Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Why Do Managers Diversify Their Firms?Agency Reconsidered
Rajesh K. AggarwalAmos Tuck SchoolDartmouth College
Hanover, NH [email protected]
(603) 646-2843
Andrew A. SamwickDepartment of Economics
Dartmouth CollegeHanover, NH 03755
[email protected](603) 646-2893
March, 2000
Abstract: The existing agency explanation for corporate diversification is based on theexistence of a diversification discount and a negative relationship between diversificationand managerial ownership. We argue that this explanation is incomplete on boththeoretical and empirical grounds. We develop a contracting model betweenshareholders and managers in which optimal incentive contracts mitigate managers’propensity to diversify. We derive comparative static predictions for the equilibriumrelationships between incentives, diversification, and firm performance. The model isconsistent with the observed negative relationship between corporate diversification andfirm value. Empirically, we show that the negative relationship that has been observedbetween diversification and managerial incentives is the result of omitted variable bias.When estimated using panel data, higher managerial incentives are associated withgreater diversification. We also find that the link between firm performance andmanagerial incentives is weaker for firms that experience changes in diversification thanit is for firms that do not experience changes in diversification. These two findingsprovide support for our agency cost explanation for diversification, in which observedchanges in diversification and incentives within firms are equilibrium responses tochanges in the level of benefits that managers derive from diversification.
We thank Sheri Aggarwal, Andrew Bernard, Michael Knetter, Praveen Kopalle, Dominic LaValle, DennisLogue, Joel Vanden, and seminar participants at Dartmouth for helpful discussions. We also thank BobBurnham for assistance with Compustat and Andy Halula for assistance with the ExecuComp database.Any errors are our own.
41 Lqwurgxfwlrq
Zk| gr pdqdjhuv fkrrvh wr glyhuvli| wkhlu �upvB D vl}deoh olwhudwxuh vxjjhvwv wkdw frusrudwh
glyhuvl�fdwlrq lv d ohdglqj h{dpsoh ri wkh djhqf| uhodwlrqvkls ehwzhhq vkduhkroghuv dqg pdqdjhuv
ghyhorshg e| Mhqvhq dqg Phfnolqj +4<:9,1 Lq odujh frusrudwlrqv/ rzqhuv ghohjdwh ghflvlrqv vxfk
dv lqyhvwphqw/ h�ruw surylvlrq/ dqg uhvrxufh doorfdwlrq wr surihvvlrqdo pdqdjhuv1 Wkhvh ghflvlrqv
duh riwhq xqrevhuydeoh ru yhu| frvwo| iru wkh rzqhuv wr prqlwru1 Lq sduwlfxodu/ lw lv w|slfdoo| yhu|
kdug iru rzqhuv wr glvfhuq zkhwkhu ru qrw glyhuvl�fdwlrq ghflvlrqv duh ydoxh0pd{lpl}lqj1 Ehfdxvh
pdqdjhuv duh qrw ixoo uhvlgxdo fodlpdqwv/ wkh| pdnh ghflvlrqv wkdw lqfuhdvh wkhlu xwlolw| zkloh
srwhqwldoo| ghfuhdvlqj wkh ydoxh ri wkh �up1 Li wkh| kdg ehwwhu lqfhqwlyhv ru juhdwhu rzqhuvkls/
wkh| zrxog pruh ixoo| lqwhuqdol}h wkh frvwv dvvrfldwhg zlwk wkhlu qrq0ydoxh0pd{lpl}lqj ghflvlrqv1
Wkh djhqf| h{sodqdwlrq lv vxssruwhg e| wzr pdlq hpslulfdo �qglqjv1 Iluvw/ d qxpehu ri sd0
shuv vxfk dv Vhuydhv +4<<9,/ Ehujhu dqg Rihn +4<<8,/ Frpphqw dqg Mduuhoo +4<<8,/ dqg Odqj dqg
Vwxo} +4<<7,/ vkrz wkdw �up ydoxh +riwhq phdvxuhg e| Wrelq*v T, lv ghfuhdvlqj lq glyhuvl�fdwlrq14
Vhfrqg/ sdshuv e| Ghqlv/ Ghqlv/ dqg Vdulq +4<<:, dqg Edwhv/ El}mdn/ dqg Ohpprq +4<<:, �qg
hylghqfh ri ohvv glyhuvl�fdwlrq lq �upv zlwk kljkhu pdqdjhuldo htxlw| rzqhuvkls1 Wkhvh �qglqjv
vxjjhvw wkdw htxlw| rzqhuvkls uhgxfhv ydoxh0ghvwur|lqj glyhuvl�fdwlrq e| uhgxflqj pdqdjhuv* ehq0
h�wv +ru/ htxlydohqwo|/ iruflqj pdqdjhuv wr lqwhuqdol}h pruh ri wkh frvwv, iurp hqjdjlqj lq djhqf|
ehkdylru1 Wkhvh wzr slhfhv ri hylghqfh sdlqw d frqvlvwhqw slfwxuh ri glyhuvl�fdwlrq uhvxowlqj iurp
djhqf| ehkdylru e| pdqdjhuv15
Xqiruwxqdwho|/ wklv slfwxuh lv lqfrpsohwh dqg vrphzkdw plvohdglqj/ rq erwk wkhruhwlfdo dqg
hpslulfdo jurxqgv1 Wkh djhqf| vwru| dv vwdwhg wuhdwv wkh ohyho ri pdqdjhuldo lqfhqwlyhv dv h{rjh0
qrxvo| ghwhuplqhg1 \hw wkh rzqhuv ri �upv fdq fkrrvh wkh ohyho ri lqfhqwlyhv/ dqg w|slfdoo| gr
vr wr lq xhqfh pdqdjhuv* dfwlrqv1 Wr wdnh dq h{wuhph irup ri wkh dujxphqw/ li glyhuvl�fdwlrq lv
frvwo|/ zk| gr rzqhuv qrw lqfuhdvh lqfhqwlyhv xqwlo pdqdjhuv fkrrvh qrw wr glyhuvli| dw dooB Fohduo|
4 Wklv hylghqfh e| lwvhoi lv qrw gh�qlwlyh/ lq wkdw �upv wkdw rswlpdoo| glyhuvli| pd| kdyh orzhu ydoxhv ri Wrelq*v T
gr wkdq �upv wkdw rswlpdoo| uhpdlq irfxvhg1 Pruh hylghqfh lv surylghg e| Mrkq dqg Rihn +4<<8,/ zkr �qg wkdw
�upv wkdw lqfuhdvh wkhlu irfxv ru ghfuhdvh glyhuvl�fdwlrq vkrz lpsuryhg �up shuirupdqfh1 Hyhq wklv/ krzhyhu/
lv qrw gh�qlwlyh lq wkdw Kxeedug dqg Sdold +4<<<, dujxh wkdw fkdqjhv lq irfxv duh rswlpdo uhvsrqvhv wr fkdqjlqj
hfrqrplf hqylurqphqwv1 Zh glvfxvv wkhvh lvvxhv ri hqgrjhqhlw| lq juhdwhu ghwdlo ehorz1
5 Wkhuh duh pdq| rwkhu srwhqwldo h{sodqdwlrqv iru glyhuvl�fdwlrq ghflvlrqv1 Wr phqwlrq wzr srvvlelolwlhv/ glyhuvl0
�fdwlrq pd| eh rswlpdo iru vrph �upv iru uhdvrqv ri lqwhuqdo fdslwdo pdunhwv/ dv lq Vwhlq +4<<:,1 Dowhuqdwlyho|/
glyhuvl�fdwlrq pd| qrw eh rswlpdo ehfdxvh lw lv wkh rxwjurzwk ri frpshwlwlrq ehwzhhq glylvlrqv iru vfdufh frusrudwh
