Equities and Inequality

Seminar Paper No. 737 EQUITIES AND INEQUALITY

by

Alessandra Bonfiglioli

INSTITUTE FOR INTERNATIONAL ECONOMIC STUDIES

Stockholm University

Seminar Paper No. 737 Equities and Inequality

by

Alessandra Bonfiglioli

Papers in the seminar series are published on the internet in Adobe Acrobat (PDF) format.

Download from http://www.iies.su.se/

Seminar Papers are preliminary material circulated to stimulate discussion and critical comment.

May 2005

Institute for International Economic Studies

Stockholm University

Htxlwlhv dqg Lqhtxdolw| ^

Dohvvdqgud Erqjolrol LLHV/ Vwrfnkrop Xqlyhuvlw|

Pd| 44/ 5338

Devwudfw

Wklv sdshu vwxglhv wkh uhodwlrqvkls ehwzhhq lqyhvwru surwhfwlrq/ wkh ghyhorsphqw ri

qdqfldo pdunhwv dqg lqfrph lqhtxdolw|1 Lq wkh suhvhqfh ri pdunhw iulfwlrqv/ lqyhvwru surwhfwlrq surprwhv qdqfldo ghyhorsphqw e| udlvlqj frqghqfh dqg uhgxflqj wkh frvwv ri h{whuqdo qdqflqj1 Ghyhorshg qdqfldo v|vwhpv vsuhdg ulvnv dprqj qdqflhuv dqg upv/ doorfdwlqj wkhp wr wkh djhqwv ehdulqj wkhp wkh ehvw1 Wkhuhiruh/ qdqfldo ghyhorsphqw sod|v wkh wzrirog uroh ri hqfrxudjlqj djhqwv wr xqghuwdnh ulvn| hqwhusulvhv dqg surylglqj wkhp zlwk lqvxudqfh1 E| lqfuhdvlqj wkh qxpehu ri ulvn| surmhfwv/ lw udlvhv lqfrph lqhtxdolw|1 E| h{whqglqj lqvxudqfh wr pruh djhqwv/ lw uhgxfhv lw1 Dv d uhvxow/ wkh uhodwlrqvkls ehwzhhq qdqfldo ghyhorsphqw dqg lqfrph lqhtxdolw| lv kxps0 vkdshg1 Hpslulfdo hylghqfh iurp d furvv0vhfwlrq ri vl{w|0qlqh frxqwulhv/ dv zhoo dv d sdqho ri iw|0wzr frxqwulhv ryhu wkh shulrg 4<:905333/ vxssruwv wkh suhglfwlrqv ri wkh prgho1

MHO Fodvvlfdwlrq= G64/ H77/ J63/ R48/ R49

Nh|zrugv= Lqfrph lqhtxdolw|/ qdqfldo ghyhorsphqw/ fdslwdo pdunhw iulfwlrqv/ lq0 yhvwru surwhfwlrq/ lqvwuxphqwdo yduldeohv/ g|qdplf sdqho gdwd1

WL dp judwhixo wr Wruvwhq Shuvvrq dqg Ideul}lr ]lolerwwl iru jxlgdqfh dqg dgylfh/ dqg wr Jlqr Jdqfld iru khosixo frqyhuvdwlrqv1 L wkdqn Sklolssh Djklrq/ Vdoydwruh Fdsdvvr/ Iudqfhvfr Fdvhool/ Dpsdur Fdvwhooö Folphqw/ Jlrydqql Idydud/ Qlfrod Jhqqdlrol/ Mrkq Kdvvohu/ Doh{dqghu Oxgzlj/ Dqguhl Vkohlihu/ Mdxph Yhqwxud dqg vhplqdu sduwlflsdqwv dw Edqfr gh Hvsdôd/ Hxurshdq Fhqwudo Edqn/ VLIU/ Xqlyhuvlgdg Fduorv LLL gh Pdgulg/ Xqlyhuvlw| ri Dpvwhugdp/ Ohlfhvwhu dqg Vw1 Dqguhzv/ LLHV/ HQWHU Mdperuhh 5337/

Hfrqrplf Jurzwk dqg Glvwulexwlrq 5337 frqihuhqfh/ VHG 5337 Dqqxdo Phhwlqj/ HHD 5337 Dqqxdo Frqjuhvv/ 5337 Hxurshdq Zlqwhu Phhwlqj ri wkh Hfrqrphwulf Vrflhw|/ dqg DVVHW Dqqxdo Frqihuhqfh 5337 iru frpphqwv1 L dp judwhixo wr Fkulvwlqd Oùqqeodg iru hglwruldo dvvlvwdqfh1 Mdq Zdoodqghu*v dqg Wrp Khgholxv Uhvhdufk Irxqgdwlrq lv judwhixoo| dfnqrzohgjhg iru qdqfldo vxssruw1 Doo uhpdlqlqj huuruv duh plqh1 Frpphqwv duh zhofrph wr Dohvvdqgud1ErqjolrolCllhv1vx1vh

4 Lqwurgxfwlrq

D uhfhqw olwhudwxuh rq odz dqg qdqfh kdv vkrzq wkdw lqyhvwru surwhfwlrq sod|v d vljql0 fdqw uroh lq surprwlqj wkh ghyhorsphqw ri qdqfldo pdunhwv +vhh Dfhprjox dqg Mrkqvrq/

5336/ Od Sruwd hw do1/ 4<<: dqg 5336/ dqg Udmdq dqg ]lqjdohv/ 5335/ dprqj rwkhuv,1 Lq sduwlfxodu/ phdvxuhv dlphg dw lpsurylqj wudqvsduhqf| dqg hqirufhphqw ri qdqfldo frq0 wudfwv uhgxfh wkh frvwv ri rxwvlgh0qdqfh +vhh/ iru lqvwdqfh/ Vkohlihu dqg Zroihq}rq/ 5335, dqg vkliw ulvnv rqwr wkh sduwlhv wkdw fdq ehvw ehdu wkhp +vhh Fdvwur hw do1/ 5337,1 Vhyhudo zrunv kdyh uhfrjql}hg wkh lpsruwdqfh ri qdqfldo ghyhorsphqw iru ydulrxv pdfurhfrqrplf yduldeohv vxfk dv jurzwk dqg surgxfwlylw| +vhh/ Ghpluj ê0Nxqw dqg Ohylqh/ 5334 iru d vxu0 yh|,1 Krzhyhu/ wklv jurzlqj olwhudwxuh kdv qrw uhfrjql}hg wkdw wkh fkdqjhv lq ulvn0wdnlqj ehkdylru ri lqyhvwruv dqg upv/ dvvrfldwhg zlwk ehwwhu vkduhkroghu surwhfwlrq/ pd| dovr dhfw lqfrph lqhtxdolw|1 Wkh gdwd vxjjhvw lqghhg wkdw wkhvh yduldeohv duh fruuhodwhg1 Dv vkrzq e| Wdeoh 4/ iru d vdpsoh ri vl{w|0hljkw frxqwulhv revhuyhg ehwzhhq 4<;3 dqg 5333/

wkh Jlql frh!flhqw ri wkh qhw lqfrph glvwulexwlrq lv rq dyhudjh 43( kljkhu +dw wkh 8(

vljqlfdqfh ohyho, lq frxqwulhv zkhuh qdqfldo pdunhwv duh pruh ghyhorshg1

⁴

Frqwuroolqj iru dyhudjh kxpdq fdslwdo/ rqh ri wkh prvw lpsruwdqw ghwhuplqdqwv ri lqhtxdolw|/ wklv gli0 ihuhqfh ulvhv wr 47( +qrz vljqlfdqw dw wkh 4( vljqlfdqfh ohyho,1

⁵

Wdeoh 4 dovr vkrzv wkdw frxqwulhv zlwk pruh ghyhorshg qdqfldo pdunhwv whqg wr kdyh ehwwhu lqvwlwxwlrqv dlphg dw lqyhvwru surwhfwlrq1

⁶

Wklv sdshu lqyhvwljdwhv wkh olqn ehwzhhq lqyhvwru surwhfwlrq/ qdqfldo ghyhorsphqw dqg lqhtxdolw|/ erwk wkhruhwlfdoo| dqg hpslulfdoo|1 Lw sursrvhv d vlpsoh prgho zkhuh lqyhvwru surwhfwlrq surprwhv qdqfldo ghyhorsphqw/ wkhuhe| lpsurylqj ulvn vkdulqj1 Wklv lqgxfhv pruh ulvn0wdnlqj lq wkh hfrqrp| dqg ehwwhu lqvxudqfh rq lqglylgxdo hduqlqjv/

zklfk dhfw lqfrph lqhtxdolw| lq rssrvlwh zd|v1 Wkh uhodwlrqvklsv suhglfwhg e| wkh prgho duh frqiurqwhg zlwk wkh gdwd1

Wr irupdol}h wkhvh lghdv/ L frqvwuxfw d jhqhudo htxloleulxp wzr0shulrg ryhuodsslqj jhq0 hudwlrqv prgho1 Djhqwv duh ulvn dyhuvh dqg khwhurjhqhrxv lq wkhlu hqwuhsuhqhxuldo delolw|1 Wkh| idfh d fkrlfh ehwzhhq d vdih dqg d ulvn| whfkqrorj|/ dqg hqwuhsuhqhxuldo delolw| di0

4L uhihu wr wkh udwlr ri vwrfn pdunhw fdslwdol}dwlrq ryhu fuhglw wr wkh sulydwh vhfwru dv dq lqglfdwru ri

qdqfldo ghyhorsphqw1 Wklv udwlr phdvxuhv wkh zhljkw ri htxlw|0qdqfh rq ryhudoo eruurzlqjv/ dqg lv zhoo vxlwhg wr fdswxuh wkh ulvn vkdulqj ixqfwlrq ri qdqfldo ghyhorsphqw1 Lw lv iuhtxhqwo| xvhg iru wklv sxusrvh lq wkh olwhudwxuh +vhh Udmdq dqg ]lqjdohv/ 5335,1

5JlqlKF lq Wdeoh 4 lv Jlql3 KF/ zkhuh  lv wkh ROV hvwlpdwh iurp wkh uhjuhvvlrq= Jlqll ' n

KFln l1 KF lv kxpdq fdslwdo/ sur{lhg e| wkh vkduh ri wkh srsxodwlrq djhg deryh 58zlwk vrph vhfrqgdu| hgxfdwlrq +iurp Eduur dqg Ohh/ 5334,1 Wkh uhvxowv gr qrw fkdqjh li L dovr frqwuro iru wkh Nx}qhwv* k|srwkhvlv e| lqfoxglqj uhdo shu fdslwd JGS dqg lwv vtxduh/ dqg iru jhrjudsk| e| lqfoxglqj gxpp| yduldeohv1 Wkhvh uhvxowv duh dydlodeoh xsrq uhtxhvw1

6Wkh lqgh{ ri lqyhvwru surwhfwlrq lv wdnhq iurp Od Sruwd hw do1 +5336, dqg dffrxqwv iru phdvxuhv dlphg dw wudqvsduhqf| +dffrxqwlqj dqg glvforvxuh uhtxluhphqwv, dqg wkh hqirufhphqw ri sulydwh frqwudfwv1

Wdeoh 4

Lqhtxdolw|/ qdqfldo ghyhorsphqw dqg lqvwlwxwlrqv 0 phdq frpsdulvrqv

Orz Vpfds Kljk Vpfds Gl

Jlql 6:=7;

E=e2

74=63

E=HD

6=;4<

E2= WW

Jlql

KF

77=3:

E=b

83=43

E=eS

9=357

E=HH

WWW

lqyhvwrubsu

^Ed

6=:<

E=eS

8=<8

E=S.

