv ghpdqg
ghwhuplqhg lq erwk h{fkdqjh udwh uhjlphv1
714
D Sxuh Iordw
Wkh urz iru Tq lq Sdqho D ri Wdeoh 5 wudfnv wkh sdwk ri ^Tq +w, Tqr `@Tqr /
wkh shufhqwdjh glhuhqfh ehwzhhq qrqwudgdeohv rxwsxw dw wlph w dqg lwv suh0dlg
ohyho154 Dowkrxjk wkh frpshqvdwhg hodvwlflw| ri ghpdqg lv rqo| 158/ vxevwlwx0
wlrq wrzdug wudghg jrrgv lqgxfhg e| dssuhfldwlrq ri wkh qrplqdo h{fkdqjh
udwh hdvlo| grplqdwhv wkh h{sdqvlrqdu| lqfrph hhfw ri kljkhu dlg rzv1
Frqvhtxhqwo|/ Tq ghfolqhv lq hyhu| fdvh1 Zkhq @ 5 6/ wkh uhfhvvlrq lq wkh
45
qrqwudgdeohv vhfwru lv surwudfwhg dqg vhyhuh dv odujh sulydwh fdslwdo lq rzv irufh
wkh qrplqdo h{fkdqjh udwh wr dssuhfldwh 54066( dw w @ 31 Iru @ =:8/ fdslwdo
lq rzv dqg qrplqdo dssuhfldwlrq duh frpsdudwlyho| prghvw> qhyhuwkhohvv/ Tq
idoov 5180818( rq lpsdfw dqg lv 1:0419( orzhu dw w @ 41
Uhfhvvlrq lv qrw wkh rqo| sureohp srolf| pdnhuv idfh1 Wkh uhdo h{fkdqjh
udwh ryhuvkrrwv lwv vwhdg|0vwdwh ohyho pxfk pruh wkdq lq wkh h{sulfh prgho/
hvshfldoo| lq wkh uxqv iru @ 561 Pruhryhu/ wkh lpsdfw rq wkh uhdo lqwhuhvw udwh
fkdqjhv gudpdwlfdoo|1 Zkhq sulfhv duh h{leoh/ wkh uhdo lqwhuhvw udwh ghfuhdvhv
whpsrudulo| iurp ;( wr 9170:19(1 Zlwk vwlfn| sulfhv/ wkh udwh mxpsv wr 47059(
lq wkh uvw |hdu1 Wklv lv d qdwxudo e|surgxfw ri wkh wudqvlwru| uhfhvvlrq= u
lv kljkhu rq wkh wudqvlwlrq sdwk ehfdxvh djjuhjdwh frqvxpswlrq vshqglqj ulvhv
ryhu wlph ^vhh wkh Hxohu htxdwlrq +43,` dv ghpdqg dqg rxwsxw uhfryhu lq wkh
qrqwudgdeohv vhfwru1
Wkh dgyhuvh lpsdfw rq wkh uhdo lqwhuhvw udwh lv lpsruwdqw/ iru lw lpsolhv wkdw
wkh vlpxodwlrq uhvxowv xqghuhvwlpdwh wkh uhdo rxwsxw orvvhv iurp rdwlqj1 Rxu
prgho dvvxphv frqvwdqw rxwsxw lq wkh wudgdeohv vhfwru1 Exw li d kljkhu uhwxuq
rq wuhdvxu| eloov lqfuhdvhv wkh frvw ri zrunlqj fdslwdo ru ghsuhvvhv lqyhvwphqw
vshqglqj/ wkhq wudgdeohv surgxfwlrq zloo frqwudfw dqg wkh ghpdqg fxuyh lq wkh
qrqwudgdeohv vhfwru zloo vkliw ixuwkhu wr wkh ohiw1 Lq d pruh hoderudwh prgho wkdw
fdswxuhg wkhvh olqndjhv/ wkh uhfhvvlrq zrxog eh ghhshu dqg pruh shuvlvwhqw wkdq
uhsruwhg khuh1
715
D Fudzolqj Shj
Wkh uhvxowv iru d fudzolqj shj lq Sdqho E ri Wdeoh 5 duh zkdw srolf| pdnhuv
guhdp derxw1 Lq dwlrq ghfuhdvhv vprrwko| zlwkrxw dq lqlwldo vslnh lq wkh sulfh
ohyho1 Wkh fxuuhqw dffrxqw uhfrugv d vpdoo vxusoxv +dq lpshufhswleoh ghflw iru
@ 6, dqg wkh uhdo h{fkdqjh udwh pryhv wrzdug lwv orqj0uxq htxloleulxp ydoxh
lq d judgxdo/ rughuo| pdqqhu1 Iru d frxsoh ri |hduv/ wkh hfrqrp| dovr hqmr|v
kljkhu rxwsxw dqg orzhu uhdo lqwhuhvw udwhv1 Zkdw pdnhv hyhu|wklqj zrun lv wkdw
wkh exgjhw0vxssruw frpsrqhqw ri dlg hhfwlyho| qdqfhv d shuihfwo| fuhgleoh
h{fkdqjh0udwh0edvhg vwdelol}dwlrq +HUEV,1 Wkh vpdoo HUEV frpsrqhqw +427
ri wkh wrwdo dlg sdfndjh, hqvxuhv wkdw lq dwlrq ghfuhdvhv prqrwrqlfdoo| hyhq
wkrxjk uhdo vshqglqj ulvhv 6160918( lq wkh vkruw uxq1
Grhv wklv phdq wkdw d fudzolqj shj zlwk ixoo| dffrpprgdwlqj prqhwdu|
srolf| vroyhv doo pdfurhfrqrplf sureohpvB Suredeo| qrw1 Ihz pdfurhfrqrplvwv
kdyh wurxeoh zlwk wkh qrwlrq wkdw sulfhv duh vwlfn| grzqzdug1 Exw duh sulfhv
vwlfn| xszdug dv zhooB Iru uhdvrqv wkdw duh kdug wr mxvwli|/ zh vxvshfw wkdw
sulfh dgmxvwphqw lv dv|pphwulf lq Vxe0Vdkdudq Diulfd dqg wkdw wkh h{sulfh
vshflfdwlrq lv fruuhfw iru pdq| eudqfkhv ri wkh qrqwudgdeohv vhfwru +h1j1/ wkh
lqirupdo vhfwru, zkhq qrplqdo sulfh lqfuhdvhv duh uhtxluhg wr fohdu wkh pdunhw1
Wkh sxuh h{sulfh prgho ri vhfwlrqv 508 pd| h{djjhudwh wkh lqlwldo xszdug
mxps lq wkh FSL/ exw wkh vwlfn|0sulfh prgho lv ryhuo| rswlplvwlf lq dvvxplqj wkh
sureohp dzd|1 Grxewohvv wkh wuxwk olhv vrphzkhuh lqehwzhhq1
8
Dowhuqdwlyh Srolflhv
Wkh orqj0uxq htxloleulxp lq dwlrq udwh ghfolqhv zkhq dlg vhuyhv lq sduw wr uhgxfh
wkh vfdo ghflw1 Vr idu vr jrrg1 Exw h{shfwdwlrqv ri orzhu lq dwlrq holflw odujh
46
sulydwh fdslwdo lq rzv1 Wklv frpsolfdwhv pdfurhfrqrplf pdqdjhphqw ehfdxvh
vwd|lqj rxw ri wkh iruhljq h{fkdqjh pdunhw lv qrw d jhqxlqh rswlrq= fhqwudo
edqnv wkdw uho| rq d sxuh rdw sdvvlyho| dftxlhvh wr +l, vwxshqgrxv dssuhfldwlrq
ri wkh qrplqdo h{fkdqjh udwh/ +ll, orzhu hpsor|phqw lq erwk wkh wudgdeohv dqg
qrqwudgdeohv vhfwruv +dvvxplqj zdjhv dqg sulfhv duh qrw h{fhswlrqdoo| h{leoh
grzqzdug,/ +lll, ryhuvkrrwlqj ri wkh uhdo h{fkdqjh udwh/ dqg +ly, odujh fxuuhqw
dffrxqw ghflwv1 D fudzolqj shj holplqdwhv wkh wkuhdw ri d kduvk uhfhvvlrq dqg
vhfxuhv juhdwhu vwdelolw| ri wkh uhdo h{fkdqjh udwh exw ohdyhv wkh jryhuqphqw
zlwk wkh sureohp ri qhjrwldwlqj dq lqlwldo elj vslnh lq wkh FSL1
Vxpplqj xs/ qhlwkhu d fudzolqj shj qru d sxuh rdw surgxfhv ixoo| dffhsw0
deoh uhvxowv1 Zh pryh rq wkhuhiruh wr wkh dqdo|vlv ri dowhuqdwlyh srolf| vwudwh0
jlhv1 Lq vhfwlrq 814 wkh fhqwudo edqn whpsrudulo| vwhulol}hv fdslwdo lq rzv> lq
vhfwlrq 815 lw rshudwhv d gluw| rdw/ lqwhuyhqlqj lq wkh iruhljq h{fkdqjh pdunhw
wr suhyhqw h{wuhph xfwxdwlrqv lq wkh qrplqdo h{fkdqjh udwh1
814
Whpsrudu| Vwhulol}dwlrq
Wkh sulfh ohyho mxpsv zkhq dlg rzv lqfuhdvh dqg wkh fhqwudo edqn pdlqwdlqv d
fudzolqj shj1 Vlqfh lq dwlrq ghfuhdvhv udslgo| diwhu wkh lqlwldo vslnh lq wkh FSL/
whpsrudu| vwhulol}dwlrq frphv wr plqg dv d vwudwhj| iru vprrwklqj wkh sdwkv ri
prqh| jurzwk dqg wkh sulfh ohyho1 Wr { lghdv/ vxssrvh wkh jryhuqphqw vhoov d
odujh eorfn ri erqgv dw w @ 3 dqg wkhq uhghhpv wkh ghew lq ixwxuh shulrgv/ yl}1=
eb @ ^e+w, er `>
@, e+w, @ er . ^e+3, er `hw =
+4:,
+4;,
Lqlwldo erqg vdohv duh e+3, er dqg wkh sdudphwhu ghwhuplqhv krz idvw wkh
ghew lv sdlg r1 Wkh vwhdg| vwdwh lv xqfkdqjhg e hyhqwxdoo| uhwxuqv wr er 1
Wdeoh 6 vkrzv wkh rxwfrph zkhq erqg vdohv dw w @ 3 duh ;( ri JGS dqg
;3( ri wkh qhzo| lvvxhg ghew lv uhghhphg ryhu whq |hduv + @ =494,155 D txlfn
vfdq ri wkh uhvxowv uhyhdov soxvvhv dqg plqxvhv1 Rq wkh soxv vlgh/ whpsrudu|
vwhulol}dwlrq lv khosixo lq vprrwklqj wkh sdwk ri wkh sulfh ohyho1 Wkh lq dwlrq udwh
gursv wr 4604;( dw w @ 3 dqg wkhq ghfolqhv prqrwrqlfdoo| wrzdug lwv vwhdg|0
vwdwh ohyho1 Wklv lv dffrpsolvkhg zlwk d pxfk vpdoohu suhidwru| vslnh lq wkh
FSL +30819( yv1 60<( lq Sdqho E ri Wdeoh 4,1 Frpsduhg wr wkh qr0vwhulol}dwlrq
fdvh/ lq dwlrq lv rqh shufhqwdjh srlqw orzhu lq wkh uvw |hdu dqg voljkwo| kljkhu
lq vxevhtxhqw |hduv1 Suhihuhqfhv ghflgh zklfk sdwk lv vxshulru/ exw zh vxvshfw
prvw srolf| pdnhuv zrxog rsw iru wkh vprrwkhu sdwk surhuhg e| whpsrudu|
vwhulol}dwlrq1
Wkh gudzedfnv ri wkh srolf| frqfhuq wkh lpsdfw rq wkh uhdo lqwhuhvw udwh dqg
wkh vl}h ri wkh lqlwldo erqg vdoh1 Lq wkh uxqv iru @ =83 wkh uhdo lqwhuhvw udwh
xfwxdwhv ehwzhhq 44 dqg 54 shufhqw lq wkh uvw |hdu1 Wklv lv zruulvrph hqrxjk/
exw zkhq @ =58 =68 wkh udwh ydxowv wr 4;076( dqg wdnhv wzr ixoo |hduv wr idoo
edfn wr <044(1 Lw lv dovr glvwxuelqj wkdw wkh prghvw uhgxfwlrq lq sulfh yrodwlolw|
uhtxluhv vr pxfk ghew wr eh vrog vr txlfno|1 Wkh dvvxpswlrq lq +4;, wkdw doo
erqg vdohv rffxu dw w @ 3 lv dq duwlfldo vlpsolfdwlrq1 D idlu lqwhusuhwdwlrq ri
wkh srolf| uxoh/ krzhyhu/ lv wkdw rshq pdunhw rshudwlrqv lqfuhdvh wkh lqwhuqdo
ghew e| :;( ri JGS lq wkh vsdq ri 90< prqwkv1 Wklv lv suredeo| wkh rxwhu
olplw ri zkdw lv ihdvleoh lq wkh Jkdqldq erqg pdunhw/ |hw wkh sulfh ohyho vslnh
vwloo h{fhhgv 5( lq yh ri wkh hljkw fdvhv1
47
Lw lv hdv| wr xqghuvwdqg lq oljkw ri wkhvh uhvxowv zk| prvw Diulfdq jryhuq0
phqwv kdyh hpsor|hg d pl{ ri vwhulol}dwlrq dqg iruhljq h{fkdqjh vdohv wr frxqwhu0
dfw wkh vkruw0uxq lq dwlrqdu| suhvvxuhv fuhdwhg e| kljk dlg rzv1 Wkh sureohp
zlwk uho|lqj rq vwhulol}dwlrq dorqh lv wkdw erqg vdohv sxvk xs wkh uhdo lqwhuhvw udwh
dqg wkhuhe| dwwudfw wkh fdslwdo lq rzv wkh| duh wu|lqj wr qhxwudol}h156 Revhuyh lq
Wdeoh 6 wkdw kljk uhdo lqwhuhvw udwhv duh dvvrfldwhg zlwk pdvvlyh ryhuvkrrwlqj ri
sulydwh fdslwdo lq rzv dqg odujh rvhw frh!flhqwv157 Wklv pdnhv olih gl!fxow iru
wkh fhqwudo edqn1 Vwhulol}dwlrq zrunv e| uhgxflqj oltxlglw| dqg udlvlqj wkh uhdo
lqwhuhvw udwh wr d ohyho wkdw lqgxfhv wkh sulydwh djhqw wr fxuwdlo h{shqglwxuh +uho0
