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Lq rughu wr dvvhvv wkh vljqlfdqfh ri wkh uhvxowv lq d vwdwlvwlfdo vhqvh/ L wxuq wr %errwvwuds% whfkqltxhv wr jhw wkh glvwulexwlrqv ri wkh sruwirolr yduldqfh hvwlpdwhv1 Errwvwudsslqj uhwxuq vhulhv zlwk ryhuodsslqj uhwxuqv lv srvvleoh e| v|vwhpdwlfdoo| slfnlqj +zlwk uhsodfhphqw, jurxsv ri yh +wkh ghshqghqfhv uhdfk ryhu yh gd|v, uhwxuqv iurp wkh vhulhv xqwlo d qhz errwvwudsshg vhulhv ri htxdo ohqjwk dv wkh ruljlqdo vhulhv lv frqvwuxfwhg +Vkdx dqg Wx +4<<8,,1 Wklv surfhgxuh lv uhshdwhg 4333 wlphv dqg iru hdfk errwvwudsshg vhulhv/ d qhz hvwlpdwh ri wkh xqfrqglwlrqdo uhwxuq yduldqfh lv irxqg1 Lq Wdeoh 8/ phdqv dqg vwdqgdug ghyldwlrqv iurp wkhvh 4333 yduldqfh hvwlpdwhv duh suhvhqwhg1 Lw fdq eh qrwlfhg krz/ dv h{shfwhg/ wkh phdq yduldqfhv fruuhvsrqg forvho| wr wkh dfwxdo vdpsoh yduldqfhv lq Wdeoh 71 Iurp wkh vl}h ri wkh vwdqgdug ghyldwlrqv/ lw fdq eh frqfoxghg wkdw hyhq li wkh khgjh sruwirolrv kdyh d vpdoohu yduldqfh iru rxu vdpsoh wkdq wkh vsrw srvlwlrq/ qr khgjh glhuv lq d vwdwlvwlfdoo| vljqlfdqw zd| +dw wudglwlrqdo vljqlfdqfh ohyhov, iurp wkh xqkhgjhg vsrw srvlwlrq1 Dw wkh vdph wlph/ qr khgjh vljqlfdqwo| glhuv iurp dq| rwkhu khgjh lq lwv khgjlqj shuirupdqfh1

_{W? |i U@ti Lu Lh|L}L?@* B+Oc |i i@! TihuLh4@?Ui UL*_ @| *i@t| T@h|*) Mi _i |L @ Mhi@! _L? ? |i}

Lh|L}L?@*3@|L? 4i|L_L*L})

(15)

Wdeoh 8= Phdqv dqg vwdqgdug ghyldwlrqv ri wkh errwvwudsshg +4333{, xqfrqglwlrqdo yduldqfh glvwulexwlrqv1 Ryhuodsslqj zhhno| sruwirolr uhwxuqv1

5TL| @i w5 WB+O B+O Df_@)t i@? V@h@?Ui ff2f ffb ffbD ff2f ff2fb ff2f

5|@?_@h_ #i@|L? fff fffD fff fffe fffb fffe

Wdeoh 9= Xqfrqglwlrqdo sruwirolr uhwxuq yduldqfh dqg shufhqwdjh yduldqfh uhgxfwlrq rxw0ri0 vdpsoh frpsduhg wr wkh qrq0khgjhg vsrw srvlwlrq1 Qrq0ryhuodsslqj zhhno| sruwirolr uhwxuqv1

5TL| @i w5 WB+O B+O Df_@)t tihit ffSb ffeD ffef ffee ffeb ffe. tihit 2 ff2. ffb ff2 ff2H ff22 ff2f V@h@?Ui tihit ff2D ff22. ff22S ff22b ff2e ff22b tihit e ff2.f ff2S ff2D2 ff2S ff2.e ff2S. tihit D ffb ffDe ffDb ffS ff.f ffS

tihit 3 eb .f eDf S 2SD tihit 2 3 2b2. 2D bef Heb 22Df I V@h@?Ui +i_U|L? tihit 3 ff fS bDH eH2 be tihit e 3 2.e SSH 2e. 3Se fbD tihit D 3 bDf SS2 eDb H eSf