uhvrxufhv/ dv lq Udmdq/ Vhuydhv/ dqg ]lqjdohv +5333,1
4
wkhuh pxvw eh frvwv dvvrfldwhg zlwk surylglqj lqfhqwlyhv dv zhoo1 Exw ehfdxvh wkhvh frvwv gr qrw
hqwhu wkh djhqf| vwru| wrog deryh/ wkdw vwru| grhv qrw ixoo| ghslfw dq htxloleulxp ri d prgho lq
zklfk glyhuvl�fdwlrq uhvxowv iurp djhqf| ehkdylru1 Wr eh vshfl�f/ wkh fxuuhqw olwhudwxuh wuhdwv
revhuyhg gl�huhqfhv lq lqfhqwlyhv dfurvv �upv dv vxerswlpdo frqwudfwv lq rwkhuzlvh lghqwlfdo �upv1
Lq frqwudvw/ zh ylhz revhuyhg gl�huhqfhv lq lqfhqwlyhv dfurvv �upv dv htxloleulxp fkrlfhv pdgh
e| khwhurjhqhrxv �upv1
Wkh nh| wr rxu prgho lv wkdw zh wuhdw wkh pdqdjhu*v lqfhqwlyhv dv hqgrjhqrxv1 Lq rxu prgho/
zh dvvxph pdqdjhuv glyhuvli| ehfdxvh wkh| ghulyh vrph sulydwh ehqh�w iurp grlqj vr1 Wkh| pd|
zlvk wr uxq d odujhu/ pruh glyhuvl�hg �up iru uhdvrqv ri suhvwljh +Mhqvhq +4<;9,/ Vwxo} +4<<3,,1
Wkh| pd| zlvk wr uxq d odujhu/ pruh glyhuvl�hg �up wr lqfuhdvh wkhlu sd| +Mhqvhq dqg Pxusk|
+4<<3,, ru wkhlu rssruwxqlwlhv iru vnlpplqj +Ehuwudqg dqg Pxoodlqdwkdq +4<<<,,1 Glyhuvli|lqj
wkh �up pd| hqwuhqfk pdqdjhuv/ pdnlqj wkhp pruh ydoxdeoh wr wkh �up +Vkohlihu dqg Ylvkq|
+4<;<,,1 Pdqdjhuv pd| glyhuvli| ehfdxvh wkh| zlvk wr uhgxfh wkh h{srvxuhv ri wkhlu sruwirolrv
wr lglrv|qfudwlf ulvn +Dplkxg dqg Ohy +4<;4,/ Pd| +4<<8,,1 Ilqdoo|/ uxqqlqj d odujhu/ pruh
glyhuvl�hg �up pd| lpsuryh d pdqdjhu*v ixwxuh fduhhu survshfwv1
Zh irfxv rq lqfhqwlyhv surylghg e| w|lqj pdqdjhuv* frpshqvdwlrq wr wkh shuirupdqfh ri wkhlu
�upv1 Wkh rswlpdo frqwudfw wudghv r� kljkhu �up ydoxh iurp uhgxfhg glyhuvl�fdwlrq djdlqvw kljkhu
frpshqvdwlrq frvwv gxh wr h{srvxuh wr ulvn1 Wkh rswlpdo frqwudfw ghshqgv rq irxu h{rjhqrxv sd0
udphwhuv wkdw jryhuq wklv wudghr�= wkh pdqdjhu*v ulvn dyhuvlrq/ wkh yduldqfh ri �up shuirupdqfh/
wkh glvxwlolw| dvvrfldwhg zlwk wdnlqj ydoxh0hqkdqflqj dfwlrqv/ dqg wkh pdjqlwxgh ri wkh sulydwh
ehqh�wv dvvrfldwhg zlwk glyhuvl�fdwlrq1 Rxu prgho fohduo| vkrzv wkdw d vshfl�f �qglqj vxfk dv
glyhuvl�fdwlrq lv ghfuhdvlqj lq lqfhqwlyhv lv qrw gh�qlwlyh derxw wkh djhqf| frvw h{sodqdwlrq iru
zk| pdqdjhuv glyhuvli|1 Lq idfw/ d �qglqj wkdw glyhuvl�fdwlrq lv lqfuhdvlqj lq lqfhqwlyhv lv htxdoo|
frqvlvwhqw zlwk wkh djhqf| frvw h{sodqdwlrq1 Erwk duh shuplwwhg dv htxloleulxp uhodwlrqvklsv lq
wkh prgho/ zlwk gl�huhqw vrxufhv ri h{rjhqrxv yduldwlrq lq wkh xqghuo|lqj sdudphwhuv1
Zh whvw rxu prgho xvlqj gdwd rq pdqdjhuldo lqfhqwlyhv iurp Vwdqgdug dqg Srru*v H{hfxFrps
gdwdvhw1 Rxu vdpsoh frqvlvwv ri frpsuhkhqvlyh gdwd iru wkh wrs �yh h{hfxwlyhv +udqnhg dqqxdoo| e|
vdodu| dqg erqxv, iurp wkh V)S 833/ V)S PlgFds 733/ dqg V)S VpdooFds 933 frpsdqlhv iurp
4<<6 wr 4<<;1 Zh xvh �up shuirupdqfh dqg glyhuvl�fdwlrq gdwd iurp Frpsxvwdw1 Rxu gdwdvhw
5
doorzv xv wr pxfk pruh fduhixoo| lvrodwh wkh uhodwlrqvkls ehwzhhq �up shuirupdqfh/ glyhuvl�fdwlrq/
dqg lqfhqwlyhv1 Zh �qg wkdw �up shuirupdqfh lv lqfuhdvlqj lq lqfhqwlyhv dqg ghfuhdvlqj lq
glyhuvl�fdwlrq/ frqvlvwhqw zlwk wkh suhylrxv olwhudwxuh1 Pruh lpsruwdqwo|/ zh �qg hylghqfh wkdw
glyhuvl�fdwlrq lv lqfuhdvlqj lq lqfhqwlyhv/ lq frqwudvw wr wkh suhylrxv olwhudwxuh1 Zh vkrz wkdw wkh
qhjdwlyh uhodwlrqvkls irxqg lq suhylrxv vwxglhv lv wkh uhvxow ri xqrevhuyhg/ �up0vshfl�f idfwruv1
Zh frqwuro iru wkhvh idfwruv e| xvlqj �up ohyho �{hg h�hfwv1 Wkh uhvxow wkdw glyhuvl�fdwlrq lv
lqfuhdvlqj lq lqfhqwlyhv vxjjhvwv wkdw fkdqjhv lq lqfhqwlyhv dqg glyhuvl�fdwlrq duh gxh wr fkdqjhv
lq wkh sulydwh ehqh�wv dvvrfldwhg zlwk glyhuvl�fdwlrq1 Wklv yduldwlrq dovr kdv lpsolfdwlrvq iru
�up ydoxh1 Dv dq dgglwlrqdo whvw/ zh frqvlghu krz �up ydoxh uhvsrqgv wr lqfhqwlyhv lq �upv
wkdw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq uhodwlyh wr �upv wkdw gr qrw1 Zh �qg wkdw wkh olqn
ehwzhhq shuirupdqfh dqg lqfhqwlyhv lv vljql�fdqwo| zhdnhu iru �upv wkdw h{shulhqfh fkdqjhv lq
glyhuvl�fdwlrq wkdq lw lv iru �upv wkdw gr qrw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq1 Wkhvh wzr
�qglqjv duh frqvlvwhqw zlwk wkh djhqf| frvw h{sodqdwlrq iru glyhuvl�fdwlrq lq zklfk revhuyhg
fkdqjhv lq �up shuirupdqfh/ glyhuvl�fdwlrq/ dqg lqfhqwlyhv zlwklq �upv duh htxloleulxp uhvsrqvhv
wr vkliwv lq wkh ohyho ri ehqh�wv pdqdjhuv ghulyh iurp glyhuvl�fdwlrq1
Wkh uhpdlqghu ri wkh sdshu lv rujdql}hg dv iroorzv1 Lq Vhfwlrq 5/ zh suhvhqw wkh sulqflsdo0djhqw
prgho ri glyhuvl�fdwlrq1 Lq Vhfwlrq 6/ zh ghvfuleh rxu gdwd rq lqfhqwlyhv/ �up shuirupdqfh/ dqg
glyhuvl�fdwlrq1 Wkh hfrqrphwulf uhvxowv duh suhvhqwhg lq Vhfwlrq 71 Vhfwlrq 8 frqfoxghv1
51 Wkhru|
Zh frqvlghu d sulqflsdo0djhqw vhwwlqj lq zklfk pdqdjhuv fkrrvh dq dfwlrq { +vxfk dv wkh dprxqw
ri h�ruw wr h{huw ru wkh ohyho ri lqyhvwphqw, dv zhoo dv wkh dprxqw ri glyhuvl�fdwlrqq1 Wkh dprxqw
ri glyhuvl�fdwlrq fdq eh wkrxjkw ri dv wkh qxpehu ri glylvlrqv ru wkh olqhv ri exvlqhvv zlwklq wkh
�up/ zkhuh q � 41 Zh dvvxph wkdw �up ydoxh lv=
� @ {� q. % +4,
zkhuh % lv d qrupdoo| glvwulexwhg vkrfn wr �up ydoxh zlwk }hur phdq dqg yduldqfh �51 Wklv
vshfl�fdwlrq lpsolhv wkdw wkh djhqw*v dfwlrq fkrlfh { dqg wkh ohyho ri glyhuvl�fdwlrq q duh dgglwlyho|
