NOTES D’ÉTUDES ET DE RECHERCHE - Publications · / phqw | sor p h q r hv glwl l j l u w h pdun xu r ode i r hv f qvhtxhq fr h k w w h \1 n u r z dph piu oleulx rxwsxwdqglq

$Page 1: NOTES D’ÉTUDES ET DE RECHERCHE - Publications · / phqw | sor p h q r hv glwl l j l u w h pdun xu r ode i r hv f qvhtxhq fr h k w w h \1 n u r z dph piu oleulx rxwsxwdqglq$
NOTES D’ÉTUDES

ET DE RECHERCHE

DIRECTION GÉNÉRALE DES ÉTUDES ET DES RELATIONS INTERNATIONALES

INCORPORATING LABOUR MARKET FRICTIONS

INTO AN OPTIMISING-BASED MONETARY

POLICY MODEL

Stéphane Moyen and Jean-Guillaume Sahuc

January 2004

NER # 105

DIRECTION GÉNÉRALE DES ÉTUDES ET DES RELATIONS INTERNATIONALESDIRECTION DES ÉTUDES ÉCONOMIQUES ET DE LA RECHERCHE

INCORPORATING LABOUR MARKET FRICTIONS

INTO AN OPTIMISING-BASED MONETARY

POLICY MODEL

Stéphane Moyen and Jean-Guillaume Sahuc

January 2004

NER # 105

Les Notes d'Études et de Recherche reflètent les idées personnelles de leurs auteurs et n'expriment pasnécessairement la position de la Banque de France. Ce document est disponible sur le site internet de laBanque de France «www.banque-France.fr».

The Working Paper Series reflect the opinions of the authors and do not necessarily express the views ofthe Banque de France. This document is available on the Banque de France Website “www.banque-France.fr”.

Lqfrusrudwlqj Oderxu Pdunhw Iulfwlrqv lqwr dq

Rswlplvlqj0Edvhg Prqhwdu| Srolf| Prgho�

Vwìskdqh Pr|hq @ dqg Mhdq0Jxloodxph Vdkxf @cKc_

@ HSHH/ Xqlyhuvlw| ri Hyu|0Ydo g*Hvvrqqh/ 7 eg Iudqêrlv Plwwhuudqg/ <4358 Hyu|/ IudqfhK Edqtxh gh Iudqfh/ Uhvhdufk Xqlw/ 64 uxh Furl{ ghv Shwlwv Fkdpsv/ :837< Sdulv/ Iudqfh

Mdqxdu| 5337+Iluvw gudiw= Rfwrehu 5335,

WZh zrxog olnh wr wkdqn Ihukdw Plkrxel dqg Mxolhq Pdwkhurq iru lqydoxdeoh vxssruw/ dqg Khuyì

Oh Elkdq/ Gdylg Pd|hv/ \yhv Vdnhv/ dqg sduwlflsdqwv dw vhplqduv dw wkh Xqlyhuvlw| ri Hyu|/ Edqtxh

gh Iudqfh/ DIVH Dqqxdo Frqjuhvv 5336/ HHD Dqqxdo Frqjuhvv 5336/ ODFHD Dqqxdo Phhwlqj 5336

iru khosixo frpphqwv dqg vxjjhvwlrqv1 Wklv sdshu uhsuhvhqwv wkh ylhzv ri wkh dxwkruv dqg vkrxog

qrw eh lqwhusuhwhg dv uh hfwlqj wkrvh ri wkh Edqtxh gh Iudqfh1 Dq| huuruv duh rxu rzq1_Fruuhvsrqglqj dxwkru1 H0pdlo dgguhvv= mhdq0jxloodxph1vdkxfCedqtxh0iudqfh1iu

4

Uìvxpì =

Fh sdslhu hvw frqvdfuì ã od phvxuh ghv h�hwv gh o*lqwurgxfwlrq g*xq pdufkì gx

wudydlo qrq Zdoudvlhq gdqv xq prgëoh pdfurìfrqrpltxh ã dqwlflsdwlrqv udwlrqqhoohv

uhsuìvhqwdqw od }rqh hxur1 Fhwwh sureoìpdwltxh v*lqvfulw gdqv ohv suìrffxsdwlrqv

uìfhqwhv gh od Edqtxh Fhqwudoh Hxursìhqqh txl fkhufkh ã dssuìkhqghu wrxwhv ohv

fdudfwìulvwltxhv gh od }rqh1 Gh fh idlw/ oh fdguh g*dqdo|vh ruljlqdo uhwhqx shuphw

g*ìwxglhu o*lpsruwdqfh uhodwlyh ghv uljlglwìv olìhv dx pdufkì ghv elhqv hw dx pdufkì

gx wudydlo vxlwh ã ghv fkrfv gh srolwltxh prqìwdluh/ whfkqrorjltxhv hw gh gìshqvhv

sxeoltxhv1 Ohv frqfoxvlrqv pdutxdqwhv gh fhwwh ìwxgh vrqw = +l, srxu uhqguh frpswh

ghv ìyroxwlrqv ìfrqrpltxhv/ ohv uljlglwìv uìhoohv vrqw xq frpsoìphqw qìfhvvdluh dx{

uljlglwìv qrplqdohv pdlv qh ohv uhpsodfhqw sdv > +ll, od g|qdpltxh ghv frxuehv gh

Skloolsv hw gh Ehyhulgjh hvw elhq uhsurgxlwh sdu oh prgëoh > +lll, ohv khxuhv wudydlooìhv

vrqw xqh yduldeoh g*dmxvwhphqw fuxfldoh > hw +ly, od g|qdpltxh ghv vdodluhv uìhov uhvwh

surf|foltxh1

Prwv0foìv = Prgëohv g*ìtxloleuh jìqìudo lqwhuwhpsruhov vwrfkdvwltxhv/ uljlglwìv

qrplqdohv/ uljlglwìv uìhoohv/ dssdulhphqw vxu oh pdufkì gx wudydlo/ shuvlvwdqfh hq0

grjëqh/ }rqh hxur1

Devwudfw=

Wklv sdshu h{dplqhv wkh h�hfwv ri lqwurgxflqj d qrq Zdoudvldq oderxu pdunhw lqwr

wkh �Qhz Qhrfodvvlfdo V|qwkhvlv� iudphzrun1 D g|qdplf vwrfkdvwlf jhqhudo htxlole0

ulxp prgho lv irupxodwhg/ vroyhg/ dqg fdoleudwhg lq rughu wr hydoxdwh lwv delolw| wr

uhsolfdwh wkh pdlq ihdwxuhv ri wkh Hxur duhd hfrqrp|1 Wklv iudphzrun doorzv xv wr

vwxg| wkh h�hfwv ri oderxu pdunhw uljlglwlhv/ qrplqdo uljlglwlhv/ dqg rwkhu iulfwlrqv wr

jlyh dffrxqw ri wkh lpsdfw ri prqhwdu| srolf|/ whfkqrorj|/ sxeolf vshqglqj/ dqg suhi0

huhqfh vkrfnv1 Rxu vlpxodwlrqv vkrz wkdw= +l, uhdo uljlglwlhv frpsohphqw exw gr qrw

vxssodqw qrplqdo uljlglwlhv/ +ll, wkh Ehyhulgjh dqg Skloolsv uhodwlrqv duh uhsurgxfhg/

+lll, krxuv zrunhg duh wrr vhqvlwlyh dq dgmxvwphqw yduldeoh/ dqg +ly, wkh uhdo zdjh

g|qdplfv lv vwloo surf|folfdo1

Nh|zrugv= GVJH prghov/ qrplqdo uljlglwlhv/ uhdo uljlglwlhv/ oderxu pdunhw

vhdufk/ hqgrjhqrxv shuvlvwhqfh/ hxur duhd1

MHO fodvvl�fdwlrq= H65/ F85/ H571

5

Uìvxpì qrq whfkqltxh =

Txhov vrqw ohv h�hwv gh od suìvhqfh gh iulfwlrqv gx pdufkì gx wudydlo vxu od g|0

qdpltxh gh o*ìfrqrplh hw od sursdjdwlrq ghv fkrfv B Elhq txh fhwwh txhvwlrq vrlw

fhqwudoh srxu od pdfurìfrqrplh hw od srolwltxh ìfrqrpltxh/ shx g*ìwxghv rqw fkhufkì

ã | uìsrqguh gdqv xq fdguh g*ìtxloleuh jìqìudo1 Srxuwdqw/ ohv frqvìtxhqfhv gh whoohv

iulfwlrqv vxu o*hpsorl/ od surgxfwlrq hw o*lq dwlrq shxyhqw íwuh frqvlgìuìhv frpph xq

sureoëph qrq qìjoljhdeoh srxu oh edqtxlhu fhqwudo hq udlvrq gh vhv lpsolfdwlrqv vxu

od wudqvplvvlrq gh od srolwltxh prqìwdluh1

Hq h�hw/ frpph o*h{soltxh xqh ìwxgh uìfhqwh gh od Edqtxh Fhqwudoh Hxursìhqqh

+EFH/ 5335,/ lo | d frh{lvwhqfh g*xq iruw wdx{ gh fk÷pdjh dx vhlq gh od }rqh hxur

+;/9 (, hw g*xq idleoh wdx{ gh sduwlflsdwlrq +9;/9 (,1 Fhod vljql�h txh ohv shu0

irupdqfhv gx pdufkì gx wudydlo hxursìhq vrqw pdxydlvhv1 Od frpsuìkhqvlrq gx

surfhvvxv g*dssdulhphqw hqwuh r�uh hw ghpdqgh gh wudydlo dssdudñw dlqvl frpph xqh

qìfhvvlwì srxu od sulvh gh gìflvlrq gh srolwltxh prqìwdluh = xq ìwudqjohphqw vxu oh

pdufkì gx wudydlo shxw fuìhu ghv suhvvlrqv lq dwlrqqlvwhv > gh wurs judqghv gl�ìuhqfhv

gh irqfwlrqqhphqw ghv pdufkìv gx wudydlo hqwuh ohv sd|v phpeuhv gh od }rqh shxyhqw

fuìhu ghv h�hwv dv|pìwultxhv vxlwh ã xq fkrf qrq dqwlflsì1

Dlqvl/ prlqv gh iulfwlrqv vxu oh pdufkì gx wudydlo gh od }rqh hxur ghyudlw hqwudñqhu

xqh uìgxfwlrq ghv h�hwv gh frxuw whuph gh od srolwltxh prqìwdluh vxu o*ìfrqrplh uìhooh1

O*remhfwli gh fhwwh ìwxgh hvw grqf gh suhqguh hq frpswh fhv uljlglwìv dx vhlq g*xq

prgëoh pdfurìfrqrpltxh hw g*hq ìwxglhu ohv h�hwv vxu od g|qdpltxh gh o*ìfrqrplh1

Srxu fhod/ qrxv frqvwuxlvrqv xq prgëoh ã dqwlflsdwlrqv udwlrqqhoohv surfkh gh fhoxl

suìvhqwì sdu od EFH +Vphwv hw Zrxwhuv/ 5336,1

O*ruljlqdolwì gh fhwwh ìwxgh hvw o*lqwurgxfwlrq g*xq pdufkì gx wudydlo qrq Zdo0

udvlhq sdu oh eldlv g*xq surfhvvxv shuphwwdqw gh suhqguh hq frpswh o*h{lvwhqfh gh

frþwv gh wudqvdfwlrq vxu oh pdufkì gx wudydlo hw mxvwl�dqw od frh{lvwhqfh g*hpsorlv

ydfdqwv hw gh fk÷phxuv1 Hq rxwuh/ od irupdwlrq ghv vdodluhv qh surylhqw sdv g*xq sur0

fhvvxv frqfxuuhqwlho devwudlw/ pdlv gh qìjrfldwlrqv hqwuh hpsor|hxuv hw wudydloohxuv1

O*dufklwhfwxuh gx prgëoh v*duwlfxoh dxwrxu gx frqfhsw gh irqfwlrq g*dssdulhphqw txl

uìvxph oh surfhvvxv gh uhqfrqwuh hqwuh ohv shuvrqqhv ã od uhfkhufkh g*xq hpsorl hw ohv

hqwuhsulvhv glvsrvdqw g*hpsorlv ydfdqwv1 Qrxv ìwdorqqrqv oh prgëoh vxu od sìulrgh

4<;805333 ã o*dlgh ghv grqqìhv glvsrqleohv ã od EFH/ sxlv dsuëv o*dyrlu uìvrox/ qrxv

frpsdurqv ohv uìvxowdwv dx{ grqqìhv d�q txh oh prgëoh vrlw uhsuìvhqwdwli gh od }rqh

hxur1 Qrxv uìdolvrqv ghv vlpxodwlrqv hw revhuyrqv ohv uìsrqvhv gx prgëoh vxlwh ã

gl�ìuhqwv fkrfv lqglylgxhov hw whpsrudluhv = xq fkrf gh srolwltxh prqìwdluh/ xq fkrf

gh gìshqvhv sxeoltxhv/ xq fkrf gh surgxfwlylwì hw xq fkrf gh suìiìuhqfh1

Oh prgëoh uhsurgxlw xqh g|qdpltxh surfkh gh fhooh gh od }rqh hxur hw soxv sdu0

6

wlfxolëuhphqw fhooh suryhqdqw ghv frxuehv gh Skloolsv +uhodwlrq qìjdwlyh hqwuh oh wdx{

gh fk÷pdjh hw o*lq dwlrq, hw gh Ehyhulgjh +uhodwlrq qìjdwlyh hqwuh oh wdx{ gh fk÷0

pdjh hw ohv hpsorlv ydfdqwv,1 Doruv txh gh qrpeuhx{ ìfrqrplvwhv rqw d!upì txh

ohv uljlglwìv uìhoohv ghydlhqw uhpsodfhu ohv uljlglwìv qrplqdohv dx vhlq g*xq prgëoh

pdfurìfrqrpltxh/ vhorq qrwuh prgëoh ohv iulfwlrqv vxu oh pdufkì gx wudydlo qh vrqw

sdv xq vxevwlwxw pdlv xq frpsoìphqw qìfhvvdluh dx{ uljlglwìv qrplqdohv1 Oh prg0

ëoh shuphw g*ìwxglhu ohv gìwhuplqdqwv hw o*ìyroxwlrq ghv pdujhv lqwhqvlyhv +ohv khxuhv

wudydlooìhv sdu hpsor|ì, hw h{whqvlyhv +oh qrpeuh g*hpsor|ìv, hw phw hq dydqw oh idlw

txh ohv khxuhv wudydlooìhv vrqw xqh yduldeoh wurs fhqwudoh hq fh vhqv txh ohv �uphv

dmxvwhqw gh pdqlëuh shx �uìdolvwh� fhwwh ghuqlëuh hq uìsrqvh ã ghv fkdqjhphqwv frq0

mrqfwxuhov rx gh ohxu vwuxfwxuh gh surgxfwlrq1 D�q gh whqwhu gh uhsruwhu ohv dmxvwh0

phqwv surqrqfìv ghv khxuhv wudydlooìhv vxu oh idfwhxu fdslwdo/ qrxv lqwurgxlvrqv xqh

yduldeoh g*xwlolvdwlrq gx fdslwdo txl qh shuphw fhshqgdqw gh glplqxhu txh idleohphqw

oh sureoëph suìfìghqw1 Wrxw frpph gdqv oh prgëoh gh od EFH/ lo qrxv hvw lpsrvvleoh

gh wurxyhu xq ghjuì �uìdolvwh� gh uljlglwì ghv sul{1 Qrxv phwwrqv dlqvl hq ìylghqfh oh

idlw txh oh edqtxlhu fhqwudo ghyudlw whqlu frpswh ghv uljlglwìv vxu oh pdufkì gx wudydlo1

Rxeolhu fh ghjuì vxssoìphqwdluh gh shuvlvwdqfh srxuudlw o*dphqhu ã ghv gìflvlrqv gh

srolwltxh prqìwdluh huurqìhv hw ã vwdelolvhu o*ìfrqrplh prlqv h!fdfhphqw1

Qrq0whfkqlfdo vxppdu|=

Zkdw duh wkh h�hfwv ri oderxu pdunhw iulfwlrqv rq wkh g|qdplfv ri wkh hfrqrp|

dqg wkh sursdjdwlrq ri vkrfnvB Hyhq wkrxjk vxfk d txhvwlrq lv fhqwudo wr pdfurhfr0

qrplfv dqg hfrqrplf srolf|/ yhu| ihz vwxglhv vrxjkw wr dqvzhu lw lq d jhqhudo htxl0

oleulxp iudphzrun1 \hw wkh frqvhtxhqfhv ri oderxu pdunhw uljlglwlhv rq hpsor|phqw/

rxwsxw dqg lq dwlrq frqvwlwxwh dq lvvxh ri juhdw lpsruwdqfh iru erwk hfrqrplvwv dqg

srolf|pdnhuv1

Dv h{sodlqhg lq d uhfhqw vwxg| rq oderxu pdunhw plvpdwfkhv surylghg e| wkh hx0

urshdq Fhqwudo Edqn +HFE/ 5335,/ wkhuh lv frh{lvwhqfh ri d shuvlvwhqwo| kljk udwh ri

xqhpsor|phqw +;19(,dqg d orz ohyho ri sduwlflsdwlrq +9;19(,1 Wklv vxjjhvwv dq lqvxi0

�flhqw delolw| ri wkh hxur duhd wr pdwfk oderxu vxsso| dqg ghpdqg1 Wkh xqghuvwdqg0

lqj ri oderxu pdunhw pdwfklqj surfhvvhv lv ri frqvlghudeoh lpsruwdqfh iru prqhwdu|

srolf|1 Iluvwo|/ erwwohqhfnv lq wkh oderxu pdunhw pd| wuljjhu lq dwlrqdu| suhvvxuhv1

Dqg vhfrqgo|/ gl�huhqfhv lq wkh oderxu pdunhw ixqfwlrqlqj dqg wkh lpsrvvlelolw| wr

xvh frxqwu|0vshfl�f prqhwdu| ru h{fkdqjh udwh srolflhv ohdgv wr dv|pphwulfdo h�hfwv

iroorzlqj d v|phwulf ru dv|phwulf vkrfn1

Frqvhtxhqwo|/ ohvv iulfwlrq rq hxur duhd oderxu pdunhw vkrxog uhgxfh wkh vkruw0uxq

h�hfwv ri prqhwdu| srolf| rq wkh uhdo hfrqrp|1 Wklv sdshu dgguhvvhv wklv lvvxh e|

