Duration Dependent UI Payments and Equilibrium Unemployment

Gxudwlrq Ghshqghqw XL Sd|phqwv dqg
Htxloleulxp Xqhpsor|phqw
Phoy|q Frohv
Dguldq Pdvwhuv
Xqlyhuvlw| ri Hvvh{
Xqlyhuvlw| ri Hvvh{
Qryhpehu 5334
Devwudfw
Wklv sdshu ghyhorsv d g|qdplfdoo| frqvlvwhqw prgho ri htxloleulxp xqhp0
sor|phqw zkhq xqhpsor|phqw lqvxudqfh +XL, sd|phqwv duh gxudwlrq ghshq0
ghqw1 Dvvxplqj wkdw wkh jryhuqphqw grhv qrw revhuyh mre rhuv/ wkhuh lv d
prudo kd}dug sureohp dv wkh rswlrq ri uhfhlylqj ixuwkhu XL sd|phqwv zkloh
xqhpsor|hg glvwruwv mre vhhnhu uhvhuydwlrq zdjhv1 H{whqglqj wkh gxudwlrq ri
XL sd|phqwv/ zkloh kroglqj wkh jhqhurvlw| ri wkh vfkhph frqvwdqw/ lqfuhdvhv
wkh glvwruwlrq rq uhvhuydwlrq zdjhv dw doo gxudwlrqv1 Vlpxodwlrqv vxjjhvw wkdw
wkh djjuhjdwh glvwruwlrq e| prylqj iurp d 9 prqwk XL vfkhph wr d rqh0|hdu
vfkhph lv uhodwlyho| vpdoo1 Krzhyhu/ dq lqghqlwh sd|phqw vfkhph kdv d odujh
lpsdfw rq htxloleulxp xqhpsor|phqw1
Nh| Zrugv= Htxloleulxp Xqhpsor|phqw/ Pdwfklqj/ Edujdlqlqj
MHO Fodvvlfdwlrq= M97/ M98/ M74
Fruuhvsrqglqj dxwkru= Ghsduwphqw ri Hfrqrplfv Xqlyhuvlw| ri Hvvh{/ Zlyhqkrh Sdun/ Frofk0
hvwhu/ FR7 6VT Hqjodqg1 dpdvwhChvvh{1df1xn
4
4
Lqwurgxfwlrq
Wklv sdshu ghyhorsv d g|qdplfdoo| frqvlvwhqw prgho ri htxloleulxp xqhpsor|phqw
zkhq xqhpsor|phqw lqvxudqfh ^XL` sd|phqwv duh gxudwlrq ghshqghqw1 Dvvxplqj
wkdw wkh jryhuqphqw grhv qrw revhuyh mre rhuv/ wkhuh lv d prudo kd}dug sureohp
dv wkh rswlrq ri uhfhlylqj ixuwkhu XL sd|phqwv zkloh xqhpsor|hg glvwruwv mre vhhnhu
uhvhuydwlrq zdjhv1 Dowkrxjk vxfk uhvhuydwlrq zdjh glvwruwlrqv duh zhoo nqrzq lq wkh
vhtxhqwldo vhdufk olwhudwxuh ^h1j1 Pruwhqvhq +4<::,/ ydq ghq Ehuj +4<<3,`/ lw kdv qrw
ehhq srvvleoh wr hpehg wkdw vwuxfwxuh zlwk gxudwlrq ghshqghqw XL sd|phqwv lqwr dq
htxloleulxp iudphzrun1 E| lqvwhdg frqvlghulqj dq h{0srvw zdjh edujdlqlqj prgho/
wklv sdshu qrw rqo| fdswxuhv wkh lpsdfw ri fkdqjlqj wkh gxudwlrq ri XL sd|phqwv rq
zrunhu uhvhuydwlrq zdjhv/ lw lv wkh uvw wr frpsxwh lwv lpsdfw rq htxloleulxp xqhp0
sor|phqw1 Wkh qglqj lv wkdw iru qdwxudo sdudphwhu ydoxhv/ h{whqglqj wkh gxudwlrq
ri XL sd|phqwv zkloh kroglqj wkh jhqhurvlw| ri wkh vfkhph frqvwdqw/ lqfuhdvhv wkh
glvwruwlrq rq uhvhuydwlrq zdjhv dw doo gxudwlrqv1 Vlpxodwlrqv vxjjhvw wkdw wkh djjuh0
jdwh glvwruwlrq e| prylqj iurp d 9 prqwk vfkhph wr d rqh0|hdu vfkhph lv uhodwlyho|
vpdoo1 Krzhyhu/ dq lqghqlwh sd|phqw vfkhph kdv d odujh lpsdfw rq htxloleulxp
xqhpsor|phqw ohyhov1 Vxfk d uhvxow dsshduv frqvlvwhqw zlwk wkh hpslulfdo qglqjv ri
Qlfnhoo +4<<:,1
Wkh lqvljkwv rhuhg duh d vljqlfdqw dgydqfh rq suhylrxv zrun rq wklv lvvxh1 Wkh
xvxdo dujxphqw iru uhgxflqj wkh gxudwlrq ri XL sd|phqwv lv wkdw wkh jryhuqphqw
qhhgv wr hqfrxudjh juhdwhu vhdufk hruw e| lqglylgxdo mre vhhnhuv1 Exw Dwnlqvrq dqg
Plfnhozuljkw +4<<4, dujxh wkdw vxfk hhfwv duh qrw odujh lq wkh X1N1 dqg fdqqrw
h{sodlq wkh odujh ulvh lq X1N1 xqhpsor|phqw vlqfh wkh 4<:3*v1 Qhyhuwkhohvv/ wkh furvv
frxqwu| hylghqfh ^h1j1 Qlfnhoo +4<<:,` hvwdeolvkhv wkdw glhuhqfhv lq XL v|vwhpv kdyh
d odujh pdfur0lpsdfw rq xqhpsor|phqw1 Wklv vxjjhvwv wkdw wkh fhqwudo fkdqqho e|
zklfk d XL v|vwhp glvwruwv d pdunhw hfrqrp| lv pruh olnho| wr eh wkurxjk glvwruwlqj
5
htxloleulxp zdjhv wkdq wkurxjk uhgxflqj mre vhdufk hruw1 Wkh dujxphqw khuh lv
qrw wkdw wkh jryhuqphqw zlvkhv wr hqfrxudjh juhdwhu vhdufk hruw/ udwkhu lw qhhgv wr
plqlplvh wkh zdjh glvwruwlrqv lqkhuhqw zlwk d sxeolf xqhpsor|phqw lqvxudqfh sur0
judp zkhq mre rhuv duh xqrevhuyhg1 Lqghhg/ wklv shuvshfwlyh vxjjhvwv d srwhqwldoo|
xvhixo uh0lqwhusuhwdwlrq ri wkh srolf| lpsdfw ri wkh X1N1 Mre Uhvwduw vfkhph1 Wklv
vfkhph shukdsv hqfrxudjhv juhdwhu vhdufk hruw e| wkh orqjhu0whup xqhpsor|hg/ exw
lw dovr jhqhudwhv yhuldeoh mre rhuv vr wkdw wkh jryhuqphqw fdq fuhgleo| wkuhdwhq wr
zlwkgudz ixuwkhu ehqhwv vkrxog d mre vhhnhu uhmhfw d vxlwdeoh hpsor|phqw rhu1
Wkh prudo kd}dug sureohp zkhq wkh jryhuqphqw grhv qrw revhuyh mre rhuv lv wkdw
d mre vhhnhu/ rq uhfhlylqj dq hpsor|phqw rhu/ kdv wkh rswlrq ri uhmhfwlqj wkdw rhu
dqg frqwlqxlqj wr uhfhlyh ixuwkhu XL sd|phqwv1 Wklv rswlrq lqfuhdvhv wkh mre vhhnhu*v
uhvhuydwlrq zdjh ^uhodwlyh wr wkh fdvh ri qr XL fryhudjh` dqg vr udlvhv htxloleulxp
zdjhv1 Hpehgglqj wklv zdjh glvwruwlrq lqwr d vwdqgdug pdwfklqj iudphzrun ^h1j1
Gldprqg +4<;4,/ Slvvdulghv +4<<3,`/ wklv sdshu lghqwlhv krz wkh gxudwlrq ri XL
sd|phqwv dhfwv htxloleulxp xqhpsor|phqw1 Vlpxodwlrqv qg wkdw prylqj iurp d
9 prqwk XL vfkhph wr dq lqghqlwh sd|phqw vfkhph/ zkloh uhgxflqj wkh ohyho ri
sd|phqwv wr nhhs jhqhurvlw| frqvwdqw/ fdq uhvxow lq d 68( lqfuhdvh lq htxloleulxp
xqhpsor|phqw/ fruuhvsrqglqj wr dq ryhudoo lqfuhdvh ri durxqg 5 shufhqwdjh srlqwv1
Wkh uhdvrq iru vxfk d odujh hpsor|phqw hhfw lv ehvw xqghuvwrrg xvlqj wkh qrwlrq
ri cfuhgleoh wkuhdwv*1 Lq htxloleulxp/ wkh qhjrwldwhg zdjh uh hfwv wkh ydoxh ri wkh
zrunhu*v rswlrq ri uhpdlqlqj xqhpsor|hg1 Dowkrxjk wkh zrunhu grhv qrw h{shfw wr
uhpdlq xqhpsor|hg lqghqlwho|/ wkh rswlrq ru cwkuhdw* ri uhfhlylqj XL sd|phqwv iru
dq lqghqlwh shulrg vljqlfdqwo| dhfwv wkh zrunhu*v uhvhuydwlrq zdjh1 Wkh uhvxowlqj
zdjh glvwruwlrq wkhq kdv d vljqlfdqw lpsdfw rq htxloleulxp xqhpsor|phqw1
Wkhuh duh wzr forvho| uhodwhg olwhudwxuhv1 Wkh fodvvlf vhdufk dssurdfk dvvxphv
upv pdnh wdnh0lw0ru0ohdyh0lw zdjh rhuv dqg zrunhuv vhdufk vhtxhqwldoo| iru mre ri0
6
ihuv1 Wdnlqj wkh zdjh rhu glvwulexwlrq dv jlyhq/ Pruwhqvhq +4<::, dqg ydq ghq Ehuj
+4<<3, ghvfuleh wkh mre vhhnhu*v rswlpdo vhdufk vwudwhj| jlyhq gxudwlrq ghshqghqw
XL sd|phqwv1 Wkh vhtxhqwldo vhdufk dvvxpswlrq lpsolhv d uhvhuydwlrq zdjh vwudw0
hj| lv rswlpdo/ dqg kljkhu XL sd|phqwv lpso| mre vhhnhuv kdyh d kljkhu uhvhuydwlrq