vhsdudeoh lq wkhlu h�hfwv rq �up ydoxh1 Wkh djhqw*v fkrlfh ri dfwlrq dqg ohyho ri glyhuvl�fdwlrq
duh dvvxphg wr eh xqrevhuydeoh1 Zkloh vkduhkroghuv frxog srwhqwldoo| prqlwru pdqdjhuv* dfwlrq
6
dqg glyhuvl�fdwlrq fkrlfhv/ grlqj vr lv frvwo|1 Grlqj vr lv sduwlfxoduo| frvwo| lq odujh/ sxeolfo|
wudghg frusrudwlrqv lq zklfk rzqhuvkls lv glvshuvhg1
Iroorzlqj Kropvwurp dqg Plojurp +4<;:,/ wkh djhqw uhfhlyhv d zdjh frqwudfw wkdw lv olqhdu lq
�up shuirupdqfh=
z @ z3 . ��= +5,
Wkh djhqw uhfhlyhv d �{hg zdjh frpsrqhqw +vdodu|, ri z3 dqg d shuirupdqfh0edvhg frpsrqhqw
ri ��1 Lq wklv vhwwlqj/ wkh djhqw*v sd|0shuirupdqfh vhqvlwlylw| lv �1 Zh fdq dovr lqwhusuhw wkh
suhylrxv htxdwlrq dv d vwdwhphqw derxw wkh djhqw*v zhdowk1 Li zh dvvxph/ dv lv wuxh ri prvw
h{hfxwlyhv/ wkdw d odujh iudfwlrq ri wkhlu zhdowk lv lqyhvwhg lq wkhlu rzq �upv/ wkhq z3 lv wkh
frpsrqhqw ri zhdowk wkdw lv lqghshqghqw ri wkh �up dqg �� lv wkh frpsrqhqw ri zhdowk wkdw lv
dwwulexwdeoh wr wkh �up1 Lq wklv fdvh/ � uhsuhvhqwv h{hfxwlyh rzqhuvkls lq wkh �up1
Wkh djhqw kdv qhjdwlyh h{srqhqwldo xwlolw| zlwk d frh!flhqw ri devroxwh ulvn dyhuvlrq ri u dqg
kdv d fhuwdlqw| htxlydohqw ri=
x @ � +{� q, . } oqq� n
5{5 � u
5�5�5= +6,
Wkh olqhdu fhuwdlqw| htxlydohqw uhvxowv iurp wkh dvvxpswlrqv wkdw wkh djhqw kdv FDUD xwlolw| dqg
wkh vkrfn wr �up ydoxh lv qrupdoo| glvwulexwhg1 Wkh �uvw whup uh hfwv wkh djhqw*v vkduh ri h{shfwhg
�up ydoxh1 Wkh djhqw kdv glvxwlolw| ri wkh dfwlrq fkrlfh jlyhq e| n
5{51 Wkh whup u
5�5�5 uhsuhvhqwv
wkh frvw ri wkh djhqw*v ulvn dyhuvlrq ru wkh suhplxp wkh djhqw kdv wr eh sdlg lq rughu wr ehdu ulvn1
Zh dvvxph wkdw wkh djhqw jhqhudwhv sulydwh ehqh�wv ri wkh irup } oqq iurp juhdwhu glyhuvl�fdwlrq/
zkhuh } A 3 lqgh{hv wkh ehqh�wv wkh djhqw ghulyhv iurp glyhuvl�fdwlrq1 Wklv ixqfwlrqdo irup
fdswxuhv wkh lghd wkdw wkhuh lv glplqlvklqj pdujlqdo xwlolw| iru wkh djhqw iurp glyhuvl�fdwlrq1 Lq
wkh Dsshqgl{/ zh frqvlghu d pruh jhqhudo vshfl�fdwlrq ri wkh pdqdjhu*v sulydwh ehqh�wv ixqfwlrq
dqg vkrz wkdw rxu uhvxowv frqwlqxh wr krog1
Wkh pdqdjhu*v sulydwh ehqh�wv pd| frph iurp suhvwljh dvvrfldwhg zlwk uxqqlqj d odujhu/ pruh
glyhuvl�hg �up1 Sulydwh ehqh�wv pd| frph ehfdxvh uxqqlqj d odujhu/ pruh glyhuvl�hg �up lq0
fuhdvhv pdqdjhuv* sd| ru wkhlu rssruwxqlwlhv iru vnlpplqj1 Sulydwh ehqh�wv pd| frph ehfdxvh
glyhuvli|lqj hqwuhqfkhv pdqdjhuv/ pdnlqj wkhp pruh ydoxdeoh wr wkh �up1 Sulydwh ehqh�wv pd|
frph ehfdxvh glyhuvl�fdwlrq uhgxfhv wkh h{srvxuh ri pdqdjhuv* sruwirolrv wr lglrv|qfudwlf ulvn1
7
Odvwo|/ sulydwh ehqh�wv pd| frph ehfdxvh uxqqlqj d odujhu/ pruh glyhuvl�hg �up lpsuryhv pdq0
djhuv* ixwxuh fduhhu survshfwv1
Wkh djhqw fkrrvhv wkh ohyho ri glyhuvl�fdwlrq dqg khu dfwlrq e| pd{lpl}lqj wkh fhuwdlqw|
htxlydohqw +6,1 Wkh sulqflsdo*v sureohp lv wr pd{lpl}h h{shfwhg �up ydoxh qhw ri frpshqvdwlrq
iru wkh djhqw jlyhq wkdw wkh djhqw zloo fkrrvh wkh dfwlrq dqg wkh ohyho ri glyhuvl�fdwlrq wr pd{lpl}h
khu xwlolw|1 Wkh wlplqj ri wkh prgho lv=
3= Sulqflsdo r�huv djhqw d frqwudfw edvhg rq shuirupdqfh1
4= Djhqw fkrrvhv olqhv ri exvlqhvv +ru dprxqw ri glyhuvl�fdwlrq, q � 4 dqg dq dfwlrq {=6
5= � lv uhdol}hg dqg wkh djhqw lv frpshqvdwhg1
Jlyhq wkh sulqflsdo*v fkrlfh ri lqfhqwlyhv/ �/ wkh djhqw*v sureohp lv=
pd{{>q
� +{� q, . } oqq� n
5{5 � u
5�5�5= +7,
Wkh �uvw rughu frqglwlrq iru glyhuvl�fdwlrq q jlyhv xv=
q� @}
�= +8,
Li wkh sulqflsdo surylghv pruh lqfhqwlyhv/ wkhq wkh djhqw fkrrvhv ohvv glyhuvl�fdwlrq1 Zkhq zh
wxuq wr wkh sulqflsdo*v sureohp ri rswlpdoo| fkrrvlqj lqfhqwlyhv ehorz/ zh vkdoo fdofxodwh krz
glyhuvl�fdwlrq dqg lqfhqwlyhv frydu| zkhq erwk duh hqgrjhqrxvo| ghwhuplqhg1
Iru wkh djhqw*v dfwlrq fkrlfh/ wkh �uvw rughu frqglwlrq jlyhv xv {� dv d ixqfwlrq ri �=
{� @�
n= +9,
Wkh sulqflsdo*v sureohp lv wr pd{lpl}h �up ydoxh qhw ri frpshqvdwlrq iru wkh djhqw jlyhq wkh
djhqw*v glyhuvl�fdwlrq dqg dfwlrq fkrlfhv1 H{shfwhg �up ydoxh qhw ri frpshqvdwlrq iru wkh djhqw
lv=
H^�`�z @ {� � q� . } oqq� � n
5+{�,5 � u
5�5�5 +:,
Khuh zh dvvxph wkdw wkh pdqdjhuldo oderu pdunhw lv frpshwlwlyh vr wkh djhqw zloo eh khog wr khu
uhvhuydwlrq xwlolw|/ zklfk zh qrupdol}h wr }hur1 Vxevwlwxwlqj wkh djhqw*v fkrlfh ri dfwlrq dqg
glyhuvl�fdwlrq lqwr htxdwlrq +:, dqg pd{lpl}lqj zlwk uhvshfw wr � |lhogv wkh sulqflsdo*v sureohp=
pd{�
�
n� }
�. } oq
}
�� �5
5n� u
5�5�5 +;,
6 Dvvxplqj 5 lv vx!flhqwo| odujh zloo jxdudqwhh wkdw ? D ��
8
Wkh �uvw rughu frqglwlrq lv=4� �
n.
}
�5� }
�� u��5 @ 3= +<,
Wkh vhfrqg rughu frqglwlrq lv=
�4
n� 5}
�6.
}
�5� u�5= +43,
Wkhuh h{lvwv d xqltxh �� 5 +3> 4,= Wr vhh wklv/ qrwh wkdw dv � $ 3/ wkh �uvw rughu frqglwlrq
lv srvlwlyh1 Dv � $ 4> wkh �uvw rughu frqglwlrq lv qhjdwlyh1 Wkhuhiruh/ wkhuh h{lvwv dq lqwhulru
vroxwlrq rq +3> 4,= Wkh vhfrqg rughu frqglwlrq lv qhjdwlyh iru doo � 5 +3> 4, lpso|lqj wkdw wkh
vroxwlrq lv xqltxh1
Rswlpdo lqfhqwlyhv �� duh d ixqfwlrq ri wkh h{rjhqrxv sdudphwhuv u> �5> n> dqg }1 Zh kdyh
wkh iroorzlqj frpsdudwlyh vwdwlfv iru ���u> �5> n> }
�=
C��
Cu@
���5
� 4
n� 5}
+��,6 .
}
+��,5 � u�5
? 3 +44,
C��
C�5@
u��
� 4
n� 5}
+��,6 .
}
+��,5 � u�5
? 3 +45,
C��
Cn@
+4� ��, @n5
� 4
n� 5}
+��,6 .
}
+��,5 � u�5
? 3 +46,
C��
C}@
� 4
+��,5 .
4
��
� 4
n� 5}
+��,6 .