7

lqfrusrudwlqj d qrq0Zdoudvldq oderxu pdunhw lqvwhdg ri d qrplqdo zdjh uljlglw| lqwr

wkh qhz jhqhudwlrq ri vpdoo0vfdoh prqhwdu| exvlqhvv prghov fdoohg �Qhz Qhrfodvvlfdo

V|qwkhvlv� prghov1 Zh wklqn wkdw wkh pdwfklqj prgho pd| surylgh d vlpsoh dqg hoh0

jdqw uhsuhvhqwdwlrq ri hxurshdq oderxu pdunhw fkdudfwhulvwlfv lq fdswxulqj wkh vdolhqw

ihdwxuhv ri wkh wkhru| ri xqhpsor|phqw1 Wkxv/ rxu pdlq remhfwlyh lv wr hydoxdwh wkh

delolwlhv ri d g|qdplf vwrfkdvwlf jhqhudo htxloleulxp prgho pl{lqj vwlfn| sulfhv dqg

oderxu pdunhw uljlglwlhv e| dffrxqwlqj iru wkh pdlq ihdwxuhv ri wkh hxur duhd/ iru doo

yduldeohv dqg iru vhyhudo vwuxfwxudo vkrfnv1

Zh vkrz wkdw wkh xqfrqglwlrqqdo vhfrqg prphqwv jhqhudwhg e| wkh fdoleudwhg

prgho duh forvh wr wkrvh lq wkh hxur duhd gxulqj wkh shulrg 4<;805333/ h{fhsw iru wkh

uhdo zdjh g|qdplfv/ zkhq erwk d kljk ghjuhh ri qrplqdo dqg oderxu pdunhw iulfwlrqv

duh dvvxphg1 Wklv lqglfdwhv wkdw oderxu pdunhw iulfwlrqv gr qrw dfw dv d vxevwlwxwh iru

qrplqdo uljlglwlhv exw dv d qhfhvvdu| frpsohphqw1 Wkxv/ dv lq wkh prgho ri wkh HFE/

rxu prgho lv qrw deoh wr dguhvv wkh vkruwfrplqj ri uhtxlulqj dq lpsodxvleoh ghjuhh

ri sulfh uljlglw| lq rughu wr pdwfk gdwd1 Vlqfh rxu prghoolqj doorzv wkh srvvlelolw| wr

lqyhvwljdwh wkh wkhruhwlfdo ghwhuplqdqwv ri wkh h{whqvlyh dqg lqwhqvlyh pdujlqv rq wkh

oderxu pdunhw/ zh fdq vhh wkdw krxuv shu zrunhu lv wrr grplqdqw dv d ohdglqj lqglfdwru

lq wkh vhqvh wkdw wkhlu yrodwlolw| lv juhdwhu wkdq wkdw ri hpsor|phqw1 Lq uhvsrqvh wr

d vwuxfwxudo vkrfn/ krxuv shu zrunhu duh wkh fuxfldo yduldeoh ri dgmxvwphqw iru �upv1

Rq wklv vlgh/ lqwurgxflqj d yduldeoh fdslwdo xwlolvdwlrq udwh khosv wr vroyh sduw ri wklv

zhdnqhvv vlqfh krxuv zrunhg duh qr orqjhu wkh rqo| qrq0suhghwhuplqhg surgxfwlrq

idfwru1 Zh vkrz wkh delolw| ri rxu prgho wr uhsurgxfh wkh oderxu pdunhw vw|ol}hg idfwv

fkdudfwhul}hg e| wkh Ehyhulgjh dqg Skloolsv fxuyhv/ exw dovr lwv lqdelolw| wr jhqhudwh

wkh revhuyhg uhdo zdjh sdwwhuq1 Ilqdoo|/ wkh idfw wkdw d fhqwudo edqnhu zklfk xvhg d

prgho zlwkrxw oderxu pdunhw uljlglwlhv zrxog kdyh doo wkh fkdqfhv wr eh plvwdnhq lq

prgli|lqj wkhlu lqwhuhvw udwh lv erxjkw wr oljkw1

8

E| sodflqj dpsol�fdwlrq dqg shuvlvwhqfh phfkdqlvpv lq irupdo jhqhudo

htxloleulxp prghov/ frqwulexwruv wr prghuq xfwxdwlrqv uhvhdufk dfklhyh dghjuhh ri fodulw| plvvlqj iurp hduolhu pdfurhfrqrplfv1 Zlwkrxw frqvlghud0

wlrq ri xqhpsor|phqw/ prghov h{sodlqhg shuvlvwhqfh lq hpsor|phqw odujho|wkurxjk shuvlvwhqfh lq gulylqj irufhv1 Zkhuh xqhpsor|phqw lv frqvlghuhg

h{solflwo|/ shuvlvwhqfh dulvhv qdwxudoo| iurp wkh wlph0frqvxplqj surfhvv risodflqj xqhpsor|hg zrunhuv lq mrev iroorzlqj dq dgyhuvh lpsxovh1

Urehuw H1 Kdoo +4<<</ s1446<,

4 Lqwurgxfwlrq

Zkdw duh wkh h�hfwv ri oderxu pdunhw iulfwlrqv rq wkh g|qdplfv ri wkh hfrqrp| dqg

wkh sursdjdwlrq ri vkrfnvB Hyhq wkrxjk vxfk d txhvwlrq lv fhqwudo wr pdfurhfrqrplfv

dqg hfrqrplf srolf|/ yhu| ihz vwxglhv vrxjkw wr dqvzhu lw lq d jhqhudo htxloleulxp

iudphzrun1

\hw wkh frqvhtxhqfhv ri oderxu pdunhw uljlglwlhv rq hpsor|phqw/ rxwsxw dqg lq0

dwlrq frqvwlwxwh dq lvvxh ri juhdw lpsruwdqfh iru erwk hfrqrplvwv dqg srolf|pdnhuv1

Dv h{sodlqhg lq d uhfhqw vwxg| rq oderxu pdunhw plvpdwfkhv surylghg e| wkh hxur0

shdq Fhqwudo Edqn +HFE/ 5335,/ wkhuh lv d jds ehwzhhq wkh hxurshdq xqhpsor|phqw

ohyho dqg wkh gl!fxowlhv lq uhfuxlwlqj zrunhuv1 Wklv frh{lvwhqfh ri xqvdwlv�hg oderxu

pdunhw vxsso| dqg ghpdqg vxjjhvwv dq lqvx!flhqw delolw| ri wkh hxur duhd wr pdwfk

oderxu vxsso| dqg ghpdqg1 Pruhryhu/ lw lv jhqhudoo| djuhhg wkdw wkh xqhpsor|phqw

udwh lq wkh hxur duhd lv kdugo| f|folfdo/ dqg wkdw lwv g|qdplfv lv pdlqo| h{sodlqhg

e| lqvwlwxwlrqdo dqg vwuxfwxudo ihdwxuhv1 Xqiruwxqdwho|/ vxfk hxurshdq oderxu pdunhw

fkdudfwhulvwlfv dv wkh orz prelolw| ri pdqsrzhu dfurvv frxqwulhv dqg wkh kljk ohyho

ri uhjxodwlrq fuhdwh d uljlg oderxu pdunhw frq�jxudwlrq +Ehuwrod/ 4<<</ Fdglrx dqg

Jxlfkdug/ 4<<</ dqg Fdglrx hw do1/ 4<<<,1

Wkh shuvlvwhqwo| kljk udwh ri xqhpsor|phqw +;19(,/ wkh orz ohyho ri sduwlflsdwlrq

+9;19(, dqg wkh xqhyhq oderxu pdunhw shuirupdqfh dffurvv hxur duhd frxqwulhv lqgl0

fdwh wkdw wkhvh lqwulqvlf iulfwlrqv fdqqrw eh qhjohfwhg dqg wkdw wkh xqghuvwdqglqj ri

oderxu pdunhw pdwfklqj surfhvvhv lv ri frqvlghudeoh lpsruwdqfh iru prqhwdu| srolf|1

Iluvwo|/ erwwohqhfnv lq wkh oderxu pdunhw pd| wuljjhu lq dwlrqdu| suhvvxuhv1 Dqg

vhfrqgo|/ gl�huhqfhv lq wkh oderxu pdunhw ixqfwlrqlqj dqg wkh lpsrvvlelolw| wr xvh

frxqwu|0vshfl�f prqhwdu| ru h{fkdqjh udwh srolflhv ohdgv wr dv|pphwulfdo h�hfwv iro0

orzlqj d v|phwulf ru dv|phwulf vkrfn1 Frqvhtxhqwo|/ ohvv iulfwlrq rq hxur duhd oderxu

pdunhw vkrxog uhgxfh wkh vkruw0uxq h�hfwv ri prqhwdu| srolf| rq wkh uhdo hfrqrp|1

Lw lv qr orqjhu srvvleoh wr flufxpyhqw wkh prghoolqj ri oderxu pdunhw iulfwlrqv lq d

9

pdfurhfrqrplf prgho rq zklfk srolf| uhfrpphqgdwlrqv duh wr eh edvhg1

Dowkrxjk uhfhqw jhqhudo htxloleulxp prghov irfxvlqj rq wkh hxur duhd hfrqrp|/

olnh Vphwv dqg Zrxwhuv +5335,/ duh vxffhvvixo dw h{sodlqlqj d qxpehu ri skhqrphqd/

wkhlu odfn ri lpsolfdwlrqv derxw wkh oderxu pdunhw dqg lwv h�hfwv rq wkh ryhudoo

hfrqrp| lv lqghhg d gudzedfn1

Wklv sdshu dgguhvvhv wklv lvvxh e| lqfrusrudwlqj d qrq0Zdoudvldq oderxu pdunhw

lqvwhdg ri d qrplqdo zdjh uljlglw| lqwr wkh qhz jhqhudwlrq ri vpdoo0vfdoh prqhwdu|

exvlqhvv prghov fdoohg �Qhz Qhrfodvvlfdo V|qwkhvlv� prghov14 Zh wklqn wkdw wkh

pdwfklqj prgho pd| surylgh d vlpsoh dqg hohjdqw uhsuhvhqwdwlrq ri hxurshdq oderxu

pdunhw fkdudfwhulvwlfv lq fdswxulqj wkh vdolhqw ihdwxuhv ri wkh wkhru| ri xqhpsor|0

phqw1 Lqghhg/ wkh olwhudwxuh rq oderxu pdunhw vhdufk dqg uhdo exvlqhvv f|fohv prghov

kdv vkrzq wkdw vxfk d phfkdqlvp jhqhudwhv uhdolvwlf g|qdplfv lq hpsor|phqw dqg

lqfuhdvhv wkh pdjqlwxgh dqg shuvlvwhqfh ri wkh lpsdfw ri surgxfwlylw| vkrfnv rq

rxwsxw15 Wkxv/ rxu pdlq remhfwlyh lv wr hydoxdwh wkh delolwlhv ri d g|qdplf vwrfkdv0

wlf jhqhudo htxloleulxp prgho pl{lqj vwlfn| sulfhv dqg oderxu pdunhw uljlglwlhv e|

dffrxqwlqj iru wkh pdlq ihdwxuhv ri wkh hxur duhd/ iru doo yduldeohv dqg iru vhyhudo

vwuxfwxudo vkrfnv1

Lq d uhfhqw zrun/ Zdovk +5336, lqfrusrudwhv d oderxu pdunhw pdwfklqj surfhvv

wrjhwkhu zlwk sulfh vwlfnlqhvv lq d fdvk0lq0dgydqfh prgho dqg vwxglhv wkh lpsolfdwlrqv

iru shuvlvwhqw rxwsxw h�hfwv ri prqhwdu| srolf| vkrfnv rq X1V1 gdwd1 Zlwklq wkh hxur

duhd hqylurqphqw/ zh h{whqg wkh vfrsh ri Zdovk*v sdshu lq rughu wr dfklhyh uhvxowv

wkdw duh frpsdudeoh wr wkrvh ghulyhg e| Vphwv dqg Zrxwhuv*v +5336,1 Iluvw/ zh wdnh

lqwr dffrxqw erwk h{whqvlyh dqg lqwhqvlyh pdujlq rq wkh oderxu pdunhw1 Vhfrqg/ zh

lqwurgxfh wkh pdlq wkhruhwlfdo hohphqwv ghyhorshg vr dv wr uhsurgxfh wkh revhuyhg

lqhuwldo g|qdplfv ri lq dwlrq dqg shuvlvwhqfh lq djjuhjdwh txdqwlwlhv1 Wklv lqfoxghv

kdelw irupdwlrq lq frqvxpswlrq ehkdylrxu/ lqyhvwphqw dgmxvwphqw frvwv/ dqg yduldeoh

fdslwdo xwlolvdwlrq1

Wkh sdshu lv rujdqlvhg dv iroorzv1 Vhfwlrq 5 lv ghyrwhg wr wkh suhvhqwdwlrq ri

wkh prqhwdu| jhqhudo htxloleulxp prgho1 Lq vhfwlrq 6 wkh prgho lv fdoleudwhg iru wkh

hxur duhd hfrqrp| xvlqj hxur duhd gdwd1 Zh h{soruh wkh ghvfulswlyh srzhu ri wkh

vlpxodwhg gdwd dqg shuirup vrph vlpxodwlrqv1 Ilqdoo|/ vhfwlrq 7 frqfoxghv dqg jlyhv

gluhfwlrqv iru ixwxuh uhvhdufk14Vhh wkh vhplqdo sdshuv ri Jrrgiulhqg dqg Nlqj +4<<:,/ Fodulgd hw do1 +4<<<, ru Zrrgirug +5336,

iru d suhvhqwdwlrq ri wkh Qhz Qhrfodvvlfdo V|qwkhvlv iudphzrun15Wkh pdlq frqwulexwlrqv duh Phu} +4<<8,/ Dqgroidwwr +4<<9,/ dqg ghq Kddq/ Udph| dqg Zdwvrq

+5333,1

:

5 Wkh Prgho Hfrqrp|

Zh frqvlghu d g|qdplf vwrfkdvwlf jhqhudo htxloleulxp prgho dorqj wkh olqhv ri Fkulv0

wldqr/ Hlfkhqedxp dqg Hydqv +5334,/ Qhlvv dqg Qhovrq +5335,/ dqg rwkhuv1 Exw rxu

vshfl�fdwlrq pdlqo| ghsduwv iurp wkrvh sdshuv zlwk uhvshfw wr wkh surshuwlhv ri wkh

oderxu pdunhw1

Zh uhpryh qrplqdo zdjh uljlglwlhv dqg iroorzlqj Eodqfkdug dqg Gldprqg +4<;<,

dqg Slvvdulghv +5333,/ wkh oderxu pdunhw vshfl�fdwlrq lv edvhg rq wkh hfrqrplfv ri

vhdufk1 Wkh edvlf lqfhqwlyh iru vhdufk dfwlylwlhv lq wkh oderxu pdunhw e| erwk zrunhuv

dqg �upv duh wkh sur�w rssruwxqlwlhv lq suhvhqw ydoxh whupv zklfk duh dvvrfldwhg

zlwk d vxffhvvixo mre pdwfk iru erwk sduwlhv1 Zdjhv duh ghwhuplqhg e| dq lpsolflw

edujdlq dw wkh lqglylgxdo ohyho/ l1h1 wkh �up hqjdjhv lq Qdvk edujdlqv zlwk hdfk

lqglylgxdo zrunhu e| wdnlqj wkh zdjh ri doo rwkhu hpsor|hhv dv jlyhq1

Qrwh dovr wkdw zh lqfrusrudwh sk|vlfdo fdslwdo dqg lqyhvwphqw edvhg rq wkh T

wkhru| zklfk pdnhv lw srvvleoh wr prgho wkh idfw wkdw dgmxvwphqw frvwv iru fdslwdo

dqg oderxu pdunhw iulfwlrqv d�hfw mrlqwo| �upv* klulqj16 Doorzlqj iru oderxu pdunhw

vhdufk wr lqwhudfw zlwk fdslwdo dgmxvwphqw frvwv lpsuryhv dovr wkh shuirupdqfh ri

lqyhvwphqw g|qdplfv dqg lq wxuq rxwsxw +Fkìurq dqg Odqjrw/ 4<<</ dqg Phu} dqg

\dvkly/ 5336,1

Wkh hfrqrp| frqvlvwv ri d jryhuqphqw dqg qxphurxv djhqwv ri wkuhh gl�huhqw

w|shv= krxvhkrogv/ zkrohvdohuv dqg uhwdlohuv1 Krxvhkrogv fkrrvh frqvxpswlrq/ erqgv/

dqg uhdo0edodqfhv vr dv wr pd{lplvh wkh suhvhqw ydoxh ri xwlolw| vwuhdpv1 Dv lq Dq0

groidwwr +4<<9,/ lw lv dvvxphg wkdw wkhuh lv dq lqvxudqfh pdunhw lq wkh hfrqrp| wkdw

xqdeohv djhqwv wr ixoo| lqvxuh djdlqvw lglrv|qfudwlf ulvnv1 Wklv dvvxpswlrq pdnhv

krxvhkrogv h{0dqwh lghqwlfdo dqg vlpsol�hv wkh dqdo|vlv1 Wkh jryhuqphqw frqvxphv

d vkduh ri �qdo jrrgv dqg frqgxfwv �vfdo dqg prqhwdu| srolf| e| xvlqj wkh qrplqdo

lqwhuhvw udwh dv lwv lqvwuxphqw1 Surgxfwlrq ri �qdo jrrgv wdnhv sodfh lq wzr vwdjhv1

Shuihfwo| frpshwlwlyh zkrohvdohuv pdqdjh wkh surgxfwlrq ri wkh vdph krprjhqhrxv

lqsxw jrrg dqg pdnh lqyhvwphqw dqg klulqj ghflvlrqv1 Ilqdoo| prqrsrolvwlf uhwdlohuv

ex| wkh lqsxw jrrg wr surgxfh gl�huhqfldwhg �qdo jrrgv vrog wr wkh krxvhkrogv dqg

vhw sulfhv dffruglqj wr wkh glvfuhwh0wlph yhuvlrq ri Fdoyr*v +4<;6, prgho1

514 Krxvhkrogv

Wkh hfrqrp| lv srsxodwhg e| d uhsuhvhqwdwlyh krxvhkrog frqvwlwxwhg e| d frqwlqxxp

ri phpehuv lqgh{hg rq wkh xqlw lqwhuydo1 Lw kdv suhihuhqfhv gh�qhg ryhu d frpsrvlwh

6Dxwkruv jhqhudoo| pdnh wkh qrquhdolvwlf exw vlpsoli|lqj dvvxpswlrq wkdw krxvhkrogv pdnh wkh

fdslwdo dffxpxodwlrq dqg xwlolvdwlrq ghflvlrqv1

;

frqvxpswlrq jrrg +F|,/ wkh hpsor|phqw*v udwh +Q|,/ krxuv zrunhg +K|,/ dqg uhdo

prqh| edodqfhv +�|@S|,1 Prqh| hqwhuv wkh xwlolw| ixqfwlrq gluhfwo| wr fdswxuh wkh

lghd wkdw uhdo edodqfhv surylgh d wudqvdfwlrq0idflolwdwlqj vhuylfh1 Wkh uhsuhvhqwdwlyh

krxvhkrog fkrrvhv d vhtxhqfh ri frqvxpswlrq +F|,/ qrplqdo prqh| +�|, dqg rqh0

shulrg erqgv +E|n�,/ wr pd{lplvh klv olihwlph xwlolw|=7

H|

"[�'f

��%R|

��S

�S � 4+F|n� � �K|,

jS3�jS �Q|n�

��?