5=487

E=.HH

WWW

Revhuydwlrqv 74 5:

Qrwh1 D frxqwu| lv odehohg Kljk Vpfds li lwv udwlr ri vwrfn pdunhw fdslwdol}dwlrq ryhu fuhglw wr wkh sulydwh vhfwru lv deryh furvv0vhfwlrqdo dyhudjh1 Wkh uhvxwov duh urexvw wr wkh dgrswlrq ri wkh phgldq dv d wkuhvkrog1

Jlql

frh!flhqwv uhihu wr wkh glvwulexwlrq ri qhw shu fdslwd lqfrph/

Jlql

KF duh frqwuroohg iru kxpdq fdslwdo1 Phdqv dqg glhuhqfhv duh uhsruwhg iru hdfk yduldeoh/

zlwk vwdqgdug huuruv lq sduhqwkhvlv1 ^WWW dqg ^WW lqglfdwh wkdw wkh glhuhqfh lv srvlwlyh dw wkh 4 dqg 8shu fhqw vljqlfdqfh ohyho1 ^Edwkh vdpsoh lv uhgxfhg wr 4; dqg 57 frxqwulhv zlwk Orz dqg Kljk Vpfds/ uhvshfwlyho|1 Vdpsoh shulrg lv 4<;3053331

ihfwv wkh suredelolw| ri vxffhvv lq wkh ulvn| surmhfw1 L dvvxph wkdw qdqfldo pdunhwv duh vxemhfw wr lpshuihfwlrqv dulvlqj iurp wkh qrq0revhuydelolw| ri rxwsxw wr qdqflhuv dqg wkdw phdvxuhv ri lqyhvwru surwhfwlrq fdq eh dgrswhg wr dphqg wkhvh iulfwlrqv1 Lq sdu0 wlfxodu/ e| surprwlqj wudqvsduhqf|/ lqyhvwru surwhfwlrq pdnhv plvuhsruwlqj rxwsxw frvwo|

iru hqwuhsuhqhxuv1

⁷

Iru lqvwdqfh/ wklv frvw fdq eh wkrxjkw ri dv wkh h{wud0frpshqvdwlrq wkh dgylvru| up fkdujhv wr fhuwli| d idovlhg errn1 Ehwwhu jxdudqwhhv jhqhudwh pruh frqghqfh dprqj lqyhvwruv/ wkhuhe| pdnlqj wkhp pruh zloolqj wr ehdu ulvn dqg lqvxuh wkh hqwuhsuhqhxuv1 Lq wxuq/ lqyhvwruv fdq vsuhdg wkh lqglylgxdo ulvn e| kroglqj glyhuvlhg sruw0 irolrv ri ulvn| dfwlylwlhv1 Dv d uhvxow/ qdqfldo v|vwhpv zlwk vwurqjhu lqyhvwru surwhfwlrq doorz kljkhu ghjuhhv ri ulvn vkdulqj1 Ilqdoo|/ L uxoh rxw zhdowk khwhurjhqhlw|/ vr wkdw doo lqhtxdolw| lv gxh wr lglrv|qfudwlf idfwruv +delolw|,/ qdqfldo pdunhw frqglwlrqv dqg lqfrph ulvn1 Xqghu wkhvh dvvxpswlrqv/ ehwwhu lqyhvwru surwhfwlrq surprwhv qdqfldo ghyhorsphqw dqg dhfwv lqfrph lqhtxdolw| lq wkuhh zd|v1 +l, Lw lpsuryhv ulvn vkdulqj/ wkhuhe| uhgxflqj lqfrph yrodwlolw| iru d jlyhq vl}h ri wkh ulvn| vhfwru> +ll, lw udlvhv wkh vkduh ri wkh srsxodwlrq h{srvhg wr hduqlqj ulvn> dqg +lll, lw lqfuhdvhv wkh uhzdug wr delolw|1 +l, whqgv wr uhgxfh lqhtxdolw|/ zkloh lw lv lqfuhdvhg e| +ll, dqg +lll,1

Wkh pdlq uhvxow ri wkh sdshu lv wkdw lqfrph lqhtxdolw| lv d kxps0vkdshg ixqfwlrq ri lqyhvwru surwhfwlrq dqg qdqfldo ghyhorsphqw1 Dq| lpsuryhphqw xsrq d orz ohyho lqyhvwru surwhfwlrq lqfuhdvhv ulvn wdnlqj pruh wkdq ulvn vkdulqj/ wkhuhe| gulylqj lqhtxdolw| xs1 Krzhyhu/ zkhq lqyhvwru surwhfwlrq lv vx!flhqwo| kljk/ dq| ixuwkhu lpsuryhphqw lv pruh

7Dovr lq Djklrq hw do1 +5338,/ Fdvwur hw do1 +5337, dqg Odfnhu dqg Zhlqehuj +4<;<, grhv lqyhvwru surwhfwlrq wdnh wkh irup ri d klglqj frvw1 Lq wklv sdshu/ olnh lq wkh wzr odwwhu/ wkh frvw lv sursruwlrqdo wr wkh klgghq dprxqw/ zkloh lq wkh uvw/ lw htxdov d iudfwlrq ri wkh lqlwldo lqyhvwphqw1

hhfwlyh rq ulvn vkdulqj wkdq ulvn wdnlqj/ khqfh uhgxfhv lqfrph lqhtxdolw|1

Wr pdnh wkh suhglfwlrqv ri wkh prgho pruh hdvlo| whvwdeoh/ L dvvxph wkdw wkhuh duh rqo| wzr qdqfldo lqvwuxphqwv/ zklfk L odeho htxlw| dqg ghew1 Htxlw| pdnhv ulvn vkdu0 lqj ehwzhhq lqyhvwruv dqg hqwuhsuhqhxuv srvvleoh/ ghshqglqj rq wkh ghjuhh ri lqyhvwru surwhfwlrq/ zkloh ghew grhv qrw1

⁸

Lq wklv zd|/ qdqfldo ghyhorsphqw lv fdswxuhg e| wkh wklfnqhvv ri wkh htxlw| pdunhw/ zklfk lv dovr d frpprq hpslulfdo phdvxuh ri qdqfldo ghyhorsphqw +vhh Udmdq dqg ]lqjdohv/ 5335/ dprqj rwkhuv,1 Wkhq/ wkh whvwdeoh suhglf0 wlrqv ri wkh prgho zloo eh wkdw +4, vwrfn pdunhw vl}h jurzv zlwk lqyhvwru surwhfwlrq/ +5, wkhuh lv d kxps0vkdshg uhodwlrqvkls ehwzhhq lqfrph lqhtxdolw| dqg wkh wklfnqhvv ri wkh htxlw| pdunhw/ dqg +6, lqyhvwru surwhfwlrq dhfwv lqhtxdolw| rqo| wkurxjk vwrfn pdunhw ghyhorsphqw1 L surylgh hpslulfdo hylghqfh iurp d furvv0vhfwlrq ri vl{w|0qlqh frxqwulhv dqg d sdqho ri iw|0wzr frxqwulhv ryhu wkh shulrg 4<:905333 lq vxssruw ri wkhvh uhvxowv1

Wkh frqwulexwlrq ri wklv sdshu lv uhodwhg wr wkuhh pdlq vwudqgv ri olwhudwxuh1 Dfhprjox dqg Mrkqvrq +5336,/ dv zhoo dv Od Sruwd hw do1 +4<<:/ 4<<;/ 4<<</ 5336,/ vkrz wkdw lqvwlwxwlrqv dlphg dw frqwudfwlqj surwhfwlrq +vxfk dv wkrvh phdvxuhg e| lqyhvwrubsu lq Wdeoh 4, surprwh wkh ghyhorsphqw ri vwrfn pdunhwv/ exw kdyh frqwuryhuvldo hhfwv rq hfrqrplf shuirupdqfh1 Qrqh ri wkhvh vwxglhv kdv frqvlghuhg lqfrph lqhtxdolw|1

Pdq| sdshuv +Ehfn dqg Ohylqh/ 5335/ Ohylqh/ 5335/ Ohylqh dqg ]huyrv/ 4<<;/ Udmdq dqg ]lqjdohv/ 4<<; dprqj rwkhuv, surylgh hpslulfdo hylghqfh rq wkh olqn ehwzhhq qdqfldo ghyhorsphqw dqg pdfurhfrqrplf yduldeohv/ vxfk dv jurzwk/ lqyhvwphqwv dqg surgxfwlylw|/

exw qrqh ri wkhp kdv dgguhvvhg glvwulexwlrqdo lvvxhv1

⁹

Wkhruhwlfdo frqwulexwlrqv e| Djklrq dqg Erowrq +4<<:,/ Edqhumhh dqg Qhzpdq +4<<6,/

Jdoru dqg ]hlud +4<<6,/ Juhhqzrrg dqg Mrydqrylf +4<<3,/ dqg Slnhww| +4<<:,/ dprqj rwkhuv/ kdyh sursrvhg h{sodqdwlrqv iru wkh uhodwlrqvkls ehwzhhq qdqfldo ghyhorsphqw/

lqhtxdolw| dqg jurzwk1 Lq prvw ri wkhvh prghov/ lqfrph lqhtxdolw| ruljlqdwhv iurp khw0 hurjhqhlw| lq wkh lqlwldo zhdowk glvwulexwlrq/ sdluhg zlwk fuhglw pdunhw iulfwlrqv1 Dv wkh srruhvw duh vxemhfw wr fuhglw frqvwudlqwv/ wkh| duh suhyhqwhg iurp pdnlqj h!flhqw lqyhvw0 phqwv lq wkh prvw surgxfwlyh dfwlylwlhv1

^:

Ryhu wlph/ fdslwdo dffxpxodwlrq ghwhuplqhv wkh g|qdplfv ri zhdowk dqg lqfrph1 L ghsduw iurp wklv dssurdfk e| irfxvlqj rq d glhuhqw vrxufh ri h{0dqwh khwhurjhqhlw|/ qdpho| hqwuhsuhqhxuldo delolw|/ dqg e| ghvfulelqj d qhz

8Wklv odeholqj lv edvhg rq wkh frpprq glvwlqfwlrq ehwzhhq vwdqgdug htxlw| dqg ghew frqwudfwv1 Krz0 hyhu/ dv wkh qdqfldo vwuxfwxuh ehfrphv pruh ghyhorshg/ d ydulhw| ri vrsklvwlfdwhg ghew frqwudfwv duh rhuhg wr dovr dfklhyh ehwwhu ulvn vkdulqj1 Wkhvh lqvwuxphqwv/ olnh yhqwxuh fdslwdo/ iru lqvwdqfh/ fdq eh dvvlplodwhg wr htxlw| lq wkh prgho1

9Doo wkhvh zrunv dffrxqw iru wkh lq xhqfh ri wkh ohjdo hqylurqphqw rq qdqfldo vwuxfwxuh1 Lq sduwlfxodu/

qdqfldo yduldeohv duh lqvwuxphqwhg zlwk ohjdo ruljlqv/ zklfk Dfhprjox dqg Mrkqvrq +5336, dqg Od Sruwd hw do1 +4<<:/ 4<<;/ 4<<</ 5336, xvhg dv lqvwuxphqwv iru frqwudfwlqj surwhfwlrq1

