6Lh @h @? @U! @h W?|ih}i?ih@| L?@*BLL tG AiLh)LuW?|ih}i?ih@| … · 4 %Zk| vkrxog L fduh derxw...
Transcript of 6Lh @h @? @U! @h W?|ih}i?ih@| L?@*BLL tG AiLh)LuW?|ih}i?ih@| … · 4 %Zk| vkrxog L fduh derxw...
6Lh�@h_ @?_ �@U!�@h_ W?|ih}i?ih@|�L?@* BLL_tG �
A�iLh) Lu W?|ih}i?ih@|�L?@* , U�@?}i�
�?|L?�L +@?}i*
#iT@h|4i?| Lu ,UL?L4�Ut
5|@?uLh_ N?��iht�|)
@?_
��,+
h@?}i*9*i*@?_�t|@?uLh_�i_�
#iUi4Mih �bbb
Devwudfw
Wklv sdshuv ghyhorsv d wkhru| ri lqwhujhqhudwlrqdo h{fkdqjh iru jhqhudwlrqvwkdw duh hlwkhu vho�vk ru kdyh qrq0g|qdvwlf dowuxlvp1 Wkh pdlq exloglqj eorfnvri wkh wkhru| duh iruzdug dqg edfnzdug lqwhujhqhudwlrqdo jrrgv +ILJv dqgELJv, dqg wkh uhodwlrqvkls ehwzhhq wkhp1 D ILJ lv d wudqvihu iurp suhvhqw wrixwxuh jhqhudwlrqv/ olnh sduhqwdo lqyhvwphqwv lq hgxfdwlrq dqg wkh suhvhuydwlrqri wkh hqylurqphqw1 D ELJ lv d wudqvihu iurp ixwxuh wr suhvhqw jhqhudwlrqv/ olnhsd|0dv0|rx0jr vrfldo vhfxulw| ru wdnlqj fduh ri hoghuo| sduhqwv1 Zh vkrz wkdwwkhuh lv d ixqgdphqwdo gl�huhqfh ehwzhhq ELJv dqg ILJv1 ELJv jhqhudwlqj dsrvlwlyh vxusoxv duh vhoi0vxvwdlqdeoh/ exw ILJv qhyhu duh1 Krzhyhu/ hyhq zlwkvho�vk jhqhudwlrqv/ rswlpdo lqyhvwphqw lq ixwxuh jhqhudwlrqv fdq wdnh sodfh liwkh htxloleulxp vrfldo qrup olqnv ELJv dqg ILJv1 Wkh wrrov ghyhorshg khuhfdq eh xvhg wr xqghuvwdqg d zlgh fodvv ri lqwhujhqhudwlrqdo sureohpv/ iurp wkhsrolwlfdo hfrqrp| ri hqylurqphqwdo wuhdwlhv wr wkh hfrqrplfv ri vhqlrulw| lqvwl0wxwlrqv1 Wzr dssolfdwlrqv duh ghyhorshg lq wkh sdshu= +4, wkh srolwlfdo hfrqrp|ri lqwhujhqhudwlrqdo sxeolf h{shqglwxuhv/ dqg +5, lqyhvwphqw lq fkloguhq zlwklqwkh idplo|1
WW �@?| |L |�@?! �@*|iU� uLh �|t �LtT�|@*�|) @?_ 4Lt| t|�4�*@|�?} hiti@hU� i?��hL?4i?|� W
@4 }h@|iu�* |L �*Mih|L �*it�?@c �@h|) 6i*_t|i�? @?_ ,h�U �@t!�? uLh |�i�h t�}}it|�L?t @?_ t�TTLh|
_�h�?} |�i ThLUitt Lu �h�||�?} |��t T@Tih� W �@?| |L |�@?! a@4it �*|c B@_� �@h*i�)c #L�} �ih?�i�4c
6h@?UitUL �@ti**�c �?_hi� �L�i?c �*i�@?_hL ��?@|c #@��_ ��|*ihc 5�i? 6i*_4@?c #hi� 6�_i?Mih}c
aihh) Bhii?c �*��ih O@h|c a@4it O�?itc ��hi�**i a@ULMtL?c �@||�i� a@U!tL?c ��@_ aL?itc aL?@|�@?
k@|3c #@��_ w@�MtL?c aL�? wi_)@h_c aig w�iM4@?c �?_hi� �@t��L*i**c a�** �Lh?�?}t|@hc 5|iT�i?
�Lhh�tc �@ti) ��**�}@?c #�?@ �*_ih��}��*@hc ALht|i? �ihttL?c a@4it �L|ihM@c +�U�@h_ �Uki*�i)c
AL__ 5@?_*ihc ki? 5�iTt*ic �?_hi� 5U�*i�uihc aL@^��4 5�*�it|hic AL4@t 5�Lt|hL4c 5|i�i A@_i*�tc
a@�4i Vi?|�h@c +�U�@h_ ~iU!�@�tih @?_ ti4�?@h T@h|�U�T@?|t @| O@h�@h_c �@*|iU�c #@��tc 5|@?uLh_c
�Lh|��it|ih?c W**�?L�t�NhM@?@c WL�@c @?_ +LU�it|ih uLh |�i�h �i*Tu�* UL44i?|t� 6�?@?U�@* t�TTLh|
uhL4 #hi� 6�_i?Mih}c +i@* �L*i}�L �L4T*�|i?ti @?_ |�i �@?! Lu 5T@�? �t }h@|iu�**) @U!?L�*i_}i_�
3
4
%Zk| vkrxog L fduh derxw ixwxuh jhqhudwlrqvB Zkdw kdyh wkh| grqh iru
phB%
Dgglvrq
%Eh qlfh wr |rxu fkloguhq/ wkh| zloo slfn |rxu qxuvlqj krph1%
Dqrq|prxv expshu vwlfnhu
%Dv rwkhuv sodqwhg ehiruh ph/ vr gr L sodqw iru p| fkloguhq1%
Wdopxg
%Wkh lpsuryhphqwv pdgh e| wkh ghdg irup d fkdujh djdlqvw wkh olylqj
zkr wdnh wkh ehqh�w ri wkhp1 111 Wkhuh vhhpv wkhq wr eh d irxqgdwlrq
lq wkh qdwxuh ri wklqjv/ lq wkh uhodwlrq zklfk rqh jhqhudwlrq ehduv wr
dqrwkhu/ iru wkh ghvfhqw ri reoljdwlrqv iurp rqh wr dqrwkhu1 Htxlw|
uhtxluhv lw1 Pxwxdo jrrg lv surprwhg e| lw1%
Mdphv Pdglvrq
%111h{shqglwxuhv rq wkh hoghuo| duh sduw ri d %vrfldo frpsdfw% ehwzhhq
jhqhudwlrqv1 Wd{hv rq dgxowv khos �qdqfh h�flhqw lqyhvwphqwv lq fklo0
guhq1 Lq uhwxuq/ dgxowv uhfhlyh sxeolf shqvlrqv dqg phglfdo sd|phqwv
zkhq rog1%
Jdu| Ehfnhu dqg Nhylq Pxusk| +4<;;,
5
� W?|hL_�U|�L?
Lqwhujhqhudwlrqdo h{fkdqjh lv xeltxlwrxv lq hfrqrplf olih1 Lw wdnhv sodfh dw wkh ohyho
ri wkh idplo|/ rujdql}dwlrq/ frppxqlw|/ qdwlrq/ dqg sodqhw1 Wudglwlrqdo h{dpsohv dw
wkh idplo| ohyho duh sduhqwdo lqyhvwphqwv lq wkh hgxfdwlrq ri wkhlu fkloguhq dqg wkh
fduh wkdw plggoh0djhg dgxowv surylgh iru wkhlu hoghuo| sduhqwv1 Wkh vhqlrulw| v|vwhp
lq srolwlfdo erglhv olnh wkh X1V1 Frqjuhvv lv dq h{dpsoh ri lqwhujhqhudwlrqdo h{fkdqjh
lq orqj0olyhg rujdql}dwlrqv1� Lq wkh Xqlwhg Vwdwhv/ wkh jryhuqphqw shuirupv lqwhu0
jhqhudwlrqdo h{fkdqjh dw wkh orfdo ohyho/ wkurxjk lqyhvwphqwv lq lqiudvwuxfwxuh dqg
sxeolf hgxfdwlrq/ dqg dw wkh qdwlrqdo ohyho/ wkurxjk lqyhvwphqw lq U)G/ wkh �qdqf0
lqj ri zduv/ dqg surjudpv olnh sd|0dv0|rx0jr vrfldo vhfxulw| dqg Phglfduh1 Ilqdoo|/
hqylurqphqwdo sureohpv vxfk dv Joredo Zduplqj dqg wkh ghsohwlrq ri wkh r}rqh
od|hu duh h{dpsohv ri lqwhujhqhudwlrqdo h{fkdqjh dw wkh lqwhuqdwlrqdo ohyho1
Wkh pdlq frqwulexwlrq ri wklv sdshu lv wr vkrz wkdw wklv glyhuvh fodvv ri sureohpv
fdq eh xqghuvwrrg xvlqj d frpprq vhw ri sulqflsohv/ wkdw duh fdswxuhg e| d vlpsoh
wkhru| ri lqwhujhqhudwlrqdo h{fkdqjh1 Lq hdfk ri wkh suhylrxv h{dpsohv wkh zhoiduh
ri d jhqhudwlrq ghshqgv rq wkh dfwlrqv wdnhq e| rwkhu jhqhudwlrqv dqg/ lq wxuq/ lwv
dfwlrqv d�hfw wkh zhoo0ehlqj ri rwkhu jhqhudwlrqv1 Wklv sdwwhuq ri lqwhujhqhudwlrqdo
vslooryhuv lv dw wkh fruh ri wkh sureohp= Gr suhvhqw jhqhudwlrqv kdyh dq lqfhqwlyh
vshqg rswlpdoo| lq rwkhu jhqhudwlrqvB Dqg li vr/ zk|B
Ri frxuvh/ wkh dqvzhu ghshqgv fuxfldoo| rq wkh ghjuhh dqg w|sh ri lqwhujhqhud0
wlrqdo dowuxlvp1 Lq d prgho zlwk lq�qlwho| olyhg g|qdvwlhv wkh sureohp ri lqwhujhq0
hudwlrqdo h{fkdqjh lv qrw sduwlfxoduo| lqwhuhvwlqj1 Diwhu doo/ iru dq lq�qlwho| olyhg
djhqw lqyhvwlqj lq rwkhu jhqhudwlrqv lv qrw dq lqwhujhqhudwlrqdo wudqvihu/ exw dq lq0
yhvwphqw lq klpvhoi1 Dowkrxjk wkh g|qdvwlf prgho kdv |lhoghg lpsruwdqw lqvljkwv/
lw lv lqydolg lq pdq| fdvhv ri lqwhuhvw1
Iluvw ri doo/ lq vrph fdvhv d prgho zlwk vho�vk jhqhudwlrqv lv d ehwwhu dssur{0
lpdwlrq ri uhdolw|1 Wdnh iru h{dpsoh wkh fdvh ri wkh vhqlrulw| v|vwhp lq wkh X1V1
Frqjuhvv1 Lw lv kdug wr eholhyh wkdw srolwlfldqv ixoo| lqwhuqdol}h wkh suhihuhqfhv ri
ixwxuh jhqhudwlrqv ri vwdwhvphq1 Ixuwkhupruh/ dowkrxjk pruh zrun uhpdlqv wr eh
grqh/ wkh vwxglhv ri Dowrqml/ Kd|dvkl dqg Nrwolnr� +4<<5/4<<:, vxjjhvwv wkdw wkh
vho�vk prgho pd| hyhq eh d jrrg dssur{lpdwlrq iru lqwhujhqhudwlrqdo h{fkdqjh
zlwklq wkh idplo|1
�5ii 5�iTt*i E�bbb� @?_ 5�iTt*i @?_ �@*iM�g E�bbf��
6
Dqrwkhu sureohp zlwk wkh g|qdvwlf prgho lv wkdw djhqwv pljkw eh dowuxlvwlf/ exw
kdyh qrq0g|qdvwlf suhihuhqfhv12 Zlwk sdwhuqdolvwlf dowuxlvp djhqwv fduh derxw krz
wkhlu dfwlrqv d�hfw ixwxuh jhqhudwlrqv/ exw qrw derxw wkh xwlolw| ri ixwxuh jhqhudwlrqv1
Iru h{dpsoh/ wkh| pljkw eh zloolqj wr sd| iru wkh froohjh hgxfdwlrq ri wkhlu fkloguhq/
exw xqzloolqj wr �qdqfh rwkhu frqvxpswlrq jrrgv1
Wklv sdshu suhvhqwv d wkhru| ri lqwhujhqhudwlrqdo h{fkdqjh zlwk qrq0g|qdvwlf
suhihuhqfhv/ lqfoxglqj wkh fdvh ri vho�vk jhqhudwlrqv1 Wkh sureohp ri rswlpdo lq0
whujhqhudwlrqdo h{fkdqjh lv sduwlfxoduo| lqwhuhvwlqj zlwk vho�vk jhqhudwlrqv ehfdxvh
wkh| idlo wr lqwhuqdol}h wkh h�hfw ri wkhlu dfwlrqv rq rwkhu jhqhudwlrqv1 Lqwxlwlyho|/
rqh pljkw h{shfw vho�vk sduhqwv wr xqghu0lqyhvw lq wkh hgxfdwlrq ri wkhlu fkloguhq
dqg vho�vk jhqhudwlrqv wr ghsohwh wkh sodqhw ri lwv qdwxudo uhvrxufhv wrr txlfno|1 Dv lw
wxuqv rxw/ wkhvh sureohpv fdq eh doohyldwhg zlwk dq dssursuldwh wudglqj uhodwlrqvkls
ehwzhhq wkh gl�huhqw jhqhudwlrqv1
Wkh �uvw sduw ri wkh sdshu ghyhorsv d edvlf prgho ri lqwhujhqhudwlrqdo h{fkdqjh1
Wkh prgho devwudfwv iurp lqvwlwxwlrqdo ghwdlov dqg hpskdvl}hv wkh nh| irufhv dw
zrun lq doo ri wkh h{dpsohv ghvfulehg deryh1 Wkh dqdo|vlv surylghv wzr pdlq lq0
vljkwv1 Iluvw/ lw lv xvhixo wr glvwlqjxlvk ehwzhhq Iruzdug Lqwhujhqhudwlrqdo Jrrgv
+ILJv, dqg Edfnzdug Lqwhujhqhudwlrqdo Jrrgv +ELJv,1 Lq eurdg whupv/ ILJv duh
wudqvihuv iurp suhvhqw wr ixwxuh jhqhudwlrqv1 H{dpsohv ri ILJv duh lqyhvwphqwv lq
fkloguhq/ lqyhvwphqwv lq orqj0olyhg lqiudvwuxfwxuh/ dqg wkh suhvhuydwlrqv ri hqylurq0
phqwdo txdolw|/ doo ri zklfk jhqhudwh d frvw iru suhvhqw jhqhudwlrqv dqg d ehqh�w iru
ixwxuh jhqhudwlrqv1 E| frqwudvw/ ELJv duh wudqvihuv iurp ixwxuh wr suhvhqw jhqhud0
wlrqv/ ru iurp |rxqj wr rog1 H{dpsohv ri ELJv duh wdnlqj fduh ri hoghuo| sduhqwv
dqg sd|0dv0|rx0jr vrfldo vhfxulw|/ zklfk dprxqw wr wudqvihuv iurp wkh |rxqj wr wkh
rog1 Wkxv/ lq ILJv wkh wudqvihuv jr iruzdug lq wlph/ iurp wkh suhvhqw wr wkh ixwxuh>
lq ELJv wkh| jr edfnzdugv/ iurp wkh suhvhqw wr wkh sdvw1
ELJv dqg ILJv jhqhudwh udwkhu gl�huhqw lqfhqwlyh sureohpv1 Wkh gl�huhqfh lv
gxh wr wkh wlplqj ri h{fkdqjh1 Frqvlghu/ dv dq h{wuhph exw looxvwudwlyh h{dpsoh/
d vho�vk idplo| dqg wkh gl�huhqfh ehwzhhq lqyhvwlqj lq fkloguhq/ d ILJ/ dqg wdnlqj
fduh ri hoghuo| sduhqwv/ d ELJ1 Orrn dw wkh ELJ �uvw1 Hyhu| shulrg d plggoh djh
dgxow qhhgv wr ghflgh zkhwkhu ru qrw wr wdnh fduh ri klv sduhqwv1 Vlqfh kh lv vho�vk/
kh zrxog udwkhu qrw gr lw1 Krzhyhu/ kh dovr zdqwv klv fkloguhq wr wdnh fduh ri klp lq
wkh ixwxuh1 Li wkh ydoxh ri ehlqj wdnhq fduh ri e| rqh*v fkloguhq rxwzhljkv wkh frvw
2�L?�_)?@t|�U @*|h��t4 �@t @*tL Mii? U@**i_ T@|ih?@*�t|�U @*|h��t4� 5ii +@) E�bH.��
7
ri wdnlqj fduh ri rqh*v sduhqwv/ wkhuh lv dq htxloleulxp lq zklfk wkh ELJ lv dozd|v
surylghg1 Dowkrxjk wkhuh duh pdq| htxloleuld wkdw vxssruw wklv rxwfrph/ doo ri wkhp
kdyh wkh iroorzlqj ihdwxuh= +dorqj wkh htxloleulxp sdwk, d jhqhudwlrq eholhyhv wkdw
wkhlu fkloguhq zloo wdnh fduh ri wkhp rqo| li wkh| wdnh fduh ri wkhlu rzq sduhqwv1
Ehfdxvh ri wkh wlplqj ri h{fkdqjh +sd| �uvw dqg uhfhlyh odwhu, wkh surylvlrq ri wkh
ELJ iru d jhqhudwlrq fdq eh frqglwlrqhg rq zkhwkhu ru qrw lw surylghg d ELJ iru
wkh suhylrxv jhqhudwlrq1
E| frqwudvw/ qrz orrn dw wkh hgxfdwlrq ILJ1 Djdlq/ iru h{srvlwlrqdo sxusrvhv
vxssrvh wkdw sduhqwv duh frpsohwho| vho�vk1 E| wkh wlph wkh| kdyh wr ghflgh wr
lqyhvw lq wkhlu fkloguhq wkh| kdyh douhdg| uhfhlyhg wkhlu rzq hgxfdwlrq1 Dv d uhvxow/
vlqfh wkh| duh vho�vk/ wkh| kdyh qr lqfhqwlyh wr surylgh wkh ILJ1 Qrwlfh wkdw wkh
wlplqj ri h{fkdqjh lv h{dfwo| wkh rssrvlwh iurp wkh rqh lq ELJv= uhfhlyh wkh ehqh�w
�uvw dqg ghflgh zkhwkhu ru qrw wr sd| odwhu1 Wklv gl�huhqfh lq wkh wlplqj ri h{fkdqjh
lpsolhv wkdw edfnzdug lqwhujhqhudwlrqdo h{fkdqjh fdq eh vhoi0vxvwdlqhg/ exw iruzdug
lqwhujhqhudwlrqdo h{fkdqjh fdqqrw1
Wkh vhfrqg nh| lqvljkw lv wkdw rswlpdo lqyhvwphqw lq ixwxuh jhqhudwlrqv fdq wdnh
sodfh hyhq zlwk vho�vk djhqwv1 Vho�vk jhqhudwlrqv fdq eh jlyhq dq lqfhqwlyh wr lqyhvw