dwlyh wr wkh qr0vwhulol}dwlrq sdwk,1 Dw wkh pdujlq/ wkh zlwkgudzdo ri rqh groodu
ri grphvwlf fxuuhqf| iurp flufxodwlrq uhgxfhv oltxlglw| vhuylfhv e| l grooduv +66
fhqwv zruwk lq Wdeoh 6,1 Zkhq wkh sulydwh djhqw h{fkdqjhv iruhljq iru grphvwlf
fxuuhqf| dw wkh fhqwudo edqn/ grooduv ri wkh fxw lq oltxlglw| vhuylfhv lv uhvwruhg/
ohdylqj d qhw orvv ri u grooduv1 Wklv lv rqo| 57( ri wkh ghfuhdvh lq oltxlglw| vhu0
ylfhv dfklhyhg iurp vhoolqj erqgv iru grphvwlf fxuuhqf| ^u@l @ @+ . , @ =57
iru glhuhqwldo fkdqjhv`1 Wkh fhqwudo edqn lv qrw srzhuohvv/ exw fdslwdo rzv
vhyhuho| frqvwudlq lwv delolw| wr pdqdjh wkh sdwk ri oltxlglw|1
815
D Pdqdjhg Iordw
1 1 1 wkh txhvwlrq ri wkh dsursuldwh h{fkdqjh udwh uhjlph iru Diulfdq
frxqwulhv uhpdlqv rshq1 Qrqh ri wkhvh frxqwulhv kdv d csxuh* rdwlqj
h{fkdqjh udwh/ rswlqj lqvwhdg iru wkh frpprq lqwhuphgldwh fdvh ri
d cpdqdjhg* rdw 1 1 1 +Ohdsh/ 4<<</ ss1459045:,
Wkh suhfhglqj uhvxowv pd| h{sodlq zk| prvw frxqwulhv suhihu pdqdjhg rdwv
wr hlwkhu d sxuh rdw ru d fudzolqj shj1 Srolf| lv wrr sdvvlyh lq d sxuh rdw=
zkloh lq dwlrq ghfuhdvhv vwurqjo|/ wkh qrplqdo h{fkdqjh udwh lv doorzhg wr dssuh0
fldwh wr wkh srlqw zkhuh rxwsxw frqwudfwv lq wkh qrqwudgdeohv vhfwru1 D fudzolqj
shj huuv lq wkh rssrvlwh gluhfwlrq/ lpshulolqj d glhuhqw wdujhw= zkhq wkh jry0
huqphqw frpplwv wr d {hg sdwk iru wkh h{fkdqjh udwh lw wkurzv dzd| wkh srolf|
lqvwuxphqw wkdw lv prvw hhfwlyh lq frpedwwlqj wkh vkruw0uxq lq dwlrqdu| suhv0
vxuhv fuhdwhg e| kljkhu dlg vshqglqj dqg dffrpsdq|lqj sulydwh fdslwdo lq rzv1
Qru grhv pruh dfwlyh prqhwdu| srolf| uhvroyh wkh wdujhwv0lqvwuxphqwv sureohp1
D fudzolqj shj frpelqhg zlwk whpsrudu| vwhulol}dwlrq uhgxfhv wkh lqlwldo sulfh
vslnh> exw/ dv zh kdyh mxvw vhhq/ wklv riwhq surgxfhv yhu| kljk uhdo lqwhuhvw udwhv
dqg pd| uhtxluh erqg vdohv rq d vfdoh wkdw lv qrw ihdvleoh1
D pdqdjhg rdw jlyhv srolf| pdnhuv wkh iuhhgrp wr qg wkh plggoh jurxqg
ehwzhhq wrr pxfk dqg wrr olwwoh lqwhuyhqwlrq1 Wkh uljkw dprxqw ri lqwhuyhqwlrq
ghshqgv/ ri frxuvh/ rq wkh zhljkwv dwwdfkhg wr wkh wdujhwv iru rxwsxw/ lq dwlrq/
wkh uhdo h{fkdqjh udwh/ dqg wkh uhdo lqwhuhvw udwh1 Udwkhu wkdq ghulyh d frpsol0
fdwhg lqwhuyhqwlrq uxoh e| rswlpl}lqj ryhu d txdgudwlf remhfwlyh ixqfwlrq wkdw
lqfrusrudwhv doo ri wkhvh wdujhwv/ zh dvvxph wkh fhqwudo edqn vhoov2ex|v iruhljq
fxuuhqf| zkhqhyhu wkh uhdo h{fkdqjh udwh +4@Sq , lv deryh2ehorz lwv orqj0uxq
htxloleulxp ohyho=
Sq Sq
> A 3=
+4<,
]b @ Sq
Htxdwlrq +4<, uhodwhv wkh rz dffxpxodwlrq ri uhvhuyhv wr ghyldwlrqv ri wkh uhdo
h{fkdqjh udwh iurp lwv wdujhw ydoxh1 Lq dgglwlrq/ ] pd| mxps dw w @ 31 Wkh
48
lqlwldo sxufkdvh ri uhvhuyhv dqg duh fkrvhq mrlqwo| wr hqvxuh wkdw wkh h{lvwlqj
qrplqdo sulfh ri wkh qrqwudghg jrrg fohduv wkh pdunhw dw w @ 31 Wkh lqwhuyhqwlrq
vwudwhj|/ lq rwkhu zrugv/ lv wr ohw wkh h{fkdqjh udwh dssuhfldwh hqrxjk wr uhgxfh
lq dwlrq exw qrw vr pxfk dv wr gulyh wkh qrqwudgdeohv vhfwru lqwr d uhfhvvlrq1
Rwkhu wdujhwv gr qrw lq xhqfh wkh lqwhuyhqwlrq uxoh> lw wxuqv rxw/ krzhyhu/ wkdw
wkh uxoh srvwxodwhg khuh dovr juhdwo| uhgxfhv yrodwlolw| ri wkh uhdo h{fkdqjh udwh
dqg wkh uhdo lqwhuhvw udwh1
Wdeoh 7 vkrzv wkh rxwfrph zkhq wkh lqlwldo vwrfn ri uhvhuyhv lv 8( ri JQS1 Dw
orqj odvw/ zh kdyh vrphwklqj wkdw fdq eh surqrxqfhg dq xqtxdolhg vxffhvv1 Lq
frqwudvw wr wkh srodu h{fkdqjh udwh uhjlphv/ wkh pdqdjhg rdw uhgxfhv lq dwlrq
lpphgldwho| zlwkrxw dq| dgyhuvh vlgh0hhfwv rq rxwsxw/ wkh fxuuhqw dffrxqw
edodqfh/ ru wkh uhdo h{fkdqjh udwh1 Wkh rqh plqru eohplvk lq wkh uhvxowv lv wkdw
wkh uhdo lqwhuhvw udwh lqlwldoo| mxpsv wr 43( lq wkh uxq iru + @ =83> @ =:8,1
Wkh xsvkrw ri doo wklv lv wkdw wkh rswlpdo h{fkdqjh udwh uhjlph olhv forvh
wr wkh fudzolqj shj hqg ri wkh srolf| vshfwuxp1 Wr txdqwli| wkh phdqlqj ri
forvh/ frqvlghu wkh sdwkv ri wkh h{fkdqjh udwh dqg uhvhuyhv dvvrfldwhg zlwk
wkh srolf| uxoh lq Wdeoh 71 Dssuhfldwlrq ri wkh qrplqdo h{fkdqjh udwh dw w @ 3
lv :04:( yv1 5507;( lq d sxuh rdw1 Fxpxodwlyh uhvhuyh sxufkdvhv duh 850;;(
dv odujh dv lq d fudzolqj shj/ zlwk wkh jxuh h{fhhglqj :8( zkhq @ 5 61
+Wkh jxuh lq sduhqwkhvhv lq wkh urz iru ] lv wkh vwrfn ri uhvhuyhv lq d fudzolqj
shj1,58
9
Rwkhu Vfhqdulrv
Lq wklv vhfwlrq zh h{dplqh wkh vhqvlwlylw| ri wkh uhvxowv wr dowhuqdwlyh vshfl0
fdwlrqv ri dlg rzv dqg vwlfn| sulfhv1 Wkh qxphulfdo uhvxowv duh uhsruwhg lq
Dsshqgl{ Wdeohv D4 dqg D51
914
Judgxdo Dlg Iorzv
Wkh uljkw w|sh ri pdqdjhg rdw dyrlgv erwk d vslnh lq wkh sulfh ohyho dqg
h{fhvvlyh dssuhfldwlrq ri wkh qrplqdo dqg uhdo h{fkdqjh udwh1 Lw lv/ krzhyhu/
d frpsolfdwhg/ lpshuihfw vroxwlrq wr wkh pdfurhfrqrplf sureohpv dvvrfldwhg
zlwk d vxgghq dlg erqdq}d= d orw ri lqirupdwlrq dqg d idlu elw ri whfkqlfdo
h{shuwlvh lv qhhghg wr fdofxodwh wkh sdudphwhuv ri wkh srolf| uxoh lq htxdwlrq
+4<,1 Dq dowhuqdwlyh/ hdvlhu0wr0lpsohphqw vwudwhj| lv wr ghihu vrph dlg wr wkh
ixwxuh1 Li fdslwdo lq rzv dqg vshqglqj lqfuhdvh judgxdoo| dorqj zlwk dlg/ wkhq
pdfurhfrqrplf vwdelolw| pd| eh frpsdwleoh zlwk d fudzolqj shj ru d sxuh rdw
zlwk frqwlqxhg rshudwlrq ri d vlpsoh/ wudqvsduhqw h{fkdqjh udwh uhjlph1
dw wkh
Sxuvxlqj wklv lghd/ vxssrvh dlg ulvhv wrzdug lwv shupdqhqw ohyho [
udwh
[+w,`> f A 3=
[b @ f^[
+53,
Ghod|hg judwlfdwlrq vkrxog qrw eh sxqlvkhg1 Wkh suhvhqw ydoxh lqfuhdvh lq dlg
lv wkh vdph wkhuhiruh dv lq wkh fdvh zkhuh [ lqfuhdvhv lqvwdqwdqhrxvo| iurp [r
wr [ 1 Wklv lpsolhv
@ [r . f . u +[ [r ,>
+54,
[
f
zkhuh u lv wkh zruog pdunhw lqwhuhvw udwh1
49
Lq Dsshqgl{ Wdeoh 4/ u lv 8( dqg wkh h{wud dlg lv skdvhg0lq vorzo| ryhu d
shulrg ri yh |hduv1 Glvdssrlqwlqjo|/ wkh uhvxowv duh vlplodu wr wkrvh lq Wdeohv
4 dqg 51 Wklv uh hfwv wkh orjlf ri Olih F|foh wkhru|1 Vlqfh wkh sulydwh djhqw
dqwlflsdwhv kljkhu dlg rzv dqg orzhu vfdo ghflwv lq wkh qhdu ixwxuh/ wkh sdwkv
iru uhdo h{shqglwxuh/ sulydwh fdslwdo rzv/ dqg rwkhu nh| pdfur yduldeohv duh
derxw wkh vdph dv zkhq dlg lqfuhdvhv lqvwdqwdqhrxvo|1 Wkh rqh h{fhswlrq lv wkh
vljqlfdqwo| ehwwhu sdwk iru qrqwudgdeohv rxwsxw lq wkh uxq iru + @ =58> @ =:8,
lq Wdeoh D41 Lq doo rwkhu fdvhv/ wkh lpsuryhphqw lq wkh wudqvlwlrq sdwk lv
lqfrqvhtxhqwldo1 Wkh vslnh lq wkh sulfh ohyho lv vwloo yhu| odujh lq d fudzolqj shj/
dqg vkdus frqwudfwlrq lq wkh qrqwudgdeohv vhfwru/ whpsrudulo| kljk uhdo lqwhuhvw
udwhv/ dqg ryhuvkrrwlqj ri wkh uhdo h{fkdqjh udwh duh vwloo vhyhuh sureohpv zkhq
wkh fxuuhqf| rdwv1 Lq vkruw/ judgxdolvp khosv/ exw qrw hqrxjk wr pdwwhu1
915
Lqhuwldo Lq dwlrq
Lq wkh vshflfdwlrq ri vwlfn| sulfhv ghyhorshg e| Fdoyr +4<;6,/ wkh sulfh ohyho
lv vwlfn| exw qrw wkh lq dwlrq udwh1 Wklv ghwdlo lv fulwlfdo1 Wkh txlfn uhvsrqvh
ri lq dwlrq lv wkh uhdvrq dq deuxsw uhgxfwlrq lq wkh udwh ri fudzo zrunv zhoo lq
wkh Fdoyr prgho1 Hduolhu zh h{suhvvhg grxewv derxw wkh qrwlrq wkdw sulfhv duh
vwlfn| xszdug1 Lq wklv vhfwlrq zh zlvk wr pdnh wkh dgglwlrqdo srlqw wkdw glhuhqw
vwlfn|0sulfh prghov jlyh glhuhqw uhvxowv1 Wkh vwurqj/ xqlirupo| srvlwlyh uhvxowv
lq wkh Fdoyr prgho gr qrw fduu| ryhu wr prghov lq zklfk vwlfn| sulfhv vwhp iurp
lqhuwldo lq dwlrq1
Wkhuh duh d ydulhw| ri zd|v wr prgho lqhuwldo lq dwlrq1 Iru looxvwudwlyh sxu0
srvhv/ zh dgrsw wkh vshflfdwlrq lq Fdoyr dqg Yhjk +4<<7,1 Lq wkhlu irupxodwlrq/
q
$b
q `>
@ $ . ^Gq +Sq > H, T
@ +q $,>
+55,
+56,
zkhuh $/ wkh udwh ri qrplqdo zdjh jurzwk/ lv suhghwhuplqhg1 Htxdwlrq +55, vd|v
wkdw upv lq wkh qrqwudgdeohv vhfwru uhdfw wr h{fhvv ghpdqg e| udlvlqj sulfhv
idvwhu wkdq zdjhv1 Wkh udwlrqdoh iru +56, lv ohvv fohdu> suhvxpdeo| zrunhuv dlp
iru zdjh lqfuhdvhv wkdw wudfn sulfh jurzwk dw wkh upv wkdw hpsor| wkhp1
Frqvlghu djdlq zkdw kdsshqv zkhq dlg lqfuhdvhv dqg wkh jryhuqphqw lpph0
gldwho| uhgxfhv wkh udwh ri fudzo " wr lwv qhz vwhdg|0vwdwh ohyho1 Diwhu vwdulqj
dw htxdwlrqv +55, dqg +56, iru wkluw| vhfrqgv/ lw vkrxog eh wudqvsduhqw wkdw wkh
sdwk wr wkh qhz vwhdg| vwdwh zloo lqyroyh dowhuqdwlqj f|fohv ri h{sdqvlrq dqg