zdjh1 Ixuwkhu/ li XL sd|phqwv ghfuhdvh zlwk xqhpsor|phqw gxudwlrq/ wkhq d mre
vhhnhu*v uhvhuydwlrq zdjh dovr idoov zlwk gxudwlrq1 H{dfwo| wkh vdph hhfw rffxuv
lq rxu iudphzrun dv erwk vwuxfwxuhv dvvxph wkh vdph prudo kd}dug sureohp 0 wkdw
wkh jryhuqphqw grhv qrw revhuyh mre rhuv dqg vr mre vhhnhuv uhwdlq wkh rswlrq ri
uhpdlqlqj xqhpsor|hg dqg frqwlqxlqj wr uhfhlyh XL ^xqwlo wkhlu XL sd|phqwv h{sluh`1
Xqiruwxqdwho| jlyhq d gxudwlrq ghshqghqw XL sd|phqw vfkhph dqg wkh fruuhvsrqglqj
qrq0vwdwlrqdu| vhdufk vwudwhjlhv ri zrunhuv/ ghwhuplqlqj wkh zdjh rhu glvwulexwlrq
hqgrjhqrxvo| ^frqvlvwhqw zlwk rswlpdo zdjh srvwlqj e| upv dqg rswlpdo mre vhdufk
e| zrunhuv` lv d iruplgdeoh sureohp1 Doeuhfkw dqg Yurpdq +5334, lv wkh rqo| sd0
shu zklfk h{solflwo| frqvlghuv wklv sureohp/ dqg grhv vr e| dvvxplqj XL sd|phqwv
h{sluh dffruglqj wr dq h{rjhqrxv Srlvvrq surfhvv1 D pruh wudfwdeoh vwuxfwxuh lv re0
wdlqhg khuh e| lqvwhdg uhsodflqj wkh wdnh0lw0ru0ohdyh0lw zdjh rhu vwuxfwxuh zlwk zdjh
edujdlqlqj1
D vhfrqg olwhudwxuh lqvwhdg dvvxphv wkdw mre vhdufk hruw lv xqrevhuyhg1 Vkdyhoo
dqg Zhlvv +4<:<, hvwdeolvk wkdw rswlpdo lqvxudqfh djdlqvw od|r ulvn lpsolhv XL sd|0
phqwv vkrxog ghfuhdvh zlwk gxudwlrq1 Lq d uhfhqw sdshu/ Iuhghulnvvrq dqg Kropoxqg
+5334, h{whqg wkrvh uhvxowv xvlqj dq htxloleulxp pdwfklqj prgho zkhuh zdjhv duh
hqgrjhqrxvo| ghwhuplqhg1 Krzhyhu dv kdv ehhq w|slfdoo| grqh lq wkh olwhudwxuh/ wkh|
ghwhuplqh zdjhv xvlqj wkh Qdvk edujdlqlqj dssurdfk dvvxplqj wkh zrunhu*v wkuhdw0
srlqw lv wkh ydoxh ri ehlqj xqhpsor|hg zlwk ixoo XL fryhudjh ^dovr vhh Eodqfkdug dqg
Gldprqg +4<<7,/ Ploodug dqg Pruwhqvhq +4<<:,/ Gdylgvrq dqg Zrrgexu| +4<<:,`1
Wklv odwwhu dvvxpswlrq kdv qr irupdo plfurhfrqrplf mxvwlfdwlrq dqg vhhpv lqfrq0
7
vlvwhqw zlwk wkh idfw wkdw zrunhuv zkr txlw duh qrw hqwlwohg wr uhfhlyh XL1 Lq frqwudvw/
khuh zh ghvfuleh d irupdo zdjh edujdlqlqj jdph zkhuh/ jlyhq mre rhuv duh qrw re0
vhuyhg/ wkh zrunhu kdv wkh rswlrq ri uhpdlqlqj xqhpsor|hg dqg frqwlqxlqj wr uhfhlyh
ixuwkhu ehqhwv gxulqj zdjh qhjrwldwlrqv1 Dvvxplqj upv dqg zrunhuv fdq frqwudfw
rq zdjhv/ wkh qhjrwldwhg zdjh wkhq ghshqgv rq wkh xqhpsor|hg zrunhu*v hqwlwohphqw
wr ixuwkhu XL1 Rxu sdshu wkhuhiruh fdswxuhv zlwklq d g|qdplfdoo| frqvlvwhqw iudph0
zrun krz d gxudwlrq ghshqghqw XL sd|phqw vfkhph dhfwv htxloleulxp zdjhv dqg
xqhpsor|phqw1
5
Wkh Prgho
Wkh dlp ri wkh sdshu lv wr xqghuvwdqg wkh pdfurhfrqrplf lqwhudfwlrq ehwzhhq d XL
surjudp zklfk rhuv d gxudwlrq ghshqghqw sd|phqw vfkhph dqg htxloleulxp zdjh
irupdwlrq lq d qrq0frpshwlwlyh oderxu pdunhw1 Dv wkh dvvxphg ghjuhh ri ulvn dyhuvlrq
ri zrunhuv lv qrw fhqwudo wr wklv lvvxh/ zh vlpsoli| e| dvvxplqj zrunhuv duh ulvn
qhxwudo14 Dv zh rplw wkh lqvxudqfh ydoxh ri XL/ zh gr qrw fodlp wr lghqwli| dq
crswlpdo* XL surjudp/ wkrxjk zh vkdoo glvfxvv wklv lvvxh ixuwkhu lq wkh Frqfoxvlrq1
Khuh zh ghprqvwudwh wkdw wkh zdjh glvwruwlrq xqghu frqvlghudwlrq fdq jhqhudwh odujh
pdfurhfrqrplf glvwruwlrqv1
Wkh lqqlwh krul}rq/ frqwlqxrxv wlph hfrqrp| frpsulvhv ri d frqwlqxxp ri zrun0
huv dqg d frqwlqxxp ri upv/ zkhuh doo duh ulvn qhxwudo dqg kdyh wkh vdph glvfrxqw
udwh o : f Wkh qxpehu ^phdvxuh` ri zrunhuv lv qrupdol}hg wr xqlw|1 Dowkrxjk wkh
qxpehu ri zrunhuv lq wkh hfrqrp| grhv qrw fkdqjh ryhu wlph/ wkhuh lv wxuqryhu1 Lq
sduwlfxodu/ hdfk zrunhu ohdyhv wkh pdunhw dffruglqj wr d Srlvvrq surfhvv zlwk sdudp0
hwhu B : f Ri frxuvh iru d vwhdg| vwdwh/ B dovr ghvfulehv wkh lq rz ri qhz xqpdwfkhg
zrunhuv1
4
Wklv dovr dyrlgv wkh vdylqjv sureohp/ zkhuh zrunhuv pljkw vhoi0lqvxuh xvlqj d vdylqjv vwudwhj|1
8
Wkurxjkrxw zh rqo| frqvlghu vwhdg| vwdwh htxloleuld1 Lq dq| vxfk htxloleulxp/ hdfk
zrunhu lv hlwkhu hpsor|hg ru xqhpsor|hg/ zkhuh L ghqrwhv wkh vwhdg| vwdwh phdvxuh
ri xqhpsor|hg zrunhuv1 Iroorzlqj Slvvdulghv +4<<3,/ wkh vwhdg| vwdwh phdvxuh ri
ydfdqflhv/ Tc zloo eh ghwhuplqhg e| d iuhh hqwu| frqglwlrq1
Ehfdxvh wkhuh duh pdwfklqj iulfwlrqv/ lw wdnhv wlph iru wkh L mre vhhnhuv wr frqwdfw
wkh T ydfdqflhv1 Zh ghvfuleh wkdw surfhvv xvlqj dq djjuhjdwh pdwfklqj ixqfwlrq
 ' ELc T zkhuh ELc f ' Efc T ' fc dqg  lv d frqwlqxrxv/ lqfuhdvlqj dqg
frqfdyh ixqfwlrq zklfk lv krprjhqhrxv ri ghjuhh 4> l1h1 wkhuh duh frqvwdqw uhwxuqv wr
pdwfklqj1 Li k ghqrwhv wkh udwh dw zklfk d mre vhhnhu frqwdfwv d ydfdqf|/ dqg ks lv
wkh duulydo udwh ri mre vhhnhuv wr dq| ydfdqf|/ v|pphwu| lpsolhv
k ' ELc T *L
dqg ks ' ELc T *T
+4,
Ri frxuvh li zh ohw ' T*L ^zklfk lv uhihuuhg wr dv oderxu pdunhw wljkwqhvv` dqg
ghqh 6E ' Ec c wkhq frqvwdqw uhwxuqv wr pdwfklqj lpsolhv wkhvh duulydo udwhv
uhgxfh wr k ' 6E dqg ks ' 6E*
Ohw ME ghqrwh wkh vwhdg|0vwdwh glvwulexwlrq ri xqhpsor|phqw vshoo ohqjwkv dfurvv wkh xqhpsor|hg1 Vhdufk lv udqgrp lq wkdw jlyhq d ydfdqf| kdv ehhq frqwdfwhg
e| dq xqhpsor|hg zrunhu/ wkdw zrunhu*v gxudwlrq lv frqvlghuhg dv d udqgrp gudz
iurp M
Dv lv vwdqgdug lq frqwlqxrxv wlph dqdo|vlv/ zh lqwurgxfh wkh frqfhsw ri wkh lq0
qlwhvlpdo wlph shulrg _| : f Wkh hyhqwxdo prghoolqj htxdwlrqv zloo eh wkrvh zklfk
hphujh lq wkh olplw dv _| dssurdfkhv 31 Zkloh xqhpsor|hg/ wkhq/ d zrunhu zlwk xq0
hpsor|phqw gxudwlrq uhfhlyhv ehqhw sd|phqw KE _| f lq wkh qh{w lqvwdqw Dq
xqhpsor|hg zrunhu dovr rewdlqv rz sd|r f wkurxjk ohlvxuh zkloh xqhpsor|hg1
Dv zrunhuv duh ulvn qhxwudo dqg wkhuh lv srvlwlyh glvfrxqwlqj/ wkh zrunhu lpphgldwho|
frqvxphv wkh ehqhw sd|phqw dqg vr rewdlqv wrwdo rz sd|r d n KE o_| zkloh
9
xqhpsor|hg1
Dv ghvfulehg lq Slvvdulghv +4<<3,/ d up pxvw sd| d {hg frvw @ : f shu xqlw wlph
wr dgyhuwlvh d ydfdqf|1 Li wkh up grhv qrw sd| wklv {hg frvw/ lw lv qrw frqwdfwhg e|
mre vhhnhuv1 Zlwk iuhh hqwu|/ wkh qxpehu ri ydfdqflhv dgmxvwv vr wkdw wkh h{shfwhg