5ihit hiThiti?|t L?_@) |L L?_@) hi|h?tc tihit 2 hiThiti?|t Ait_@) |L Ait_@) hi|h?tc i|U W? |t @)c W Lh! | ?L?Lih*@TT?} hi|h?t | @*4Lt| @** @|LULhhi*@|L? hi4Li_

Wkh ryhuodsslqj qdwxuh ri wkh uhwxuqv +lq wkh whvw shulrg, reylrxvo| lqgxfhv ghshqghqfhv lq wkh uhwxuq vhulhv deryh1 Wr vwxg| wkh hhfw ri wklv rq wkh uhodwlyh khgjh shuirupdqfh/ Wdeoh 9 vkrzv wkh vdph hqwulhv dv Wdeoh 7/ exw qrz fdofxodwhg iru qrq0ryhuodsslqj uhwxuq vhulhv zkhuh doprvw doo dxwrfruuhodwlrq lq wkh uhwxuqv lv uhpryhg1 Iurp wkh yh glhuhqw whvw vhulhv lw fdq eh vhhq krz wkh frqfoxvlrqv gudzq iurp Wdeoh 7 uhpdlq ydolg1 Doo wkh glhuhqw khgjhv v|vwhpdwlfdoo| uhgxfh wkh sruwirolr yduldqfh frpsduhg wr wkh vsrw yduldqfh hyhq wkrxjk wkh uhgxfwlrq lv pxfk

vpdoohu iru vrph vhulhv +iru lqvwdqfh vhulhv 7, wkdq iru rwkhuve_{1 Rqfh pruh/ hyhq iru wkh qrq0}

ryhuodsslqj uhwxuq vhulhv/ wkh qdlyh khgjh dqg wkh ROV khgjh shuirup ehwwhu wkdq wkh frqglwlrqdo khgjhv1

Dv d qdo yduldwlrq ri wklv wkhph/ wkh 79< revhuydwlrq orqj whvw shulrg lv vsolw lqwr wkh wkuhh

e_{Ai h|L}L?@* B+O i_}i @U|@**) ?Uhi@tit |i @h@?Ui uLh |i uLh| ?L?Lih*@TT?} tihit}

(16)

Wdeoh := Xqfrqglwlrqdo sruwirolr uhwxuq yduldqfh dqg shufhqwdjh yduldqfh uhgxfwlrq rxw0ri0 vdpsoh frpsduhg wr wkh qrq0khgjhg vsrw srvlwlrq1 Wkh wkuhh vxeshulrgv1

5TL| @i w5 WB+O B+O Df_@)t tMTihL_ ffH fff fff2 ffff fff2 ffe V@h@?Ui tMTihL_ 2 ff.S ff.2 ffDe ff.f ffHH ff.e tMTihL_ ff.S fffS ff2 ff2D fff ff

tMTihL_ 3 .2D DDH Hf DbH Hb I V@h@?Ui +i_U|L? tMTihL_ 2 3 fbb Sfe D2 3fb fe tMTihL_ 3 SSb efH efSf Sf DD.

Ai |hii tMTihL_t ULhhitTL?_ |L |i |hii |4i TihL_t Lu i^@* *i?}| bb.2f |L bbHf.2c bbHf.2e |L bbbffHc @?_ bbbffb |L bbbf2

vxeshulrgv ri htxdo ohqjwk1 Dv fdq eh vhhq lq Wdeoh :/ wkh khgjlqj shuirupdqfh glhuv vrphzkdw ehwzhhq wkh wkuhh vxeshulrgv exw iru doo khgjhv dqg wlph shulrgv/ wkh khgjhg srvlwlrqv ydu| ohvv wkdq wkh xqkhgjhg vsrw srvlwlrq1 Lq sduwlfxodu/ iru wkh vshfldo fdvh ri wkh Ruwkrjrqdo JDUFK khgjh/ lw fdq fohduo| eh vhhq krz wkh shuirupdqfh ghwhulrudwhv lq shulrg wzr> suredeo| gxh wr wkh kljk uhwxuq yduldqfh lq wklv shulrg1 Wkh kljk yrodwlolw| vsloov ryhu wr erwk khgjh udwlrv dqg sruwirolr uhwxuqv dqg/ dv phqwlrqhg deryh/ wkh shuirupdqfh ri wkh Ruwkrjrqdo JDUFK whfkqltxh lv sduwlfxoduo| vhqvlwlyh wr kljko| yrodwloh wlph shulrgv1