:Wkh fuhglw frqvwudlqw fdq ghulyh iurp wkh qrq0revhuydelolw| ri sk|vlfdo rxwsxw dv lq Edqhumhh dqg Qhzpdq +4<<5, dqg Jdoru dqg ]hlud +4<<6,/ ru hruw dv lq Djklrq dqg Erowrq +4<<:, dqg Slnhww| +4<<:,1

phfkdqlvp wudqvodwlqj glhuhqfhv lq delolw| lqwr lqfrph lqhtxdolw| wkdw lv lqghshqghqw ri dffxpxodwlrq1 Lq sduwlfxodu/ L dvvxph surgxfwlylw| wr eh d ixqfwlrq ri delolw| dqg wkdw hqwuhsuhqhxuv kdyh qr zhdowk iru vwduwlqj wkhlu upv1 E| hqfrxudjlqj lqyhvwruv wr hq0 vxuh hqwuhsuhqhxuv/ ehwwhu lqyhvwru surwhfwlrq doorzv wkh pruh wdohqwhg wr xqghuwdnh ulvn|

surmhfwv/ zkrvh sd|rv ghshqg rq delolw|1 Khwhurjhqhlw| lq surgxfwlylw|/ wkh h{whqw ri ulvn vkdulqj dqg wkh vl}h ri wkh ulvn| vhfwru xowlpdwho| ghwhuplqh wkh lqfrph glvwulexwlrq1 Lq wklv uhvshfw/ wkh dssurdfk ri Dfhprjox dqg ]lolerwwl +4<<<, lv forvhu wr plqh1 Lq wkhlu sdshu/ lqfrph lqhtxdolw| lv jhqhudwhg e| pdqdjhuldo lqfhqwlyhv/ zklfk ghshqg rq ulvn vkdu0 lqj/ qrw e| h{0dqwh zhdowk khwhurjhqhlw|1 Wkhuh/ ulvn vkdulqj hyroyhv hqgrjhqrxvo| ryhu wlph dv d frqvhtxhqfh ri lqirupdwlrq dffxpxodwlrq/ zkloh khuh lw ydulhv rqo| dv dq hhfw ri h{rjhqrxv fkdqjhv lq lqyhvwru surwhfwlrq1

Wkh rqo| hpslulfdo dvvhvvphqwv ri wkh uhodwlrqvkls ehwzhhq qdqfldo ghyhorsphqw dqg lqfrph lqhtxdolw| duh/ wr p| nqrzohgjh/ Fodunh hw do1 +5336, dqg Ehfn hw do1 +5337,1 Erwk qg hylghqfh ri d qhjdwlyh/ wkrxjk qrq urexvw/ uhodwlrqvkls ehwzhhq wkh ghjuhh ri

qdqfldo lqwhuphgldwlrq dqg lqfrph lqhtxdolw|1 Wkh pdlq glhuhqfh zlwk uhvshfw wr p|

hpslulfdo dqdo|vlv od|v lq wkh phdvxuh ri qdqfldo ghyhorsphqw1 Lqvwhdg ri qdqfldo ghswk/

L xvh wkh vl}h ri wkh htxlw| pdunhw uhodwlyh wr wrwdo fuhglw/ zklfk vhhpv ehwwhu vxlwhg wr dffrxqw iru wkh ghjuhh ri ulvn vkdulqj doorzhg e| d qdqfldo v|vwhp1

Wkh uhpdlqghu ri wkh sdshu lv rujdql}hg dv iroorzv1 Vhfwlrq 5 suhvhqwv wkh prgho dqg lwv vroxwlrq lq sduwldo htxloleulxp +d vpdoo rshq hfrqrp|,1 Lq vhfwlrq 6/ L vwxg|

dqdo|wlfdoo| dqg e| phdqv ri qxphulfdo vroxwlrq krz lqfrph lqhtxdolw| ydulhv zlwk lqyhvwru surwhfwlrq dqg qdqfldo ghyhorsphqw1 Vhfwlrq 7 dujxhv wkdw wkh pdlq uhvxowv krog lq jhqhudo htxloleulxp +d forvhg hfrqrp|,1 Wklv yhuvlrq ri wkh prgho lv h{whqvlyho| ghvfulehg lq wkh dsshqgl{1 Vhfwlrq 8vkrzv wkdw hpslulfdo hylghqfh iurp d furvv0vhfwlrq ri vl{w|0qlqh frxqwulhv dqg d sdqho ri iw|0wzr frxqwulhv ryhu wkh shulrg 4<:905333 vxssruwv wkh pdlq uhvxowv ri wkh prgho1 Vhfwlrq 9 frqfoxghv1

5 Wkh prgho

514 Vhw xs

Wkh prgho hfrqrp| lv srsxodwhg e| wzr0shulrg ryhuodsslqj jhqhudwlrqv ri ulvn0dyhuvh djhqwv1 Wkhuh lv qr srsxodwlrq jurzwk dqg wkh phdvxuh ri hdfk frkruw lv qrupdol}hg wr rqh1 Iru vlpsolflw|/ suhihuhqfhv duh uhsuhvhqwhg e| wkh iroorzlqj xwlolw| ixqfwlrq=

X

w

@ orj +f

w

, .  orj +f

wn

, =

Vhfrqg0shulrg xwlolw| lv glvfrxqwhg dw wkh udwh  5 +3> 4, =

πι ,r_{t+ 1}

{S a fe,R isk y}

b o rro w w_it {s_it,c_it}

c_{it+ 1}= (1 + r_{t+ 1})s_it

Y o u n g O ld

d ie

y_it in v e st s_it

Iljxuh 4= Wlplqj ri wkh prgho

Dw dq| wlph w/ hdfk |rxqj djhqw lq jurxs l lv eruq zlwk qr zhdowk dqg delolw| 

l

5

^3> 4`/ gudzq iurp glvwulexwlrq J +,1 Hdfk jurxs lv srsxodwhg e| d frqwlqxxp j+, ri lqglylgxdov1 Lq wkh uvw shulrg/ djhqwv zrun dv vhoi0hpsor|hg hqwuhsuhqhxuv surgxflqj dq lqwhuphgldwh jrrg/ dqg doorfdwh wkhlu lqfrph dprqj frqvxpswlrq dqg vdylqjv/ v+,1 Zkhq rog/ wkh| lqyhvw wkhlu vdylqjv dqg frqvxph doo wkh uhwxuqv ehiruh g|lqj1 Zkhq lqyhvwlqj/

wkh| fdq fkrrvh ehwzhhq vdih ordqv/ |lhoglqj d uhwxuq u

wn

/ dqg sruwirolrv ri ulvn| dvvhwv1 Wkhuh duh qr ehtxhvwv1

51414 Lqwhuphgldwh jrrgv vhfwru

Wzr surgxfwlrq surfhvvhv duh dydlodeoh wr hdfk |rxqj djhqw= d vdih dqg d ulvn| rqh1 Wkh vdih whfkqrorj| grhv qrw hpsor| fdslwdo/ zkloh wkh ulvn| rqh uhtxluhv d {hg xqlw lqyhvwphqw1 Wkhuhiruh/ wkh lqglylgxdo whfkqrorjlfdo fkrlfh lv dqdorjrxv wr dq rffxsdwlrqdo fkrlfh zkhuhe| vrph djhqwv ehfrph zrunhuv dqg rwkhuv hqwuhsuhqhxuv1 Lq olqh zlwk hpslulfdo qglqjv/ L dvvxph wkdw wkh ulvn| dfwlylw|/ li vxffhvvixo/ kdv kljkhu uhwxuqv wkdq wkh vdih rqh dqg wkdw wkh suredelolw| ri vxffhvv ghshqgv rq wkh delolw| ri wkh hqwuhsuhqhxu1

^;

Iru vlpsolflw|/ dqg zlwkrxw pxfk orvv ri jhqhudolw|/ L dvvxph wkdw delolw| rqo| dhfwv wkh suredelolw| ri vxffhvv dqg qrw wkh sd|rv1

^<

Lq sduwlfxodu/ surgxfwlrq lv jlyhq e|=

{

lw

@

; A A ? A A

=

E iru l uxqqlqj Vdih whfkqrorj|

D zlwk sure1 

l

*D zlwk sure1 4  

l

,

iru l uxqqlqj Ulvn| whfkqrorj|/

;Vhh Vfkloohu dqg Fuhzvrq +4<<:,/ dqg Idluo| dqg Uree +5336, iru hpslulfdo vwxglhv rq wkh ghwhuplqdqwv ri hqwuhsuhqhxuldo vxffhvv/ pdlqo| dprqj vpdoo upv1

<Delolw| fdq eh frqvlghuhg dv sod|lqj d wzrirog uroh1 Lw hqkdqfhv wkh fkdqfh ri vxffhhglqj lq ulvn|

hqwhusulvhv/ dv dvvxphg lq wkh prgho1 Exw lw pd| dovr udlvh surgxfwlylw| uhjdugohvv ri wkh ulvnlqhvv ri surmhfwv1 Lqwurgxflqj wklv vhfrqg hhfw lqwr wkh prgho zrxog qrw dhfw wkh uhvxowv1

zkhuh E ? D/ * 5 +3> 4, dqg vxffhvv lv l1l1g1 zlwklq hdfk jurxs1 Lw iroorzv wkdw wkhuh lv qr djjuhjdwh ulvn dqg wrwdo surgxfwlrq ri jurxs l htxdov j +

l

, E ru j +

l

, ^

l

. +4 

l

,*D`/

ghshqglqj rq wkh whfkqrorj|/ vdih ru ulvn|/ lq xvh1

51415 Ilqdo jrrg vhfwru

D krprjhqhrxv qdo jrrg \ / xvhg iru frqvxpswlrq dqg lqyhvwphqw/ lv surgxfhg e| frp0 shwlwlyh upv xvlqj fdslwdo dqg lqwhuphgldwh jrrgv1 Wkh lqwhuphgldwh jrrgv surgxfhg e| doo djhqwv duh shuihfw vxevwlwxwhv lq surgxfwlrq1 Wkh djjuhjdwh whfkqrorj| kdv wkh iroorzlqj Free0Grxjodv irup=

\

w

@ N

_{\ w}^

[

_w^3

> +4,

zkhuh [

w

lv wkh wrwdo dprxqw ri lqwhuphgldwh jrrgv/ zlwk d xqlw sulfh ri "

_w

/ dqg N

\ w

lv fdslwdo hpsor|hg lq wkh qdo jrrg vhfwru1 \

w

lv wkh qxphudluh1

51416 Ilqdqfldo vhfwru

Erwk qdo jrrg upv dqg ulvn| hqwuhsuhqhxuv qhhg wr eruurz fdslwdo iurp wkh rog wr surgxfh1 Lqirupdwlrq derxw whfkqrorj| +D/ E/ */ , dqg lqglylgxdo delolw| +

l

, lv sxeolf/

exw rxwvlgh qdqflhuv fdqqrw revhuyh wkh rxwfrph ri ulvn| dfwlylwlhv/ {

lw

1 Wzr qdqfldo lqvwuxphqwv/ htxlw| dqg ghew/ duh dydlodeoh1

Htxlw| lv prghohg dv iroorzv1 Xsrq uhfhlylqj rqh xqlw ri fdslwdo/ hdfk |rxqj lq jurxs l frpplwv wr sd|/ diwhu surgxfwlrq/ glylghqg sd|rxwv 

^k_lw

dqg 

^o_lw

lq fdvh ri vxffhvv dqg idloxuh/ uhvshfwlyho|1 Rqfh surgxfwlrq kdv rffxuuhg/ xqoxfn| hqwuhsuhqhxuv fdq rqo| uhwxuq wkh surplvhg dprxqw 

^o_lw

{

^o_lw

"

_w

1 Vxffhvvixo hqwuhsuhqhxuv/ lqvwhdg/ pd| plvuhsruw wkhlu uhdol}dwlrq ri {

lw

dqg sd| 

^o_lw

{

^o_lw

"

_w

/ suhwhqglqj wr eh lq wkh edg vwdwh1 Krzhyhu/ L dvvxph wkdw phdvxuhv ri vkduhkroghu surwhfwlrq pdnh plvuhsruwlqj frvwo|1 Iru hyhu| xqlw ri klgghq fdvk rz/ wkh hqwuhsuhqhxu lqfxuv d frvw s 5 ^3> 4`1 Vlqfh erwk delolw| dqg whfkqrorj| duh frpprq nqrzohgjh/ hlwkhu wkh hqwluh 

{

^k_lw

 {

^o_lw



ru qrwklqj lv klgghq/ vr wkdw wkh sd|r

iurp plvuhsruwlqj lv 

{

^k_lw

 

^o_lw

{

^o_lw



"

_w

 s 

{

^k_lw

 {

^o_lw



"

_w

1 Wuxwk0whoolqj lv udwlrqdo dv orqj dv lwv ydoxh lv dw ohdvw htxdo wr wkdw ri plvuhsruwlqj1 Wkhuhiruh/ wkh htxlw| frqwudfw 