glvfrxqwhg surw e| dgyhuwlvlqj lv }hur1
Zdjhv duh ghwhuplqhg e| edujdlqlqj1 Ri frxuvh lq vwdwlrqdu| hqylurqphqwv wkhuh
lv d forvh uhodwlrqvkls ehwzhhq wkh Qdvk edujdlqlqj dssurdfk dqg wkh Uxelqvwhlq
prgho ri edujdlqlqj ^h1j1 Elqpruh +4<;:,/ Elqpruh hw do1 +4<;9,`1 Zh uhfrqvlghu
wkdw uhodwlrqvkls lq ghwdlo ehorz1 Iru qrz/ qrwh wkdw jlyhq wkh zrunhu*v gxudwlrq
f dqg wkdw d jdlq wr wudgh h{lvwv/ wkh edujdlqlqj jdph zloo lpso| d ^uhgxfhg
irup` htxloleulxp zdjh djuhhphqw W E Jlyhq wkdw djuhhphqw/ d frqwudfw lv wkhq
zulwwhq zklfk vshflhv wkdw zdjh lq doo ixwxuh shulrgv1 Wkh fruuhvsrqglqj htxloleulxp
sd|rv wr wkh up dqg zrunhu ^jlyhq frqwdfw dqg o duh dvvxphg wr eh
Z s E '
& W E W E c
dqg Z E '
onB
onB
zkhuh & : f lv pdwfk surgxfwlylw|1
Qrwh/ wkh deryh sd|r ixqfwlrqv lpsolflwo| dvvxph qr rq0wkh0mre vhdufk/ qr txlwv
dqg qr od|r ulvn 0 wkh mre lv iru olih ^xqwlo wkh zrunhu txlwv wkh oderxu pdunhw`1
Dvvxplqj qr rq0wkh0mre vhdufk lv d vwdqgdug vlpsoli|lqj dvvxpswlrq15 Uxolqj rxw
txlwv lv vwudljkwiruzdug li zh dvvxph d zrunhu zkr txlwv lv qrw hqwlwohg wr uhfhlyh XL
sd|phqwv ^zklfk lv xvxdoo| wkh fdvh`1 Dv zh vkdoo vhh/ uhfhlylqj XL sd|phqwv sxwv d
zrunhu lq d vwurqjhu edujdlqlqj srvlwlrq zklfk udlvhv wkh qhjrwldwhg zdjh1 Txlwwlqj
wr vhdufk iru dqrwkhu ^lghqwlfdo` hpsor|hu zlwk qr hqwlwohphqw wr XL sd|phqwv lv d
uhwurjudgh vwhs zklfk qr zrunhu zrxog wdnh lq htxloleulxp1
Dvvxplqj qr od|r ulvn lv dovr d vlpsoli|lqj dvvxpswlrq> lq hvvhqfh zh frqvlghu dq
5
Vhh Exughww dqg Pruwhqvhq +4<<;, iru wkh frpsolfdwlrqv wkdw pljkw dulvh zkhq wkhuh lv rq0wkh0
mre vhdufk1
:
lq rz0rxw rz prgho zkhuh vfkrro0ohdyhuv uhsodfh uhwlulqj zrunhuv1 Lqwurgxflqj od|r
ulvn/ vd| e| dvvxplqj up vshflf surgxfwlylw| vkrfnv dv ghvfulehg lq Pruwhqvhq dqg
Slvvdulghv +4<<7,/ zrxog lqwurgxfh uh0hqwlwohphqw hhfwv1 Lq sduwlfxodu/ d odlg0r
zrunhu zkrvh XL sd|phqwv kdyh h{sluhg zrxog qg wkdw jhwwlqj uh0hpsor|hg uh0
hqwlwohv klp2khu wr ixwxuh XL sd|phqwv ^shukdsv diwhu d fhuwdlq txdolfdwlrq shulrg`1
Lq frqwudvw/ wkh ydoxh ri wklv uh0hqwlwohphqw hhfw iru d zrunhu zkr kdv mxvw ehhq odlg
r lv }hur dv kh2vkh lv douhdg| ixoo| hqwlwohg wr uhfhlyh XL1 Frohv dqg Pdvwhuv +5334,
hvwdeolvk zlwklq d vwrfkdvwlf ^qrq0vwhdg|0vwdwh` pdwfklqj iudphzrun wkdw vxfk uh0
hqwlwohphqw hhfwv duh hpsor|phqw vwdelolvlqj ryhu wkh f|foh1 Krzhyhu khuh zh irfxv
rq vwhdg| vwdwh/ dqg vr uhvwulfwlqj dwwhqwlrq wr dq lq rz0rxw rz prgho ri wxuqryhu
frqyhqlhqwo| devwudfwv iurp wkrvh hhfwv16
514
Wkh Vwudwhjlf Edujdlqlqj Jdph1
W|slfdoo| rqh wklqnv ri wkh Qdvk edujdlqlqj vroxwlrq dv d uhgxfhg irup dssur{lpdwlrq
iru wkh vwudwhjlf edujdlqlqj dssurdfk1 Dowkrxjk wkh uhodwlrqvkls ehwzhhq wkh wzr
iudphzrunv kdv ehhq fohduo| ghvfulehg lq Elqpruh +4<;:,/ Elqpruh/ Uxelqvwhlq dqg
Zrolqvn| +4<;9,/ wkhuh lv vrph frqixvlrq rq wkh uroh ri Qdvk edujdlqlqj cwkuhdwsrlqwv*
lq wkh htxloleulxp pdwfklqj olwhudwxuh1 Lq idfw dv orqj dv edujdlqlqj lv mrlqwo| h!flhqw
dqg zkloh edujdlqlqj srzhu uhpdlqv d iuhh sdudphwhu/ wkhq w|slfdoo| wkh fkrlfh ri
cwkuhdwsrlqw* pdnhv olwwoh txdolwdwlyh glhuhqfh lq d pdwfklqj htxloleulxp
Wr vhh wklv frqvlghu wkh h{wuhph fdvh zkhuh upv kdyh doo wkh edujdlqlqj srzhu/
6
Li zh kdg dvvxphg ulvn dyhuvh zrunhuv/ rplwwlqj od|r ulvn zrxog eh d pruh lpsruwdqw ghihfw ri
wkh prgho 0 ulvn dyhuvh zrunhuv dqg od|r ulvn wrjhwkhu lpso| wkh XL v|vwhp lqfuhdvhv wkh ydoxh ri
dq| pdwfk dqg vr lv srwhqwldoo| hpsor|phqw hqkdqflqj1 Exughww dqg Pruwhqvhq +4<;3, h{soruh wklv
ihdwxuh ri d XL v|vwhp lq ghwdlo1 Exw zlwk ulvn qhxwudo zrunhuv/ wkh XL v|vwhp jhqhudwhv qr vxfk
hhfw dqg vr lqfoxglqj od|r ulvn zrxog frpsolfdwh wkh iudphzrun zlwkrxw surgxflqj dq| xvhixo
lqvljkw1
;
w ' 1 Wklv lpsolhv wkdw zrunhuv fdq qhyhu rewdlq dq| vxusoxv iurp d pdwfk1 Khqfh/
iru dq| fkrvhq wkuhdwsrlqwv frqvlvwhqw zlwk sulydwho| h!flhqw edujdlqlqj ^h1j1 wkrvh
frqvlvwhqw zlwk vrph euhdngrzq udwh ri wkh xqghuo|lqj vwudwhjlf edujdlqlqj jdph`/ d
pdwfklqj htxloleulxp dqg wkh fkrlfh ri w '  lpsolhv wkh htxloleulxp zdjh rxwfrph
lv dq hpsor|phqw frqwudfw zkrvh ydoxh wr wkh zrunhu lv htxdo wr wkh ydoxh ri ehlqj
xqhpsor|hg iruhyhu ^dv d zrunhu fdq qhyhu h{wudfw dq| vxusoxv e| ehfrplqj hpsor|hg`1
Wklv lv dovr wkh orzhvw zdjh zklfk lv frqvlvwhqw zlwk lqglylgxdo zrunhu udwlrqdolw|1
Wkh vdph lqvljkw krogv zkhq zrunhuv kdyh doo wkh edujdlqlqj srzhu w ' f Dv upv
fdqqrw rewdlq dq| vxusoxv wkurxjk edujdlqlqj/ wkhq uhjdugohvv ri wkh fkrvhq wkuhdw0
srlqw ^frqvlvwhqw zlwk vrph euhdngrzq udwh ri wkh xqghuo|lqj vwudwhjlf edujdlqlqj
jdph`/ d pdwfklqj htxloleulxp zrxog lpso| d zdjh htxdo wr wkh ydoxh ri rxwsxw1 Dq
lqwhuphgldwh fkrlfh ri w 5 Efc  wkhuhiruh sdudphwhulvhv krz pxfk ^uhgxfhg irup` vxu0
soxv zrunhuv rewdlq lq d pdwfklqj htxloleulxp frqvlvwhqw zlwk lqglylgxdo udwlrqdolw|1
Wkh srlqw ehlqj wkdw zkloh edujdlqlqj srzhu uhpdlqv d iuhh sdudphwhu/ wkh fkrlfh ri
wkuhdwsrlqw 0 zkhwkhu lw lv wkh ydoxh ri frqwlqxhg vhdufk ^dq lqqlwh euhdngrzq udwh`
ru wkh ydoxh ri edujdlqlqj iruhyhu ^d }hur euhdngrzq udwh` ru vrph zhljkwhg dyhudjh
^d qlwh/ srwhqwldoo| hqgrjhqrxv/ euhdngrzq udwh` 0 w|slfdoo| sod|v olwwoh uroh17
Ri frxuvh wkhuh duh h{fhswlrqv1 Rqh lv zkhq wkh irfxv lv rq wkh olplwlqj iulfwlrqohvv
fdvh zkhuh o $ f ^h1j1 Uxelqvwhlq dqg Zrolqvn| +4<;7,/ Jdoh +4<;:,/ Pruwhqvhq dqg
Zuljkw +5333,`18 D vhfrqg lv zkhq sd|rv hyroyh g|qdplfdoo|1 Iru h{dpsoh xvlqj
7
Qrw vxusulvlqjo| vrph vshflfdwlrqv duh pdwkhpdwlfdoo| pruh frqyhqlhqw wkdq rwkhuv1 Iru h{0
dpsoh/ zkhq wkh wkuhdwsrlqwv duh wkh ydoxh ri frqwlqxhg vhdufk/ Krvlrv +4<<3, lghqwlhv wkh Qdvk
edujdlqlqj srzhu zklfk lpsohphqwv wkh vrfldoo| h!flhqw rxwfrph1 Pruh vshflfdoo|/ frqvwdqw uh0