}
+��,5 � u�5
A 3= +47,
Htxdwlrqv +44, dqg +45, duh dq lpphgldwh frqvhtxhqfh ri dvvxplqj wkdw pdqdjhuv duh ulvn dyhuvh1
Pdqdjhuv uhfhlyh ihzhu lqfhqwlyhv �� dv ulvn dyhuvlrq lqfuhdvhv ru wkh yduldqfh ri wkh shuirupdqfh
phdvxuh lqfuhdvhv17 Htxdwlrq +46, vkrzv wkdw lqfhqwlyhv ghfuhdvh dv wkh glvxwlolw| ri wkh dfwlrq
fkrlfh lqfuhdvhv1 Dv lw ehfrphv lqfuhdvlqjo| frvwo| wr lqgxfh wkh djhqw wr wdnh wkh dfwlrq/ wkh
sulqflsdo zloo uhvsrqg e| uhgxflqj wkh lqfhqwlyhv vkh surylghv iru wkh djhqw wr wdnh wkh dfwlrq1
Wkh �uvw wkuhh frpsdudwlyh vwdwlfv duh vwdqgdug iru olqhdu sulqflsdo0djhqw prghov +vhh Kropvwurp
dqg Plojurp +4<;:,,1
Lq wklv sdshu/ zh h{whqg wkh prgho wr dqdo|}h pdqdjhuv* lqfhqwlyhv lq uhodwlrq wr glyhuvl�fdwlrq1
Htxdwlrq +47, vkrzv wkdw lqfhqwlyhv lqfuhdvh dv wkh sulydwh ehqh�w dvvrfldwhg zlwk glyhuvl�fdwlrq
lqfuhdvhv1 Wkh lqwxlwlrq iru wklv uhvxow lv wkdw lqfhqwlyhv duh xvhg wr r�vhw wkh pdqdjhu*v sul0
ydwh ehqh�w iurp glyhuvl�fdwlrq1 Li sulydwh ehqh�wv lqfuhdvh/ wkh pdqdjhu pxvw eh jlyhq pruh7 Djjduzdo dqg Vdpzlfn +4<<<d/ 4<<<e, vkrz wkdw
Yk
Yj5 f lv vwurqjo| vxssruwhg hpslulfdoo|1 Lq wkrvh sdshuv/
zh vkrz wkdw pdqdjhuv dw �upv zlwk wkh odujhvw yduldqfhv ri vwrfn uhwxuqv kdyh sd|0shuirupdqfh vhqvlwlylwlhv wkdw
duh dq rughu ri pdjqlwxgh vpdoohu wkdq pdqdjhuv dw �upv zlwk wkh vpdoohvw yduldqfhv ri vwrfn uhwxuqv1 Zh dujxh
wkdw wklv surylghv ydolgdwlrq ri wkh sulqflsdo0djhqw prgho1
9
lqfhqwlyhv dv sduw ri wkh rswlpdo frqwudfw wr suhyhqw wkh pdqdjhu iurp hqjdjlqj lq hyhq pruh
ydoxh0ghvwur|lqj glyhuvl�fdwlrq1
Lq rughu wr whvw wkh prgho edvhg rq wkh ghwhuplqdqwv ri �/ zh zrxog qhhg wr revhuyh }1 Li zh
�qg wkdw C��
C}A 3/ wkhq wklv zrxog frqvwlwxwh vwurqj vxssruw iru wkh prgho1 Frqyhuvho|/ li zh �qg
wkdw C��
C}? 3/ wkhq zh nqrz wkdw wkh prgho/ dw ohdvw lq lwv edvlf irup/ lv zurqj1 Xqiruwxqdwho|/
} lv qrw gluhfwo| revhuydeoh lq d odujh furvv0vhfwlrq ri �upv/ qru duh uhdvrqdeoh sur{lhv dydlodeoh
lq wkh vhqvh wkdw wkh| zrxog eh xqfruuhodwhg zlwk rwkhu �up0vshfl�f idfwruv1 Krzhyhu/ zh fdq
uholdeo| revhuyh �/ q/ dqg � lq d odujh sdqho ri �upv1 Lq rughu wr whvw wkh wkhru|/ zh wkhuhiruh
ghulyh frpsdudwlyh vwdwlf suhglfwlrqv ri krz wkhvh wkuhh rxwfrphv zloo fkdqjh dv wkh xqghuo|lqj
h{rjhqrxv sdudphwhuv u/ �5/ n/ dqg } ydu| dfurvv �upv dqg ryhu wlph1
Zh vwduw e| vhhlqj krz glyhuvl�fdwlrq lv d�hfwhg e| lqfhqwlyhv1 Iru wkh djhqw*v glyhuvl�fdwlrq
fkrlfh q�/ zh xvh wkh �uvw0rughu frqglwlrq +8,1 Wkh rswlpdo �� iurp htxdwlrq +<, lv d ixqfwlrq ri
wkh h{rjhqrxv sdudphwhuv u/ �5/ n> dqg }1 Zh vxevwlwxwh ���u> �5> n> }
�lqwr htxdwlrq +8, wr jhw=
q� @}
�� +u> �5> n> },= +48,
Zh �uvw wdnh wkh ghulydwlyh ri q� zlwk uhvshfw wr wkh h{rjhqrxv sdudphwhuv dqg wkhq fdofxodwh
krz q� ydulhv zlwk �� jlyhq d fkdqjh lq wkh h{rjhqrxv sdudphwhu1 Wkh frpsdudwlyh vwdwlfv zlwk
uhvshfw wr wkh h{rjhqrxv sdudphwhuv duh=
Cq�
Cu@ � }
+��,5C��
CuA 3 +49,
Cq�
C�5@ � }
+��,5C��
C�5A 3
Cq�
Cn@ � }
+��,5C��
CnA 3
Cq�
C}@
4
��� }
+��,5C��
C}
@4
��
# � 4n� }
+��,6� u�5
� 4n� 5}
+��,6. }
+��,5� u�5
$A 3=
Iru ulvn dyhuvlrq u/ wkh yduldqfh ri wkh shuirupdqfh phdvxuh �5/ dqg wkh glvxwlolw| ri wkh dfwlrq
fkrlfh n/ wkh rswlpdo ohyho ri glyhuvl�fdwlrq fkdqjhv gxh wr wkhvh sdudphwhuv rqo| wkurxjk wkhlu
h�hfw rq lqfhqwlyhv ��1 Ehfdxvh rswlpdo lqfhqwlyhv ghfuhdvh dv wkhvh sdudphwhuv lqfuhdvh/ glyhu0
vl�fdwlrq lqfuhdvhv1 Wkh lqwxlwlrq lv wkdw lqfuhdvlqj wkhvh sdudphwhuv orzhuv lqfhqwlyhv hlwkhu wr
:
lqvxodwh wkh pdqdjhu iurp ulvn ru wr uhgxfh wkh frvw ri lqgxflqj wkh pdqdjhu wr wdnh wkh frvwo|
dfwlrq1 Exw lqfhqwlyhv duh zkdw frqvwudlq wkh pdqdjhu*v glyhuvl�fdwlrq ghflvlrq1 Dv lqfhqwlyhv
ghfuhdvh/ wkh pdqdjhu glyhuvl�hv pruh1
Iru sulydwh ehqh�wv ri glyhuvl�fdwlrq }/ wkh rswlpdo ohyho ri glyhuvl�fdwlrq fkdqjhv iru wzr
uhdvrqv1 Iluvw/ juhdwhu sulydwh ehqh�wv pdnh glyhuvl�fdwlrq pruh dwwudfwlyh iru pdqdjhuv/ dqg
wklv lqfuhdvhv glyhuvl�fdwlrq1 Vhfrqg/ juhdwhu sulydwh ehqh�wv lqfuhdvh lqfhqwlyhv zklfk uhgxfh
glyhuvl�fdwlrq1 Ehfdxvh lqfhqwlyhv duh frvwo| wr surylgh/ wkh �uvw h�hfw grplqdwhv wkh vhfrqg vr
wkh ohyho ri glyhuvl�fdwlrq lv lqfuhdvlqj lq wkh sulydwh ehqh�wv ri glyhuvl�fdwlrq1
Lq rughu wr whvw wkh prgho zh qrz h{dplqh krz q� ydulhv zlwk �� lq htxloleulxp jlyhq d fkdqjh
lq dq h{rjhqrxv sdudphwhu=8
Cq�
C��
����Cu
@Cq�
Cu!C��
Cu? 3 +4:,
Cq�
C��
����C�
5
@Cq�
C�5!C��
C�5? 3
Cq�
C��
����Cn
@Cq�
Cn!C��
Cn? 3
Cq�
C��
����C}
@Cq�
C}
�����
�@��+u>�5>n>},
!C��
C}A 3=
Wkhvh h{suhvvlrqv uhodwh wkh rswlpdo ohyho ri glyhuvl�fdwlrq wr wkh rswlpdo dprxqw ri lqfhqwlyhv
jlyhq d fkdqjh lq dq h{rjhqrxv sdudphwhu1 Wkhvh h{suhvvlrqv ghvfuleh wkh ehkdylru ri q� dqg
���lq rwkhu zrugv/ lq htxloleulxp1 Iru ulvn dyhuvlrq/ wkh yduldqfh ri wkh shuirupdqfh phdvxuh/ dqg
wkh glvxwlolw| ri wkh dfwlrq fkrlfh/ glyhuvl�fdwlrq lv ghfuhdvlqj lq lqfhqwlyhv ehfdxvh/ dv h{shfwhg/
lqfhqwlyhv r�vhw glyhuvl�fdwlrq1 Li wkh pdqdjhu ghulyhv juhdwhu sulydwh ehqh�wv iurp glyhuvli|lqj/
juhdwhu lqfhqwlyhv dovr r�vhw glyhuvl�fdwlrq/ exw qrw hqrxjk wr suhyhqw wkh pdqdjhu iurp glyhuvl0
i|lqj pruh1 Iru juhdwhu sulydwh ehqh�wv/ dq lqfuhdvh lq lqfhqwlyhv lv dvvrfldwhg zlwk dq lqfuhdvh
lq glyhuvl�fdwlrq1 Zkhq frqiurqwhg zlwk d pdqdjhu zlwk kljkhu sulydwh ehqh�wv/ rzqhuv surylgh
vwurqjhu lqfhqwlyhv wr frxqwhudfw wkh sulydwh ehqh�wv1 Surylglqj wkhvh lqfhqwlyhv frphv dw d frvw
wr wkh rzqhuv lq wkh irup ri surylglqj pruh lqvxudqfh wr wkh pdqdjhu wr r�vhw wkh lqfuhdvhg ulvn1
Dowkrxjk lqfhqwlyhv lqfuhdvh wr r�vhw wkh lqfuhdvh lq sulydwh ehqh�wv/ lqfhqwlyhv gr qrw lqfuhdvh
vx!flhqwo| wr suhyhqw wkh pdqdjhu iurp juhdwhu glyhuvl�fdwlrq19
8 Htxdwlrq +4:, gl�huv iurp htxdwlrq +8, lq wkdw htxdwlrq +4:, krogv dw wkh htxloleulxp fkrlfhv ri E?Wc kW� zkhuhdv
htxdwlrq +8, ghvfulehv ?
Wdv d ixqfwlrq ri k1 Htxdwlrq +4:, frlqflghv zlwk htxdwlrq +8, li wkh h{rjhqrxv vrxufh ri
yduldwlrq lv oc &c ru j
2exw gl�huv li wkh h{rjhqrxv vrxufh ri yduldwlrq lv 5�
9
;
Qrz zh wxuq wr �up ydoxh1 Lw lv fohdu wkdw �up ydoxh ghshqgv rq wkh h{rjhqrxv sdudphwhuv
u/ �5/ n/ dqg } rqo| wkurxjk wkhlu lpsdfw rq lqyhvwphqw rq wkh djhqw*v dfwlrq { dqg wkh djhqw*v
glyhuvl�fdwlrq fkrlfh q1 Zh wdnh wkh ghulydwlyh ri � zlwk uhvshfw wr wkh h{rjhqrxv sdudphwhuv
dqg wkhq fdofxodwh krz � ydulhv zlwk �� dqg zlwk q� jlyhq d fkdqjh lq wkh h{rjhqrxv sdudphwhu1
H{shfwhg �up ydoxh/
H+�, @ {� � q� @��
n� }
��> +4;,
ydulhv zlwk wkh h{rjhqrxv sdudphwhuv lq wkh iroorzlqj zd|=
CH+�,
Cu@
4
n
C��
Cu.
}
+��,5C��
Cu? 3 +4<,
CH+�,
C�5@
4
n
C��
C�5.
}
+��,5C��
C�5? 3
CH+�,
Cn@ ���
n5.