�? . 4+K|n�,

j?n�

j?

�

.�6

�6 � 4

��|n�

S|n�

�j63�j6

&+4,

vxemhfw wr d vhulhv ri uhdo shulrg exgjhw frqvwudlqwv=

F|n� .�|n�

S|n�.

E|n�n�

+4 . l|n�,S|n�� Z|n�Q|n�K|n� .

E|n�

S|n�.

�|n�3�

S|n��W|n� .�|n� +5,

zkhuh � 5 +3> 4, uhsuhvhqwv wkh glvfrxqw idfwru dqg %R| lv d jhqhudo vkrfn wr suhihu0

hqfhv wkdw d�hfwv wkh lqwhuwhpsrudo vxevwlwxwlrq ri krxvhkrogv1 Lw lv dvvvxphg wr

iroorz d �uvw0rughu dxwruhjuhvvlyh surfhvv zlwk l1l1g1 Qrupdo huuru whup= oq+%R| , @�4� �R

�oq +�%R, . �R oq+%

R|3�, . h�c|1

Lq htxdwlrq +4,/ �S ghqrwhv wkh lqwhuwhpsrudo hodvwlflw| ri vxevwlwxwlrq ri frq0

vxpswlrq/ �? lv wkh hodvwlflw| ri oderxu ghvxwlolw| zlwk uhvshfw wr krxuv zrunhg/ �6uhsuhvhqwv wkh hodvwlflw| ri prqh| kroglqjv zlwk uhvshfw wr wkh lqwhuhvw udwh1 Suhihu0

hqfhv ryhu frqvxpswlrq wdnh rq d qrq wlph vhsdudeoh irup fdswxulqj wkh lghd wkdw

krxvhkrogv pd| h{klelw kdelw irupdwlrq lq wkhlu frqvxpswlrq sdwwhuqv1 Wkh sdudp0

hwhu � 5 ^3> 4, uhsuhvhqwv wkh kdelw irupdwlrq sdudphwhu phdvxulqj wkh h�hfw ri vwrfn

rq fxuuhqw xwlolw|1 Lq wklv sdshu zh zrun zlwk vwulfwo| srvlwlyh � lq oljkw ri hylghqfh

wkdw grlqj vr uhgxfhv vrph ri wkh hpslulfdo vkruwfrplqjv ri txdqwlwdwlyh exvlqhvv

f|foh prghov +Erogulq/ Fkulvwldqr dqg Ilvkhu/ 4<<</ ru Ixkuhu/ 5333,18 Wkh kdelw

vwrfn lv vxssrvhg wr htxdo wkh ohyho ri djjuhjdwh frqvxpswlrq lq wkh suhylrxv shulrg/

K| @ F|3�1

Lq htxdwlrq +5,/ Z| ghqrwhv wkh krxuo| uhdo zdjh/ l| ghqrwhv wkh qrplqdo lqwhuhvw

udwh/ W| ghqrwhv wkh uhdo oxps0vxp wd{ +jryhuqphqw wudqvihuv, dqg �| lv wkh vxp ri

wkh glylghqgv ghulyhg iurp uhwdlohuv +��| , dqg zkrohvdohuv +�o

| ,17Wkh shuihfw lqvxudqfh v|vwhp pdnhv wkh uhsuhvhqwdwlyh krxvhkrog d zhljkwhg dyhudjh ri hpsor|hg

dqg xqhpsor|hg krxvhkrogv/ zkhuh wkh zhljkw lv wkh hpsor|phqw udwh1 Wkdw*v zk| wkh hpsor|phqw

udwh hqwhuv wkh xwlolw| ixqfwlrq dqg wkh exgjhw frqvwudlqw1 E| vlpsol�fdwlrq zh vxssrvh wkdw wkhuh

lv qr ghvxwlolw| wr vhdufk d mre18Ixkuhu +5333, vkrzv wkdw kdelw irupdwlrq doorzv wkh prgho wr pdwfk wkh uhvsrqvh ri uhdo vshqglqj

wr prqhwdu|0srolf| vkrfnv1 Lw lv d uhdo prwlydwlrq iru xvlqj kdelw irupdwlrq dv dq d sulrul ghvludeoh

prgl�fdwlrq wr wkh vwdqgdug prgho1

<

Wkh frqvxpswlrq jrrg F| lv d Gl{lw0Vwljolw} djjuhjdwh ri d pxowlsolflw| ri gl�hu0

hqfldwhg jrrgv/ lqgh{hg e| } 5 ^3> 4`/

F| @

�] �

fF| +},

"3�" g}

� ""3�

+6,

zkhuh wkh sdudphwhu � A 4 lv wkh hodvwlflw| ri vxevwlwxwlrq ehwzhhq gl�huhqfldwhg

uhwdlo jrrgv +ru htxlydohqwo| wkh sulfh hodvwlflw| ri ghpdqg,1 Jlyhq sulfh S| +}, iru

wkh �qdo jrrgv/ wklv suhihuhqfh vshfl�fdwlrq lpsolhv wkh krxvhkrog*v ghpdqg iru jrrg

} lv

F| +}, @

�S| +},

S|

�3"

F| +7,

zkhuh wkh djjuhjdwh uhwdlo sulfh lqgh{ S| lv gh�qhg dv

S| @

�] �

fS| +},

�3" g}� �

�3"

= +8,

Zlwk �| wkh Odjudqjh pxowlsolhu rq +5,/ wkh rswlpdo krxvhkrog ehkdylrxu |lhogv

wkh iroorzlqj �uvw0rughu frqglwlrqv=

�| @ %R| +F| � �K|,3 �

jS > +9,

%R|

��|

S|

�3 �

j6

@ �| � �H|�|n�S|S|n�

> +:,

�| @ +4 . l|,�H|�|n�S|S|n�

= +;,

515 Oderxu Pdunhw Pdwfklqj

Dw wkh pdfurhfrqrplf ohyho/ wkh odz ri prwlrq ri djjuhjdwh hpsor|phqw +Q|, lv

Q|n� @ +4� v,Q| .P| +<,

zkhuh v 5 ^3> 4` lv d jlyhq h{rjhqhrxv mre vhsdudwlrq udwh/ frqvwdqw ryhu wlph/ wkdw

hqvxuhv wkdw d sursruwlrq v ri doo �oohg mrev glvdsshduv dw hdfk lqvwdqw/ dqg P| lv wkh

pdvv ri uhfuxwlqjv dw shulrg w1 Wkxv/ pdwfklqjv zklfk wdnh sodfh dw wkh shulrg w duh

rqo| surgxfwlyh dw wkh iroorzlqj shulrg1

Wkh pdwfklqj ixqfwlrq lv d yhu| frqyhqlhqw k|srwkhwlfdo frqfhsw zkrvh edvlf lghd

lv wkdw wkh uhfuxlwlqj h�ruw ri hpsor|huv dqg wkh vhdufk h�ruw ri zrunhuv vhuyh dv lq0

43

sxwv lq d pdunhw pdwfklqj ixqfwlrq wkdw jhqhudwhv qhz kluhv19 Wkh mre ydfdqflhv +Y|,

dqg xqhpsor|hg djhqwv +X| @ 4�Q|, duh udqgrpo| pdwfkhg zlwk hdfk rwkhu1 Wkh

djjuhjdwh rz ri mre pdwfkhv duh ghwhuplqlvwlf dqg jlyhq e| wkh iroorzlqj pdwfklqj

whfkqrorj|=

P| @ P +X|> Y|, @ �pXk| Y

�3k| +43,

zkhuh � 5 +3> 4, dqg �p A 3 lv d vfdoh sdudphwhu1 Wkh pdwfklqj whfkqrorj| h{klelwv

frqvwdqw uhwxuqv wr vfdoh1 Zh fkrrvh d Free0Grxjodv irup iru lwv vlpsolflw|1

Wkh mre ydfdqflhv dqg xqhpsor|hg zrunhuv wkdw duh pdwfkhg wrjhwkhu lq shulrg w

duh udqgrpo| vhohfwhg iurp wkh vhwv Y| dqg X|1 Khqfh/ wkh vwrfkdvwlf surfhvv jryhuqlqj

wkh vwdwh ri ydfdqw mrev gxulqj dq lqwhuydo ri wlph lv Srlvvrq zlwk udwh

� | @P +X|> Y|,

Y|= +44,

Lq rwkhu zrugv/ � | fdq eh lqwhusuhwhg dv wkh lqvwdqwdqhrxv suredelolw| ri d ydfdqf|

ehlqj �oohg1 Dovr/ wkh dyhudjh vwhdg|0vwdwh gxudwlrq ri d mre ydfdqf| lv 4@�� 1

Vlploduo|/ wkh lqvwdqwdqhrxv suredelolw| wkdw dq xqhpsor|hg zrunhu �qgv d ydfdqw

srvlwlrq lv jlyhq e|=

(| @P +X|> Y|,

X|+45,

zklfk phdqv wkdw wkh dyhudjh vwhdg|0vwdwh gxudwlrq ri xqhpsor|phqw lv 4@�(1

516 Zkrohvdohuv

Zh frqvlghu d uhsuhvhqwdwlyh �up zklfk dfwv rq d shuihfw frpshwlwlrq pdunhw dqg

pdnhv lqyhvwphqw dqg klulqj ghflvlrqv1 Hdfk shulrg/ wklv �up xvhv sk|vlfdo fdslwdo

+N|, dqg oderxu +wrwdo krxuv/ Q|K|, dv lqsxwv lq rughu wr surgxfh d krprjhqhrxv

zkrohvdoh jrrg +[�| , zklfk fdqqrw eh frqvxphg dqg zloo eh vrog wr uhwdlohuv dw

uhodwlyh sulfh | @ S`| @S| wr surgxfh d gl�huhqfldwhg �qdo jrrg1 Wkh surgxfwlrq

whfkqrorj| lv jlyhq e|[�| @ i +y|N|>Q|K|,

@ %@| +y|N|,# +Q|K|,

�3# +46,

zkhuh � 5 +3> 4, > y| lv wkh fdslwdo xwlolvdwlrq udwh dqg %@| lv dq h{rjhqrxv whfkqrorj|

vkrfn dvvxphg wr iroorz d �uvw0rughu dxwruhjuhvvlyh surfhvv zlwk l1l1g1 Qrupdo huuruwhup= oq+%@| , @ +4� �@, oq +�%

@, . �@ oq+%@|3�, . h2c|1

9Ilupv kdyh mrev wkdw duh �oohg ru ydfdqw dqg zrunhuv kdyh d mre ru duh xqhpsor|hg exw rqo| wkh

ydfdqw mrev duh r�huhg dqg xqhpsor|hg shrsoh duh hqjdjhg lq vhdufk1 Wklv dvvxpswlrq lpsolhv wkdw

wkh wzr dfwlylwlhv ri surgxfwlrq ri jrrgv dqg wudgh lq oderxu pdunhw duh vwulfwo| vhsdudwh dfwlylwlhv1

44

Wkh prghoolvdwlrq ri lqyhvwphqw fdq eh olqnhg wr Wrelq*v T0prgho/ zklfk frxsohv

lqyhvwphqw ghflvlrqv wr iruzdug0orrnlqj vwrfn pdunhw ydoxdwlrqv ri wkh �up1: Wklv

prgho fdq eh ghulyhg iurp wkh wkhru| li lw lv dvvxphg wkdw lqyhvwphqw lv vxemhfw

wr dgmxvwphqw frvwv/ zklfk duh d frqyh{ ixqfwlrq ri wkh udwh ri fkdqjh ri wkh �up*v

fdslwdo vwrfn1 D qhfhvvdu| frqglwlrq lv frqyh{lw| zklfk lpsolhv wkdw wkhvh lqvwdoodwlrq

frvwv lqfuhdvh dw dq lqfuhdvlqj udwh dqg wrr idvw dq dffxpxodwlrq ri fdslwdo lv pruh

frvwo|1

Wkh �up*v vwrfn ri sk|vlfdo fdslwdo hyroyhv dffruglqj wr=

N|n� @ +4� � +y|,,N| . L| +47,

zkhuh L| ghqrwhv wlph w sxufkdvhv ri lqyhvwphqw jrrgv dqg � +y|, d srvlwlyh/ lqfuhdvlqj

dqg frqyh{ ixqfwlrq ri wkh xwlolvdwlrq udwh gh�qhg e|

� +y|, @ ��y_|

g+48,

wkdw uh hfwv wkh idfw wkdw d kljkhu xwlolvdwlrq udwh udlvhv wkh ghsuhfldwlrq udwh ri

fdslwdo +Nlqj dqg Uhehor/ 4<<<,1 �� A 3 lv d vfdoh sdudphwhu1

Wkh ixqfwlrqqdo irup fkrvhq khuh iru wkh dgmxvwphqw frvwv lv jlyhq e|=

D +L|>N|>y|, @�

5

�L|N|

� � +y|,

�2

N| +49,

zlwk � A 31

Wkh uhsuhvhqwdwlyh �up fkrrvhv vhtxhqfhv ri ydfdqflhv/ lqyhvwphqw/ dqg xwlolvdwlrq

udwh lq rughu wr pd{lplvh wkh h{shfwhg vxp ri glvfrxqwhg sur�wv/ wdnlqj dv jlyhq d

shu ydfdqf| frvw +),=

pd{tT|n� cU|n� cy|n��

H|

;?="[�'f

��|n��|

^|n�i +y|n�N|n� >Q|n�K|n�,

�Z|n�Q|n�K|n� � )Y|n� � +L|n� .D +L|n� >N|n�>y|n�,,`j +4:,

vxemhfw wr wkh iroorzlqj frqvwudlqwv=

Q|n�n� @ +4� v,Q|n� . � |n�Y|n�> +4;,

N|n�n� @ +4� � +y|n�,,N|n� . L|n� = +4<,

Wkh �uvw0rughu frqglwlrqv ri wklv surjudp duh jlyhq e|=:Vhh Jhuwohu dqg Jlofkulvw +5333, iru dq dssudlvdo ri wkh pdfurhfrqrplf frqvhtxhqfhv ri lqyhvw0

phqw ghod|v lq d vwdjjhuhg0sulfhv iudphzrun1

45

)

� |@ �H|

��|n��|

�|n�i

�

�|n��Z|n�K|n� . +4� v,

)

� |n�

��> +53,

4 .D�

U|@ �H|

��|n��|

�|n�i

�

g|n��D

�

g|n�. +4� �,

�4 .D

�

U|n�

��> +54,

|i�

y|@ N|�

�

y|= +55,

517 Zdjh dqg Krxuv Ghwhuplqdwlrq

Zdjh dqg krxuv zrunhg duh ghwhuplqhg e| wkh jhqhudol}hg Qdvk0edujdlqlqj vroxwlrq1Lqghhg/ wkh pdwfklqj ehwzhhq dq xqhpsor|hg shuvrq dqg d �up zkr frruglqdwh

hdfk rwkhu jlyhv ulvh wr d vxusoxv zklfk pxvw eh vkduhg ehwzhhq wkh phhwlqj sdlu1

Wklv vkdulqj wdnhv sodfh dw wkh pdwfk ohyho wkurxjk d elodwhudo dqg ghfhqwudol}hg

zdjh2krxuv qhjrfldwlrq1 Nqrzlqj wkdw wkhuh duh d uhsuhvhqwdwlyh krxvhkrog dqg d

uhsuhvhqwdwlyh �up/ zh duh orfdwhg gluhfwo| dw wkh v|pphwulf htxloleulxp vroxwlrq ri

wkh prgho1

Irupdoo|/ wkh vxusoxv jhqhudwhg e| d vxffhvvixo pdwfk ehwzhhq dq xqhpsor|hg

zrunhu dqg d ydfdqw mre lv wkh pdujlqdo ydoxh ri hpsor|phqw1 Rqh fdq vkrz +vhh

Dsshqgl{ D iru ghwdlov, wkdw krxuo| uhdo zdjh dqg krxuv zrunhg duh jlyhq e|=

Z| @ �

�+4� �,

|\|Q|K|

.)

K|

Y|X|

�. +4� �,

#%R|

�? +K|,�

j?

