EH\RQG EDODQFHG JURZWK
Sl|dekd Nrqjvdpxw|/ Vhujlr Uhehor} dqg Gdq|dqj [lh{
Ghfhpehu/ 5333
Devwudfw
Edodqfhg jurzwk prghov duh frpprqo| xvhg lq pdfurhfrqrplfv ehfdxvh
wkh| duh frqvlvwhqw zlwk wkh zhoo0nqrzq Ndogru idfwv uhjduglqj hfrqrplf
jurzwk1 Wkhvh prghov/ krzhyhu/ duh lqfrqvlvwhqw zlwk rqh ri wkh prvw
vwulnlqj uhjxodulwlhv ri wkh jurzwk surfhvvwkh pdvvlyh uhdoorfdwlrq ri oderu
iurp djulfxowxuh lqwr pdqxidfwxulqj dqg vhuylfhv1 Wklv sdshu suhvhqwv d
vlpsoh prgho frqvlvwhqw zlwk erwk wkh Ndogru idfwv dqg wkh g|qdplfv ri
vhfwrudo oderu uhdoorfdwlrq1
Nh| zrugv= Jurzwk/ Vwuxfwxudo Fkdqjh/ Ndogru Idfwv1
MHO Fodvvlfdwlrq= R47/ R741
Zh ehqhwhg iurp wkh ghwdlohg frpphqwv ri wkh hglwru/ Rud}lr Dwwdqdvlr/ dqg ri wzr dqrq|0
prxv uhihuhhv1 Zh duh dovr wkdqnixo wr Urehuw Eduur/ Pduldqqh Ed{whu/ Urehuw Kdoo/ Urehuw
Nlqj/ Khqu| Vlx/ Urehuw Vrorz/ Ure Yljixvvrq/ dqg wr vhplqdu sduwlflsdqwv dw Ehuq/ Ervwrq
Xqlyhuvlw|/ Kduydug/ Plfkljdq/ Urfkhvwhu/ Ylujlqld/ dqg wkh Zruog Edqn iru wkhlu vxjjhvwlrqv1
Uhvhdufk vxssruw iurp QVI judqw VUE0<844<49 dqg iurp d Krqj Nrqj Xqlyhuvlw| ri Vflhqfh
dqg Whfkqrorj| GDJ judqw lv judwhixoo| dfnqrzohgjhg1
|Lqwhuqdwlrqdo Prqhwdu| Ixqg1
}Qruwkzhvwhuq Xqlyhuvlw|/ QEHU dqg FHSU1
{Krqj Nrqj Xqlyhuvlw| ri Vflhqfh dqg Whfkqrorj| dqg Lqwhuqdwlrqdo Prqhwdu| Ixqg1
41 Lqwurgxfwlrq
Edodqfhg jurzwk prghov duh zlgho| xvhg lq pdfurhfrqrplfv ehfdxvh wkh| duh
frqvlvwhqw zlwk wkh zhoo0nqrzq Ndogru idfwv uhjduglqj hfrqrplf jurzwk1 Ndogru
vwuhvvhg wkdw wkh jurzwk udwh ri rxwsxw/ wkh fdslwdo0rxwsxw udwlr/ wkh uhdo lqwhuhvw
udwh/ dqg wkh oderu lqfrph vkduh duh doo urxjko| frqvwdqw ryhu wlph1 Wkh frqvwdqf|
ri wkhvh juhdw udwlrv surylghv d jrrg fkdudfwhul}dwlrq ri wkh orqj uxq ehkdylru
ri wkh X1V1 hfrqrp|1
Mxvw dv lpsruwdqw dv wkhvh uhjxodulwlhv vwuhvvhg e| Ndogru lv wkh pdvvlyh uhdoor0
fdwlrq ri oderu iurp djulfxowxuh lqwr pdqxidfwxulqj dqg vhuylfhv wkdw dffrpsdqlhv
wkh jurzwk surfhvv1 Wklv uhdoorfdwlrq surfhvv/ riwhq fdoohg vwuxfwxudo fkdqjh/
kdv ehhq grfxphqwhg e| dxwkruv vxfk dv Fodun +4<73,/ Nx}qhwv +4<8:,/ dqg Fkhq0
hu| +4<93,1 D ihz qxpehuv khos wr sxw wklv skhqrphqrq lqwr shuvshfwlyh1 Lq 4;:3
wkh X1V1 vkduh ri hpsor|phqw lq djulfxowxuh zdv 73(1 Rqh kxqguhg |hduv odwhu/
djulfxowxuh dffrxqwhg iru rqo| 7( ri hpsor|phqw1 Vhuylfhv/ zklfk dffrxqwhg iru
53( ri hpsor|phqw lq 4;:3/ devruehg 73( ri wkh oderu irufh e| 4<:31 Zh uhihu
wr wkh pdlq uhjxodulwlhv ri wklv uhdoorfdwlrq surfhvv dv wkh Nx}qhwv idfwv1
Wkh pdfurhfrqrplfv dqg jurzwk olwhudwxuh/ zklfk pdnhv khdy| xvh ri edodqfhg
jurzwk prghov/ jhqhudoo| glvuhjdugv wkh gudpdwlf vhfwrudo uhdoorfdwlrq ri oderu
h{shulhqfhg e| doo h{sdqglqj hfrqrplhv1 Lq frqwudvw/ wkhuh lv d olwhudwxuh rq
vwuxfwxudo fkdqjh wkdw ljqruhv wkh Ndogru idfwv/ lq sduw ehfdxvh lw irfxvhv rq d
orqjhu wlph shulrg iru zklfk wkhvh idfwv pd| qrw dsso| +h1j1 Edxpro +4<9:,/
Sdvlqhwwl +4<;4,/ Sdun +4<<8,/ Hfkhyduuld +4<<:,/ dqg Odlwqhu +5333,,1
Lv wkhuh d jurzwk prgho wkdw lv frqvlvwhqw zlwk erwk wkh Ndogru idfwv dqg
wkh pdvvlyh vhfwrudo oderu uhdoorfdwlrq h{shulhqfhg lq wkh X1V1 gxulqj wkh odvw
fhqwxu|B Dw uvw vljkw wkh dqvzhu wr wklv txhvwlrq lv qr1 Diwhu doo/ rqh surshuw|
ri edodqfhg jurzwk prghov lv wkdw wkh iudfwlrq ri fdslwdo dqg oderu doorfdwhg
4
wr glhuhqw lqgxvwulhv uhpdlq frqvwdqw ryhu wlph1 Zh vkrz wkdw wkh wzr vhw ri
idfwv krzhyhu fdq eh uhfrqflohg/ surylghg wkdw d nqlih0hgjh frqglwlrq lv vdwlvhg1
Wkh prgho zh sursrvh glvsod|v d jhqhudol}hg edodqfhg jurzwk +JEJ, sdwkd
wudmhfwru| wkdw uhwdlqv wkh nh| ihdwxuhv ri edodqfhg jurzwk dqg lv frqvlvwhqw zlwk
wkh g|qdplfv ri vwuxfwxudo fkdqjh1
Edodqfhg jurzwk sdwkv duh hdv| wr vwxg|1 Wkh idfw wkdw doo yduldeohv jurz
dw d frqvwdqw udwh wudqvirupv wkh v|vwhp ri glhuhqfh htxdwlrqv wkdw ghvfulehv
wkh hfrqrp|*v frpshwlwlyh htxloleulxp lqwr d v|vwhp ri vwdwlf htxdwlrqv wkdw fdq
eh hdvlo| vroyhg1 Wklv v|vwhp dovr gholyhuv wkh yhfwru ri lqlwldo ydoxhv iru wkh
fdslwdo vwrfnv wkdw lv frqvlvwhqw zlwk edodqfhg jurzwk1 Wkh jhqhudol}hg edodqfhg
jurzwk sdwk lq rxu prgho vkduhv wkhvh dwwudfwlyh ihdwxuhv1 Wkh JEJ sdwk dqg