Lw kdv ehhq vkrzq krz wkh qrq0khgjhg vsrw srvlwlrq lv/ ryhudoo/ pruh yrodwloh wkdq wkh khgjh sruwirolrv/ lqglfdwlqj krz khgjlqj vsrw srvlwlrqv zlwk ixwxuhv frqwudfwv rq wkh Qruglf Srzhu H{fkdqjh fdq eh surwdeoh iru d yduldqfh0plqlpl}lqj wudghu1 Wr ixuwkhu hydoxdwh wkh shuirupdqfh ri wkh glhuhqw khgjhv/ L kdyh fkrvhq wr orrn dw dqrwkhu shuirupdqfh phdvxuh> krz riwhq wkh zhhno| sruwirolr uhwxuq lv dfwxdoo| vpdoohu +lq dq devroxwh vhqvh, wkdq wkh zhhno| vsrw uhwxuq1 Lq Wdeoh ;/ L frxqw wkh qxpehu ri wlphv +rxw ri 79<, wkh devroxwh zhhno| uhwxuq ri wkh

khgjhg srvlwlrqv lv vpdoohu wkdq wkh devroxwh zhhno| vsrw uhwxuqD_{1 Zkloh wkh qdlyh khgjh qrz}

shuirupv uhodwlyho| zruvh/ wkh wzr JDUFK khgjhv shuirup htxdoo| zhoo dv wkh ROV khgjh1 Hyhq wkrxjk wkh prylqj dyhudjh khgjh lv mxvw voljkwo| ehwwhu wkdq wkh qdlyh khgjh/ lw lv fohdu krz

wkh frqglwlrqdo khgjhv whqg wr uhgxfh wkh yduldqfh dv riwhq dv wkh xqfrqglwlrqdo khgjhv/ hyhq

li wkh|/ rq dyhudjh/ gr qrw uhpryh dv pxfk ri wkh yduldelolw| dv wkh xqfrqglwlrqdo khgjhv1 Lw

vkrxog dovr eh qrwlfhg wkdw wkh sruwirolr uhwxuqv duh dfwxdoo| odujhu wkdq wkh vsrw uhwxuqv lq

D_{At t @? @*|ih?@|i 4i@thi Lu |i @h@M*|) Lu |i _gihi?| TLh|uL*Lt Ai *@h}i @h@?Ui Lu @ T@h|U*@h}

TLh|uL*L 4}| Mi _i |L @ t4@** ?4Mih Lu ih) *@h}i hi|h?tc ii? |L} 4Lt| Lu |i hi|h?t @hi t4@**ih |@? |i L|ih TLh|uL*Lt 5U @ TLh|uL*L tL*_ TihuLh4 hi*@|i*) Mi||ih | |t @*|ih?@|i @h@M*|) 4i@thi

(17)

Wdeoh ;= Wkh qxpehu ri wlphv +rxw ri wkh 79< zhhno| uhwxuqv, wkdw wkh khgjh sruwirolrv devroxwh zhhno| uhwxuq lv vpdoohu +lq dq devroxwh vhqvh, wkdq wkh devroxwh zhhno| vsrw uhwxuq1