+�? . 4,�|

$> +56,

+4� �,2|\|Q|K|

@ %R|K

�

j?

|

�|+57,

zkhuh 3 � � � 4 lv wkh uhodwlyh edujdlqlqj srzhu ri zrunhuv1

518 Uhwdlohuv

Wkhuh lv d frqwlqxxp ri prqrsrolvwlfdoo| frpshwlwlyh uhwdlohuv lqgh{hg e| } rq wkh

xqlw lqwhuydo1 Hdfk ri wkhp lv lq�qlwlyho| olyhg dqg surgxfhv d gl�huhqfldwhg �qdo

jrrg \| +}, zlwk d whfkqrorj| wkdw wudqvirupv rqh xqlw ri zkrohvdoh jrrgv lqwr rqh

xqlw ri uhwdlo jrrgv/ vr wkdw \| +}, @ [�| +},1 Ilupv rq wkh uhwdlo vhfwru sxufkdvh

rxwsxw iurp zkrohvdoh surgxfhuv dw wkh sulfh | +zklfk ehfrphv wkh �up*v uhdo

pdujlqdo frvw, dqg gluhfwo| vhoo wr krxvhkrogv1

Iru wkh vdnh ri vlpsolflw|/ zh dvvxph wkdw wkh jryhuqphqw dqg wkh zkrohvdohu

kdyh wkh vdph rswlpdo lqwudwhpsrudo doorfdwlrqv iru hdfk gl�huhqfldwhg jrrgv dv wkh

46

krxvhkrog1 Wklv lpsolhv wkdw wkh ghpdqg fxuyh idflqj hdfk uhwdlohu lv jlyhq e|=

\| +}, @

�S| +},

S|

�3"

\|= +58,

Ilqdo rxwsxw pd| wkhq eh hlwkhu wudqviruphg lqwr d vlqjoh w|sh ri frqvxpswlrq

jrrg/ lqyhvwhg/ frqvxphg e| wkh jryhuqphqw/ xvhg xs lq ydfdqf| srvwlqj frvwv/ ru

fdslwdo dgmxvwphqw frvwv1 Lq sduwlfxodu/ wkh hfrqrp|0zlgh uhvrxufh frqvwudlqw lv jlyhq

e|=

\| @ F| . L| .J| . )Y| .D|= +59,

Zh lqwurgxfh d qrplqdo uljlglw| lq wkh irup ri vwdjjhuhg sulfh vhwwlqj dv ghyhorshg e|

Fdoyr +4<;6,1 Hdfk shulrg/ uhwdlohuv pd| uhvhw wkhlu sulfhv zlwk suredelolw| +4� !, >

lqghshqghqw ri wkh hodsvhg wlph vlqfh wkh| uhylvhg wkhlu sulfhv1 Wkhvh gudzlqjv duh

lqghshqgdqw ri klvwru| dqg zh gr qrw qhhg wr nhhs wudfn ri �upv fkdqjlqj sulfhv1

Wkh h{shfwhg wlph ryhu zklfk wkh sulfh lv �{hg/ l1h1 wkh h{shfwhg zdlwlqj wlph xqwlo

wkh qh{w sulfh dgmxvwphqw/ lv wkhuhiruh ��3� 1 Wkh uhpdlqlqj iudfwlrq ! ri �upv wkdw

duh dvvxphg wr dgmxvw wkhlu suhylrxv shulrg*v sulfhv iroorzv wkh vlpsoh uxoh=

S| +}, @ �|3�S|3� +}, = +5:,

Dv h{sodlqhg e| Fkulvwldqr hw doll +5334,/ wklv vshfl�fdwlrq lv suhihuuhg ehfdxvh

wkh vwdqgdug vshfl�fdwlrq S| +}, @ ��S|3� +},/ zkhuh �� lv wkh vwhdg| vwdwh jurvv udwh

ri lq dwlrq/ grhv qrw jhqhudwh vx!flhqw lq dwlrq lqhuwld1

Wkh remhfwlyh ixqfwlrq ri wkh uhwdlohuv zkr kdyh wkh srvvlelolw| wr dgmxvw wkhlu

sulfhv lq shulrg w lpsolhv wkdw wkh| fkrrvh S W| +}, wr pd{lplvh

H|

"[�'f

+!�,��|n��|

�S W| +},

S|n��|n�

�\|n� +}, +5;,

vxemhfw wr wkh ghpdqg fxuyh +58,1

��b|n�b|

lv wkh uhohydqw glvfrxqw idfwru ehwzhhq w dqg w. m> zkhuh b|n�b|

lv wkh udwlr

ri pdujlqdo xwlolw| ri frqvxpswlrq dw w . m wr pdujlqdo xwlolw| dw w1 \|n� +}, lv wkh

�up*v ghpdqg ixqfwlrq iru lwv rxwsxw dw wlph w . m frqglwlrqdo rq wkh sulfh vhw dw

wlph w1

Frqvhtxhqwo|/ diwhu vwdqgdug pdqlsxodwlrqv/ wkh �uvw0rughu frqglwlrq dvvrfldwhg

wr wkh pd{lplvdwlrq ri +5;, lv jlyhq e|=

S W| +}, @

�

�� 4

H|

S"�'f +!�,

� b|n�b|

S "|n�\|n�|n�

H|

S"�'f +!�,

� b|n�b|

S "3�|n� \|n�

+5<,

47

zkhuh ""3� lv wkh vwhdg| vwdwh jurvv pdunxs1

Ilqdoo|/ vlqfh wkhuh lv qr �up0vshfl�f idfwruv lq xhqflqj sulflqj ghflvlrqv/ wkh

iudfwlrq +4� !, ri wkh uhwdlohuv wkdw dgmxvw lq w fkrrvhv wkh vdph qhz sulfh S W| dqg

wkh vdph ohyho ri rxwsxw/ dqg wkh dyhudjh sulfh ri �upv wkdw gr qrw dgmxvw lv vlpso|

odvw shulrg*v sulfh ohyho vfdohg e| odvw shulrg*v lq dwlrq +�|3�S|3�,1 Wkh g|qdplfv ri

wkh frqvxpswlrq0edvhg sulfh lqgh{ lv wkhq/;

S| @k! +�|3�S|3�,

�3" . +4� !,S W|�3"

l �

�3"= +63,

519 Ilvfdo dqg Prqhwdu| Srolf|

Zh qrz forvh wkh prgho e| vshfli|lqj wkh jryhuqphqw*v ehkdylrxu1 Wkh jryhuqphqw

frqgxfwv erwk �vfdo dqg prqhwdu| srolflhv1 Zh dvvxph wkdw h{rjhqhrxv jryhuqphqw

h{shqglwxuh +J|, duh �qdqfhg e| oxps0vxp wd{dwlrq/ dv zhoo dv prqh| dqg erqgv

fuhdwlrq1 Vlqfh zh gr qrw frqvlghu glvwruwlrqdu| wd{hv/ wkh jryhuqphqw idfhv wkh

iroorzlqj exgjhw frqvwudlqw=

J| @�| � �|3�

S|.

E|n�@ +4 . l|,�E|

S|. W| +64,

Wkh odz ri prwlrq iru jryhuqphqw vshqglqj lv jlyhq e|=

oq+J|, @�4� �}

�oq��J�. �} oq+J|3�, . %}|

zkhuh %}| lv d l1l1g1 jryhuqphqw vshqglqj vkrfn/ dqg �} ? 41

Zh dvvxph wkdw wkh vkruw uxq lqwhuhvw udwh +l|, lv wkh lqvwuxphqw sulylohjhg e|

prqhwdu| dxwkrulw|1 Wkh prqhwdu| dxwkrulw| dgrswv d ihhgedfn uxoh wkdw kdv wkh

qrplqdo udwh dgmxvw wr ghyldwlrqv ri hfrqrp|0zlgh lq dwlrq iurp lwv vwhdg| vwdwh

ydoxh dqg rxwsxw iurp lwv qdwxudo ydoxh/ l1h1 wkh htxloleulxp ohyho ri rxwsxw xqghu

frpsohwh sulfh h{lelolw| +\ ?| ,1 Lq dgglwlrq/ zh doorz iru sduwldo dgmxvwphqw wr fdswxuh

wkh lqwhuhvw udwh vprrwklqj wkdw vhhpv dssduhqw lq wkh gdwd1 Wkh ihhgedfn uxoh lv

jlyhq e|

+4 . l|, @ +4 . l|3�,��

%�S|S|3�

��Z�

\|\ ?|

��+&�3��

h{s�%�|�

+65,

zkhuh %�| lv dq l1l1g prqhwdu| srolf| vkrfn/ dqg #� 5 +3> 4, > #Z A 4 dqg #+ A 31

Zh fdq qrwlfh wkdw/

� hyhq wkrxjk wkh qrplqdo lqwhuhvw udwh lv wkh prqhwdu| srolf| wrro/ wkh ihhgedfn

uxoh lqgluhfwo| ghwhuplqhv �| vlqfh wkh fhqwudo edqn pxvw dgmxvw wkh prqh|

vxsso| wr vdwlvi| prqh| ghpdqg +htxdwlrq +:,,/ jlyhq wkh fkrlfh ri l|>;Vhh \xq +4<<9, ru Zrrgirug +5336,1

48

� lq htxloleulxp wkh h{fhvv ri vxsso| ri erqgv pxvw eh }hur= E| @ 31

6 Txdqwlwdwlyh Hydoxdwlrq

Wkh pdlq jrdo ri wklv vwxg| lv wr hydoxdwh wkh frqwulexwlrq ri lqwurgxflqj wkh vhdufk0

wkhruhwlf iudphzrun lqwr d prqhwdu| srolf| prgho1 Wrzdugv wklv hqg/ wklv vhfwlrq

hydoxdwhv wkh shuirupdqfh ri dowhuqdwlyh prghov ghshqglqj rq wkh dvvxphg ghjuhh ri

uljlglwlhv1 Zh suhvhqw rxu fkrlfh ri fdoleudwlrq dqg wkh frpsdulvrqv ehwzhhq prghov

dqg wkhlu hpslulfdo frxqwhusduwv xvlqj wkh xqfrqglwlrqdo vhfrqg prphqwv1 Ilqdoo|/

wkh lpsxovh uhvsrqvh ixqfwlrqv ri wkh vhohfwhg prgho duh frpsxwhg1 Wkh| vkrz

wkh wudqvplvvlrq phfkdqlvpv ri wkh vwuxfwxudo vkrfnv dqg looxvwudwh wkh g|qdplf

surshuwlhv ri wkh jhqhudo prgho1

614 Vroxwlrq dqg Prgho Sdudphwhulvdwlrq

Lq rughu wr jhw wkh prgho lq d wudfwdeoh irup iru frqgxfwlqj srolf| vlpxodwlrqv zh

qhhg wr orrn iru dq dssur{lpdwh dqdo|wlfdo vroxwlrq e| wudqviruplqj wkh prgho lqwr

d v|vwhp ri orj0olqhdu gl�huhqfh htxdwlrqv1 Wkh vwudwhj| lv wr xvh d �uvw rughu Wd|oru

dssur{lpdwlrq durxqg wkh vwhdg| vwdwh +zlwk }hur lq dwlrq, wr uhsodfh wkh htxdwlrqv

zlwk dssur{lpdwlrqv/ zklfk duh olqhdu lq wkh orj0ghyldwlrqv ri wkh yduldeohv1 Wkh

uhvxowlqj v|vwhp/ h{suhvvhg lq whupv ri shufhqwdjh ghyldwlrqv durxqg wkh vwhdg|0vwdwh

lv suhvhqwhg lq Dsshqgl{ E1

Zh wkhq vroyh wkh prgho xvlqj wkh phwkrgv ghyhorshg e| Dqghuvrq dqg Prruh

+4<;8, zklfk doorzv wr frpsxwh vroxwlrqv iru udwlrqdo h{shfwdwlrqv prghov1 Wkh dojr0

ulwkp ghwhuplqhv zkhwkhu wkh prgho kdv d xqltxh vroxwlrq/ dq lq�qlw| ri vroxwlrqv ru

qr vroxwlrqv dw doo/ dqg surgxfhv d pdwul{ frgli|lqj wkh olqhdu frqvwudlqwv jxdudqwhh0

lqj dv|pswrwlf frqyhujhqfh1 Wkh xqltxhqhvv ri vroxwlrqv wr wkh v|vwhp uhtxluhv wkdw

wkh wudqvlwlrq pdwul{ fkdudfwhul}lqj wkh olqhdu v|vwhp kdyh dq dssursuldwh qxpehu

ri h{sorvlyh dqg vwdeoh hljhqydoxhv +Eodqfkdug dqg Nkdq frqglwlrqv,1

Wkh sdudphwhu ydoxhv duh slqqhg grzq vr wkdw wkh hxur duhd prgho hfrqrp|

xfwxdwhv durxqg lwv vwdwlrqdu| vwdwh ryhu wkh shulrg 4<;8053331 Wkh fkrlfh ri wkh

shulrg ri fdoleudwlrq dqvzhuv d wzrirog dlp= dssrlqwlqj wkh orqjhvw shulrg zkloh

dyrlglqj wrr vljql�fdqw euhdnv1< Wkh hxur duhd gdwd uhwdlqhg iru wkh fdoleudwlrq

<Fdoleudwlrq lv xvhg lqvwhdg ri hvwlpdwlrq iru wzr uhdvrqv1 Iluvw/ Hxurshdq gdwd shuwdlqlqj wr

wkh oderxu pdunhw duh vhogrp frpsohwh +h1j1 krxuv zrunhg dqg ydfdqflhv duh xvxdoo| qrw dydlodeoh,1

Hvwlpdwlqj wkh prgho zlwk vxfk dq lqfrpsohwh gdwdvhw zrxog lqgxfh d ohyho ri sdudphwhu xqfhuwdlqw|

wkdw jrhv eh|rqg wkh dffhswdeoh olplwv1 Vhfrqg/ vlqfh wkh hxur duhd zdv fuhdwhg rqo| uhfhqwo|/

lwv ehkdylrxu fdq eh lqihuuhg iurp lwv sdvw udwkhu wkdq gluhfwo| hvwlpdwhg iurp wkh suhylrxv mrlqw

49

uhvxow iurp wkh �dxjphqwhg� gdwdedvh xvhg e| Idjdq/ Khqu| dqg Phvwuh +5334, iru

wkh Duhd Zlgh Prgho ri wkh HFE1 Wkh prgho lv fdoleudwhg wr txduwhuo| gdwd1

Wkh glvfrxqw udwh dqg wkh frh!flhqw ri uhodwlyh ulvn dyhuvlrq dsshdu lq vwdqgdug

GVJH prghov1 Wkh vxemhfwlyh glvfrxqw udwh � lv vhw htxdo wr 31<</ zklfk jlyhv dq

dqqxdo vwhdg| vwdwh uhdo lqwhuhvw udwh htxdo wr irxu shufhqw1 Zh dvvljq ydoxhv iru wkh

lqwhuwhpsrudo hodvwlflw| ri vxevwlwxwlrq +3=9, dqg hodvwlflw| ri oderxu ghvxwlolw| +3=75,

vlplodu wr wkrvh hvwlpdwhg e| Vphwv dqg Zrxwhuv +5336,1 Vdkxf +5335, ru Vphwv dqg

Zrxwhuv +5336, frqvlghuhg ydoxhv ri � udqjlqj iurp 318: wr 31<91 Khuh/ zh uhwdlq dq

lqwhuphgldwh ydoxh ri 3=:81

Frqfhuqlqj wkh pdwfklqj surfhvv dqg wkh oderxu pdunhw/ zh iroorz Shwurqjror dqg

Slvvdulghv +5334, vxuyh| ri hpslulfdo vwxglhv iru wkh Free0Grxjodv pdwfklqj ixqfwlrq

sdudphwhu dqg vhw � @ 3=81 Wkh uhodwlyh edujdlqlqj srzhu ri zrunhuv lv vhw wr � @ 3=8

vr wkdw hpsor|huv dqg zrunhuv kdyh wkh vdph edujdlqlqj vwuhqjwk1 Dffruglqj wr wkh

hxur duhd gdwd/ wkh QDLUX lv hvwlpdwhg dw ;19( zklfk lpsolhv d ydoxh iru �Q ri 31<471

Wkh vwhdg|0vwdwh ydoxh ri wkh vhsdudwlrq udwh lv jlyhq e| v @��( �X

�@�4� �X

�=

Dffruglqj wr wkh DZPgdwdedvh/ wkh vkduh ri jryhuqphqw vshqglqj lq wkh JGS��J@�\

�lv htxdo wr 49155( dqg wkh vkduh ri frqvxpswlrq lq JGS

��F@�\

�lv 95189(1 Wkh udwh

ri fdslwdo ghsuhfldwlrq lv vhw dw 5( lq rughu wr pdnh wkh vkduh ri lqyhvwphqw uhodwlyh wr

JGS��L@�\ @ 53=55(

�frpsdwleoh zlwk wkh frh!flhqw ri fdslwdo

��N@�\ @ <=9;

�1 Wkh

fdslwdo vkduh sdudphwhu zdv rewdlqhg e| hvwlpdwlqj d surgxfwlrq ixqfwlrq e| ROV1

Wkh hvwlpdwhg sdudphwhu frxog qrw uhmhfw � @ 3=681 Pruhryhu/ jxlghg e| wkh hpslu0

lfdo zrun ri Edvx dqg Nlpedoo +4<<:,/ zh vhw wkh hodvwlflw| ri pdujlqdo ghsuhfldwlrq

zlwk uhvshfw wr wkh xwlolvdwlrq udwh +g, wr xqlw|1

Wkh uhdfwlrq ixqfwlrq ri wkh prqhwdu| dxwkrulw| lv dvvxphg wr eh dq lqhuwldo

Wd|oru uxoh zlwk wkh xvxdo sdudphwhu ydoxhv +vhh Fodulgd hw do1/ 4<<;,= #� @ 3=<> #Z @

4=8 dqg #+ @ 3=81

Wkh ghjuhh ri qrplqdo uljlglw| ghwhuplqhg e| wkh iudfwlrq ri �upv wkdw gr qrw

dgmxvw wkhlu sulfh +!, dqg wkh ghjuhh ri uhdo uljlglw| hpdqdwlqj iurp wkh oderxu pdunhw

yld wkh wzr vwhdg|0vwdwh suredelolwlhv �� dqg �(/ duh pruh gl!fxow wr jdxjh1 Wkh| zloo

eh wdnhq dv iuhh sdudphwhuv dqg zh zloo xvh wkh furvv0fruuhodwlrqv wr dvvhvv sodxvleoh

ydoxhv1

Wdeoh 4 suhvhqwv dq ryhuylhz ri wkh ydoxhv ri wkh fdoleudwhg sdudphwhuv dv wkh|

zhuh xvhg lq wkh vlpxodwlrqv1

ehkdylrxu ri lwv phpehuv1 Pruhryhu/ wkh sureohpv ri djjuhjdwlrq dqg wkh hqwu| ri qhz phpehuv

pdnh wkh txdolw| ri wkh gdwd ghedwdeoh dqg uhtxluh dgglwlrqdo dgmxvwphqwv1

4:

615 Xqfrqglwlrqdo Vhfrqg Prphqwv

Dq lqirupdo dvvhvvphqw ri wkh txdqwlwdwlyh shuirupdqfh ri wkh prgho dqg g|qdplf

sursdjdwlrq phfkdqlvpv fdq eh frqgxfwhg e| frpsdulqj wkh vhfrqg prphqwv ri wkh

vlpxodwhg vhulhv ri fhuwdlq nh| pdfurhfrqrplf yduldeohv lpsolhg e| wkh ehqfkpdun

prgho zlwk wkhlu revhuydeoh frxqwhusduwv1 Wkdw dovr zloo hqdeoh xv wr hydoxdwh wkh

ghjuhhv ri qrplqdo dqg uhdo uljlglw| qhfhvvdu| iru wkh hxur duhd1

Wkh vdpsoh prphqwv duh frpsxwhg iru Krgulfn0Suhvfrww �owhuhg gdwd dqg zh xvh

Prqwh Fduor vlpxodwlrq ri wkh prgho wr surgxfh dq dyhudjh ri 43333 vlpxodwhg vhwv

ri wlph vhulhv zlwk ohqjwk ri 931 Zh vlpxodwhg wkh prgho iru irxu vhwv ri sdudphwhuv

ghshqglqj rq wkh ohyho ri sulfh dqg oderxu pdunhw uljlglwlhv=

41 Vshfl�fdwlrq 4= ! @ 3=:8 +sulfhv duh �{hg iru rqh |hdu,/ �( @ 3=8 +wkh gxudwlrq

ri xqhpsor|phqw lv 9 prqwkv, dqg �� @ 3=<8 +wkh gxudwlrq ri ydfdqflhv lv wkuhh

prqwkv,>

51 Vshfl�fdwlrq 5= ! @ 3=:8 +sulfhv duh �{hg iru rqh |hdu,/ �( @ 3=58 +wkh gxudwlrq

ri xqhpsor|phqw lv 45 prqwkv, dqg �� @ 3=8 +wkh gxudwlrq ri ydfdqflhv lv vl{

prqwkv,>

61 Vshfl�fdwlrq 6= ! @ 3=< +sulfhv duh �{hg iru wzr |hduv dqg d kdoi,/ �( @ 3=8 +wkh

gxudwlrq ri xqhpsor|phqw lv 9 prqwkv, dqg �� @ 3=<8 +wkh gxudwlrq ri ydfdqflhv

lv wkuhh prqwkv,>

71 Vshfl�fdwlrq 7= ! @ 3=< +sulfhv duh �{hg iru wzr |hduv dqg d kdoi,/ �( @ 3=58

+wkh gxudwlrq ri xqhpsor|phqw lv 45 prqwkv, dqg �� @ 3=8 +wkh gxudwlrq ri

ydfdqflhv lv vl{ prqwkv,1

Uhvxowv duh vkrzq lq Iljxuhv 4d wr 4g1 Wkh juh| eduv uhsuhvhqw wkh gdwd furvv

fruuhodwlrqv dqg wkh eodfn rqhv duh wkrvh lpsolhg e| wkh vlpxodwhg prgho1 Lw lv reylrxv

wkdw wkh prgho zlwk d vwdqgdug ghjuhh ri qrplqdo uljlglw| +! @ 3=:8, lv qrw deoh wr

jhqhudwh wkh vdpsoh g|qdplf furvv fruuhodwlrqv dowkrxjk dvvxplqj d kljkhu ghjuhh ri

uhdo uljlglw| lpsuryhv wkh jhqhudo �w ri wkh g|qdplf furvv fruuhodwlrqv1

Lq idfw/ zh kdyh uholhg rq d yhu| kljk ghjuhh ri sulfh uljlglw| +! @ 3=<, lq rughu

wr pdwfk wkh gdwd1 Rqh lpsruwdqw uhdvrq iru wkh uhodwlyho| kljk ghjuhh ri qrplqdo

vwlfnlqhvv lq sulfhv frphv iurp wkh idfw wkdw wkh vhqvlwlylw| ri pdujlqdo frvw wr rxwsxw

lv forvho| uhodwhg wr d �up*v delolw| wr dgmxvw lwv lqsxw1 Lq rxu prgho/ wkh wzr qrq0

suhghwhuplqhg yduldeohv +fdslwdo xwlolvdwlrq udwh dqg krxuv shu zrunhu, lqwurgxfh

dgglwlrqdo pdujlq e| zklfk �upv fdq uhvsrqg wr xqdqwlflsdwhg vkrfnv/ uhgxflqj wkh

h�hfw ri rxwsxw rq pdujlqdo frvw1 Lq rwkhu zrugv/ fdslwdo xwlolvdwlrq udwh dqg krxuv

4;

shu zrunhu uhvxow lq d dwwhqlqj ri wkh pdujlqdo frvw vfkhgxoh wkhuhe| lqwurgxflqj

wkh srvvlelolw| ri hqgrjhqrxv sulfh vwlfnlqhvv +h�hfw uhlqirufhg e| wkh dvvxpswlrq ri

frqvwdqw uhwxuqv wr vfdoh lq wkh surgxfwlrq ixqfwlrq,1 Rq wkh rwkhu kdqg/ vwdqgdug

vwlfn|0sulfh prghov zlwk fdslwdo duh vxemhfw wr lqfuhdvlqj vkruw0uxq pdujlqdo frvwv/

zklfk lq wxuq gdpshqv wkh uhvsrqvh ri rxwsxw1 Wkh uhdo h�hfw ri vkrfnv rq rxwsxw

lq vxfk prghov lv frqvhtxhqwo| zhdn/ dqg fdq rqo| eh dffrpsolvkhg e| dvvxplqj d

uhodwlyho| kljk ghjuhh ri qrplqdo uljlglw|1

Lq dgglwlrq/ zkhq zh lqwurgxfh kljk gxudwlrqv ri xqhpsor|phqw dqg ydfdqflhv

+vshfl�fdwlrq 7,/ wkh odj dqg ohdg furvv fruuhodwlrqv iru doprvw doo wkh yduldeohv lq wkh

prgho duh txlwh forvh wr wkrvh ri wkh gdwd/ erwk lq vljq dqg pdjqlwxgh1 Iru h{dpsoh/

zh fdq revhuyh wkdw frqvxpswlrq/ lqyhvwphqw/ dqg hpsor|phqw duh vwurqjo| surf|fol0

fdo zkloh fdslwdo ru lqwhuhvw udwhv duh df|folfdo1 Wkh prgho shuirupv uhdvrqdeo| zhoo

zlwk uhvshfw wr xqhpsor|phqw1

Fruuhodwlrqv ehwzhhq xqhpsor|phqw dqg rxwsxw duh jhqhudoo| frxqwhuf|folfdo dv

uh hfwhg e| wkh gdwd dqg wkh qhjdwlyh fruuhodwlrq ehwzhhq lq dwlrq dqg xqhpsor|0

phqw ghvfulehv d Skloolsv fxuyh uhodwlrq1 Wklv lv qrw vxusulvlqj dv lw lv d xvxdo ihdwxuh

lq prghov lqfoxglqj vkruw uxq qrq0qhxwudolw| ri prqh| dqg oderxu pdunhw vhdufk +vhh

iru h{dpsoh Fkìurq dqg Odqjrw/ 4<<</ ru Frroh| dqg Txdgulql/ 4<<<,1 Dv hpskd0

vl}hg lq wkh iruphu sdshu/ wkh vw|ol}hg idfw dvvrfldwhg zlwk wkh Skloolsv fxuyh lv ylhzhg

dv dq lpsruwdqw wrro lq wkh frqgxfw ri prqhwdu| srolf|1 Wkxv/ d prgho dlplqj dw

lqiruplqj wkh prqhwdu| srolf| ghedwh/ vxfk dv rxuv/ pxvw txdolwdwlyho| dffrxqw iru

wkh Skloolsv0fxuyh1

Dowkrxjk zh gr qrw kdyh d vhulhv ri ydfdqflhv/ Fkduw 5 ri wkh HFE grfxphqw

+5335/ s14:, doorzv xv wr vd| wkdw hxur duhd gdwd glvsod| d vwurqj qhjdwlyh fruuhod0

wlrq ehwzhhq ydfdqflhv dqg xqhpsor|phqw143 Wklv idfw lv uh hfwhg lq rxu vlpxodwhg

furvv fruuhodwlrqv +qrw uhsuhvhqwhg khuh exw dydlodeoh, dqg vr zhoo uhsuhvhqwhg e| rxu

wkhruhwlfdo prgho1 Wklv phdqv wkdw wkh pdwfklqj surfhvv dvvxpswlrq lv vx!flhqw wr

ghvfuleh wkh g|qdplf ri wkh iulfwlrqdo xqhpsor|phqw vxppdul}hg e| wkh Ehyhulgjh

fxuyh1

Krzhyhu/ wkh prvw vhulrxv zhdnqhvv ri wkh prgho zlwk vwdjjhuhg sulfh dqg oderxu

pdunhw vhdufk lv lwv lqdelolw| wr jhqhudwh wkh fruuhfw g|qdplf sdwwhuq iru uhdo zdjhv144

Frqwhpsrudqhrxvo|/ rqh fdq vhh wkdw zh idfh wkh xvxdo gl!fxow| ri oderxu pdunhw

vhdufk prgho wr dffrxqw iru wkh orz surf|folflw| ri uhdo zdjhv1 E| dgglqj h{whu0

43Wkh Ehyhulgjh fxuyh iru wkh hxur duhd surylghg e| wkh HFE lv sur{lhg e| wkh djjuhjdwh ri qlqh

frxqwulhv fryhulqj 97( ri wkh }rqh144Vklphu +5336, dujxhg wkdw d vhdufk dqg pdwfklqj prgho lq zklfk zdjhv duh ghwhuplqhg e| Qdvk

edujdlqlqj fdqqrw jhqhudwh vxevwdqwldo pryhphqwv dorqj d grzqzdug vorslqj Ehyhulgjh fxuyh lq

uhvsrqvh wr vkrfnv1

4<

qdo kdelw rq frqvxpswlrq zh kdyh h{shfwhg wkdw shuvlvwhqw frqvxpswlrq pryhphqw

zloo pdnh wkh pdujlqdo ghvxwlolw| ri zrun +lq whupv ri frqvxpswlrq, dqg wkxv uhdo

zdjhv ohvv surf|folfdo1 Xqiruwxqdwho|/ zdjhv duh vwloo wrr surf|folfdo1 Wkh glyhujhqfh

ehwzhhq gdwd dqg wkh prgho vxjjhvwv wkdw ixwxuh zrun frxog irfxv rq prgli|lqj

wkh zdjh htxdwlrq1 D phdq lv wr pdnh lw sduwldoo| edfnzdug0orrnlqj ru/ dv vkrzq

lq Fkìurq dqg Odqjrw +5335,/ doorzlqj iru qrq vhsdudeoh suhihuhqfhv ehhwzhhq frq0

vxpswlrq dqg ohlvxuh1

Ilqdoo|/ rqh fdq fdofxodwh d vlpsoh phdvxuh wr hydoxdwh wkh �w ri d g|qdplf

vwuxfwxudo hfrqrplf prgho lq xvlqj d prgl�hg urrw phdq vtxduhg huuru fulwhuld iru

wkh furvv0fruuhodwlrqv +fdoohg UPVHFF,1 Lw lv gh�qhg dv wkh urrw ri wkh vxp ri wkh

vtxduhg ri wkh gl�huhqfh ehwzhhq gdwd dqg prgho furvv0fruuhodwlrqv=

UPVHFF @

3Cyxxw 4

�

�[J'�

H[,'3H

kFruu

�{JKr&c| > {

JKr&c|n,

��Fruu

�{r�6&c| > {

r�6&c|n,

�l24Dzkhuh {r|@|e| @ i|r|@|e| > fr|@|e| > �r|@|e| > Lr|@|e| > qr|@|e| > xr|@|e| > lr|@|e| > zr|@|e

| > nr|@|e| j lv d yhfwru

ri revhuydeoh + vwdwh @ rev, ru vlpxodwhg + vwdwh @ vlp, yduldeohv/ R lv wkh qxpehu ri

yduldeohv lq {|/ o lv wkh qxpehu ri odjv dqg ohdgv ri wkh furvv0fruuhodwlrqv/ dqg � lv d

vfdoh sdudphwhu1 Wdeoh 5 surylghv d vxppdu| ri wkh UPVHFF iru wkh irxu vshfl�fd0

wlrqv1 Lq mxvw wkh vdph zd| dv vkrzq judsklfdoo|/ lw lv qrwlfhg wkdw wkh lqfuhdvh lq wkh

ghjuhh ri uhdo uljlglwlhv pdnhv lw srvvleoh wr ghfuhdvh wkh gl�huhqfhv ehwzhhq revhuyhg

dqg vlpxodwhg dxwrfruuhodwlrqv dssur{lpdwho| 8( +pdlqo| wkh fruuhodwlrqv uhodwhg wr

wkh oderxu pdunhw, dqg wkdw wkh lqfuhdvh lq wkh ghjuhh ri qrplqdo uljlglw| ghfuhdvhv

wkhp e| 48(1 Wklv frq�upv wkh fuxfldo dvshfw ri wkh ghjuhh ri sulfh uljlglw| dqg wkh

frpsohphqwdulw| ri wkh uljlglw| rq oderxu pdunhw1

Zh pdlqwdlq wkh vshfl�fdwlrq 7 lqgxflqj wkh kljkhvw ghjuhhv ri qrplqdo dqg uhdo

uljlglwlhv lq wkh iroorzlqj vxevhfwlrq1

616 Lpsxovh Uhvsrqvhv

Wklv vxevhfwlrq suhvhqwv wkh g|qdplfv ri wkh prgho dqg pruh vshfl�fdoo| wkh lpsxovh

uhvsrqvhv wr rqh0vwdqgdug ghyldwlrq vkrfnv wr doo wkh xqghuo|lqj prgho vkrfnv1 Wkh

lpsxovh uhsrqvhv duh ghslfwhg lq Iljxuhv 5 wkurxjk 81 Lq hdfk fdvh/ zh vlpxodwh wkh

uhvsrqvh wr d srvlwlyh lqqrydwlrq ri 4( lq wkh uhohydqw iruflqj yduldeoh*v surfhvv1 Wklv

ohdgv wr shuvlvwhqw lqfuhdvhv lq wkh ohyho ri lqwhuhvw udwh/ wkh ohyho ri whfkqrorj|/ wkh

ohyho ri jryhuqphqw vshqglqj dqg wkh ohyho ri suhihuhqfh/ zlwk wkh ghjuhh ri shuvlvwhqfh

ghshqglqj rq wkh DU +4, frh!flhqwv ri wkh uhohydqw vwrfkdvwlf surfhvvhv1

Wkh lpsxovh uhvsrqvh ixqfwlrqv frq�up wkh suhvhqfh ri erwk wkh Skloolsv fxuyh

dqg wkh Ehyhulgjh fxuyh1

53

61614 Prqhwdu| Srolf| Vkrfn

Iljxuh 5 uhsruwv wkh uhvsrqvhv wr dq lqfuhdvh lq wkh qrplqdo lqwhuhvw udwh1 Wklv vkrfn

lv d shuwxuedwlrq ri wkh prqhwdu| srolf| uxoh dqg wkhuhiruh/ lw wuljjhuv wkh lpsolhg

fruuhfwlrq phfkdqlvpv1

Iroorzlqj wklv vkrfn/ krxvhkrogv uhgxfh wkhlu frqvxphu vshqglqj +04(, dv wkh

uhdo lqwhuhvw udwh lqfuhdvhv +319(,1 Ilupv uhvsrqg wr wkh klnh lq lqwhuhvw udwh e|

vkduso| uhgxflqj wkhlu lqyhvwphqw vshqglqj +04;(, dqg ghfuhdvlqj krxuv shu zrunhu

+0515(, dqg fdslwdo xwlolvdwlrq udwkhu wkdq hpsor|phqw1 Wklv uhvxow fdq eh h{sodlqhg

e| wkh idfw wkdw krxuv duh wkh rqo| surgxfwlrq idfwru zklfk lv qrw suhghwhuplqhg1

Wklv fdxvhv d odujh ghfuhdvh lq pdujlqdo frvw1 Lq whupv ri frqwulexwlrqv wr JGS/ wkh

ghfolqh lq lqyhvwphqw lv vwurqjhu wkdq wkdw lq frqvxpswlrq1 Lq dwlrq ghfuhdvhv vorzo|

gxh wr sulfh uljlglwlhv1

Vlqfh ydfdqflhv uh hfw uhfuxlwlqj h�ruwv dqg pryh lq uhvsrqvh wr wkh h{shfwdwlrq

ri wkh sur�wdelolw| ri d vxffhvvixo pdwfk/ wkh| gurs +0;(, iroorzlqj wkh ghfuhdvh lq wkh

pdujlqdo frvw +0818(,1 Krzhyhu/ zh fdq qrwlfh wkdw wklv yduldeoh lv wkh �uvw wr vwduw

lwv �qdo kxps vkdsh sdwwhuq1 Wkh idoo lq hpsor|phqw +0316(, lqgxfhv dq lqfuhdvh

ri wkh suredelolw| wkdw d ydfdqf| lv �oohg/ zklfk whqgv wr lqfuhdvh h{shfwhg sur�wv

dqg wkhq ydfdqflhv1 Wklv h�hfw grplqdwhv rqo| diwhu vrph shulrgv zklfk h{sodlqv

wkh sduwlfxodu g|qdplfv ri ydfdqflhv1 Dv hpskdvl}hg e| Fkìurq dqg Odqjrw +5335,/

uhdo zdjhv h{shulhqfh d odujh ghfuhdvh +0:18(, ehfdxvh wkhlu g|qdplfv lv vwurqjo|

surf|folfdo dqg pruh suhflvho| lq rxu prgho/ wkh| duh wrr vwurqjo| uhodwhg wr wkh

ydfdqflhv0xqhpsor|phqw udwlr1

Doo yduldeohv ghfd| vorzo| edfn wr wkhlu vwhdg|0vwdwh ydoxhv/ dqg wkh g|qdplf

uhvsrqvhv glvsod| wkh w|slfdo kxps vkdshg sdwwhuq1

Dv zh kdyh mxvw vhhq lw/ d nh| phfkdqlvp lv wkdw �upv pdlqo| dgmxvw wrwdo krxuv

+Q|K|, yld krxuv shu zrunhu +wkh lqwhqvlyh pdujlq,1 Dowkrxjk wklv h�hfw lv wrr

lpsruwdqw lq rxu vwxg| dqg frqwudu| wr zkdw pdq| shrsoh vd|/ lw lv qrw glvfrqqhfwhg

iurp uhdolw|1 Dv Iljxuh 9 iru wkh wkuhh odujhu frxqwulhv ri wkh hxur duhd vkrzv lw/

wkh hyroxwlrq ri wkh dqqxdo jurzwk udwh ri krxuv zrunhg lv dv yrodwloh dv wkdw ri

hpsor|phqw145

61615 Whfkqrorj| Vkrfn

Iljxuh 6 vkrzv wkh h�hfwv ri dq lpsuryhphqw lq wrwdo idfwru surgxfwlylw|1 Wkh rxw0

sxw uhvsrqvh lv dxwrpdwlfdoo| dqg txlfno| srvlwlyh dqg nhhsv exloglqj xs judgxdoo|