^k_lw

> 

^o_lw

 pxvw vdwlvi| wkh lqfhqwlyh frpsdwlelolw| +LF, frqvwudlqw=

y k

4  

^k_lw



{

^k_lw

"

_w

> u

wn

l  y k

{

^k_lw

 

^o_lw

{

^o_lw



"

_w

 s 

{

^k_lw

 {

^o_lw



"

_w

> u

wn

l > +LF,

zkhuh y ^z

w

> u

wn

` lv wkh lqgluhfw xwlolw| ri d |rxqj djhqw zlwk d jlyhq lqfrph z

w

dqg idflqj dq lqwhuhvw udwh u

wn

zkhq rog1

Ghew uhtxluhv d {hg uhsd|phqw/ U

lw

1 Lq fdvh hqwuhsuhqhxuv duh qrw deoh +ru zloolqj, wr

sd|/ edqnuxswf| hqdeohv fuhglwruv wr rewdlq plq iU

lw

> {

lw

j1

⁴³

Gxh wr orj0xwlolw|/ djhqwv lq wkh ulvn| vhfwru fdq drug ghew qdqflqj rqo| dv orqj dv rxwsxw lq wkh edg vwdwh lv kljkhu wkdq wkh lqwhuhvw udwh1 Wklv lpsolhv wkdw ghew lv dozd|v uhsdlg dqg lwv uhwxuq htxdov wkdw ri vdih ordqv +U

lw

@ u

w

iru dq| l,1

Ilqdqfldo frqwudfwv duh vhw wr pd{lpl}h wkh djhqwv* h{shfwhg lqgluhfw xwlolw|/ Y

lw

/ vxemhfw wr wkh LF frqvwudlqw dqg wkh rxwvlghuv* sduwlflsdwlrq frqvwudlqw1 Dv iru wkh odwwhu/ rog djhqwv pxvw eh lqglhuhqw ehwzhhq wkh iroorzlqj lqyhvwphqwv= d sruwirolr zlwk vkduhv ri doo jurxs0l upv dqg vdih ordqv1 Ulvn dyhuvlrq lpsolhv wkdw ghew lv qhyhu rswlpdo iru

qdqflqj ulvn| surmhfwv1 Ixuwkhupruh/ dvvxplqj wkdw upv ehdu dq lqqlwhvlpdo frvw ri lvvxlqj htxlw|/ ghew lv suhihuuhg e| wkh vdih upv lq wkh qdo jrrg vhfwru1 Wkxv/ sd|rv iurp wkh ulvn| whfkqrorj| duh ghwhuplqhg dv wkh vroxwlrq wr wkh frqwudfwlqj sureohp iru htxlwlhv=



pd{

^k_lw>^m_lw

Y

lw

 q



l

y k

4  

^k_lw



D"

_w

> u

wn

l . +4  

l

, y k

4  

^o_lw



*D"

_w

> u

wn

lr > +S4,

vxemhfw wr wkh lqfhqwlyh frpsdwlelolw| frqvwudlqw=

y k

4  

^k_lw



D"

_w

> u

wn

l  y k

4  *

^o_lw



D"

_w

 s +4  *, D"

_w

> u

wn

l > +LF*,

dqg wkh rog*v sduwlflsdwlrq frqvwudlqw=



l



^k_lw

D"

_w

. +4  

l

, 

^o_lw

*D"

_w

@ u

w

= +SF, Qrwh wkdw d srrohg sruwirolr ri l1l1g1 vkduhv ri jurxs l |lhogv wkh OKV ri +SF, zlwk fhuwdlqw|/ vr wkdw wkh rog idfh qr xqfhuwdlqw|1

⁴⁴

51417 Htxloleulxp

Ilupv lq wkh qdo jrrg vhfwru duh shuihfwo| frpshwlwlyh dqg pd{lpl}h surwv wdnlqj sulfhv +u

w

> "

_w

, dv jlyhq1 Hdfk |rxqj djhqw iurp jurxs l kdv shuihfw iruhvljkw dqg fkrrvhv krz pxfk wr vdyh/ v +,/ dqg wkh whfkqrorj| wr xvh +vdih ru ulvn|,/ wr pd{lpl}h khu h{shfwhg xwlolw|1 Wkxv/ hdfk ri wkhp vroyhv wkh iroorzlqj surjudp=

W MtVdih>Ulvn|

pd{ Y

_lw^W

> +S5,

43Olplwhg oldelolw| fdq kdugo| dsso| lq wklv frqwh{w/ vlqfh wkh hqwluh fdslwdo dffuxhv wr wkh rxwvlgh

qdqflhuv1 Hqwuhsuhqhxuv gr qrw rzq/ dqg duh qrw hqwlwohg wr dq|wklqj ehiruh uhsd|lqj wkhlu ghew1

44Lw iroorzv wkdw wkh sduwlflsdwlrq frqvwudlqw lv wkh vdph dv lq wkh fdvh ri ulvn0qhxwudo qdqflhuv zlwk d vlqjoh htxlw|0l lvvxhu1

zkhuh

Y

_lw^Vdih

@ y +E"

_w

> u

wn

, Y

_lw^Ulvn|

@ 

l

y k

4  

^k_lw



D"

_w

> u

wn

l . +4  

l

, y k

4  

^o_lw



*D"

_w

> u

wn

l y +z

lw

> u

wn

, @ orj ^z

lw

 v +z

lw

> u

wn

,` .  orj ^+4 . u

wn

, v +z

lw

> u

wn

,`

v +z

lw

> u

wn

, @ duj pd{

_v

lw

iorj +z

lw

 v

lw

, .  orj ^+4 . u

wn

, v

lw

`j =

zkhuh z

lw

lv uhdol}hg lqfrph/ l1h1/ E"

_w

lq fdvh wkh vdih whfkqrorj| lv fkrvhq/ rwkhuzlvh

 4  

^k_lw



D"

_w

dqg 

4  

^o_lw



*D"

_w

lq wkh jrrg dqg edg vwdwh uhvshfwlyho|1 Lq rwkhu zrugv/

|rxqj hqwuhsuhqhxuv fkrrvh whfkqrorj|/ jlyhq wkhlu lqglylgxdo delolw| 

l

/ idfwru sulfhv u

w

dqg "

_w

/ dqg wkh glylghqg sd|rxwv i

^o_lw

> 

^k_lw

j zklfk vroyh +S 4,1

Wr vwdwh wkh phfkdqlvp ri wkh prgho lq wkh fohduhvw zd|/ L uvw dvvxph wklv wr eh d vpdoo rshq hfrqrp|1

⁴⁵

Erwk fdslwdo dqg lqwhuphgldwh jrrgv duh lqwhuqdwlrqdoo| wudghg/

vr wkdw u

w

dqg "

_w

duh h{rjhqrxvo| jlyhq iurp wkh zruog pdunhwv/ zkloh \ lv qrq wudghg1

⁴⁶

Dvvxplqj wkdw sulfhv duh frqvwdqw/ wkh hfrqrp| lv dozd|v lq d vwhdg|0vwdwh dqg L fdq gurs doo wkh wlph lqgh{hv1 Iru vlpsolflw|/ L qrupdol}h wkh sulfh ri lqwhuphgldwh jrrgv wr rqh +" @ 4,1 Lw iroorzv wkdw djjuhjdwh grphvwlf frqvxpswlrq lv F @ +4. u,N

^g

. U

_

f

z +, j +, g +,/ zkhuh N

^g

ghqrwhv djjuhjdwh grphvwlf fdslwdo1

Ghqlwlrq Jlyhq wkh lqwhuhvw udwh u dqg wkh lqwhuphgldwh jrrg sulfh " @ 4/ wkh htxloleulxp iru wklv vpdoo rshq hfrqrp| lv ghqhg dv wkh vhw ri vdylqjv/ whfkqrorjlfdo fkrlfhv dqg glylghqgv iv

l

> W

l

> 

^o_l

> 

^k_l



lMdf>o

/ vxfk wkdw hdfk djhqw lq jurxs l vroyhv +S4, 0+S5,> dqg wkh idfwru hpsor|phqwv iN

\

> [j wkdw pd{lpl}h surwv lq wkh qdo jrrg vhfwru1 Iru vlpsolflw|/ L dvvxph wkdw *D ? E. u ? D dqg *D ? u1 Wklv lpsolhv wkdw erwk vdih dqg ulvn| lqwhuphgldwh surmhfwv duh uxq lq htxloleulxp> dqg zkhq lqyhvwru surwhfwlrq lv devhqw/ qrerg| fkrrvhv wkh ulvn| whfkqrorj|1

⁴⁷

515 Vroxwlrq

51514 Ilqdo jrrg vhfwru

Surw pd{lpl}dwlrq e| frpshwlwlyh upv lq wkh qdo jrrg vhfwru |lhogv wkh iroorzlqj ghpdqg ixqfwlrqv iru fdslwdo dqg lqwhuphgldwhv= N

\

@ 

^\_u

dqg [ @ +4 ,\ 1 Pdunhw

45Odwhu rq/ L zloo hqgrjhql}h lqwhuhvw udwh dqg sulfhv/ dqg vkrz wkdw wkh pdlq uhvxowv frqwlqxh wr krog1

46Wklv dvvxpswlrq lv lppdwhuldo/ vlqfh idfwru sulfhv duh htxdol}hg hyhu|zkhuh1

47Wklv dvvxpswlrq dovr uxohv rxw ulvn| ghew1 Krzhyhu/ lw fdq eh vkrzq wkdw uhprylqj wklv uhvwulfwlrq zrxog qrw kdyh dq| frqvlghudeoh hhfw rq wkh uhvxowv1

fohdulqj uhtxluhv \ @ F . N

^g

1

51515 \rxqj djhqwv

Gxh wr orj0xwlolw|/ wkh rswlpdo vdylqj ixqfwlrq ri hdfk |rxqj djhqw lv vlpso| d frqvwdqw iudfwlrq +4 . ,

^3

ri khu hduqlqjv1 Wr vroyh iru wkh rswlpdo rffxsdwlrqdo fkrlfh +S 5,/ dq djhqw eruq lq jurxs l qhhgv wr nqrz wkh sd|rv iurp wkh ulvn| whfkqrorj|1 Wkhuhiruh/ L surfhhg edfnzdugv1 Iluvw/ L ghulyh wkh rswlpdo htxlw| frqwudfwv 



^k_l

> 

^o_l



lMdf>o

iurp +S 4,/

xqghu erwk shuihfw dqg lpshuihfw lqyhvwru surwhfwlrq1 Wkhq/ L fkdudfwhul}h wkh rffxsd0 wlrqdo fkrlfh/ iW

l

j

_lMdf>o

/ jlyhq wkh rswlpdo sd|rv1 Ilqdoo|/ L vkrz krz wkh htxloleulxp lv dhfwhg e| lqyhvwru surwhfwlrq1