wkh fruuhvsrqglqj yhfwru ri lqlwldo frqglwlrqv fdq eh fkdudfwhul}hg dqdo|wlfdoo|/
hyhq wkrxjk vrph yduldeohv kdyh wlph0ydu|lqj jurzwk udwhv1
Rxu sdshu lv rujdql}hg dv iroorzv1 Vhfwlrq 5 vxppdul}hv eulh | wkh pdlq
hpslulfdo idfwv wkdw prwlydwh rxu dqdo|vlv1 Vhfwlrq 6 suhvhqwv rxu prgho1 D qdo
vhfwlrq glvfxvvhv srvvleoh dssolfdwlrqv dqg h{whqvlrqv ri rxu prgho1
51 Wkh Hpslulfdo Idfwv
Lq dgglwlrq wr revhuylqj wkdw wkh udwh ri hfrqrplf h{sdqvlrq glhuv zlgho| dfurvv
frxqwulhv/ Ndogru sursrvhg wkh iroorzlqj zhoo0nqrzq vhw ri hpslulfdo uhjxodulwlhv=
Wkh Ndogru Idfwv
4 0 Shu fdslwd rxwsxw jurzv dw d udwh wkdw lv urxjko| frqvwdqw>
5 0 Wkh fdslwdo0rxwsxw udwlr lv urxjko| frqvwdqw>
6 0 Wkh uhdo udwh ri uhwxuq wr fdslwdo lv urxjko| frqvwdqw>
7 0 Wkh vkduhv ri oderu dqg fdslwdo lq qdwlrqdo lqfrph duh urxjko| frqvwdqw1
Wkhvh vw|ol}hg idfwv/ zklfk vxjjhvw wkdw vhyhudo djjuhjdwh juhdw udwlrv hyroyh
5
vprrwko| ryhu wlph/ kdyh kdg dq hqruprxv lpsdfw rq wkh frqvwuxfwlrq ri jurzwk
prghov1 Duh wkh| wrr vw|ol}hg wr eh idfwvB Wkh uvw sdqho ri Iljxuh 4/ zklfk
ghslfwv wkh orjdulwkp ri shu fdslwd X1V1 uhdo JGS iurp 4<35 wr 4<<< phdvxuhg dw
dq dqqxdo iuhtxhqf|/ vkrzv wkdw wkh jurzwk udwh ri rxwsxw lv lqghhg uhpdundeo|
vwdeoh1 Wklv ylvxdo lpsuhvvlrq lv frquphg e| irupdo vwdwlvwlfdo whvwv zklfk gr qrw
uhmhfw wkh k|srwkhvlv wkdw wkh phdq udwh ri jurzwk kdv ehhq wkh vdph lq wkh uvw
dqg lq wkh vhfrqg sduwv ri wkh vdpsoh +vhh Vwrnh| dqg Uhehor +4<<8,,1 Wkh vhfrqg
sdqho ri Iljxuh 4 vkrzv wkh X1V1 fdslwdo0rxwsxw udwlr iru wkh shulrg 4<5<04<<;14
Zkloh wklv udwlr urvh gxulqj wkh Juhdw Ghsuhvvlrq/ lw kdv ehhq uhpdundeo| vwdeoh
gxulqj wkh srvw0zdu shulrg1 Wkh wklug sdqho ri Iljxuh 4 uhsruwv wkh dqqxdo uhdo
udwh ri uhwxuq rq wkh X1V1 vwrfn pdunhw frpslohg e| Vlhjho +4<<8, iru glhuhqw
wlph shulrgv15 Wkhuh lv uhpdundeo| olwwoh yduldwlrq lq wklv uhdo udwh ri uhwxuq16
Wkh odvw sdqho ri Iljxuh 4 vkrzv wkdw wkh yduldwlrq lq wkh oderu lqfrph vkduh lq
wkh shulrg 4<8<04<<; lv uhodwlyho| vpdoo1
Wkh gdwd glvsod|hg lq Iljxuh 4 vkrzv wkdw wkh Ndogru idfwv duh d jrrg vkruw0
kdqg ghvfulswlrq ri wkh X1V1 jurzwk surfhvv1 Exw zkloh wkhvh idfwv vxjjhvw wkdw
wkh jurzwk surfhvv lv vprrwk/ wklv lpsuhvvlrq lv txlfno| vkdwwhuhg rqfh zh pryh
eh|rqg wkhvh djjuhjdwh vwdwlvwlfv wr wkh vlpsohvw ohyho ri lqgxvwu| glvdjjuhjdwlrq1
4
Lq rughu wr rewdlq wkh orqjhvw frqvlvwhqw wlph vhulhv iru wkh fdslwdo vwrfn zh h{foxghg sxeolf
dqg uhvlghqwldo fdslwdo1
5
Wkh kljk uhdo uhwxuq wr wkh X1V1 vwrfn pdunhw gxulqj wkh 4<<3*v grhv qrw lqydolgdwh wkh
revhuydwlrq wkdw wkh dyhudjh uhdo udwh ri uhwxuq vhhpv frqvwdqw ryhu wlph1 Xvlqj wkh Leerwvrq
dqg Dvvrfldwhv +4<<<, gdwd iru wkh uhdo udwh ri uhwxuq wr wkh Vwdqgdug dqg Srruv 833 lqgh{/ rqh
fdqqrw uhmhfwhg wkh k|srwkhvlv wkdw wkh h{shfwhg uhdo udwh ri uhwxuq kdv ehhq frqvwdqw dfurvv
ghfdghv iru wkh shulrg 4<6304<<<1 Wklv sduwo| uh hfwv wkh idfw wkdw wkh kljk yrodwlolw| ri vwrfn
pdunhw uhwxuqv pdnhv lw gl!fxow wr hvwlpdwh wkh dyhudjh udwh ri uhwxuq1 Vhh Phuwrq +4<;3, iru
d glvfxvvlrq ri wkh gl!fxowlhv dvvrfldwhg zlwk hvwlpdwlqj h{shfwhg uhwxuqv1
6
Vlhjho +4<<8, dovr uhsruwv wkh uhdo uhwxuq rq erqgv/ zklfk zdv voljkwo| kljkhu lq wkh ehjlqqlqj
ri wkh vdpsoh wkdq lq wkh hqg1 Wklv wlph yduldwlrq pd|/ krzhyhu/ uh hfw wkh idfw wkdw wkh erqg
sruwirolr xvhg lq wkh uvw sduw ri wkh vdpsoh frpsulvhg ulvnlhu vhfxulwlhv +pxqlflsdo dqg xwlolw|
erqgv,/ wkdq wkh Wuhdvxu| eloov ihdwxuhg lq wkh vhfrqg sduw ri wkh vdpsoh1
6
Wkh Nx}qhwv Idfwv
Wdeoh 4 vxppdul}hv wkh pdlq hohphqwv ri wkh vwuxfwxudo fkdqjh wkdw kdv wdnhq
sodfh lq wkh X1V1 dqg lq rwkhu jurzlqj hfrqrplhv gxulqj wkh odvw 433 |hduv1
Iljxuh 5 looxvwudwhv wkh idfwv vxppdul}hg lq wklv wdeoh1 Lwv uvw sdqho ghslfwv
wkh hyroxwlrq ri X1V1 hpsor|phqw vkduhv lq Djulfxowxuh/ Pdqxidfwxulqj/ dqg Vhu0
ylfhv iurp 4;9< wr 4<<;17 Wkh ghfolqh lq wkh djulfxowxudo zrunirufh dqg wkh ulvh lq
wkh vhuylfh vhfwru duh vdolhqw lq wklv jxuh1 Wkh vhfrqg sdqho ri Iljxuh 5 vkrzv wkh
hyroxwlrq ri djjuhjdwh frqvxpswlrq h{shqglwxuh vkduhv iurp 4<73 wr 4<<<1 Ryhu
wlph wkh dyhudjh X1V1 frqvxphu kdv lqfuhdvhg wkh vkduh ri h{shqglwxuh ghyrwhg wr