wxuqv wr pdwfklqj lpsolhv d zdjh h{lvwv zklfk lqwhuqdolvhv wkh uhohydqw h{whuqdolwlhv/ dqg vrfldo
rswlpdolw| uhtxluhv wkdw wkh dvvxphg edujdlqlqj srzhu dqg wkuhdwsrlqw lpsohphqw wkdw sulfh1 D
glhuhqw wkuhdwsrlqw zrxog lpso| d glhuhqw edujdlqlqj srzhu1 Ri frxuvh wkh dojheud lv prvw hohjdqw
iru wkh Krvlrv +4<<3, fdvh1
8
Lq wklv fdvh/ wkh ydoxh ixqfwlrqv wdnh duelwudulo| odujh ydoxhv/ zkloh wkh vxusoxv wr dq| pdwfk
<
d prqhwdu| prgho ri vhdufk/ Frohv dqg Zuljkw +4<<;, vkrz wkdw htxloleulxp wudg0
lqj f|fohv duh srvvleoh zkhq wkh whupv ri wudgh duh ghwhuplqhg e| ^iruzdug orrnlqj`
vwudwhjlf edujdlqlqj/ exw fdqqrw h{lvw li d vwdwlf Qdvk edujdlqlqj uxoh lv lpsrvhg1
Dv djhqwv rxjkw wr eh iruzdug orrnlqj lq wkh edujdlqlqj sureohp ^dv wkh| duh lq doo
rwkhu dvshfwv ri wkh prgho`/ g|qdplf frqvlvwhqf| uhtxluhv wkdw wkh whupv ri wudgh duh
ghwhuplqhg e| vwudwhjlf edujdlqlqj zkhq sd|rv hyroyh g|qdplfdoo|1
Wkh edujdlqlqj sureohp khuh fruuhvsrqgv wr wklv vhfrqg fdvh 0 XL sd|phqwv fkdqjh
zlwk gxudwlrq 0 dqg vr g|qdplf frqvlvwhqf| uhtxluhv ghwhuplqlqj wkh whupv ri wudgh
xvlqj wkh vwudwhjlf edujdlqlqj dssurdfk1 Krzhyhu frqvlvwhqw zlwk wkh deryh dujx0
phqwv/ zh ohdyh edujdlqlqj srzhu dv d iuhh sdudphwhu exw qrwh wkdw wkh ghvfulswlrq
ri wkh edujdlqlqj jdph zloo lpso| sduwlfxodu vwudwhjlf cwkuhdwsrlqwv*1
Zkhq d mre vhhnhu dqg d up zlwk dq xqoohg ydfdqf| phhw/ dvvxph wkh| erwk
revhuyh wkh mre vhhnhu*v fxuuhqw gxudwlrq ri xqhpsor|phqw 1 Wkh djuhhg zdjh lv
ghwhuplqhg e| vwudwhjlf edujdlqlqj zlwk udqgrp dowhuqdwlqj rhuv zlwk shulrg _| :
f ehwzhhq frxqwhurhuv1 Wkh fuxfldo dvvxpswlrq lv wkdw wkh jryhuqphqw grhv qrw
revhuyh rhuv ri hpsor|phqw/ dqg vr wkh zrunhu frqwlqxhv wr uhfhlyh XL ehqhwv KE diwhu uhmhfwlqj dq rhu1
Dw wkh ehjlqqlqj ri wlph lqwhuydo d|c | n _|/ wkh up dqg wkh zrunhu uvw ghflgh
zkhwkhu wr frqwlqxh edujdlqlqj1 Li hlwkhu fkrrvhv wr vhsdudwh wkhq wkh zrunhu*v sd|r
lv wkh h{shfwhg ydoxh ri frqwlqxhg vhdufk/ zkloh wkh up*v sd|r lv }hur lq d iuhh hqwu|
htxloleulxp1 Li erwk djuhh wr edujdlq/ Qdwxuh zlwk suredelolw| w 5 dfc o fkrrvhv wkh
up wr pdnh d frqwudfw rhu c dqg zlwk suredelolw|  w fkrrvhv wkh zrunhu wr
pdnh dq rhu1 Li wkh frqwudfw rhu lv dffhswhg/ wkh pdwfk lv frqvxppdwhg dqg wkh
sd|rv duh Zs ' d& o*Eo n Bc Z ' *Eo n B Li wkh frqwudfw rhuhg e| rqh
sduw| lv uhmhfwhg e| wkh rwkhu/ wkhuh lv d rqh0shulrg ghod| gxulqj zklfk wkhuh lv qr
ehfrphv duelwudulo| vpdoo dv djhqwv ehfrph duelwudulo| sdwlhqw1 Vpdoo prghoolqj glhuhqfhv fdq
srwhqwldoo| kdyh odujh hhfwv lq wklv fdvh1
43
surgxfwlrq1 Gxulqj wklv ghod|/ wkh up uhfhlyhv d }hur rz sd|r/ zkloh wkh zrunhu
rewdlqv ^ n KE o_|1 Wkh vhtxhqfh lv wkhq uhshdwhg ryhu wlph lqwhuydo d| n _|c | n 2_|/
jlyhq wkh lqfuhdvhg xqhpsor|phqw gxudwlrq n _|1 Ri frxuvh htxloleulxp zloo uh hfw
wkh zrunhu*v zruvhqlqj edujdlqlqj srvlwlrq 0 klv XL sd|phqwv pd| vrrq h{sluh1
Zh pdnh wkh vwdqgdug wlh0euhdnlqj dvvxpswlrqv> wkdw dq djhqw dffhswv d frqwudfw
rhu li lqglhuhqw wr grlqj vr/ dqg dq djhqw zkr lv lqglhuhqw ehwzhhq frqwlqxhg
edujdlqlqj dqg vhsdudwlrq fkrrvhv wr frqwlqxh edujdlqlqj1 Wkh uvw wlh0euhdn dv0
vxpswlrq lv vwdqgdug dqg lv qhfhvvdu| iru h{lvwhqfh ri dq htxloleulxp/ wkh vhfrqg
sod|v qr lpsruwdqw uroh1
Wr vlpsoli| pdwwhuv/ zh dvvxph wkurxjkrxw wkdw xqhpsor|phqw ehqhwv duh qrq0
lqfuhdvlqj zlwk gxudwlrq dqg wkdw n KEf &c zklfk lpso| wkdw d jdlq wr wudgh
dozd|v h{lvwv ehwzhhq d up dqg dq xqhpsor|hg zrunhu1
Dv lv vwdqgdug lq wkh pdwfklqj olwhudwxuh/ wkh zrunhu*v rxwvlgh rswlrq 0 zklfk lv wr
vhsdudwh dqg frqwlqxh vhdufk 0 lv qhyhu elqglqj rq wkh edujdlqlqj htxloleulxp ^lghq0
wlfdo upv dqg d srvlwlyh glvfrxqw udwh lpso| lw lv dozd|v ehwwhu wr nhhs edujdlqlqj
wkdq eh xqpdwfkhg`1 Ixuwkhu/ srvlwlyh glvfrxqwlqj vxjjhvwv wkdw wkh prvw qdwxudo
edujdlqlqj htxloleulxp lv rqh zkhuh wkh up dqg zrunhu dozd|v uhdfk lpphgldwh
djuhhphqw1 Zh uhihu wr vxfk dq rxwfrph dv dq Lpphgldwh Wudgh Htxloleulxp ^LWH`1
Fodlp 41 Iru dq| gxudwlrq fc dqg lq wkh olplw dv _| $ fc dq LWH h{lvwv/ lv
xqltxh dqg lpsolhv htxloleulxp zdjh djuhhphqw
W E ' E w& n w
] "
e3EonBE|3 Eo n Bd n KE|o_|
+5,
Ehiruh surylqj Fodlp 4/ zh uvw vkrz wkdw lw lq idfw fruuhvsrqgv wr d sduwlfxodu
Qdvk edujdlqlqj ghfrpsrvlwlrq1 Ghqh wkh zrunhu*v glvdjuhhphqw sd|r _ E dv
_ E '
] "
e3EonBE|3 d n KE|o_|c
44
zklfk dw gxudwlrq lv wkh zrunhu*v ydoxh ri uhpdlqlqj xqhpsor|hg iruhyhu1 Dovr
ghqh cvxusoxv* E dv
E ' &*Eo n B _ E ] "
e3EonBE|3 d& KE|o_|c
+6,
zkhuh wkh dvvxpswlrq n KE| & iru doo | jxdudqwhhv E : f iru doo Wkh deryh
zdjh htxdwlrq lv lq idfw htxlydohqw wr
W E *Eo n B ' _ E n E wE (
+7,
l1h1 wkh zrunhu qhjrwldwhv d frqwudfw zlwk ydoxh htxdo wr klv glvdjuhhphqw sd|r _ E 0 wkh ydoxh ri uhpdlqlqj xqhpsor|hg iruhyhu 0 soxv d vkduh ri wkh vxusoxv E : f
Dovr qrwh wkdw dv XL sd|phqwv idoo zlwk gxudwlrq/ wkhq erwk wkh zrunhu*v glvdjuhhphqw
sd|r _ dqg wkh htxloleulxp zdjh djuhhphqw W idoo zlwk gxudwlrq1
Wkh up*v fruuhvsrqglqj sd|r Z s E ' d& W E o*Eo n B lv
Z s E ' wE (
l1h1 wkh up rewdlqv d frqvwdqw vkduh ri wkh vxusoxv1 Dv suhylrxvo| h{sodlqhg/ qrwh
wkdw w '  lpsolhv wkh zrunhu qhjrwldwhv wkh ydoxh ri ehlqj xqhpsor|hg iruhyhu/ zkloh
w ' f lpsolhv wkh zdjh htxdov wkh ydoxh ri rxwsxw ^wkh up pdnhv }hur surw`1 Khqfh
w 5 dfc o sdudphwhulvhv krz pxfk ^uhgxfhg irup` vxusoxv zrunhuv rewdlq ^frqvlvwhqw
zlwk lqglylgxdo udwlrqdolw|` zkloh wkh vwudwhjlf edujdlqlqj dssurdfk lpsolhv wkhvh
sulfhv duh g|qdplfdoo| frqvlvwhqw 0 erwk djhqwv suhihu lpphgldwh djuhhphqw dw zdjh
W E wkdq ghihu wudgh1
515
Wkh ghulydwlrq ri Fodlp 41
Zh txlfno| vnhwfk wkh uhohydqw dujxphqw dqg uhihu wkh uhdghu wr Frohv dqg Zuljkw
+4<<;, iru d pruh irupdo dssurdfk1 Il{ _| : f dqg ohw W E| ghqrwh wkh h{shfwhg zdjh