lq ILJv e| olqnlqj wkhp zlwk ELJv1 Wr vhh wkh lqwxlwlrq/ frqvlghu djdlq wkh vho�vk
idplo| dqg vxssrvh wkdw wkh plggoh0djhg dgxow eholhyhv wkdw wrpruurz klv fkloguhq
zloo wdnh fduh ri klp rqo| li= +4, kh wdnhv fduh ri klv rzq sduhqwv dqg +5, kh lqyhvwv
rswlpdoo| lq wkhlu hgxfdwlrq1 Lq rwkhu zrugv/ wkh frvw ri ex|lqj d ELJ iru klpvhoi
lv sd|lqj iru klv fkloguhq*v hgxfdwlrq dqg wdnlqj fduh ri klv sduhqwv1 Li ehlqj wdnhq
fduh r� lq rog djh lv ydoxdeoh hqrxjk/ wkh plggoh0djhg sduhqw surylghv erwk wkh
ELJ dqg wkh ILJ1 Ri frxuvh/ wklv zrunv rqo| li wkh frvw ri surylglqj d ILJ lv orz
hqrxjk dqg wkh ydoxh ri wkh ELJ lv kljk hqrxjk1 Exw lq vrph fdvhv wkh olqn lv deoh
wr jhqhudwh rswlpdo lqyhvwphqw lq ixwxuh jhqhudwlrqv1
Wkh edvlf wkhru| ri ELJv dqg ILJv fdq eh dssolhg wr d zlgh fodvv ri sureohpv1
Wkh vhfrqg sduw ri wkh sdshu h{soruhv wzr qdwxudo dssolfdwlrqv= +4, wkh srolwlfdo
hfrqrp| ri lqwhujhqhudwlrqdo sxeolf h{shqglwxuhv/ dqg +5, lqyhvwphqw lq fkloguhq
zlwklq wkh idplo|1 Pdq| rwkhu dssolfdwlrqv duh srvvleoh1
2 �hi��L�t w�|ih@|�hi
Wkhuh h{lvwv d odujh olwhudwxuh rq lqwhujhqhudwlrqdo sureohpv/ zklfk iru wkh prvw
sduw kdv irfxvhg rq frqfuhwh sureohpv olnh ehtxhvwv/ wkh idplo|/ wkh hqylurqphqw/ ru
8
wkh h�hfw ri wkh jryhuqphqw ghew1 E| frqwudvw/ wkh jrdo ri wklv sdshu lv wr surylgh d
frpprq iudphzrun iru lqwhujhqhudwlrqdo sureohpv1 Vhyhudo rwkhu sdshuv kdyh dovr
dwwhpswhg wr gr wklv1 Vdqgohu dqg Vplwk +4<:9, dqg Vdqgohu +4<:;/4<;5, duh wkh
�uvw uhihuhqfhv nqrzq e| wkh dxwkru wr ghyhors wkh frqfhsw ri %lqwhujhqhudwlrqdo
jrrgv1% Wkhvh sdshuv irfxv rq fkdudfwhul}lqj wkh rswlpdolw| frqglwlrqv iru wkh
surylvlrq ri lqwhujhqhudwlrqdo jrrgv/ exw ljqruh wkh lqfhqwlyh sureohpv wkdw duh dw
wkh khduw ri wkh wkhru| ri ELJv dqg ILJv1� Grhohpdq dqg Vdqgohu +4<<;, vwxg|
wzr dqg wkuhh shulrg ryhuodsslqj jhqhudwlrq prghov lq zklfk hduolhu jhqhudwlrqv
fdq pdnh lqyhvwphqwv wkdw ehqh�w odwhu jhqhudwlrqv1 Diwhuzdugv/ odwhu jhqhudwlrqv
yroxqwdulo| fkrrvh zkhwkhu wr uhixqg suhylrxv jhqhudwlrqv iru wkhlu h�ruwv1 Wkh|
vkrz wkdw xqghu0lqyhvwphqw wdnhv sodfh ehfdxvh odwhu jhqhudwlrqv gr qrw kdyh dq
lqfhqwlyh wr sd| iru wkh lqyhvwphqw rqfh wkh| kdyh uhfhlyhg lw1 Lq wklv vhqvh/ wkh| od|
rxw wkh ixqgdphqwdo pdunhw dqg srolwlfdo idloxuh ~ zklfk wkh| uhihu wr dv %plvvlqj
pdunhwv dqg plvvlqj yrwhuv%~ zklfk lv dw wkh fruh ri wklv sdshu/ exw wkh| gr qrw
h{soruh krz lqwhujhqhudwlrqdo h{fkdqjh fdq ryhufrph wkhvh srolwlfdo dqg pdunhw
idloxuhv1
Wkh wkhru| ri lqwhujhqhudwlrqdo h{fkdqjh ghyhorshg lq wklv sdshu lv dq dssolfd0
wlrq ri wkh wkhru| ri uhshdwhg jdphv zlwk ryhuodsslqj jhqhudwlrqv ri sod|huv +Vdodqw
+4<<4,/ Ndqgrul +4<<5,/ Vplwk +4<<5,,1 Iurp d jdph wkhruhwlfdo srlqw ri ylhz/ wkh
rqo| lqqrydwlrq lv wr srlqw rxw dqg h{sorlw wkh glvwlqfwlrq ehwzhhq edfnzdug dqg
iruzdug lqwhujhqhudwlrqdo h{fkdqjh1 Wkh sdshu dovr xvhv ri wkh zhoo0nqrzq idfw wkdw
olqndjhv dfurvv jdphv fdq khos lq vxvwdlqlqj frrshudwlrq1 Ehuqkhlp dqg Zklqvwrq
+4<<3, vkrz wkdw frrshudwlrq dprqj +lq�qlwho|0olyhg, roljrsrolvwv lv pruh olnho| wr
dulvh zkhq wkh| frpshwh vlpxowdqhrxvo| lq vhyhudo lqgxvwulhv +vhh dovr Ehqgru dqg
Prrnkhumhh +4<<3,,1 Irophu hw do1 +4<<6, dsso| vlplodu lghdv wr lqwhuqdwlrqdo fr0
rshudwlrq lq hqylurqphqwdo sureohpv1 Doo ri wkhvh sdshuv vwxg| frrshudwlrq dprqj
lq�qlwho|0olyhg djhqwv zkr sod| vhyhudo jdphv vlpxowdqhrxvo|1 Krzhyhu/ wklv sdshu
dssolhv wkhvh lghdv wr lqwhujhqhudwlrqdo h{fkdqjh dqg hpskdvl}hv wkh glvwlqfwlrq eh0
wzhhq ILJv dqg ELJv= iruzdug lqwhujhqhudwlrqdo h{fkdqjh fdq eh vxvwdlqhg rqo| e|
olqnlqj lw wr d jdph zlwk wkh rssrvlwh wlplqj ri h{fkdqjh1
D vljql�fdqw qxpehu ri sdshuv kdyh vwxglhg wkh vxvwdlqdelolw| ri edfnzdug lq0
whujhqhudwlrqdo h{fkdqjh lq gl�huhqw frqwh{wv1 Vhh/ dprqj rwkhuv/ Erkq +4<;;,/
Frroh| dqg Vrduhv +4<<<,/ Kdpprqg +4<:8,/ Kdqvvrq dqg Vwxduw +4<;<,/ Nrfkhu0
�5ii @*tL 5�*�it|hi E�bbec�bbD��
9
odnrwd +4<<;,/ Nrwolnr�/ Shuvvrq/ dqg Vyhqvvrq +4<;;, dqg Nuhsv +4<<3,1 Krzhyhu/
rqo| d vpdoo qxpehu ri sdshuv kdyh vwxglhg edfnzdug dqg iruzdug lqwhujhqhud0
wlrqdo h{fkdqjh wrjhwkhu1 Ri sduwlfxodu uhohydqfh duh Ehfnhu dqg Pxusk| +4<;;,
dqg Erogulq dqg Prqwhv +4<;;, zkr/ dv lq wkh �uvw dssolfdwlrq ghyhorshg ehorz/
dovr vwxg| wkh srolwlfdo hfrqrp| ri lqwhujhqhudwlrqdo sxeolf h{shqglwxuhv1 Ehfnhu
dqg Pxusk| vxjjhvwhg wkdw rqh frxog wklqn ri rog djh vrfldo vhfxulw| surjudpv dqg
hgxfdwlrqdo lqyhvwphqwv dv d odujh lqwhujhqhudwlrqdo wudgh lq zklfk hyhu| qhz jhq0
hudwlrq uhfhlyhv hgxfdwlrq iurp lwv sduhqwv dqg lq h{fkdqjh sd|v wkhlu uhwluhphqw
ehqh�wv1 Krzhyhu/ wkh| glg qrw vwxg| wkh g|qdplf frqvlvwhqf| ri wkhvh duudqjh0
phqwv1 Erogulq dqg Prqwhv vwxg| d wkuhh shulrg ROJ prgho lq zklfk h{shqglwxuhv
lq sxeolf hgxfdwlrq dqg vrfldo vhfxulw| duh ghflghg e| pdmrulw| uxoh1 Wkh| vkrz
wkdw wkh rswlpdo doorfdwlrq fdq eh vxvwdlqhg xvlqj wuljjhu vwudwhjlhv vlplodu wr wkh
rqhv vwxglhg lq wklv sdshu1e
� �@t�U �L_i* Lu W?|ih}i?ih@|�L?@* , U�@?}i
Frqvlghu d vlpsoh ryhuodsslqj jhqhudwlrqv prgho1 Hyhu| shulrg w @ ===>�4> 3> 4> ===
d qhz jhqhudwlrq lv eruq dqg olyhv iru wkuhh shulrgv= w/ w . 4/ dqg w . 51 Djhqwv
duh lqidqwv lq wkh �uvw shulrg/ plggoh0djhg lq wkh vhfrqg/ dqg rog lq wkh wklug1
Wkh| uhfhlyh dq hqgrzphqw ru zdjh lq wkh vhfrqg shulrg/ dqg fdq vdyh +ru eruurz,
iru uhwluhphqw xvlqj d vwrudjh whfkqrorj| zlwk d frqvwdqw udwh ri uhwxuq 4 . u1 D
jhqhudwlrq frqvlvwv ri d vlqjoh lqglylgxdo1
Hyhu| shulrg w wkh plggoh0djhg jhqhudwlrq w�4 fdq lqyhvw lq d Iruzdug Lqwhujhq0
hudwlrqdo Jrrg +ILJ, wkdw rqo| ehqh�wv wkdw qh{w jhqhudwlrq1 Ohw i| ghqrwh wkh ohyho
ri lqyhvwphqw lq shulrg w1 Wkh ILJ fdq eh surgxfhg dw rqo| wzr ohyhov= i| 5 i3> 4j1
Hyhu| shulrg/ wkh plggoh0djhg fdq dovr lqyhvw lq d Edfnzdug lqwhujhqhudwlrqdo Jrrg
+ELJ, wkdw rqo| ehqh�wv wkh suhylrxv jhqhudwlrq1 Ohw e| 5 i3> 4j ghqrwh wkh ohyho
ri lqyhvwphqw lq wkh ELJ1 Wkh frvw ri lqyhvwlqj lq wkh ILJ lv I A 3/ wkh frvw ri
lqyhvwlqj lq wkh ELJ lv E A 31D Wkh wlplqj ri ghflvlrq pdnlqj lv looxvwudwhg lq
Iljxuh 41
Wr vlpsoli| wkh h{srvlwlrq zh vwduw zlwk wkh fdvh ri vho�vk jhqhudwlrqv dqg dgg
eA�i TL*�|�U@* iUL?L4) 4L_i* Lu �?|ih}i?ih@|�L?@* i U�@?}i Thiti?|i_ �ihi @?_ |�i L?i �?�L*_h�? @?_ �L?|it E�bbH� �ihi _i�i*LTi_ �?_iTi?_i?|*)� A�i TL*�|�U@* iUL?L4) 4L_i* Thiti?|i_�? 5iU|�L? . �t @ hi��ti_ �iht�L? Lu +@?}i* E�bb.��
DA�i |�iLh) hi4@�?t �?U�@?}i_ �u |�iti ULt|t @hi 4L_i**i_ @t ��|�*�|)� ULt|tc ���U� 4@) Mi4Lhi @TThLTh�@|i uLh tL4i @TT*�U@|�L?t *�!i �?|ih}i?ih@|�L?@* i U�@?}i ��|��? |�i u@4�*)�
:
period t
Y M O
Y M O
Y M O
t-BIG
t-FIG t+1-BIG
t-1-FIG
generation t
generation t-1
Iljxuh 4= Wlplqj ri h{fkdqjh
qrq0g|qdvwlf dowuxlvp diwhuzdugv1 Wkh suhihuhqfhv ri jhqhudwlrq w duh jlyhq e|
X|+f6> fJ> i|> e|n2, @ x+f6, . �x+fJ, . Y 8 +i|, . Y �+e|n2,>
zkhuh Y 8 +4, A Y 8 +3, dqg Y �+4, A Y �+3,1 Djhqwv rqo| fduh derxw wkhlu rzq
frqvxpswlrq/ dqg derxw uhfhlylqj d ILJ zkhq wkh| duh |rxqj dqg d ELJ zkhq
wkh| duh rog1 Fkloguhq gr qrw ghulyh xwlolw| iurp frqvxpswlrq/ exw wkh| fduh derxw
wkh ILJ wkdw wkh| jhw iurp wkh suhylrxv jhqhudwlrq1S Ilqdoo|/ x+3, @ �4/ zklfk
lpsolhv wkdw djhqwv kdyh d yhu| vwurqj suhihuhqfh iru frqvxplqj d srvlwlyh dprxqw
lq erwk shulrgv1
Wkh iroorzlqj qrwdwlrq zloo vlpsoli| wkh h{srvlwlrq ehorz1 Ohw
�WE�6c�J� @ dujpd{3 �
J
E�no�$j$�6
x+z6 � �, . �x++4 . u,� .zJ,
ghqrwh wkh rswlpdo ohyho ri vdylqjv iru dq djhqw wkdw kdv lqfrph z6 lq plggoh djh
dqg zJ lq rog djh1 +Wkh hqgrzphqw ri wkh rog lv }hur/ exw lq htxloleulxp wkh| pd|
uhfhlyh wudqvihuv ri wkh frqvxpswlrq jrrg,1 Dovr/ ohw
yW+z6> zJ, @ x+z6 � �WE�6c�J�, . �x++4 . u,�WE�6c�J� .zJ,
ghqrwh wkh lqgluhfw xwlolw| ri frqvxpswlrq1 Ilqdoo|/ wr plqlpl}h qrwdwlrq wlph vxe0
vfulswv dozd|v uhihu wr wkh shulrg lq zklfk wkh uhohydqw hyhqw lv wdnlqj sodfh1 Iru
h{dpsoh/ i| lv wkh ohyho ri ILJ lqyhvwphqw lq shulrg w dqg z| duh wkh zdjhv lq wkdw
shulrg +zklfk duh sdlg wr wkh plggoh0djhg ri jhqhudwlrq w� 4,1
S�t �i ��** tii Mi*L�c |�i hit�*|t i@t�*) i |i?_ |L |�i U@ti Lu ?L?�_)?@t|�U @*|h��t4 @?_ |L |�i
U@ti Lu �4T�hi 6WBtc ��ihi |�i }i?ih@|�L? ThL_�U�?} |�i 6WB }i|t tL4i Lu |�i Mi?i�|t�
;
Xqghu wkhvh dvvxpswlrqv wkh prgho ri lqwhujhqhudwlrqdo h{fkdqjh uhgxfhv wr dq
lq�qlwho| uhshdwhg jdph wkdw wkh jhqhudwlrqv sod| zlwk hdfk rwkhu1 Hyhu| shulrg w/
dv looxvwudwhg lq Iljxuh 4/ jhqhudwlrq w� 4 slfnv dq dfwlrq +i|> e|, 5 i3> 4j � i3> 4j1
Wkh sd|r� ri d jhqhudwlrq ghshqgv rqo| rq klv dfwlrqv/ wkh dfwlrqv ri wkh suhylrxv
jhqhudwlrq/ dqg wkh dfwlrqv ri wkh qh{w jhqhudwlrq1 Wkh klvwru| k| ri suhylrxv
ghflvlrqv lv nqrzq/ zkhuh k| @ ++i|3�> e|3�,> +i|32> e|32,> ===, ghqrwhv hyhu| dfwlrq
wdnhq sulru wr shulrg w1 D vwudwhj| iru jhqhudwlrq w04 lv d ixqfwlrq v|+k|, wkdw
vshfl�hv dq dfwlrq frqwlqjhqw rq wkh hqwluh klvwru| ri sod|1 Dq htxloleulxp lv vlpso|
d vxejdph shuihfw htxloleulxp ri wklv jdph1
e �WB5 �t 6WBtG |�i Uh�U�@* hL*i Lu |�i |�4�?} Lu i �
U�@?}i
Lq wklv vw|ol}hg prgho ri lqwhujhqhudwlrqdo h{fkdqjh wkh rqo| gl�huhqfh ehwzhhq
ILJv dqg ELJv lv wkh wlplqj ri h{fkdqjh1 Lq erwk fdvhv wkh vwuxfwxuh ri h{fkdqjh lv
vlplodu= ex| vrphwklqj iru jhqhudwlrq { dqg uhfhlyh vrphwklqj iurp jhqhudwlrq |1
Wkh wlplqj ri h{fkdqjh/ krzhyhu/ lv udwkhu gl�huhqw1 Lq wkh fdvh ri ELJv/ djhqwv sd|
�uvw/ e| surylglqj d ELJ iru wkh suhylrxv jhqhudwlrq/ dqg ehqh�w odwhu/ e| uhfhlylqj
d ELJ iurp wkh qh{w jhqhudwlrq1 E| frqwudvw/ djhqwv uhfhlyh wkhlu rzq ILJ �uvw dqg
sd| rqo| odwhu e| surylglqj d ILJ iru wkh qh{w jhqhudwlrq1
Wkh jrdo ri wklv vhfwlrq lv wr vkrz wkdw wklv vlpsoh gl�huhqfh lq wkh wlplqj ri
h{fkdqjh kdv lpsruwdqw lpsolfdwlrqv iru wkh w|sh ri lqwhujhqhudwlrqdo h{fkdqjh wkdw
fdq wdnh sodfh1 Wzr frqfhswv duh xvhixo lq dfklhylqj wklv jrdo1 Iluvw/ lv wkh vxusoxv
jhqhudwhg e| d ELJ/ zklfk lv htxdo wr wkh ydoxh ri %frrshudwlqj% lq wkh ELJ1 Iru
jhqhudwlrq w� 4 wkh vxusoxv lv jlyhq e|
^yW+z| �E> 3, . Y �+4,`� ^yW+z|> 3, . Y �+3,`=
Wkh �uvw whup lv wkh sd|r� li wkh ELJ lv surgxfhg hyhu| shulrg1 Wkh vhfrqg whup
lv wkh sd|r� li wkh ELJ lv qhyhu surgxfhg1
Dqrwkhu xvhixo qrwlrq lv vhoi0vxvwdlqdelolw|1 Wr xqghuvwdqg wklv qrwlrq frqvlghu