vhuylfhv dqg uhgxfhg wkh vkduh ghyrwhg wr djulfxowxudo surgxfwv1 Wkhvh g|qdp0
lfv duh dvvrfldwhg zlwk wkh ulvh lq shu fdslwd lqfrph revhuyhg ryhu wklv shulrg1
Wkh idfw wkdw wkh vkduh ri h{shqglwxuhv ghyrwhg wr wkh frqvxpswlrq ri vhuylfhv lq0
fuhdvhv/ zkloh wkh vkduh ghyrwhg wr djulfxowxudo jrrgv ghfuhdvhv dv lqfrph ulvhv kdv
ehhq zhoo grfxphqwhg lq sdqho gdwd vwxglhv ri frqvxpswlrq sdwwhuqv +Krxwkdnnhu
dqg Wd|oru +4<:3,/ Elov dqg Nohqrz +4<<;,,1
Wdeoh 4
Wkh Nx}qhwv Idfwv
Vkduh ri
Wrwdo Hpsor|phqw
Djulfxowxuh
Pdqxidfwxulqj
Vhuylfhv
ghfolqhv
vwdeoh8
lqfuhdvhv
7
Vkduh ri Wrwdo
Frqvxpswlrq
H{shqglwxuhv
ghfolqhv
vwdeoh
lqfuhdvhv
Frqvwuxfwlrq dqg Plqlqj zhuh lqfoxghg lq Pdqxidfwxulqj/ zkloh Wudqvsruw dqg Frppxql0
fdwlrqv zhuh lqfoxghg lq Vhuylfhv1
8
Wklv ghvfulswlrq uh hfwv rxu irfxv rq wkh odvw rqh kxqguhg |hduv1 Sulru wr wklv shulrg wkhuh
kdv ehhq d ulvh lq wkh lpsruwdqfh ri pdqxidfwxulqj/ vhh Odlwqhu +5333,1
7
Duh wkh vhfwrudo pryhphqwv grfxphqwhg lq Iljxuh 5 shfxoldu wr wkh X1V1 hfrq0
rp|/ ru duh wkh| d jhqhudo ihdwxuh ri hfrqrplf ghyhorsphqwB Nrqjvdpxw hw do
+4<<<, vwxglhv erwk d orqj0uxq gdwd vhw frpsulvlqj 55 frxqwulhv dqg d furvv0vhfwlrq
gdwd vhw ri 456 qrq0vrfldolvw frxqwulhv iru wkh shulrg 4<:304<;<1 Erwk gdwd vhwv
frqup wkh ghyhorsphqw uhjxodulwlhv ghslfwhg lq Iljxuh 51 Jurzwk lq shu fdslwd
lqfrph whqgv wr eh dffrpsdqlhg e| d ulvh lq vhuylfhv dqg d ghfolqh lq wkh djulfxo0
wxudo vhfwru/ erwk lq whupv ri oderu hpsor|phqw dqg uhodwlyh zhljkw lq JGS1
61 Wkh Prgho
Rxu prgho kdv wkuhh vhfwruv ri dfwlylw| +djulfxowxuh/ pdqxidfwxulqj dqg vhuylfhv,
zklfk vkduh surgxfwlrq ixqfwlrqv wkdw duh lghqwlfdo xs wr d frqvwdqw ri sursru0
wlrqdolw|1 Zh devwudfw iurp wkh suhvhqfh ri odqg dqg ri lqwhuqdwlrqdo wudgh/ wr
pdlqwdlq d vwuxfwxuh wkdw lv dv forvh dv srvvleoh wr wkdw ri vwdqgdug jurzwk prg0
hov19 Zh fdvw rxu prgho lq frqwlqxrxv wlph exw dqdorjrxv uhvxowv fdq eh rewdlqhg
lq glvfuhwh wlph1
Surgxfwlrq dqg Dffxpxodwlrq Whfkqrorj|
Wkhuh duh rqo| wzr idfwruv ri surgxfwlrq/ fdslwdo +g| , dqg oderu1 Zh qrupdol}h
wr rqh wkh wrwdo dprxqw ri oderu dydlodeoh lq wkh hfrqrp| dw hyhu| srlqw lq wlph1
Wkh surgxfwlrq vwuxfwxuh lv dv iroorzv=
| ' 8 E
| g| c | f| c
+614,

| n g | n Bg| '  8 E
| g| c | f| c
+615,
9
Iru dq dqdo|vlv ri vwuxfwxudo fkdqjh lq zklfk odqg sod|v d nh| uroh lq wkh dqdo|vlv vhh
Jrrgiulhqg dqg PfGhuprww +4<<8,1 Nrqjvdpxw +4<<8, qgv olwwoh hylghqfh wkdw rshqqhvv wr
wudgh lq xhqfhv wkh ehkdylru ri vhfwrudo vkduhv1
8
7| ' 7 8 E7| g| c |7 f| c
+616,

7
| n | n | ' c
+617,
| n | n |7 ' c
+618,
f | ' f| }c
+619,
gf c ff : fc jlyhq1
+61:,
Wkh ixqfwlrq 8 Ec lv dvvxphg wr eh ri fodvv 2 / krprjhqrxv ri ghjuhh rqh/
frqfdyh/ dqg lqfuhdvlqj lq erwk dujxphqwv1 Wkh yduldeohv dqg ghqrwh/
uhvshfwlyho|/ wkh iudfwlrq ri fdslwdo dqg oderu ghyrwhg wr vhfwru 1 Fdslwdo dqg oderu
duh iuhho| preloh dfurvv vhfwruv1 Wkh yduldeoh f| ghqrwhv wkh ohyho ri whfkqrorjlfdo
surjuhvv zklfk zh dvvxph wr eh oderu dxjphqwlqj1 Wkh h{lvwhqfh ri d edodqfhg
jurzwk sdwk uhtxluhv wklv irup ri whfkqlfdo surjuhvv1 Vlqfh zh vhhn wr jhqhudol}h
wkh frqfhsw ri edodqfhg jurzwk/ zh uhwdlqhg wkh oderu dxjphqwlqj fkdudfwhu ri
whfkqlfdo surjuhvv1
Rxwsxw ri wkh djulfxowxuh +| , dqg vhuylfhv +7| , vhfwruv fdq eh xvhg iru frq0
vxpswlrq1
Wkh rxwsxw ri wkh pdqxidfwxulqj vhfwru fdq eh frqvxphg +| , ru
lqyhvwhg +g | n Bg| ,1 Wkh dvvxpswlrq wkdw rqo| pdqxidfwxulqj rxwsxw fdq eh lq0
yhvwhg lv frqvlvwhqw zlwk wkh X1V1 lqsxw0rxwsxw wdeohv1 Dffruglqj wr wkhvh wdeohv
wkh pdqxidfwxulqj dqg frqvwuxfwlrq vhfwruv surgxfhg ehwzhhq <3( dqg <6( ri
lqyhvwphqw gxulqj wkh shulrg 4<8; wr 4<;:1:
:
Wkh X1V1 lqsxw0rxwsxw wdeohv xvhg lq wkhvh fdofxodwlrqv zhuh sxeolvkhg lq wkh iroorzlqj lvvxhv
ri wkh Vxuyh| ri Fxuuhqw Exvlqhvv= Qryhpehu 4<97/ Iheuxdu| 4<:7/ Pd| 4<;7/ Dsulo 4<;;/ dqg
Dsulo 4<<71
9
H!flhqf| lq Surgxfwlrq
Vlqfh fdslwdo dqg oderu duh iuhho| preloh/ dq h!flhqw doorfdwlrq uhtxluhv wkdw
wkh pdujlqdo udwh ri wudqvirupdwlrq eh htxdwhg dfurvv wkh wkuhh surgxfwlrq vhfwruv/
zklfk lpsolhv=

7
| ' | ' | ' 
|
|
|7
+61;,
Vlqfh wkh surgxfwlrq ixqfwlrqv ri wkh glhuhqw vhfwruv duh sursruwlrqdo/ wkh