frqwudfwlrq1 Lq wkh vkruw uxq/ qrqwudgdeohv rxwsxw dqg q lqfuhdvh1 Exw wkh
lqlwldo h{sdqvlrqdu| skdvh pxvw eh iroorzhg e| d frqwudfwlrqdu| skdvh li q
lv wr wuhn grzqzdug lq wkh gluhfwlrq ri "1 Ehfdxvh q lqfuhdvhv lqlwldoo|/ wkh
frqwudfwlrqdu| skdvh lv riwhq surorqjhg dqg ghhs1 Dsshqgl{ Wdeoh D5 uhsruwv
uhvxow iru @ 4 dqg @ 81 Dowkrxjk sulfh dgmxvwphqw lv idvw dqg lq dwlrq lv
qrw kljko| lqhuwldo/ wkh h{sdqvlrqdu| skdvh lv h{fhhglqjo| eulhi dqg wkh vxevh0
txhqw uhfhvvlrq odvwv 509 |hduv1 Lq uxqv zkhuh @ 5/ +qrw uhsruwhg khuh, wkh
uhdo h{fkdqjh udwh dovr ryhuvkrrwv lwv orqj0uxq ohyho e| d frqvlghudeoh dprxqw1
Zh vkrxog dfnqrzohgjh wkdw vrph ri rxu rwkhu uhvxowv fkdqjh li wkh Fdoyr0
Yhjk vshflfdwlrq pluuruv uhdolw|1 Lq sduwlfxodu/ zkloh d pdqdjhg rdw frqwlqxhv
wr grplqdwh d fudzolqj shj dqg d sxuh rdw +frpsduh Sdqhov E dqg D lq Wdeoh
D5,/59 lw grhv qrw fxuh doo pdfurhfrqrplf sureohpv= vlqfh zdjh dqg sulfh lq0
dwlrq lq wkh qrqwudgdeohv vhfwru ghfuhdvh rqo| zkhq upv rshudwh zlwk h{fhvv
4:
fdsdflw|/ d uhfhvvlrq lv lqhylwdeoh uhjdugohvv ri krz wkh h{fkdqjh udwh lv pdq0
djhg1 Wklv frqfoxvlrq suredeo| grhv qrw dsso| wr doo w|shv ri dlg1 Lqwxlwlrq
vxjjhvwv/ iru h{dpsoh/ wkdw vshqglqj dlg prqh| wr lqfuhdvh vxsso| pljkw uhgxfh
lqhuwldo lq dwlrq zlwkrxw vxemhfwlqj wkh hfrqrp| wr d uhfhvvlrq1 Wkhuh lv qr
sdlq0iuhh vroxwlrq/ krzhyhu/ zkhq dlg dhfwv rqo| djjuhjdwh ghpdqg1
:
Frqfoxglqj Uhpdunv
Wkh g|qdplf uhvsrqvh wr shuvlvwhqw r!fldo fdslwdo rzv lv olqnhg wr wkh ghjuhh
ri exgjhw vxssruw wkh| surylgh dqg wkh vwuhqjwk ri sulydwh sruwirolr vxevwlwx0
wlrq1 Zkhq wkhvh wdnh hyhq ruglqdu| ydoxhv/ sruwirolr dgmxvwphqwv grplqdwh wkh
vkruw0uxq g|qdplfv dqg surgxfh vrph glvwlqfwo| xqsohdvdqw wudghrv1 D sxuh
rdw/ lq sduwlfxodu/ shuirupv yhu| srruo|1 Sruwirolr suhvvxuhv surgxfh d qrp0
lqdo dssuhfldwlrq wkdw lv dq rughu ri pdjqlwxgh odujhu wkdq wkh uhtxluhg uhdo
dssuhfldwlrq/ dqg xqohvv wkh sulfhv ri qrqwudghg jrrgv duh shuihfwo| h{leoh/ wkh
uhdo h{fkdqjh udwh ryhuvkrrwv dqg vxevwlwxwlrq hhfwv gulyh wkh hfrqrp| lqwr
d ghhs uhfhvvlrq1 D fudzolqj shj grhv ehwwhu/ exw doorzv d vkruw0uxq vslnh lq
lq dwlrq> erqg vwhulol}dwlrq fdq suhyhqw wkh lq dwlrq vslnh/ exw rqo| dw wkh frvw
ri d udslgo| ulvlqj lqwhuhvw exughq1 Lq rxu suhihuuhg pdqdjhg rdw vfhqdulr/
wkh fhqwudo edqn xvhv xqvwhulol}hg iruhljq h{fkdqjh lqwhuyhqwlrq wr wdujhw wkh
prghvw uhdo dssuhfldwlrq qhhghg wr devrue wkh dlg lq rz1 Uhdo lqwhuhvw udwhv
wkhq vwd| orz dqg pdfurhfrqrplf dgmxvwphqw lv udslg1 Rxu dqdo|vlv vxjjhvwv
wkdw Diulfdq fhqwudo edqnv kdyh ehhq fruuhfw wr lqwhuyhqh vxevwdqwldoo| lq wkh
idfh ri uhfhqw lqfuhdvhv lq dlg/ dqg wr glvfrxqw wkh dujxphqw wkdw udslg grphvwlf
oltxlglw| h{sdqvlrq qhfhvvdulo| fdoov iru d frpelqdwlrq ri erqg vwhulol}dwlrq dqg
fohdqhu rdwlqj1
Rxu vlpxodwlrqv kdyh ehhq frqqhg wr dlg vxujhv fkdudfwhulvwlf ri wkrvh
uhfhlyhg e| KLSF frxqwulhv lq wkh odwh 4<<3v1 Wkh ulgh zloo eh pruh vshfwdfxodu/
ri frxuvh/ li grqruv iroorz wkh uhfrpphqgdwlrqv ri wkh XQ dqg wkh Frpplvvlrq
rq Diulfd +5338,/ zklfk frxog surgxfh d grxeolqj ri dlg wr frxqwulhv olnh Jkdqd
ryhu wkh qh{w ghfdgh1 Rxu phvvdjh lq wklv hyhqw lv vwudljkwiruzdug= li d sruwlrq
ri wkh dgglwlrqdo dlg vxevwlwxwhv iru grphvwlf prqhwdu| qdqfh/ rdwlqj zloo
gholyhu d pxfk odujhu uhdo dssuhfldwlrq wkdq lv uhtxluhg wr devrue wkh vxujh lq
dlg1 D qduurz irfxv rq prqhwdu| wdujhwv zloo lq wklv fdvh eh srwhqwldoo| vhyhuho|
glvuxswlyh> wkh dssursuldwh vwdqfh lv rqh ri vxevwdqwldo dqg xqvwhulol}hg iruhljq
h{fkdqjh lqwhuyhqwlrq1
Zh forvh zlwk vrph wkrxjkwv derxw wzr h{whqvlrqv ri wkh dqdo|vlv wkdw zrxog
whvw wkh urexvwqhvv ri rxu frqfoxvlrqv lq d eurdghu srolf| frqwh{w15: Wkh uvw
frqfhuqv dlg rzv wkdw vxssruw sxeolf lqyhvwphqw1 Zh kdyh htxdwhg dlg zlwk
wudqvihu sd|phqwv wr wkh srru +l1h1/ wkh uhsuhvhqwdwlyh sulydwh djhqw,1 Lw lv
dovr ghvluhdeoh wr lqyhvwljdwh wkh uhshufxvvlrqv ri dlg wkdw qdqfhv uhkdelolwdwlrq
ri vrfldo dqg sk|vlfdo lqiudvwuxfwxuh1 Wklv w|sh ri dlg eulqjv pdq| qhz hhfwv
lqwr sod|1 Li surgxfwlyh fdsdflw| lqfuhdvhv sursruwlrqdwho| lq wkh wudgdeohv dqg
qrqwudgdeohv vhfwruv/ wkhq dssuhfldwlrq ri wkh uhdo h{fkdqjh udwh zloo eh vwulfwo|
whpsrudu|1 Ixuwkhupruh/ li sulydwh fdslwdo dqg lqiudvwuxfwxuh duh frpsohphqwv/
dlg pd| surgxfh odujh pxowlsolhu hhfwv dqg d qrqwulyldo lqfuhdvh lq wd{ uhyhqxh
lq wkh orqj uxq15; Wkh frpsolfdwlrqv wkdw durvh khuh iurp sulydwh fdslwdo lq rzv
dxjphqwlqj dlg rzv zrxog wkhq pdwhuldol}h lq wkh fdvh zkhuh doo dlg lv vshqw1
Uhodwhg wr wklv/ zh frqmhfwxuh wkdw surgxfwlyh dlg dlg wkdw kdv d vwurqj
4;
srvlwlyh lpsdfw rq shupdqhqw lqfrph dqg wkh htxloleulxp sulydwh fdslwdo vwrfn
zloo holflw lpphgldwh/ odujh lqfuhdvhv lq sulydwh frqvxpswlrq dqg lqyhvwphqw1
Lq wkh vkruw uxq/ wkhuhiruh/ lw pljkw suryh yhu| gl!fxow wr frqwdlq lq dwlrqdu|
suhvvxuhv1 Wklv sxvkhv wkh rswlpdo pdqdjhg rdw pruh lq wkh gluhfwlrq ri wkh
plggoh jurxqg ehwzhhq d {hg h{fkdqjh udwh dqg d sxuh rdw1 Krz pxfk pruh
lv qrw fohdu devhqw fduhixo dqdo|vlv1 Iru zkdw lw lv zruwk/ rxu sulru lv wkdw wkh
pdfurhfrqrplf wudghrv dvvrfldwhg zlwk dlg dqg wkh uljkw srolf| lqwhuyhqwlrq
duh vhqvlwlyh wr wkh w|sh ri dlg1
Wkh vhfrqg h{whqvlrq dfnqrzohgjhv wkdw Diulfdq fhqwudo edqnv kdyh wr zruu|
derxw pruh wkdq mxvw dlg vkrfnv zkhq ghflglqj rq wkh dssursuldwh h{fkdqjh udwh
uhjlph1 Zh duh fxuuhqwo| zrunlqj rq d vwdwlrqdu|/ glvfuhwh0wlph yhuvlrq ri rxu
prgho lq zklfk dlg vkrfnv frpshwh zlwk rwkhu lpsruwdqw vkrfnv iru srolf|pdn0
huv* dwwhqwlrq dqg vrph sruwlrq ri dlg pd| lq idfw uhsuhvhqw d uhvsrqvh wr rwkhu
vkrfnv +h1j1/ wr wkh whupv ri wudgh,1 Zh orrn iru ghvludeoh lqwhuyhqwlrq dqg
vwhulol}dwlrq uxohv/ jlyhq d sodxvleoh orvv ixqfwlrq dqg jlyhq wkh revhuyhg mrlqw
glvwulexwlrq ri vkrfnv dqg dlg1 Wklv dssurdfk olqnv wkh dqdo|vlv lq wkh fxuuhqw
sdshu zlwk wkh jurzlqj olwhudwxuh rq prqhwdu| srolf| uxohv lq wkh rshq hfrqrp|
+h1j1/ Vyhqvvrq/ 5333,1 Wkh frqfoxvlrqv zh kdyh hpskdvl}hg khuh lqfoxglqj
wkh phulwv ri pdqdjhg rdwlqj dqg wkh olplwhg uroh iru erqg vwhulol}dwlrq vhhp olnho| wr vxuylyh li wkh hqylurqphqw lv grplqdwhg e| dxwrqrprxv dqg uhd0
vrqdeo| shuvlvwhqw fkdqjhv lq dlg1 Zkdw uhpdlqv wr eh vhhq lv zkhwkhu wkhvh
frqfoxvlrqv frqvwlwxwh d vhulrxv fkdoohqjh/ xqghu pruh jhqhudo flufxpvwdqfhv/ wr
uxohv wkdw lqfrusrudwh juhdwhu h{fkdqjh udwh h{lelolw| dqg2ru pruh djjuhvvlyh
erqg rshudwlrqv1
4<
Dsshqgl{
Lq wklv dsshqgl{ zh vroyh iru wkh vwhdg|0vwdwh rxwfrph dqg iru wkh g|qdplf
v|vwhpv wkdw frqwuro wkh wudqvlwlrq sdwk lq d sxuh rdw dqg d fudzolqj shj1
L1 Wkh Vwhdg|0Vwdwh Rxwfrph
Dfurvv vwhdg| vwdwhv/ p
b @ Ib @ ]b @ Hb @ 31 Lpsrvlqj wkhvh frqglwlrqv ohdgv
wr u @ > " @ / dqg
!4
!5
H
p
@
@
@
@
YH Sq + . ,>
YH Sq >
Sq Tq . TW . [>
Sq +j . e, [=
+D4,
+D5,
+D6,
+D7,
Lq wkh orqj uxq/ sulydwh vshqglqj ulvhv e| wkh ixoo dprxqw ri wkh dlg lq rz dqg
uhyhqxh iurp wkh lq dwlrq wd{ fryhuv wkh vfdo ghflw diwhu judqwv1 Qrwh dovr/
iurp +D4, dqg +D5,/ wkdw orzhu lq dwlrq dwwudfwv fdslwdo lq rzv rqo| li grphvwlf
dqg iruhljq fxuuhqf| duh Hgjhzruwk vxevwlwxwhv +l1h1/ !54 ? 3,1
Htxdwlrqv +D4,0+D7, dqg wkh pdunhw0fohdulqj frqglwlrq lq wkh qrqwudgdeohv
vhfwru
+D8,
Gq +Sq > H, @ Tq
fdq eh vroyhg iru Sq > > H> p> dqg I dv d ixqfwlrq ri wkh dlg lq rz [1 Uhfdoo
wkdw wkh jryhuqphqw lqfuhdvhv wudqvihuv wr wkh sulydwh vhfwru e| g+Sq j, @ #g[
dqg wkdw Y +, dqg !+, duh qhvwhg FHV0FUUD ixqfwlrqv=
+44@ ,@+4,
H 44@ nr . n4 Sq4
Y +Sq > H, @
>
4 4@
q
@+4, r44@
n5 p
+4,@ . n6 I +4,@
>
!+p>
I , @ k
4 4@
zkhuh/ wr uhshdw/ p
pSq dqg I I Sq > lv wkh hodvwlflw| ri vxevwlwxwlrq
ehwzhhq wudghg dqg qrqwudghg frqvxphu jrrgv/ lv wkh hodvwlflw| ri vxevwlwxwlrq
ehwzhhq grphvwlf dqg iruhljq fxuuhqf|> dqg lv wkh lqwhuwhpsrudo hodvwlflw| ri
53
vxevwlwxwlrq1 Iru wklv xwlolw| ixqfwlrq /
gH
@
g[
>
4 n
+D9,
gSq
Sq
@
g[
>
H
+D:,
g
gp
p
gI
I
vn . +4 #,+4 n, g[
>
+D;,
+4 n,+4 ,
H
4
g[
vn
@
.