45Dv zh mxvw kdyh dqqxdo dqg qrw txduwhuo| gdwd/ zh kdyh qrw ehhq deoh wr frpsduh wkh hpslulfdo

krxuv2rxwsxw fruuhodwlrqv zlwk wkrvh jhqhudwhg e| wkh prgho1

54

+31;8(,1 Wkh vkrfn udlvhv frqvxpswlrq +318(, vlqfh krxvhkrogv lqfuhdvh wkhlu vshqg0

lqj1 Wkhlu uhdo zdjhv duh lqgh{hg wr surgxfwlylw| dqg lqfuhdvhg judgxdoo| exw vljqli0

lfdqwo| +4(,1 Dv qrwhg ehiruh/ wkh| iroorz ixuwkhupruh wkh ydfdqflhv0xqhpsor|phqw

udwlr/ wkxv frq�uplqj wkh suhfhglqj phfkdqlfdo h�hfw1

Vlqfh rxwsxw ulvhv e| ohvv wkdq srwhqwldo rxwsxw/ wkh uhvxowlqj qhjdwlyh rxwsxw

jds sxwv grzqzdug suhvvxuh rq sulfhv/ zklfk doorzv wkh prqhwdu| dxwkrulwlhv wr

uhgxfh lqwhuhvw udwh1 Khqfh/ prqhwdu| srolf| lv dffrpprgdwlqj/ dqg sulfhv gr qrw

fkdqjh pxfk +wkh uhvsrqvh ri lq dwlrq lv qhjdwlyh +03136(, dqg h{klelwv shuvlvwhqfh,1

Lqyhvwphqw dqg ydfdqflhv dovr ulvh e| 516( dqg 4(/ uhvshfwlyho|1

Wzr ihdwxuhv pxvw eh qrwhg frqfhuqlqj wkh hpsor|phqw g|qdplfv1 Iluvw/ jlyhq

wkdw wkh dprxqw ri qrplqdo sulfh uljlglw| lpsduwhg e| wkh qrplqdo dqg uhdo iulfwlrqv

lv yhu| vxevwdqwldo/ �upv fdq phhw wkhlu ghpdqg zlwk ohvv oderxu lqsxw +wrwdo krxuv

idoo +0318(,, jlyhq wkh lqfuhdvh lq surgxfwlylw|1 Rxu prgho lv wkhq frqvlvwhqw zlwk

wkh �qglqjv ri Jdol +4<<<, rq RHFG frxqwulhv dqg Vphwv dqg Zrxwhuv +5336, rq

hxur duhd gdwd1 Frqwudu| wr wkh Grwvh|*v +5335, fodlp/ rqh fdq surgxfh d qhjdwlyh

fruuhodwlrq ehwzhhq surgxfwlylw| dqg wrwdo krxuv lq wkh suhvhqfh ri dq lqwhuhvw udwh

uxoh dqg vwlfn| sulfhv1 Vhfrqg/ frqwudu| wr wkh hylghqfh/ �upv pdlqo| dgmxvw wrwdo

krxuv yld lqglylgxdo krxuv dqg qrw yld hpsor|phqw1

61616 Vkrfn wr Jryhuqphqw Vshqglqj

Iljxuh 7 sorwv wkh g|qdplf uhvsrqvhv ri vhohfwhg yduldeohv wr d vkrfn wr jryhuqphqw

frqvxpswlrq1 Vxfk d vkrfn dozd|v udlvhv rxwsxw +3147(,/ zlwk pruh shuvlvwhqw vkrfnv

ohdglqj wr juhdwhu lqfuhdvhv1 Wkdw lv/ zh revhuyh pxowlsolhu h�hfwv zlwk shuvlvwhqw

jryhuqphqw vshqglqj vkrfnv1 Qhjdwlyh lqwhuhvw udwh h�hfwv eulqj sulydwh frqvxpswlrq

ehorz lwv vwhdg| vwdwh ydoxh +03139(, wkrxjk iroorzlqj d kxps0vkdshg sdwwhuq +gxh

wr wkh suhvhqfh ri kdelw irupdwlrq,/ dqg wkhq frqvxpswlrq judgxdoo| uhwxuqv wr lwv

vwhdg| vwdwh ydoxh1 Xqghu wkh ghpdqg vkrfn/ wkhuh h{lvwv dq h{fhvv ghpdqg lq wkh

jrrgv pdunhw dw wkh suhydlolqj lqwhuhvw udwh/ dqg wkh lqwhuhvw udwh pxvw jr xs wr fohdu

wkh jrrgv pdunhw +31345(,1 Wkhq/ fdslwdo vwrfn dqg lqyhvwphqw idoo +03137( dqg

�3155(/ uhvshfwlyho|,1

Zlwk d srvlwlyh lqfrph h�hfw rq ohlvxuh/ shuvlvwhqw fkdqjhv lq jryhuqphqw vshqg0

lqj dozd|v kdyh d srvlwlyh h�hfw rq wrwdo krxuv zrunhg1 Exw krxuv shu zrunhu dqg hp0

sor|phqw uhvsrqg gl�huhqwo|1 Krxuv zrunhg duh ghwhuplqhg e| qhjrfldwlrq zkhuhdv

hpsor|phqw lv ghwhuplqhg e| mre ghvwuxfwlrq dqg fuhdwlrq lq wkh oderxu pdunhw1

Fkdqjhv lq hpsor|phqw lq wklv prgho ghshqg fuxfldoo| rq wkh ghflvlrq e| wkh �up wr

fuhdwh d ydfdqw mre dw vrph frvw1 Dq lqfuhdvh lq jryhuqphqw vshqglqj xqdpeljxrxvo|

udlvhv krxuv zrunhg shu zrunhu +3144(,/ exw pd| lqfuhdvh ru ghfuhdvh wkh hpsor|0

55

phqw1 Wkh �up lqfuhdvhv ru ghfuhdvhv mre rshqlqjv edvhg rq wkh h{shfwhg ydoxh ri

d kluhg zrunhu wr wkh �up1 D kljkhu ydoxh ri d kluhg zrunhu wr wkh �up hqfrxudjhv

wkh �up wr fuhdwh pruh ydfdqflhv1 Wkh wzr idfwruv d�hfwlqj wkh ydoxh duh wkh uhdo

lqwhuhvw udwh dqg wkh joredo vxusoxv lq hdfk shulrg1 Zh revhuyh wkdw hyhq wkrxjk wkh

joredo vxusoxv lqfuhdvhv lq uhvsrqvh wr d ghpdqg vkrfn/ wkh qhjdwlyh uhdo lqwhuhvw udwh

h�hfw rq wkh ydoxh ri d kluhg zrunhu vwloo grplqdwhv wkh srvlwlyh hfrqrplf uhqw h�hfw/

wkxv ydfdqflhv ghfuhdvh +0313;(, mxvw olnh wkh hpsor|phqw +031338(,1

61617 Suhihuhqfh Vkrfn

Iljxuh 8 uhsruwv wkh uhvsrqvhv wr d suhihuhqfh vkrfn1 Wkh vkrfn dfwv gluhfwo| rq

frqvxpswlrq e| lqfuhdvlqj lw e| 3159( dqg pdnhv lw srvvleoh wr lqfuhdvh rxwsxw e|

314;(1 Zh qrwlfh wkdw wkh suhihuhqfh vkrfn kdv d vwurqjhu lpsdfw rq rxwsxw wkdq

wkh jryhuqphqw vshqglqj vkrfn1

Mxvw olnh wkh suhfhglqj ghpdqg vkrfn/ lw lv fohdu wkdw lqfuhdvhg ryhudoo ghpdqg

sxwv xszdug suhvvxuh rq uhdo idfwru sulfhv/ uhdo pdujlqdo frvw/ dqg lq dwlrq1 Lq

rughu wr vwhp wkhvh lq dwlrqdu| suhvvxuhv/ wkh uhdo lqwhuhvw udwh ulvhv lqgxflqj d

vljql�fdqw qhjdwlyh furzglqj0rxw h�hfw rq lqyhvwphqw +�3188(,1 Wkh lqfuhdvh lq

fdsdflw| qhfhvvdu| wr pdwfk wkh lqfuhdvhg ghpdqg ghulyhv iurp d ulvh lq wkh xwlolvdwlrq

ri lqvwdoohg fdslwdo +vr d ghfuhdvh lq fdslwdo gxulqj vhyhudo shulrgv, dqg dq lqfuhdvh

lq wrwdo krxuv1

Khuh djdlq/ wkh pdwfklqj phfkdqlvp wkdw ghwhuplqhv hpsor|phqw lpsolhv dq

lqfuhdvh lq krxuv shu zrunhu +3137(, dqg lq hpsor|phqw +3134(, dv vhyhudo YDU

prghov vxjjhvw lw lq wkh olwhudwxuh1

617 Vrph Ohvvrqv iru Prqhwdu| Srolf|

Ehiruh frqfoxglqj/ zh kdyh wr foduli| wzr lpsruwdqw srlqwv iru wkh prqhwdu| srolf|

ghflvlrqv1

Iluvw/ vlqfh wkh lqwurgxfwlrq ri oderxu pdunhw iulfwlrqv kdv d vwurqj lpsdfw rq

wkh ryhudoo g|qdplfv ri wkh prgho/ wkh srolf| uhfrpphqgdwlrqv fdq ydu| d juhdw ghdo

dffruglqj wr zkhwkhu d prgho zlwkrxw oderxu pdunhw uljlglwlhv ru d pruh frpsohwh rqh

lv xvhg dv d srolf| jxlgh1 Wkh suhylrxv vwxg| ri wkh furvv0fruuhodwlrqv dqg wkh uhvsrqvh

ixqfwlrqv kdv doorzhg wr ghprqvwudwh wkdw wkh lqwurgxfwlrq ri iulfwlrqv rwkhu wkdq

wkrvh rq wkh pdunhw ri jrrgv h{dfhuedwhv wkh hqgrjhqrxv shuvlvwhqfh1 Frqvhtxhqwo|/

wkh prqhwdu| dxwkrulwlhv zklfk xvhg d prgho zlwkrxw oderxu pdunhw uljlglwlhv zrxog

kdyh doo wkh fkdqfhv wr eh plvwdnhq lq prgli|lqj wkhlu lqwhuhvw udwh1 Wkh vwdelolvdwlrq

ri wkh hfrqrp| zrxog eh pxfk orqjhu wkdq wkdq wkh| krshg1

56

Vhfrqg/ wkh frpsdulvrq ri vhyhudo prqhwdu| srolf| uxohv jlyhv vrph lqwhuhvwlqj

uhvxowv1 Zh duh lqwhuhvwhg lq frpsdulqj wkuhh uxohv= +4, dq lq dwlrq wdujhwlqj uxoh/

+5, wkh Wd|oru0w|sh uxoh uhwdlqhg xqwlo qrz/ dqg +6, dq dxjphqwhg Wd|oru0w|sh uxoh=

+4, l| @ #�l|3� . +4� #�, ^#Z�|` . %�|

+5, l| @ #�l|3� . +4� #�,�#Z�| . #+ +|| � |?| ,

�. %�|

+6, l| @ #�l|3� . +4� #�,�#Z�| . #+ +|| � |?| , . #� +x| � x?| ,

�. %�|

Iljxuh : vkrzv wkh uhvsrqvhv ri rxwsxw/ lq dwlrq/ hpsor|phqw dqg lqwhuhvw udwh

iroorzlqj wkh wzr hfrqrplf srolf| vkrfnv1 Wkh gdvkhg olqhv uhvsrqvhv duh wkrvh ri

wkh prgho lqfoxglqj dq lq dwlrq wdujhwlqj uxoh/ wkh vrolg olqhv duh wkrvh ri rxu prgho/

dqg wkh grwwhg olqh duh wkrvh ri wkh prgho lqfoxglqj wkh xqhpsor|phqw0dxjphqwhg

Wd|oru0w|sh uxoh1

Rqh fdq kljkoljkw wkh idfw wkdw dq lq dwlrq wdujhwlqj uxoh jlyhv zruvh uhvxowv

lq whupv ri vwdelolvdwlrq wkdq d Wd|oru0w|sh uxoh1 Wklv lv qrw d qhz uhvxow vlqfh

lw lv reylrxv wkdw dgglqj dgglwlrqqdo yduldeohv lq d uxoh doorzv lpsuryhg vwdelolvlqj

surshuwlhv1 Krzhyhu/ dv vkrzq lq Iljxuh ;/ wr sxw d pruh lpsruwdqw zhljkw rq

wkh rxwsxw jlyhv ehwwhu uhvxowv +vhh iru h{dpsoh wkh uxoh hvwlpdwhg e| Vdkxf/ 5335,1

Pruhryhu/ dv lq wkh fdvh zkhq lw frphv iurp wr wkh �qdqfldo pdunhw/ rqh pd| zrqghu

zkhwkhu wkh prqhwdu| dxwkrulwlhv vkrxog lqfoxgh d oderxu pdunhw vodfn yduldeoh/ vxfk

dv wkh xqhpsor|phqw udwh/ lq wkhlu prqhwdu| srolf| uxoh1 Rxu vlpxodwlrqv vxjjhvw

wkdw wkh lqwurgxfwlrq ri wkh xqhpsor|phqw udwh lq wkh uxoh +zlwk wkh vdph zhljkw dv

wkh rxwsxw iru h{dpsoh, voljkwo| khosv wr dfklhyh idvwhu lq dwlrq vwdelolvdwlrq dqg kdv

qr vljql�fdwlyh h�hfw rq wkh rwkhu yduldeohv vwdelolvdwlrq1 Ilqdoo|/ zh fdq vd| wkdw

dxjphqwlqj wkh uxoh zlwk d oderxu pdunhw yduldeoh lv qrw vshfldoo| dq lpsuryhphqw1

7 Vxppdu| dqg Frqfoxglqj Uhpdunv

Suhylrxv zrunv xvlqj frpshwlwlyh GVJH prgho kdyh surylghg uhdvrqdeoh ghvfulswlrqv

ri wkh gdwd rq uhdo yduldeohv1 Krzhyhu/ vxfk zrunv glg qrw fdswxuh dw doo ru edgo| wkh

oderxu pdunhw ihdwxuhv dowkrxjk zh nqrz wkdw wkh ixqfwlrqlqj ri wkh oderxu pdunhw

d�hfwv exvlqhvv f|foh g|qdplfv dqg lv fuxfldo iru prqhwdu| srolf| ghflvlrqv1 Lw zrxog

dsshdu lpshudwlyh wr prgho xqhpsor|phqw dv wkh rxwfrph ri dq htxloleulxp surfhvv1

Wklv sdshu dlpv dw �oolqj wklv jds lq ghyhorslqj dq rswlplvlqj0edvhg prqhwdu|

srolf| prgho zlwk fdslwdo/ vwlfn| sulfhv/ dqg d qrq0zdoudvldq oderxu pdunhw lq wkh

irup ri d vlpsoh oderxu pdunhw vhdufk phfkdqlvp1 Wklv hqdeohv xv wr vwxg| wkh

uhvshfwlyh uroh ri oderxu pdnhw iulfwlrqv dqg qrplqdo iulfwlrqv lq dffrxqwlqj iru wkh

hpslulfdo vhfrqg prphqwv revhuyhg rq hxur duhd gdwd1

57

Zh kdyh vkrzq wkdw wkh xqfrqglwlrqqdo vhfrqg prphqwv jhqhudwhg e| wkh fdol0

eudwhg prgho duh forvh wr wkrvh lq wkh hxur duhd/ h{fhsw iru wkh uhdo zdjh g|qdplfv/

zkhq erwk d kljk ghjuhh ri qrplqdo dqg oderxu pdunhw iulfwlrqv duh dvvxphg1 Wklv

lqglfdwhv wkdw oderxu pdunhw iulfwlrqv gr qrw dfw dv d vxevwlwxwh iru qrplqdo uljlglwlhv

exw dv d qhfhvvdu| frpsohphqw1 Wkxv/ dv lq Vphwv dqg Zrxwhuv +5336,/ rxu prgho lv

qrw deoh wr dguhvv wkh vkruwfrplqj ri uhtxlulqj dq lpsodxvleoh ghjuhh ri sulfh uljlglw|

lq rughu wr pdwfk gdwd1

Frqwudu| wr wkh iruphu sdshu/ rxu prgho doorzv wkh srvvlelolw| wr lqyhvwljdwh

wkh wkhruhwlfdo ghwhuplqdqwv ri wkh h{whqvlyh dqg lqwhqvlyh pdujlqv rq wkh oderxu

pdunhw1 Xqiruwxqdwho|/ zh duh qrw deoh wr pdwfk wkh xvxdo hpslulfdo YDU uhvsrqvhv

ri lqglylgxdo krxuv zrunhg uhodwlyh wr hpsor|phqw1 Lqghhg/ zh �qg wkdw krxuv shu

zrunhu lv wrr grplqdqw dv d ohdglqj lqglfdwru lq wkh vhqvh wkdw wkhlu yrodwlolw| lv

juhdwhu wkdq wkdw ri hpsor|phqw1 Lq uhvsrqvh wr d vwuxfwxudo vkrfn/ krxuv shu zrunhu

duh wkh fuxfldo yduldeoh ri dgmxvwphqw iru �upv1 Rq wklv vlgh/ lqwurgxflqj d yduldeoh

fdslwdo xwlolvdwlrq udwh khosv wr vroyh sduw ri wklv zhdnqhvv vlqfh krxuv zrunhg duh qr

orqjhu wkh rqo| qrq0suhghwhuplqhg surgxfwlrq idfwru1

Zh kdyh vkrzq wkh delolw| ri rxu prgho wr uhsurgxfh wkh oderxu pdunhw vw|ol}hg

idfwv fkdudfwhul}hg e| wkh Ehyhulgjh dqg Skloolsv fxuyhv/ exw dovr lwv lqdelolw| wr jhq0

hudwh wkh revhuyhg uhdo zdjh sdwwhuq1 Doorzlqj iru frqvxpswlrq gl�huhqfhv ehwzhhq

xqhpsor|hg dqg hpsor|hg djhqw fdq khos xv wr fruuhfw wklv gudzedfn/ dv vkrzq lq

Fkìurq dqg Odqjrw +5335,1

Ilqdoo|/ lw pljkw eh lqwhuhvwlqj iru ixuwkhu uhvhdufk wr xvh wklv w|sh ri prgho wr

lqyhvwljdwh wkh lpsdfw ri oderxu pdunhw iulfwlrqv rq wkh ghulydwlrq ri wkh rswlpdo

prqhwdu| srolf|/ dqg/ pruh sduwlfxoduo| wkhlu h�hfwv rq wkh joredo zhoiduh1

58

Dsshqgl{ D= Uhdo Zdjh dqg Krxuv Zrunhg Ghulydwlrqv

Ohw 8| eh wkh ydoxh ixqfwlrq ri wkh �up lq shulrg w1 Iru d zdjh Z| wkh �up*v

h{shfwhg uhwxuq iurp d mre lv jlyhq e| wkh pdujlqdo ydoxh ri hpsor|phqw=

C 8|

CQ|@ +4� �,

|\|Q|

�Z|K| . ��|n��|

CQ|n�

CQ|

C 8|n�

CQ|n�

@ +4� �,|\|Q|

�Z|K| . ��|n��|

+4� v,C 8

|n�

CQ|n�

@ +4� �,|\|Q|

�Z|K| .)