uhodwlyh sulfhv ri djulfxowxuh dqg vhuylfhv lq whupv ri pdqxidfwxulqj jrrgv duh
jlyhq e|=
'  * c
7 '  *7 Xvlqj wkhvh uhodwlyh sulfhv dqg wkh h!flhqf| frqglwlrq +61;, zh fdq uhzulwh wkh
hfrqrp|*v uhvrxufh frqvwudlqw dv=
| n g | n Bg| n | n 7 7| '  8 Eg| c f| +61<,
Suhihuhqfhv
Jlyhq wkh hfrqrp|*v surgxfwlrq vwuxfwxuh/ vhfwrudo pryhphqwv pxvw ruljlqdwh
iurp glhuhqfhv lq wkh lqfrph hodvwlflw| ri ghpdqg iru wkh glhuhqw jrrgv1 Zh
dvvxph wkdw suhihuhqfhv duh wlph0vhsdudeoh1 Rxu prphqwdu| xwlolw| vshflfdwlrq
hpehgv glhuhqw lqfrph hodvwlflwlhv lq d sduvlprqlrxv zd| wkdw lv idploldu iurp
zrun rq wkh olqhdu h{shqglwxuh v|vwhp; =
]
L'
" 34| dE| 7 q | E7| n 7
7 w o 3j 
e
_|

j
f
;
+6143,
Vhh Dwnhvrq dqg Rjdnl +4<<9, iru uhfhqw hpslulfdo zrun xvlqj wklv fodvv ri suhihuhqfhv1
:
7 7/
7 duh doo vwulfwo| srvlwlyh dqg wkdw q n nw ' 1
Zh dvvxph wkdw j/ q/ / 4/ /
Wkhvh suhihuhqfhv lpso| wkdw wkh lqfrph hodvwlflw| ri ghpdqg lv ohvv wkdq rqh
iru djulfxowxudo jrrgv/ htxdo wr rqh iru pdqxidfwxulqj jrrgv/ dqg juhdwhu wkdq
rqh iru vhuylfhv1 Wkh yduldeoh 7 fdq eh lqwhusuhwhg dv wkh ohyho ri vxevlvwhqfh
frqvxpswlrq/ zkloh 77 fdq eh ylhzhg dv uhsuhvhqwlqj krph surgxfwlrq ri vhuylfhv1
Wkh Frpshwlwlyh Htxloleulxp
Wkh frpshwlwlyh htxloleulxp iru wklv hfrqrp| frlqflghv zlwk wkh Sduhwr Rswl0
pdo vroxwlrq1 Wklv vroxwlrq fdq eh fkdudfwhul}hg e| pd{lpl}lqj +6143, vxemhfw wr
+61<,1 Wkh hfrqrp|*v uhdo lqwhuhvw udwh lv jlyhq e|=
o '  8 E&c  Bc
+6144,
zkhuh & ' g*f Wkh rswlpdo doorfdwlrq ri frqvxpswlrq dfurvv vhfwruv uhtxluhv=
7
E| |
'
c
q
+6145,
7
7 E7| n 7
|
'
+6146,
w
Wkh rswlpdo sdwk iru wkh frqvxpswlrq ri pdqxidfwxulqj jrrgv pxvw vdwlvi|=
o4

'

j
+6147,
D Edodqfhg Jurzwk Sdwk
Vxssrvh/ iru wkh prphqw wkdw 7 ' 77 ' f1 Lw lv fohdu iurp +61<, wkdw wkh rqo|
sdwk dorqj zklfk doo yduldeohv h{sdqg dw d frqvwdqw udwh uhtxluhv wkdw | / | / 7|
dqg g| jurz dw udwh }1 Htxdwlrqv +6144, dqg +6147, ghwhuplqh wkh vwhdg| vwdwh
ydoxh ri &=
 8 E&c  B ' j} n 4
;
+6148,
Wklv htxdwlrq kdv d vlpsoh lqwhusuhwdwlrq1 Wkh rqo| frqvwdqw udwh ri jurzwk wkdw
lv ihdvleoh iru wklv hfrqrp| wr dgrsw lv }1 Wkh hfrqrp| zloo iroorz d edodqfhg
jurzwk sdwk zkhqhyhu lwv vwrfn ri fdslwdo lv frqvlvwhqw zlwk d uhdo lqwhuhvw udwh
wkdw ohdgv krxvhkrogv wr fkrrvh wr h{sdqg wkhlu frqvxpswlrq ri wkh wkuhh jrrgv
dw udwh }1
D Jhqhudol}hg Edodqfhg Jurzwk Sdwk
Ohw xv qrz uhwxuq wr wkh fdvh lq zklfk 7 dqg 77 duh vwulfwo| srvlwlyh1 Lq wklv
fdvh d edodqfhg jurzwk sdwk grhv qrw h{lvw1 Htxdwlrqv +6145,/ +6146, dqg +6147,
lpso| wkdw hyhq zkhq wkh uhdo lqwhuhvw udwh lv frqvwdqw krxvhkrogv gr qrw fkrrvh
wr h{sdqg dqg 7 dw frqvwdqw udwhv1
Zh zloo vhdufk iru d sdwk dorqj zklfk wkh uhdo lqwhuhvw udwh lv frqvwdqw1 Zh
fkrrvh wklv surshuw| ri edodqfhg jurzwk dv rxu vwduwlqj srlqw ehfdxvh/ xqolnh
rwkhu ihdwxuhv ri d edodqfhg jurzwk sdwk +h1j1 wkh frqvwdqf| ri wkh jurzwk udwh
ri rxwsxw,/ lw kdv fohdu/ wudfwdeoh lpsolfdwlrqv lq pxowl0vhfwru prghov1
Ghqlwlrq D Jhqhudol}hg Edodqfhg Jurzwk Sdwk lv d wudmhfwru| dorqj zklfk wkh
uhdo lqwhuhvw udwh lv frqvwdqw1
Htxdwlrq +6144, lpsolhv wkdw & kdv wr eh frqvwdqw lq rughu iru wkh uhdo lqwhuhvw
udwh wr eh frqvwdqw1 Wkh hfrqrp|*v uhvrxufh frqvwudlqw fdq eh zulwwhq dv=
| n g | n Bg| n | n 7 7| '  8 E&c f| +6149,
Wkh uljkw kdqg vlgh ri wklv htxdwlrq h{sdqgv dw udwh }1 Rq wkh ohiw kdqg vlgh | /
g | / dqg Bg| jurz dw udwh }/ exw | dqg 7| gr qrw1 Dw uvw jodqfh wkh uhtxluhphqw
ri d frqvwdqw uhdo lqwhuhvw udwh dsshduv lqfrpsdwleoh zlwk wkh v|vwhp ri glhuhqwldo
htxdwlrqv wkdw ghvfulehv wkh frpshwlwlyh htxloleulxp1 Vxssrvh/ krzhyhu/ wkdw wkh
iroorzlqj uhvwulfwlrq/ zklfk zh zloo glvfxvv odwhu/ krogv=
<
7 7 ' 7
7 +614:,
Wklv lpsolhv wkdw 7 77 7 ' f/ zklfk doorzv xv wr uh0zulwh wkh uhvrxufh frq0
vwudlqw dv=
7 n 7 E7| n 7
7 '  8 E&c f| | n g | n Bg| n E| +614;,
Vlqfh erwk | 7 dqg 7| n 77 jurz dw udwh }/ doo wkh whupv lq wklv h{suhvvlrq
jurz dw d frqvwdqw udwh1 Wklv suryhv wkh iroorzlqj sursrvlwlrq=
7 7 ' 7
7 1
Sursrvlwlrq D Jhqhudol}hg Edodqfhg Jurzwk sdwk h{lvwv zkhqhyhu Wkh JEJ sdwk iru wklv prgho ihdwxuhv frqvwdqw uhodwlyh sulfhv/ d frqvwdqw