@i w5 WB+O B+O Df_@)t ?4Mih Lu |4it 2Hf fS fS fD 2H

I Lu |i u** t@4T*i Db.f SD2D SD2D SDf Dbb

derxw 68 wr 73( ri wkh zhhnv1

Vr idu/ zh fdq frqfoxgh wkdw lw kdv ehhq srvvleoh wr xvh ixwxuhv khgjhv rq Qrug Srro wr uhgxfh wkh yduldqfh lq wkh Qruglf hohfwulflw| pdunhw lq wkh odvw wzr |hduv/ zkloh wkh shuirupdqfh ri wkh glhuhqw khgjh sruwirolrv grhv qrw jhqhudoo| glhu vljqlfdqwo| iurp hdfk rwkhu dqg dovr ghshqgv rq wkh fkrlfh ri hydoxdwlrq phdvxuh dv zhoo dv wkh wlph shulrg1 Wkh idluo| zhdn shuirupdqfh ri wkh pruh hoderudwh JDUFK khgjhv frpsduhg wr wkh vlpsoh ROV khgjh pljkw eh h{sodlqhg e| hvwlpdwlrq sureohpv ru wkh idfw wkdw JDUFK prghov gr qrw dozd|v shuirup dv zhoo rxw0 ri0vdpsoh dv lq0vdpsoh1 Wkhuh duh qr lqglfdwlrqv ri vhyhuh hvwlpdwlrq sureohpv/ krzhyhu/ dqg wkh sureohpv dvvrfldwhg zlwk iruhfdvwv iurp JDUFK prghov hvwlpdwhg rq gdlo| gdwd vkrxog eh txlwh olplwhg dw vxfk vkruw krul}rqv dv rqh zhhn1 Zkhq lw frphv wr Ruwkrjrqdo JDUFK/ zklfk kdv sulpdulo| ehhq ghyhorshg iru odujh kljko| fruuhodwhg pxowlglphqvlrqdo sureohpv/ wkh zhdn shuirupdqfh frxog sduwo| eh h{sodlqhg e| d euhdngrzq ri wkh ruwkrjrqdol}dwlrq whfkqltxh lq shulrgv ri kljk yrodwlolw| dqg dv|pphwulfdoo| ehkdylqj zhdno| fruuhodwhg dvvhwv1

e Ai L?_|L?@* V@h@?Ui

Vwxg|lqj wkh uhgxfwlrq ri wkh frqglwlrqdo lqvwhdg ri wkh xqfrqglwlrqdo yduldqfh jlyhv vrphzkdw glhuhqw uhvxowv1 Dvvxplqj wkdw wkh wuxh uhwxuq surfhvvhv/ dqg wkh frqglwlrqdo fryduldqfh pdwul{/ duh jhqhudwhg e| hlwkhu ri wkh wzr JDUFK prghov jlyhv xv wkh srvvlelolw| wr frpsduh wkh uhodwlyh shuirupdqfh ri wkh gdwd0jhqhudwlqj JDUFK prgho dqg wkh rwkhu prghov lq plqlpl}lqj wkh frqglwlrqdo yduldqfh +Edloolh dqg P|huv +4<<4,/ Vhskwrq +4<<6, dqg Ehud/ Jdufld dqg Urk +4<<:,,1 Khgjlqj wkh vsrw srvlwlrq hdfk gd| lq wkh whvw shulrg dqg wdnlqj wkh dyhudjh ydoxh ri wkh frqglwlrqdo yduldqfh ri wkh vsrw dqg khgjh sruwirolr uhwxuqv/ surylghv d phdvxuh iru hdfk sruwirolr wkdw vkrxog eh dv vpdoo dv srvvleoh1

Lq Wdeoh </ wkh +dyhudjh, frqglwlrqdo yduldqfhv dqg yduldqfh uhgxfwlrqv +rxw0ri0vdpsoh, ri wkh glhuhqw khgjhv frpsduhg wr wkh rshq vsrw srvlwlrq duh suhvhqwhg iru wzr glhuhqw fkrlfhv ri

xqghuo|lqj fryduldqfh pdwul{S_{1 Wkh frqvwdqw fruuhodwlrq JDUFK prgho lv +qrw xqh{shfwhgo|,}

S_{W? A@M*it bc fc @?_ |i TihUi?|@}i hi_U|L? Lu |i @ih@}i ELih |i |it| TihL_t UL?_|L?@* @h@?Uit}

(18)

Wdeoh <= Sruwirolr uhwxuq frqglwlrqdo yduldqfh +dyhudjh ydoxh ryhu wkh whvw shulrg, dqg shufhqwdjh uhgxfwlrq ri wklv dyhudjh frqglwlrqdo yduldqfh rxw0ri0vdpsoh frpsduhg wr wkh qrq0khgjhg vsrw srvlwlrq1 Ryhuodsslqj frqglwlrqdo zhhno| sruwirolr yduldqfhv1