.4#
>
+D<,
4 n +4 ,
4 n
H
+ ,p vn
4
g[
@ .4# > +D43,
l+4 ,
4 n
4 n H
@ zkhuh
p
@
lp
lp . I
i
@
I
@ 4 p
lp . I
duh wkh vkduhv ri oltxlglw| vhuylfhv surylghg e| grphvwlf dqg iruhljq fxuuhqf|>
p@H> n + . ,4 > v Sq e@H> l @ . lv wkh qrplqdo lqwhuhvw udwh> dqg
@ + p . i ,@l lv wkh hodvwlflw| ri prqh| ghpdqg zlwk uhvshfw wr lq dwlrq1
Xqghu wkh dvvxpswlrq wkdw # ? 4 v@/ wkh vfdo ghflw dqg lq dwlrq idoo1
Wklv hqvxuhv wkdw p ulvhv1 Wkh lpsdfw rq I lv xqfhuwdlq/ exw wkhuh lv d yhu|
vwurqj suhvxpswlrq wkdw iruhljq fxuuhqf| kroglqjv zloo ghfuhdvh1 Revhuyh lq
+D43, wkdw l+4 ,@p @ +l . I@H,+4 , lv wkh udwlr ri oltxlglw| vhuylfhv wr
qdwlrqdo lqfrph/ vfdohg grzq e| 4 1 Wkh uhflsurfdo ri wklv/ zklfk pxowlsolhv
/ lv d kxjh qxpehu1 Sulydwh fdslwdo rzv rxw wkhuhiruh rqo| zkhq grphvwlf
dqg iruhljq fxuuhqf| duh h{wuhpho| zhdn vxevwlwxwhv1
LL1 Ioh{leoh H{fkdqjh Udwhv
Lq d sxuh rdw wkh g|qdplf v|vwhp frqvlvwv ri
+ . ,
H+u ,>
p
b @ Sq +j . ue, [ "p>
Ib @ Sq Tq . TW . [ H>
Hb
@
+D44,
+D45,
+D46,
zkhuh p dqg H duh mxps yduldeohv dqg I lv d vwdwh yduldeoh1 Wr vroyh wkh
v|vwhp/ zh qhhg wr jxuh rxw krz u dqg " ydu| zlwk p/ I / dqg H1 ^Htxdwlrq
+4, douhdg| uhodwhv Sq wr H1` Zrunlqj wrzdug wklv hqg/ qrwh iurp +4,/ +5, dqg
+43, wkdw
+u ,=
+D47,
Sb @S @ @ " .
54
Htxdwlrqv +:,/ +;,/ dqg +D47, fdq eh vroyhg iru / "/ dqg u1 Wkh vroxwlrqv iru
u dqg " duh
^+ ,p gp@p + p . i ,gI@I . gH@H`>+D48,
+ . ,
+ ,i gI
gH
+ i . p , gp
.
.
.
.
+D49,
>
g" @ p
I
H
gu
@
Wkh uhtxlvlwh pdfklqhu| lv qrz lq sodfh1 Olqhdul}lqj +D44,0+D46, durxqg
wkh vwhdg| vwdwh +p > I > H , surgxfhv
65
6
5
6 5
p
b
p p
f4 f5
f6
7 Ib 8 @ 7 3
3
n 4 8 7 I I 8 >
+D47,
b
f
f9
H H
f
H
7
8
zkhuh
y
f4
f5
f6
@ @+ . ,
+ i . p ,
vy+ ,p
. .
>
Sq ey+ p . I , p + , i
.
.
@
>
I
I . y >
@ v
.
@
+ ,p y+ . ,
>
+ p . I ,y+ . ,
I@H
f7
@
f8
@
f9
@ y+ . ,@=
Wkh v|vwhp lv vdggohsrlqw vwdeoh1 + Vdggohsrlqw vwdelolw| uhtxluhv f5 f7 f4 f8 ? 3/
zklfk krogv iru ? 41, Rq wkh xqltxh sdwk wkdw frqyhujhv wr wkh vwdwlrqdu|
htxloleulxp/
p+w, pr
I +w, Ir
H+w, Hr
@ p pr U4 +I Ir ,h6 w >
U5
@ +I Ir ,+4 h6 w ,>
@ H Hr I Ir 6 w
h >
U5
zkhuh
U4
@
6 f9 . f8 U5
B 3>
f7
U5
@
n 4
A 3>
6
55
+D48,
+D49,
+D4:,
dqg 6 lv wkh v|vwhp*v qhjdwlyh hljhqydoxh1 Qrwh wkdw +D48, dqg +D4:, fdq eh
zulwwhq dv
U4
^I +w, I ` B 3
U5
p+w, p
@
H+w, H @ ^I +w, I `@U5 A 3=
+D4;,
+D4<,
Wkhvh duh wkh htxdwlrqv iru wkh PP dqg NN vfkhgxohv lq Iljxuh 5 lq wkh wh{w1
Lw lv fohdu iurp +D4:, wkdw h{shqglwxuh ryhuvkrrwhv lwv vwhdg|0vwdwh ohyho dw
b Ib ? 3/ ;w/ wkh uhdo lqwhuhvw udwh lv orzhu
w @ 31 Ixuwkhupruh/ vlqfh H>
u+w, @ 6
4 n I Ir 6 w
h ?
HU5
dqg fxuuhqw dffrxqw +FD, ghflwv shuvlvw wkurxjkrxw wkh dgmxvwphqw surfhvv
FD+w, @ Ib +w, @ 6 +I Ir ,h6 w ? 3=
Pruh zrun lv uhtxluhg wr vkrz wkdw wkh sulfh ohyho ghfuhdvhv rq lpsdfw dqg
wkh lq dwlrq udwh lv frqwlqxrxvo| orzhu1 Uhfdoo wkdw wkh qrplqdo prqh| vxsso|
lv suhghwhuplqhg1 Wkxv
h+3, hr
hr
@ p+3, pr
pr
@ p pr U4 +I Ir ,
.
=
pr
U5 pr
Diwhu vxevwlwxwlqj iru p pr dqg I Ir / wklv ehfrphv
;
<
A
A
A
A
A
A
?
@ g[
U5 6 f9 I + ,p N
4
h+3, hr
.
@
? 3>
A
hr
+ ,p +4 n,
f7 p l+4 ,
4 n A
HU5
A
A
A
A
~}
>
=
Srvlwlyh iru I ?Ir
zkhuh
N@
+D53,
vn
. 4 # A 3=
4 n
Wkh vroxwlrq iru wkh mxps lq wkh sulfh ohyho lv rewdlqhg iurp +4,/ +5,/ +D4:,/
dqg +D53,=
S +3, Sr
Sr
@,
S +3, Sr
Sr
h+3, hr
H+3, Hr
. n
h
Hr
; r
A
A
A
? U 4
I + ,p N
5
@
n .
A
4 n + ,p
H
l+4 ,
4 n
A
A
~}
~}
=
@
Srvlwlyh iru A
Srvlwlyh iru I AIr
6<
A
A
:A
@
9
: g[
9 6
.
9
n:
? 3=
8A HU5
7 f7 + ,p
A
~}
A
>
5
Srvlwlyh iru A
56
+D54,
Ilqdoo|/ htxdwlrq +D47, dqg wkh uvw0rughu frqglwlrqv +:, dqg +;, |lhog
+u . ,
n5 p 4@
=
@
n6 I
u+ . , +D55,
p@I ulvhv dqg u idoov/ vr pxvw ghfuhdvh dw w @ 31 Wklv jxdudqwhhv frqwlqxrxvo|
orzhu lq dwlrq rq wkh wudqvlwlrq sdwk wr wkh qhz vwhdg| vwdwh1 +Diwhu mxpslqj
dw w @ 3/ wkh sdwk ri lv frqwlqxrxv/ zlwk b @ k+I Ir ,1 Iru k A 3/ b ? 31
Zkhq k ? 3/ b A 3/ lpso|lqj wkdw dssurdfkhv lwv vwhdg|0vwdwh ohyho iurp
ehorz1,
LLL1 D Fudzolqj Shj
D fudzolqj shj jlyhv ulvh wr wkh v|vwhp
Hb
Mb
+ . ,
H+u ,>
@ Sq +j . ue, . Sq Tq . TW H "p>
@
+D44,
+D56,
zkhuh M p . I 1 Zh dvvxph wkh udwh ri fxuuhqf| ghsuhfldwlrq " lv uhgxfhg
wr lwv qhz vwhdg|0vwdwh ohyho lq rqh vwhs dw w @ 31 Wkh lqsxwv qhhghg wr vroyh
+D44, dqg +D56, duh wkxv olplwhg wr wkh uhgxfhg irupv wkdw vkrz krz u dqg
p ydu| zlwk M dqg H rq wkh wudqvlwlrq sdwk1 Wkhvh duh exulhg lq +:, dqg +;,1
Diwhu vxevwlwxwlqj iru iurp +D47, dqg uhsodflqj I zlwk M p/ wkh uvw0rughu
frqglwlrqv |lhog5<
gp @
gu
zkhuh
@
p
gH .
^ . i + ,`gM>
I
l
M
gH gM >
I + . , H
+D57,
+D58,
@ ^i l . p +5 . p @l i ,` . p 5 @l=
Urxwlqh dojheud qrz gholyhuv
Mb
q49
@
q4;
Hb
q4:
q4;
M M
H H
>
+D59,
zkhuh
q49
@
p
Sq el
.
^ . i + ,`
I + . , I q4:
@
vMl
5 +4 . v,
.
4>
.
I + . ,
q4;
@
l+ . ,
=
+ . ,
Xqghu wkh zhdn uhvwulfwlrq A v/ wkh vwhdg| vwdwh lv d vdggoh srlqw dqg wkh
vroxwlrqv iru M dqg H uhdg63
M+w, Mr
H+w, Hr
@ +M Mr ,+4 h5 w ,>
@ H Hr +M Mr ,U6 h5 w >
57
+D5:,
+D5;,
zkhuh 5 lv wkh v|vwhp*v qhjdwlyh hljhqydoxh dqg
U6 @
q4;
A 3=
q4; +M@H, 5 +I@H,
Wr orfdwh wkh srvlwlrq ri M / dgg wkh vroxwlrqv iru p dqg I lq +D<, dqg +D43,=
<
;
A
A
?
p
vn . +4 #,+4 n, @ g[
M
=
. ^ . i + ,`
M Mr @
A
A
l
+4 n,+4 ,
> H
= 4 n
Lpsdfw ri H%
Lpsdfw ri &
+D5<,
Kljkhu vshqglqj lqfuhdvhv wrwdo fxuuhqf| ghpdqg sursruwlrqdwho|/ exw wkh lp0
sdfw ri orzhu lq dwlrq ghshqgv rq lqlwldo frqglwlrqv +r / i , dqg wkh uhodwlyh
pdjqlwxghv ri wkh vxevwlwxwlrq sdudphwhuv dqg 1 Iru vx!flhqwo| odujh/ wkh
vhfrqg whup lv qhjdwlyh dqg odujhu lq devroxwh ydoxh wkdq wkh uvw1 Vroylqj iru
wkh erughuolqh ydoxh ri surgxfhv
M ? Mr
l A +4 . @i , .
l+4 ,+ . ,
M
= +D63,
i ^+ . , v . +4 #,` H
~}
Srvlwlyh iru #?4v@
LY1 Whpsrudu| Vwhulol}dwlrq
Zkhq wkh jryhuqphqw hqjdjhv lq whpsrudu| vwhulol}dwlrq/
eb @ ^e+w, er `=
+D64,
Wklv dowhuv rqo| rqh htxdwlrq lq wkh h{sulfh fudzolqj shj yduldqw ri wkh prgho1
Wkh sxeolf vhfwru exgjhw frqvwudlqw lv qrz
p
b . Sq eb @ Sq +j . ue, . [ . ]b "p>
+D65,
vr +D56, fkdqjhv wr
Mb @ Sq +j . ue, . Sq +e er , . Sq Tq . TW H "p=
+D66,
Surfhhglqj dv ehiruh |lhogv
M+w, Mr
H+w, Hr
@ M Mr . k5 h5 w . ^e+3, er `U7 hw >
@ H Hr . k5 U6 h5 w . ^e+3, er `U8 hw >
+D67,
+D68,
zkhuh
U7
U8
@ + . ,+q4; M@I . ,@K>
@ + . ,q4; H@I K>
K
@ 5 . +q4; M@I q49 , .