� |+4� v, +66,

Ohw M| eh wkh ydoxh ixqfwlrq ri wkh krxvhkrog lq shulrg w1 Wkh krxvhkrog*v

h{shfwhg uhwxuq iurp d mre lv jlyhq e| wkh pdujlqdo ydoxh ri hpsor|phqw=

C M|

CQ|@ �|Z|K| � %R|

�?�? . 4

+K|,j?n�

j? . �CQ|n�

CQ|

C M|n�

CQ|n�

@ �|Z|K| � %R|�?

�? . 4+K|,

j?n�

j? . � +4� v� (|,C M

|n�

CQ|n�+67,

D uhdol}hg mre pdwfk |lhogv vrph sxuh hfrqrplf uhqw/ zklfk lv htxdo wr wkh vxp ri

wkh h{shfwhg vhdufk frvwv ri wkh �up dqg wkh zrunhu1 Zh dvvxph wkdw wkh prqrsro|

uhqw lv vkduhg dffruglqj wr wkh Qdvk vroxwlrq wr d edujdlqlqj sureohp1 Wkh uhdo zdjh

lv wkhq ghwhuplqhg dffruglqj wr wkh pd{lplvdwlrq ri wkh iroorzlqj Qdvk fulwhulrq

zkhuh wkh vxsoxv ri hdfk djhqwv lv jlyhq e| wkh pdujlqdo ydoxh ri xqhpsor|phqw

phdvxuhg lq whup ri frqvxpswlrq jrrgv=

Z| @ dujpd{t`|�

�C M

|

�|CQ|

�1 �C 8

|

CQ|

�E�31�

+68,

Wkh �uvw rughu frqglwlrq jlyhv wkh iroorzlqj vxusoxv vkdulqj uxoh=

�C 8

|

CQ|@ +4� �,

C M|

�|CQ|+69,

Lwhudwlqj +69, rqh shulrg lq wkh ixwxuh dqg pxowlso|lqj e|�

�|zh rewdlq=

��H|

#�|n�C

8|n�

�|CQ|n�

$@ +4� �,�H|

#C M

|n�

�|CQ|n�

$+6:,

Xvlqj wkh idfw wkdw �H|

#�|n��|

C 8|n�

CQ|n�

$@

)

� |/ zh kdyh=

)

� |@

+4� �,

��

C M|n�

�|CQ|n�+6;,

59

E| frpelqlqj wklv odvw h{suhvvlrq zlwk wkh h{suhvvlrqv ri wkh vxusoxvhv dqg wkh

vkdulqj uxoh zh fdq ghulyh wkh zdjh h{suhvvlrq=

Z| @ �

�+4� �,

|\|Q|K|

.)

K|

Y|X|

�. +4� �,

#%R|

�? +K|,�

j?

+�? . 4,�|

$+6<,

Wkhq krxuv zrunhg duh ghwhuplqhg e| pd{lplvlqj wkh mrlqw vxusoxv +V|,/

V| @C M

|

�|CQ|.

C 8|

CQ|+73,

vr wkh �uvw rughu frqglwlrq lv

CV|CK|

@ +4� �,2|\|Q|K|

� %R|�|

Ck

j?j?n�

+K|,j?n�

j?

lCK|

@ 3 +74,

Ilqdoo|/ zh rewdlq=

+4� �,2|\|Q|K|

@ %R|K

�

j?

|

�|+75,

5:

Dsshqgl{ E= Wkh Orj0Olqhdulvhg Prgho

� Frqvxpswlrq

af| @ �af|3� . ^+4� �,�S`�a%R| � a�|

�� Hxohu htxdwlrq

a�| @ H|a�|n� .a~| � H|a�|n�

� Lq dwlrq

a�| @4

4 . �a�|3� .

�

4 . �H|a�|n� .

+4� �!, +4� !,

+4 . �,!a|

� Krxuvak| @

4

+4� �,a|| � �

+4� �,

�en| . ay|�� 4

+4� �,a%@| � aq|

� Fdslwdo dffxpxodwlrq

an|n� @�4� ��

�an| . ��

�eL| � gay|�

� Djjuhjdwh frqvwudlqw

a|| @�F�\af| .

�L�\eL| . �J

�\aj| .

) �Y�\

ay|

� Lqyhvwphqw

aL| @

��

��

�\�N.

�+4� ��,

��

��H|

a�|n� � a�|�.

�� \

�� N

�H|

a|n� . H|a||n��

��

�4 .

� ��\

�� N

�H|

an|n� . an| . gay| � g

�4 .�

�

�H|ay|n� . �H| aL|n�

� Hpsor|phqw

aq|n� @ +4� v, aq| . v ap|

� Pdujlqdo frvwv

a| @+4 . �?,

�?ak| � a�| � a|| . aq| .a%R|

� Mre ydfdqflhv

ay| @ ap| .�� +4� �, ��\

) �Q

�H|

a|n� . H|a||n� � H|aq|n��. H|

a�|n� � a�|

.�+4� v, +H|ay|n� � H| ap|n�,� �� Z �K

)

�H| az|n� . H|

ak|n��

5;

� Fdsdflw| xwlolvdwlrq

ay| @4

g

�a| . a|| � an|

�� Xqhpsor|phqw

ax| @ ��Q�Xaq|

� Zdjhv

az| @� +4� �, ��\

�Z �K �Q

�a| . a|| � aq|

�� ?+4� �,+4� �,2 ��\

+4 . �?, �Z �K �Q

�a�| � a%R|

�.

�+4� �,+4� �,2 ��\

+4 . �?, �Z �K �Q� � +4� �, ��\

�Z �K �Q� �) �Y

�Z �K �X

�ak|

.�) �Y�Z �K �X

+ay| � ax|,

� Jryhuqphqw vshqglqj

aj| @ �}aj|3� . %}|

� Lqwhuhvw udwh uxoh

a~| @ #�a~|3� . +4� #�,�#Za�| . #+ +a|| � a|?| ,

�. %�|

� Pdwfklqj ixqfwlrq

ap| @ �ax| . +4� �, ay|

� Suhihuhqfh vkrfn

a%R| @ �Ra%R|3� . h�c|

� Whfkqrorj| vkrfn

a%@| @ �@a%@|3� . h2c|

5<

Uhihuhqfhv

^4` Dqghuvrq/ J1/ Prruh/ J1/ 4<;81 D olqhdu dojheudlf surfhgxuh iru vroylqj olqhdu

shuihfw iruhvljkw prghov/ Hfrqrplfv Ohwwhuv 4:/ 57:05851

^5` Dqgroidwwr/ G1/ 4<<91 Exvlqhvv f|fohv dqg oderxu pdunhw vhdufk/ Dphulfdq Hfr0

qrplf Uhylhz ;9/ 44504651

^6` Edvx/ V1/ Nlpedoo/ P1/ 4<<:1 F|folfdo surgxfwlylw| zlwk xqrevhuyhg lqsxw yduld0

wlrq/ Zrunlqj Sdshu q�8<48/ QEHU1

^7` Ehuwrod/ J1/ 4<<<1 Oderxu pdunhwv lq wkh hxurshdq xqlrq/ plphr/ Xqlyhuvlwã gl

Wrulqr1

^8` Eodqfkdug/ R1/ Gldprqg/ S1/ 4<;<1 Wkh Ehyhulgjh fxuyh/ Eurrnlqjv Sdshuv rq

Hfrqrplf Dfwlylw| 4/ 40:91

^9` Erogulq/ P1/ Fkulvwldqr/ O1/ Ilvkhu/ M1/ 53331 Kdelw shuvlvwhqfh/ dvvhw uhwxuqv

dqg wkh exvlqhvv f|foh/ Uhvhdufk ghsduwphqw vwd� uhsruw q�5;3/ Ihghudo Uhvhuyh

Edqn ri Plqqhdsrolv1

^:` Fdglrx/ O1/ Jxlfkdug/ V1/ 4<<<1 Od glyhuvlwì ghv pdufkìv gx wudydlo hq hxursh =

txhoohv frqvìtxhqfhv srxu o*xqlrq prqìwdluh/ 4ëuh sduwlh/ Grfxphqw gh Wudydlo

q�<<043/ FHSLL1

^;` Fdglrx/ O1/ Jxlfkdug/ V1/ Pdxuho/ P1/ 4<<<1 Od glyhuvlwì ghv pdufkìv gx wudydlo

hq hxursh = txhoohv frqvìtxhqfhv srxu o*xqlrq prqìwdluh/ 5ëph sduwlh/ Grfxphqw

gh Wudydlo q�<<044/ FHSLL1

^<` Fdoyr/ J1/ 4<;61 Vwdjjhuhg sulfhv lq d xwlolw|0pd{lpl}lqj iudphzrun/ Mrxuqdo ri

Prqhwdu| Hfrqrplfv 45/ 6;606<;1

^43` Fkìurq/ D1/ Odqjrw/ I1/ 4<<<1 Wkh Skloolsv dqg Ehyhulgjh fxuyhv uhylvlwhg/ Hfr0

qrplfv Ohwwhuv 9</ 6:406:91

^44` Fkìurq/ D1/ Odqjrw/ I1/ 53351 Oderxu pdunhw vhdufk dqg uhdo exvlqhvv f|fohv=

uhfrqflolqj Qdvk edujdlqlqj zlwk wkh uhdo zdjh g|qdplfv/ plphr/ Xqlyhuvlwì gx

Pdlqh1

^45` Fkulvwldqr/ O1/ Hlfkhqedxp/ P1/ Hydqv/ F1/ 53341 Qrplqdo uljlglwlhv dqg wkh

g|qdplf h�hfwv ri d vkrfn wr prqhwdu| srolf|/ Zrunlqj Sdshu q�533403;/ Ihghudo

Uhvhuyh Edqn ri Fklfdjr1

63

^46` Fodulgd/ U1/ Jdol/ M1/ Jhuwohu/ P1/ 4<<<1 Wkh vflhqfh ri prqhwdu| srolf|= d qhz

nh|qhvldq shuvshfwlyh/ Mrxuqdo ri Hfrqrplf Olwhudwxuh 6:/ 499404:3:1

^47` Fodulgd/ U1/ Jdol/ M1/ Jhuwohu/ P1/ 4<<;1 Prqhwdu| srolf| uxohv lq sudfwlfh= vrph

lqwhuqdwlrqdo hylghqfh/ hxurshdq Hfrqrplf Uhylhz 75/ 43660439:1

^48` Frroh|/ W1/ Txdgulql/ Y1/ 4<<<1 D Qhrfodvvlfdo prgho ri wkh Skloolsv fxuyh uhod0

wlrq/ Mrxuqdo ri Prqhwdu| Hfrqrplfv 77/ 49804<61

^49` ghq Kddq/ Z1/ Udph|/ J1/ Zdwvrq/ M1/ 53331 Mre ghvwuxfwlrq dqg sursdjdwlrq

ri vkrfnv/ Dphulfdq Hfrqrplf Uhylhz <3/ 7;507<;1

^4:` Grwvh|/ P1/ 53351 Vwuxfwxuh iurp vkrfnv/ Hfrqrplf Txduwhuo| ri wkh Ihghudo

Uhvhuyh Edqn ri Ulfkprqg ;;/ 6:07:1

^4;` HFE/ 53351 Oderxu pdunhw plvpdwfkhv lq hxur duhd frxqwulhv/ pdufk1

^4<` Idjdq/ J1/ Khqu|/ M1/ Phvwuh/ U1/ 53341 Dq duhd0zlgh prgho +DZP, iru wkh

hxur0duhd/ Zrunlqj Sdshu q�75/ hxurshdq Fhqwudo Edqn1

^53` Ixkuhu/ M1/ 53331 Kdelw irupdwlrq lq frqvxpswlrq dqg lwv lpsolfdwlrqv iru

prqhwdu|0srolf| prghov/ Dphulfdq Hfrqrplf Uhylhz <3/ 69:06<31

^54` Jdol/ M1/ 4<<<1 Whfkqrorj|/ hpsor|phqw/ dqg wkh exvlqhvv f|foh= gr whfkqrorj|

vkrfnv h{sodlq djjuhjdwh xfwxdwlrqvB/ Dphulfdq Hfrqrplf Uhylhz ;</ 57<05:41

^55` Jhuwohu/ P1/ Jlofkulvw/ V1/ 53331 Kxps0vkdshg rxwsxw lq d udwlrqdo h{shfwdwlrqv

iudphzrun= wkh uroh ri lqyhvwphqw ghod|v/ plphr/ Qhz0\run Xqlyhuvlw|1

^56` Jrrgiulhqg/ P1/ Nlqj/ U1/ 4<<:1 Wkh qhz Qhrfodvvlfdo v|qwkhvlv dqg wkh uroh ri

prqhwdu| srolf|/ QEHU Pdfurhfrqrplfv Dqqxdo/ PLW Suhvv/ Fdpeulgjh PD1

^57` Kdoo/ U1H1/ 4<<<1 Oderxu pdunhw iulfwlrqv dqg hpsor|phqw xfwxdwlrqv1 Lq=

Wd|oru/ M1/ Zrrgirug/ P1 +Hgv1,/ Kdqgerrn ri Pdfurhfrqrplfv/ yro 6/ Qruwk0

Kroodqg/ Dpvwhugdp1

^58` Nlqj/ U1/ Uhehor/ V1/ 4<<<1 Uhvxvflwdwlqj uhdo exvlqhvv f|fohv/ Lq= Wd|oru/ M1/

Zrrgirug/ P1 +Hgv1,/ Kdqgerrn ri Pdfurhfrqrplfv/ yro 6/ Qruwk0Kroodqg/ Dp0

vwhugdp1

^59` Phu}/ P1/ 4<<81 Vhdufk lq wkh oderxu pdunhw dqg wkh uhdo exvlqhvv f|foh/ Mrxuqdo

ri Prqhwdu| Hfrqrplfv 69/ 59<06331

64

^5:` Phu}/ P1/ \dvkly/ H1/ 53361 Wkh ydoxh ri oderu dqg wkh pdunhw ydoxh ri �upv/

plphr/ Xqlyhuvlw| ri Erqq1

^5;` Qhlvv/ N1/ Qhovrq/ H1/ 53351 Wkh uhdo lqwhuhvw udwh jds dv dq lq dwlrq lqglfdwru/

Pdfurhfrqrplfv G|qdplfv :/ 56<05951

^5<` Shwurqjror/ E1/ Slvvdulghv/ F1/ 53341 Orrnlqj lqwr wkh eodfn er{= d vxuyh| ri wkh

pdwfklqj ixqfwlrq/ Mrxuqdo ri Hfrqrplf Olwhudwxuh 6;/ 6<307641

^63` Slvvdulghv/ F1/ 53331 Htxloleulxp Xqhpsor|phqw Wkhru|/ Eodfnzhoo/ R{irug1

^64` Vdkxf/ M0J1/ 53351 D ck|eulg* prqhwdu| srolf| prgho= hylghqfh iurp wkh hxur

duhd/ Dssolhg Hfrqrplfv Ohwwhuv </ <7<0<881

^65` Vklphu/ U1/ 53361 Wkh f|folfdo ehkdylru ri htxloleulxp xqhpsor|phqw dqg yd0

fdqflhv= hylghqfh dqg wkhru|/ plphr/ Sulqfhwrq Xqlyhuvlw|1

^66` Vphwv/ I1/ Zrxwhuv/ U1/ 53361 Dq hvwlpdwhg g|qdplf vwrfkdvwlf jhqhudo htxlole0

ulxp prgho ri wkh hxur duhd/ Mrxuqdo ri wkh hxurshdq Hfrqrplf Dvvrfldwlrq 4/

4456044:81

^67` \xq/ W1/ 4<<91 Qrplqdo sulfh uljlglw|/ prqh| vxsso| hqgrjhqhlw|/ dqg exvlqhvv

f|fohv/ Mrxuqdo ri Prqhwdu| Hfrqrplfv 6:/ 67806:31

^68` Zdovk/ F1/ 53361 Oderxu pdunhw vhdufk/ vwlfn| sulfhv/ dqg lqwhuhvw udwh srolflhv/

plphr/ Xqlyhuvlw| ri Fdoliruqld1

^69` Zrrgirug/ P1/ 53361 Lqwhuhvw dqg Sulfhv= Irxqgdwlrqv ri d Wkhru| ri Prqhwdu|