dq hyhq vlpsohu h{fkdqjh jdph lq zklfk wkhuh duh rqo| ELJv1 Khuh/ wkh rqo| ghflvlrq
wkdw djhqwv pdnh lv zkhwkhu ru qrw wr surgxfh d ELJ iru wkh suhylrxv jhqhudwlrq1 D
ELJ lv vhoi0vxvwdlqdeoh li wkhuh lv dq htxloleulxp lq wkh vlpsohu jdph lq zklfk rqo|
ELJv duh surgxfhg hyhu| shulrg1 Lqwxlwlyho|/ d ELJ lv vhoi0vxvwdlqdeoh li lw jhqhudwhv/
<
rq lwv rzq/ hqrxjk lqfhqwlyhv wr vxvwdlq edfnzdug lqwhujhqhudwlrqdo h{fkdqjh1 Wkh
gh�qlwlrq ri vhoi0vxvwdlqdelolw| iru ILJv lv dqdorjrxv1
SURSRVLWLRQ 4= Wkhuh lv d ixqgdphqwdo dv|pphwu| ehwzhhq iruzdug dqg
edfnzdug lqwhujhqhudwlrqdo h{fkdqjh= +4, ELJv wkdw jhqhudwh d srvlwlyh vxu0
soxv iru hyhu| jhqhudwlrq duh vhoi0vxvwdlqdeoh> +5, ILJv duh qrw vhoi0vxvwdlqdeoh
hyhq zkhq wkh| jhqhudwh dq duelwudulo| odujh vxusoxv iru hyhu| jhqhudwlrq1
Wkh surri ri wklv sursrvlwlrq lv d vwudljkwiruzdug dssolfdwlrq ri wkh wkhru| ri
uhshdwhg jdphv1 Frqvlghu �uvw wkh fdvh lq zklfk wkhuh lv rqo| d ELJ dqg vxssrvh
wkdw lw jhqhudwhv d vxusoxv iru hyhu| jhqhudwlrq1 Zh qhhg wr vkrz wkdw wkhuh lv dq
htxloleulxp lq zklfk wkh ELJ lv dozd|v surgxfhg1 Wr gr vr/ frqvlghu wkh iroorzlqj
wuljjhu0vwudwhjlhv=
v|+k|, @
+e| @ 4 li e|3� @ e|32 @ === @ 4e| @ 3 rwkhuzlvh
= +4,
Xqghu wkhvh vwudwhjlhv d jhqhudwlrq surgxfhv wkh ELJ li/ dqg rqo| li/ hyhu| suhylrxv
jhqhudwlrq kdv grqh wkh vdph1
Wr hvwdeolvk wkdw wkh vwudwhjlhv lq +4, duh dq htxloleulxp zh qhhg wr vkrz wkdw
hyhu| jhqhudwlrq kdv dq lqfhqwlyh wr iroorz lw jlyhq wkdw hyhu| rwkhu jhqhudwlrq grhv
vr1 Frqvlghu wkh lqfhqwlyhv ri jhqhudwlrq w � 4 zkr/ lq shulrg w/ fdq �qg lwvhoi lq
wzr w|shv ri klvwrulhv1 Iluvw/ wkhuh duh klvwrulhv lq zklfk d suhylrxv jhqhudwlrq kdv
idlohg wr surgxfhg wkh ELJ1 Lq wklv fdvh/ dv +4, vshfl�hv/ wkh ehvw uhvsrqvh lv qrw
wr surgxfh wkh ELJ vlqfh wkh dfwlrqv ri wkh qh{w jhqhudwlrq duh �{hg dw e|n� @ 31
Vhfrqg/ wkhuh duh klvwrulhv lq zklfk hyhu| suhylrxv jhqhudwlrq kdv surylghg wkh ELJ1
Lq wklv fdvh jhqhudwlrq w� 4 jhwv
x+z| �E � �WE�|3�cf�, . �x++4 . u,�WE�|3�cf�, . Y �+4,
li lw surylghv wkh ELJ/ dqg
x+z| � �WE�|3�cf�, . �x++4 . u,�WE�|3�cf�
, . Y �+3,
li lw grhv qrw1 Fohduo|/ jhqhudwlrq w� 4 surylghv wkh ELJ dv orqj dv
Y �+4,� Y �+3, � yW+z|> 3,� yW+z| �E> 3,> +5,
l1h1/ dv orqj dv wkh ELJ jhqhudwhv d vxusoxv1 Zh fdq frqfoxgh wkdw li +5, lv vdwlv�hg
iru hyhu| jhqhudwlrq/ wkh wuljjhu0vwudwhjlhv duh dq htxloleulxp lq zklfk wkh ELJ lv
dozd|v surgxfhg1
43
Iru wkh vhfrqg sduw ri wkh surri frqvlghu wkh fdvh lq zklfk wkhuh duh rqo| ILJv1
Lw lv hdv| wr vhh wkdw wkhuh lv d xqltxh htxloleulxp lq zklfk qr ILJv duh surgxfhg1
Vlqfh djhqwv uhfhlyh wkhlu rzq ILJ ehiruh wkh| kdyh wr pdnh d ghflvlrq/ surylglqj
d ILJ iru wkh qh{w jhqhudwlrq lv d sxuh wudqvihu1 Wkxv/ uhjdugohvv ri wkh vxusoxv
jhqhudwhg e| wkh ILJ/ lw lv qhyhu surgxfhg1 Wklv frqfoxghv wkh surri1
Wkh wlplqj ri h{fkdqjh lv hvvhqwldo wr xqghuvwdqg zk| ELJv wkdw jhqhudwh d vpdoo
exw srvlwlyh vxusoxv duh vhoi0vxvwdlqdeoh exw ILJv qhyhu duh1 Surylglqj d ELJ ru d
ILJ iru vrphrqh hovh lv d frvwo| dfwlrq wkdw jhqhudwlrqv gr qrw zdqw wr xqghuwdnh1
Wkh| gr vr rqo| li wklv lv wkh rqo| zd| ri jhwwlqj d jrrg wkdw wkh| fduh derxw1 Lq
wkh fdvh ri ELJv/ frrshudwlrq lv srvvleoh ehfdxvh djhqwv pxvw fkrrvh �uvw wr ex| d
ELJ iru vrphrqh hovh/ dqg rqo| odwhu uhfhlyh wkh ELJ wkdw wkh| fduh derxw1 Wklv
doorzv wkh vrfldo qrup wr frqglwlrq wkh surgxfwlrq ri wkh ELJ wkdw d jhqhudwlrq
fduhv derxw rq wkhlu ehkdylru wrzdugv suhylrxv jhqhudwlrqv1 E| frqwudvw/ lq wkh
fdvh ri ILJv/ d jhqhudwlrq uhfhlyhv lwv rzq ILJ dw eluwk dqg lw grhv qrw fduh derxw
krz lwv dfwlrqv d�hfw ixwxuh ehkdylru1
Wkh wuljjhu0vwudwhjlhv ghvfulehg lq +4, duh vrphzkdw gudfrqldq dqg xquhdolvwlf1
Lq sduwlfxodu/ xqghu wklv vrfldo qrup lqwhujhqhudwlrqdo h{fkdqjh froodsvhv li d vlq0
joh jhqhudwlrq idlov wr surgxfh wkh ELJ1 Krzhyhu/ li lqwhujhqhudwlrqdo frrshudwlrq
lv ihdvleoh zlwk wuljjhu0vwudwhjlhv/ wkhq w|slfdoo| lw lv dovr ihdvleoh zlwk qrq0wuljjhu
vwudwhjlhv1 Iru h{dpsoh/ d yduldwlrq ri wkh suhylrxv dujxphqw vkrzv wkdw wkh vwudwh0
jlhv
v|+k|, @
;A?A=
e| @ 4 li e|3� @ e|32 @ === @ 4e| @ 4 li e|3& @ e|3E&n�� @ 3 dqg e|3� @ 4 iru doo m 9@ n> n . 4e| @ 3 rwkhuzlvh
+6,
duh dovr dq htxloleulxp wkdw vxssruw wkh surgxfwlrq ri wkh ELJv1 Exw lq wklv fdvh d
vlqjoh %ghyldwlrq% grhv qrw froodsvh doo lqwhujhqhudwlrqdo h{fkdqjh1 Wkh �uvw jhqhu0
dwlrq wkdw idlov wr surgxfh wkh ELJ lv sxqlvkhg e| qrw uhfhlylqj d ELJ lq rog djh/
exw diwhuzdugv frrshudwlrq uhvxphv1 Pruh frpsolfdwhg vwudwhjlhv duh srvvleoh1.
Wkh uhvw ri wkh sdshu pdnhv h{whqvlyh xvhg ri wuljjhu vwudwhjlhv1 Wklv lv mxvwl�hg
e| wkh iroorzlqj zhoo nqrzq uhvxow1 Lq wklv fodvv ri jdphv/ li lqwhujhqhudwlrqdo frrs0
hudwlrq fdq eh vxvwdlqhg xvlqj qrq0wuljjhu0vwudwhjlhv/ wkhq lw fdq dovr eh vxvwdlqhg
.��@t!@h E�bbH� t�L�t |�@|c �? |��t |)Ti Lu L�ih*@TT�?} }i?ih@|�L? }@4itc |�i i �t|i?Ui Lu ULLT�ih@|��i i^��*�Mh�@ _iTi?_t Uh�U�@**) L? |�i LMtih�@M�*�|) Lu |�i i?|�hi ��t|Lh) Lu T*@)� W? T@h|�U�*@hc?L�ULLTih@|�L? �t |�i �?�^�i i^��*�Mh��4 ��i? }i?ih@|�L?t U@? LMtih�i @| 4Lt| |�i @U|�L?t Lu |�i*@t| ? Thi_iUittLht�
44
zlwk wuljjhu0vwudwhjlhv1 Wkxv/ rqh fdq xvh wuljjhu0vwudwhjlhv wr hvwdeolvk qhfhvvdu|
frqglwlrqv iru lqwhujhqhudwlrqdo frrshudwlrq1 Krzhyhu/ dv wkh suhylrxv sdudjudsk
vkrzv/ wklv grhv qrw phdq wkdw wuljjhu0vwudwhjlhv duh wkh rqo| zd| ri vxssruwlqj
frrshudwlrq1 Wkh| duh d vlpso| frqyhqlhqw dqdo|wlf ghylfh/ qrw wkh prvw uhdolvwlf
ghvfulswlrq ri wkh htxloleulxp vrfldo qrup1 D vwudljkwiruzdug lpsolfdwlrq ri wklv
uhvxow lv wkdw Sursrvlwlrq 4 fdq eh vwuhqjwkhq= ELJv duh vhoi0vxvwdlqdeoh li dqg rqo|
li wkh| jhqhudwh d qrq0qhjdwlyh vxusoxv iru hyhu| jhqhudwlrq1 Wklv iroorzv gluhfwo|
iurp +5, lq wkh surri ri Sursrvlwlrq 41
Wkh pxowlsoh htxloleuld sureohp lv vhyhuh dqg xqdyrlgdeoh lq wklv fodvv ri jdphv1
Lq sduwlfxodu wkhuh duh dozd|v htxloleuld lq zklfk wkh ELJ lv qhyhu surgxfhg1 Diwhu
doo/ vlqfh surgxflqj d ELJ lv frvwo|/ d jhqhudwlrq grhv vr rqo| li lw eholhyhv wkdw lwv
dfwlrqv zloo d�hfw wkh ehkdylru ri wkh qh{w jhqhudwlrq1 Dv d uhvxow/ v|+k|, @ 3 iru doo
k| lv dozd|v dq htxloleulxp1 Wklv %edg% htxloleulxp h{lvwv hyhq li wkh ELJ jhqhudwhv
dq duelwudulo| odujh vxusoxv1
D w�?!�?} 6WBt @?_ �WBt
Dowkrxjk ILJv duh qrw vhoi0vxvwdlqdeoh/ lq wklv vhfwlrq zh vkrz wkdw wkhuh duh htxl0
oleuld lq zklfk wkh| duh surylghg1 Ixuwkhupruh/ wkh uhvxowv vkrz wkdw wkhuh lv dq
lpsruwdqw uhodwlrqvkls ehwzhhq edfnzdug dqg iruzdug lqwhujhqhudwlrqdo h{fkdqjh=
ILJv duh surylghg rqo| zkhq wkh| duh %olqnhg% wr ELJv1
SURSRVLWLRQ 5= ILJv duh surylghg lq hyhu| shulrg li dqg rqo| li +4, iru hyhu|
jhqhudwlrq/ wkh vxusoxv jhqhudwhg e| wkh ELJ lv odujhu wkdq wkh frvw ri surylglqj
wkh ILJ> dqg +5, wkh htxloleulxp vwudwhjlhv olqn ELJv dqg ILJv e| pdnlqj
frrshudwlrq rq ILJv d qhfhvvdu| frqglwlrq iru frrshudwlrq rq ELJv1
Wr suryh wklv uhvxow qrwh wkdw wzr w|shv ri vwudwhjlhv duh srvvleoh zkhq jhq0
hudwlrqv slfn ELJv dqg ILJv1 Lq wkh �uvw w|sh wkhuh lv qr olqn ehwzhhq ELJv dqg
ILJv/ wkh klvwru| ri ELJv lq�xhqfhv rqo| wkh fkrlfh ri ELJv dqg wkh klvwru| ri ILJv
lq�xhqfhv rqo| wkh fkrlfh ri ILJv1 Wkhvh vwudwhjlhv fdq eh zulwwhq dv
v|+k|, @ +e|+e|3�> e|32> ===,> i|+i|3�> i|32> ===,,=
Lw lv hdv| wr vhh wkdw wkh vhw ri qr0olqn htxloleuld lv jlyhq vlpso| e| wkh mx{wdsrvlwlrq
ri wkh htxloleuld ghvfulehg lq wkh suhylrxv vhfwlrq1 Wkxv/
v|+k|, @ +3> 3,
45
dqg
v|+k|, @
+e| @ 4/ i| @ 3 li e|3� @ e|32 @ === @ 4e| @ i| @ 3 rwkhuzlvh
duh wzr srvvleoh qr0olqn htxloleuld1 Lq wkh �uvw qr lqwhujhqhudwlrqdo h{fkdqjh wdnhv
sodfh/ lq wkh vhfrqg rqo| ELJv duh surgxfhg1
E| frqwudvw/ lq wkh vhfrqg w|sh ri vwudwhjlhv jlyhq e|
v|+k|, @ +e|+k|,> i|+k|,,
wkhuh lv d olqn ehwzhhq ELJv dqg ILJv1 Khuh wkh fkrlfh ri ELJv ghshqgv rq wkh
klvwru| ri erwk ELJv dqg ILJv1 Wklv olqn kdv lpsruwdqw frqvhtxhqfhv iru wkh sur0
gxfwlrq ri ILJv1 Lq sduwlfxodu/ frqvlghu wkh wuljjhu0vwudwhjlhv
v|+k|, @
+e| @ i| @ 4 li i|3� @ e|3� @ i|32 @ e|32 @ === @ 4e| @ i| @ 3 rwkhuzlvh
> +7,
zkhuh idloxuh wr surgxfh hlwkhu d ELJ ru d ILJ froodsvhv erwk w|shv ri lqwhujhqhud0
wlrqdo wudgh1
Dv ehiruh/ wr vkrz wkdw wkh vwudwhjlhv lq +7, duh dq htxloleulxp zh qhhg wr vkrz
wkdw hyhu| jhqhudwlrq kdv dq lqfhqwlyh wr iroorz wkhp dw hyhu| srvvleoh klvwru|/
jlyhq wkdw hyhu| rwkhu jhqhudwlrq grhv vr1 Rqfh pruh/ vwduw e| orrnlqj dw klvwrulhv
lq zklfk wkhuh zdv d suhylrxv euhdngrzq lq lqwhujhqhudwlrqdo frrshudwlrq1 Khuh
jhqhudwlrq w� 4 nqrzv wkdw/ uhjdugohvv ri klv dfwlrqv/ wkh qh{w jhqhudwlrq zloo qrw
surylgh wkh ELJ1 Wkh ehvw uhvsrqvh/ dv +7, vshfl�hv/ lv wr surgxfh qhlwkhu wkh ELJ
qru wkh ILJ1
Qrz frqvlghu wkh klvwru| lq zklfk hyhu| suhylrxv jhqhudwlrq kdv surylghg erwk
jrrgv1 Li jhqhudwlrq w� 4 frrshudwhv lw jhwv d sd|r�
x+z| �E � I � �WE�|3�38cf�, . �x++4 . u,�WE�|3�38cf�
, . Y 8 +4, . Y �+4,=
Rq wkh rwkhu kdqg/ wkh sd|r� dw wkh ehvw srvvleoh ghyldwlrq lv jlyhq e|
x+z| � �WE�|cf�, . �x++4 . u,�WE�|cf�
, . Y 8 +4, . Y �+3,
Fohduo|/ jhqhudwlrq w� 4 surylghv wkh ELJ dqg wkh ILJ dv orqj dv
Y �+4,� Y �+3, � yW+z|3�> 3,� yW+z|3� � +E . I ,> 3,= +8,
Lq rwkhu zrugv/ frrshudwlrq lv srvvleoh dv orqj dv wkh vxusoxv jhqhudwhg e| wkh ELJ
rxwzhljkv wkh frvw ri surylglqj erwk wkh ELJ dqg wkh ILJ1 Wklv frqfoxghv wkh surri1
46
Wkh nh| lqvljkw ehklqg wklv uhvxow lv wkdw d vhoi0vxvwdlqdeoh ELJ soxv d orz frvw
ILJ orrnv olnh d vhoi0vxvwdlqdeoh ELJ1 Li hyhu|rqh ehkdyhv dffruglqj wr +7,/ wkh rqo|
zd| wkdw d jhqhudwlrq fdq sxufkdvh lwv rzq ELJ lv wr surylgh erwk wkh ELJ dqg
wkh ILJ1 Exw wkhq wkh fkrlfh wkdw hyhu| jhqhudwlrq idfhv lv wr jlyh xs E . I zkhq
plggoh0djhg wr uhfhlyh Y �+4, zkhq rog1 Wklv orrnv h{dfwo| olnh d ELJ wkdw frvwv
E . I 1
Fdq wkh olqn ehwzhhq ELJv dqg ILJv jhqhudwh rswlpdo lqyhvwphqw lq ixwxuh
jhqhudwlrqvB \hv/ dv orqj dv wkh vxusoxv jhqhudwhg e| wkh ELJv rxwzhljkv wkh frvw ri
surylglqj wkh ELJv1 Krzhyhu/ ryhu0lqyhvwphqw lq ixwxuh jhqhudwlrqv lv dovr srvvleoh1
D jhqhudwlrq lqyhvwv lq wkh ILJ rqo| dv zd| ri pdlqwdlqlqj frrshudwlrq lq wkh ELJ1
Lw grhv qrw fduh derxw wkh ehqh�wv jhqhudwhg e| wkh ILJ/ rqo| derxw lwv frvwv1 Wkxv/
lw lv lqgl�huhqw ehwzhhq lqyhvwlqj lq h�flhqw dqg lqh�flhqw ILJv1