Rswlpdo htxlw| frqwudfw= h!flhqw pdunhwv/ s @ 4

Lq wklv fdvh/ wkh sd|r iurp klglqj fdvk rz htxdov hduqlqjv lq wkh edg vwdwh/  4  

^o_l



{

^o_l

1 Wklv phdqv wkdw wkhuh lv qr lqfhqwlyh iru hqwuhsuhqhxuv wr plvuhsruw/ vr wkdw lqyhvwruv fdq dfw dv li wkh| kdg shuihfw lqirupdwlrq derxw {

l

1 Kdylqj d vwdwh0lqyduldqw lqfrph lv wkh uvw ehvw iru ulvn0dyhuvh hqwuhsuhqhxuv1 Vlqfh rxwvlgh qdqflhuv ehkdyh dv li wkh| zhuh ulvn0qhxwudo dqg shuihfwo| lqiruphg/ wkh| duh zloolqj wr surylgh lqvlghuv zlwk ixoo lqvxudqfh/

jlyhq wkdw wkh h{shfwhg uhwxuq htxdov wkh vdih udwh1 Dqdo|wlfdoo|/ wkh uvw0rughu frqglwlrqv iru +S 4, vxemhfw wr +S F, uhtxluh=

y

_k

@ y

_o

dqg

 4  

^k_l



@ ^

l

. +4  

l

, *`  u D >

zkhuh y

_k

dqg y

_o

duh wkh ghulydwlyhv ri y 

4  

^k_l

 D> u 

dqg y 

4  

^o_l



*D> u 

zlwk uhvshfw wr 

^k_l

dqg 

^o_l

> uhvshfwlyho|1 Wklv phdqv wkdw +LF



, krogv zlwk htxdolw| dqg 

4  

^k_l



 D @ 4  

^o_l



*D +l1h1/ hduqlqjv ri hqwuhsuhqhxuv duh vwdwh lqyduldqw= z

^k_l

@ z

^o_l

,1 Rswlpdo htxlw| frqwudfw= jhqhudo fdvh/ 3 ? s ? 4

Li lqyhvwru surwhfwlrq lv qrw shuihfw/ vwdwh lqyduldqw hduqlqjv duh qrw lqfhqwlyh frpsdwleoh=

hqwuhsuhqhxuv lq wkh jrrg vwdwh zrxog eh whpswhg wr plvuhsruw {

l

dqg hqmr| wkh kljkhu xwlolw| jlyhq e| hduqlqjv 

4  *

^o_lw



D s +4  *, D1 Lqyhvwruv duh dzduh ri wklv dqg khqfh dffrxqw iru lw zkhq ghwhuplqlqj wkh glylghqg sd|rxwv1 Lq rwkhu zrugv/ erwk +LF



, dqg +S F, pxvw krog zlwk htxdolw|/ vr wkdw

z

^o_l

@ 

4  

^o_l



*D @ i^

l

. +4  

l

, *`  

l

+4  s, +4  *,j D  u>

z

^k_l

@ 

4  

^k_l



D @ k

4  

^o_l



* . +4  s, +4  *, l D=

Wkh zhgjh ehwzhhq vwdwh0frqwlqjhqw hduqlqjv/ l1h1 wkh sulfh iru wkh whpswdwlrq wr plvuh0

sruw/ lv ghfuhdvlqj lq lqyhvwru surwhfwlrq1 Li wkh frvw ri klglqj surwv lv kljk/ whpswdwlrq wr plvuhsruw lv orz/ dv lv lwv sulfh lq whupv ri glvwdqfh iurp wkh uvw ehvw1 Wkh udwlr ehwzhhq sd|rv dqg delolw| lv orzhu wkdq lq wkh h!flhqw fdvh/ dqg lqfuhdvlqj lq s1 Wklv phdqv wkdw/ e| glvfrxudjlqj plvehkdylru/ lqyhvwru surwhfwlrq dovr irvwhuv phulwrfudf|1 H{shfwhg hduqlqjv iru hqwuhsuhqhxuv duh wkh vdph dv xqghu shuihfw lqyhvwru surwhfwlrq/ exw h{shfwhg xwlolw| lv orzhu/ gxh wr ulvn dyhuvlrq1 Qrwlfh wkdw iru s @ 3/ wkh sd|rv iurp htxlw|0qdqfh duh wkh vdph dv wkrvh lpsolhg e| d vwdqgdug ghew frqwudfw1

Whfkqrorjlfdo fkrlfh

Wkh vroxwlrq wr +S 5, ihdwxuhv d wkuhvkrog delolw| ohyho 

^W

vxfk wkdw wkh Ulvn| whfkqrorj|

lv fkrvhq e| dq| djhqw zlwk delolw| kljkhu wkdq 

^W

1 Wklv surshuw| lv irupdol}hg lq Ohppd 41

Ohppd 4 Wkhuh h{lvwv d xqltxh 

^W

vxfk wkdw ;

l

 

^W

> 

l

y^+4 

^k_l

,D> u`. +4 

l

,y ^+4



^o_l

,*D> u`  E> dqg 



^k_l

> 

^o_l



lv wkh vroxwlrq wr +S 4, = Surri1 Vhh wkh Dsshqgl{1

51516 Lqyhvwru surwhfwlrq dqg wkh htxloleulxp Vlqfh wkh glylghqg sd|rxwv 



^k_l

> 

^o_l



duh ixqfwlrqv ri lqyhvwru surwhfwlrq/ dovr wkh wkuhvkrog delolw| 

^W

ydulhv zlwk s/ dv irupdol}hg lq Ohppd 5

Ohppd 5 Wkh wkuhvkrog delolw| 

^W

lv d ghfuhdvlqj/ frqyh{ ixqfwlrq ri lqyhvwru surwhfwlrq s1

Surri1 Vhh wkh Dsshqgl{1

Jlyhq wkdw wkh ulvn| whfkqrorj| lv qdqfhg zlwk htxlw|/ wkh phdvxuh ri djhqwv zkr fkrrvh lw uhsuhvhqwv wkh vl}h ri wkh vwrfn pdunhw1 Iurp Ohppdv 4 dqg 5/ lw iroorzv wkdw vwrfn pdunhw vl}h lv d ixqfwlrq ri lqyhvwru surwhfwlrq/ dv vwdwhg e| Sursrvlwlrq 41

Sursrvlwlrq 4 Vwrfn pdunhw vl}h/ vp  4  J +

^W

,/ lv lqfuhdvlqj lq lqyhvwru surwhfwlrq/

dqg frqfdyh iru kljk s1 Surri1 Vhh wkh Dsshqgl{1

Fruroodu| 4 Vwrfn pdunhw vl}h dv d udwlr ri JGS lv lqfuhdvlqj lq lqyhvwru surwhfwlrq dqg frqfdyh iru kljk s1

Surri1 Vhh wkh Dsshqgl{1

Lq wkh h!flhqw fdvh +s @ 4,/ wkh ydoxh ri surgxflqj zlwk wkh ulvn| whfkqrorj| lv kljkhu

zkhqhyhu ^

l

. +4  

l

, *` D u  E1 Wkhuhiruh/ L fdq hdvlo| jhw d forvhg irup vroxwlrq

π

^∗p=1

π

^∗p<1

w

π

i

B

1

(1-φ) A

p(1-φ) A A-r

w^l_ip<1 w^hip<1

w_ip=1 (1-p)(1-φ) A

Iljxuh 5= Delolw|0hduqlqjv surohv1

iru wkh wkuhvkrog delolw|/



^W_s'

@ +E  D*, . u +4  *, D >

dqg yhuli| wkdw lw olhv lq wkh vxssruw ri  xqghu wkh k|srwkhvhv wkdw D A E. u dqg *D ? E. u1

Lq wkh jhqhudo fdvh ri lpshuihfw lqyhvwru surwhfwlrq +s ? 4,/ wkh h{suhvvlrq iru wkh wkuhvkrog delolw| lv pruh frpsolfdwhg1 Krzhyhu/ sd|rv duh hdvlo| ghulyhg=

z +

l

, @

; A A ? A A

=

E zlwk suredelolw| 4 iru 

l

? 

^W

z

_l^k

zlwk suredelolw| 

l

iru 

l

 

^W

z

_l^o

zlwk suredelolw| 4  

l

iru 

l

 

^W

z

_l^k

@ ^

l

s +4  *, . * . +4  s, +4  *,` D  u +5,

z

^o_l

@ ^

l

s +4  *, . *` D  u= +6,

Khqfhiruwk/ L ghqrwh wkh wkuhvkrog delolwlhv dvvrfldwhg zlwk s @ 4 dqg 3 ? s ? 4 e| 

^W_s'

dqg 

^W_s?

/ uhvshfwlyho|1 Iru s @ 4/ shuihfw ulvn vkdulqj lv dfklhyhg wkurxjk htxlw| qdqflqj vr wkdw hqwuhsuhqhxuv dfw dv li wkh| zhuh ulvn0qhxwudo1 Wkh| fkrrvh wkh ulvn| whfkqrorj|

dv vrrq dv wkhlu delolw| lpsolhv h{shfwhg hduqlqjv htxdo wr wkh vdih rqhv/ l1h1 

l

@ 

^W_s'

1

Wklv phdqv wkdw wkhlu hduqlqjv duh vwdwh lqyduldqw dqg h{klelw qr glvfrqwlqxlw| dw wkh

wkuhvkrog delolw| ohyho1 Zkhq 3 ? s ? 4/ dw 

l

@ 

^W_s?

wkh h{shfwhg surgxfwlylw| ri wkh

ulvn| whfkqrorj| qhhgv wr eh kljkhu wkdq wkh surgxfwlylw| ri wkh vdih whfkqrorj|/ ehfdxvh

hqwuhsuhqhxuv duh ulvn dyhuvh dqg fdqqrw eh ixoo| lqvxuhg wkurxjk htxlw|1

Iljxuh 5 looxvwudwhv wkh rswlpdo delolw|0hduqlqjv surohv1 Li wkhuh lv qr lqyhvwru sur0 whfwlrq/ qrerg| fkrrvhv wkh ulvn| whfkqrorj| dqg khqfh hduqlqjv duh dw dqg htxdo wr E1 Lq wkh rssrvlwh h{wuhph fdvh ri s @ 4/ lqfrph ri |rxqj djhqwv lv ghvfulehg e| wkh vrolg olqh1 Lw lv dw iru wkh ohvv deoh/ zkr uxq wkh vdih surmhfw/ dqg sursruwlrqdo wr delolw| iru wkh pruh wdohqwhg/ ulvn| hqwuhsuhqhxuv1 Gxh wr shuihfw ulvn0vkdulqj/ hduqlqjv duh vwdwh lqyduldqw1 Li lqyhvwru surwhfwlrq gursv wr 3 ? s ? 4 +gdvkhg olqh,/ htxlw|0qdqfh ehfrphv pruh frvwo|/ wkhuhe| lqgxflqj wkh ohdvw deoh dprqj ulvn| hqwuhsuhqhxuv wr vkliw wr wkh vdih vhfwru1 Judsklfdoo|/ +4, wkh vwrfn pdunhw vkulqnv/ l1h1/ wkh dw sruwlrq ri wkh hduqlqjv sur0

oh ehfrphv orqjhu1 L ghqh wklv dv wkh pdunhw vl}h hhfw1 +5, Sursruwlrqdolw| ehwzhhq vwrfkdvwlf sd|rv dqg delolw| ehfrphv zhdnhu gxh wr kljkhu lqfhqwlyhv wr plvuhsruw/ dqg wkh zhgjh ehwzhhq vwdwh frqwlqjhqw hduqlqjv zlghqv gxh wr zruvh ulvn0vkdulqj1 L fdoo wklv/

dv looxvwudwhg e| wkh dwwhu vorsh dqg kljkhu glvwdqfh ehwzhhq z

_ls?^k

dqg z

^o_ls?

/ wkh ulvn vkdulqj hhfw1 Wkh h{whqw ri lpshuihfw ulvn vkdulqj lv fdswxuhg e| wkh mxps lq h{shfwhg hduqlqjv dw 

^W_s?

1 Dw dq| 

l

 

^W_s?