Srolf|/ Sulqfhwrq Xqlyhuvlw| Suhvv1

65

Wdeoh 4Hxur duhd prgho fdoleudwlrq

Ghvfulswlrq Sdudphwhu Txduwhuo| Ydoxh

Lqwhuwhpsrudo hodvwlflw| ri vxevwlwxwlrq �S 31:73

Hodvwlflw| ri zrun h�ruw �? 31753

Glvfrxqw idfwru � 31<<3

Kdelw irupdwlrq sdudphwhu � 31:83

Suredelolw| ri qrw uhvhwwlqj sulfh ! 31:83031<33

Fdslwdo vkduh � 31683

Udwh ri ghsuhfldwlrq � 31353

Sulfh hodvwlflw| ri ghpdqg � 44

Fdslwdo dgmxvwphqw frvw sdudphwhu � 9

Xwlolvdwlrq udwh hodvwlflw| g 4

Ydfdqf| frvw sdudphwhu ) 31433

Edujdlqlqj srzhu � 31833

Hodvwlflw| lq wkh pdwfklqj ixqfwlrq � 31833

Odjjhg lqwhuhvw udwh frh!flhqw lq wkh uxoh #� 31<33

Lq dwlrq frh!flhqw lq wkh uxoh #Z 41833

Rxwsxw jds frh!flhqw lq wkh uxoh #+ 31833

Xqhpsor|phqw udwh X 313;9

DU+4, sdudphwhu/ suhihuhqfh vkrfn �R 31;83

DU+4, sdudphwhu/ whfkqrorj| vkrfn �@ 31<83

DU+4, sdudphwhu/ jryhuqhphqw vshqglqj vkrfn �} 31<83

Yduldqfh ri wkh lqwhuhvw udwh vkrfn �20� 31433

Yduldqfh ri wkh suhihuhqfh vkrfn �20R 31683

Yduldqfh ri wkh whfkqrorj| vkrfn �20@ 31933

Yduldqfh ri wkh jryhuqphqw vshqglqj vkrfn �20} 31633

66

Wdeoh 5Wkh UPVHFF fulwhuld

Prgho Phdq Yduldqfh Jdlq

Vshfl�fdwlrq 4+ehqfkpdun,

431<37 71;75 0

Vshfl�fdwlrq 5 4316;5 71:3; 8135;(

Vshfl�fdwlrq 6 <174: 51539 481:<4(

Vshfl�fdwlrq 7 <1563 41:75 4;146:(

67

Ilj1 4d1 Frpsdulvrq ri furvv fruuhodwlrqv ri wkh GVJH prgho dqg wkh gdwd1+Vshfl�fdwlrq 4,1

68

Ilj1 4e1 Frpsdulvrq ri furvv fruuhodwlrqv ri wkh GVJH prgho dqg wkh gdwd1+Vshfl�fdwlrq 5,1

69

Ilj1 4f1 Frpsdulvrq ri furvv fruuhodwlrqv ri wkh GVJH prgho dqg wkh gdwd1+Vshfl�fdwlrq 6,1

6:

Ilj1 4g1 Frpsdulvrq ri furvv fruuhodwlrqv ri wkh GVJH prgho dqg wkh gdwd1+Vshfl�fdwlrq 7,1

6;

Ilj1 51 Uhvsrqvhv wr d prqhwdu| srolf| vkrfn1

Ilj1 61 Uhvsrqvhv wr d whfkqrorj| vkrfn1

6<

Ilj1 71 Uhvsrqvhv wr d jryhuqphqw vshqglqj vkrfn1

Ilj1 81 Uhvsrqvhv wr d suhihuhqfh vkrfn1

73

Ilj1 91 Dqqxdo jurzwk udwh ri wkh krxuv zrunhg dqg hpsor|phqw1Vrxufh= Exuhdx ri Oderxu Vwdwlvwlfv

74

Ilj1 :1 G|qdplf uhvsrqvhv ri vhyhudo uxohv1

Ilj1 ;1 G|qdplf uhvsrqvhv dffruglqj wr wkh zhljkw rq rxwsxw lq wkh uxoh1

75

Notes d'Études et de Recherche

1. C. Huang and H. Pagès, “Optimal Consumption and Portfolio Policies with an InfiniteHorizon: Existence and Convergence,” May 1990.

2. C. Bordes, « Variabilité de la vitesse et volatilité de la croissance monétaire : le casfrançais », février 1989.

3. C. Bordes, M. Driscoll and A. Sauviat, “Interpreting the Money-Output Correlation: Money-Real or Real-Real?,” May 1989.

4. C. Bordes, D. Goyeau et A. Sauviat, « Taux d'intérêt, marge et rentabilité bancaires : le casdes pays de l'OCDE », mai 1989.

5. B. Bensaid, S. Federbusch et R. Gary-Bobo, « Sur quelques propriétés stratégiques del’intéressement des salariés dans l'industrie », juin 1989.

6. O. De Bandt, « L'identification des chocs monétaires et financiers en France : une étudeempirique », juin 1990.

7. M. Boutillier et S. Dérangère, « Le taux de crédit accordé aux entreprises françaises : coûtsopératoires des banques et prime de risque de défaut », juin 1990.

8. M. Boutillier and B. Cabrillac, “Foreign Exchange Markets: Efficiency and Hierarchy,”October 1990.

9. O. De Bandt et P. Jacquinot, « Les choix de financement des entreprises en France : unemodélisation économétrique », octobre 1990 (English version also available on request).

10. B. Bensaid and R. Gary-Bobo, “On Renegotiation of Profit-Sharing Contracts in Industry,”July 1989 (English version of NER n° 5).

11. P. G. Garella and Y. Richelle, “Cartel Formation and the Selection of Firms,” December1990.

12. H. Pagès and H. He, “Consumption and Portfolio Decisions with Labor Income andBorrowing Constraints,” August 1990.

13. P. Sicsic, « Le franc Poincaré a-t-il été délibérément sous-évalué ? », octobre 1991.

14. B. Bensaid and R. Gary-Bobo, “On the Commitment Value of Contracts underRenegotiation Constraints,” January 1990 revised November 1990.

15. B. Bensaid, J.-P. Lesne, H. Pagès and J. Scheinkman, “Derivative Asset Pricing withTransaction Costs,” May 1991 revised November 1991.

16. C. Monticelli and M.-O. Strauss-Kahn, “European Integration and the Demand for BroadMoney,” December 1991.

17. J. Henry and M. Phelipot, “The High and Low-Risk Asset Demand of French Households: AMultivariate Analysis,” November 1991 revised June 1992.

18. B. Bensaid and P. Garella, “Financing Takeovers under Asymetric Information,” September1992.

19. A. de Palma and M. Uctum, “Financial Intermediation under Financial Integration andDeregulation,” September 1992.

20. A. de Palma, L. Leruth and P. Régibeau, “Partial Compatibility with Network Externalitiesand Double Purchase,” August 1992.

21. A. Frachot, D. Janci and V. Lacoste, “Factor Analysis of the Term Structure: a ProbabilisticApproach,” November 1992.

22. P. Sicsic et B. Villeneuve, « L'afflux d'or en France de 1928 à 1934 », janvier 1993.

23. M. Jeanblanc-Picqué and R. Avesani, “Impulse Control Method and Exchange Rate,”September 1993.

24. A. Frachot and J.-P. Lesne, “Expectations Hypothesis and Stochastic Volatilities,” July 1993revised September 1993.

25. B. Bensaid and A. de Palma, “Spatial Multiproduct Oligopoly,” February 1993 revisedOctober 1994.

26. A. de Palma and R. Gary-Bobo, “Credit Contraction in a Model of the Banking Industry,”October 1994.

27. P. Jacquinot et F. Mihoubi, « Dynamique et hétérogénéité de l'emploi en déséquilibre »,septembre 1995.

28. G. Salmat, « Le retournement conjoncturel de 1992 et 1993 en France : une modélisationVAR », octobre 1994.

29. J. Henry and J. Weidmann, “Asymmetry in the EMS Revisited: Evidence from the CausalityAnalysis of Daily Eurorates,” February 1994 revised October 1994.

30. O. De Bandt, “Competition Among Financial Intermediaries and the Risk of ContagiousFailures,” September 1994 revised January 1995.

31. B. Bensaid et A. de Palma, « Politique monétaire et concurrence bancaire », janvier 1994révisé en septembre 1995.

32. F. Rosenwald, « Coût du crédit et montant des prêts : une interprétation en terme de canallarge du crédit », septembre 1995.

33. G. Cette et S. Mahfouz, « Le partage primaire du revenu : constat descriptif sur longuepériode », décembre 1995.

34. H. Pagès, “Is there a Premium for Currencies Correlated with Volatility? Some Evidencefrom Risk Reversals,” January 1996.

35. E. Jondeau and R. Ricart, “The Expectations Theory: Tests on French, German andAmerican Euro-rates,” June 1996.

36. B. Bensaid et O. De Bandt, « Les stratégies “stop-loss” : théorie et application au ContratNotionnel du Matif », juin 1996.

37. C. Martin et F. Rosenwald, « Le marché des certificats de dépôts. Écarts de taux àl'émission : l'influence de la relation émetteurs-souscripteurs initiaux », avril 1996.

38. Banque de France - CEPREMAP - Direction de la Prévision - Erasme - INSEE - OFCE,« Structures et propriétés de cinq modèles macroéconomiques français », juin 1996.

39. F. Rosenwald, « L'influence des montants émis sur le taux des certificats de dépôts »,octobre 1996.

40. L. Baumel, « Les crédits mis en place par les banques AFB de 1978 à 1992 : une évaluationdes montants et des durées initiales », novembre 1996.

41. G. Cette et E. Kremp, « Le passage à une assiette valeur ajoutée pour les cotisationssociales : Une caractérisation des entreprises non financières “gagnantes” et “perdantes” »,novembre 1996.

42. S. Avouyi-Dovi, E. Jondeau et C. Lai Tong, « Effets “volume”, volatilité et transmissionsinternationales sur les marchés boursiers dans le G5 », avril 1997.

43. E. Jondeau et R. Ricart, « Le contenu en information de la pente des taux : Application aucas des titres publics français », juin 1997.

44. B. Bensaid et M. Boutillier, « Le contrat notionnel : efficience et efficacité », juillet 1997.

45. E. Jondeau et R. Ricart, « La théorie des anticipations de la structure par terme : test à partirdes titres publics français », septembre 1997.

46. E. Jondeau, « Représentation VAR et test de la théorie des anticipations de la structure parterme », septembre 1997.

47. E. Jondeau et M. Rockinger, « Estimation et interprétation des densités neutres au risque :Une comparaison de méthodes », octobre 1997.

48. L. Baumel et P. Sevestre, « La relation entre le taux de crédits et le coût des ressourcesbancaires. Modélisation et estimation sur données individuelles de banques », octobre 1997.

49. P. Sevestre, “On the Use of Banks Balance Sheet Data in Loan Market Studies : A Note,”October 1997.

50. P.-C. Hautcoeur and P. Sicsic, “Threat of a Capital Levy, Expected Devaluation and InterestRates in France during the Interwar Period,” January 1998.

51. P. Jacquinot, « L’inflation sous-jacente à partir d’une approche structurelle des VAR : uneapplication à la France, à l’Allemagne et au Royaume-Uni », janvier 1998.

52. C. Bruneau et O. De Bandt, « La modélisation VAR structurel : application à la politiquemonétaire en France », janvier 1998.

53. C. Bruneau and E. Jondeau, “Long-Run Causality, with an Application to InternationalLinks between Long-Term Interest Rates,” June 1998.

54. S. Coutant, E. Jondeau and M. Rockinger, “Reading Interest Rate and Bond FuturesOptions’ Smiles: How PIBOR and Notional Operators Appreciated the 1997 French SnapElection,” June 1998.

55. E. Jondeau et F. Sédillot, « La prévision des taux longs français et allemands à partir d’unmodèle à anticipations rationnelles », juin 1998.

56. E. Jondeau and M. Rockinger, “Estimating Gram-Charlier Expansions with PositivityConstraints,” January 1999.

57. S. Avouyi-Dovi and E. Jondeau, “Interest Rate Transmission and Volatility Transmissionalong the Yield Curve,” January 1999.

58. S. Avouyi-Dovi et E. Jondeau, « La modélisation de la volitilité des bourses asiatiques »,janvier 1999.

59. E. Jondeau, « La mesure du ratio rendement-risque à partir du marché des euro-devises »,janvier 1999.

60. C. Bruneau and O. De Bandt, “Fiscal Policy in the Transition to Monetary Union: AStructural VAR Model,” January 1999.

61. E. Jondeau and R. Ricart, “The Information Content of the French and German GovernmentBond Yield Curves: Why Such Differences?,” February 1999.

62. J.-B. Chatelain et P. Sevestre, « Coûts et bénéfices du passage d’une faible inflation à lastabilité des prix », février 1999.

63. D. Irac et P. Jacquinot, « L’investissement en France depuis le début des années 1980 », avril1999.

64. F. Mihoubi, « Le partage de la valeur ajoutée en France et en Allemagne », mars 1999.

65. S. Avouyi-Dovi and E. Jondeau, “Modelling the French Swap Spread,” April 1999.

66. E. Jondeau and M. Rockinger, “The Tail Behavior of Stock Returns: Emerging VersusMature Markets,” June 1999.

67. F. Sédillot, « La pente des taux contient-elle de l’information sur l’activité économiquefuture ? », juin 1999.

68. E. Jondeau, H. Le Bihan et F. Sédillot, « Modélisation et prévision des indices de prixsectoriels », septembre 1999.

69. H. Le Bihan and F. Sédillot, “Implementing and Interpreting Indicators of Core Inflation: TheFrench Case,” September 1999.

70. R. Lacroix, “Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part I,”December 1999.

71. R. Lacroix, “Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II,”December 1999.

72. R. Lacroix, “Testing the Null Hypothesis of Stationarity in Fractionally Integrated Models,”December 1999.

73. F. Chesnay and E. Jondeau, “Does correlation between stock returns really increase duringturbulent period?,” April 2000.

74. O. Burkart and V. Coudert, “Leading Indicators of Currency Crises in Emerging Economies,”May 2000.

75. D. Irac, “Estimation of a Time Varying NAIRU for France,” July 2000.

76. E. Jondeau and H. Le Bihan, “Evaluating Monetary Policy Rules in Estimated Forward-Looking Models: A Comparison of US and German Monetary Policies,” October2000.

77. E. Jondeau and M. Rockinger, “Conditional Volatility, Skewness, ans Kurtosis: Existenceand Persistence,” November 2000.

78. P. Jacquinot et F. Mihoubi, « Modèle à Anticipations Rationnelles de la COnjonctureSimulée : MARCOS », novembre 2000.

79. M. Rockinger and E. Jondeau, “Entropy Densities: With an Application to AutoregressiveConditional Skewness and Kurtosis,” January 2001.

80. B. Amable and J.-B. Chatelain, “Can Financial Infrastructures Foster EconomicDevelopment? ,” January 2001.

81. J.-B. Chatelain and J.-C. Teurlai, “Pitfalls in Investment Euler Equations,” January 2001.

82. M. Rockinger and E. Jondeau, “Conditional Dependency of Financial Series: An Applicationof Copulas,” February 2001.

83. C. Florens, E. Jondeau and H. Le Bihan, “Assessing GMM Estimates of the Federal ReserveReaction Function,” March 2001.

84. J.-B. Chatelain, “Mark-up and Capital Structure of the Firm facing Uncertainty,” June 2001.

85. B Amable, J.-B. Chatelain and O. De Bandt, “Optimal capacity in the Banking Sector andEconomic Growth,” June 2001.

86. E. Jondeau and H. Le Bihan, “Testing for a Forward-Looking Phillips Curve. AdditionalEvidence from European and US Data,” December 2001.

87. G. Cette, J. Mairesse et Y. Kocoglu, « Croissance économique et diffusion des TIC : le cas dela France sur longue période (1980-2000) », décembre 2001.

88. D. Irac and F. Sédillot, “Short Run Assessment of French Economic activity Using OPTIM,”January 2002.

89. M. Baghli, C. Bouthevillain, O. de Bandt, H. Fraisse, H. Le Bihan et Ph. Rousseaux, « PIBpotentiel et écart de PIB : quelques évaluations pour la France », juillet 2002.

90. E. Jondeau and M. Rockinger, “Asset Allocation in Transition Economies,” October 2002.

91. H. Pagès and J.A.C Santos, “Optimal Supervisory Policies and Depositor-Preferences Laws,”October 2002.

92. C. Loupias, F. Savignac and P. Sevestre, “Is There a Bank Lending Channel in France ?Evidence from Bank Panel Data,” November 2002.

93. M. Ehrmann, L. Gambacorta, J. Martínez-Pagés, P. Sevestre and A. Worms, “Financialsystems and The Role in Monetary Policy transmission in the Euro Area,” November 2002.

94. S. Avouyi-Dovi, D. Guégan et S. Ladoucette, « Une mesure de la persistance dans les indicesboursiers », décembre 2002.

95. S. Avouyi-Dovi, D. Guégan et S. Ladoucette, “What is the Best Approach to Measure theInterdependence between Different Markets? ,” December 2002.

96. J.-B. Chatelain and A. Tiomo, “Investment, the Cost of Capital and Monetray Policy in theNineties in France: A Panel Data Investigation,” December 2002.

97. J.-B. Chatelain, A. Generale, I. Hernando, U. von Kalckreuth and P. Vermeulen, “FirmInvestment and Monetary Policy Transmission in the Euro Area,” December 2002.

98. J.-S. Mésonnier, « Banque centrale, taux de l’escompte et politique monétaire chez HenryThornton (1760-1815) », décembre 2002.

99. M. Baghli, G. Cette et A. Sylvain, « Les déterminants du taux de marge en France et quelquesautres grands pays industrialisés : Analyse empirique sur la période 1970-2000 », janvier2003.

100. G. Cette and C. Pfister, “The Challenges of the “New Economy” for Monetary Policy,”January 2003.

101. C. Bruneau, O. De Bandt, A. Flageollet and E. Michaux, “Forecasting Inflation usingEconomic Indicators: the Case of France,” May 2003.

102. C. Bruneau, O. De Bandt and A. Flageollet, “Forecasting Inflation in the Euro Area,” May2003.

103. E. Jondeau and H. Le Bihan, “ML vs GMM Estimates of Hybrid Macroeconomic Models(With an Application to the “New Phillips Curve”),” September 2003.

104. J. Matheron and T.-P. Maury, “Evaluating the Fit of Sticky Price Models,” January 2004.

105. S. Moyen and J.-G. Sahuc, “Incorporating Labour Market Frictions into an Optimising-BasedMonetary Policy Model,” January 2004.

Pour tous commentaires ou demandes sur les Notes d'Études et de Recherche, contacter la bibliothèque du Centre derecherche à l'adresse suivante :

For any comment or enquiries on the Notes d'Études et de Recherche, contact the library of the Centre de recherche at thefollowing address :

BANQUE DE FRANCE41-1391 - Centre de recherche75049 Paris Cedex 01tél : (0)1 42 92 49 55fax : (0)1 42 92 62 92email : [email protected]

Documents

NOTES D’ÉTUDES ET DE RECHERCHE - Publications · / phqw | sor p h q r hv glwl l j l u w h pdun xu r ode i r hv f qvhtxhq fr h k w w h \1 n u r z dph piu oleulx rxwsxwdqglq