45
djuhhphqw dw gxudwlrq | lq dq LWH Qrz frqvlghu dq| gxudwlrq f dqg vxssrvh
Qdwxuh fkrrvhv wkh up wr pdnh d zdjh rhu/ 1 E| dffhswlqj wkdw rhu/ wkh zrunhu
rewdlqv h{shfwhg sd|r *Eo n B Krzhyhu/ vkrxog wkh zrunhu uhmhfw wkdw rhu/ wkh
zrunhu zloo uhfhlyh XL sd|phqw KE iru wkh vxevhtxhqw shulrg ^wkh jryhuqphqw grhv
qrw revhuyh mre rhuv` dqg/ lq dq LWH/ h{shfwv djuhhphqw qh{w shulrg dw h{shfwhg
zdjh W E n _| Wkh zrunhu*v h{shfwhg sd|r e| uhmhfwlqj wkh mre rhu lv wkhuhiruh
%
&
W E n _|
 B_|
d n KE o_| n
 n o_|
onB
Wkh zrunhu*v rswlpdo edujdlqlqj vwudwhj| kdv wkh uhvhuydwlrq zdjh surshuw|= wkh
zrunhu uhmhfwv dq| zdjh rhu zklfk kdv ohvv ydoxh wkdq wkh frqwlqxdwlrq ydoxh ri
edujdlqlqj1 Wkdw uhvhuydwlrq zdjh/ ghqrwhg - E c lv wkhuhiruh
%
&
- E  B_|
W E n _|
'
d n KE o_| n
c
onB
 n o_|
onB
dqg wkh zrunhu lv mxvw lqglhuhqw wr dffhswlqj zdjh rhu ' - Prvw lpsruwdqwo|/
qrwh wkdw jlyhq W E n _|c wkh zrunhu*v uhvhuydwlrq zdjh dw gxudwlrq lv vwulfwo|
lqfuhdvlqj lq wkh XL sd|phqw KE Ri frxuvh wkh vdph dujxphqw dssolhv vkrxog Qdwxuh fkrrvh wkh zrunhu wr pdnh
d zdjh rhu1 Wkh up eholhyhv wkdw li lw uhmhfwv wkdw rhu/ wkhq wkh| zloo uhdfk
djuhhphqw qh{w shulrg dw h{shfwhg zdjh W E n _| Wkh up*v uhvhuydwlrq zdjh/
ghqrwhg -s E c lv wkhuhiruh
%
&
& -s E  B_| & W E n _|
'
onB
 n o_|
onB
D qlfh lqvljkw lv wkdw wkh glhuhqfh ehwzhhq wkhvh wzr uhvhuydwlrq zdjhv lv wkh vxusoxv
wkdw lv orvw vkrxog d rqh0shulrg ghod| rffxu1 Wr vhh wklv/ dgg xs wkh deryh wzr
htxdwlrqv dqg uh0duudqjh wr rewdlq
-s E - E  B_|
d& KE o _|c
'
onB
 n o_|
46
+8,
zkhuh n KE & jxdudqwhhv wkdw wkh uljkw kdqg vlgh ri +8, lv vwulfwo| srvlwlyh1 Dv
wkh uhvhuydwlrq zdjh ri wkh up lv vwulfwo| juhdwhu wkdq wkh uhvhuydwlrq zdjh ri wkh
zrunhu/ htxloleulxp dozd|v uhvxowv lq lpphgldwh djuhhphqw1 Li wkh up pdnhv wkh
zdjh rhu/ lw h{wudfwv wkdw rqh0shulrg vxusoxv e| rhulqj wkh zrunhu*v uhvhuydwlrq
zdjh/ zklfk wkh zrunhu dffhswv1 Vlploduo| li wkh zrunhu pdnhv wkh rhu/ kh h{wudfwv
wkdw vxusoxv e| rhulqj wkh up*v uhvhuydwlrq zdjhc zklfk wkh up dffhswv1
Khqfh wkh h{shfwhg zdjh djuhhphqw dw gxudwlrq lv
W E ' w- E n E w-s E Xvlqj wkh deryh wr vxevwlwxwh rxw - E c -s E dqg uhduudqjlqj lpsolhv=
%
 B_|
 B_| W
E w&
E n _| '
Eo n B_| wd n KE o n
E  n o_|
 n o_|
 B_|
W
&
+9,
Wklv uhfxuvlyh htxdwlrq ghvfulehv wrgd|*v h{shfwhg zdjh djuhhphqw jlyhq wkh sod|hu*v
h{shfwdwlrqv rq wkh h{shfwhg zdjh djuhhphqw wrpruurz vkrxog hlwkhu wxuq grzq wkh
rwkhu*v rhu1 Vroylqj wklv ^xqvwdeoh` iruzdug orrnlqj glhuhqfh htxdwlrq/ qrwlqj wkdw
dq LWH uhtxluhv d erxqghg vroxwlrq W E| 5 dfc &o iru doo |c lpsolhv wkh xqltxh vroxwlrq
W
E ' E w& n w
"
[
'f
%
 B_|
 n o_|
&n
Eo n Bd n KE n _|o_|
+:,
Ohwwlqj _| $ fchtxdwlrq +8, lpsolhv -s E c - E $ W c dqg vr W ghvfulehv wkh
dfwxdo zdjh djuhhphqw lq wklv olplw1 +:, wkhq lpsolhv wkh Fodlp1
Qrwh wkdw dv _| $ fc wkhq W E| - E| ehfrphv duelwudulo| vpdoo1 +9, wkhuhiruh
ghvfulehv wkh zrunhu*v uhvhuydwlrq zdjh lq wkh edujdlqlqj jdph dv _| ehfrphv vpdoo1
Lw lv zruwk frqwudvwlqj wklv uhvhuydwlrq zdjh rxwfrph zlwk wkh vhtxhqwldo vhdufk
dssurdfk zkhuh lqvwhdg upv srvw zdjhv dqg 8 ghvfulehv wkh glvwulexwlrq ri zdjh
rhuv1 Wkh xvxdo uhfxuvlyh dujxphqwv ^vhh ydq ghq Ehuj +4<<3, iru h{dpsoh` lpso|
wkh uhvhuydwlrq zdjh ri d zrunhu dw gxudwlrq c ghqrwhg -E c vdwlvhv wkh glhuhqfh
htxdwlrq=
%
 B_|
k ] "
 B_|
-E n _| '
-E Eo nB_| d n KE o n
d 8 Eo_
 n o_|
 n o_|
o n B -E n_|
47
&
zklfk kdv d yhu| vlplodu vwuxfwxuh wr +9,1 Lqghhg/ wklv uhvhuydwlrq zdjh lv dovr d
glvfrxqwhg vxp ri ixwxuh d n KE|o1 Krzhyhu wkh dgglwlrqdo qrq0olqhdu whup lpsolhv
d forvhg irup vroxwlrq grhv qrw h{lvw/ zklfk lv zk| wkh deryh edujdlqlqj dssurdfk
lv pruh wudfwdeoh iru fkdudfwhulvlqj htxloleulxp1 Qhyhuwkhohvv wkh xqghuo|lqj prudo
kd}dug sureohp lv lghqwlfdo 0 ixwxuh XL sd|phqwv glvwruw fxuuhqw uhvhuydwlrq zdjhv1
6
Wkh Pdwfklqj Htxloleulxp1
Zh wdnh dv jlyhq wkh jryhuqphqw*v XL surjudp Kc zkhuh KE lv d srvlwlyh dqg ghfuhdv0
lqj ixqfwlrq ri c zlwk n KEf & Jlyhq htxloleulxp zdjhv W ghqhg lq Fodlp
4/ d Pdwfklqj Htxloleulxp lv d vwhdg| vwdwh wulsoh iLc Tc Mj zkhuh xqhpsor|phqw L
dqg wkh glvwulexwlrq ri xqfrpsohwhg xqhpsor|phqw vshoov ME duh frqvlvwhqw zlwk
vwhdg| vwdwh wxuqryhu/ zkloh ydfdqflhv T duh frqvlvwhqw zlwk iuhh hqwu| ^vhh Slvvdulghv
+4<<3, iru h{dpsoh`1 Zh fkdudfwhulvh hdfk frpsrqhqw lq wxuq1
614
Vwhdg|0Vwdwh Ydfdqf| Fuhdwlrq
Lq d vwhdg| vwdwh dqg ryhu dq| eulhi lqwhuydo _|/ wkh ydoxh f wr kroglqj dq xqoohg
ydfdqf| lv jlyhq e|/
f '

d@_| n ks _|H dZ s E o n E ks _|f o  n o_|
Qrwh/ @_| lv wkh rz frvw wr kroglqj dq xqoohg ydfdqf|1 Zlwk suredelolw| ks _|c wkh
up frqwdfwv d zrunhu zlwk vrph xqhpsor|phqw gxudwlrq dqg rewdlqv h{shfwhg
surw HdZ s E o c zkhuh d Pdwfklqj Htxloleulxp lpsolhv kdv glvwulexwlrq M Li wkh
up lv qrw frqwdfwhg e| d mre vhhnhu/ wkh ydfdqf| uhpdlqv xqoohg zlwk h{shfwhg
sd|r f Iuhh hqwu| ri ydfdqflhv lpsolhv f ' fc dqg vr wkh deryh lpsolhv
@ ' ks H dZs E o
48
+;,
ghvfulehv wkh dssursuldwh iuhh hqwu| frqglwlrq1
615
Vwhdg|0Vwdwh Xqhpsor|phqw
Vwhdg|0vwdwh xqhpsor|phqw lpsolhv
B ' ELc T n BLc
zkhuh wkh ohiw kdqg vlgh ghvfulehv wkh lq rz ri pdunhw hqwudqwv lqwr wkh srro ri
xqhpsor|phqw/ dqg wkh uljkw kdqg vlgh ghvfulehv wkh rz ri zrunhuv rxw ri wkh srro
ri xqhpsor|phqw1 Dv k ' ELc T *Lc vwhdg| vwdwh xqhpsor|phqw lpsolhv
L'
616
B
k n B
+<,
Vwhdg|0Vwdwh ME Qrwh wkdw wkh h{lw udwh ri xqhpsor|hg zrunhuv lv qrw gxudwlrq ghshqghqw 0 hdfk h{lwv
dw udwh ^k n Bo Li LE ghqrwhv wkh phdvxuh ri xqhpsor|hg zrunhu zkr kdyh ehhq
xqhpsor|hg qr orqjhu wkdq gxudwlrq c wkhq jlyhq xqhpsor|phqw lq rz B : fc
LE '
] f
B i TdEk n B|o_|c
zkhuh i TdEk n B|o lv wkh suredelolw| d zrunhu grhv qrw qg zrun ehiruh gxudwlrq