Doo ri wkh htxloleuld lq wklv prgho fdq eh glylghg lqwr wkuhh fdwhjrulhv1 Iluvw/
wkhuh duh Pdunryldq ru klvwru| lqghshqghqw htxloleuld lq zklfk qr lqwhujhqhudwlrqdo
wudgh/ edfnzdug ru iruzdug/ wdnhv sodfh1 Vhfrqg/ wkhuh duh klvwru| ghshqghqw qrq0
olqndjh htxloleuld lq zklfk rqo| ELJv duh surgxfhg1 Ilqdoo|/ wkhuh duh klvwru| gh0
shqghqw htxloleuld zlwk olqndjh lq zklfk erwk ELJv duh ILJv duh surgxfhg1 D
frpsdulvrq ri wkhvh fdwhjrulhv |lhogv wkh iroorzlqj lqvljkwv=
41 Lqyhvwphqw lq ixwxuh jhqhudwlrqv lv srvvleoh hyhq zlwk vho�vk jhqhudwlrqv1 Iru
vrph sdudphwhuv/ wkh olqndjh vwudwhj| pd| hyhq |lhog rswlpdo lqwhujhqhud0
wlrqdo h{fkdqjh1
51 Rswlpdo lqyhvwphqw lq ixwxuh jhqhudwlrqv fdq wdnh sodfh rqo| li= +4, ELJv dqg
ILJv duh olqnhg lq wkh htxloleulxp vrfldo qrup/ dqg +5, wkh frvw ri surylglqj
wkh ILJ lv qrw wrr odujh dqg wkh vxusoxv jhqhudwhg e| wkh ELJ lv odujh hqrxjk1
61 Vlqfh ILJv duh surgxfhg rqo| zkhq ELJv duh dovr surgxfhg/ wkhuh lv d eldv lq
idyru ri edfnzdugv lqwhujhqhudwlrqdo h{fkdqjh1
71 Wkh ehqh�wv jhqhudwhg e| wkh ILJ sod| qr uroh rq lwv vxvwdlqdelolw|/ rqo| wkh
surgxfwlrq frvwv pdwwhu1 Wkxv/ d ILJ wkdw jhqhudwhv duelwudulo| odujh ehqh�wv/
exw lv frvwo|/ zloo qrw eh surgxfhg1 Zkhuhdv d ILJ wkdw jhqhudwhv orzhu qhw
ehqh�wv/ exw lv uhodwlyho| fkhds/ fdq eh vxvwdlqhg1
Wkhvh uhvxowv duh dw zrun lq d zlgh udqjh ri sureohpv/ iurp wkh srolwlfdo hfrqrp|
ri wkh hqylurqphqw wr wkh hfrqrplfv ri wkh idplo|1
47
D qdwxudo h{whqvlrq ri wkh prgho lv wr frqvlghu wkh fdvh lq zklfk wkhuh duh
pxowlsoh ILJv dqg ELJv1 Vxssrvh/ dv ehiruh/ wkdw doo ri wkhvh jrrgv fdq eh surgxfhg
dw wzr ohyhov +3 dqg 4, dqg wkdw suhihuhqfhv duh dgglwlyho| vhsdudeoh lq hdfk jrrg1
Vrph ri wkh ELJv pljkw eh vhoi0vxvwdlqdeoh/ rwkhuv pd| qrw1
SURSRVLWLRQ 6= +4, Wkh surylvlrq ri dq h{shqvlyh ILJ fdq eh vxvwdlqhg e|
olqnlqj lw wr vhyhudo ELJv1 Wklv lv ihdvleoh dv orqj dv/ iru hyhu| jhqhudwlrq/ wkh
vxp ri wkh vxusoxvhv jhqhudwhg e| wkh ELJv lv odujhu wkdq wkh frvw ri surylglqj
wkh ILJ1 +5, D qrq0vhoi0vxvwdlqdeoh ELJ lv surylghg lq htxloleulxp li dqg rqo|
li lw lv olqnhg wr d vhoi0vxvwdlqdeoh ELJ wkdw jhqhudwhv d odujh hqrxjk vxusoxv1
Wkh surri ri wklv uhvxow lv d vwudljkwiruzdug uhshwlwlrq ri suhylrxv dujxphqwv dqg
lv rplwwhg1 Wkh nh| wr wkh �uvw sduw ri wkh uhvxow lv wkdw wzr ELJv wkdw jhqhudwh d
vxusoxv orrn olnh d ELJ wkdw jhqhudwhv dq hyhq odujhu vxusoxv1 Dv d uhvxow/ vhyhudo
ELJv fdq eh olqnhg wrjhwkhu wr surylgh lqfhqwlyhv wr vxssruw d ILJ1 Li ELJv 4 wr q
duh olqnhg wrjhwkhu wkhq wkh lqfhqwlyh frqvwudlqw lq +8, ehfrphv
?[�'�
+Y ��+4,� Y ��+3,, � yW+z|> 3,� yW+z| � +?[�'�
E� . I ,> 3,>
zklfk jlyhv pruh lqfhqwlyh ohyhudjh wr vxssruw iruzdug lqwhujhqhudwlrqdo h{fkdqjh1
Lw lv dovr hdv| wr vhh wkdw d qrq0vxvwdlqdeoh ELJ fdq eh vxssruwhg e| olqnlqj lw zlwk
d vxvwdlqdeoh rqh1 Lq vrph vhqvh/ surgxflqj d qrq0vxvwdlqdeoh ELJ lv dqdorjrxv wr
surgxflqj d ILJ1
Wkh srvvlelolw| ri d edg rxwfrph lq ELJv lv hvvhqwldo wr surylgh lqfhqwlyhv iru
lqyhvwphqw lq ixwxuh jhqhudwlrqv1 Krzhyhu/ dq lqfuhdvh lq wkh vl}h ri wkh vxusoxv
jhqhudwhg e| wkh ELJ fdq eh d pl{hg eohvvlqj1 Frqvlghu wkh fdvh lq zklfk Y �+3, ??
3> l1h1/ d jhqhudwlrq wkdw grhvq*w jhw lwv ELJ jhwv d yhu| orz sd|r�1 Khuh wkh ELJ
jhqhudwhv d yhu| odujh vxusoxv1 Krzhyhu/ wr dyrlg wkh edg htxloleulxp lq zklfk wkh
ELJ lq qrw surgxfhg/ djhqwv pljkw eh whpswhg wr orrn iru dq h{rjhqrxv frpplwphqw
ghylfh1 Wklv zrxog eh ydoxdeoh ehfdxvh lw holplqdwhv wkh srvvlelolw| ri d yhu| edg
rxwfrph1 Exw lw dovr holplqdwhv wkh jrrg htxloleuld lq zklfk ILJv duh surgxfhg1
Ixuwkhupruh/ vlqfh Y �+4, � Y �+3, lv yhu| odujh/ wkh ELJ surylghv d odujh dprxqw
ri lqfhqwlyh ohyhudjh wkdw frxog eh xvhg wr vxssruw wkh surgxfwlrq ri d odujh fodvv
ri ILJv1
Lq vrph dssolfdwlrqv zh pljkw zdqw wr xqghuvwdqg wkh frqglwlrqv xqghu zklfk
lqwhujhqhudwlrqdo frrshudwlrq ehjlqv1 Xqiruwxqdwho|/ jlyhq wkh pxowlsolflw| ri htxl0
48
oleuld/ d suhflvh dqvzhu iru ELJv fdqqrw eh jlyhq1 Li ELJv jhqhudwh d vxusoxv lq
hyhu| shulrg/ iru hyhu| qdwxudo qxpehu n wkhuh lv dq htxloleulxp lq zklfk wkh �uvw
n�4 jhqhudwlrqv gr qrw surgxfh lqwhujhqhudwlrqdo jrrgv/ dqg hyhu| jhqhudwlrq eruq
diwhuzdugv sod|v rqh ri wkh frrshudwlyh vwudwhjlhv1 Krzhyhu/ jlyhq wkh qhhg iru d
olqn ehwzhhq ELJv dqg ILJv/ vrphwklqj fdq eh vdlg derxw wkh wlplqj dw zklfk fr0
rshudwlrq lq ILJv pxvw ehjlq1 Zh nqrz wkdw d jhqhudwlrq zloo �qdqfh d ILJ rqo| li
lw lv qhfhvvdu| iru jhwwlqj d ELJ lq rog djh1 Wkxv/ frrshudwlrq rq ELJv pxvw dulvh/
dw wkh odwhvw/ rqh shulrg diwhu ILJv duh �uvw surgxfhg1 Wklv rffxuv/ iru h{dpsoh/ lq
wkh iroorzlqj htxloleulxp=
v|+k|, @ +e| @ 3> i| @ 3, iru w ? n /
v&+k&, @ +e� @ 3> i& @ 4, /
dqg/ iru w A n/
v|+k|, @
+e| @ i| @ 4 li i|3� @ e|3� @ === @ i&n� @ e&n� @ 4 dqg i& @ 4e| @ i| @ 3 rwkhuzlvh
=
Wkhuh duh dovr htxloleuld lq zklfk iru d zkloh jhqhudwlrqv frqglwlrq frrshudwlrq rq
ELJv rq wkh klvwru| ri ELJv/ dqg wkh olqn zlwk ILJv lv lqwurgxfhg rqo| odwhu rq1
S , |i?t�L?t
Wkh edvlf prgho ri lqwhujhqhudwlrqdo h{fkdqjh lv yhu| vw|ol}hg1 Jhqhudwlrqv duh frp0
sohwho| vho�vk/ wkh| gr qrw ehqh�w dw doo iurp lqyhvwlqj lq ILJv ru ELJv/ dqg wkhuh
lv rqo| d rqh shulrg odj ehwzhhq wkh surgxfwlrq dqg wkh frqvxpswlrq ri wkh ILJ1
Wkhvh dvvxpswlrqv duh sureohpdwlf lq vrph dssolfdwlrqv1 Iru h{dpsoh/ d qdwxudo
zd| ri prghoolqj idplolhv lv wr dvvxph wkdw sduhqwv kdyh dowuxlvwlf exw sdwhuqdolvwlf
suhihuhqfhv1 Dovr/ ILJv olnh lqyhvwphqw lq sxeolf lqiudvwuxfwxuh ehqh�w pdq| jhq0
hudwlrqv/ lqfoxglqj wkh rqh wkdw pdnhv wkh lqyhvwphqw1 Wkh jrdo ri wklv vhfwlrq lv
wr vkrz wkdw wkhvh frpsolfdwlrqv fdq hdvlo| eh lqfrusrudwhg zlwkrxw fkdqjlqj wkh
lqvljkwv ri wkh edvlf wkhru|1H
HA�i i |i?t�L? Lu |�i |�iLh) |L �?L?�*�?i@h� iUL?L4�it �? ���U� �?|ihit| h@|it @?_ �@}it _iTi?_
L? |�i U@T�|@* t|LU! �t ?L| UL?t�_ihi_ Mi*L�� OL�i�ihc UL?UiT|�@**) �| �t t|h@�}�|uLh�@h_� A�i L?*)_�gihi?Ui �t |�@| �? tL4i U@tit @}i?|t |@!i �?|L @UUL�?| |�i igiU| Lu |�i�h @U|�L?t L? |�i U@T�|@*t|LU!� `�i? |��t �@TTi?t UL?_�|�L?t *�!i ED� ?ii_ |L Mi 4L_��i_ |L �?U*�_i |�iti igiU|tc M�| |�i!i) �?t�}�|t hi4@�? �?U�@?}i_� 6Lh i @4T*ic tii �LL*i) @?_ 5L@hit Ebb� @?_ �L*_h�? @?_ �L?|itEbH� uLh @ ?L?�*�?i@h 4L_i* Lu |�i T@)�@t�)L��}L tLU�@* tiU�h�|) �WB�
49
S�� ��*|��}i?ih@|�L?@* 6WBt
Frqvlghu �uvw d pruh jhqhudo surgxfwlrq vwuxfwxuh iru ILJv1 Dv ehiruh/ hyhu| jhq0
hudwlrq kdv wr ghflgh zkhwkhu ru qrw wr surgxfh d ILJ dw d frvw I A 31 Krzhyhu/
wkh ILJ qrz pd| ehqh�w pruh wkdq rqh jhqhudwlrq/ dqg wkhuh pd| eh d orqj odj
ehwzhhq wkh surgxfwlrq dqg wkh frqvxpswlrq ri wkh ILJ1 Dq h{dpsoh ri vxfk d ILJ
lv lqyhvwphqw lq orqj0whup U)G/ zkhuh wkh ehqh�wv dsshdu rqo| vhyhudo jhqhudwlrqv
diwhu wkh lqyhvwphqw lv pdgh/ dqg hyhu| jhqhudwlrq eruq diwhuzdugv ehqh�wv iurp
wkh lqyhqwlrq1
Jhqhudo surgxfwlrq vwuxfwxuhv fdq eh prghoohg xvlqj wkh iroorzlqj xwlolw| ixqf0
wlrq
X|+=, @ x+f6, . �x+fJ, ."[&'f
�&Y8 +i|3&, . Y �+e|n2,>
zkhuh �& lv d vhtxhqfh ri srvlwlyh zhljkwv vdwlvi|lqjS"
&'f �& ? 41 Iru h{dpsoh/
wkh edvlf prgho lv d vshfldo fdvh ri wklv vshfl�fdwlrq zlwk �f @ 4 dqg �& @ 3 iru dq|
n A 31 D ILJ wkdw ehqh�wv hyhu| jhqhudwlrq eruq 43 shulrgv diwhu wkh lqyhvwphqw
lv pdgh/ exw wkdw dovr h{klelwv ghsuhfldwlrq/ fdq eh uhsuhvhqwhg e| �& @ 3 iru
n @ 3> ===> < dqg �& @ �&3�f +3 ? � ? 4, iru doo n A <1
Lw lv hdv| wr vhh wkdw wkh suhylrxv uhvxowv uhpdlq xqfkdqjhg1 Wkh nh| lv wr qrwlfh
wkdw/ dowkrxjk wkh qhz surgxfwlrq ixqfwlrq orrnv pruh frpsolfdwhg/ wkh lqfhqwlyhv
ri wkh gl�huhqw jhqhudwlrqv kdyh qrw fkdqjhg1 Lq sduwlfxodu/ wkh wuljjhu0vwudwhj| lq
+7, jhqhudwhv surgxfwlrq ri ILJv dqg ELJv li/ dqg rqo| li/ +8, krogv1 Wkh lqwxlwlrq
lv vlpsoh1 Vlqfh jhqhudwlrq w grhv qrw ghulyh dq| ydoxh iurp wkh ILJ/ lw lv lqgl�huhqw
ehwzhhq surgxflqj d ILJ wkdw ehqh�wv jhqhudwlrq w.4/ rqh wkdw ehqh�wv jhqhudwlrq
w.4333> ru rqh wkdw ehqh�wv hyhu| ixwxuh jhqhudwlrq1 Diwhu doo/ wkh rqo| uhdvrq wkdw
wkh jhqhudwlrq surgxfhv wkh ILJ lv wr nhhs frrshudwlrq jrlqj lq wkh ELJv1
Dq lqwhuhvwlqj gl�huhqfh zlwk wkh edvlf prgho kdv wr gr zlwk wkh irup ri wkh
sxqlvkphqwv wkdw vxssruw frrshudwlrq1 Lq wkh edvlf prgho/ jhqhudwlrq w nqrzv wkdw
li lw grhvq*w surgxfh wkh ILJ iru jhqhudwlrq w . 4 lw zloo eh sxqlvkhg e| wkhp1 Lq
wklv fdvh wkh jhqhudwlrq fduu|lqj rxw wkh sxqlvkphqw lv wkh vdph jhqhudwlrq wkdw
lv kxuw zkhq wkh ILJ lv qrw surgxfhg1 E| frqwudvw/ frqvlghu d ILJ wkdw ehqh�wv
hyhu| jhqhudwlrq eruq 43 shulrgv diwhu lw lv surgxfhg1 Zk| vkrxog jhqhudwlrq w. 4
sxqlvk khuhB Diwhu doo/ lw grhv qrw fduh derxw wkh shulrg w ILJ1 Li wkh vrfldo qrup
lv d wuljjhu0vwudwhj|/ jhqhudwlrq w . 4 sxqlvkhv e| qrw surgxflqj wkh ELJ ehfdxvh
lw nqrzv wkdw lqwhujhqhudwlrqdo h{fkdqjh froodsvhv diwhu d vlqjoh ghyldwlrq1 Li wkh
4:
vrfldo qrup lv qrw d wuljjhu vwudwhj|/ jhqhudwlrq w.4 sxqlvkhv ehfdxvh lw nqrzv wkdw
lw zloo qrw eh uhzdughg iru khoslqj d ghyldwru1
S�2 �L?�_)?@t|�U �*|h��t4 @?_ �W4T�hi� 6WBt
Wkh edvlf wkhru| lv dovr urexvw wr wkh lqwurgxfwlrq ri qrq0g|qdvwlf dowuxlvp1 Wkh
nh| gl�huhqfh lv wkdw qrz jhqhudwlrqv uhfhlyh ehqh�wv iurp surgxflqj d ILJ1 D
vlpsoh frpsolfdwlrq ri wkh edvlf prgho doorzv xv wr lqfrusrudwh wklv h�hfw1
Vxssrvh wkdw wkh ELJ ghflvlrq lv glvfuhwh/ e| 5 i3> 4j/ exw wkh ILJ ghflvlrq lv
frqwlqxrxv= i| 5 ^3>4,1 i| fdq eh lqwhusuhwhg dv wkh dprxqw ri wkh sulydwh jrrg
lqyhvwhg lq ILJv1 Dovr/ vxssrvh wkdw suhihuhqfhv duh jlyhq e|
X|+=, @ x+f6, . �x+fJ, . +4� �,Y 8 +i|, . �Y 8 +i|n�, . Y �+e|n2,>
zkhuh � 5 +3> 4, lv d sdudphwhu wkdw uh�hfwv wkh ghjuhh wr zklfk wkh jhqhudwlrq
surgxflqj wkh ILJ ehqh�wv iurp lw1 Li � @ 3 wkh prgho uhgxfhv wkh edvlf fdvh1 Li
� @ 4 ILJv gr qrw jhqhudwh lqwhujhqhudwlrqdo vslooryhuv1b
Ohw iW| ghqrwh wkh h�flhqw ohyho ri ILJv +dw dq lqwhulru doorfdwlrq, dqg ei| wkh ohyhori ILJv wkdw d jhqhudwlrq fkrrvhv li lw rqo| wdnhv lqwr dffrxqw lwv suhihuhqfhv> l1h1/
wkh ohyho wkdw lw fkrrvhv lq wkh devhqfh ri jdph wkhruhwlf frqvlghudwlrqv1 Fohduo|/
iW| A ei|= Lq frqwudvw wr wkh vho�vk fdvh/ zlwk qrq0g|qdvwlf dowuxlvp hyhu| jhqhudwlrq
zdqwv wr surgxfh vrph ri wkh ILJ1 Wkxv/ wkh frq�lfw lv qrw ryhu surgxflqj d srvlwlyh