4
n
C��
Cn.
}
+��,5C��
Cn? 3
CH+�,
C}@
4
n
C��
C}� 4
��.
}
+��,5C��
C}
@4
n
# � 4+��,5
. 4��
� 4n� 5}
+��,6. }
+��,5� u�5
$� 4
��
# � 4n� }
+��,6� u�5
� 4n� 5}
+��,6. }
+��,5� u�5
$
@
}
+��,7� }
+��,6. 4
��n
� 4n� 5}
+��,6. }
+��,5� u�5
? 3>
ehfdxvh �� 5 +3> 4,1 Zh kdyh xvhg htxdwlrq +<, wr vlpsoli| wkh h{suhvvlrq iru CH+�,
C}1
Wkh uhvxowv lq +4<, duh lqwxlwlyh1 Dv ulvn dyhuvlrq/ wkh yduldqfh ri wkh shuirupdqfh phdvxuh/
dqg wkh glvxwlolw| ri wkh dfwlrq fkrlfh lqfuhdvh/ �up ydoxh ghfuhdvhv ehfdxvh wkh rswlpdo frqwudfw
Lq sulqflsoh/ zh frxog dovr vhh krz wkh djhqw*v dfwlrq fkrlfh %
Wlv d�hfwhg e| fkdqjhv lq wkh h{rjhqrxv sdudphwhuv1
Wklv lv xvhixo li wkh dfwlrq fkrlfh lv phdvxudeoh +h1j1/ wkh dfwlrq fkrlfh lv lqyhvwphqw�vhh Djjduzdo dqg Vdpzlfn
+4<<<f, iru d pruh wkrurxjk glvfxvvlrq ri wklv fdvh,1 Lw lv qrw hpslulfdoo| xvhixo li wkh dfwlrq fkrlfh lv qrw phdvxudeoh
+h1j1/ wkh dfwlrq fkrlfh lv h�ruw/ dv lq d vwdqgdug sulqflsdo0djhqw prgho,1 Wkh frpsdudwlyh vwdwlfv iru wkh djhqw*v
dfwlrq fkrlfh %
Wduh=
Y%
W
Yo
'
�
&
Yk
W
Yo
f
Y%
W
Yj
2'
�
&
Yk
W
Yj
2 f
Y%
W
Y&
' 3
k
W
&
2n
�
&
Yk
W
Y&
f
Y%
W
Y5
'
�
&
Yk
W
Y5
: f�
Zh dovr kdyh iru d jlyhq vrxufh ri h{rjhqrxv yduldwlrq=
Y%
W
Yk
W
����Y�
'
Y%
W
Y�
*
Yk
W
Y�
: fc � M toc j2c &c 5��
Lq rwkhu zrugv/ wkh djhqw*v dfwlrq fkrlfh lv dozd|v lqfuhdvlqj lq lqfhqwlyhv uhjdugohvv ri wkh vrxufh ri h{rjhqrxv
yduldwlrq1
<
vshfl�hv wkdw ihzhu lqfhqwlyhv duh jlyhq1 Li wkh djhqw*v sulydwh ehqh�wv ri glyhuvl�fdwlrq lqfuhdvh/
wkhuh duh wzr h�hfwv1 Iluvw/ glyhuvl�fdwlrq lqfuhdvhv/ zklfk orzhuv �up ydoxh1 Vhfrqg/ lqfhqwlyhv
lqfuhdvh wr sduwldoo| r�vhw wkh lqfuhdvhg glyhuvl�fdwlrq/ zklfk lq wxuq ohdgv wkh pdqdjhu wr wdnh
pruh ri wkh dfwlrq {/ wkhuhe| udlvlqj �up ydoxh1 Wkh �uvw h�hfw grplqdwhv wkh vhfrqg dqg vr
djjuhjdwh �up ydoxh lv orzhuhg1
Jlyhq d fkdqjh lq dq h{rjhqrxv sdudphwhu/ �up ydoxh frydulhv zlwk fkdqjhv lq �� lq wkh
iroorzlqj zd|v=
CH+�,
C��
����Cl
@CH+�,
Cl@C��
ClA 3> l 5 iu> �5> nj dqg +53,
CH+�,
C��
����C}
@CH+�,
C}@C��
C}? 3=
Li wkh xqghuo|lqj vrxufh ri h{rjhqrxv yduldwlrq lv ulvn dyhuvlrq/ wkh yduldqfh ri wkh shuirupdqfh
phdvxuh/ ru wkh glvxwlolw| ri wkh dfwlrq fkrlfh/ �up ydoxh lv lqfuhdvlqj lq lqfhqwlyhv1 Li wkh
xqghuo|lqj vrxufh ri yduldwlrq lv sulydwh ehqh�wv/ wkhq dq lqfuhdvh lq lqfhqwlyhv lv dvvrfldwhg zlwk
d ghfuhdvh lq �up ydoxh ehfdxvh glyhuvl�fdwlrq zloo dovr lqfuhdvh1
Zh kdyh iru q�=CH+�,
Cq�
����Cl
@CH+�,
Cl@Cq�
Cl? 3> l 5 iu> �5> n> }j= +54,
Wkh djhqw fkrrvhv d kljkhu ohyho ri glyhuvl�fdwlrq wkdq zrxog wkh sulqflsdo +jlyhq rxu dvvxpswlrqv/
wkh sulqflsdo zrxog fkrrvh wkh plqlpxp ohyho ri glyhuvl�fdwlrq,1 Wkhuhiruh/ dq| lqfuhdvh lq
glyhuvl�fdwlrq uhgxfhv �up ydoxh1
Lq wklv prgho/
� @ {�����u> �5> n> }
�> n�� q�+��
�u> �5> n> }
�> }, . %= +55,
Ehfdxvh wkh ohyho ri glyhuvl�fdwlrq q� ghshqgv rq lqfhqwlyhv ��/ uhjuhvvlqj �up ydoxh rq lqfhqwlyhv
fdq eh dpeljxrxv1 Wr vhh wklv/ qrwlfh wkdw lq htxdwlrq +53, deryh wkdw CH+�,
C��
fdq eh hlwkhu srvlwlyh
ru qhjdwlyh ghshqglqj xsrq wkh vrxufh ri h{rjhqrxv yduldwlrq1 Krzhyhu/ htxdwlrq +54, vkrzv
wkdw CH+�,
Cq�
lv dozd|v qhjdwlyh/ uhjdugohvv ri wkh vrxufh ri h{rjhqrxv yduldwlrq1 Li zh frqglwlrq
rq glyhuvl�fdwlrq/ wkhq �up ydoxh zloo eh lqfuhdvlqj lq lqfhqwlyhv1 Lq rughu wr hvwlpdwh htxdwlrq
+55,/ li zh zhuh wr uhjuhvv=
� @ �3. �
4�. �
5q. % +56,
43
zh vkrxog vhh �4A 3 dqg �
5? 3 lq doo fdvhv/ uhjdugohvv ri wkh vrxufh ri h{rjhqrxv yduldwlrq1
Wkh prgho lv wkhq lghqwl�hg e| h{dplqlqj Cq�
C��1 Li hpslulfdoo| Cq
�
C��@ 3/ wkhq wklv lpsolhv wkdw
glyhuvl�fdwlrq lv qrw gulyhq e| djhqf| frqvlghudwlrqv1 Li Cq�
C��? 3/ wkhq glyhuvl�fdwlrq lv gulyhq
e| djhqf| frqfhuqv dqg wkh vrxufhv ri h{rjhqrxv yduldwlrq wkdw fkdqjh lqfhqwlyhv/ glyhuvl�fdwlrq/
dqg �up ydoxh duh ulvn dyhuvlrq/ wkh yduldqfh ri vkrfnv/ ru wkh glvxwlolw| ri wkh dfwlrq fkrlfh1 Wklv
lv wkh �qglqj ri sdshuv vxfk dv Ghqlv/ Ghqlv/ dqg Vdulq +4<<:, dqg Edwhv/ El}mdn/ dqg Ohpprq
+4<<:,1 Li Cq�
C��A 3/ wkhq glyhuvl�fdwlrq lv gulyhq e| djhqf| frqfhuqv dqg wkh vrxufh ri h{rjhqrxv
yduldwlrq wkdw fkdqjhv lqfhqwlyhv/ glyhuvl�fdwlrq/ dqg �up ydoxh lv wkh ohyho ri sulydwh ehqh�wv wkdw
pdqdjhuv hqmr| iurp uxqqlqj d glyhuvl�hg �up1
Wr vxppdul}h/ dffruglqj wr wkh wkhru|/ yduldwlrq lq �up shuirupdqfh/ glyhuvl�fdwlrq/ dqg
lqfhqwlyhv pxvw eh wkh uhvxow ri gl�huhqfhv lq wkh irxu xqghuo|lqj sdudphwhuv�ulvn dyhuvlrq/ wkh
yduldqfh ri �up shuirupdqfh/ wkh glvxwlolw| ri wkh dfwlrq fkrlfh/ ru sulydwh ehqh�wv ri glyhuvl�fd0
wlrq1 Rxu prgho kdv irxu whvwdeoh suhglfwlrqv1 Iluvw/ frqwuroolqj iru wkh ohyho ri glyhuvl�fdwlrq/
wkh prgho suhglfwv wkdw �up shuirupdqfh zloo eh lqfuhdvlqj lq lqfhqwlyhv1 Wklv lv frqvlvwhqw zlwk
wkh hylghqfh lq Djjduzdo dqg Vdpzlfn +4<<<f,1 Vhfrqg/ frqwuroolqj iru wkh ohyho ri lqfhqwlyhv/
wkh prgho suhglfwv wkdw �up shuirupdqfh zloo eh ghfuhdvlqj lq glyhuvl�fdwlrq1 Wklv lv frqvlvwhqw
zlwk Vhuydhv +4<<9,/ Ehujhu dqg Rihn +4<<8,/ Frpphqw dqg Mduuhoo +4<<8,/ dqg Odqj dqg Vwxo}*v
+4<<7, hylghqfh iurp wkh 4<;3v1 Wklug/ li wkh xqghuo|lqj vrxufh ri yduldwlrq zlwklq �upv lv ulvn
dyhuvlrq/ wkh yduldqfh ri �up shuirupdqfh/ ru wkh glvxwlolw| ri wkh pdqdjhu*v dfwlrq fkrlfh/ wkhq