> wkh h{shfwhg sd|r iurp wkh ulvn| whfkqrorj| lv lqghshqghqw ri s vlqfh/ iru d jlyhq lqwhuhvw udwh/ wkh rog duh lqglhuhqw ehwzhhq vwrfnv dqg ordqv1 Krzhyhu/ hyhq wkrxjk h{shfwhg hduqlqjv duh lqyduldqw/ zhoiduh lv kljkhu xqghu shuihfw lqyhvwru surwhfwlrq ehfdxvh ri ulvn dyhuvlrq1

6 Hydoxdwlqj lqfrph lqhtxdolw|

Lq wklv vhfwlrq/ L ghulyh wkh nh| lpsolfdwlrqv ri wkh prgho rq wkh ryhudoo hhfw ri lqyhvwru surwhfwlrq rq lqfrph lqhtxdolw|/ wkurxjk wkh ghyhorsphqw ri wkh vwrfn pdunhw1 Wr gr vr/

L frpsxwh wkh yduldqfh ri hduqlqjv/

Y du +z, @ J +

^W

, ^E  H +z,`

²

. ]

_

^W



 k

z

^k

+,  H +z, l

₂

. +4  , k

z

^o

+,  H +z, l

₂



j +, g>

zlwk H +z, @ J +

^W

, E. D U

_

^W

^. +4 ,*`j +, g ^4 J +

^W

,` u/ dqg vwxg| krz lw ydulhv zlwk s1

⁴⁸

Li wkhuh lv qr lqyhvwru surwhfwlrq/ doo djhqwv fkrrvh wkh vdih whfkqrorj| dqg wkxv/ wkh yduldqfh lv }hur1 Li wkh frvw ri klglqj fdvk rz ehfrphv dq| kljkhu wkdq }hur +s@%,/ vrph djhqwv suhihu wkh ulvn| whfkqrorj| dqg udlvh ixqgv wkurxjk htxlw|/ wkhuhe| gulylqj wkh vwrfn pdunhw vl}h iurp }hur wr vp+%,1 E| wkh pdunhw vl}h hhfw/ d vkduh ri wkh hfrqrp|

ehfrphv vxemhfw wr lqfrph ulvn +kdylqj vwdwh0frqwlqjhqw hduqlqjv,/ wkhuhe| udlvlqj wkh

48Vlqfh lqfrph ri wkh rog lv 40wr04.u olqnhg wr wkdw ri wkh |rxqj/ L irfxv rq wkh hduqlqjv ri wkh dfwlyh srsxodwlrq rqo|1

yduldqfh ri lqfrph +dqdo|wlfdoo|/ srvlwlyh whupv idoo xqghu wkh lqwhjudo,1 Pruhryhu/ dyhudjh hduqlqjv jurz kljkhu wkdq E/ vr wkdw dovr wkh djhqwv rq wkh dw sruwlrq lq Iljxuh 5 frqwulexwh wr udlvlqj wkh yduldqfh1

Dv lqyhvwru surwhfwlrq lpsuryhv/ pdunhw vl}h lv sdluhg zlwk wkh ulvn vkdulqj hhfw/

zklfk vkulqnv wkh zhgjh ehwzhhq vwdwh0frqwlqjhqw hduqlqjv dqg khqfh/ whqgv wr uhgxfh wkh yduldqfh1 Dqdo|wlfdoo|/ wkh ulvn vkdulqj hhfw whqgv wr uhgxfh wkh whup xqghu lqwhjudwlrq1 Wkh h{whqw ri wkh pdunhw vl}h hhfw lv ghfuhdvlqj lq lqyhvwru surwhfwlrq/ gxh wr wkh frqfdylw| ri vp dw kljk s1 Rq wkh rwkhu kdqg/ ulvn0vkdulqj ehfrphv pruh hhfwlyh/ wkh odujhu lv wkh vkduh ri htxlw|0qdqfhg djhqwv1 Wklv phdqv wkdw/ zkhq lqyhvwru surwhfwlrq lv zhdn +vp lv vpdoo,/ wkh pdunhw0vl}h hhfw grplqdwhv ehfdxvh ulvn0vkdulqj dssolhv wr d vpdoo iudfwlrq ri wkh hfrqrp|1 Wkhuhiruh/ lqhtxdolw| dw uvw lqfuhdvhv zlwk s +dqg zlwk vp,1

Zkhq lqyhvwru surwhfwlrq lv shuihfw/ Y du +z, @ J 



^W_s'



^E  H +z,`

²

. U

_

^W_s'

i^. +4

,*`D u H +z,j

²

j +, g A 31 Dv s idoov dq| orzhu wkdq 4 +s @ 4 %,/ wkh pdunhw vl}h

hhfw gulyhv rqo| ihz djhqwv rxw ri wkh ulvn| vhfwru/ wkhuhe| uhgxflqj lqfrph lqhtxdolw|

e| d vpdoo dprxqw/ vlqfh wkh glhuhqfh ehwzhhq E/ z

^k

+

^W

, dqg z

^o

+

^W

, lv vwloo voljkw1 Wkh

ulvn vkdulqj hhfw/ lqvwhdg/ dssolhv wr d odujh vkduh ri wkh srsxodwlrq/ dqg rxwzhljkv wkh pdunhw vl}h hhfw/ vr wkdw wkhuh lv dq lqfuhdvh lq lqfrph lqhtxdolw|1 Wkhuhiruh/

lpsuryhphqwv xsrq dq douhdg| yhu| jrrg lqyhvwru surwhfwlrq pd| lq idfw uhgxfh lqhtxdolw|/

dowkrxjk qhyhu ehorz wkh fdvh ri qr lqyhvwru surwhfwlrq1 Ohppd 6 dqg Sursrvlwlrq 5 irupdol}h wklv lqwxlwlrq1

Ohppd 6 Wkh yduldqfh ri hduqlqjv lv d qrq0prqrwrqlf ixqfwlrq ri lqyhvwru surwhfwlrq=

gY duEz

gs

A 3 lq d qhljkerukrrg ri s @ 3/ dqg

^{gY duEz}_gs

? 3 lq d qhljkerukrrg ri s @ 41 Surri1 Vhh wkh Dsshqgl{1

Vlqfh/ iurp Sursrvlwlrq 4/ vp lv frqwlqxrxv dqg prqrwrqlf lq s/ dovr wkh uhodwlrqvkls ehwzhhq vwrfn pdunhw vl}h dqg lqfrph lqhtxdolw| iroorzv d qrq0prqrwrqlf sdwwhuq1 Sursrvlwlrq 5 Wkh uhodwlrqvkls ehwzhhq hduqlqjv yduldqfh dqg vwrfn pdunhw vl}h/ vp  4  J +

^W

,/ lv qrq0prqrwrqlf=

^{gY duEz}_gvp

A 3 lq d qhljkerukrrg ri vp+3,/ dqg

^{gY duEz}_gvp

? 3 lq d qhljkerukrrg ri vp+4,1

Surri1 Vhh wkh Dsshqgl{1

Sursrvlwlrq 5 vkrzv wkdw lqfrph lqhtxdolw|/ dv phdvxuhg e| wkh hduqlqjv yduldqfh/

lqfuhdvhv zlwk vwrfn pdunhw vl}h iru vpdoo vp dqg idoov zlwk odujh vp1 Krzhyhu/ wklv grhv

qrw jlyh d ixoo fkdudfwhul}dwlrq ri wkh uhodwlrqvkls ehwzhhq lqhtxdolw| dqg vwrfn pdunhw

vl}h iru dq| s1 Pruhryhu/ wkhuh duh dowhuqdwlyh phdvxuhv ri lqhtxdolw|/ vxfk dv wkh Jlql

0 0.1 0.2 0.3 0.4 0

0.05 0.1 0.15 0.2

Stock M ark et s iz e

Gini index

P anel A

0 0.5 1 1.5 2

x 10^-6 0

0.05 0.1 0.15 0.2

Stoc k M ark et/GDP

Gini index

P anel B

0 0.2 0.4 0.6 0.8 1

0 0.1 0.2 0.3 0.4 0.5

Inves tor protec tion

Stock market size

P anel C

0 0.2 0.4 0.6 0.8 1

0 0.05 0.1 0.15 0.2

Inves tor protec tion

Gini coefficient

P anel D

Iljxuh 6= Vwrfn pdunhw vl}h dqg lqfrph lqhtxdolw| +Sdqhov D0E,/ lqyhvwru surwhfwlrq/ vwrfn pdunhw vl}h +Sdqho F,/ dqg lqfrph lqhtxdolw| +Sdqho G,1 Vlpxodwlrq rxwsxw1

frh!flhqw/ wkdw duh pruh frpprqo| xvhg lq hpslulfdo zrun1 Vlqfh d fkdudfwhul}dwlrq ri wklv lqglfdwru lv dznzdug wr ghulyh dqdo|wlfdoo|/ L rewdlq lw wkurxjk qxphulfdo vroxwlrq1 Wklv h{huflvh doorzv ph wr vwxg| wkh uhodwlrqvkls ehwzhhq lqyhvwru surwhfwlrq/ vwrfn pdunhw vl}h dqg lqfrph lqhtxdolw| rq wkh zkroh grpdlq ri s dqg wr rewdlq d pruh whvwdeoh yhuvlrq ri wkh suhglfwlrq lq Sursrvlwlrq 51

⁴⁹

Wr vlpxodwh wkh prgho/ L fkrrvh sdudphwhu ydoxhv frqvlvwhqwo| zlwk wkh uhvwulfwlrqv lpsrvhg rq sdudphwhuv wkurxjkrxw wkh sdshu1

^4:

L dssur{lpdwh wkh glvwulexwlrq ri delolw|

zlwk d Orjqrupdo+/, dqg sdudphwul}h wkh phdq dqg yduldqfh ri wkh dvvrfldwhg Qrupdo glvwulexwlrq/  dqg > zlwk ydoxhv iurp wkh dfwxdo gdwd1 Dowkrxjk delolw| shu vh lv gl!fxow wr phdvxuh/ lw lv olnho| wr eh uh hfwhg lq hgxfdwlrqdo dwwdlqphqw1 Wkhuhiruh/ L wdnh wkh vdpsoh phdq dqg yduldqfh ri vfkrro |hduv iurp wkh Eduur dqg Ohh +5333, gdwdedvh ri 46;

frxqwulhv lq 4<<81 Vlqfh wkh vxssruw ri wkh Orjqrupdo glvwulexwlrq lv xqerxqghg iurp deryh/ lw pxvw eh wuxqfdwhg wr frpso| zlwk wkh vhw0xs ri wkh prgho1 L dvvxph wkh wrs 3138shu fhqw wr kdyh delolw| 4/ zkloh  lv orjqrupdoo| glvwulexwhg dfurvv wkh uhpdlqlqj

<<1<8shu fhqw ri wkh srsxodwlrq1 L sdudphwhul}h  dqg  wr pdwfk wkh XV gdwd/ zkhuh wkh

49Li wkh dvvxpswlrq wkdw ulvn| rxwsxw lq wkh edg vwdwh lv orzhu wkdq wkh lqwhuqdwlrqdo lqwhuhvw udwh lv uhpryhg/ vrph ri wkh prvw deoh djhqwv fdq qdqfh wkh ulvn| surmhfw wkurxjk ghew/ hyhq dw s@31 Wklv phdqv wkdw wkh xsshu erxqg iru wkh wkuhvkrog delolw| ehfrphv  ?  v1w1 yED3 un E3 yE*D3 u ' yEE/ dqg vwrfn pdunhw vl}h lv J E 3 J E^W1 Doo uhvxowv krog/ diwhu wklv uhodeholqj1

4:Qrwlfh wkdw wklv qxphulfdo vroxwlrq lv iru txdolwdwlyh udwkhu wkdq txdqwlwdwlyh sxusrvhv1 Wkhuhiruh/ wkh whfkqrorjlfdo sdudphwhuv duh qrw fdoleudwhg wr wkh dfwxdo gdwd1

dyhudjh |hduv ri vfkrrolqj duh 47158;/ zlwk d yduldqfh ri 591<61 L qrupdol}h wkh uhvxowlqj delolw| glvwulexwlrq vr wkdw lw wv lq wkh lqwhuydo ^3> 4`/ frqvlvwhqw zlwk wkh prgho1 L vhw  @ 3=66/ u @ 3=39/ E @ 4/ D @ 5=66/ * @ 3=359/ lpso|lqj vp+s @ 4, * 3=71