ohyho ri ILJv/ exw ryhu surgxflqj pruh wkdq wkh vkruw0vljkwhg dprxqw1 Lq vrph
vhqvh/ djhqwv surgxfh wzr jrrgv= +l, d qrq0lqwhujhqhudwlrqdo jrrg wkdw frvwv ei|/ dqg+ll, d sxuh ILJ jlyhq e| h{shqglwxuhv deryh ei|1
Wklv yduldwlrq ri wkh prgho dovr fryhuv wkh fdvh ri lpsxuh ILJv1 Dq lpsxuh ILJ
lv d jrrg wkdw ehqh�wv wkh jhqhudwlrq surgxflqj lw dqg ixwxuh jhqhudwlrqv1 Lq rwkhu
zrugv/ dq lpsxuh ILJ kdv vkruw0uxq dqg orqj0uxq ehqh�wv1 D jrrg h{dpsoh ri dq
lpsxuh ILJ lv vdylqj wkh udlq iruhvwv/ zklfk ehqh�wv fxuuhqw dqg ixwxuh jhqhudwlrqv1
SURSRVLWLRQ 7= Lq wkh fdvh ri lpsxuh ILJv ru qrq0g|qdvwlf dowuxlvp/ wkh
rswlpdo dprxqw ri ILJv lv surylghg lq hyhu| shulrg li dqg rqo| li= +4, iru
hyhu| jhqhudwlrq/ wkh vxusoxv jhqhudwhg e| wkh ELJ lv odujhu wkdq wkh +xwlolw|,
frvw ri surylglqj wkh rswlpdo dprxqw ri ILJ> dqg +5, wkh htxloleulxp vwudwhjlhv
bA�i M@t�U |�iLh) U@? @*tL i@t�*) Mi i |i?_i_ |L |�i U@ti Lu |�L�t�_i_ ?L?�_)?@t|�U @*|h��t4�
A��t �@h�@|�L? Lu |�i 4L_i* �t �ti_ Mi*L� �? |�i @TT*�U@|�L? |L �?�it|4i?| �? U��*_hi? ��|��? |�i
u@4�*)�
4;
olqn ELJv dqg ILJv e| pdnlqj frrshudwlrq rq ILJv d qhfhvvdu| frqglwlrq iru
frrshudwlrq rq ELJv1
Vlqfh wkh surri ri wklv uhvxow lv doprvw lghqwlfdo wr wkh surri ri Sursrvlwlrq 5/ rqo|
d vnhwfk lv surylghg1 Iluvw/ wr fkhfn wkh frqglwlrqv xqghu zklfk rswlpdo lqyhvwphqw
fdq wdnh sodfh zh fdq xvh wkh wuljjhu0vwudwhjlhv
v|+k|, @
+e| @ 4> i| @ iW| li i|3& @ iW| dqg e|3& @ 4 iru doo n
e| @ 3> i| @ ei| rwkhuzlvh>
zklfk olqn ELJv dqg ILJv e| frqglwlrqlqj surylvlrq ri wkh ELJ rq wkh rswlpdo sur0
ylvlrq ri wkh ILJ1 Vhfrqg/ rqh fdq vkrz wkdw wkh qhfhvvdu| dqg vx�flhqw frqglwlrqv
iru wkhvh vwudwhjlhv wr eh dq htxloleulxp duh jlyhq e|
+Y �+4,� Y �+3,, . �+Y �+iW| ,� Y �+ ei|,, � yW+z| � ei|> 3,� yW+z| � +E . iW| ,> 3,=
Wklv frqglwlrq/ dqdorjrxv wr +8,/ vwdwhv wkdw wkh vxusoxv jhqhudwhg e| wkh ELJ
pxvw eh odujhu wkdq wkh frvw ri lqyhvwlqj lq ILJv eh|rqg wkh vkruw0vljkwhg dprxqw1
Ilqdoo|/ lw lv hdv| wr vhh wkdw lq dq| qr0olqn vwudwhj| hyhu| jhqhudwlrq fkrrvhv ei|1Wkxv/ zh fdq frqfoxgh wkdw wkh lqwurgxfwlrq ri qrq0g|qdvwlf dowuxlvp ru %lp0
sxuh% ILJv grhv qrw fkdqjh wkh pdlq uhvxowv ri wkh wkhru|1 Wr lqgxfh d jhqhudwlrq
wr lqyhvw deryh wkh vkruw0vljkwhg dprxqw lw lv vwloo qhfhvvdu| wr olqn ELJv dqg ILJv1
Wkh lqwxlwlrq lv vlpsoh1 Iurp wkh srlqw ri ylhz ri wkh jhqhudwlrq pdnlqj wkh lqyhvw0
phqw/ dq| h{shqglwxuh lq ILJv eh|rqg zkdw lw lqwhuqdol}hv orrnv olnh d ILJ ehfdxvh
wkh frvwv ri dgglwlrqdo surylvlrq rxwzhljk wkh ehqh�wv1
S�� W?|ih}i?ih@|�L?@* Ah@?tuiht @?_ ,?_L�4i?| ,giU|t
Wkh suhylrxv uhvxowv vkrz wkdw ILJv duh surylghg/ ru surylghg rswlpdoo| lq wkh fdvh
ri qrq0g|qdvwlf dowuxlvp/ rqo| li wkh| duh olqnhg zlwk d ELJ1 D qdwxudo txhvwlrq
iroorzv= Fdq wkh surgxfwlrq ri ILJv eh vxssruwhg xvlqj wudqvihuv ri wkh frqvxpswlrq
jrrgB Diwhu doo/ jhqhudwlrq w . 4 frxog frpshqvdwh jhqhudwlrq w iru surgxflqj lwv
ILJ e| jlylqj dzd| sduw ri lwv hqgrzphqw1 Wkh dqvzhu lv |hv dqg iroorzv iurp wkh
idfw wkdw lqwhujhqhudwlrqdo wudqvihuv duh d ELJ1 Krzhyhu/ dv zh zloo vhh ehorz/ wklv
ELJ lv qrw dozd|v vhoi0vxvwdlqdeoh1
Wklv txhvwlrq lv sduwlfxoduo| uhohydqw zkhq ILJv jhqhudwh hqgrzphqw h�hfwv> l1h1/
zkhq d jhqhudwlrq*v hqgrzphqw ghshqgv rq zkhwkhu suhylrxv jhqhudwlrqv lqyhvwhg
lq ILJv1 Qdwxudo h{dpsohv duh lqyhvwphqwv lq lqiudvwuxfwxuh/ U)G dqg kxpdq
fdslwdo h{shqglwxuhv1
4<
D vlpsoh zd| ri lqfrusrudwlqj hqgrzphqw h�hfwv lv wr uhwxuq wr wkh edvlf prgho/
exw pdnh wkh hqgrzphqwv d ixqfwlrq ri wkh klvwru| ri ILJv1 Lq sduwlfxodu/ vxssrvh
wkdw
z|+k|, @
++4 . �,z|3�+k|, li i|3� @ 4
z|3�+k|, rwkhuzlvh> +9,
zkhuh � A 3 lv wkh hqgrzphqw h�hfw1�f Khuh/ wkh zdjh ri jhqhudwlrq w lv htxdo wr
wkh hqgrzphqw ri wkh suhylrxv jhqhudwlrq li wkhuh lv qr lqyhvwphqw lq wkh ILJ/ exw
jurzv e| +4 . �, dv d uhvxow ri wkh lqyhvwphqw1 Zh fdq wklqn ri � dv wkh jurvv udwh
ri uhwxuq ri lqyhvwlqj lq wkh ILJ1
Wr nhhs wklqjv vlpsoh vxssrvh wkdw lqyhvwlqj lq wkh ILJ frvwv d iudfwlrq ! 5
+3> 4, ri wkh hqgrzphqw ri wkh jhqhudwlrq pdnlqj wkh lqyhvwphqw/ zkhuh ! fdq
eh lqwhusuhwhg dv wkh iudfwlrq ri oderu lqfrph wkdw lv ghyrwhg wr lqfuhdvlqj wkh
surgxfwlyh fdsdflw| ri wkh hfrqrp|1 Dvvxph dovr wkdw ILJv kdyh qr xwlolw| h�hfwv1
+Dq h{dpsoh ri wklv w|sh ri ILJ lv d qduurz lqwhusuhwdwlrq ri lqyhvwphqwv lq kxpdq
fdslwdo1,
Wr h{soruh wkh uroh ri lqwhujhqhudwlrqdo wudqvihuv frqvlghu dq h{fkdqjh jdph
lq zklfk hyhu| jhqhudwlrq slfnv dq dfwlrq +W|> i|, 5 ?n � i3> 4j1 Lq wklv fdvh wkh
wudqvihuv/ zklfk dprxqw wr d ELJ/ duh frqwlqxrxv dqg wkh ILJ lv glvfuhwh1
SURSRVLWLRQ 8= Frqvlghu dq htxloleulxp lq zklfk +4, suhvhqw jhqhudwlrqv
lqyhvw lq lqfuhdvlqj wkh hqgrzphqw ri wkh qh{w jhqhudwlrq dqg +5, wkh qh{w
jhqhudwlrq frpshqvdwhv wkhp zlwk d iudfwlrq � ri wkhlu hqgrzphqw1 Wklv htxl0
oleulxp lv ihdvleoh rqo| li wkh udwh ri uhwxuq ri lqyhvwlqj lq ILJv h{fhhgv wkh
udwh ri uhwxuq ri wkh vwrudjh whfkqrorj|= � � u. +4 . u,�>1
Rqfh pruh/ vlqfh wkh surri ri wklv uhvxow lv d vpdoo yduldwlrq ri suhylrxv dujx0
phqwv/ rqo| wkh nh| vwhsv duh suhvhqwhg1 Iluvw qrwh wkdw d vhtxhqfh ri wudqvihuv iW|j
lv d ELJ= jlyh d wudqvihu wr wkh suhylrxv jhqhudwlrq zkhq |rxqj dqg lq h{fkdqjh
uhfhlyh d wudqvihu zkhq rog1 Dovr/ vlqfh djhqwv fdq eruurz dqg vdyh dw wkh udwh
4 . u/ wkh| fduh derxw wkh udwh ri uhwxuq lpsolflw lq wkh wudqvihuv/ exw qrw derxw
wkhlu wlplqj1 Dv d uhvxow/ wklv ELJ lv vhoi0vxvwdlqdeoh rqo| li W|n� � +4 . u,W| iru doo
w1 Lqwxlwlyho|/ wkh %wudqvihu jdph%�� dprxqwv wr d yroxqwdu| vdylqjv surjudp wkdw
lv dwwudfwlyh rqo| li lw sd|v d ehwwhu udwh ri uhwxuq wkdq wkh vwrudjh whfkqrorj|1
�f+iU@** |�@| �| �t |�i i?_L�4i?| Lh �@}i |�@| }i?ih@|�L? |3 � }i|t �? 4�__*i @}ic ���U� |@!itT*@Ui �? Tih�L_ |� A�ihiuLhic �| U@? Mi @ u�?U|�L? Lu �| ' Es|3�c K|3�c �����
��A��t |h@?tuih }@4i �@t �ht| t�}}it|i_ M) 5@4�i*tL? E�bDH� @?_ �@t @*tL Mii? t|�_�i_ M)O@44L?_ E�b.D��
53
Qh{w/ dv ehiruh/ wkh ILJ lv surgxfhg rqo| li +4, wkh jhqhudwlrqv sod| klvwru|
ghshqghqw vwudwhjlhv wkdw olqn ELJv dqg ILJv/ dqg +5, wkh vxusoxv jhqhudwhg e|
wkh ELJ lv odujhu wkdq wkh frvw ri surylglqj wkh ILJ1 Wkh ELJ*v vxusoxv lv jlyhq
e| W|n� � +4 . u,W|1 Lw lv hdv| wr fkhfn wkdw wkh wuljjhu0vwudwhj| olqnlqj ILJv dqg
wudqvihuv lv dq htxloleulxp rqo| li/ iru hyhu| w dqg k|/
W|n� � +4 . u,+W| . !z|+k|,,/ +:,
zkhuh !z|+k|, lv wkh frvw ri surylglqj wkh ILJ1 Fohduo|/ d vhtxhqfh ri wudqvihuv
vdwlv�hv +:, rqo| li lw jurzv idvwhu wkdq wkh lqwhuhvw udwh/ zklfk lv srvvleoh rqo| li
� A u1 Qrz frqvlghu wudqvihuv ri wkh irup W|+k|, @ �z|+k|,1 Wkhvh wudqvihuv vdwlvi|
wkh htxloleulxp frqglwlrq rqo| li
�+4 . �,z|+k|, � z|+k|,+�. !,+4 . u, iru doo w>
zklfk lv vdwlv�hg rqo| li
� � u . +4 . u,!
�=
Frqvlghu wkh lpsolfdwlrqv ri wklv frqglwlrq1 Lq wklv prgho vrflhw| kdv wzr lqyhvw0
phqw whfkqrorjlhv= wkh vwrudjh whfkqrorj| dqg wkh ILJv1 Erwk ri wkhp wudqvirup
xqlwv ri wkh frqvxpswlrq jrrg lq rqh shulrg lqwr xqlwv ri wkh frqvxpswlrq jrrg lq
wkh iroorzlqj shulrg1 Li � A u/ lw lv vrfldoo| rswlpdo wr lqyhvw rqo| rq ILJv1 Lghdoo|/
suhvhqw jhqhudwlrqv zrxog lqyhvw lq ILJv dqg ixwxuh jhqhudwlrqv zrxog xvh wkh lq0
fuhdvh lq wkhlu hqgrzphqw wr frpshqvdwh wkhp1 Krzhyhu/ Sursrvlwlrq 9 vkrzv wkdw
wkh lqfhqwlyh frqglwlrqv duh pruh vwulqjhqw wkdq wkh frqglwlrqv iru vrfldo rswlpdolw|1
Lq sduwlfxodu/ wklv duudqjhphqw lv g|qdplfdoo| frqvlvwhqw rqo| li wkh ILJ*v udwh ri
uhwxuq h{fhhgv wkh rqh ri wkh vwrudjh whfkqrorj| e| dw ohdvw +4 . u,�>1
. �TT*�U@|�L? �G �L*�|�U@* ,UL?L4) Lu W?|ih}i?ih@|�L?@*
, Ti?_�|�hit
Wkh edvlf prgho ri lqwhujhqhudwlrqdo h{fkdqjh fdq eh dssolhg wr d zlgh fodvv ri
sureohpv1 Lq wkh uhvw ri wkh sdshu zh h{soruh vrph ri wkhvh dssolfdwlrqv1 Wkh �uvw
dssolfdwlrq lv wr vwxg| wkh srolwlfdo hfrqrp| ri lqwhujhqhudwlrqdo sxeolf h{shqgl0
wxuhv1 Lq prvw qdwlrqv/ d vljql�fdqw dprxqw ri lqwhujhqhudwlrqdo h{fkdqjh wdnhv
sodfh wkurxjk wkh jryhuqphqw1 Surplqhqw h{dpsohv duh sd|0dv0|rx0jr surjudpv
wkdw ehqh�w wkh hoghuo|/ olnh Vrfldo Vhfxulw| dqg Phglfduh +ELJv,/ dqg h{shqglwxuhv
54
lq sxeolf hgxfdwlrq/ U)G/ dqg lqiudvwuxfwxuh +ILJv,1 Lq wkh X1V1 vrph ri wkhvh
surjudpv wdnh sodfh dw wkh ihghudo ohyho/ rwkhuv/ olnh hgxfdwlrq/ duh fduulhg rxw dw
wkh vwdwh ohyho1 Lq wklv vhfwlrq zh suhvhqw d g|qdplf prgho ri wkh srolwlfdo hfrqrp|
ri lqwhujhqhudwlrqdo h{shqglwxuhv dw wkh ihghudo ru fhqwudo ohyho/ dqg vkrz wkdw wkh
xqghuo|lqj srolwlfdo irufhv duh hdvlo| xqghuvwrrg lq whupv ri wkh wkhru| ri ELJv dqg
ILJv1�2
.�� �L_i*
Frqvlghu dq hfrqrp| zlwk d vrphzkdw uhdolvwlf ghprjudsklf vwuxfwxuh lq zklfk
hyhu| shulrg d qhz jhqhudwlrq ri djhqwv lv eruq dqg olyhv iru ;3 shulrgv1 Djhqwv duh
fkloguhq iru wkh �uvw 53 shulrgv/ zrunhuv iru wkh qh{w 78 shulrgv/ dqg uhwluh dw djh
981 Hyhu| jhqhudwlrq kdv d frqwlqxxp ri djhqwv zlwk pdvv 41 Zrunhuv lq shulrg
w uhfhlyh d zdjh z|+d,/ zklfk pljkw ghshqg rq wkh djh ri wkh zrunhu1 Wklv frxog
uh�hfw/ iru h{dpsoh/ gl�huhqfhv lq hgxfdwlrq ohyhov dfurvv frkruwv1 Iru vlpsolflw|/
vxssrvh wkdw zdjhv gr qrw ghshqg rq wkh vl}h ri wkh fdslwdo vwrfn/ dqg wkdw wkh|
jurz dw d frqvwdqw jurzwk udwh 1 Wkh lqwhuhvw udwh lv �{hg dqg htxdo wr 4 . u dqg/
dv ehiruh/ djhqwv fdq eruurz dqg ohqg dw wklv udwh1�� Ixuwkhupruh/ dvvxph wkdw wkh
lqwhuhvw udwh h{fhhgv wkh udwh ri jurzwk ri zdjhv/ vr wkdw wkh hfrqrp| lv g|qdplfdoo|
h�flhqw1
Wkhuh duh wzr jryhuqphqw surjudpv= +4, sd|0dv0|rx0jr vrfldo vhfxulw|/ dqg +5, d
jhqhulf ILJ wkdw fdq eh lqwhusuhwhg dv hqylurqphqwdo surwhfwlrq/ orqj0whup U)G/ ru
dq| rwkhu sxeolf h{shqglwxuh wkdw glvsursruwlrqdwho| ehqh�wv wkh |rxqj1 Ghflvlrqv
rq wkhvh surjudpv duh pdgh e| pdmrulw| uxoh1 Djhqwv fdq yrwh rqo| diwhu wkh|
ehfrph zrunhuv dw djh 541
Wkh sd|0dv0|rx0jr vrfldo vhfxulw| v|vwhp lv fkdudfwhul}hg e| d vhtxhqfh ri +oxps0
vxp, sd|uroo wd{hv W|/ zklfk duh dozd|v htxdo wr d iudfwlrq � ri zdjhv1 Wkh v|vwhp lv
edodqfhg shulrg e| shulrg dqg wkxv hdfk uhwluhh uhfhlyhv ehqh�wv E| @ 6W|1�e D sd|0
�26Lh @? @?@*)t�t Lu |�i TL*�|�U@* iUL?L4) Lu �?�it|4i?| �? u�|�hi }i?ih@|�L?t @| |�i *LU@* *i�i*tii �L?*i) @?_ +@?}i* E�bbb�c kL|*�!Lg @?_ +Lti?|�@* E�bb��c @?_ 5L@hit E�bbb��
��A�iti T@h|�@* i^��*�Mh��4 @tt�4T|�L?t t�4T*�u) |�i @?@*)t�t Lu |�i 4L_i*c M�| ?L?i Lu |�i�?t�}�|t _�tU�tti_ Mi*L� _iTi?_ L? |�i4� �*tLc |L @�L�_ _i@*�?} ��|� MLhhL��?} UL?t|h@�?|tc �i@tt�4i |�@| @}i?|t U@? MLhhL� �? �?|ih?@|�L?@* �?@?U�@* 4@h!i|t @| |�i h@|i � n o�
�e i @tt�4i |�@| |�i @}i?|t< hi|�hi4i?| @}i �t i L}i?L�t*) }��i? @?_ |�@| tLU�@* tiU�h�|) Mi?i�|tt|@h| @| |�@| _@|i� A��tc �? |��t t�4T*i 4L_i* tLU�@* tiU�h�|) _Lit ?L| _�t|Lh| hi|�hi4i?| _iU�t�L?t��? �?|ihit|�?} ^�it|�L?c �L�i�ihc �t ��) tL 4@?) hi|�hi4i?| ThL}h@4t @hL�?_ |�i �Lh*_ �?|hL_�Uit�U� _�t|Lh|�L?t� A�L T@Tiht @__hitt�?} |��t �tt�i @hi #�@4L?_ @?_ ��hh*iit E�b.H� @?_ ��**�}@?@?_ 5@*@����@h|�? E�bbb��
55
dv0|rx jr vrfldo vhfxulw| v|vwhp dprxqwv wr d vhtxhqfh ri edfnzdug lqwhujhqhudwlrqdo
wudqvihuv dqg wkxv lv dqdorjrxv wr wkh wudqvihu ELJ glvfxvvhg lq Vhfwlrq 81
Wkh jhqhulf ILJ fdq rqo| eh surgxfhg dw wzr ohyhov/ i| 5 i3> 4j1 Wkh frvw ri
surgxflqj wkh ILJ lv eruq htxdoo| e| doo wd{sd|huv/ dq dvvxpswlrq wkdw lv mxvwl�hg
li ILJv duh �qdqfhg rxw ri jhqhudo uhyhqxhv1 Wkh +oxps0vxp, frvw iru hdfk wd{sd|hu
ri surgxflqj wkh w0ILJ lv I|1 Wr nhhs wklqjv vlpsoh zh dovr dvvxph wkdw +4, rqo|
fkloguhq dqg xqeruq jhqhudwlrqv ehqh�w iurp surgxflqj d ILJ dqg +5, I| lv d frq0
vwdqw iudfwlrq ri djjuhjdwh zdjhv1 Xqghu wkhvh dvvxpswlrqv/ wd{sd|huv ehqh�w iurp
wkh surgxfwlrq ri sdvw ILJv/ exw qrw iurp wkh surgxfwlrq ri fxuuhqw ru ixwxuh ILJv1
Wkhvh wzr uhvwulfwlrqv duh pdgh iru dqdo|wlfdo frqyhqlhqfh/ exw duh qrw qhfhvvdu|
iru wkh uhvxowv ru wkhlu lqwhusuhwdwlrq1
Dv ehiruh/ ohw k| @ i+W|3�> i|3�,> +W|32> i|32,> ===j ghqrwh wkh klvwru| ri jryhuq0
phqw srolf|1 Wkh suhihuhqfhv ri jhqhudwlrq w duh jlyhq e|
Y|+f+4,> ===> f+;3,> k|n2�, @Hf[
@'2�
�@32�x+f+d,> k|n2�,= +;,
Xqghu wkhvh suhihuhqfhv djhqwv gr qrw frqvxph ehiruh wkh| ehfrph zrunhuv/ fduh
derxw ILJv surgxfhg ehiruh wkhlu eluwk ru gxulqj wkhlu fklogkrrg/ dqg duh qrw
d�hfwhg e| ILJv surgxfhg diwhu wkh| uhdfk dgxowkrrg1 +Wklv iroorzv iurp wkh idfw
wkdw Y|+=, rqo| ghshqgv rq k|n2�,1
Hyhu| shulrg yrwhuv fkrrvh vrfldo vhfxulw| srolf| dqg zkhwkhu ru qrw wr �qdqfh
wkh ILJ1 Krzhyhu/ wkh dqdo|vlv lv vlpsol�hg li zh dvvxph wkdw wkh vl}h ri wkh ehqh�wv
dqg wudqvihuv duh h{rjhqrxvo| jlyhq dqg wkdw yrwhuv rqo| ghflgh zkhwkhu ru qrw wr
h{hfxwh wkhp1 Ohw iW |j ghqrwh wkh h{rjhqrxvo| jlyhq v|vwhp1 Lq wklv fdvh wkh srolf|
vsdfh lq shulrg w lv jlyhq e| wkh idploldu
S| @ ie| @ 4> e| @ 3j � ii| @ 4> i| @ 3j=
Wklv dvvxpswlrq lv qrw dv uhvwulfwlyh dv lw vhhpv1 Li d v|vwhp iW |j fdq eh vxssruwhg
dv dq htxloleulxp ri wkh xquhvwulfwhg jdph/ wkhq lw dovr dulvhv dv dq htxloleulxp zlwk
wkh uhvwulfwhg srolf| vsdfh1 Wkxv/ wkh uhvwulfwhg dqdo|vlv ixoo| fkdudfwhul}hv wkh vhw
ri wudqvihuv wkdw fdq eh vxssruwhg lq wkh jhqhudo fdvh1
Ohw v|+d> k|, 5 S| ghqrwh wkh +klvwru| ghshqghqw, yrwlqj vwudwhj| iru dq djhqw ri
djh d lq shulrg w/ dqg ohw v ghqrwh d frpsohwh ghvfulswlrq ri wkh ehkdylru ri hyhu|
djhqw lq hyhu| shulrg1 Jlyhq v zh fdq frqvwuxfw wkh ixqfwlrqv
Z�+v> k|, dqg Z8 +v> k|, +<,
56
zklfk ghqrwh wkh rxwfrph ri wkh hohfwlrq/ iru ELJv dqg ILJV/ li wkh hfrqrp| uhdfkhv
shulrg w xqghu wkh klvwru| k|= Dqrwkhu xvhixo remhfw lv
kS+v> +e|> i|,> k|,>
zklfk ghqrwhv wkh frqwlqxdwlrq rxwfrphv ri fkrrvlqj +e|> i|, diwhu klvwru| k|> l1h1/ lw
ghvfulehv wkh rxwfrph ri wkh hohfwlrq lq shulrgv w.4/ w.5/ 111 1 kS lv frpsxwhg e|
lwhudwlqj +<,1
Wr fkdudfwhul}h wkh htxloleuld ri wkh yrwlqj jdph zh qhhg wr ghulyh djhqwv* suhi0
huhqfhv ryhu suhvhqw dqg ixwxuh sxeolf srolf|1 Frqvlghu d yrwhu ri djh d lq shulrg
w1 Vlqfh wkh yrwhu grhv qrw ehqh�w iurp wkh surgxfwlrq ri qhz ILJv/ dqg lv deoh wr
eruurz dqg ohqg dw wkh udwh 4. u/ kh rqo| fduhv derxw wkh h�hfw ri sxeolf srolf| rq
klv exgjhw frqvwudlqw1 Wkxv/ klv suhihuhqfhv ryhu sxeolf srolf| duh jlyhq e|
X|+d> i+e&> i&,j&D|, @ SY �
| +d> i+e&> i&,j&D|, . SY 8
| +d> i+e&> i&,j&D|,>
zkhuh SY �| ghqrwhv wkh suhvhqw ydoxh ri doo suhvhqw dqg ixwxuh vrfldo vhfxulw| frq0
wulexwlrqv dqg SY 8| ghqrwhv wkh suhvhqw ydoxh ri wkh wd{hv wkdw wkh djhqw zloo kdyh
wr sd| lq wklv dqg vxevhtxhqw shulrgv li wkh vhtxhqfh ii&j&D| ri ILJv lv surgxfhg1
+Ehqh�wv duh srvlwlyh dqg wd{hv duh qhjdwlyh qxpehuv,1 Lq rwkhu zrugv/ SY �| dqg
SY 8| ghqrwh wkh h�hfw wkdw ELJv dqg ILJv srolf| kdyh rq wkh djhqw*v exgjhw frq0
vwudlqw1
Srolwlfdo Htxloleulxp= D yhfwru vW ri yrwlqj vwudwhjlhv lv d srolwlfdo htxloleulxp
li/ iru doo d> w> dqg k|/ lw vdwlv�hv
vW| +d> k|, 5 dujpd{K|cs|
X|+d> +e|> i|,> kS+vW> +e|> i|,> k|,,=
Wzr dvvxpswlrqv duh exlow lqwr wklv qrwlrq ri htxloleulxp1 Wkh �uvw rqh lv vlqfhuh
yrwlqj= djhqwv yrwh iru wkhlu idyrulwh srolf| hyhq wkrxjk wkh| duh qhyhu slyrwdo
yrwhuv1 Wklv dvvxpswlrq lv vwdqgdug lq wkh srolwlfdo hfrqrp| olwhudwxuh dqg lv d zd|
ri dyrlglqj wkh sdudgr{ ri yrwlqj= zk| gr yrwhuv yrwh dw dooB Lw dovr holplqdwhv d orw
ri %edg% htxloleuld1 Lq idfw/ zlwkrxw vlqfhuh yrwlqj dq| srolf| frxog eh vxssruwhg
dv dq htxloleulxp1 Wkh vhfrqg dvvxpswlrq lv wkdw yrwhuv duh qrw vkruw0vljkwhg/ wkh|
wdnh lqwr dffrxqw wkh h�hfw wkdw fxuuhqw hohfwrudo rxwfrphv kdyh rq ixwxuh hohfwlrqv1
57
.�2 �L*�|�U@* ,UL?L4) Lu �@)�@t�)L��}L 5LU�@* 5iU�h�|)
Dv ehiruh/ lw lv xvhixo wr dqdo|}h �uvw wkh srolwlfdo htxloleuld ri d vlpsohu fdvh lq
zklfk wkhuh lv rqo| vrfldo vhfxulw|1 Xvlqj wkh lqvljkwv iurp wkh edvlf prgho wkh
dqdo|vlv lv udwkhu vlpsoh1
Wkh nh| lv wr qrwlfh wkdw wkh frqwlqxdwlrq ydoxh ri vrfldo vhfxulw| lpsuryhv zlwk
djh1 Wkh suhvhqw ydoxh ri wkh v|vwhp lv srvlwlyh iru uhwluhhv/ vlqfh wkh| rqo| uhfhlyh
ehqh�wv/ dqg iru wkrvh wkdw duh forvh hqrxjk iru uhwluhphqw1 Lq idfw/ li wkh vrfldo
vhfxulw| v|vwhp lv edodqfhg/ sd|uroo wd{ udwhv dqg zdjh jurzwk udwhv duh frqvwdqw/
dqg wkh hfrqrp| lv g|qdplfdoo| h�flhqw zh kdyh wkdw
SY �| +98, A SY �
| +97, A === A SY �| +54,= +43,
Ohw d4�?| eh wkh |rxqjhvw djh/ lq shulrg w/ dw zklfk wkh frqwlqxdwlrq ydoxh ri vrfldo
vhfxulw| lv qrq0qhjdwlyh +l1h1/ SY �| +d4�?| , � 3 dqg SY �
| +d4�?| � 4, ? 3,1 Dovr/ ohw
d6e_| ghqrwh wkh phgldq djh ri wkh yrwlqj srsxodwlrq1
SURSRVLWLRQ 9= Vrfldo vhfxulw| fdq dulvh dv d srolwlfdo htxloleulxp lq hyhu|
shulrg dv orqj dv wkh phgldq yrwhu lv dozd|v d zrunhu zlwk d srvlwlyh frqwlqx0
dwlrq ydoxh iru vrfldo vhfxulw| +d6e_| � d4�?| iru doo w,1
Wkh surri ri wklv uhvxow lv dqdorjrxv wr wkh surri wkdw ELJv duh vhoi0vxvwdlqdeoh
li wkh| jhqhudwh d srvlwlyh vxusoxv1 Lq sduwlfxodu/ lw lv vx�flhqw wr vkrz wkdw wkh
iroorzlqj yrwlqj vwudwhjlhv duh d srolwlfdo htxloleulxp zkhq d6e_| � d4�?| =
v|+d> k|, @
;A?A=e| @ 4 li d A 98e| @ 4 li d4�?| � d � 98 dqg e|3& @ 4 iru doo ne| @ 3 rwkhuzlvh
= +44,
Wkh lqfhqwlyhv ri uhwluhhv duh vwudljkwiruzdug= vlqfh wkh| duh qhw ehqh�fldulhv/
wkh| dozd|v yrwh iru vrfldo vhfxulw|1 Wkh lqfhqwlyhv ri djhqwv |rxqjhu wkdq d4�?| duh
dovr vwudljkwiruzdug1 Vlqfh wkh frqwlqxdwlrq ydoxh ri vrfldo vhfxulw| lv qhjdwlyh iru
wkhp/ wkh| dozd|v yrwh djdlqvw vrfldo vhfxulw|1 Wkhvh wzr hohphqwv duh lqfrusrudwhg
lqwr +44,1
Wklqjv duh pruh frpsolfdwhg iru plggoh0djhg yrwhuv zlwk djhv ehwzhhq d4�?| dqg
981 Li wkh rqo| fkrlfh lv wr nloo ru vdyh vrfldo vhfxulw| iruhyhu/ wkh djhqwv duh lq
idyru ri nhhslqj wkh v|vwhp1 Krzhyhu/ vlqfh wkh| kdyh wr sd| sd|uroo wd{hv xqwlo
wkhlu uhwluhphqw/ wkh| zrxog suhihu wr vxvshqg vrfldo vhfxulw| lq wkh vkruw0whup dqg
uhlqvwdwh lw zkhq wkh| uhwluh1
58
Xqghu +44,/ wklv jurxs yrwhv iru vrfldo vhfxulw| dv orqj/ dqg rqo| dv orqj dv/
vrfldo vhfxulw| kdv dozd|v ehhq fkrvhq e| wkh srolwlfdo surfhvv1 Lq rwkhu zrugv/
plggoh0djhg yrwhuv sod| d wuljjhu0vwudwhj|1 Wr vhh wkdw +44, lv dq htxloleulxp lw lv
hqrxjk wr qrwlfh wkdw iurp wkh srlqw ri ylhz ri wkh plggoh0djhg/ yrwlqj iru vrfldo
vhfxulw| lv dqdorjrxv wr surylglqj d ELJ lq wkh edvlf wkhru|1 Wklv iroorzv iurp wkh
gh�qlwlrq ri htxloleulxp= djhqwv yrwh vlqfhuho| dqg wdnh wkh uhvsrqvh ri ixwxuh yrwhuv
dv jlyhq1 Wkxv/ vlqfh wkh hoghuo| yrwh iru vrfldo vhfxulw|/ wkh plggoh0djhg jurxs
dozd|v ghwhuplqhv srolf| dqg lv sod|lqj dq lqwhujhqhudwlrqdo h{fkdqjh jdph zlwk
ixwxuh jhqhudwlrqv ri plggoh0djhg yrwhuv/ wkh rqhv wkdw zloo ghwhuplqh wkh vrfldo
vhfxulw| ehqh�wv ri fxuuhqw zrunhuv1 Exw wkhq/ dv zh vkrzhg ehiruh/ wkh wuljjhu0
vwudwhjlhv gh�qhg lq +44, duh dq htxloleulxp dv orqj dv wkh vrfldo vhfxulw| jhqhudwhv
d vxusoxv iru dw ohdvw kdoi ri wkh srsxodwlrq> wkdw lv/ dv orqj dv SY �| +d, � 3 iru doo
d � d6e_| 1 Wklv frqglwlrq lv vdwlv�hg zkhq d4�?| � d6e_
| 1
Dw �uvw vljkw wklv srolwlfdo hfrqrp| prgho grhv qrw �w wkh iudphzrun ri wkh
edvlf wkhru|1 Wkhuh lv d frqwlqxxp ri yrwhuv/ djhqwv gr qrw ghwhuplqh srolf| e|
wkhpvhoyhv/ dqg yrwhuv pdnh ghflvlrqv lq hyhu| shulrg ri wkhlu dgxow olyhv1 Krzhyhu/
wkh suhylrxv dujxphqw vkrzv wkdw zlwk vlqfhuh yrwlqj wkh srolwlfdo hfrqrp| prgho
fdq eh uhgxfhg wr d ELJ jdph dprqj wkh %slyrwdo% plggoh djhg jhqhudwlrqv1
Wkh frqwulexwlrq ri wklv vhfwlrq ri wkh sdshu lv qrw wr surylgh d qhz prgho ri
wkh srolwlfv ri vrfldo vhfxulw|1 Erkq +4<<;,/ Erogulq dqg Prqwhv +4<<;,/ Frroh| dqg
Vrduhv +4<<<,/ dqg Kdqvrq dqg Vwxduw +4<;<, kdyh vwxglhg vlplodu prghov1 Wkh
jrdo khuh lv wr vkrz wkdw frpsolfdwhg prghov ri lqwhujhqhudwlrqdo h{fkdqjh fdq eh
xqghuvwrrg lq vlpsoh whupv xvlqj wkh lghdv ri ELJv dqg ILJv1 Lqflghqwdoo|/ Erkq
dovr vwxglhv d prgho zlwk d uhdolvwlf ghprjudsklf vwuxfwxuh dqg vkrzv wkdw sd|0dv0
|rx0jr vrfldo vhfxulw| lv vxssruwdeoh dv orqj dv wkh phgldq yrwhu lv rog hqrxjk1 Kh
vkrzv wkdw klvwrulfdoo| wkh frqglwlrq d4�?| ? d6e_| kdv ehhq vdwlv�hg e| wkh X1V1
srsxodwlrq dqg wkdw wklv zloo frqwlqxh wr eh wuxh lq wkh ixwxuh1 Wklv surylghv dw
ohdvw sduw ri wkh h{sodqdwlrq iru zk| wkh Dphulfdq Vrfldo Vhfxulw| v|vwhp uhpdlqv
srolwlfdoo| yldeoh hyhq wkrxjk lw lv qrw dfwxduldoo| idlu1
.�� �L*�|�U@* ,UL?L4) Lu W?�it|4i?| �? 6�|�hi Bi?ih@|�L?t
Qrz ohw*v dgg wkh jhqhulf ILJ1 Zloo d vho�vk hohfwrudwh �qdqfh lqyhvwphqwv wkdw gr
qrw ehqh�w dq|rqh zkr yrwhvB Wkh edvlf wkhru| ri ELJv dqg ILJv surylghv d vlpsoh
dqvzhu1 Lw ghshqgv rq +4, zkhwkhu yrwlqj vwudwhjlhv olqn vrfldo vhfxulw| dqg ILJv/
59
dqg +5, rq zkhwkhu wkh frqwlqxdwlrq ydoxh ri vrfldo vhfxulw| iru wkh slyrwdo plggoh