glyhuvl�fdwlrq zloo eh ghfuhdvlqj lq lqfhqwlyhv1 Li wkh xqghuo|lqj vrxufh ri yduldwlrq lv wkh pdjql0
wxgh ri wkh sulydwh ehqh�wv ri glyhuvl�fdwlrq/ wkhq glyhuvl�fdwlrq zloo eh lqfuhdvlqj lq lqfhqwlyhv1
Irxuwk/ iru �upv h{shulhqflqj yduldwlrq lq ulvn dyhuvlrq/ wkh yduldqfh ri �up shuirupdqfh/ ru wkh
glvxwlolw| ri wkh pdqdjhu*v dfwlrq fkrlfh/ shuirupdqfh zloo eh hyhq pruh vwurqjo| lqfuhdvlqj lq
lqfhqwlyhv wkdq lw zloo eh iru �upv h{shulhqflqj qr yduldwlrq lq wkh xqghuo|lqj sdudphwhuv1 Frq0
yhuvho|/ iru �upv h{shulhqflqj yduldwlrq lq wkh pdjqlwxgh ri wkh sulydwh ehqh�wv ri glyhuvl�fdwlrq/
shuirupdqfh zloo eh pruh zhdno| lqfuhdvlqj +ru srwhqwldoo| ghfuhdvlqj, lq lqfhqwlyhv wkdq lw zloo
eh iru �upv h{shulhqflqj qr yduldwlrq lq wkh xqghuo|lqj sdudphwhuv1
44
61 Gdwd
Wklv vhfwlrq ghvfulehv wkh gdwd vrxufhv wkdw zh xvh wr whvw wkh frpsdudwlyh vwdwlf suhglfwlrqv ri rxu
sulqflsdo0djhqw prgho1 Zh xvh Vwdqgdug dqg Srru*v H{hfxFrps gdwdvhw wr frqvwuxfw rxu phdvxuh
ri pdqdjhuldo lqfhqwlyhv1 H{hfxFrps frqwdlqv gdwd rq doo dvshfwv ri frpshqvdwlrq iru wkh wrs
�yh h{hfxwlyhv +udqnhg dqqxdoo| e| vdodu| dqg erqxv, dw hdfk ri wkh �upv lq wkh V)S 833/ V)S
Plgfds 733/ dqg V)S VpdooFds 9331 Gxh wr hqkdqfhg ihghudo uhsruwlqj uhtxluhphqwv iru �vfdo
|hduv hqglqj diwhu Ghfhpehu 48/ 4<<5/ zh fdq phdvxuh lqfhqwlyhv iurp 4<<6 wr 4<<;1: Ilqdqfldo
dqg rshudwlqj gdwd iru wkh H{hfxFrps vdpsoh frpsdqlhv duh gudzq iurp wkh Frpsxvwdw gdwdvhw1
Prqwko| phdvxuhv ri vwrfn uhwxuqv iurp wkh Fhqwhu iru Uhvhdufk rq Vhfxulw| Sulfhv +FUVS, duh
xwlol}hg lq fdofxodwlrqv ri wkh yduldqfh ri uhwxuqv1
Pdqdjhuv fdq uhfhlyh sd|0shuirupdqfh lqfhqwlyhv iurp d ydulhw| ri vrxufhv1 Wkh ydvw pdmrulw|
ri wkhvh lqfhqwlyhv duh gxh wr rzqhuvkls ri vwrfn dqg vwrfn rswlrqv1 Mhqvhq dqg Pxusk| +4<<3,
fduhixoo| djjuhjdwh sd|0shuirupdqfh lqfhqwlyhv lqwr d vlqjoh sd|0shuirupdqfh vhqvlwlylw|1 Wkh|
�qg wkdw wkh w|slfdo FHR uhfhlyhv dssur{lpdwho| '6158 ri frpshqvdwlrq shu wkrxvdqg groodu
lqfuhdvh lq vkduhkroghu zhdowk1 Ri wklv dprxqw/ '5183 lv gxh wr wkh phgldq FHR*v kroglqjv ri
vwrfn lq wkh �up dqg '3148 lv gxh wr rzqhuvkls ri vwrfn rswlrqv1 Lqfuhdvhv lq wkh suhvhqw ydoxh
ri fxuuhqw dqg ixwxuh frpshqvdwlrq dqg ghfuhdvhv lq wkh suredelolw| ri glvplvvdo duh uhvsrqvleoh
iru '3163 hdfk1 Djjduzdo dqg Vdpzlfn +4<<<d, vkrz wkdw lqfhqwlyhv iurp vwrfn dqg rswlrqv duh
urxjko| wzhqw| wlphv pruh lpsruwdqw wkdq dqqxdo frpshqvdwlrq dv d vrxufh ri lqfhqwlyhv iru erwk
FHRv dqg rwkhu wrs pdqdjhuv1 Wkxv/ rxu xvh ri sd|0shuirupdqfh vhqvlwlylwlhv edvhg rq vwrfn
dqg rswlrq rzqhuvkls fdswxuhv wkh exon ri wrwdo lqfhqwlyhv1 Pxfk ri wkh pdqdjhuldo hqwuhqfkphqw
olwhudwxuh kdv irfxvhg rq lqfhqwlyhv iurp vwrfn rzqhuvkls1 Rxu phdvxuh ri lqfhqwlyhv lv pruh
lqfoxvlyh lq wkdw lw dovr fryhuv rswlrqv1 Iru wklv uhdvrq/ zh uhihu wr rxu h{sodqdwru| yduldeoh dv
wkh sd|0shuirupdqfh vhqvlwlylw| ru �SSV� udwkhu wkdq �rzqhuvkls1�
H{hfxFrps frqwdlqv suhflvh gdwd rq h{hfxwlyhv* kroglqjv ri vwrfn lq wkhlu rzq frpsdqlhv dqg
judqwv ri rswlrqv gxulqj wkh fxuuhqw |hdu1 Iru vwrfn/ wkh sd|0shuirupdqfh vhqvlwlylw| lv vlpso| wkh
iudfwlrq ri wkh �up wkdw wkh h{hfxwlyh rzqv1 D FHR zkr krogv 6 shufhqw ri wkh vwrfn rxwvwdqglqj
: Wkh H{hfxFrps gdwd duh froohfwhg gluhfwo| iurp wkh frpsdqlhv* sur{| vwdwhphqwv dqg uhodwhg �olqjv zlwk wkh
Vhfxulwlhv H{fkdqjh Frpplvvlrq1 Rxu dqdo|vlv lq wklv sdshu xvhv gdwd iurp wkh Rfwrehu 4<<< uhohdvh ri wkh gdwd1
Vhh Vwdqgdug dqg Srru*v +4<<8, iru ixuwkhu grfxphqwdwlrq1
45
lq khu �up zloo uhfhlyh '63 shu wkrxvdqg groodu fkdqjh lq vkduhkroghu zhdowk1 Iru rswlrqv/ wkh
sd|0shuirupdqfh vhqvlwlylw| lv wkh iudfwlrq ri wkh �up*v vwrfn rq zklfk wkh rswlrqv duh zulwwhq
pxowlsolhg e| wkh rswlrqv* ghowdv1
Iru rswlrqv judqwhg lq wkh fxuuhqw |hdu/ frpsdqlhv pxvw uhsruw wkh qxpehu ri vhfxulwlhv/ wkh
h{huflvh sulfh/ dqg wkh h{huflvh gdwh1 Iroorzlqj Vwdqgdug dqg Srru*v +4<<8,/ zh dvvxph wkdw
rswlrqv zloo eh h{huflvhg ; |hduv wkurxjk wkhlu whup iru rswlrqv judqwhg lq 4<<7 ru hduolhu1 Iru
rswlrq judqwv lq 4<<8 dqg odwhu/ zh dvvxph wkh rswlrqv zloo eh h{huflvhg : |hduv wkurxjk wkhlu
whup1 Zh xvh wkh fruuhvsrqglqj ; dqg : |hdu }hur0frxsrq Wuhdvxu| erqg udwhv dv wkh ulvn0iuhh
udwhv ri uhwxuq1 Wkh ulvn0iuhh lqwhuhvw udwhv xvhg iru 4<<5 wkurxjk 4<<; duh 9176/ 8186/ :1;7/ 817</
9167/ dqg 81:: shufhqw/ uhvshfwlyho|1 Lq dsso|lqj wkh Eodfn0Vfkrohv irupxod/ zh xvh wkh glylghqg
|lhog iru wkh frpsdq| uhsruwhg e| H{hfxFrps dqg fdofxodwh wkh vwdqgdug ghyldwlrq ri prqwko|
vwrfn uhwxuqv iru hdfk frpsdq| xvlqj gdwd iurp FUVS1 Zh xvh xs wr �yh |hduv ri sulru prqwko|
uhwxuqv wr frpsxwh yduldqfhv1 Li d �up glg qrw kdyh dw ohdvw wzhoyh sulru prqwko| uhwxuqv iru d
jlyhq |hdu/ zh lpsxwh wkh yduldqfh1; Zh pxowlso| wklv ydoxh e|s45 wr jhw wkh vwdqgdug ghyldwlrq
ri frqwlqxrxvo| frpsrxqghg dqqxdo uhwxuqv +yrodwlolw|,1
Iru rswlrqv judqwhg lq suhylrxv |hduv/ wkh sur{| vwdwhphqw uhsruwv rqo| wkh djjuhjdwh qxpehu
ri vhfxulwlhv dqg wkh djjuhjdwh �lqwulqvlf ydoxh� ri wkh rswlrqv wkdw duh lq wkh prqh|1 Wkh lqwulqvlf
ydoxh ri hdfk rswlrq lv wkh vwrfn sulfh dw wkh hqg ri wkh �vfdo |hdu ohvv wkh rswlrq*v h{huflvh sulfh1
Iroorzlqj Pxusk| +4<<<,/ zh wuhdw doo h{lvwlqj rswlrqv dv d vlqjoh judqw zlwk d �yh |hdu uhpdlqlqj