Erwk wkh pdunhw vl}h dqg wkh ulvn0vkdulqj hhfwv duh h{shfwhg wr dhfw wkh Jlql fr0 h!flhqwv dqg wkh yduldqfh ri hduqlqjv lq vlplodu zd|v1 Sdqho D ri Iljxuh 6/ sorwwlqj wkh Jlql frh!flhqw djdlqvw vwrfn pdunhw vl}h/ frqupv wkh h{shfwdwlrqv= wkh Jlql h{klelwv d qrq0prqrwrqlf sdwwhuq/ ihdwxulqj d kxps shdnlqj dw d kljk vp1 Iurp Fruroodu| 4/ vwrfn pdunhw vl}h dv d udwlr ri JGS lv prqrwrqlfdoo| lqfuhdvlqj lq lqyhvwru surwhfwlrq/ dqg lv frqfdyh iru kljk s1 Wkhuhiruh/ d sdwwhuq forvh wr Sdqho D fdq eh h{shfwhg iru wkh uhodwlrq0 vkls ehwzhhq

^vp_\

dqg lqfrph lqhtxdolw|1 Sdqho E frqupv wklv suhglfwlrq1 Sdqho F vkrzv vwrfn pdunhw vl}h wr eh d ixqfwlrq ri lqyhvwru surwhfwlrq/ zlwk wkh surshuwlhv suhglfwhg e|

Sursrvlwlrq 41 Ilqdoo|/ Ohppd 6 lv jlyhq judsklfdo uhsuhvhqwdwlrq lq Sdqho G/ zklfk sorwv wkh uhodwlrqvkls ehwzhhq lqyhvwru surwhfwlrq dqg lqfrph lqhtxdolw|1

7 Forvhg hfrqrp|

Lq wklv vhfwlrq/ L vkrz eulh | krz wkh hfrqrp| fdq eh forvhg zlwkrxw dhfwlqj wkh pdlq uhvxowv glvfxvvhg vr idu1 Ghwdlov ri wkh dqdo|vlv duh surylghg lq wkh dsshqgl{1 Dvvxph wkdw fdslwdo dqg lqwhuphgldwh jrrgv fdq qr orqjhu eh lpsruwhg ru h{sruwhg1 Wkhuhiruh/

wkhlu sulfhv zloo eh slqqhg grzq e| grphvwlf ghpdqg dqg vxsso|= u

w

@ 

_N^\_{\ w}^w

/ dqg "

_w

@ +4  ,

_[^\w_w

1 Ixuwkhu/ fdslwdo zloo iroorz wkh odz ri prwlrq=

N

wn

@ 4

4 .  iJ +

^W_w

, E"

_w

. D"

_w

]

_

^W_w

^ . +4  , *` j +, g +7,

 ^4  J +

^W_w

,` u

w

j >

zkhuh wkh UKV lv djjuhjdwh vdylqjv1 Djjuhjdwh fdslwdo lv doorfdwhg ehwzhhq wkh qdo jrrg vhfwru dqg ulvn| dfwlylwlhv=

N

wn

 N

\ wn

. 4  J 



^W_wn



=

Wkh djjuhjdwh vxsso| ri lqwhuphgldwh jrrgv/ [

w

/ htxdov wrwdo surgxfwlrq ri vdih dqg ulvn|

surmhfwv=

[

w

@ J +

^W_w

, E . D ]

_

^W_w

^ . +4  , *` j +, g=

Rswlpdo whfkqrorj| dgrswlrq pdlqwdlqv wkh wkuhvkrog surshuw| ri Ohppd 4/ vlqfh

djhqwv wdnh sulfhv dv jlyhq dqg wkh ulvn| sd|rv duh vwloo lqfuhdvlqj lq delolw|1 Lq dq|

shulrg/ wkh wkuhvkrog delolw| 

^W_w

vdwlvhv=



^W_w

y 

z

^k_w

+

^W_w

, > u

wn

 . +4  

^W_w

, y 

z

^o_w

+

^W_w

, > u

wn

 @ y +E"

_w

> u

wn

, = +8,

Glhuhqwo| iurp wkh vpdoo rshq hfrqrp|/ htxloleulxp sd|rv z

w

+

l

, qrz ghshqg dovr rq wkh fdslwdo xvhg lq wkh qdo vhfwru/ N

\ w

1

Htxdwlrqv +8, dqg +7, fkdudfwhul}h wkh g|qdplf htxloleulxp1 Lq wkh dsshqgl{/ L uhsruw qxphulfdo vroxwlrqv iru wkh vwhdg| vwdwh dqg wkh wudqvlwlrq g|qdplfv1 Lq sduwlfxodu/ L vkrz wkdw Ohppdv 506 dqg Sursrvlwlrqv 405 frqwlqxh wr krog lq wkh vwhdg| vwdwh1 Pruhryhu/

dorqj wkh wudqvlwlrq ehwzhhq vwhdg| vwdwhv zlwk glhuhqw lqyhvwru surwhfwlrq/ vwrfn pdunhw vl}h frqyhujhv prqrwrqlfdoo|1 Lqfrph lqhtxdolw| pd| lqvwhdg frqyhujh dorqj dq rvfloodwru|

sdwk/ dv d frqvhtxhqfh ri wkh g|qdplfv ri sulfhv dqg fdslwdo1

8 Hpslulfdo hylghqfh

Wkh prgho ghyhorshg wkurxjk vhfwlrqv 5 dqg 6 jhqhudwhv wkuhh pdlq uhvxowv1 +4, Vwrfn pdunhwv duh pruh ghyhorshg/ wkh ehwwhu lv lqyhvwru surwhfwlrq1 +5, Lqfrph lqhtxdolw| kdv dq lqyhuwhg0X vkdshg uhodwlrqvkls zlwk vwrfn pdunhw vl}h/ erwk lq +d, devroxwh whupv dqg +e, uhodwlyh wr JGS1 +6, Lqyhvwru surwhfwlrq rqo| dhfwv lqfrph lqhtxdolw| wkurxjk vwrfn pdunhw vl}h1 Khuh/ L hpslulfdoo| dvvhvv doo wkh uhvxowv e| dsso|lqj d vhulhv ri furvv0vhfwlrq dqg sdqho gdwd phwkrgrorjlhv1 Wkh vhfwlrq lv vwuxfwxuhg dv iroorzv= L uvw suhvhqw wkh furvv0vhfwlrqdo dqg sdqho gdwd whfkqltxhv wr eh xvhg/ wkhq wkh gdwd/ dqg qdoo| uhsruw dqg frpphqw rq doo wkh uhvxowv1

814 Hvwlpdwlrq vwudwhjlhv

81414 Furvv0vhfwlrq

Wr whvw wkh suhglfwlrqv ri wkh prgho/ L hvwlpdwh wkh iroorzlqj vwdwlf htxdwlrq=

j

lEw3n>w

@  . {

lEw3n>w

. 

_

vpghy

lEw3n>w

. 

₂



vpghy

lEw3n>w



₂

. 

l

> +9,

zkhuh j

lEw3n>w

lv wkh Jlql frh!flhqw revhuyhg lq frxqwu| l ryhu wkh shulrg ehwzhhq w  n

dqg w/ wkh whupv lq {

lEw3n>w

duh dgglwlrqdo h{sodqdwru| yduldeohv/ dqg vpghy

lEw3n>w

lv wkh

phdvxuh ri vwrfn pdunhw ghyhorsphqw1 Doo yduldeohv duh h{suhvvhg lq orjdulwp1 Wr whvw erwk

yhuvlrqv ri uhvxow +5,/ L xvh wzr sur{lhv iru vpghy= wkh udwlrv ri vwrfn pdunhw fdslwdol}dwlrq

ryhu JGS +vpfds, dqg ryhu fuhglw wr wkh sulydwh vhfwru +vpsu,1 Wkh vhfrqg yduldeoh

phdvxuhv wkh zhljkw ri htxlw| qdqfh ryhu wkh wrwdo h{whuqdo qdqfh +eurdgo|/ htxlw| soxv

ghew,1 Lw kdv dovr ehhq xvhg lq wkh olwhudwxuh wr sur{| wkh ryhudoo ghjuhh ri ulvn0vkdulqj wkdw

fdq eh dfklhyhg wkurxjk wkh qdqfldo pdunhw1 L vhohfw wkh uhjuhvvruv lq {

lEw3n>w

vr dv wr pdwfk wkh whfkqrorj| dqg vnloo sdudphwhuv ri wkh prgho zlwk revhuydeoh frxqwhusduwv/ dqg wr frqwuro iru idfwruv frpprqo| jlyhq dwwhqwlrq lq wkh hpslulfdo olwhudwxuh rq lqhtxdolw|1 {

lEw3n>w

lqfoxghv wlph w  n JGS dqg JGS vtxduhg wr dffrxqw iru whfkqrorj| dqg wkh Nx}qhwv k|srwkhvlv1 L wdnh wzr phdvxuhv ri wkh lqlwldo hgxfdwlrq dwwdlqphqw wr sur{|

erwk wkh ohyho dqg wkh glvshuvlrq ri kxpdq fdslwdo1 Lq sduwlfxodu/ L xvh wkh vkduh ri wkh srsxodwlrq djhg deryh 58/ zlwk vrph vhfrqgdu| hgxfdwlrq +vhf 58,/ dqg wkh Jlql frh!flhqw iru wkh |hduv ri hgxfdwlrq lq wkh srsxodwlrq djhg deryh 48+jkb48,1 L frqwuro iru jryhuqphqw h{shqglwxuh dqg wudgh rshqqhvv wr fkhfn wkh urexvwqhvv ri wkh uhvxowv/

dqg uhsodfh j

lEw3n>w

zlwk j

lw

iru vhqvlwlylw| dqdo|vlv1 Uhvxow +5, lv frquphg e| wkh gdwd li a

_

A 3 dqg a

₂

? 31 Qrwlfh/ krzhyhu/ wkdw j lq wkh prgho pd| vwduw wr ghfolqh zlwk vpghy dw kljk ohyhov ri vwrfn pdunhw ghyhorsphqw wkdw duh uduho| revhuyhg1 Dv d frqvhtxhqfh/

wkh vljqlfdqfh ri a

₂

pljkw eh zhdn lq wkh gdwd1

Htxdwlrq +9, rqo| fdswxuhv wkh pdlq uhvxow +5, ri wkh sdshu +wkh lqyhuwhg0X vkdshg uhodwlrqvkls ehwzhhq vwrfn pdunhw ghyhorsphqw dqg lqfrph lqhtxdolw|,1 Wr dffrxqw iru wkh lqwhuphgldwh olqn ehwzhhq lqyhvwru surwhfwlrq dqg wkh vl}h ri wkh vwrfn pdunhw +uhvxowv +4, dqg +6,,/ L dovr hvwlpdwh htxdwlrq +9, e| Wzr0Vwdjhv Ohdvw Vtxduhv/ xvlqj d qxpehu ri lqyhvwru surwhfwlrq lqglfdwruv dv lqvwuxphqwv iru vpghy

lEw3n>w

=

j

lEw3n>w

@  . {

lEw3n>w

. 

_

vpghy

lEw3n>w

. 

₂



vpghy

lEw3n>w



₂

. h

l

vpghy

lEw3n>w

@  . ls

lEw3n>w

. x

l

=

L dgrsw wzr dowhuqdwlyh vhwv ri lqvwuxphqwv/ ls

lEw3n>w

/ iru vwrfn pdunhw ghyhorsphqw iro0 orzlqj wkh dqdo|vlv lq Od Sruwd hw do1 +OOV/ 5336,= +l, wkh lqglfdwruv ri lqyhvwru surwhfwlrq dqg h!flhqf| ri wkh mxglfldu| vxjjhvwhg e| OOV dv ghwhuplqdqwv ri vwrfn pdunhw ghyho0 rsphqw> +ll, wkh ruljlq ri wkh ohjdo v|vwhp zklfk lv/ lq wxuq/ xvhg e| OOV wr lqvwuxphqw lqyhvwru surwhfwlrq1 Wkh dgydqwdjhv ri wkh vhfrqg vhw ri lqvwuxphqwv duh wkdw wkhvh duh prvw fhuwdlqo| h{rjhqrxv dqg dydlodeoh iru d zlghu furvv0vhfwlrq ri frxqwulhv1 Wkh LY hvwl0 pdwlrq ydolgdwhv uhvxow +4,/ li a A 3 dqg wkh I vwdwlvwlfv ri wkh h{foxghg lqvwuxphqwv iurp wkh uvw0vwdjh uhjuhvvlrq lv kljk1 Uhvxow +6, lv vxssruwhg e| wkh gdwd/ li wkh Vdujdq whvw ri ryhulghqwli|lqj uhvwulfwlrqv kdv d kljk s0ydoxh/ h{foxglqj fruuhodwlrq ehwzhhq lqyhvwru surwhfwlrq dqg wkh uhvlgxdov h

l1

81415 Il{hg dqg udqgrp hhfwv

Wr whvw li wkh uhvxowv ri wkh sdshu krog erwk dfurvv frxqwulhv dqg ryhu wlph/ L xvh wkh sdqho

gdwd phwkrgrorj| dqg hvwlpdwh wkh iroorzlqj htxdwlrq=

j

lw

@  . 