I V@h@?Ui +i_U|L?c WB+O L @|h 3 3. SS . D 3ff. I V@h@?Ui +i_U|L?c B+O L @|h 3 bSD .2 DH2 fS

Wdeoh 43= Shufhqwdjh uhgxfwlrq ri wkh frqglwlrqdo sruwirolr yduldqfh +dyhudjh ydoxh ryhu wkh whvw shulrg, rxw0ri0vdpsoh frpsduhg wr wkh frqglwlrqdo vsrw yduldqfh1 Qrq0ryhuodsslqj frqglwlrqdo zhhno| sruwirolr yduldqfhv1

@i w5 WB+O B+O Df_@)t tihit 3.S S. . DD f. tihit 2 3.2 S2 .f De 3fS I V@h +i_U|L?c WB+O L @|h tihit 3He2 SD . e2. 3fDe tihit e 3Sb S2 .fb D22 3fe tihit D 3D.D Db .S D fe

tihit 3ffe b2. fS e. 2. tihit 2 3fD bfb .f D 2Df I V@h +i_U|L?c B+O L @|h tihit 2 ff2 ee . bH tihit e f b.e 2HS eHe 2.2 tihit D .H f2e SH HbS eSf

wkh ehvw prgho zkhq lw lv lwvhoi dvvxphg wr kdyh jhqhudwhg wkh gdwd1 Wkh ROV khgjh lv wkh vhfrqg ehvw/ grplqdwlqj wkh rwkhu JDUFK prgho/ Ruwkrjrqdo JDUFK1 Rq wkh rwkhu kdqg/ zkhq wkh Ruwkrjrqdo JDUFK prgho lv dvvxphg wr kdyh jhqhudwhg wkh gdwd lw lv dovr surgxflqj wkh ehvw khgjh1 Wklv wlph wkh elyduldwh JDUFK khgjh shuirupv ehwwhu wkdq wkh ROV khgjh1 Wkh udqnlqj ri wkh yhu| ehvw khgjhv qrw vxusulvlqjo| fkdqjhv zkhq fkdqjlqj wkh dvvxpswlrq ri wkh fryduldqfh pdwul{/ exw wkrvh khgjhv wkdw shuirup edgo| lq rqh fdvh/ duh dovr vkrzq wr shuirup edgo| lq wkh rwkhu fdvh1 Wkh ehvw khgjh lq wkh xqfrqglwlrqdo yduldqfh hydoxdwlrq/ wkh qdlyh khgjh/ lv qrz lqvwhdg wkh zruvw shuiruphu/ dqg zkloh wkh prylqj dyhudjh prgho hduolhu

t Thiti?|i_ W?t|i@_c *LL!?} @| |i @ih@}i Lu |i TihUi?|@}i hi_U|L?t Lih |i |it| TihL_t }it i @U|*) |i t@4i hi*@|i TihuLh4@?Ui @?_ hi*@|i h@?!?} Lu |i _gihi?| i_}i TLh|uL*Lt

(19)

Wdeoh 44= Sruwirolr uhwxuq frqglwlrqdo yduldqfh dqg shufhqwdjh uhgxfwlrq ri wkh frqglwlrqdo yduldqfh rxw0ri0vdpsoh frpsduhg wr wkh qrq0khgjhg vsrw srvlwlrq1 Wkh wkuhh vxeshulrgv1

5TL| @i w5 WB+O B+O Df_@)t tMTihL_ ffS ff.D ffD2 ffD2 ffDe ff.f L?_ V@h@?Uic tMTihL_ 2 ffbf ffe2 ffSS ffSf ff.f ffHS WB+O L @|h tMTihL_ ffbD ff22 ffH2 ffH ffHe ffb tMTihL_ ffSD ffDS ffeSb ffeD ffe2 ffSf L?_ V@h@?Uic tMTihL_ 2 ffS. ffDS ff2H fff ff2be ffDD B+O L @|h tMTihL_ ff2fe ff2. ffbf ffH. ffHe ffbH

tMTihL_ 3 3HH DDe DH2 eb 3DSS I V@h +i_U|L?c tMTihL_ 2 3 3D.f SS .Se Df . WB+O L @|h tMTihL_ 3 3bf. S.f .fb DDf 2f2 tMTihL_ 3 D.e f2 bD . f I V@h +i_U|L?c tMTihL_ 2 3 fS fDe .S bbD b B+O L @|h tMTihL_ 3 3S SHS H. bHf 2H.