djjuhjdwh oderu lqfrph vkduh/ d frqvwdqw jurzwk udwh iru fdslwdo dqg dj0
juhjdwh rxwsxw/ d frqvwdqw fdslwdo0rxwsxw udwlr/ dqg wlph0ydu|lqj vhfwrudo
jurzwk udwhv dqg hpsor|phqw vkduhv lq wkh wkuhh vhfwruv1 Wkh hpsor|phqw
vkduh ghfolqhv lq djulfxowxuh/ ulvhv lq vhuylfhv/ dqg lv vwdeoh lq pdqxidfwxulqj1
Wkh lqlwldo ydoxh ri & frqvlvwhqw zlwk wkh JEJ sdwk lv jlyhq e| htxdwlrq
+6148,1
Wkh jurzwk udwhv ri rxwsxw lq djulfxowxuh dqg vhuylfhv duh jlyhq e|=
|
| 7
' }
c
|
|
7 |
7| n 77
' }
7|
7|
Xvlqj h!flhqf| frqglwlrq +61;, zh qg wkdw=
| ' }
| ' fc
|7 ' }
7
c
f| 8 E&c 
77
7 f| 8 E&c 
43
Wkh vkduh ri oderu lq djulfxowxuh ghfolqhv/ zkloh wkh vkduh lq vhuylfhv h{sdqgv1
Wkh udwhv ri fkdqjh ri erwk idfwru vkduhv frqyhujh wr }hur lq wkh orqj uxq1 Wkh wzr
sdqhov ri Iljxuh 6/ vkrz wkh hyroxwlrq ri wkh hpsor|phqw vkduhv dqg wkh rxwsxw
vkduh ri wkh wkuhh vhfwruv iru d qxphulfdo h{dpsoh1< Wkh idfw wkdw wkh hpsor|phqw
vkduhv frlqflgh zlwk wkh rxwsxw vkduhv lv dq lpsolfdwlrq ri wkh surgxfwlrq ixqfwlrqv
ehlqj lghqwlfdo xs wr d frqvwdqw ri sursruwlrqdolw|143 Dv wkh hfrqrp| jurzv wkh
lpsruwdqfh ri 7 dqg 77 ghfolqhv dqg wkh hfrqrp| frqyhujhv wr d vwdqgdug edodqfhg
jurzwk sdwk1 Wklv lv frqvlvwhqw zlwk wkh X1V1 h{shulhqfh= wkh vhfwrudo uhdoorfdwlrq
ri oderu rxw ri djulfxowxuh kdv ehhq olplwhg vlqfh wkh 4<:3*v dqg wkhuh kdv ehhq d
vorzgrzq lq wkh h{sdqvlrq ri vhuylfh hpsor|phqw1
Wudqvlwlrq G|qdplfv
Dqdorjrxv wr d edodqfhg jurzwk prgho/ wklv hfrqrp| ihdwxuhv vrph wudqvl0
wlrqdo g|qdplfv zkhqhyhu wkh lqlwldo ydoxh ri & lv lqfrpsdwleoh zlwk wkh JEJ
sdwk1 Iru wklv vlpsoh hfrqrp| wkhvh wudqvlwlrq g|qdplfv duh hdv| wr fkdudfwhul}h/
ehfdxvh wkh prgho kdv wkh vdph vwdelolw| surshuwlhv dv wkh rqh vhfwru qhrfodvvlfdo
jurzwk prgho1 Wr vhh wklv xvh htxdwlrqv +6145, dqg +6146, wr vxevwlwxwh | 7 dqg
7| n 77 lqwr wkh xwlolw| ixqfwlrq dqg lq wkh uhvrxufh frqvwudlqw +61<, dqg uh0zulwh
wkh sodqqlqj sureohp iru wklv hfrqrp| dv=
Wkh sdudphwhu ydoxhv xvhg lq wklv h{dpsoh duh= D @ 733> V @ 583/ @ 3=4/ @ 3=48/
@ 3=:8/ @ 6/ @ 3=34/ @ 3=38/ j @ 3=34;/ [3 @ 433/ ED @ 7> EP @ 4/ EV @ 5=81 Wkh
ixqfwlrq I +=, lv dvvxphg wr eh Free0Grxjodv zlwk d fdslwdo vkduh ri 3=71
43
Wkh uhtxluhphqw wkdw wkh vxevlvwhqfh whupv D dqg V eh vwulfwo| srvlwlyh wr jhqhudwh vwuxf0
wxudo fkdqjh pd| dsshdu wr frqwudglfw Edxpro*v +4<9:, uhvxowv rq xqedodqfhg jurzwk1 Klv prgho
kdv wzr vhfwruv/ pdqxidfwxulqj dqg vhuylfhv1 Klv Sursrvlwlrq 4 lpsolflwo| dvvxphv d prphqwdu|
xwlolw| ixqfwlrq ri wkh irup x @ Vw4 Pw 1 Erwk jrrgv duh surgxfhg rqo| zlwk oderu/ dqg rqo|
pdqxidfwxulqj ehqhwv iurp whfkqlfdo surjuhvv= Vw @ EV QwV / Pw @ EP QwP [w 1 Lw lv hdv| wr
vhh wkdw wklv prgho ihdwxuhv qr vwuxfwxudo fkdqjh> lw kdv d edodqfhg jurzwk sdwk dorqj zklfk
erwk Q V dqg Q P duh frqvwdqw1 Wr surgxfh vwuxfwxudo fkdqjh +Sursrvlwlrq 5, Edxpro dvvxphv
wkdw suhihuhqfhv ru jryhuqphqw srolf| vrphkrz ohdg wkh hfrqrp| wr pdlqwdlq d frqvwdqw udwlr/
Vw @Pw 1 Wklv reylrxvo| irufhv oderu wr rz iurp pdqxidfwxulqj lqwr vhuylfhv1
<
44
" 34| | 3j 
e
_|c
]

4@ L '
j
f
vxemhfw wr wkh frqvwudlqw=
|
n g | n Bg| '  8 Eg| c f| c
dqg wkh lqlwldo frqglwlrqv gf dqg ff 1
Wkh JEJ Uhvwulfwlrq
Wkh JEJ sdwk h{lvwv rqo| zkhq wkh uhvwulfwlrq +614:, krogv1 Zh duh xvhg wr wkh
pdq| uhvwulfwlrqv wkdw duh qhfhvvdu| iru prghov wr glvsod| edodqfhg jurzwk= oderu0
dxjphqwlqj whfkqlfdo surjuhvv/ lvrhodvwlf prphqwdu| xwlolw| dqg/ lq pxowlvhfwru
prghov/ furvv0sdudphwhu uhvwulfwlrqv vlplodu wr +614:,/ w|lqj wrjhwkhu sdudphwhuv
ri suhihuhqfhv dqg whfkqrorj| +vhh h1j1 Hydqv/ Krqndsrkmd dqg Urphu +4<<;,,1 Lw
lv shukdsv/ qrw vxusulvlqj/ wkdw wr jhqhudwh ulfkhu g|qdplfv zh qhhg dq dgglwlrqdo
sdudphwhu uhvwulfwlrq1
Rqh lqwhusuhwdwlrq ri rxu hfrqrp| lv wkdw hdfk djhqw kdv d srvlwlyh hqgrzphqw
7 Uhvwulfwlrq
ri vhuylfhv 77 dqg d qhjdwlyh hqgrzphqw ri djulfxowxudo jrrgv 1
+614:, uhtxluhv wkdw wkh pdunhw ydoxh ri wkhvh hqgrzphqwv 7 77 7 eh htxdo
wr }hur1
Wkhuh lv hylghqfh ri vhfwrudo uhdoorfdwlrq ri hpsor|phqw rxw ri djulfxowxuh lqwr
vhuylfhv iru doo jurzlqj frxqwulhv1
Lq frqwudvw/ hylghqfh lq idyru ri wkh Ndogru
idfwv lv ohvv frpshoolqj iru hfrqrplhv rwkhu wkdq wkh X1V1 Wklv vxjjhvwv wkdw