| Lqwhjudwlrq lpsolhv
LE '
B
d i TiEk n B joc
k n B
dqg dv ME LE *Lc zh rewdlq
ME '  i TiEk n B j
49
+43,
617
Htxloleulxp
Lq dq| Pdwfklqj Htxloleulxp iLc Tc Mjc zh fdq ghqh htxloleulxp oderxu pdunhw
wljkwqhvv W ' T*L Qrwh/ wkh pdwfklqj ixqfwlrq lpsolhv k ' 6EW dqg +<, lpsolhv
f m W zkhuh
L ' B*dk n Bo Ixuwkhu/ +43, lpsolhv M ME
f m '  i TiE6E n B j
ME
+44,
W lv wlhg grzq e| wkh iuhh hqwu| frqglwlrq +;,1 Dv htxloleulxp zdjh irupdwlrq lpsolhv
Z s E ' wE c zkhuh lv wkh vxusoxv ixqfwlrq ghqhg hduolhu/ dqg dv wkh pdwfklqj
ixqfwlrq lpsolhv ks ' 6EW *W c wkhq wkh iuhh hqwu| frqglwlrq +;, uhtxluhv qglqj d
W zklfk vdwlvhv
@'
6E ] "
f m wE _ME
f
+45,
Li d vroxwlrq W h{lvwv/ zh kdyh lghqwlhg d Pdunhw Htxloleulxp zkhuh Lc M duh dv
ghvfulehg deryh dqg T ' W L
Dvvxplqj w : f dqg wkdw wkh Pdwfklqj Ixqfwlrq kdv vwdqgdug surshuwlhv ^wkdw iru
: fc ks ' 6E* lv frqwlqxrxv dqg vwulfwo| ghfuhdvlqj lq c zlwk *4<f 6E* '
4c *4<" 6E* ' fo lpsolhv d qrq0ghjhqhudwh Pdwfklqj Htxloleulxp h{lvwv dqg
lv xqltxh19
7
Glvfxvvlrq dqg Vlpxodwlrqv
Rxu irfxv khuh lv rq wkh hhfw ri gxudwlrq ghshqghqw xqhpsor|phqw ehqhwv rq
htxloleulxp xqhpsor|phqw1 Lq sduwlfxodu/ zh qrz uhvwulfw dwwhqwlrq wr xqhpsor|phqw
9
e m !" , uvw rughu vwrfkdvwlfdoo| grplqdwhv K+
e m !# ,= Dv # lv
Qrwh wkdw !" ? !# lpsolhv K+
vwulfwo| srvlwlyh dqg lqfuhdvlqj iru 3> wkhq iru 5 +3> 4`> wkh lqwhjudo whup rq wkh uljkw kdqg
vlgh +UKV, ri +45, lv vwulfwo| srvlwlyh dqg ghfuhdvhv zlwk != Wkh surshuwlhv ri wkh pdwfklqj ixqfwlrq
wkhq lpso| wkh UKV lv d frqwlqxrxv dqg vwulfwo| ghfuhdvlqj ixqfwlrq ri ! iru ! A 3> zkhuh wkh
UKV ehfrphv duelwudulo| odujh dv ! $ 3> dqg frqyhujhv wr }hur dv ! $ 4= Khqfh iru dq| d A 3> d
Pdwfklqj htxloleulxp h{lvwv dqg lv xqltxh1
4:
ehqhw vfkhphv ri wkh irup
KE '
;
A
? Kf
A
=
iru A
f rwkhuzlvh1
Wkh srolf| sdudphwhuv duh wkh ohyho ri ehqhw sd|phqwv Kf c dqg wkh gxudwlrq ri wkh
vfkhph A
Ri frxuvh kroglqj Kf frqvwdqw zkloh lqfuhdvlqj A lpsolhv d pruh jhqhurxv ehqhw
vfkhph/ dqg lpsolhv doo zdjhv iru A lqfuhdvh1 Wr lghqwli| d sxuh gxudwlrq hhfw/
zh frqvlghu d frpshqvdwhg fkdqjh zkhuh Kf lv uhgxfhg dv A lqfuhdvhv vr wkdw wkh
h{shfwhg frvw ri wkh XL vfkhph lv khog frqvwdqw1
Jlyhq k c wkh h{shfwhg frvw ri XL sd|phqwv shu mre vhhnlqj hqwudqw/ ghqrwhg K c
lv
K '
] "
f
e3Ek nB KE|_|c
dv hdfk xqhpsor|hg zrunhu h{lwv wkh vwdwh ri xqhpsor|phqw dw udwh B n k Khqfh
jlyhq srolf| sdudphwhuv EKf c A c jhqhurvlw|
Kf d e3Ek nBA o
K '
k n B
+46,
Qrz { K : f dqg frqvlghu krz yduldwlrqv lq EKf c A vdwlvi|lqj +46, dhfw htxloleulxp
zdjhv1 Fodlp 4 lpsolhv
W E ' E w& n w
] "
e3EonBE|3 Eo n Bd n KE|o_|
Reylrxvo| li K ' fc wkh htxloleulxp zdjh uhgxfhv wr ' E w& n w Wr irfxv rq
wkh zdjh glvwruwlrq jhqhudwhg e| wkh XL vfkhph/ ghqh { ' W E dE w& n woc
zklfk lv wkh zdjh lqfuhdvh dw gxudwlrq gxh wr wkh XL vfkhph1 Wkh deryh jlyhv
{ ' w
] "
;
A
?
' A
=
e3EonBE|3 Eo n BKE|_|
wKf d e3EonBdA 3 o o iru A
f iru A
4;
D fulwlfdo lqvljkw lv wkdw dowkrxjk wkh zrunhu dqwlflsdwhv ehfrplqj uh0hpsor|hg
dw udwh k c wkh zdjh glvwruwlrq { grhv qrw ghshqg rq k Wkh zrunhu*v uhvhuydwlrq
zdjh lqvwhdg ghshqgv rq wkh ydoxh ri uhpdlqlqj xqhpsor|hg lqghqlwho|/ dqg lw lv wkh
rswlrq ri frqwlqxlqj wr uhfhlyh XL sd|phqwv lq wkh ixwxuh zklfk glvwruwv W Ixuwkhu/
wkh ydoxh ri wkdw rswlrq uh hfwv wkh zrunhu*v udwh ri wlph suhihuhqfh o : f
Dovr qrwh wkdw wkh wlph irup ri wklv zdjh ghyldwlrq lv forvho| uhodwhg wr wkdw
lghqwlhg lq wkh vhtxhqwldo vhdufk olwhudwxuh zlwk gxudwlrq ghshqghqw XL wkh ^uhvhu0
ydwlrq` zdjh ghfuhdvhv dv $ Ac exw wkh fkdqjh lv vpdoo iru A odujh/ dqg odujh
dv dssurdfkhv A ^vhh Pruwhqvhq +4<::,/ ydq ghq Ehuj +4<<3,`1
Iru jlyhq K c zh fdq xvh +46, wr vxevwlwxwh rxw Kf zklfk jlyhv
{E c A '
 e3EonBdA 3 o
wEk n BK
 e3Ek nBA
iru A Wklv htxdwlrq ghvfulehv wkh zdjh glvwruwlrq dw dq| gxudwlrq A e|
ydu|lqj EKf c A zkloh kroglqj jhqhurvlw|/ K c frqvwdqw1
Fodlp 51 Jlyhq k dqg iru o k c {E c A lv vwulfwo| lqfuhdvlqj lq A iru doo
f A > l1h1 fhwhulv sdulexv/ dq lqfuhdvh lq wkh gxudwlrq ri wkh XL vfkhph ^zkloh
kroglqj jhqhurvlw| K frqvwdqw`/ lqfuhdvhv zdjhv dw doo gxudwlrqv A 1
Surri= Glhuhqwldwlqj wkh htxdwlrq iru { zlwk uhvshfw wr A jlyhv=
Y
d{E c A o
YA
E e3Ek nBA Eo n Be3EonBdA 3 o E e3EonBdA 3 o Ek n Be3Ek nBA
'
wEk n BK
d e3Ek nBA o2
E e3Ek nBA Eo n Be3EonBA E e3EonBA Ek n Be3Ek nBA
wEk n BK
d e3Ek nBA o2
l
e3EonBA wEk n BK k
3Ek nBA
3Ek 3oA
'
Eo
n
B
n
Ek
Ek
n
Be
oe
d e3Ek nBA o2
Lqvshfwlrq hvwdeolvkhv wkdw wkh eudfnhwhg whup lq wkh odvw htxdwlrq deryh lv vwulfwo|
lqfuhdvlqj lq A Dv wkh eudfnhwhg whup lv }hur dw A ' fc wkh eudfnhwhg whup lv vwulfwo|
srvlwlyh iru doo A : fc zklfk hvwdeolvkhv wkh Fodlp1
4<
Ljqrulqj dq| htxloleulxp ihhgedfn hhfwv 0 wkdw wkh zdjh glvwruwlrq dovr fkdqjhv
htxloleulxp k 0 Fodlp 5 hvwdeolvkhv wkdw lqfuhdvlqj wkh gxudwlrq ri wkh XL vfkhph/
zkloh uhgxflqj Kf wr krog jhqhurvlw| frqvwdqw/ sxvkhv xs htxloleulxp zdjhv1 ^Qrwh wkdw
o k lv wkh qdwxudo fdvh> h1j1 lq wkh XN wkh dyhudjh gxudwlrq ri xqhpsor|phqw
lv durxqg 59 zhhnv/ zklfk lpsolhv dq dqqxdo pdwfklqj udwh k ' 2c zkloh dqqxdo
glvfrxqw udwhv duh w|slfdoo| dvvxphg wr eh durxqg 8(1` Wkh xqghuo|lqj lqvljkw lv
wkdw zkhq mre rhuv duh xqrevhuydeoh/ hdfk zrunhu*v uhvhuydwlrq zdjh ghshqgv rq wkh
zrunhu*v rswlrq ydoxh ri uhpdlqlqj xqhpsor|hg dqg frqwlqxlqj wr uhfhlyh ixuwkhu XL
sd|phqwv1 Dv wkh zrunhu*v udwh ri wlph suhihuhqfh o k c h{whqglqj wkh gxudwlrq
ri XL sd|phqwv zkloh kroglqj jhqhurvlw| frqvwdqw lpsolhv wkh rswlrq ri uhpdlqlqj
xqhpsor|hg lqfuhdvhv lq ydoxh1
Wr looxvwudwh wkh srwhqwldo pdjqlwxgh ri wklv zdjh glvwruwlrq/ wkh iroorzlqj xvhv d
qxphulfdo vlpxodwlrq edvhg rq wkh sdudphwhu ydoxhv fkrvhq e| Ploodug dqg Pruwhqvhq