q4;
+q4: H q49 M,=
I
Dw w @ 3/ M mxpsv grzqzdug e| wkh vdph dprxqw dv e mxpsv xszdug1 Wkxv
k5 @ Mr M ^e+3, er `+4 . U7 ,
58
QRWHV
41 Wkh Sryhuw| Uhgxfwlrq Vwudwhj| Sdshu +SUVS,/ duwlfxodwhv d frxqwu|*v
phglxp0whup pdfurhfrqrplf dqg sxeolf h{shqglwxuh surjudp1 Lq wkh
pdmrulw| ri frxqwulhv wkh SUVS dqwlflsdwhv lqfuhdvhg sxeolf h{shqglwxuhv
qdqfhg lq sduw e| vxvwdlqhg lqfuhdvhv lq qhw dlg rzv/ lqfoxglqj iurp ghew
uholhi sd|phqwv dulvlqj iurp wkh Kljko| Lqghewhg Srru Frxqwulhv +KLSF,
lqlwldwlyh1
51 D jurzlqj olwhudwxuh hpskdvl}hv wkh lpsruwdqfh ri fdslwdo rzv lq vxe0
Vdkdudq Diulfd1 Vhh/ iru h{dpsoh/ Dvhd dqg Uhlqkduw +4<<9,/ Eklqgud hw
do +4<<<,/ Froolhu hw do +5335,/ dqg Ihgghunh dqg Olx +5335,1 Hpslulfdo
zrun e|/ dprqjvw rwkhuv/ Ilhoglqj +4<<7,/ Dgdp +4<<<,/ Khqvwulgjh +4<<<,
dqg Qdfkhjd +5334, qgv vljqlfdqw fxuuhqf|0vxevwlwxwlrq hhfwv rq wkh
ghpdqg iru grphvwlf prqhwdu| djjuhjdwhv1
61 Glvvdwlvidfwlrq zlwk wkh srolf| fkrlfhv lv hylghqw lq Rxdqhv/ Q|dzdwd dqg
Mrqdvvhq +5334, udglfdo vxjjhvwlrq +s154, wkdw dlg lq rzv vkrxog qrw h{0
fhhg d frxqwu|*v vwhulol}dwlrq fdsdflw|1
71 Fdoyr/ Ohlghupdq dqg Uhlqkduw +4<<7, dujxh wkdw lw lv ehvw wr devrue
fdslwdo lq rzv wkurxjk d rdw rq wkh jurxqgv wkdw dssuhfldwlrq ri wkh
qrplqdo h{fkdqjh udwh uhfrqflohv dssuhfldwlrq ri wkh uhdo udwh zlwk zlwk
orzhu lq dwlrq1 Vfkdgohu hw do1 +4<<6, dqg Ihuqdqgh}0Duldv dqg Prqwlho
+4<<9, zruu|/ krzhyhu/ wkdw rdwlqj pd| uhvxow qrw rqo| lq h{wuhph yrodwlo0
lw| ri wkh qrplqdo h{fkdqjh udwh exw dovr lq juhdwhu dssuhfldwlrq ri wkh
uhdo udwh1 Dvvhvvphqwv ri vwhulol}dwlrq duh htxdoo| glyhuvh dqg lqfrqfoxvlyh1
Fdoyr +4<<4, dqg Fdoyr/ Ohlghupdq dqg Uhlqkduw krog wkdw vwhulol}dwlrq
lv vhoi0ghihdwlqj= wkh kljkhu uhdo lqwhuhvw udwhv wkdw dffrpsdq| erqg vdohv
zruvhq lq dwlrqdu| suhvvxuhv e| lqfuhdvlqj wkh vfdo ghflw> pruhryhu/
kljkhu lqwhuhvw udwhv dwwudfw dgglwlrqdo fdslwdo lq rzv/ qhfhvvlwdwlqj ixu0
wkhu erqg vdohv/ hwf1 Hfkrlqj wklv srvlwlrq/ Vfkdgohu hw do1 uvw dvvhuw wkdw
vwhulol}dwlrq lv glvfuhglwhg dv d uhvsrqvh wr fdslwdo lq rzv +s16,/ exw wkhq
dfnqrzohgjh wkdw vwhulol}dwlrq lv riwhq hhfwlyh lq lqvxodwlqj dq hfrqrp|
iru vkruw shulrgv ri wlph iurp vrph ri wkh xqzdqwhg hhfwv ri vxujhv lq
lq rzv +s163,1 Wklv odwwhu ylhz lv forvh wr wkdw ri Orsh}0Phmld +4<<<,/
Nkdq dqg Uhlqkduw +4<<8,/ Khog dqg V}dodfkpdq +4<<;,/ dqg Ihuqdqgh}0
Duldv dqg Prqwlho +4<<9,/ zkr frqwhqg wkdw vwhulol}dwlrq lv hhfwlyh lq wkh
vkruw uxq exw kdug wr vxvwdlq ehfdxvh ri ulvlqj vfdo frvwv1
81 Jkdqd kdv ehhq vwuxjjolqj r dqg rq iru wzhqw| |hduv wr qg wkh uljkw
srolf| uhvsrqvh wr odujh dlg lq rzv1 Vhh \rxqjhu +4<<5, iru dq dffrxqw ri
wkh 4<;:04<<7 shulrg1
91 Iru vpdoo fkdqjhv/ fdq eh wuhdwhg dv d frqvwdqw1 Lq wkh qxphulfdo
vlpxodwlrqv/ ydulhv hqgrjhqrxvo| zlwk Sq 1 +Zh gr qrw dvvxph Free0
Grxjodv suhihuhqfhv1,
:1 Zh kdyh rplwwhg vrph lqwhuphgldwh vwhsv1 Wkh uvw lv
b
Sq Hb
YHS
@ +u ,>
.
YHH Gq
Sq H
59
zkhuh YHS CYH @CSq 1 ^Qrwh iurp +5, wkdw " @ Sbq @Sq 1` Wr jhw ulg
ri wkh dznzdug Ylm whupv/ uhfdoo Ur|*v lghqwlw| Gq @ YS +Sq > H,@YH +Sq > H,=
Iru krprwkhwlf suhihuhqfhv/ YHS @YHH Gq @ 4=Zh dovr kdyh iurp +4,
wkdw gSq @Sq @ +.,4 gH@H= Vxevwlwxwlqj iru Sbq @Sq dqg iru YHS @YHH Gq
surgxfhv htxdwlrq +43, lq wkh wh{w1
;1 Iru vlpsolflw|/ zh ljqruh lqwhuhvw sd|phqwv rq uhvhuyhv1 Wklv hqvxuhv wkdw
wkh orqj0uxq lpsdfw ri dlg rq uhdo lqfrph dqg wkh vfdo ghflw lv lqghshq0
ghqw ri wkh h{fkdqjh udwh uhjlph1
<1 Lq wkh odwwhu fdvh/ wkh iudfwlrq ri dlg uhvhuyhg iru exgjhw vxssruw vkrxog
eh kdoyhg lq rughu wr nhhs wkh lpsdfw rq wkh vfdo ghflw wkh vdph1
431 D uhfhqw LPI vwxg| vwuhvvhv wklv srlqw= Dlg dovr vhuyhv dv d zd| iru
wkh jryhuqphqw wr qdqfh lwv grphvwlf h{shqglwxuhv/ dv dq dowhuqdwlyh wr
grphvwlf wd{ uhyhqxh ru eruurzlqj/ hlwkhu iurp wkh sxeolf ru iurp wkh
fhqwudo edqn1 Lw pd| vhhp/ wkhuhiruh/ wkdw wkh qdqflqj ri h{shqglwxuhv
vxfk dv wkh klulqj ri qxuvhv lv dq dowhuqdwlyh xvh iru dlg/ lq dgglwlrq wr
lpsruwv1 Exw wklv dssurdfk wr wkh ixqfwlrq ri dlg lv plvohdglqj> diwhu doo/
wkh sxusrvh ri dlg lv qrw wr doorz wkh grphvwlf h{shqglwxuh1 Diwhu doo/ wkh
wkh jryhuqphqw frxog dozd|v vlpso| eruurz iurp wkh fhqwudo edqn +l1h1/
sulqw prqh|, wr qdqfh wkhvh h{shqglwxuhv1 +Ehuj/ 5338/ s16,
441 Vhh Ooxfk hw do1 +4<::/ fkdswhu 6,/ Ghdwrq dqg Pxhooedxhu +4<;3/ s1:4,/
Eoxqghoo +4<;;/ s168,/ dqg Eoxqghoo/ Sdvkdughv/ dqg Zhehu +4<<6/ Wdeoh
6e/ s18;4,1
451 1580183 lv wkh udqjh ghqhg e| wkh orzhu0 dqg xsshu0erxqg hvwlpdwhv ri iru Jkdqd lq Rjdnl/ Rvwu|/ dqg Uhlqkduw +4<<9,1
461 Vhh Ndplq dqg Hulfvvrq +4<<6,/ Vdydvwdqr +4<<9,/ dqg Edolqr/ Ehqqhww/
dqg Eruhqv}whlq +4<<<,1
471 Wkh Jkdqdldq jryhuqphqw ghglfdwhv 53( ri KLSF ghew uholhi wr ghflw
uhgxfwlrq +LPI 5337/ s164,1 Hpslulfdo hvwlpdwhv iru Jkdqd sodfh # dw
156/ uljkw rq wkh uhjuhvvlrq olqh iru Diulfd1 +Vhh vhfwlrq 514,
481 Wkh sdwkv iru lq dwlrq/ wkh uhdo lqwhuhvw udwh/ wkh fxuuhqw dffrxqw edodqfh/
hwf1 zhuh jhqhudwhg e| vxevwlwxwlqj wkh olqhdul}hg vroxwlrqv iru wkh ydul0
deohv lq wkh fruh g|qdplf v|vwhp lqwr wkh vwdwlf qrqolqhdu prgho1 Wklv
vhpl0Qrydohv surfhgxuh uhwdlqv pruh ri wkh qrqolqhdu vwuxfwxuh ri wkh
prgho dqg wkhuhe| uhgxfhv olqhdul}dwlrq huuru1 Lq wkh ixoo Qrydohv surfh0
gxuh/ wkh olqhdul}hg vroxwlrq iru wkh fruh g|qdplf v|vwhp lv xvhg rqo| wr
lpsrvh vwdelolw| frqglwlrqv rq wkh uhodwlrqvkls ehwzhhq wkh sdwkv ri wkh
vwdwh yduldeohv dqg wkh sdwkv ri wkh mxps yduldeohv1 Wkh vroxwlrq sdwkv iru
doo hqgrjhqrxv yduldeohv +u> > hwf1, dqg iru wkh vwdwh yduldeohv duh frp0
sxwhg iurp wkh ruljlqdo qrqolqhdu prgho1 Zh frpsxwhg iwhhq vroxwlrqv
xvlqj erwk wkh vhpl0Qrydohv dqg ixoo Qrydohv surfhgxuhv1 Wkh uhvxowv zhuh
yhu| forvh lq hyhu| fdvh +riwhq glhuhqfhv glg qrw dsshdu xqwlo wkh wklug
ru irxuwk ghflpdo sodfh,1 Vlqfh wkh vhpl0Qrydohv surfhgxuh lv idvwhu dqg
hdvlhu wr surjudp/ zh xvhg lw wr jhqhudwh wkh vroxwlrqv1
5:
491 Wkh vroxwlrq lv hydoxdwhg dw wkh lqlwldo vwhdg| vwdwh zkhuh Sq @ 4> u @ >
dqg @ "1
4:1 Dlg lv ixqqhohg wr wkh sulydwh vhfwru wkurxjk oxps0vxp wudqvihuv1 Vlqfh
r @ =83/ dssur{lpdwho| kdoi ri wkh h{wud dlg prqh| lv vshqw rq qrqwudghg
jrrgv1 Li dlg qdqfhg vrph surmhfw wkdw lqyroyhg d odujhu frpsrqhqw
ri qrqwudgdeohv vshqglqj/ wkh lqlwldo lqfuhdvh lq wkh sulfh ohyho zrxog eh
juhdwhu1 Zkhq doo dlg lv vshqw rq qrqwudghg jrrgv/ iru h{dpsoh/ wkh
xszdug mxps lq S dw w @ 3 lv derxw wzlfh dv odujh dv lq Wdeoh 51
4;1 Gxh wr frqwlqxrxv0wlph frpsrxqglqj/ wkh lqfuhdvh lq wkh sulfh ohyho ryhu
wkh fdohqgdu |hdu lv juhdwhu wkdq 43( zkhq Sb @S @ @ =43 +l1h1/ h=58 4 @
=5;7,1 Wkh jxuh uhsruwhg iru lq dwlrq lq wkh uvw |hdu lv wkh frqvwdqw ohyho
ri lq dwlrq wkdw surgxfhv wkh vdph lqfuhdvh lq wkh sulfh ohyho dw w @ 4 dv
lq wkh prgho1
4<1 Iruhfdvwv duh pdwkhpdwlfdoo| fruuhfw dqg zhljkwhg e| wkh suredelolw| wkh
sulfh txrwh zlo eh lq irufh dw wlph w1
531 Wr vroyh wkh rdwlqj udwh prgho/ uhdo prqh| edodqfhv phdvxuhg lq xqlwv
ri wkh qrqwudghg jrrg kdv wr eh lqwurgxfhg dv d vwdwh yduldeoh1
541 Zh dvvxph idvw sulfh dgmxvwphqw= @ 8 lq Wdeohv 6 dqg 71
551 Sd|lqj r wkh ghew pruh txlfno| uhvxowv lq kljkhu uhdo lqwhuhvw udwhv1
561 Wklv gudzedfn ri vwhulol}dwlrq lv hpskdvl}hg e| Vfkdgohu hw do1 +4<<6, dqg