djhg yrwhuv rxwzhljkv wkh frvw ri sxufkdvlqj wkh ILJv1
Dv ehiruh/ li d6e_| � d4�?| iru doo w wkhuh duh htxloleuld zlwk vrfldo vhfxulw| exw qrw
ILJv1 Exw htxloleuld zlwk sxeolf lqyhvwphqw lq ixwxuh jhqhudwlrqv duh dovr srvvleoh1
Ohw SY �n8| +d, ghqrwh wkh h�hfw iru dq djhqw ri djh d ri kdylqj vrfldo vhfxulw| dqg
ILJv lq hyhu| shulrg iurp w rqzdugv1 Fohduo|/
SY �n8| +d, ? SY �
| +d, iru doo d � 54>
vlqfh djhqwv qrz sd| iru vrfldo vhfxulw| dqg ILJv1 Ixuwkhupruh/ dv orqj dv wkh frvw
ri wkh ILJv grhvq*w �xfwxdwh wrr pxfk zh kdyh wkdw
SY �n8| +98, A SY �n8
| +97, A === A SY �n8| +54,>
zklfk lv jxdudqwhhg e| wkh dvvxpswlrq wkdw wkh frvw ri ILJv lv d frqvwdqw iudfwlrq
ri djjuhjdwh zdjhv1 Li wkh ILJ lv yhu| h{shqvlyh wkhq SY �n8| +d, frxog eh qhjdwlyh
hyhq iru uhwluhhv1 Krzhyhu/ li wkh ILJ lv vpdoo uhodwlyh wr vrfldo vhfxulw|/ ru li
vrfldo vhfxulw| ehqh�wv duh yhu| jhqhurxv/ wkhuh lv dq djh ed4�?| ? ;3 vxfk wkdw wkh
frqwlqxdwlrq ydoxh ri wkh mrlqw ELJ dqg ILJ srolf| lv srvlwlyh1
SURSRVLWLRQ := Li d6e_| � ed4�?| iru doo w wkhuh duh srolwlfdo htxloleuld lq zklfk
vrfldo vhfxulw| dqg wkh jhqhulf ILJ duh surylghg lq hyhu| shulrg1 Wkhvh htxl0
oleuld duh vxssruwhg e| yrwlqj vwudwhjlhv wkdw olqn vrfldo vhfxulw| dqg wkh ILJ1
Wr suryh wklv uhvxow lw lv hqrxjk wr vkrz wkdw wkh iroorzlqj yrwlqj vwudwhj| lv dq
htxloleulxp zkhq d6e_| � ed4�?| =
v|+d> k|, @
+e| @ i| @ 4 li ed4�?| � d dqg e|3& @ i|3& @ 4 iru doo n A 3e| @ i| @ 3 rwkhuzlvh
= +45,
Wkh dujxphqw lv dqdorjrxv wr wkh surri wkdw ILJv fdq eh vxssruwhg e| olqnlqj wkhp
zlwk ELJv1 Frqvlghu dq| yrwhu roghu wkdq ed4�?| 1 Wklv yrwhu suhihuv qrw wr �qdqfh wkh
ILJ dqg wr kdyh d vrfldo vhfxulw| v|vwhp rqo| gxulqj klv uhwluhphqw1 Krzhyhu/ li wkh
fkrlfh lv ehwzhhq vrfldo vhfxulw| dqg ILJv/ ru qrqh ri wkh wzr surjudpv/ wkh yrwhu
zloo idyru nhhslqj erwk srolflhv1 Ixuwkhupruh/ vlqfh djhqwv yrwh vlqfhuho| dqg wdnh
ixwxuh yrwlqj vwudwhjlhv dv jlyhq/ wklv djhqw lv sod|lqj dq lqwhujhqhudwlrqdo jdph
zlwk ixwxuh yrwhuv lq wkh djh udqjh ed4�?| wr ;31 Wkxv/ klv lqfhqwlyhv orrn h{dfwo|
olnh wkh rqhv ri wkh plggoh0djhg djhqw lq wkh edvlf prgho1 Iurp Sursrvlwlrq 5 lw
5:
iroorzv wkdw wkh wuljjhu0vwudwhjlhv lq +45, duh dq htxloleulxp dv orqj dv SY �n8| +d,
lv qrq0qhjdwlyh iru d pdmrulw| ri wkh hohfwrudwh/ zklfk lv vdwlv�hg li d6e_| � ed4�?| 1
Qrwh wkdw qrz wkh rqo| yrwhuv zlwk d grplqdqw vwudwhj| duh wkrvh ehwzhhq 54
dqg d4�?| |hduv rog/ zkr dozd|v yrwh djdlqvw vrfldo vhfxulw| dqg djdlqvw wkh jhqhulf
ILJ1 Djhqwv ehwzhhq d4�?| dqg ed4�?| zrxog olnh wr kdyh vrfldo vhfxulw|/ exw qrw li lw
lv olqnhg e| wkh ILJ1 Djhqwv roghu wkdq ed4�?| zrxog suhihu wr kdyh vrfldo vhfxulw|
zlwkrxw ILJv/ exw duh zloolqj wr �qdqfh ILJv li wklv lv wkh rqo| zd| ri pdnlqj vxuh
wkdw ixwxuh yrwhuv zloo �qdqfh wkhlu vrfldo vhfxulw| ehqh�wv1
Sursrvlwlrq ; vkrzv wkdw lqyhvwphqw lq ixwxuh jhqhudwlrqv fdq wdnh sodfh hyhq li
suhvhqw jhqhudwlrqv duh vho�vk dqg gr qrw ehqh�w iurp wkh h{shqglwxuhv1 Krzhyhu/
dv lq wkh edvlf wkhru|/ wklv fdq kdsshq rqo| li yrwlqj vwudwhjlhv olqn vrfldo vhfxulw|
zlwk ILJv vxfk dv lqyhvwphqwv lq wkh hqylurqphqw dqg sxeolf hgxfdwlrq1 Ri frxuvh/
zlwk lpsxuh ILJv ru dowuxlvwlf jhqhudwlrqv wkhuh lv vrph lqyhvwphqw lq ILJv hyhq li
wkh olqn lv qrw suhvhqw1 Krzhyhu/ lq wkh devhqfh ri g|qdvwlf dowuxlvp/ djhqwv w|slfdoo|
gr qrw lqyhvw wkh rswlpdo dprxqw zlwkrxw d olqn wr wkh ELJ1
D vxusulvlqj frpsdudwlyh vwdwlf lv wkdw/ frqwlqjhqw rq ehlqj lq dq htxloleulxp
wkdw olqnv vrfldo vhfxulw| dqg ILJv/ wkh djlqj ri wkh srsxodwlrq fdq khos lqyhvwphqw
lq ixwxuh jhqhudwlrqv1 Wkh uhdvrq lv wkdw iru zrunhuv wkh frqwlqxdwlrq ydoxh ri vrfldo
vhfxulw| lqfuhdvhv zlwk djh1 Dv d uhvxow/ roghu zrunhuv kdyh pruh vxusoxv wkdw fdq
eh xvhg wr vxssruw wkh surgxfwlrq ri ILJv1
Rwkhu suhglfwlrqv ri wkh edvlf prgho duh dovr dw zrun khuh1 Iluvw/ sxuh lqyhvw0
phqwv lq ixwxuh jhqhudwlrqv wdnh sodfh rqo| zkhq ELJv/ olnh vrfldo vhfxulw|/ duh
dovr surgxfhg1 Lq wklv vhqvh wkhuh lv d eldv lq idyru ri edfnzdugv lqwhujhqhudwlrqdo
h{fkdqjh= sxeolf h{shqglwxuhv rq wkh hoghuo| duh pruh olnho| wr dulvh wkdq sxeolf
h{shqglwxuhv lq ixwxuh jhqhudwlrqv1 Vhfrqg/ wkh ehqh�wv jhqhudwhg e| ILJv sod|
qr uroh rq wkh srolwlfdo fdofxodwlrqv ri vho�vk yrwhuv/ rqo| wkh frvwv ri surgxflqj
wkhp pdwwhu1 Dv d uhvxow/ ILJv wkdw jhqhudwh duelwudulo| odujh ehqh�wv/ exw duh yhu|
frvwo|/ zloo qrw eh surgxfhg1 E| frqwudvw/ ILJv wkdw jhqhudwh orzhu qhw ehqh�wv/ exw
duh uhodwlyho| fkhds fdq eh vxvwdlqhg1 Wkxv/ wkh prgho suhglfwv wkdw frvwo| ILJv
duh ohvv olnho| wr eh surgxfhg dqg wkdw wkh qhw ehqh�wv surgxfhg e| d ILJ vkrxog
qrw d�hfw lwv ohyho ri ixqglqj1 Lq wklv vhqvh/ h{shqvlyh exw srwhqwldoo| yhu| ydoxdeoh
ILJv olnh dyrlglqj joredo zduplqj ru vsdfh h{sorudwlrq pd| eh xqghu0ixqghg/ zkloh
fkhdshu exw ohvv dwwudfwlyh ILJv/ olnh plqru hqylurqphqwdo lpsuryhphqwv/ pd| eh
ixqghg1
5;
Vrfldo Vhfxulw| lv qrw wkh rqo| ELJ wkdw fdq eh xvhg wr vxssruw lqyhvwphqw lq
ixwxuh jhqhudwlrqv1 Dq| jryhuqphqw surjudp wkdw glvsursruwlrqdwho| ehqh�wv ru
kxuwv wkh rog fdq dovr eh xvhg1 H{dpsohv ri vxfk surjudpv duh Phglfduh/ fdslwdo
wd{dwlrq/ ru d frpelqdwlrq ri wkh wzr1
Lq wkh fdslwdo wd{dwlrq ELJ/ yrwhuv fkrrvh lq hyhu| shulrg wkh fdslwdo wd{ udwh
iru wkdw shulrg1 \rxqj yrwhuv zrxog olnh wr h{sursuldwh wkh vdylqjv ri wkh hoghuo|/
exw gr qrw zdqw wr eh h{sursuldwhg zkhq wkh| duh rog1 Wkh edg htxloleulxp lq wklv
ELJ lv udwkhu julp= qr rqh vdyhv ehfdxvh wkh| nqrz wkdw wkhlu vdylqjv zloo eh wd{hg
dzd|1 Wr dyrlg wklv rxwfrph vrflhwlhv pljkw zdqw wr pdnh xvh ri dq h{rjhqrxv
frqvwlwxwlrqdo frqvwudlqw djdlqvw fdslwdo wd{dwlrq1 Wklv zrxog suhyhqw d yhu| edg
rxwfrph exw zrxog dovr holplqdwh d orw lqfhqwlyh ohyhudjh wkdw frxog eh xvhg wr
vxssruw lqyhvwphqw lq ixwxuh jhqhudwlrqv1
Rqh pljkw eh whpswhg wr wklqn wkdw xvlqj ghew wr �qdqfh ILJv zrxog jhw ulg ri
wkhvh sureohpv1 Diwhu doo/ e| xvlqj ghew rqh frxog lqyhvw lq ixwxuh jhqhudwlrqv dqg
sdvv wkhp wkh eloo1 Wklv lqwxlwlrq lv lqfruuhfw1 Wkh sureohp lv wzrirog1 Iluvw/ li wkh
jryhuqphqw kdv wkh dxwkrulw| wr lvvxh ghew wr �qdqfh ILJv/ lw dovr kdv wkh dxwkrulw|
wr lvvxh ghew wr �qdqfh frqvxpswlrq1 Khqfh/ suhvhqw yrwhuv dozd|v lqwhuqdol}h wkh
frvw ri lqyhvwlqj lq ILJv dqg wkh sureohp uhpdlqv1 D srvvleoh vroxwlrq zrxog eh wr
lqwurgxfh d fdslwdo exgjhw frqvwudlqw xqghu zklfk wkh jryhuqphqw fdq lvvxh ghew
rqo| wr lqyhvw lq ixwxuh jhqhudwlrqv1 Wkh sureohp zlwk wklv vroxwlrq lv wkdw lw lv
gl�fxow wr gh�qh suhflvho| zkdw lv dq lqyhvwphqw dqg zkdw lv qrw1�D Ixuwkhupruh/
hyhq li wklv sureohp frxog eh vroyhg/ ixwxuh jhqhudwlrqv zrxog vwloo kdyh wr yrwh wr
vhuylfh wkh ghew1
H �TT*�U@|�L? 2G � �5i*�t�� A�iLh) Lu |�i �*|h��t|�U
6@4�*)
Dqrwkhu qdwxudo dssolfdwlrq ri ELJv dqg ILJv duh wkh hfrqrplfv ri wkh idplo|/ zkhuh
d vljql�fdqw dprxqw ri lqwhujhqhudwlrqdo h{fkdqjh wdnhv sodfh1 Sduhqwv lqyroyhphqw
dqg h{shqglwxuhv d�hfw wkhlu fkloguhq*v kxpdq fdslwdo dqg hprwlrqdo zhoo0ehlqj�S
+ILJv,1 Plggoh0djhg sduhqwv dovr surylgh wdqjleoh dqg lqwdqjleoh ehqh�wv wr hoghuo|
sduhqwv +ELJv,1
�D� hiUi?| Thit�_i?|�@* UL44�tt�L? L? U@T�|@* M�_}i|�?} @hh��i_ @| |��t UL?U*�t�L?� 5ii �hit��_i?|<t �L44�tt�L? |L 5|�_) �@T�|@* ��_}i|�?} E�bbb��
�SWu )L� _L ?L| |��?! |�@| |��t �t @? iUL?L4�U }LL_c UL?t�_ih |�i @4L�?| Lu hitL�hUit |�@| @hi_i�L|i_ i�ih) )i@h |L Tt)U�L*L}�U@* UL�?ti*�?} @?_ |�ih@T)�
5<
Hyhq fdvxdo revhuydwlrq vxjjhvwv wkdw dowuxlvp sod|v dq lpsruwdqw uroh lq wkh
hfrqrplfv ri wkh idplo|1 Krzhyhu/ lw lv lpsruwdqw wr gl�huhqwldwh ehwzhhq sdwhu0
qdolvwlf dqg g|qdvwlf dowuxlvp1 Wr wkh nqrzohgjh ri wkh dxwkru/ wkhuh lv qr vwurqj
hylghqfh lq idyru ri wkh g|qdvwlf prgho/ dqg vrph hylghqfh djdlqvw lw1�. Wklv pr0
wlydwhv wkh vwxg| ri prghov ri wkh idplo| edvhg rq wzr0vlghg sdwhuqdolvwlf dowuxlvp/
zkhuh djhqwv fduh derxw wkhlu hoghuo| sduhqwv dqg derxw wkhlu fkloguhq1�H Wklv prgho
kdv lpsolfdwlrqv wkdw duh gl�huhqw iurp wkh vwdqgdug g|qdvwlf prgho dqg wkdw fdq
eh xvhg wr frpsduh wkh wzr prghov hpslulfdoo|1 Ixuwkhupruh/ lw dovr surylghv qhz
lqvljkwv lqwr wkh uhodwlrqvkls ehwzhhq jryhuqphqw srolf| dqg idplo| ehkdylru1
Frqvlghu d vlpsoh prgho ri dq lpshuihfwo| dowuxlvwlf idplo|1 Djhqwv olyh iru
wkuhh shulrgv1 Wkh| duh fkloguhq lq wkh �uvw shulrg/ sduhqwv lq wkh vhfrqg/ dqg
judqgsduhqwv lq wkh wklug1 Dw dq| wlph wkhuh duh wkuhh frh{lvwlqj jhqhudwlrqv1
Hdfk shulrg wkh sduhqw fkrrvhv krz pxfk wr lqyhvw lq klv fklog dqg krz pxfk wr
khos klv hoghuo| sduhqwv1 Ohw i| dqg e| ghqrwh/ uhvshfwlyho|/ wkh dprxqw ri uhvrxufhv
ghyrwhg wr wkh fkloguhq dqg wkh hoghuo| lq shulrg w1 Wklv qrwdwlrq hpskdvl}hv wkdw
lqyhvwlqj lq d fklog lv d ILJ dqg khoslqj dq hoghuo| sduhqw lv d ELJ1
Wkh suhihuhqfhv ri jhqhudwlrq w duh jlyhq e|
X|+=, @ x+f6, . �x+fJ, . Y 8 +i|, . �8Y 8 +i|n�, . ��Y �+e|n�, . Y �+e|n2,/
zkhuh ��> �8 5 ^3> 4, ghqrwh wkh ghjuhh wr zklfk lw lqwhuqdol}hv wkh lqwhujhqhudwlrqdo
vslooryhu rq wkh |rxqj dqg rog1 Lq wkh vho�vk prgho �S @ �} @ 31 Wkxv/ wkh prgho
doorzv iru vho�vk dqg sdwhuqdolvwlf jhqhudwlrqv1 Ilqdoo|/ ohw ei| ghqrwh wkh dprxqw ri
lqyhvwphqw lq fkloguhq wkdq sduhqwv pdnh lq wkh devhqfh ri jdph wkhruhwlf h�hfwv
dqg iW| wkh rswlpdo dprxqw ri lqyhvwphqw1 Gh�qh ee| dqg eW| vlploduo|1 Lw lv qdwxudo
wr dvvxph wkdw iW| A ei| dqg eW| Aee|1
Iurp wkh edvlf wkhru|/ lw iroorzv wkdw zlwkrxw jryhuqphqw lqwhuyhqwlrq wkhuh duh
htxloleuld lq zklfk sduhqwv fkrrvh vkruw0vljkwhgo| dqg xqghu0lqyhvw lq wkh fkloguhq
dqg wkh hoghuo|> htxloleuld lq zklfk wkh plggoh0djhg lqyhvw rswlpdoo| lq wkh hoghuo|/
exw qrw lq wkh fkloguhq> dqg htxloleuld zlwk rswlpdo dqg hyhq ryhu0lqyhvwphqw lq
�.5ii �*|L?��c w�c 6� O@)@t��c @?_ w� kL|*�!Lg E�bb2c�bb.���H6Lh @? i Ui**i?| hi��i� Lu |�i *�|ih@|�hi Lu |�i iUL?L4�Ut Lu |�i u@4�*) tii w@�|?ih E�bb.�� �t
u@h @t |�i @�|�Lh !?L�tc |��t �t |�i �ht| T@Tih |L t|�_) @ |h�*) _)?@4�U 4L_i* Lu |�i u@4�*) ��|�|�L�t�_i_ @*|h��t4� w@�|?ih E�bHH� t|�_�it @ |�L Tih�L_ 4L_i* �? ���U� T@hi?|t 4@!i _iU�t�L?tMiuLhi |�i�h U��*_hi?� OL�i�ihc �? |�@| uh@4i�Lh! 4�*|��}i?ih@|�L?@* �?Ui?|��it Lu |�i |)Ti �W |@!iU@hi Lu 4) T@hi?|t tL |�@| 4) U��*_hi? ��** |@!i U@hi Lu 4i� U@??L| @h�ti� A�iti |)Ti Lu �?Ui?|��it@hi @| |�i ULhi Lu |�i |�iLh) Lu �WBt @?_ 6WBt�
63
erwk1 Krzhyhu/ wkhuh lv qr htxloleuld lq zklfk sduhqwv lqyhvw rswlpdoo| lq wkh fklo0
guhq exw qrw lq wkh hoghuo|1
Vlqfh sduhqwv duh dowuxlvwlf/ wkh| dozd|v vshqg vrph uhvrxufhv rq wkh rog dqg
rq wkhlu fkloguhq1 Krzhyhu/ rswlpdo lqyhvwphqw uhtxluhv dgglwlrqdo lqfhqwlyhv1 Wkh
lqfhqwlyh wr wdnh rswlpdo fduh ri wkh hoghuo| vwhpv iurp ghvluh eh wdnhq fduh lq rog
djh1 Wklv ELJ lv vhoi0vxvwdlqdeoh dv orqj dv wkh ydoxh ri wkh rswlpdo fduh surylghg
e| rqh*v fkloguhq rxwzhljkv wkh frvw ri wdnlqj rswlpdo fduh ri rqh*v sduhqwv1 E| frq0
wudvw/ wkh ILJ %lqyhvw dq dgglwlrqdo iW| �ei| xqlwv lq fkloguhq% lv qrw vhoi0vxvwdlqdeoh1
Sduhqwv lqyhvw wkh h{wud uhvrxufhv lq fkloguhq li/ dqg rqo| li/ wkh| eholhi wkdw wklv lv
wkh rqo| zd| ri sxufkdvlqj rswlpdo fduh lq rog djh1 Dv lq wkh edvlf wkhru|/ rswlpdo
lqyhvwphqw lq ILJv lv vxssruwhg zlwk d idplo| qrup wkdw olqnv ELJv dqg ILJv1 Lq
wklv qrup/ djhqwv uhfhlyh rswlpdo fduh lq rog djh rqo| li= +4, wkh| wrrn rswlpdo fduh
ri wkhlu rzq hoghuo| sduhqwv/ dqg +5, wkh| lqyhvwhg rswlpdoo| lq wkhlu fkloguhq1
Jryhuqphqw srolf| kdv lqwhuhvwlqj dqg vxusulvlqj lpsolfdwlrqv lq wklv prgho ri
wkh idplo|1 Lq sduwlfxodu/ jryhuqphqw lqwhuyhqwlrqv rq ELJv furzg rxw ELJ dqg ILJ
surylvlrq zlwklq wkh idplo|1 Wr vhh wklv/ vxssrvh wkdw wkh jryhuqphqw lqwurgxfhv d
odz wkdw irufhv wkh plggoh0djhg wr surylgh rswlpdoo| iru wkhlu sduhqwv1 Dq h{dpsoh lv
rog djh sxeolf krxvlqj wkdw lv �qdqfhg zlwk wd{hv rq wkh plggoh0djhg1 Wkhq sduhqwv
nqrz wkdw wkhlu fkloguhq zloo kdyh wr surylgh wkhp zlwk rswlpdo fduh zkhq wkh| duh
lq rog djh ~ hyhq li wkh fduh lv surylghg lqgluhfwo| wkurxjk jryhuqphqw vhuylfhv1 Exw
wklv holplqdwhv wkh srvvlelolw| ri d idplo| qrup wkdw/ e| olqnlqj ILJv dqg ELJv/
surylghv lqfhqwlyhv wr lqyhvw rswlpdoo| lq fkloguhq1 Dv d uhvxow/ wkh lqwurgxfwlrq ri
d jryhuqphqw ELJ furzgv rxw lqyhvwphqw lq fkloguhq zlwklq wkh idplo|1
Ri frxuvh/ wklv dvvxphv wkdw wkh jryhuqphqw lqwhuyhqhv rqo| lq ELJv1 Rqh frxog
dujxh wkdw wkh sureohp glvdsshduv li wkh jryhuqphqw lqwhuyhqhv lq erwk ELJ dqg
ILJv1 Exw/ dw ehvw/ wklv fdq rqo| eh d sduwldo vroxwlrq1 Iluvw ri doo/ jryhuqphqw
surjudpv uhtxluh uhyhqxh wkdw pxvw eh udlvhg zlwk frvwo| glvwruwlrqdu| wd{hv1 Vhf0
rqg/ wkhvh surjudpv duh qrw olnho| wr eh wdloruhg rswlpdoo| wr wkh vshfl�f qhhgv ri
gl�huhqw idplolhv1 Ilqdoo|/ dqg shukdsv prvw lpsruwdqwo|/ wkh qdwxuh ri vrph ELJv
dqg ILJv lv vxfk wkdw wkh| fdq rqo| eh surylghg lq wkh frqwh{w ri wkh idplo|1 Iru
h{dpsoh/ wkhuh grhv qrw vhhp wr d vxevwlwxwh iru wkh lpsdfw wkdw sduhqwv* fduh dqg
oryh kdyh rq wkh hprwlrqdo dqg fkdudfwhu ghyhorsphqw ri fkloguhq1
64
b �L?U*�t�L?t
Pdq| sureohpv ri lqwhujhqhudwlrqdo h{fkdqjh vkduh d frpprq vwuxfwxuh zklfk lv
fdswxuhg e| wkh gl�huhqfh ehwzhhq ELJv dqg ILJv dqg wkh uhodwlrqvkls ehwzhhq
wkhp1 Eurdgo| vshdnlqj/ ILJv duh iruzdug wudqvihuv/ iurp suhvhqw wr ixwxuh jhqhu0
dwlrqv/ dqg ELJv duh edfnzdug wudqvihuv/ iurp |rxqj wr rog1 Wklv gl�huhqfh lq wkh
wlph ri h{fkdqjh kdv lpsruwdqw lpsolfdwlrqv iru wkh w|sh ri lqwhujhqhudwlrqdo wudgh
wkdw fdq eh vxvwdlqhg1 ELJv wkdw jhqhudwh d srvlwlyh vxusoxv duh vhoi0vxvwdlqdeoh/
exw ILJv qhyhu duh1 Ixuwkhupruh/ wudqvihuv wr ixwxuh jhqhudwlrqv wdnh sodfh lq htxl0
oleulxp rqo| li jhqhudwlrqv olqn ELJv dqg ILJv1 Dv zh vdz lq wkh dssolfdwlrqv/ wkhvh
irufhv duh dw zrun lq d zlgh udqjh ri sureohpv/ iurp wkh srolwlfdo hfrqrp| ri sxeolf
lqwhujhqhudwlrqdo h{shqglwxuhv wr lqyhvwphqw e| sulydwh �upv1
Wkh wkhru| ri ELJv dqg ILJv kdv srvlwlyh dqg qrupdwlyh dssolfdwlrqv1 Rq wkh
srvlwlyh vlgh/ lw fdq dssolhg wr xqghuvwdqg wkh hfrqrplf sureohpv lq zklfk lqwhu0
jhqhudwlrqdo h{fkdqjh lv rqh ri wkh nh| irufhv dw zrun1 Ehvlghv wkh wkuhh sureohpv
vwxglhg deryh/ rwkhu srvvleoh dssolfdwlrqv duh lqwhujhqhudwlrqdo ulvn0vkdulqj>�b %vh0
qlrulw|% lqvwlwxwlrqv olnh wkh XV1 Frqjuhvv/2f dfdghpld/ dqg wkh jryhuqdqfh vwuxfwxuh
ri pdq| frpsdqlhv> wkh srolwlfdo hfrqrp| ri ghew dqg wd{dwlrq> rswlpdo wd{dwlrq
lq wkh suhvhqfh ri srolwlfdo frqvwudlqwv> dqg wkh srolwlfdo hfrqrp| ri lqwhuqdwlrqdo
lqwhujhqhudwlrqdo jrrgv olnh wkh joredo folpdwh1
Rq wkh qrupdwlyh vlgh/ wkh wkhru| fdq dovr eh xvhg wr wu| wr ghvljq ehwwhu
lqwhujhqhudwlrqdo lqvwlwxwlrqv1 Vxssrvh/ iru h{dpsoh/ wkdw ixwxuh hpslulfdo dqdo|vlv
vkrzv wkdw yrwhuv gr qrw olqn ELJv dqg ILJv/ dqg wkdw wkhuh lv xqghu0lqyhvwphqw lq
ixwxuh jhqhudwlrqv1 Rqh frxog wkhq orrn iru sodxvleoh prgl�fdwlrqv wr wkh hohfwrudo
dqg frqjuhvvlrqdo v|vwhpv wkdw fuhdwh wkh qhfhvvdu| olqn1
+iuihi?Uit
^4` Dowrqml/ O1/ I1 Kd|dvkl/ dqg O1 Nrwolnr� +4<<5, %Lv wkh H{whqghg Idplo| Dowux0
lvwlfdoo| OlqnhgB Gluhfw Whvwv Xvlqj Plfur Gdwd/% Dphulfdq Hfrqrplf Uhylhz/
Ghfhpehu/ 44::0<;1
�b5ii +@?}i* @?_ ~iU!�@�tih E�bbb� @?_ |�i hiuihi?Uit |�ihi�?�2f5ii 5�iTt*i E�bbb� @?_ 5�iTt*i @?_ �@*iM�g E�bbf��
65
^5` Dowrqml/ O1/ I1 Kd|dvkl/ dqg O1 Nrwolnr� +4<<:, %Sduhqwdo Dowuxlvp dqg Lqwhu
Ylyrv Wudqvihuv= Wkhru| dqg Hylghqfh/% Mrxuqdo ri Srolwlfdo Hfrqrp|/ Ghfhp0
ehu/ 44540991
^6` Eduur/ Urehuw +4<:7, %Duh Jryhuqphqw Erqgv Qhw ZhdowkB% Mrxuqdo ri Srolw0
lfdo Hfrqrp|/ ;5/ 43<80444;1
^7` Ehfnhu/ Jdu| dqg Nhylq Pxusk| +4<;;, %Wkh Idplo| dqg wkh Vwdwh/% Mrxuqdo
ri Odz dqg Hfrqrplfv/ yro1 [[[L/ Dsulo= 404;1
^8` Ehqgru/ Mrqdwkdq dqg Glols Prrnkhumhh +4<<3, %Qrupv/ Wklug0Sduw| Vdqf0
wlrqv/ dqg Frrshudwlrq/% Mrxuqdo ri Odz/ Hfrqrplfv/ dqg Rujdql}dwlrq/ yro1 9/
Vsulqj= 6608:1
^9` Ehuqkhlp/ Grxjodv dqg Plfkdho Zklqvwrq +4<<3, %Pxowlpdunhw Frqwdfw dqg
Frooxvlyh Ehkdylru/% Udqg Mrxuqdo ri Hfrqrplfv/ 54=40591
^:` Ekdvndu/ Y1 +4<<;, %Lqirupdwlrqdo Frqvwudlqwv dqg wkh Ryhuodsslqj Jhqhud0
wlrqv Prgho= Iron dqg Dqwl0Iron Wkhruhpv/% Uhylhz ri Hfrqrplf Vwxglhv/ 98=
46807<1
^;` Erkq/ Khqqlqj +4<<;, %Zloo Vrfldo Vhfxulw| Uhpdlq Yldeoh dv wkh X1V1 Srsx0
odwlrq lv DjlqjB% X1F1 Vdqwd Eduedud/ pdqxvfulsw1
^<` Erogulq/ Plfkhoh dqg Dqd Prqwhv +4<<;, %Lqwhujhqhudwlrqdo Wudqvihu Lqvwl0
wxwlrqv= Sxeolf Hgxfdwlrq dqg Sxeolf Shqvlrqv/% Xqlyhuvlw| ri Plqqhvrwd/
pdqxvfulsw1
^43` Frqoh|/ Mrkq dqg Dqwrqlr Udqjho +4<<<, %Lqwhujhqhudwlrqdo Vslooryhuv dqg Lq0
whumxulvglfwlrqdo Frpshwlwlrq/% Vwdqirug plphr1
^44` Frroh|/ Wkrpdv dqg Mrujh Vrduhv +4<<<, %D Srvlwlyh Wkhru| ri Vrfldo Vhfxulw|
Edvhg rq Uhsxwdwlrq/% Mrxuqdo ri Srolwlfdo Hfrqrp|/ yro1 43:/ 4= 46804931
^45` Gldprqg/ S1 dqg M1 Pluuohhv +4<:;, %D Prgho ri Vrfldo Lqvxudqfh zlwk Yduldeoh
Uhwluhphqw/% Mrxuqdo ri Sxeolf Hfrqrplfv/ 43+6, 5<806691
^46` Grhohpdq/ M1 dqg W1 Vdqgohu +4<<;, %Wkh Lqwhujhqhudwlrqdo Fdvh ri Plvvlqj
Pdunhwv dqg Plvvlqj Yrwhuv/% Odqg Hfrqrplfv/ :7 +4,=40481
66
^47` Irophu/ Khqn/ hw do1 +4<<6, %Lqwhufrqqhfwhg Jdphv dqg Lqwhuqdwlrqdo Hqylurq0
phqwdo Sureohpv/% Hqylurqphqwdo dqg Uhvrxufh Hfrqrplfv/ 6= 6460681
^48` Kdpprqg/ Shwhu +4<:8, %Fkdulw|= Dowuxlvp ru Frrshudwlyh HjrlvpB% lq Do0
wuxlvp/ Prudolw|/ dqg Hfrqrplfv/ hg1 H1 Skhosv1
^49` Kdqvvrq/ L1 dqg F1 Vwxduw +4<;<,/ %Vrfldo Vhfxulw| dv Wudgh Dprqj Olylqj
Jhqhudwlrqv/% Dphulfdq Hfrqrplf Uhylhz/ :<+8,= 44;5044<81
^4:` Ndqgrul/ Plfklklur +4<<4, %Uhshdwhg Jdphv Sod|hg e| Ryhuodsslqj Jhqhud0
wlrqv ri Sod|huv/% Uhylhz ri Hfrqrplf Vwxglhv/ 8<+4,= ;40<51
^4;` Nrfkhuodnrwd/ Qdud|dqd +4<<;,/ %Prqh| lv Phpru|/% Mrxuqdo ri Hfrqrplf
Wkhru|/ Dxjxvw= 5650841
^4<` Nrwolnr�/ O1/ W1 Shuvvrq/ dqg O1 Vyhqvvrq +4<;;, %Vrfldo Frqwudfwv dv Dvvhwv=
D Srvvleoh Vroxwlrq wr wkh Wlph0Frqvlvwhqf| Sureohp/% Dphulfdq Hfrqrplf
Uhylhz/ :;= 99509::1
^53` Nrwolnr�/ O1 dqg U1 Urvhqwkdo +4<<6, %Vrph Lqh�flhqf| Lpsolfdwlrqv ri Jhq0
hudwlrqdo Srolwlfv dqg H{fkdqjh/% Hfrqrplfv dqg Srolwlfv/ 8= 5:0751
^54` Nuhsv/ G1 +4<<3, %Frusrudwh Fxowxuh dqg Hfrqrplf Wkhru|/% Wkh Irxqgdwlrqv
ri Srolwlfdo Hfrqrp|/ M1 Dow dqg N1 Vkhsvoh +hgv1,/ Fdpeulgjh= Kduydug Xql0
yhulvw| Suhvv1
^55` Odlwqhu/ Mrkq +4<<:, %Lqwhujhqhudwlrqdo dqg Lqwhukrxvhkrog Hfrqrplf Olqnv/%
Kdqgerrn ri Srsxodwlrq dqg Idplo| Hfrqrplfv/ P1 Urvhq}zhlj dqg R1 Vwdun
hglwruv/ fkdswhu 81 Qruwk0Kroodq
^56` Pxooljdq/ F1 dqg [1 Vdod0l0Pduwlq +4<<<, %Jhurqwurfudf|/ Uhwluhphqw/ dqg Vr0
fldo Vhfxulw|/% QEHU zrunlqj sdshu &:44:1
^57` Suhvlghqw*v Frpplvvlrq wr Vwxg| Fdslwdo Exgjhwlqj +4<<<,/ Zdvklqjwrq G1F1
^58` Udqjho/ D1 +4<<:, %Edfnzdug dqg Iruzdug Lqwhujhqhudwlrqdo Jrrgv/% Kduydug
pdqxvfulsw1
^59` Udqjho/ D1 dqg U1 ]hfnkdxvhu/ %Fdq Pdunhwv dqg Srolwlfdo Lqvwlwxwlrqv Jhqhu0
dwh Rswlpdo Lqwhujhqhudwlrqdo Ulvn Vkdulqj/% lq M1 Fdpsehoo dqg P1 Ihogvwhlq/
67
hgv1/ Ulvn Dvshfwv ri Lqyhvwphqw Edvhg Vrfldo Vhfxulw| Uhirup/ Fklfdjr Xql0
yhuvlw| Suhvv/ iruwkfrplqj 53331
^5:` Ud|/ Gheudm +4<;:, %Qrqsdwhuqdolvwlf Lqwhujhqhudwlrqdo Dowuxlvp/% Mrxuqdo ri
Hfrqrplf Wkhru|/ 74+4,=4450651
^5;` Vdodqw/ Gdylg +4<<4, %D Uhshdwhg Jdph zlwk Ilqlwho| Olyhg Ryhuodsslqj
^5<` Jhqhudwlrqv ri Sod|huv/% Jdphv dqg Hfrqrplf Ehkdylru/ 6+5,= 57708<1
^63` Vdpxhovrq/ Sdxo +4<8;, %Dq H{dfw Frqvxpswlrq0Ordq Prgho ri Lqwhuhvw zlwk
ru zlwkrxw wkh Vrfldo Frqwulydqfh ri Prqh|/% Mrxuqdo ri Srolwlfdo Hfrqrp|/
99=79:0;51
^64` Vdqgohu/ W1 +4<:;, %Lqwhuuhjlrqdo dqg Lqwhujhqhudwlrqdo Vslooryhu Dzduhqhvv/%
Vfrwwlvk Mrxuqdo ri Srolwlfdo Hfrqrp|/ 58 +6,=5:60;71
^65` Vdqgohu/ W1 +4<;5, %D Wkhru| ri Lqwhujhqhudwlrqdo Foxev/% Hfrqrplf Lqtxlu|/
[[=4<4053;1
^66` Vdqgohu/ W1 dqg N1 Vplwk +4<:9, %Lqwhuwhpsrudo dqg Lqwhujhqhudwlrqdo H�0
flhqf|/% Mrxuqdo ri Hqylurqphqwdo Hfrqrplfv dqg Pdqdjhphqw/ 5=4840<1
^67` Vkhsvoh/ Nhqqhwk +4<<<, %Iurp Jhqhudwlrq wr Jhqhudwlrq= D Irupdo Dqdo|vlv
ri Lqwhuwhpsrudo Vwudwhjlf Lqwhudfwlrq/% pdqxvfulsw1
^68` Vkhsvoh/ N1 dqg E1 Qdohex� +4<<3, %Wkh Frpplwphqw wr Vhqlrulw| lq Vhoi0
Jryhuqlqj Jurxsv/% Mrxuqdo ri Odz/ Hfrqrplfv/ dqg Rujdql}dwlrq/ 9= 780:51
^69` Vloyhvwuh/ Mrdtxlp +4<<7, %Dq H�flhqf| Dujxphqw iru Vxvwdlqdeoh Xvh/% XF0
Gdylv Zrunlqj sdshu &<70441
^6:` Vloyhvwuh/ Mrdtxlp +4<<8, %Txdvlolqhdu/ Ryhuodsslqj Jhqhudwlrq Hfrqrplhv/%
XF0Gdylv Zrunlqj sdshu <803<1
^6;` Vplwk/ Orqhv +4<<5, %Iron Wkhruhpv lq Ryhuodsslqj Jhqhudwlrqv Jdphv/%
Jdphv dqg Hfrqrplf Ehkdylru/ 7+6,=75907<1
^6<` Vrduhv/ Mrujh +4<<<, %Eh|rqg Vhuudqr yv1 Sulhvw= Qdwlrqdo Ixqglqj ri Hgxfd0
wlrq/% Jhrujh Zdvklqjwrq Xqlyhuvlw| plphr1