+4<<:, ^khqfhiruwk PP` lq wkhlu fdoleudwlrqv ri wkh X1V1 hfrqrp|1
Dvvxplqj d
Free0Grxjodv pdwfklqj ixqfwlrq  ' L 3# T # c Wdeoh 4 uhsruwv wkh PP ydoxhv iru
c oc #c wc & zkhuh wkh dvvxphg wlph xqlw lv rqh txduwhu1
Wr irfxv rq wkh prudo kd}dug lpsolfdwlrqv ri qrq0revhuydeoh mre rhuv/ wkh wkhru|
vhfwlrq zdv vlpsolhg e| dvvxplqj qr mre ghvwuxfwlrq1 Dv d uhvxow/ vwhdg| vwdwh mre
wxuqryhu htxdov B1 Wkh sxusrvh ri wkh vlpxodwlrqv wkdw iroorz lv wr ghprqvwudwh krz
odujh wkh uhvxowlqj zdjh glvwruwlrq rq xqhpsor|phqw fdq eh xvlqj d edvholqh hfrqrp|
lq zklfk wkh xqhpsor|phqw jxuhv fruuhvsrqg urxjko| wr dfwxdo hfrqrplf dfwlylw| lq
wkh XV1 Wkh Fxuuhqw Srsxodwlrq Vxuyh| ^FSV` lqglfdwhv wkdw ehwzhhq 4<;8 dqg 4<<8/
wkh dyhudjh xqhpsor|phqw udwh dqg wkh dyhudjh gxudwlrq ri xqhpsor|phqw zhuh 917(
dqg 48 zhhnv uhvshfwlyho|1 Wr w wkhvh dyhudjhv/ vwhdg| vwdwh uhtxluhv wkdw wkh lq rz
ri mre vhhnhuv B ' ffDDD shu txduwhu ^e| frpsdulvrq/ Froh dqg Urjhuvrq +4<<<, xvh
31388 zkhq ghvfulelqj djjuhjdwh mre ghvwuxfwlrq udwhv`1
53
&
o
#
w
B
@
Kf
4
315;8 3134 319 31: 13888 ;189 3158
Wdeoh 4= Vlpxodwlrq Sdudphwhu Ydoxhv
Wkh xqhpsor|phqw lqvxudqfh v|vwhp lq wkh X1V1 lv frqvlghuhg wr eh AK ' 2 txdu0
whuv zlwk d uhsodfhphqw udwh ri durxqg 3181 Wkh uhpdlqlqj sdudphwhu ydoxhv @ dqg Kf
duh fkrvhq wr dssur{lpdwh wklv uhsodfhphqw udwh zkloh pdwfklqj wkh xqhpsor|phqw
jxuhv iurp wkh FSV1 Wdeoh4 ghvfulehv wkrvh sdudphwhu ydoxhv/ dqg urz 5 lq Wdeoh 5
ghvfulehv wkh fruuhvsrqglqj pdunhw htxloleulxp1:
Jlyhq wkhvh sdudphwhu ydoxhv/ Wdeoh 5 ghvfulehv wkh hhfw ri fkdqjlqj wkh gxudwlrq
ri sd|phqwv lq d XL vfkhph zkloh kroglqj jhqhurvlw| frqvwdqw Iru hdfk vfkhph/
qhzo| xqhpsor|hg zrunhuv h{shfw wr uhfhlyh 614 zhhnv ri pdwfk rxwsxw lq wrwdo XL
sd|phqwv ^derxw 9 zhhnv ri zdjhv`1; Wkh vhfrqg dqg wklug froxpqv ghvfuleh wkh
7 lv wkh dyhudjh zdjh sdlg lq wkh hfrqrp| zkloh lv wkh dyhudjh gxudwlrq
vfkhph1 ri xqhpsor|phqw1
Dv ghprqvwudwhg e| Fodlp 5/ lqfuhdvlqj A ^zkloh kroglqj K frqvwdqw` lqfuhdvhv
wkh rswlrq ydoxh ri uhpdlqlqj xqhpsor|hgc dqg vr lqfuhdvhv zdjhv iru doo A 1 Wdeoh
5 ghprqvwudwhv wkhvh hhfwv duh srwhqwldoo| odujh1 Jrlqj wr dq lqghqlwh sd|phqw
vfkhph ^iurp urz 5 wr urz 7` lpsolhv d 4<( lqfuhdvh lq dyhudjh pdunhw zdjhv1 Wkh
fruuhvsrqglqj lqfuhdvh lq xqhpsor|phqw lv durxqg 68( ^mxvw ryhu wzr shufhqwdjh
srlqwv` dqg wkh dyhudjh gxudwlrq ri xqhpsor|phqw lqfuhdvhv iurp 48 wr 53 zhhnv1
Krzhyhu/ prvw ri wklv fkdqjh rffxuv zkhq zh pryh iurp wkh rqh |hdu wr wkh lqghqlwh
:
Wkh ydoxh iru d pd| orrn h{fhvvlyho| odujh xqghu lwv xvxdo lqwhusuhwdwlrq dv dq dgyhuwlvlqj frvw1
Lq dfwxdolw|/ lw kdv wr fdswxuh doo ri wkh fdslwdo frvwv dvvrfldwhg zlwk mre fuhdwlrq1
;
zlwk W @ 5 dqg e! @ 3=58> wkh frpsxwhg vwhdg| vwdwh frvw ri wkh XL vfkhph lv 3134641 Qrwh
wkdw dv wkh lq rz lv wkh vdph dfurvv vfkhphv/ wkh vwhdg| vwdwh frvw ri wkh XL vfkhph shu hqwudqw
lv dovr frqvwdqw1
54
oJ
A
r
zhhnv
3
3
4
Kf
7
0
L
7
I
zhhnv
317<< 914:
4718
46
31698 31838 915:
471:
5
59
31583 31844 916;
4813
6
85
31538 31857 9195
4818
7
4
31485 31939 ;195
5315
Wdeoh 5= Vlpxodwlrq Uhvxowv
sd|phqw vfkhph 0 wkh glvwruwlrq lv uhodwlyho| vpdoo iru d vkliw iurp 9 prqwkv wr rqh
|hdu1
Iljxuh 4 sorwv wkh zdjh ixqfwlrqv W E iru hdfk ri wkh srolf| sdudphwhuv EKf c A Dv lpsolhg e| fodlp 5/ wkhvh zdjh ixqfwlrqv vkliw xs dv A lqfuhdvhv1 Dsduw iurp
wkh fdvh A ' 4c wkhvh zdjh ixqfwlrqv ghfuhdvh zlwk gxudwlrq/ zkhuh d zrunhu*v
edujdlqlqj srvlwlrq ghwhulrudwhv wkh forvhu wkh h{slu| gdwh ri klv2khu XL hqwlwohphqw1
Qrwh wkdw htxloleulxp xqhpsor|phqw ohyhov fkdqjh zlwk wkhvh srolf| sdudphwhuv1
Rq hdfk zdjh ixqfwlrq ghvfulehg lq jxuh 4/ zh kdyh dovr pdunhg wkh dyhudjh gxud0
wlrq ri xqhpsor|phqw ^dv ghvfulehg lq Wdeoh 5`1 Iru wkhvh sdudphwhu ydoxhv/ wkh
glvwruwlrq rq ^dqg Lo lv vpdoo iru A vpdoo ^qr pruh wkdq rqh |hdu`1 Wkh lpsolhg
hpsor|phqw hodvwlflw| zlwk uhvshfw wr dyhudjh zdjhv lv rqo| 4( lq wklv uhjlrq ^jrlqj
iurp urz 4 wr urz 6 lq Wdeoh 5`1 Krzhyhu wkh hpsor|phqw glvwruwlrq jrlqj wr wkh
lqghqlwh sd|phqw fdvh lv uhodwlyho| odujh1
Dv doo duh ulvn qhxwudo/ zh fdqqrw ghvfuleh wkh lqvxudqfh ydoxh ri hdfk XL vfkhph1
Qhyhuwkhohvv lw lv zhoo nqrzq zkhq doo duh ulvn qhxwudo/ wkdw wkh pdunhw rxwfrph lv qrw
h!flhqw xqohvv wkh Krvlrv frqglwlrq krogv ^Krvlrv +4<<3,`1 Iru wkh deryh sdudphwhu
ydoxhv ^dqg K ' fo zrunhuv kdyh cwrr olwwoh* edujdlqlqj srzhu ^dv  w ' f  # '
55
feo/ dqg d zhdn wkuhdwsrlqw ^zklfk lv wkh ydoxh ri ehlqj xqhpsor|hg iruhyhu/ udwkhu
wkdq wkh htxloleulxp ydoxh ri ehlqj xqhpsor|hg`1 Wkh qhjrwldwhg zdjh lq urz 3/ iru
wkh fdvh K ' fc lv wkhuhiruh ehorz wkh Krvlrv rswlpxp1 Htxloleulxp wkhuh lpsolhv cwrr
pxfk* ydfdqf| fuhdwlrq1
Dv upv pdnh }hur h{shfwhg surw/ wkh Xwlolwduldq Vrfldo Zhoiduh phdvxuh L7`
fruuhvsrqgv wr wkh vwhdg| vwdwh rz xwlolw| ri doo zrunhuv/ zklfk e| wkh deryh lv
L7` ' d Lo n B
] "
f
e3Ek nB| d n KE|o_|
' d Lo n B_ Ef
Jlyhq wkh deryh sdudphwhu ydoxhv dqg Wdeoh 5/ wklv zhoiduh phdvxuh lpsolhv wkdw urz
7/ wkh lqghqlwh XL vfkhph/ lv lq idfw wkh suhihuuhg XL v|vwhp1 E| lpsurylqj wkh
edujdlqlqj srvlwlrq ri zrunhuv/ wklv XL vfkhph udlvhv htxloleulxp zdjhv forvhu wr wkh
Krvlrv zdjh ohyho ^dw zklfk srlqw doo frqjhvwlrq h{whuqdolwlhv duh ixoo| lqwhuqdolvhg`1
Ri frxuvh iru glhuhqw sdudphwhuv/ vd| zrunhuv kdyh wrr pxfk edujdlqlqj srzhu/
wkh rssrvlwh lqvljkw zrxog dsso| 0 urz }hur lq Wdeoh 5/ zklfk fdq dowhuqdwlyho| eh
lqwhusuhwhg dv pdnlqj d oxps vxp sd|phqw ri K dw ' fc zrxog wkhq eh suhihuuhg
0 doo rwkhu XL vfkhphv glvwruw zdjhv ixuwkhu dzd| iurp wkh Krvlrv rswlpxp1
8
Frqfoxvlrq
Wklv sdshu kdv ghyhorshg d g|qdplfdoo| frqvlvwhqw prgho ri htxloleulxp xqhpsor|0