shukdsv uhvwulfwlrq +614:, krogv pruh forvho| iru wkh X1V1 hfrqrp| wkdq iru rwkhu
frxqwulhv1
Lw lv qdwxudo wr dvn zkdw wkh prgho*v lpsolfdwlrqv duh zkhq htxdwlrq +614:,
grhv qrw krog1 Zh h{soruh wklv txhvwlrq lq wkh Dsshqgl{1 Zh vkrz wkdw wkh
htxloleulxp ri dq hfrqrp| lq zklfk wkh JEJ frqvwudlqw grhv qrw krog frqyhujhv
45
dv|pswrwlfdoo| wr wkh JEJ sdwk1 Zh dovr fkdudfwhul}h wkh ehkdylru ri wkh uhdo
lqwhuhvw udwh gxulqj wklv dgmxvwphqw surfhvv1
Zh kdyh h{soruhg qxphulfdoo| wkh ehkdylru ri wkh uhdo lqwhuhvw udwh zkhq wkh
JEJ frqvwudlqw grhv qrw krog1 Zh irxqg wkdw ghyldwlrqv iurp wkh JEJ frqvwudlqw
wkdw surgxfh vpdoo fkdqjhv lq wkh sdwwhuq ri oderu uhdoorfdwlrq ohdg wr qhjoljleoh
pryhphqwv lq wkh uhdo lqwhuhvw udwh1 Odujh ylrodwlrqv ri wkh JEJ frqvwudlqw
surgxfh prghudwh pryhphqwv lq wkh uhdo lqwhuhvw udwh exw fkdqjh gudpdwlfdoo|
wkh sdwwhuq ri vhfwrudo uhdoorfdwlrq144
71 H{whqvlrqv
Wkh prgho suhvhqwhg khuh fdq eh jhqhudol}hg dqg xvhg lq rwkhu vhwwlqjv1 Wzr
qdwxudo h{whqvlrqv duh= +l, wr lqwurgxfh glhuhqw vhfwrudo surgxfwlrq ixqfwlrqv>
dqg +ll, wr doorz iru glhuhqw vhfwrudo udwhv ri whfkqlfdo surjuhvv/ vr wkdw wkh
uhodwlyh sulfhv ri wkh glhuhqw jrrgv fdq ydu| ryhu wlph145 D pruh jhqhudo yhuvlrq
ri rxu prgho fdq dffrpprgdwh erwk ri wkhvh skhqrphqd +vhh Nrqjvdpxw hw do
Iru h{dpsoh/ zh uhgxfhg V iurp 583 +wkh ydoxh xvhg lq wkh frqvwuxfwlrq ri Iljxuh 6, wr 5331
Dv d frqvhtxhqfh/ wkh uhdo lqwhuhvw udwh zdv qr orqjhu frqvwdqw exw lwv yduldwlrq zdv yhu| vpdoo=
lw lqfuhdvhg iurp 917( wr 91:( ryhu d wkluw| |hdu shulrg dqg wkhq vorzo| dv|pswrwhg wr 917(1
Wklv uhgxfwlrq lq V kdg d vpdoo lpsdfw rq wkh sdwwhuq ri oderu uhdoorfdwlrqwkh iudfwlrq ri wrwdo
oderu uhdoorfdwhg wr wkh vhuylfh vhfwru ihoo e| 6(1 Zkhq zh uhgxfhg V wr }hur wkh pryhphqwv
lq wkh uhdo lqwhuhvw udwh ehfdph pruh surqrxqfhgwkh uhdo lqwhuhvw udwh lqfuhdvhg iurp 917( wr
;19( ryhu d wkluw| |hdu shulrg dqg wkhq dv|pswrwhg wr 917(1 Wklv fkdqjh lq V kdg d odujh
lpsdfw rq vhfwrudo uhdoorfdwlrq sdwwhuqv= wkh iudfwlrq ri wrwdo oderu uhdoorfdwhg wrzdug vhuylfhv
ihoo iurp 76( wr 5:(1 Li zh { V dqg orzhu D wkh hhfw rq wkh ehkdylru ri wkh uhdo lqwhuhvw udwh
lv vlplodu lq pdjqlwxgh1 Krzhyhu/ iru uhdvrqv h{sodlqhg lq wkh Dsshqgl{/ wkh uhdo lqwhuhvw udwh
idoov lqlwldoo| lqvwhdg ri ulvlqj1
45
Mrujhqvrq dqg Jroors +4<<5, hvwlpdwh wkdw surgxfwlylw| jurzwk kdv ehhq kljk lq djulfxowxuh
dqg orz lq wkh vhuylfh vhfwru1 Krzhyhu/ surgxfwlylw| hvwlpdwhv duh yhu| vhqvlwlyh wr phdvxuhphqw
huuru lq wkh gh dwruv xvhg wr frpsxwh uhdo rxwsxw1 Wkhvh gh dwruv riwhq idlo wr wdnh lqwr dffrxqw
wkh fkdqjhv lq wkh txdolw| ri wkh glhuhqw jrrgv wkdw rffxu ryhu wlph1 Vkdslur dqg Zlofr{ +4<<9,
glvfxvv wkh eldvhv dvvrfldwhg zlwk lqfuhdvhv lq wkh txdolw| ri phglfdo vhuylfhv1 Kruqvwhlq dqg
Nuxvhoo +4<<9, uhylhz wkh sureohpv dvvrfldwhg zlwk surgxfwlylw| phdvxuhphqw lq wkh vhuylfh
vhfwru1
44
46
+4<<<,,1 Wkhvh pruh jhqhudo prghov frqwlqxh wr uhtxluh nqlih0hgjh frqglwlrqv
vlplodu wr +614:, wr jxdudqwhh wkh h{lvwhqfh ri wkh JEJ sdwk1 Krzhyhu/ wkhvh
JEJ frqvwudlqwv whqg wr eh pruh frpsoh{ dqg pruh gl!fxow wr lqwhusuhw wkdq
+614:,1
Rwkhu orqj uxq hpslulfdo uhjxodulwlhv fdq eh hdvlo| dffrpprgdwhg zlwklq rxu
prgho1 Wzr h{dpsohv duh wkh orqj uxq ghfolqh lq shu fdslwd krxuv zrunhg dqg
Zdjqhu*v odz/ wkh orqj uxq lqfuhdvh lq wkh udwlr ri jryhuqphqw vshqglqj wr wrwdo
rxwsxw1
Zh irfxvhg rq wkh gudpdwlf uhdoorfdwlrq ri hpsor|phqw wkdw kdv wdnhq sodfh
lq djulfxowxuh/ pdqxidfwxulqj dqg vhuylfhv1 Exw uhdoorfdwlrq lv dovr suhvhqw zlwklq
wkh pdqxidfwxulqj dqg wkh vhuylfh vhfwru1 Zh duh krshixo wkdw wkh prgholqj
whfkqltxhv xvhg lq wklv sdshu zloo eh xvhixo lq wklqnlqj derxw vwuxfwxudo fkdqjh
dw d pruh glvdjjuhjdwhg ohyho1
Ilqdoo|/ zh vxvshfw wkdw rwkhu frpelqdwlrqv ri suhihuhqfhv dqg whfkqrorjlhv
fdq jhqhudwh jhqhudol}hg edodqfhg jurzwk sdwkv1 Ilqglqj wkhvh lv dq h{flwlqj
fkdoohqjh wr ixwxuh uhvhdufk1
Uhihuhqfhv
^4` Dwnhvrq/ Dqguhz dqg Pdvdr Rjdnl Zhdowk0Ydu|lqj Lqwhuwhpsrudo Hodvwlf0
lwlhv ri Vxevwlwxwlrq= Hylghqfh iurp Sdqho dqg Djjuhjdwh Gdwd/ Mrxuqdo ri
Prqhwdu| Hfrqrplfv/ 6;= 83:0867/ 4<<91