Fdoyr/ Ohlghupdq dqg Uhlqkduw +4<<7,1
571 Lqwhuhvwlqjo|/ qxphurxv hpslulfdo hvwlpdwhv qg rvhw frh!flhqwv forvh wr
wkrvh lq Wdeoh 91 Vhh Djhqru dqg Prqwlho +4<<</ s1537,1
581 Qrwh wkdw lq wkh fdvh zkhuh @ =83 dqg @ =:8 uhvhuyh sxufkdvhv dw
w @ 3 duh juhdwhu wkdq lq d fudzolqj shj1 Wklv pdnhv dq rgg lpsuhvvlrq1
Vkrxogq*w d pdqdjhg rdw lqyroyh ohvv/ qrw pruh/ lqwhuyhqwlrq wkdq d
fudzolqj shjB Fhwhulv sdulexv/ wkh dqvzhu lv |hv1 Exw rwkhu wklqjv duh
qrw htxdo lq Wdeohv 5 dqg :1 Iru @ =83 dqg @ =:8/ lq dwlrq dqg wkh
udwh ri fxuuhqf| ghsuhfldwlrq " ghfuhdvh pruh lq wkh vkruw uxq zkhq wkh
jryhuqphqw rshudwhv d pdqdjhg rdw lqvwhdg ri d fudzolqj shj1 +" @ =3<6
dw w @ 31 Lq d fudzolqj shj/ " lv frqvwdqw dw wkh vwhdg|0vwdwh lq dwlrq udwh/
14641, Wklv ohdgv wr odujhu fdslwdo lq rzv dqg juhdwhu uhvhuyh dffxpxodwlrq
lq wkh vkruw uxq hyhq wkrxjk dssuhfldwlrq ri wkh qrplqdo h{fkdqjh udwh
ehduv vrph ri wkh exughq ri dgmxvwphqw1
591 Zh kdyh qrw suhvhqwhg uhvxowv iru d sxuh rdw dqg lqhuwldo lq dwlrq1 Wkh|
duh wrr dzixo wr frqwhpsodwh1
5:1 Iru d frxsoh ri uhdvrqv/ zh gr qrw frqvlghu wkh dvvxpswlrq wkdw dlg lv
shupdqhqw wr eh hvshfldoo| olplwlqj1 Iluvw/ hpslulfdo phdvxuhv ri dlg jhq0
hudoo| vkrz vwurqj shuvlvwhqfh lq Diulfdq frxqwulhv1 Hyhq diwhu uhprylqj d
olqhdu wuhqg/ iru h{dpsoh/ wkh yduldqfh ri yduldeohv olnh uhdo dlg shu fdslwd
ru wkh dlg0wr0JQS udwlr whqgv wr eh grplqdwhg e| orz0iuhtxhqf| frpsr0
qhqwv1 ^Wkxv zkloh Exolu dqg Dqqdq +5334, hpskdvl}h wkh yrodwlolw| ri dlg/
wkhlu dqdo|vlv dssolhv wr wkh vkruw0uxq f|foh l1h1/ wkh frpsrqhqw wkdw
5;
uhpdlqv diwhu xvlqj wkh Krgulfn0Suhvfrww owhu wr uhpryh d vorz0prylqj
qrqolqhdu wuhqg1 Wkh wuhqg lwvhoi vkrzv yhu| vxevwdqwldo shuvlvwhqfh/
hyhq zkhq dssolhg wr olqhduo| ghwuhqghg dlg vhulhv1` Vhfrqg/ lqwxwlwlrq
vxjjhvwv wkdw whpsrudu| dlg lq rzv zloo surgxfh uhvxowv txdolwdwlyho| vlp0
lodu wr exw txdqwlwdwlyho| zhdnhu wkdq lq wkh fdvh ri shupdqhqw dlg rzv1
+Wkh suhvhqw prgho dssolhv/ ri frxuvh/ li wkh jryhuqphqw frqyhuwv whpsr0
udu| dlg lqwr shupdqhqw dlg e| vshqglqj rqo| lwv dqqxlw| ydoxh1,
5;1 Wkhru| vxjjhvwv wkdw wkh furzglqj0lq hhfw rq sulydwh lqyhvwphqw frxog
eh txlwh vwurqj1 Vhh Ex!h +4<<8,1
5<1 Vlqfh wkh| zloo vkruwo| eh xvhg lq olqhdul}lqj +D44, dqg +D56,/ wkh vroxwlrqv
lq +D57, dqg +D58, duh hydoxdwhg dw wkh vwdwlrqdu| htxloleulxp1
631 Wkh vwhdg| vwdwh lv d vdggoh srlqw l
q4: q49 M@H ? 3>
ru
5
6
9M
:
v + . , 7 + . i , . +4 i M@I ,8 ? 3=
I
~}
?4
Wkh vhfrqg dqg wklug whupv lq wkh vwdelolw| frqglwlrq duh qhjdwlyh1 Wkh
uvw whup lv srvlwlyh/ krzhyhu/ ehfdxvh wkh ihhgedfn hhfwv ehwzhhq fkdqjhv
lq h{shqglwxuh/ wkh uhdo h{fkdqjh udwh/ dqg wkh uhdo lqwhuhvw sd|phqwv rq
wkh lqwhuqdo ghew duh pxwxdoo| uhlqiruflqj1 Wklv lv d qxlvdqfh/ qrw d vhulrxv
sureohp1 Lqvwdelolw| lv d wkuhdw rqo| li lv xqxvxdoo| vpdoo dqg yduldwlrqv
lq wkh uhdo h{fkdqjh udwh xquhdolvwlfdoo| odujh1 Hyhq lq wkh h{wuhph fdvh
zkhuh @ =;3 dqg uhdo lqwhuhvw sd|phqwv rq wkh lqwhuqdo ghew duh 43( ri
qdwlrqdo lqfrph/ A =43 hqvxuhv vwdelolw|1
5<
Uhihuhqfhv
Dgdp/ F1V1/4<<</ Ilqdqfldo Olehudol}dwlrq dqg Fxuuhqf| Ghpdqg lq ]dp0
eld1 Mrxuqdo ri Diulfdq Hfrqrplhv ; +6,/ 59;06391
Djhqru/ S1 dqg S1 Prqwlho/ 4<<</ Ghyhorsphqw Pdfurhfrqrplfv/ 5qg hgl0
wlrq +Sulqfhwrq/ Q1M1> Sulqfhwrq Xqlyhuvlw| Suhvv,1
Dvhd/ S1N1/ dqg F1P1 Uhlqkduw/ 4<<9/ Oh Sul{ gh o*Dujhqw= Krz +Qrw, wr
Ghdo zlwk Fdslwdo Lq rzv1 Mrxuqdo ri Diulfdq Hfrqrplhv 8+6,/ 56405:41
Edolqr/ W1/ D1 Ehqqhww/ dqg H1 Eruhqv}whlq/ 4<<</ Prqhwdu| Srolf| lq
Groodul}hg Hfrqrplhv1 LPI Rffdvlrqdo Sdshu/ Qr1 4:41
Ehuj/ D1/ 5338/ Kljk Dlg Lq rzv Fdvh Vwxg|= Jkdqd1 Plphr +Lqwhuqd0
wlrqdo Prqhwdu| Ixqg,1
Eklqgud/ Q1/ V1 Jul!wkv0Mrqhv/ Mrqdwkdq Ohdsh/ dqg Pdwwkhz Pduwlq/
4<<</ Sulydwh Fdslwdo Iorzv wr Diulfd= Shufhswlrq dqg Uhdolw|1 Wkh Kdjxh/
Irqgdg1
Eoxqghoo/ U1/ 4<;;/ Frqvxphu Ehkdylru= Wkhru| dqg Hylghqfh D Vxu0
yh|1 Hfrqrplf Mrxuqdo <;/ 490981
Eoxqghoo/ U1/ S1 Sdvkdughv/ dqg J1 Zhehu/ 4<<6/ Zkdw gr zh Ohduq derxw
Frqvxphu Ghpdqg Sdwwhuqv iurp Plfur GdwdB Dphulfdq Hfrqrplf Uh0
ylhz ;6/ 8:308<:1
Ex!h/ H1/ 4<<8/ Sxeolf Lqyhvwphqw/ Sulydwh Lqyhvwphqw/ dqg Lq dwlrq1
Mrxuqdo ri Hfrqrplf G|qdplfv dqg Frqwuro 4</ 45560457:1
Ex!h/ H1/ 5336/ Wljkw Prqh|/ Lqwhuhvw udwhv dqg Lq dwlrq lq Vxe0Vdkdudq
Diulfd1 LPI Vwd Sdshuv1
Ex!h/ H1/ F1 Dgdp/ V1 R*Frqqhoo/ dqg F1 Sdwwloor/ 5336/ H{fkdqjh
Udwh Srolf| dqg wkh Pdqdjhphqw ri R!fldo dqg Sulydwh Fdslwdo Iorzv
lq Diulfd1 Zrunlqj Sdshu +Lqwhuqdwlrqdo Prqhwdu| Ixqg,1
Exolu/D1 dqg D1M1 Dqqdq/ 5334/ Krz Yrodwloh dqg Xqsuhglfwdeoh duh
Dlg Iorzv dqg Zkdw duh wkh Srolf| LpsolfdwlrqvB LPI Zrunlqj Sdshu
34249:1
Fdyor/ J1/ 4<;6/ Vwdjjhuhg Sulfhv lq d Xwlolw|0Pd{lpl}lqj Iudphzrun1
Mrxuqdo ri Prqhwdu| Hfrqrplfv 45+6,/ <;60<<;1
Fdoyr/ J1/ 4<<4/ Wkh Shulov ri Vwhulol}dwlrq1 LPI Vwd Sdshuv 6;+7,/
<540591
Fdoyr/ J1 O1 Ohlghupdq/ dqg F1 Uhlqkduw/ 4<<7/ Wkh Fdslwdo Lq rzv
Sureohp= Frqfhswv dqg Lvvxhv1 Frqwhpsrudu| Hfrqrplf Srolf| 45/ 870
991
63
Fdoyr/ J1 dqg F1 Uhlqkduw/ 5333/ Ihdu ri Iordwlqj1 Txduwhuo| Mrxuqdo
ri Hfrqrplfv 44: +5,/ 6:<073;1
Fdoyr/ J1 dqg F1 Yhjk/ 4<<6/ H{fkdqjh0Udwh0Edvhg0Vwdelol}dwlrq xqghu
Lpshuihfw Fuhglelolw|1 Lq/ K1 Iulvfk dqg D1 Zrujrwwhu/ hgv1/ Rshq Hfrq0
rp| Pdfurhfrqrplfv +Qhz \run/ Vw1 Pduwlq*v Suhvv,1
Fdoyr/ J1 dqg F1 Yhjk/ 4<<7/ Vwdelol}dwlrq G|qdplfv dqg Edfnzdug0
Orrnlqj Frqwudfwv1 Mrxuqdo ri Ghyhorsphqw Hfrqrplfv/ 76/ 8<0;51
Froolhu/S1/ D1Krh"hu/ dqg F1Sdwwloor/ 5335/ Diulfd*v H{rgxv= Fdslwdo
Ioljkw dqg wkh Eudlq Gudlq dv Sruwirolr Ghflvlrqv1 Plphr1
Ghdwrq/ D1 dqg G1 Pxhooedxhu/ 4<;3/ Hfrqrplfv dqg Frqvxphu Ehkdylru
+Qhz \run/ Fdpeulgjh Xqlyhuvlw| Suhvv,1
Frpplvvlrq iru Diulfd/ 5338/ Rxu Frpprq Lqwhuhvw= Uhsruw ri wkh Frp0
plvvlrq iru Diulfd +zzz1frpplvvlrqiru diulfd1ruj,
Ihgghunh/ M0Z1 dqg Z1Olx/ 5335/ Prghoolqj wkh Ghwhuplqdqwv ri Fdslwdo
Iorzv dqg Fdslwdo Ioljkw= Zlwk dq Dssolfdwlrq wr Vrxwk Diulfdq Gdwd
iurp 4<9304<<81 Hfrqrplf Prghoolqj 4<+6,= 74<0771
Ihuqdqgh}0Duldv/ H1 dqg S1 Prqwlho/ 4<<9/ Wkh Vxujh lq Fdslwdo Lq rzv
lq Ghyhorslqj Frxqwulhv= Survshfwv dqg Srolf| Uhvsrqvh1 Zruog Edqn
Hfrqrplf Uhylhz 43/ 840::1
Ilhoglqj/ G1/ 4<<7/ Prqh| Ghpdqg lq Irxu Diulfdq Frxqwulhv1 Mrxuqdo
ri Hfrqrplf Vwxglhv 54/ 606:1
Jxswd/ V1/ Fohphqwv/ E1M1/ Edogdffl/ H1 dqg F1 Pxodv0Judqdgrv/ 5335/
H{shqglwxuh frpsrvlwlrq/ Ilvfdo Dgmxvwphqw dqg Jurzwk lq Orz0Lqfrph
Frxqwulhv1 LPI Zrunlqj Sdshu/ Qr1352::1
Jlrydqqlql/ D1 dqg E1 Wxuwoherrp/ 4<<7/ Fxuuhqf| Vxevwlwxwlrq1 Lq/
I1 ydq ghu Sorhj/ hg1/ Kdqgerrn ri Lqwhuqdwlrqdo Pdfurhfrqrplfv +Fdp0
eulgjh/ PD> Eodfnzhoo,1
Khog/ J1 dqg U1 V}dodfkpdq/ 4<<;/ H{whuqdo Fdslwdo Iorzv lq Odwlq
Dphulfd dqg wkh Fduleehdq lq wkh 4<<3v= H{shulhqfhv dqg Srolflhv1
FHSDO Uhylhz 97/ 5<07:1
Khqvwulgjh/Q1P1/ 4<<</ Gh0prqhwlvdwlrq/ Lq dwlrq dqg Frhh= wkh Gh0
pdqg iru Prqh| lq Xjdqgd1 Mrxuqdo ri Diulfdq Hfrqrplhv ;+6,/ 67806;8
Lqwhuqdwlrqdo Prqhwdu| Ixqg/ 5336/ Jkdqd= Vhohfwhg Lvvxhv1 LPI Frxq0
wu| Uhsruw/ Qr13624671
Lqwhuqdwlrqdo Prqhwdu| Ixqg/ 5337/ Jkdqd= Vhfrqg Uhylhz Xqghu wkh
Sryhuw| Uhgxfwlrq dqg Jurzwk Idflolw| dqg Uhtxhvw iru Zdlyhu ri Qrq0
revhuydqfh ri Shuirupdqfh Fulwhuld1 +Suhsduhg e| wkh Diulfdq Ghsduw0
phqw1,
64
Ndplq/ V1 dqg Q1 Hulfvvrq/ 4<<6/ Groodul}dwlrq lq Dujhqwlqd1 Lqwhu0