phqw zkhq XL sd|phqwv duh gxudwlrq ghshqghqw1 Wkh qglqj lv wkdw iru qdwxudo
sdudphwhu ydoxhv +wkdw lpso| o k / h{whqglqj wkh gxudwlrq ri XL sd|phqwv zkloh
kroglqj wkh jhqhurvlw| ri wkh vfkhph frqvwdqw/ lqfuhdvhv wkh glvwruwlrq rq uhvhuydwlrq
zdjhv dw doo gxudwlrqv1 Vlpxodwlrqv vxjjhvw wkdw dq lqghqlwh sd|phqw vfkhph kdv d
sduwlfxoduo| odujh lpsdfw rq htxloleulxp zdjhv dqg xqhpsor|phqw ohyhov1
Wr looxvwudwh fohduo| wkh qdwxuh ri wkh prudo kd}dug sureohp/ wklv sdshu kdv dv0
56
vxphg wkdw zrunhuv duh ulvn qhxwudo1 Exw dv wkhuh lv qr lqvxudqfh uroh iru XL lq wklv
fdvh/ zh kdyh plqlplvhg dq| zhoiduh glvfxvvlrqv1 Dq lpsruwdqw gluhfwlrq iru ixwxuh
uhvhdufk lv wr doorz vwulfwo| ulvn dyhuvh zrunhuv1 Li zrunhuv dovr kdyh cwrr pxfk* edu0
jdlqlqj srzhu vr wkdw pdunhw zdjhv duh srwhqwldoo| wrr kljk ^lq wkh Krvlrv vhqvh`/
wkh jryhuqphqw wkhq kdv d wudgh0r ehwzhhq surylglqj h!flhqw lqvxudqfh djdlqvw
xqhpsor|phqw ulvn/ dqg glvwruwlqj pdunhw zdjhv1 Xqiruwxqdwho| vxfk dq h{whqvlrq
lv frpsoh{1 Wkh fhqwudo gl!fxow| lv wkdw jlyhq gxudwlrq ghshqghqw XL sd|phqwv/ wkh
htxloleulxp zdjh edujdlqlqj rxwfrph zlwk d vwulfwo| ulvn dyhuvh zrunhu lv ghvfulehg
e| d qrq0olqhdu glhuhqwldo htxdwlrq zklfk kdv qr forvhg irup vroxwlrq ^vhh Frohv dqg
Zuljkw +4<<;, iru h{dpsoh`1 Dowkrxjk lw vkrxog eh srvvleoh wr frpsxwh qxphulfdo
htxloleuld/ wkh fohdq wkhruhwlfdo lqvljkwv rewdlqhg deryh duh qhfhvvdulo| orvw1 Qhy0
huwkhohvv/ lqwxlwlrq vwurqjo| vxjjhvwv d Vkdyhoo0Zhlvv w|sh surjudp zloo eh rswlpdo1
Lq Vkdyhoo dqg Zhlvv +4<:<,/ wkh jryhuqphqw uhgxfhv XL sd|phqwv zlwk gxudwlrq wr
uhgxfh wkh ydoxh ri uhpdlqlqj xqhpsor|hg dqg vr hqfrxudjh juhdwhu mre vhdufk hruw1
Wkh vdph lqvljkw dssolhv khuh vkrxog zrunhuv kdyh wrr pxfk edujdlqlqj srzhu1 E|
uhgxflqj XL sd|phqwv zlwk gxudwlrq/ wkh jryhuqphqw uhgxfhv wkh ydoxh ri uhpdlqlqj
xqhpsor|hg zklfk/ wklv wlph/ uhgxfhv wkh glvwruwlrq rq zrunhu uhvhuydwlrq zdjhv1 Dv
lq Vkdyhoo dqg Zhlvv +4<:<,/ wkh jryhuqphqw fdq wkhq rhu uhodwlyho| jhqhurxv XL sd|0
phqwv iru vkruw gxudwlrqv/ dqg vr surylgh uhdvrqdeoh lqvxudqfh iru hpsor|hg zrunhuv
djdlqvw od|r ulvn/ zkloh plqlplvlqj wkh prudo kd}dug glvwruwlrq rq htxloleulxp zdjh
irupdwlrq1 Frpsxwlqj vxfk htxloleuld dqg hvwdeolvklqj irupdoo| wklv lqwxlwlrq lv ohiw
iru ixwxuh uhvhdufk1
57
Uhihuhqfhv
Doeuhfkw/ M1 dqg V1 Yurpdq +5334,/ Htxloleulxp Vhdufk zlwk Wlph Ydu|lqj Xqhp0
sor|phqw Ehqhwv plphr/ Jhrujhwrzq Xqlyhuvlw|1
Dwnlqvrq/ D1 dqg M1 Plfnohzuljkw +4<<4, Xqhpsor|phqw Frpshqvdwlrq dqg Oderxu
Pdunhw Wudqvlwlrqv= d Fulwlfdo Uhylhz Mrxuqdo ri Hfrqrplf Olwhudwxuh/ 5</
49:<04:5:1
Elqpruh/ N1 +4<;:, Shuihfw Htxloleuld lq Edujdlqlqj Prghov/ lq Wkh Hfrqrplfv
ri Edujdlqlqj/ Nhq Elqpruh dqg Sduwkd Gdvjxswd/ hgv1 R{irug/ X1N1= Edvlo
Eodfnzhoo1
Elqpruh/ N1/ D1 Uxelqvwhlq/ dqg D1 Zrolqvn|/ +4<;9, Wkh Qdvk Edujdlqlqj Vroxwlrq
lq Hfrqrplf Prghoolqj Udqg Mrxuqdo ri Hfrqrplfv/ 4:/ 4:90;;1
Eodqfkdug/ R1 dqg S1 Gldprqg/ +4<<7, Udqnlqj/ Xqhpsor|phqw Gxudwlrq dqg
Zdjhv/ Uhylhz ri Hfrqrplf Vwxglhv/ 94/ 74:0671
Exughww/ N1 dqg G1 Pruwhqvhq +4<;3, Vhdufk/ Od|0rv dqg Oderu Pdunhw Htxlole0
ulxp/ Mrxuqdo ri Srolwlfdo Hfrqrp|/ ;;/ 9850:51
Froh/ K1 dqg U1 Urjhuvrq/ +4<<<, Fdq wkh Pruwhqvhq0Slvvdulghv Pdwfklqj Prgho
Pdwfk wkh Exvlqhvv F|foh IdfwvB Lqwhuqdwlrqdo Hfrqrplf Uhylhz/ 73/ <660931
Frohv/ P1 dqg D1 Pdvwhuv +5334, Xqhpsor|phqw Lqvxudqfh dqg wkh F|folfdo Sdwwhuq
ri Xqhpsor|phqw/ plphr Xqlyhuvlw| ri Hvvh{/ XN1
Frohv/ P1 dqg U1 Zuljkw/ +4<<;, D G|qdplf Htxloleulxp Prgho ri Vhdufk/ Edu0
jdlqlqj dqg Prqh| Mrxuqdo ri Hfrqrplf Wkhru|/ ;6/ 650871
Gdylgvrq/ F1 dqg V1 Zrrgexu|/ +4<<:, Rswlpdo Xqhpsor|phqw Lqvxudqfh/ Mrxu0
qdo ri Sxeolf Hfrqrplfv/ 97/ 68<0;:1
58
Gldprqg/ S1 +4<;4, Zdjh Ghwhuplqdwlrq dqg H!flhqf| lq Vhdufk Htxloleulxp/
Uhylhz ri Hfrqrplf Vwxglhv/ 7</ 54:05;1
Iuhgulnvvrq/ S1 dqg E1 Kropxqg/ +5334, Rswlpdo Xqhpsor|phqw Lqvxudqfh lq
Vhdufk Htxloleulxp/ Mrxuqdo ri Oderu Hfrqrplfv/ 4</ 6:30<<1
Jdoh/ G1 +4<;:, Olplw Wkhruhpv iru Pdunhwv zlwk Vhtxhqwldo Edujdlqlqj/ Mrxuqdo
ri Hfrqrplf Wkhru|/ 76/ 530871
Krvlrv/ D1 +4<<3, Rq wkh H!flhqf| ri Pdwfklqj dqg Uhodwhg Prghov ri Vhdufk dqg
Xqhpsor|phqw/ Uhylhz ri Hfrqrplf Vwxglhv/ 8:/ 5:<0<;1
Ploodug/ V1 dqg G1 Pruwhqvhq/ +4<<:, Wkh Xqhpsor|phqw dqg Zhoiduh Hhfwv ri
Oderxu Pdunhw Srolf|= D Frpsdulvrq ri wkh XVD dqg wkh XN lq Xqhpsor|0
phqw Srolf|/ Vqrzhu/ G1 dqg gh od Ghkhvd/ J1 hgv1 Fdpeulgjh= Fdpeulgjh
Xqlyhuvlw| Suhvv +iru FHSU,1
Pruwhqvhq/ G1 +4<::, Xqhpsor|phqw Lqvxudqfh dqg Mre Vhdufk Ghflvlrqv/ Lqgxv0
wuldo dqg oderxu Uhodwlrqv Uhylhz/ 63/ 83804:1
Pruwhqvhq/ G1 dqg F1 Slvvdulghv +4<<7,= Mre Fuhdwlrq dqg Mre Ghvwuxfwlrq lq wkh
Wkhru| ri Xqhpsor|phqw/ Uhylhz ri Hfrqrplf Vwxglhv/ 94/ 6<:07481
Pruwhqvhq/ G1 dqg U1 Zuljkw +5333, Frpshwlwlyh Sulflqj dqg H!flhqf| lq Vhdufk
Htxloleulxp/ plphr/ Xqlyhuvlw| ri Shqqv|oydqld1
Qlfnhoo/ V1 +4<<:, Xqhpsor|phqw dqg Oderxu Pdunhw Uljlglwlhv= Hxursh yhuvxv
Qruwk Dphulfd Mrxuqdo ri Hfrqrplf Shuvshfwlyhv/ 4416/ 880:71
Slvvdulghv/ F1 +4<<3,1 Htxloleulxp Xqhpsor|phqw Wkhru|1 R{irug= Edvlo Eodfnzhoo1
Uxelqvwhlq/ D1 dqg D1 Zrolqvn| Htxloleulxp lq d Pdunhw zlwk Vhtxhqwldo Edujdlq0
lqj/ Hfrqrphwulfd/ 86/ 44660831
59
Vkdyhoo/ V1 dqg O1 Zhlvv +4<:<, Wkh Rswlpdo Sd|phqw ri Xqhpsor|phqw Lqvxudqfh
Ehqhwv ryhu Wlph Mrxuqdo ri Srolwlfdo Hfrqrp|/ ;:/ 467:0951
ydq ghq Ehuj/ J1 +4<<3, Qrqvwdwlrqdulw| lq Mre Vhdufk Wkhru|/ Uhylhz ri Hfr0
qrplf Vwxglhv/ 8:/ 5880::1
5:
0.62
0.60
T =infinity
0.58
indicates average unemployment
duration for each series
0.56
T =13 weeks
T =26 weeks
0.54
T =52 weeks
0.52
0.50
0.48
0.46
0
10
20
30
40
50
60
Iljxuh 4= Zdjh yhuvxv Gxudwlrq ri Xqhpsor|phqw lq Zhhnv
5;
70