whup dqg dq h{huflvh sulfh vxfk wkdw wkh lqwulqvlf ydoxh ri doo rswlrqv lv htxdo wr wkdw uhsruwhg rq
wkh sur{| vwdwhphqw1 Dsduw iurp kdylqj wr lpsxwh wkh h{huflvh sulfh dqg |hduv uhpdlqlqj xqwlo
h{huflvh/ wkh phwkrgrorj| iru rswlrqv judqwhg lq suhylrxv |hduv lv wkh vdph dv iru fxuuhqw rswlrq
judqwv1
Zh h{sorlw H{hfxFrps*v vdpsolqj iudph dqg h{dplqh wkh lqfhqwlyhv wr wkh wrs pdqdjhphqw
whdp1 FHR vwdwxv lv uhsruwhg gluhfwo| lq H{hfxFrps dqg shuwdlqv wr wkh h{hfxwlyh zkr khog wkdw
srvlwlrq iru wkh pdmrulw| ri wkh |hdu1 Wkh sd|0shuirupdqfh vhqvlwlylw| iru wkh wrs pdqdjhphqw
whdp lv gh�qhg dv wkh SSV iru wkh FHR soxv irxu wlphv wkh dyhudjh SSV ri wkh rwkhu h{hfxwlyhv
dw wkh �up zkrvh lqirupdwlrq lv uhsruwhg lq d jlyhq |hdu1 Wklv frqyhqwlrq vwdqgdugl}hv wkh vl}h
; Iru �upv wkdw zhuh plvvlqj gdwd rq yduldqfh iru vrph |hduv/ zh xvh wkh yduldqfh ri wkh qh{w dydlodeoh |hdu*v
uhwxuqv1 Iru �upv wkdw kdg plvvlqj gdwd rq yduldqfh lq doo |hduv/ zh xvh wkh vdpsoh*v dyhudjh yduldqfh lq hdfk
|hdu1 Rplwwlqj wkhvh revhuydwlrqv grhv qrw vljql�fdqwo| fkdqjh rxu uhvxowv1
46
ri wkh whdp dw �yh iru doo �upv hyhq li gdwd duh plvvlqj iru vrph h{hfxwlyhv ru pruh wkdq �yh
h{hfxwlyhv duh uhsruwhg lq d jlyhq |hdu1
Wkh �uvw wzr urzv ri Wdeoh 4 suhvhqw ghvfulswlyh vwdwlvwlfv rq wkh sd|0shuirupdqfh vhqvlwlylwlhv
ri wkh wrs pdqdjhphqw whdp dqg wkh FHR iru wkh �upv lq rxu vdpsoh1 Wkh phdq wrs pdqdjh0
phqw whdp kdv d frpelqhg sd|0shuirupdqfh vhqvlwlylw| htxdo wr :146 shufhqw ri wkh �up1 Wkh
lqwhusuhwdwlrq ri wklv qxpehu lv wkdw li wkh ydoxh ri vkduhkroghu zhdowk lqfuhdvhv e| '4333 ryhu wkh
frxuvh ri d |hdu/ wkhq wkh ydoxh ri wkh vwrfn dqg rswlrq kroglqjv ri wkh wrs pdqdjhphqw whdp zloo
lqfuhdvh e| ':41631 Wkh glvwulexwlrq ri pdqdjhphqw lqfhqwlyhv dfurvv �upv lv vnhzhg wr wkh uljkw/
zlwk phgldq lqfhqwlyhv vxevwdqwldoo| orzhu dw 6146 shufhqw1 Wkh FHR ri hdfk �up kdv lqfhqwlyhv
ri 7149 shufhqw ri wkh �up dw wkh phdq dqg 4167 shufhqw dw wkh phgldq1 Rwkhu shufhqwlohv ri wkh
glvwulexwlrqv duh dovr uhsruwhg/ vkrzlqj frqvlghudeoh yduldwlrq lq lqfhqwlyhv lq wkh H{hfxFrps
vdpsoh1
Wkh qh{w urz ri Wdeoh 4 shuwdlqv wr rxu phdvxuh ri �up shuirupdqfh/ Wrelq*v T/ zklfk lv
fdofxodwhg iurp Frpsxvwdw1 Wrelq*v T lv htxdo wr wkh udwlr ri wkh vxp ri wkh pdunhw ydoxh ri
htxlw| dqg wkh errn ydoxh ri ghew wr wkh errn ydoxh ri dvvhwv1 T lv frpprqo| xvhg dv d phdvxuh
ri �up sur�wdelolw| dqg shuirupdqfh +Prufn/ Vkohlihu/ dqg Ylvkq| +4<;;,/ PfFrqqhoo dqg Vhuydhv
+4<<3,/ dqg Klpphoehuj/ Kxeedug/ dqg Sdold +4<<<,,1 Rxu fdofxodwlrq uh hfwv dyhudjh T dqg
devwudfwv iurp wkh h�hfw ri wd{hv rq �up ydoxh1 Lq rxu vdpsoh/ wkh phdq dqg phgldq ydoxhv ri
T duh 5147 dqg 4193/ uhvshfwlyho|1 Wkh plggoh ;3 shufhqw ri wkh �upv kdyh T ydoxhv ehwzhhq 413:
dqg 61961
Wkh qh{w wkuhh urzv ri Wdeoh 4 suhvhqw ghvfulswlyh vwdwlvwlfv rq wkuhh phdvxuhv ri glyhuvl�fdwlrq1
Wkh �uvw lv wkh qxpehu ri vhjphqwv uhsruwhg e| frpsdq| pdqdjhphqw lq Frpsxvwdw*v Lqgxvwu|
Vhjphqw �oh1 Wkh phdq qxpehu ri vhjphqwv lv dssur{lpdwho| 5 +514:<9, zkloh wkh phgldq lv 4
vhjphqw1 Dssur{lpdwho| 93( ri wkh �upv lq rxu vdpsoh duh vlqjoh0vhjphqw �upv1 Wkh vhfrqg
phdvxuh ri glyhuvl�fdwlrq lv wkh qxpehu ri gl�huhqw 70gljlw VLF frghv lq zklfk wkh �up rshudwhv1
Wkh wklug phdvxuh ri glyhuvl�fdwlrq lv wkh qxpehu ri gl�huhqw 50gljlw VLF frghv lq zklfk wkh �up
rshudwhv1 Wkhvh phdvxuhv ri glyhuvl�fdwlrq duh vlplodu wr wkrvh xvhg e| Ghqlv/ Ghqlv/ dqg Vdulq
+4<<:, dqg Frpphqw dqg Mduuhoo +4<<8,1< Doo wkuhh ri rxu phdvxuhv duh kljko| fruuhodwhg dqg doo
< Wkrvh sdshuv lqfoxgh wkuhh rwkhu phdvxuhv ri glyhuvl�fdwlrq= wkh iudfwlrq ri �upv zlwk pxowlsoh vhjphqwv/ d
uhyhqxh0edvhg Khu�qgdko Lqgh{/ dqg dq dvvhw0edvhg Khu�qgdko Lqgh{1 Zh h{foxgh wkh �uvw ri wkhvh rwkhu wkuhh
ehfdxvh lw lv d yhu| zhdn phdvxuh ri glyhuvl�fdwlrq wkdw lv xvhixo sulpdulo| lq Frpphqw dqg Mduuhoo*v +4<<8, wlph0
47
ri rxu uhvxowv duh urexvw wr wkh fkrlfh ri phdvxuh1 Zh uhsruw uhvxowv iru wkh qxpehu ri gl�huhqw
70gljlw VLFv1
Wkh uhpdlqghu ri Wdeoh 4 suhvhqwv wkh ghvfulswlyh vwdwlvwlfv iru rwkhu yduldeohv wkdw zh frqwuro
iru lq rxu hfrqrphwulf vshfl�fdwlrqv iru T ru glyhuvl�fdwlrq1 Zh lqfoxgh lqyhvwphqw/ zklfk lv
htxdo wr fdslwdo h{shqglwxuhv iru surshuw|/ sodqw/ dqg htxlsphqw glylghg e| wkh vwrfn ri qhw
surshuw|/ sodqw/ dqg htxlsphqw1 Lqyhvwphqw udwhv duh 58 shufhqw dw wkh phdq dqg 54 shufhqw dw
wkh phgldq1 Zh lqfoxgh wkh qdwxudo orj ri vdohv wr dffrxqw iru gl�huhqfhv lq �up vl}h1 Zh lqfoxgh
wkh udwlr ri fdslwdo +qhw surshuw|/ sodqw/ dqg htxlsphqw, wr vdohv wr frqwuro iru dvvhw wxuqryhu1 Lq
wkh uhjuhvvlrqv suhvhqwhg ehorz/ zh dovr lqfoxgh wkh vtxduhv ri wkhvh wzr yduldeohv1 Zh lqfoxgh
wkh udwlr ri fdvk rz wr fdslwdo ehfdxvh pdq| vwxglhv edvhg rq wkh zrun ri Id}}dul/ Kxeedug/
dqg Shwhuvhq +4<;;, kdyh vkrzq d uhodwlrqvkls ehwzhhq fdvk rz dqg lqyhvwphqw1 Wkh h�hfw ri
ohyhudjh lv fdswxuhg e| wkh udwlr ri orqj0whup ghew wr dvvhwv1 Zh lqfoxgh wkh vwdqgdug ghyldwlrq
ri groodu uhwxuqv wr vkduhkroghuv +fdofxodwhg iurpFUVS/ dv ghvfulehg deryh, wr doorz iru dq h�hfw
ri ulvn rq sur�wdelolw| dqg glyhuvl�fdwlrq1 Ilqdoo|/ zh lqfoxgh frqwurov iru wkh udwlr ri uhvhdufk