^5` Edxpro/ Zlooldp Pdfurhfrqrplfv ri Xqedodqfhg Jurzwk= Wkh Dqdwrp| ri
Xuedq Fulvlv/ Dphulfdq Hfrqrplf Uhylhz/ 8:= 7480759/ 4<9:1
^6` Elov/ Pdun dqg Shwh Nohqrz Xvlqj Frqvxphu Wkhru| wr Whvw Frpshwlqj
Exvlqhvv F|foh Prghov/ Mrxuqdo ri Srolwlfdo Hfrqrp|/ 439= 5660594/ 4<<;1
47
^7` Fkhqhu|/ Kroolv E1 Sdwwhuqv ri Lqgxvwuldo Jurzwk/ Dphulfdq Hfrqrplf Uh0
ylhz/ 83= 9570987/ 4<931
^8` Fodun/ Frolq Wkh Frqglwlrqv ri Hfrqrplf Surjuhvv/ PdfPloodq/ Orqgrq/
4<731
^9` Hfkhyduuld/ Fulvwlqd Fkdqjlqj Vhfwrudo Frpsrvlwlrq Dvvrfldwhg zlwk Hfr0
qrplf Jurzwk/ Lqwhuqdwlrqdo Hfrqrplf Uhylhz/ 6;= 7640785/ 4<<:1
^:` Hydqv/ Jhrujh/ Vhssr Krqndsrkmd dqg Sdxo Urphu Jurzwk F|fohv/ Dphu0
lfdq Hfrqrplf Uhylhz/ ;;= 7<80848/ 4<<;1
^;` Jrrgiulhqg/ Pduylq dqg Mrkq PfGhuprww Hduo| Ghyhorsphqw/ Dphulfdq
Hfrqrplf Uhylhz/ ;8= 4490466/ 4<<81
^<` Klvwrulfdo Vwdwlvwlfv ri wkh Xqlwhg Vwdwhv= Frorqldo Wlphv wr 4<:3/ Frpphufh
Ghsduwphqw/ Fhqvxv Exuhdx/ 4<:81
^43` Kruqvwhlq/ Dqguhdv dqg Shu Nuxvhoo Fdq Whfkqrorj| Lpsuryhphqwv Fdxvh
Surgxfwlylw| VorzgrzqvB/ QEHU Pdfurhfrqrplfv Dqqxdo 4<<9/ 44= 53<0
58</ 4<<91
^44` Krxwkdnnhu/ K1 V1 dqg Ohvwhu Wd|oru Frqvxphu Ghpdqg lq wkh Xqlwhg Vwdwhv=
Dqdo|vlv dqg Surmhfwlrqv/ Kduydug Xqlyhuvlw| Suhvv/ 4<:31
^45` Leerwvrq Dvvrfldwhv/ Vwrfnv/ Erqgv/ Eloov/ dqg Lq dwlrq 4<<< \hduerrn/ 4<<</
Fklfdjr/ LO1
^46` Mrujhqvrq/ Gdoh dqg Iudqn Jroors Surgxfwlylw| Jurzwk lq X1V1 Djulfxowxuh=
D Srvwzdu Shuvshfwlyh/ Dphulfdq Mrxuqdo ri Djulfxowxudo Hfrqrplfv/ :7/ 6=
:780:83/ 4<<51
48
^47` Nrqjvdpxw/ Sl|dekd Vwuxfwxudo Fkdqjh dqg Orqj Uxq Jurzwk/ plphr/
Xqlyhuvlw| ri Urfkhvwhu/ 4<<81
^48` Nrqjvdpxw/ Sl|dekd/ Vhujlr Uhehor dqg Gdq|dqj [lh Eh|rqg Edodqfhg
Jurzwk/ Zrunlqj Sdshu/ Qruwkzhvwhuq Xqlyhuvlw|/ 4<<<1
^49` Nx}qhwv/ Vlprq Txdqwlwdwlyh Dvshfwv ri wkh Hfrqrplf Jurzwk ri Qdwlrqv=
LL/ Hfrqrplf Ghyhorsphqw dqg Fxowxudo Fkdqjh Vxssohphqw wr Yro1 Y +7,=
60444/ 4<8:1
^4:` Odlwqhu/ Mrkq Vwuxfwxudo Fkdqjh dqg Hfrqrplf Jurzwk/ Uhylhz ri Hfr0
qrplf Vwxglhv/ 9:= 878094/ 53331
^4;` Phuwrq/ Urehuw F1 Rq Hvwlpdwlqj wkh H{shfwhg Uhwxuq rq wkh Pdunhw= Dq
H{sorudwru| Lqyhvwljdwlrq/ Mrxuqdo ri Ilqdqfldo Hfrqrplfv/ ;= 656094/ 4<;31
^4<` Sdun/ Vxqjln Wudqvlwlrqdo G|qdplfv ri Vwuxfwxudo Fkdqjhv/ plphr/ Xql0
yhuvlw| ri Urfkhvwhu/ 4<<81
^53` Sdvlqhwwl/ Oxljl O1 Vwuxfwxudo Fkdqjh dqg Hfrqrplf Jurzwk = D Wkhruhwlfdo
Hvvd| rq wkh G|qdplfv ri wkh Zhdowk ri Qdwlrqv/ Fdpeulgjh= Fdpeulgjh
Xqlyhuvlw| Suhvv/ 4<;41
^54` Vkdslur/ Pdwkhz dqg Gdylg Zlofr{ Plvphdvxuhphqw lq wkh Frqvxphu Sulfh
Lqgh{= Dq Hydoxdwlrq/ QEHU Pdfurhfrqrplfv Dqqxdo 4<<9/ <60475/ 4<<91
^55` Vlhjho/ Mhuhp| Vwrfnv iru wkh Orqj Uxq/ Luzlq Surihvvlrqdo Sxeolvklqj/ Qhz
\run/ 4<<81
^56` Vwrnh|/ Qdqf| dqg Vhujlr Uhehor Jurzwk Hhfwv ri Iodw0Udwh Wd{hv/ Mrxu0
qdo ri Srolwlfdo Hfrqrp|/ 436= 84<0883/ 4<<81
49
Figure 1: The Kaldor Facts
U.S. Real GDP per capita, 1902-1999
(in logarithms)
11
10.5
10
9.5
9
8.5
8
7.5
7
1902-06
1925
1935
1945
1955
1965
1975
1985
Sources: Historical Statistics of the U.S.; Economic Report of the President; and U.S. Census Bureau.
U.S. Capital-Output Ratio, 1929-1998
3
2.5
2
1.5
1
0.5
0
1929
1939
1949
1959
1969
1979
1989
Sources: Fixed assets and consumer durable goods. Survey of current business, May 1997, April 2000.
NIPA (B.E.A. website).
1995
Figure 1: The Kaldor Facts (cont.)
Annual, Real, Geometrically Compounded Returns to U.S. Stock
8
7
6
5
4
3
2
1
0
1802-1870
1871-1925
1926-1992
Source: Siegel (1995)
U.S. Share of Labor Income in Total Income,
1959-1998
60
59
58
57
56
55
54
53
1959
1963
1967
1972
1977
1982
1987
1992
Source: Survey of Current Business, August 1996, and June 2000.
1994
1998
Figure 2: The Kuznets Facts
U.S. Employment Shares by Sector, 1869-1998
80
70
60
50
40
30
20
10
0
1869
1909
1929-37
Agriculture
1953-57
Industry
1970
Services
Sources: Historical Statistics of the United States, 1975 edition.
Statistical Abstract of the United States, 1999.
U.S. Consumption Shares by Sector, 1940-1999
0.6
0.5
0.4
0.3
0.2
0.1
0
1940
1945
1950
1955
Agriculture
1960
1965
1970
Services
1975
1980
1985
Manufacturing
Source: Economic Report of the President (1990,2000).