Wdeoh 45= Wkh qxpehu ri wlphv wkdw wkh frqglwlrqdo khgjh sruwirolr yduldqfh lv vpdoohu wkdq wkh frqglwlrqdo vsrw yduldqfh +rxw ri wkh 79< zhhno| yduldqfhv,1

@i w5 WB+O B+O Df_@)t ?4Mih Lu |4itc WB+O L@h@?Ui @|h H eSH eSb eSe e. ?4Mih Lu |4itc B+O L@h@?Ui @|h .. eS e2H eSb 22

I Lu |i u** t@4T*ic WB+O L@h@?Ui @|h .2. bb.b ffff bHb .bb I Lu |i u** t@4T*ic B+O L@h@?Ui @|h ..e HH.f b2S ffff SHSS

shuiruphg dv zhoo dv wkh JDUFK prghov/ lw qrz eduho| uhgxfhv wkh yduldqfh dw doo1 Lq Wdeoh </ L dvvxph/ d sulrul/ wkdw uhwxuq vhulhv iroorz JDUFK prghov dqg wkh uhodwlyh udqnlqj ri wkh glhuhqw prghov lv wkhuhiruh ri qr pdmru lqwhuhvw> wkh wzr JDUFK prghov reylrxvo| grplqdwh wkh rwkhu prghov1 Lqvwhdg/ wkh irfxv vkrxog eh rq wkh devroxwh uhgxfwlrq lq yduldqfh frpsduhg wr wkh vsrw srvlwlrq/ dv zhoo dv wkh devroxwh shuirupdqfh ri wkh JDUFK prghov frpsduhg wr wkh vlpsohu prghov1 Iurp wklv/ lw vkrxog dsshdu zkhwkhu prghoolqj wkh khgjh udwlr lq wklv pdunhw zlwk JDUFK prghov lv zruwk zkloh1 Wkh dqvzhu wr wklv txhvwlrq qdoo| ghshqgv rq krz frvwo| d g|qdplf JDUFK khgjh lv/ lq whupv ri wudqvdfwlrq frvwv hwf1/ frpsduhg wr wkh vlpsohu vwdwlf khgjhv1

Dv lq wkh xqfrqglwlrqdo hydoxdwlrq lq wkh odvw vxevhfwlrq/ zh frqwlqxh e| orrnlqj dw qrq0 ryhuodsslqj uhwxuq vhulhv dv zhoo dv vxevdpsohv ri wkh zkroh whvw shulrg1 Lq Wdeohv 43 dqg 44/

(20)

zh vhh krz wkh uhvxowv iurp Wdeoh < uhpdlq vwdeoh erwk iru wkh qrq0ryhuodsslqj vhulhv dqg wkh

glhuhqw vxevdpsohv._{> wkh shuirupdqfh ri wkh glhuhqw khgjhv fkdqjhv yhu| olwwoh iurp vhulhv wr}

vhulhv lq Wdeoh 43 dqg hyhq li wkhuh lv vrph fkdqjh lq shuirupdqfh iurp vxevdpsoh wr vxevdpsoh lq Wdeoh 44/ wklv grhv qrw dhfw wkh uhodwlyh udqnlqj ri wkh glhuhqw khgjhv1

Lq d vlplodu zd| dv grqh lq Wdeoh ; iru wkh xqfrqglwlrqdo hydoxdwlrq/ L qrz orrn dw wkh qxpehu ri wlphv wkh frqglwlrqdo sruwirolr yduldqfh lv vpdoohu wkdq wkh qrq0khgjhg vsrw srvlwlrq yduldqfh ryhu wkh whvw shulrg1 Lq Wdeoh 45/ lw lv revhuyhg krz wkh udqnlqj iurp wkh hduolhu Wdeohv </ 43/ dqg 44 uhpdlqv xqfkdqjhg/ dqg wkdw wkh JDUFK prgho wkdw lv dvvxphg wr kdyh

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