qdwlrqdo Ilqdqfh Glvfxvvlrq Sdshuv/ Qr1793 +Erdug ri Jryhuqruv ri wkh
Ihghudo Uhvhuyh V|vwhp,1
Nkdq/ P1 dqg F1 Uhlqkduw/ 4<<8/ Fdslwdo Iorzv lq wkh DSHF Uhjlrq1
LPI Rffdvlrqdo Sdshu/ Qr14551
Ohdsh/ M1/ 4<<</ Uhdolw|= Wkh Lpsdfw ri Fdslwdo Iorzv dqg Srolf| Uh0
vsrqvhv1 Lq/ Q1 Eklqgud hw do1/ Sulydwh Fdslwdo Iorzv wr Diulfd= Shufhs0
wlrq dqg Uhdolw| +Wkh Kdjxh/ Irqgdg,1
Ooxfk/ F1/ D1 Srzhoo/ dqg U1 Zlooldpv/ 4<::/ Sdwwhuqv lq Krxvhkrog Gh0
pdqg dqg Vdylqj +Orqgrq/ R{irug Xqlyhuvlw| Suhvv,1
Orsh}0Phmld/ D1/ 4<<</ Odujh Fdslwdo Iorzv= D Vxuyh| ri wkh Fdxvhv/
Frqvhtxhqfhv/ dqg Srolf| Uhvsrqvh1 LPI Zrunlqj Sdshu/ Qr1<<24:1
Pdutxh}/ M1/ 4<;:/ Prqh| Ghpdqg lq Rshq Hfrqrplhv1 Mrxuqdo ri
Lqwhuqdwlrqdo Prqh| dqg Ilqdqfh 9/ 49:04:;1
Qdfkhjd/ M0F1/ 5334/ Ilqdqfldo Olehudol}dwlrq/ Prqh| Ghpdqg dqg Lq0
dwlrq lq Xjdqgd1 LPI Zrunlqj Sdshu Qr1 34244;1
Qrydohv/ D1 hw do1/ 4<<</ Vroylqj Qrqolqhdu Udwlrqdo H{shfwdwlrqv Prghov
e| Hljhqydoxh0Hljhqyhfwru Ghfrpsrvlwlrqv1 Lq/ U1 Pdulprq dqg D1 Vfrww/
hgv1/ Frpsxwdwlrqdo Phwkrgv iru wkh Vwxg| ri G|qdplf Hfrqrplhv +Qhz
\run/ R{irug Xqlyhuvlw| Suhvv,1
Rjdnl/ P1/ M1 Rvwu|/ dqg F1 Uhlqkduw/ 4<<9/ Vdylqj Ehkdylru lq Orz0 dqg
Plggoh0Lqfrph Ghyhorslqj Frxqwulhv1 LPI Vwd Sdshuv 76/ 6;0:41
Rxdqhv/ D1/ R1 Q|dzdwd/ dqg P1 Mrqdvvhq/ 5334/ Xjdqgd= Lvvxhv lq
wkh Lpsohphqwdwlrq ri Prqhwdu| Srolf|1 Lqwhuqdwlrqdo Prqhwdu| Ixqg/
plphr +Prqhwdu| dqg H{fkdqjh Ddluv Ghsduwphqw,1
Udpluh}0Urmdv/ F1/ 4<;8/ Fxuuhqf| Vxevwlwxwlrq lq Dujhqwlqd/ Ph{lfr
dqg Xuxjxd|1 Lqwhuqdwlrqdo Prqhwdu| Ixqg Vwd Sdshuv 65/ 95<099:1
Vdydvwdqr/ P1/ 4<<9/ Groodul}dwlrq lq Odwlq Dphulfd= Uhfhqw Hylghqfh
dqg Srolf| Lvvxhv/ lq Wkh Pdfurhfrqrplfv ri Lqwhuqdwlrqdo Fxuuhqflhv/
hglwhg e| S1 Pl}hq dqg H1 Shqwhfrvw +Eurrnhog/ Yhuprqw> Hgzdug Hojdu,1
Vfkdgohu/ V1/ P1 Fdufrylf/ D1 Ehqqhw/ dqg U1 Ndkq / 4<<6/ Uhfhqw H{sh0
ulhqfhv zlwk Vxujhv lq Fdslwdo Lq rzv/ LPI Rffdvlrqdo Sdshu Qr1 43;1
Vyhqvvrq/ O1/ 5333/ Rshq0Hfrqrp| Lq dwlrq Wdujhwlqj1 Mrxuqdo ri Lq0
whuqdwlrqdo Hfrqrplfv 83/ 48804;61
\rxqjhu/ V1/ 4<<5/ Dlg dqg wkh Gxwfk Glvhdvh= Pdfurhfrqrplf Pdqdjh0
phqw Zkhq Hyhu|erg| Oryhv \rx1 Zruog Ghyhorsphqw 53/ 48;:048<:1
65
Table 1: Transition paths under pure float and crawling peg
-0.3%
-0.2%
-0.1%
-0.1%
0.0%
0.0%
0.0%
14.3%
13.9%
13.6%
13.5%
13.4%
13.3%
13.1%
15.2%
15.0%
14.8%
14.8%
14.7%
14.7%
14.6%
3.2%
17.3%
4.8%
19.8%
9.6%
8.9%
8.6%
8.3%
8.2%
8.1%
8.0%
9.4%
8.8%
8.5%
8.3%
8.2%
8.1%
8.0%
0.87
0.88
0.88
0.89
0.89
0.89
0.89
0.94
0.92
0.91
0.90
0.90
0.90
0.89
0.91
0.90
0.90
0.90
0.89
0.89
0.89
0.3%
0.2%
0.1%
0.1%
0.1%
0.0%
0.0%
-0.5%
-0.3%
-0.2%
-0.1%
-0.1%
-0.1%
0.0%
1.3%
0.9%
0.6%
0.4%
0.3%
0.2%
0.0%
0.6%
0.4%
0.2%
0.1%
0.1%
0.1%
0.0%
CA
7.3%
19.1%
7.4%
7.6%
7.7%
7.8%
7.9%
7.9%
8.0%
0.90
0.90
0.89
0.89
0.89
0.89
0.89
-1.2%
-0.7%
-0.5%
-0.3%
-0.2%
-0.1%
0.0%
RER
5.5%
16.1%
8.3%
8.2%
8.1%
8.1%
8.0%
8.0%
8.0%
0.85
0.86
0.87
0.88
0.88
0.89
0.89
r
9.0%
19.0%
7.0%
7.2%
7.4%
7.6%
7.7%
7.8%
8.0%
[1]
Panel B: Crawling Peg
0.88
0.88
0.89
0.89
0.89
0.89
0.89
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
12.0%
12.2%
12.3%
12.3%
12.4%
12.4%
12.5%
Panel A: Pure Float
7.6%
7.7%
7.8%
7.9%
7.9%
7.9%
8.0%
0.89
0.89
0.89
0.89
0.89
0.89
0.89
-2.3%
-1.5%
-1.0%
-0.7%
-0.4%
-0.3%
0.0%
10.8%
10.7%
10.6%
10.6%
10.6%
10.6%
10.5%
3.00
Inflation
tau
14.0%
14.2%
14.4%
14.5%
14.5%
14.5%
14.6%
8.0%
8.0%
8.0%
8.0%
8.0%
8.0%
8.0%
0.81
0.83
0.85
0.87
0.87
0.88
0.89
-2.4%
-1.6%
-1.1%
-0.7%
-0.5%
-0.3%
0.0%
10.2%
10.6%
10.9%
11.1%
11.2%
11.3%
11.4%
CA
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
13.1%
13.1%
13.1%
31.3%
13.1%
13.1%
13.1%
6.4%
6.6%
6.9%
7.1%
7.4%
7.6%
8.0%
0.80
0.83
0.85
0.86
0.87
0.88
0.89
-3.7%
-2.4%
-1.6%
-1.0%
-0.7%
-0.4%
0.0%
RER
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
7.9%
9.3%
10.3%
11.0%
11.5%
11.8%
12.5%
7.5%
7.4%
7.5%
7.6%
7.7%
7.8%
8.0%
0.76
0.80
0.83
0.85
0.87
0.87
0.89
r
sigma
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
8.3%
9.2%
9.7%
10.0%
10.2%
10.3%
10.5%
6.9%
6.6%
6.6%
6.8%
7.1%
7.4%
8.0%
Inflation
0.75
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
4.1%
6.4%
8.1%
9.3%
10.0%
10.5%
11.4%
2.00
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
Notes: sigma and tau denote the elasticity of substitution between domestic and foreign currency and of intertemporal substitution respectively.
Inflation is the rate of inflation; r the real interest rate; RER the real exchange rate and CA the current account balance.
[1] The numbers in parentheses in cells for t=0 and t=1 are, respectively, the percentage increase in the price level at t=0 and the
inflation rate in the first year inclusive of the initial price level jump.
Table 2: Transition paths under pure float and crawling peg when nontradable prices are sticky
1.1%
0.7%
0.4%
0.2%
0.1%
0.1%
0.0%
3.3%
1.1%
0.4%
0.2%
0.1%
0.1%
0.0%
3.6%
1.3%
0.5%
0.2%
0.1%
0.1%
0.0%
Panel B: Crawling Peg
1.00
0.94
0.91
0.90
0.90
0.89
0.89
1.3%
0.9%
0.6%
0.4%
0.3%
0.2%
0.0%
5.3%
1.8%
0.6%
0.2%
0.1%
0.0%
0.0%
Panel A: Pure Float
4.3%
7.1%
7.9%
8.1%
9.1%
8.1%
8.0%
1.00
0.94
0.92
0.91
0.90
0.90
0.89
0.3%
0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
5.1%
1.5%
0.5%
0.2%
0.1%
0.0%
0.0%
3.00
Qn
19.0%
16.5%
15.5%
15.0%
14.8%
14.7%
14.6%
6.4%
8.2%
8.5%
8.4%
8.3%
8.2%
8.0%
1.00
0.92
0.90
0.89
0.89
0.89
0.89
0.4%
0.4%
0.3%
0.2%
0.1%
0.1%
0.0%
6.5%
2.1%
0.7%
0.2%
0.1%
0.0%
0.0%
CA
-2.5%
-0.7%
-0.2%
-0.1%
0.0%
0.0%
0.0%
17.1%
14.8%
14.0%
13.6%
13.4%
13.3%
13.1%
0.2%
5.0%
6.9%
7.6%
7.8%
7.9%
8.0%
1.00
0.93
0.91
0.90
0.90
0.89
0.89
-0.2%
-0.3%
-0.2%
-0.2%
-0.1%
0.0%
0.0%
RER
-0.5%
-0.2%
-0.1%
-0.1%
0.0%
0.0%
0.0%
-5.5%
-1.6%
-0.4%
-0.1%
0.0%
0.0%
0.0%
18.3%
14.6%
13.2%
12.7%
12.5%
12.5%
12.5%
2.7%
6.6%
7.7%
8.0%
8.1%
8.1%
8.0%
1.00
0.92
0.89
0.89
0.89
0.89
0.89
r
0.83
0.87
0.88
0.89
0.89
0.89
0.89
0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
-4.5%
-1.7%
-0.8%
-0.4%
-0.2%
-0.1%
0.0%
15.8%
12.4%
11.3%
10.9%
10.7%
10.6%
10.5%
-1.5%
4.1%
6.4%
7.3%
7.7%
7.8%
8.0%
Inflation
14.3%
9.3%
8.3%
8.0%
8.0%
8.0%
8.0%
0.80
0.86
0.88
0.89
0.89
0.89
0.89
-2.5%
-1.6%
-1.0%
-0.7%
-0.4%
-0.3%
0.0%
-8.7%
-3.0%
-1.1%
-0.4%
-0.2%
-0.1%
0.0%
18.1%
13.6%
12.0%
11.5%
11.4%
11.3%
11.4%
Qn
tau
14.4%
14.3%
14.5%
14.5%
14.6%
14.6%
14.6%
18.0%
10.4%
8.6%
8.2%
8.0%
8.0%
8.0%
0.73
0.80
0.84
0.86
0.87
0.88
0.89
-2.1%
-1.6%
-1.1%
-0.7%
-0.5%
-0.3%
0.0%
-5.4%
-2.3%
-1.1%
-0.6%
-0.4%
-0.2%
0.0%
CA
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
9.5%
12.0%
12.8%
13.1%
13.1%
13.1%
13.1%
19.7%
10.1%
8.1%
7.7%
7.6%
7.7%
8.0%
0.68
0.78
0.83
0.86
0.87
0.88
0.89
-3.9%
-2.5%
-1.6%
-1.0%
-0.6%
-0.4%
0.0%
RER
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
7.5%
9.2%
10.5%
11.2%
11.6%
11.9%
12.5%
26.1%
11.9%
8.7%
8.0%
7.8%
7.8%
8.0%
0.67
0.76
0.81
0.84
0.86
0.87
0.89
r
sigma
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
0.6%
6.7%
9.0%
9.8%
10.1%
10.3%
10.5%
23.6%
11.1%
8.3%
7.6%
7.5%
7.6%
8.0%
Inflation
0.75
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
3.0%
6.1%
8.3%
9.5%
10.2%
10.6%
11.4%
2.00
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
Notes: see Table 1. Qn is the suppy of non-tradables.