1990
Employment
0.6
Figure 3
Generalized Balanced Growth Path Output Shares
0.6
0.55
0.55
0.5
0.5
Services
Services
0.45
0.45
0.4
0.4
Manufacturing
Manufacturing
0.35
0.35
0.3
0.3
Agriculture
Agriculture
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0
20
40
60
time
80
100
0.1
0
20
40
60
time
80
100
D1 Dsshqgl{
Zkdw kdsshqv zkhq wkh JEJ frqvwudlqw grhv qrw krogB
Wklv dsshqgl{ glvfxvvhv d yhuvlrq ri wkh prgho lq zklfk wkh JEJ frqvwudlqw
7 7 *
7 9' f1 Wr vlpsoli| rxu
grhv qrw krogzh dvvxph wkdw 0 '  E7*
glvfxvvlrq zh irfxv rq wkh fdvh ri Free0Grxjodv surgxfwlrq ixqfwlrqv1 Zh df0
frpsolvk wkh iroorzlqj remhfwlyhv= +l, zh vkrz krz wr xvh d skdvh gldjudp zlwk
prylqj lvrfolqhv wr fkdudfwhul}h wkh g|qdplfv ri wkh prgho> +ll, zh vkrz wkdw wkh
hfrqrp|*v htxloleulxp wudmhfwru| frqyhujhv dv|pswrwlfdoo| wr wkh JEJ sdwk> +lll,
zh fkdudfwhul}h wkh hfrqrp|*v uhdo lqwhuhvw udwh g|qdplfv1
Zlwkrxw orvv ri jhqhudolw|/ ohw xv dvvxph wkdw wkh frqvwdqw 0 lv qhjdwlyh1 Eh0
fdxvh wkh wkuhh vhfwruv kdyh vlplodu surgxfwlrq ixqfwlrqv/ zh fdq djjuhjdwh wkhvh
vhfwruv vr wkdw wkh frpshwlwlyh htxloleulxp lv wkh rxwfrph ri wkh iroorzlqj rswl0
pl}dwlrq sureohp=
] " 3j

e34| _|c
4@
j
f

vxemhfw wr= g '  g k f 3k  Bg n 0
+D14,
zkhuh f jurzv dw h{rjhqrxv udwh ri }1
Ohw b eh wkh fr0vwdwh yduldeoh dvvrfldwhg zlwk g1 Wkh uvw rughu frqglwlrqv
duh=
b
 3j ' c
b ' 4b b k g k3 f 3k B Wkh wudqvyhuvdolw| frqglwlrq lv ,6 gbe34 | ' f1 Ghqh wkh iroorzlqj wudqv0
|<"
' bf j 1 Zh fdq uhzulwh wkh uvw rughu frqglwlrqv
' g*f/ b
iruphg yduldeohv= g
dv iroorzv=
dqg b
lq whupv ri g
% &3*j
_g

b
k n 0c
'  g
EB n }g
_|
f
k
l
_b
k
3

' b 4 n B n j} k g
_|
Zh fdqqrw hpsor| d vwdqgdug skdvh gldjudp ehfdxvh f lv wlph ghshqghqw dqg
khqfh wkh v|vwhp ri glhuhqwldo htxdwlrqv lv qrw dxwrqrprxv1 Zh fdq/ krzhyhu/
4:
xvh d skdvh gldjudp zlwk prylqj lvrfolqhv wr ghvfuleh wkh g|qdplfv ehfdxvh f
ghshqgv rq wlph lq dq h{solflw idvklrq/ qdpho| f ' ff e} | 1
Dv dq h{dpsoh/ zh xvh d skdvh gldjudp zlwk prylqj lvrfolqhv wr ghslfw wkh
htxloleulxp wudmhfwru| zkhq gf *ff ' dE4 n B n j} * Ek o*Ek3 ~
λ
8
~
K0 --locus
~
K τ --locus
~ --locus
K
~
K
Iljxuh 7= Wlph ydu|lqj orfl
~
λ
~
K τ --locus
~
K
Iljxuh 8= Gluhfwlrqv iru Lpphgldwh Pryhphqwv dw wlph Lq Iljxuh 7/ wkh yhuwlfdo olqh uhsuhvhqwv wkh htxdwlrq _b*_|
' f1 Wkh grzqzdug
vorslqj fxuyh rq wkh wrs lv wkh orfxv dorqj zklfk _g*_| ' f zkhq | ' f1 Wkh
fxuyh lq wkh plggoh uhsuhvhqwv wkh vdph orfxv zkhq | ' +zh zloo dexvh odqjxdjh
orfxv,1 Wkh fxuyh dw wkh erwwrp uhsuhvhqwv wkh srlqwv dorqj
dqg fdoo lw wkh g
lv frqvwdqw zkhq | ' 41
zklfk g
4;
Dw dq| wlph wkh iroorzlqj skdvh gldjudp lqglfdwhv wkh gluhfwlrqv ri pryhphqw
dqg b1
iru g
Zlwk wkh wzr Iljxuhv deryh xqghuvwrrg/ zh fdq qrz gudz wkuhh uhsuhvhqwdwlyh
sdwkv1 Wkh wudmhfwru| lq wkh plggoh lv wkh htxloleulxp wudmhfwru|1
~
λ~
λ
~ --locus
K0 --locus
88
~
--locus
~K --locus
K
~~
KK
Iljxuh 9= Uhsuhvhqwdwlyh Wudmhfwrulhv
lv ehorz wkh g
b
f
Wr xqghuvwdqg wkh wrs wudmhfwru|/ qrwh wkdw wkh lqlwldo Eg/
orfxv dqg wkhuhiruh wkh lpphgldwh gluhfwlrq ri pryhphqw lv wrzdug wkh ohiw1 Exw
f lv forvh wr erwk wkh g
b
f orfxv dqg wkh yhuwlfdo olqh/ wkh pdjqlwxgh
vlqfh Eg/
zloo eh deryh
b
ri wkh pryhphqw lv vpdoo1 Diwhu d vkruw zkloh/ vd| dw | ' / Eg/
orfxv dqg wkhuhiruh wkh wudmhfwru| pryhv grzq wr wkh uljkw1 Wklv pryhphqw
g
frqwlqxhv xqwlo wkh sdwk klwv wkh yhuwlfdo olqh1 Diwhu wklv srlqw wkh wudmhfwru|
pryhv xs wr wkh uljkw1
lv idu ehorz
b
Wr xqghuvwdqg wkh erwwrp wudmhfwru|/ qrwh wkdw wkh lqlwldo Eg/
wkh gf orfxv dqg wkhuhiruh wkh ohiwzdug pryhphqw lv vwurqj dw wkh ehjlqqlqj1 Lq
| olhv xqghu g
b
| orfxv iru doo |1 Rqfh
idfw/ wkh pryhphqw lv vr vwurqj wkdw Eg/
wkh wudmhfwru| sdvvhv g" orfxv/ wkhuh lv qr wxuqlqj edfn1
b
Wkh htxloleulxp orfxv lv wkh xqltxh sdwk zklfk vwduwv dw dq dssursuldwh Eg/
| frphv wr eh deryh dqg vwd|v deryh wkh g
b
| orfxv
vr wkdw dv wlph hodsvhv/ Eg/
dqg lq wkh phdqwlph Eg/ b| vwd|v wr wkh ohiw ri wkh yhuwlfdo olqh1
Wr vhh wkh surshuw| ri wkh htxloleulxp sdwk zlwk 0 qhjdwlyh/ qrwh wkdw g| *f|
uvw ghfolqhv dqg wkhq lqfuhdvhv dqg dssurdfkhv wkh vwhdg| vwdwh ohyho1 Wkhuhiruh/
wkh uhdo lqwhuhvw udwh lqfuhdvhv uvw dqg wkhq frphv edfn wr wkh ruljlqdo ohyho1
Zkhq 0 lv srvlwlyh wkh sdwkv ri wkh uhdo lqwhuhvw udwh dqg ri g| *f| duh wkh pluuru
lpdjh ri wkh sdwkv fruuhvsrqglqj wr 0 qhjdwlyh1
4<