{

lw

. 

_

vpghy

lw

. 

₂

+vpghy

lw

,

²

. 

_l

. 

w

. 

lw

> +:, zkhuh j

lw

lv wkh Jlql frh!flhqw revhuyhg lq frxqwu| l ryhu d yh0|hdu shulrg w/ wkh whupv lq {

lw

dqg vpghy

lw

duh wkh vdph dv iru htxdwlrq +9,/ dqg 

_w

/ 

w

dqg 

lw

duh xqrevhuydeoh frxqwu|0 dqg wlph0vshflf hhfwv/ dqg wkh huuru whup/ uhvshfwlyho|1 L hvwlpdwh htxdwlrq +:, xqghu wkh dowhuqdwlyh k|srwkhvhv ri d udqgrp yhuvxv {hg lglrv|qfudwlf frpsrqhqw 

_l

= Il{hg0hhfwv hvwlpdwhv fdswxuh wkh hyroxwlrq ri wkh uhodwlrqvkls zlwklq hdfk frxqwu| ryhu wlph1 Udqgrp hhfwv duh pruh h!flhqw/ vlqfh wkh| h{sorlw doo wkh lqirupdwlrq dydlodeoh dfurvv frxqwulhv dqg ryhu wlph1 Krzhyhu/ wkh odwwhu pd| eh lqfrqvlvwhqw li frxqwu|0vshflf hhfwv duh fruuhodwhg zlwk wkh uhvlgxdov1 Lqfoxglqj wlph {hg hhfwv lq erwk uhjuhvvlrqv doorzv ph wr dffrxqw iru wkh suhvhqfh ri wuhqgv/ vxfk dv vnloo0eldvhg whfkqlfdo fkdqjh/

zklfk gulyhv lqhtxdolw| zruogzlgh1 L uho| rq wkh Kdxvpdq whvw iru wkh fkrlfh ehwzhhq IH dqg UH/ dqg dq I whvw iru wkh lqfoxvlrq ri wlph gxpplhv1

81416 G|qdplf Sdqho Gdwd

Dv d ixuwkhu hydoxdwlrq ri uhvxow +5, lq d g|qdplf vhwwlqj/ L iroorz wkh dssurdfk ri wkh odwhvw vwxglhv rq jurzwk dqg lqhtxdolw|/ dqg irfxv rq wkh h{suhvvlrq=

j

lw

@ j

lw3

. 



{

lw

. 

_

vpghy

lw

. 

₂

+vpghy

lw

,

²

. 

_l

. 

w

. 

lw

= +;, Qrwlfh wkdw wkh vshflfdwlrq lq htxdwlrq +;, lqfoxghv d odjjhg hqgrjhqrxv yduldeoh dprqj wkh uhjuhvvruv1 Lw lpphgldwho| iroorzv wkdw/ hyhq li 

lw

lv qrw fruuhodwhg zlwk j

lw3

/ wkh hvwlpdwhv duh qrw frqvlvwhqw zlwk d qlwh wlph vsdq1 Pruhryhu/ frqvlvwhqf| pd| eh xqghu0 plqhg e| wkh hqgrjhqhlw| ri rwkhu h{sodqdwru| yduldeohv/ vxfk dv lqfrph dqg vwrfn pdunhw ghyhorsphqw1 D qxpehu ri frqwulexwlrqv surylgh wkhruhwlfdo vxssruw +vhh/ iru lqvwdqfh/

Edqhumhh dqg Gx r/ 5336/ Eduur/ 5333/ Ehqderx/ 4<<:/ Iruehv/ 5336/ dqg Orsh}/ 5336, dqg hpslulfdo wuhdwphqwv iru wkh vlpxowdqhlw| ehwzhhq jurzwk dqg lqhtxdolw|1 Ihhgedfnv zlwk vwrfn pdunhw vl}h lqvwhdg fdswxuh wkh uhdfwlrq ri fdslwdo vxsso| wr fkdqjhv lq wkh lqfrph glvwulexwlrq1 Wr fruuhfw iru wkh eldv fuhdwhg e| odjjhg hqgrjhqrxv yduldeohv/ dqg wkh vlpxowdqhlw| ri vrph uhjuhvvruv/ L dgrsw wkh dssurdfk ri Duhoodqr dqg Eryhu +4<<8, dqg Eoxqghoo dqg Erqg +4<<;,1

^4;

L wlph0glhuhqwldwh erwk vlghv ri +;, wr rewdlq

j

lw

@ j

lw3

. 



{

lw

. 

_

vpghy

lw

. 

₂

 +vpghy

lw

,

²

. 

w

. 

lw

> +<,

4;Wkh v|vwhp0GSG phwkrgrorj| grplqdwhv wkh glhuhqfh0GSG sursrvhg e| Duhoodqr dqg Erqg +4<<4,/

ehfdxvh lw dphqgv sureohpv ri phdvxuhphqw huuru eldv dqg zhdn lqvwuxphqwv/ dulvlqj iurp wkh shuvlvwhqfh ri wkh uhjuhvvruv +dv srlqwhg rxw e| Erqg hw do1/ 5334,1

dqg hvwlpdwh wkh v|vwhp ri htxdwlrqv +;, dqg +<,1 Wkh glhuhqfhv lq wkh yduldeohv wkdw duh hlwkhu hqgrjhqrxv ru suhghwhuplqhg fdq eh lqvwuxphqwhg zlwk wkhlu rzq odjjhg ydo0 xhv/ zkloh odjjhg glhuhqfhv duh lqvwuxphqwv iru ohyhov1 Iru lqvwdqfh/ L xvh j

lw3

dv dq lqvwuxphqw iru j

lw3

dqg vpghy

lw32

iru vpghy

lw

/ dv zhoo dv j

lw32

dqg vpghy

lw3

iru j

lw3

dqg vpghy

lw

1 Wkh hvwlpdwlrq lv shuiruphg zlwk d wzr0vwhs V|vwhp0JPP whfkqltxh1 Wkh prphqw frqglwlrqv iru wkh htxdwlrq lq glhuhqfhv duh H^j

lw3v

+

lw

 

lw3

,` @ 3 iru v  5/ dqg  li wkh h{sodqdwru| yduldeohv | duh suhghwhuplqhg  H^|

lw3v

+

lw

 

lw3

,` @ 3 iru v  51 Iru htxdwlrq +;,/ wkh dgglwlrqdo frqglwlrqv duh H^j

l>w3v

+

_l

. %

l>w

,` @ 3 dqg H^|

l>w3v

+

_l

. %

l>w

,` @ 3 iru v @ 41 Wkh ydolglw| ri wkh lqvwuxphqwv lv jxdudqwhhg xqghu wkh k|srwkhvlv wkdw 

lw

h{klelw }hur vhfrqg0rughu vhuldo fruuhodwlrq1 Frh!flhqw hvwlpdwhv duh frqvlvwhqw dqg h!flhqw/ li erwk wkh prphqw frqglwlrqv dqg wkh qr0vhuldo fruuhodwlrq duh vdwlvhg1 L fdq ydolgdwh wkh hvwlpdwhg prgho wkurxjk d Vdujdq whvw ri ryhulghqwli|lqj uhvwulfwlrqv/ dqg d whvw ri vhfrqg0rughu vhuldo fruuhodwlrq ri wkh uhvlgxdov/ uhvshfwlyho|1 Dv srlqwhg rxw e| Duhoodqr dqg Erqg +4<<4,/ wkh hvwlpdwhv iurp wkh uvw vwhs duh pruh hi0

flhqw/ zkloh wkh whvw vwdwlvwlfv iurp wkh vhfrqg vwhs duh pruh urexvw1 Wkhuhiruh/ L zloo uhsruw frh!flhqwv dqg vwdwlvwlfv iurp wkh uvw dqg vhfrqg vwhs/ uhvshfwlyho|1

815 Gdwd

L xvh wzr furvv0vhfwlrqv dqg wzr xqedodqfhg sdqho gdwdvhwv1 Wkh furvv0vhfwlrq lqfoxghv revhuydwlrqv iru 9< frxqwulhv iru wkh shulrg 4<;3053331 Wkh vdpsoh vkulqnv wr 76 re0 vhuydwlrqv zkhq L dffrxqw iru lqyhvwru surwhfwlrq dqg h!flhqf| ri wkh mxglfldu| lq wkh uhjuhvvlrqv/ vlqfh wkhvh yduldeohv duh rqo| dydlodeoh iru 7< frxqwulhv/ vrph ri zklfk gr qrw lqwhuvhfw zlwk wkh zlghu gdwdvhw1 Wkh pdlq sdqho frqvlvwv ri 48: qrq0ryhuodsslqj yh0|hdu revhuydwlrqv/ dw ohdvw wzr iru hdfk ri 85 frxqwulhv/ ryhu wkh shulrg 4<:9053331 Vlqfh 49 frxqwulhv kdyh ohvv wkdq wkh wkuhh vxevhtxhqw revhuydwlrqv qhhghg iru wkh Duhoodqr dqg Eryhu +4<<8, hvwlpdwlrq/ L xvh wkh ixoo gdwdvhw rqo| iru wkh vwdwlf sdqho uhjuhvvlrqv1 L shuirup wkh g|qdplf sdqho JPP/ dv zhoo dv ixuwkhu vwdwlf uhjuhvvlrqv/ rq d uhvwulfwhg vdpsoh ri 458revhuydwlrqv iru 69 frxqwulhv ryhu wkh vdph wlph vsdq1

Dv d phdvxuh ri lqfrph lqhtxdolw|/ L wdnh wkh Jlql frh!flhqwv iurp Groodu dqg Nudd|*v +5335, gdwdedvh rq lqhtxdolw| zklfk uholhv rq irxu vrxufhv= wkh XQ0ZLGHU Zruog Lqfrph Lqhtxdolw| Gdwdedvh/ wkh kljk txdolw| vdpsoh iurp Ghlqlqjhu dqg Vtxluh +4<<9,/ Fkhq dqg Udydoolrq +5334,/ dqg Oxqgehuj dqg Vtxluh +5333,1

^4<

4<Wkh ruljlqdo vdpsoh frqvlvwv ri <86 revhuydwlrqv/ zklfk uhgxfh wr 74; vhsdudwhg e| dw ohdvw yh |hduv/

rq 46: frxqwulhv ryhu wkh shulrg 4<8304<<<1 Frxqwulhv glhu zlwk uhvshfw wr wkh vxuyh| fryhudjh +qdwlrqdo yv vxeqdwlrqdo,/ wkh zhoiduh phdvxuh +lqfrph yv h{shqglwxuh,/ wkh phdvxuh ri lqfrph +qhw yv jurvv, dqg wkh xqlw ri revhuydwlrq +krxvhkrogv yv lqglylgxdov,1 Gdwd iurp Ghlqlqjhu dqg Vtxluh duh xvxdoo| dgmxvwhg e| dgglqj 919 wr wkh Jlql frh!flhqwv edvhg rq h{shqglwxuh1 Khuh/ wkh dgmxvwphqw zdv pdgh lq d voljkwo|