Table 3: Transition path under crawling peg with temporary sterilization [1]
sigma
tau
Inflation
r
RER
CA
[2]
0.75
0.25
0.35
0.50
2.00
0.25
0.35
0.50
3.00
0.25
0.35
t=0
t=1
t=2
Long Run
18.1%
16.6%
15.7%
14.6%
1.5%
18.8%
t=0
t=1
t=2
Long Run
17.8%
16.2%
15.3%
14.1%
0.8%
17.7%
t=0
t=1
t=2
Long Run
16.9%
15.4%
14.5%
13.1%
0.0%
t=0
t=1
t=2
Long Run
14.5%
13.6%
13.1%
12.5%
4.2%
18.1%
t=0
t=1
t=2
Long Run
14.1%
13.1%
12.5%
11.7%
3.4%
16.9%
t=0
t=1
t=2
Long Run
13.4%
12.2%
11.5%
10.5%
2.1%
14.9%
t=0
t=1
t=2
Long Run
13.0%
12.2%
11.8%
11.4%
5.6%
18.0%
t=0
t=1
t=2
Long Run
12.7%
11.7%
11.2%
10.6%
4.7%
16.8%
F
[3]
[4]
Offset
[5]
42.7%
17.1%
11.3%
8.0%
0.97
0.92
0.89
0.89
2.2%
0.8%
0.1%
0.0%
0.066
0.095
0.116
0.143
0.126
0.132
0.136
0.143
0.75
29.0%
14.5%
10.6%
8.0%
0.99
0.93
0.90
0.89
2.6%
1.1%
0.3%
0.0%
0.069
0.097
0.118
0.146
0.124
0.132
0.137
0.146
0.69
21.0%
12.7%
10.0%
8.0%
1.00
0.94
0.91
0.89
2.9%
1.4%
0.6%
0.0%
0.071
0.100
0.120
0.151
0.121
0.131
0.138
0.151
0.64
23.5%
12.6%
9.7%
8.0%
0.92
0.90
0.88
0.89
0.9%
0.1%
-0.3%
0.0%
0.028
0.048
0.065
0.125
0.102
0.096
0.092
0.125
0.93
19.7%
11.9%
9.6%
8.0%
0.94
0.90
0.89
0.89
1.3%
0.4%
-0.1%
0.0%
0.029
0.048
0.064
0.084
0.091
0.089
0.087
0.084
0.77
17.3%
11.4%
9.4%
8.0%
0.96
0.92
0.89
0.89
1.8%
0.8%
0.1%
0.0%
0.029
0.046
0.061
0.083
0.077
0.079
0.080
0.083
0.60
18.2%
10.9%
9.0%
8.0%
0.90
0.88
0.87
0.89
0.3%
-0.3%
-0.6%
0.0%
0.013
0.027
0.039
0.049
0.088
0.074
0.064
0.049
0.94
16.7%
10.8%
9.0%
8.0%
0.91
0.89
0.87
0.89
0.7%
-0.1%
-0.4%
0.0%
0.013
0.025
0.035
0.047
0.072
0.063
0.057
0.047
0.76
Notes: See Table 1.
[1] Bond sales at t=0 are equivalent to 7.8% of GDP.
[2] The numbers in parentheses in cells for t=0 and t=1 are, respectively, the percentage increase in the price level at t=0
and the inflation rate in the first year inclusive of the initial price level jump.
[3] F denotes the (private) stock of foreign currency (as a percentage of GDP) where F0=0.15.
[4] The number in parenthesis is the value of F when there is no temporary sterilization.
[5] The offset coefficient is calculated as [F(0)ns-F(0)]/[b(0)-b0] where F(0) and F(0)ns are the post-jump values of
foreign currency holdings at t=0 with and without sterilization.
Table 4: Transition paths under a managed float
sigma
0.75
tau
0.25
0.50
2.00
0.25
0.50
3.00
0.25
Inflation
r
RER
CA
Z
[1]
[2]
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
13.3%
13.9%
14.2%
14.4%
14.5%
14.5%
14.6%
8.6%
3.0%
8.2%
8.1%
8.0%
8.0%
8.0%
0.90
0.89
0.89
0.89
0.89
0.89
0.89
0.2%
0.1%
0.1%
0.0%
0.0%
0.0%
0.0%
0.068
0.065
0.063
0.062
0.061
0.061
0.061
0.074
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
10.5%
11.8%
12.4%
12.7%
12.9%
13.0%
13.1%
10.0%
8.9%
8.5%
8.3%
8.1%
8.1%
8.0%
0.93
0.91
0.90
0.90
0.89
0.89
0.89
1.1%
0.6%
0.4%
0.2%
0.1%
0.1%
0.0%
0.084
0.079
0.076
0.074
0.073
0.072
0.071
0.080
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
7.1%
7.3%
7.5%
7.6%
7.7%
7.8%
8.0%
0.86
0.87
0.88
0.88
0.88
0.89
0.89
-0.9%
-0.6%
-0.4%
-0.2%
-0.2%
-0.1%
0.0%
0.078
0.082
0.085
0.087
0.088
0.089
0.091
0.098
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
11.3%
10.9%
10.7%
10.6%
10.6%
10.6%
10.5%
7.9%
7.9%
8.0%
8.0%
8.0%
8.0%
8.0%
0.89
0.89
0.89
0.89
0.89
0.89
0.89
-0.1%
-0.1%
0.0%
0.0%
0.0%
0.0%
0.0%
0.107
0.111
0.113
0.114
0.114
0.115
0.115
0.123
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
10.5%
10.9%
11.1%
11.2%
11.3%
11.3%
11.4%
7.1%
7.1%
7.2%
7.4%
7.6%
7.7%
8.0%
0.83
0.85
0.87
0.87
0.88
0.88
0.89
-1.7%
-1.1%
-0.7%
-0.4%
-0.3%
-0.1%
0.0%
0.086
0.094
0.100
0.103
0.105
0.106
0.109
0.113
Notes: See Table 1.
[1] Z denotes official reserves, where Z0 = 0.05
[2] Corresponding level of reserves at t=0 and t=Long Run under crawling peg.
0.071
0.083
0.102
0.124
0.122
0.25
tau
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
13.2%
13.2%
13.0%
12.9%
12.7%
12.6%
13.1%
14.1%
14.3%
14.3%
14.2%
14.1%
14.0%
14.6%
12.8%
8.8%
8.0%
7.8%
7.8%
7.9%
8.0%
0.82
0.87
0.88
0.88
0.88
0.88
0.89
0.85
0.87
0.88
0.88
0.88
0.88
0.89
-5.3%
-3.5%
-2.3%
-1.5%
-1.0%
-0.6%
0.0%
-2.9%
-1.9%
-1.2%
-0.8%
-0.5%
-0.3%
0.0%
-3.3%
-2.1%
-1.3%
-0.8%
-0.5%
-0.4%
0.0%
CA
-7.5%
-2.5%
-0.8%
-0.3%
-0.1%
-0.1%
0.0%
-3.4%
-1.2%
-0.4%
-0.2%
-0.1%
-0.1%
0.0%
-3.9%
-0.9%
-0.1%
0.1%
0.1%
0.1%
0.0%
-1.0%
0.0%
0.2%
0.2%
0.1%
0.1%
0.0%
Qn
Panel B: Pure Float and Sticky Prices
17.8%
15.9%
15.0%
14.5%
14.2%
14.0%
14.6%
16.1%
9.9%
8.4%
8.1%
8.0%
8.0%
8.0%
0.74
0.80
0.83
0.85
0.86
0.87
0.89
-5.1%
-3.5%
-2.3%
-1.5%
-1.0%
-0.7%
0.0%
-4.5%
-1.9%
-0.9%
-0.5%
-0.3%
-0.2%
0.0%
RER
-1.6%
-0.7%
-0.2%
0.0%
0.1%
0.1%
0.0%
12.7%
13.2%
13.1%
12.9%
12.6%
12.5%
13.1%
18.3%
9.6%
7.8%
7.5%
7.5%
7.6%
8.0%
0.68
0.78
0.82
0.85
0.86
0.87
0.89
-6.7%
-4.4%
-2.8%
-1.8%
-1.2%
-0.7%
0.0%
r
0.94
0.93
0.92
0.91
0.90
0.89
0.89
-0.8%
-0.1%
0.2%
0.3%
0.3%
0.3%
0.0%
10.2%
10.3%
10.7%
11.0%
11.1%
11.3%
12.5%
24.4%
11.4%
8.6%
7.9%
7.8%
7.8%
8.0%
0.67
0.76
0.81
0.83
0.85
0.86
0.89
Inflation
3.4%
17.5%
8.9%
9.4%
9.3%
9.1%
8.8%
8.6%
8.0%
0.97
0.95
0.93
0.92
0.91
0.90
0.89
-2.7%
-1.4%
-0.7%
-0.3%
-0.1%
0.0%
0.0%
2.9%
7.4%
9.0%
9.5%
9.6%
9.6%
10.5%
22.2%
10.6%
8.1%
7.5%
7.4%
7.5%
8.0%
CA
1.7%
14.9%
9.4%
9.3%
9.0%
8.8%
8.6%
8.4%
8.0%
0.89
0.90
0.90
0.90
0.89
0.89
0.89
-1.9%
-0.8%
-0.3%
0.0%
0.1%
0.1%
0.0%
5.3%
7.1%
8.5%
9.3%
9.8%
10.1%
11.4%
RER
6.0%
17.0%
7.1%
7.8%
8.2%
8.4%
8.4%
8.4%
8.0%
0.93
0.92
0.91
0.91
0.90
0.89
0.89
-3.4%
-1.8%
-0.9%
-0.4%
-0.2%
-0.1%
0.0%
[1]
4.0%
139.0%
8.1%
8.4%
8.4%
8.5%
8.4%
8.3%
8.0%
0.87
0.88
0.89
0.89
0.89
0.89
0.89
r
Table A1: Transition paths under pure float and crawling peg when aid is increased gradually
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
10.9%
11.5%
11.7%
11.8%
11.8%
11.8%
12.5%
7.6%
17.0%
6.9%
7.2%
7.7%
8.1%
8.2%
8.2%
8.0%
Panel A: Crawling Peg
sigma
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
9.8%
10.1%
10.1%
10.1%
10.0%
10.0%
10.5%
3.00
Inflation
0.75
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
9.1%
10.0%
10.5%
10.6%
10.7%
10.7%
11.4%
2.00
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
Notes: see Tables 1 and 2.
Table A2: Transition paths under crawling peg and managed float when sticky prices stem from inertial inflation
0.9%
0.7%
0.3%
0.2%
0.1%
0.0%
0.0%
0.0%
-1.8%
-1.0%
-0.5%
-0.3%
-0.2%
0.0%
0.0%
-1.5%
-0.8%
-0.4%
-0.2%
-0.1%
0.0%
Panel B: Pure Float and Sticky Prices
0.92
0.89
0.89
0.89
0.89
0.89
0.89
1.0%
0.8%
0.4%
0.2%
0.1%
0.1%
0.0%
0.0%
-1.7%
-1.0%
-0.5%
-0.3%
-0.2%
0.0%
Panel A: Crawling Peg
-2.4%
6.5%
6.6%
6.8%
7.0%
7.2%
8.0%
0.93
0.89
0.89
0.89
0.89
0.89
0.89
1.0%
0.7%
0.3%
0.2%
0.1%
0.0%
0.0%
0.0%
-2.0%
-1.2%
-0.7%
-0.4%
-0.3%
0.0%
3.00
Qn
16.9%
17.3%
16.3%
15.7%
15.3%
15.1%
14.6%
0.0%
7.0%
7.2%
7.4%
7.5%
7.6%
8.0%
0.93
0.89
0.89
0.89
0.89
0.89
0.89
1.0%
0.8%
0.4%
0.2%
0.1%
0.1%
0.0%
0.0%
-1.8%
-1.0%
-0.6%
-0.4%
-0.2%
0.0%
CA
2.8%
-1.5%
-2.1%
-1.3%
-0.3%
0.2%
0.0%
16.9%
16.3%
15.0%
14.3%
13.9%
13.7%
13.1%
-4.6%
6.1%
6.0%
6.1%
6.2%
6.4%
8.0%
0.93
0.88
0.89
0.89
0.89
0.89
0.89
0.9%
0.7%
0.3%
0.2%
0.1%
0.0%
0.0%
RER
1.5%
0.6%
0.1%
0.0%
0.0%
0.1%
0.0%
2.9%
-2.2%
-2.2%
-0.9%
-0.1%
0.1%
0.0%
16.8%
16.7%
15.2%
14.4%
13.9%
13.6%
12.5%
-2.0%
6.0%
6.4%
6.5%
6.8%
7.0%
8.0%
0.92
0.88
0.88
0.89
0.89
0.89
0.89
r
1.00
0.88
0.86
0.87
0.89
0.90
0.89
1.5%
1.0%
0.6%
0.3%
0.2%
0.1%
0.0%
4.4%
-2.0%
-2.8%
-1.6%
-0.3%
-0.4%
0.0%
17.6%
15.5%
13.8%
12.8%
12.2%
11.8%
10.5%
-5.3%
5.5%
5.6%
5.7%
5.9%
6.2%
8.0%
Inflation
-0.3%
6.7%
10.2%
10.5%
9.4%
8.4%
8.0%
1.00
0.89
0.87
0.89
0.90
0.90
0.89
0.8%
-0.1%
-0.4%
-0.3%
-0.1%
0.0%
0.0%
4.6%
-2.9%
-2.9%
-1.2%
0.0%
0.3%
0.0%
16.7%
16.1%
14.5%
13.6%
13.0%
12.6%
11.4%
Qn
tau
23.3%
18.2%
14.8%
13.5%
13.8%
14.3%
14.6%
0.7%
7.9%
10.2%
9.8%
8.8%
8.2%
8.0%
1.00
0.85
0.83
0.85
0.88
0.90
0.89
0.7%
0.5%
0.2%
0.1%
0.0%
0.0%
0.0%
5.4%
-2.2%
-3.2%
-1.8%
-0.3%
0.5%
0.0%
CA
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
22.3%
15.9%
12.7%
12.3%
12.8%
13.2%
13.1%
-5.7%
3.7%
9.5%
10.7%
9.6%
8.3%
8.0%
1.00
0.86
0.85
0.87
0.89
0.90
0.89
0.3%
-0.4%
-0.6%
-0.5%
-0.2%
-0.1%
0.0%
RER
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
24.2%
17.0%
12.1%
10.5%
11.0%
12.0%
12.5%
-5.1%
6.0%
10.0%
9.9%
8.8%
8.0%
8.0%
1.00
0.84
0.81
0.84
0.88
0.90
0.89
r
sigma
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
23.5%
13.9%
9.5%
9.0%
9.8%
10.5%
10.5%
-8.4%
2.3%
9.2%
10.8%
9.6%
8.2%
8.0%
Inflation
0.75
0.50
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
24.9%
16.5%
10.9%
9.0%
9.6%
10.8%
11.4%
2.00
0.25
t=0
t=1
t=2
t=3
t=4
t=5
Long Run
Notes: see Tables 1 and 2.
© Copyright 2026 Paperzz