dqg ghyhorsphqw wr fdslwdo dqg dgyhuwlvlqj wr fdslwdo143
Zh uhvwulfw rxu vdpsoh wr wkrvh �up0|hduv lq zklfk whdp sd|0shuirupdqfh vhqvlwlylw|/ glyhuvl0
�fdwlrq/ dqg T fdq eh frqvwuxfwhg1 Zlwklq wkdw vdpsoh ri :378 �up0|hduv iru 4935 �upv/ wkh odvw
irxu yduldeohv duh plvvlqj iru vhyhudo kxqguhg ru pruh revhuydwlrqv/ dv vkrzq lq wkh �uvw froxpq ri
Wdeoh 41 Lq wkh hpslulfdo zrun ehorz/ zh vhw wkh ydoxhv ri wkhvh yduldeohv wr }hur iru revhuydwlrqv
zkhuh wkh| duh plvvlqj dqg lqfoxgh d gxpp| yduldeoh iru zkhwkhu wkh gdwd zhuh ruljlqdoo| plvvlqj1
71 Hpslulfdo Uhvxowv
Rxu prgho suhglfwv dq htxloleulxp uhodwlrqvkls ehwzhhq �up shuirupdqfh/ pdqdjhuldo lqfhqwlyhv/
dqg glyhuvl�fdwlrq1 Rxu hpslulfdo whvwv ri wkdw prgho frqvlvw ri uhjuhvvlrqv ri shuirupdqfh rq
lqfhqwlyhv dqg glyhuvl�fdwlrq dqg uhjuhvvlrqv ri glyhuvl�fdwlrq rq lqfhqwlyhv1 Wklv ghvljq iroorzv
qdwxudoo| iurp wkh wkhruhwlfdo prgho�pdqdjhuv fkrrvh wkh ohyho ri glyhuvl�fdwlrq dv d ixqfwlrq ri
wkhlu lqfhqwlyhv/ dqg �up shuirupdqfh lv uhodwhg wr erwk glyhuvl�fdwlrq dqg lqfhqwlyhv1 Krzhyhu/
vhulhv frqwh{w1 Zh h{foxgh wkh wzr Khu�qgdko phdvxuhv ehfdxvh vrph ri rxu hvwlpdwhv uhtxluh xv wr dqdo|}h
glvfuhwh fkdqjhv lq glyhuvl�fdwlrq/ zklfk fdq rqo| eh phdvxuhg uholdeo| e| h{dplqlqj wkh qxpehu ri vhjphqwv1 Dv
lq Ghqlv/ Ghqlv/ dqg Vdulq +4<<:, dqg Frpphqw dqg Mduuhoo +4<<8,/ rxu uhvxowv edvhg rq wkh ohyho ri glyhuvl�fdwlrq
duh lqyduldqw wr wkh phdvxuh ri glyhuvl�fdwlrq xvhg1 Lq wkhlu uhjuhvvlrq dqdo|vlv/ Ghqlv/ Ghqlv/ dqg Vdulq +4<<:,
irfxv rq wkh vhjphqw phdvxuhv ri glyhuvl�fdwlrq1
43Wkhvh yduldeohv duh wkh vdph frqwuro yduldeohv xvhg e| Klpphoehuj/ Kxeedug/ dqg Sdold +4<<<,1
48
lw lv lpsruwdqw wr uhfrjql}h wkdw wkh frh!flhqwv rq lqfhqwlyhv dqg glyhuvl�fdwlrq gr qrw uhsuhvhqw
wkh pdujlqdo h�hfw ri dq h{rjhqrxv fkdqjh lq pdqdjhuldo lqfhqwlyhv dqg glyhuvl�fdwlrq rq �up
shuirupdqfh1 Lqvwhdg/ wkh hvwlpdwhg frh!flhqwv whvw wkh ydolglw| ri wkh wkhruhwlfdo prgho e|
yhuli|lqj wkdw wkh hqgrjhqrxv uhodwlrqvklsv dprqj wkh yduldeohv duh frqvlvwhqw zlwk wkh prgho*v
suhglfwlrqv edvhg rq vkliwv lq d vxevhw ri wkh h{rjhqrxv sdudphwhuv1
Zh ehjlq e| hvwlpdwlqj uhjuhvvlrqv ri wkh iroorzlqj irup=
Tlw @ �3. �
4SSVlw . �
5qlw .
N[n@4
�n{n
lw.
<;[w@<7
�w . �l . %lw= +57,
Lq wklv htxdwlrq/ wkh ghshqghqw yduldeoh lv Wrelq*v T1 Wkh lqghshqghqw yduldeohv duh SSV +lq0
fhqwlyhv, dqg q +glyhuvl�fdwlrq,1 Wkh rwkhu fryduldwhv +olvwhg lq Wdeoh 4, duh ghqrwhg e| {nlw1 Wkh
vshfl�fdwlrq dovr lqfoxghv |hdu h�hfwv/ ghqrwhg e| �w/ dqg �up ohyho �{hg h�hfwv/ ghqrwhg e| �l1
Iru hdfk htxdwlrq wkdw zh hvwlpdwh/ zh uhsruw hljkw vshfl�fdwlrqv1 Wdeohv 5 dqg 6 suhvhqw wkh
hvwlpdwhv ri htxdwlrq +57,1 Wdeoh 5 suhvhqwv uhvxowv iru wkh wrs pdqdjhphqw whdp/ dqg Wdeoh 6
suhvhqwv uhvxowv iru FHRv dv dq lqglfdwlrq ri wkh urexvwqhvv ri wkh pdlq uhvxowv1 Wkh �uvw froxpq
lq hdfk wdeoh suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv/ h{foxglqj wkh rwkhu fryduldwhv dqg wkh
�{hg h�hfwv +l1h1/ �n @ 3>;n dqg �l @ 3>;l,1 Wkh vhfrqg froxpq lqfoxghv wkh �{hg h�hfwv exw qrw
wkh rwkhu fryduldwhv1 Wkh wklug froxpq suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv lqfoxglqj wkh
rwkhu fryduldwhv exw qrw wkh �{hg h�hfwv1 Wkh irxuwk froxpq lqfoxghv erwk wkh rwkhu fryduldwhv
dqg wkh �{hg h�hfwv1 Wkh prvw urexvw whvwv ri wkh prgho duh edvhg lqfoxgh erwk wkh �{hg h�hfwv
dqg wkh rwkhu fryduldwhv1 Zh vkrz wkh rwkhu wkuhh uhvxowv sulpdulo| wr looxvwudwh krz wkh uhvxowv
duh d�hfwhg zkhq srwhqwldoo| frqirxqglqj idfwruv duh qrw frqwuroohg iru lq wkh uhjuhvvlrq1
Lq Wdeoh 5/ wkh frh!flhqw rq wkh SSV whup lv hvwlpdwhg wr eh srvlwlyh lq doo ri wkh vshfl�fdwlrqv1
Lw lv pruh vwdwlvwlfdoo| vljql�fdqw/ wkrxjk vpdoohu lq vl}h/ zkhq �{hg h�hfwv duh lqfoxghg1 Wkh
srvlwlyh dqg vljql�fdqw frh!flhqw rq wkh SSV whup lv frqvlvwhqw zlwk wkh uhvxowv lq Djjduzdo dqg
Vdpzlfn +4<<<f,/ zkr dovr hvwlpdwhg slhfhzlvh0olqhdu vshfl�fdwlrqv ri T rq lqfhqwlyhv dqg yhul�hg
wkdw wkh uhodwlrqvkls lv srvlwlyh ryhu wkh hqwluh udqjh ri lqfhqwlyhv1 Vhyhudo sulru sdshuv/ lqfoxglqj
Prufn/ Vkohlihu/ dqg Ylvkq| +4<;;,/ PfFrqqhoo dqg Vhuydhv +4<<3,/ dqg Klpphoehuj/ Kxeedug/
dqg Sdold +4<<<,/ kdg irxqg hlwkhu qr uhodwlrqvkls ru d qrqprqrwrqlf uhodwlrqvkls ehwzhhq T dqg
lqfhqwlyhv xvlqj ohvv frpsuhkhqvlyh gdwd1 Wkh frh!flhqw rq wkh glyhuvl�fdwlrq whup lv hvwlpdwhg
wr eh qhjdwlyh dqg vljql�fdqw lq doo irxu vshfl�fdwlrqv/ frqvlvwhqw zlwk wkh uhvxowv lq Vhuydhv
49
+4<<9,/ Ehujhu dqg Rihn +4<<8,/ Frpphqw dqg Mduuhoo +4<<8,/ dqg Odqj dqg Vwxo} +4<<7, wkdw
ruljlqdoo| grfxphqwhg wkh glyhuvl�fdwlrq glvfrxqw1 Wdeoh 6 surylghv hvvhqwldoo| vlplodu uhvxowv iru
FHRv1 Wkh frh!flhqw rq wkh SSV whup lv hvwlpdwhg wr eh srvlwlyh dqg vljql�fdqw lq wkh �uvw
wkuhh uhjuhvvlrqv dqg srvlwlyh exw qrw vljql�fdqw lq wkh uhjuhvvlrq wkdw lqfoxghv erwk �{hg h�hfwv
dqg rwkhu fryduldwhv1 Wkh frh!flhqw rq wkh glyhuvl�fdwlrq whup lv hvwlpdwhg wr eh qhjdwlyh dqg
vljql�fdqw lq doo irxu vshfl�fdwlrqv/ frqvlvwhqw zlwk rxu uhvxowv iru wkh wrs pdqdjhphqw whdp
Wkh �{hg h�hfwv uhjuhvvlrqv surylgh d pruh urexvw whvw ri wkh frpsdudwlyh vwdwlfv suhglfwlrqv
ri wkh prgho1 Lqfoxglqj d gxpp| yduldeoh iru hdfk �up uhpryhv wkh h�hfw ri dq| �up0vshfl�f
fkdudfwhulvwlf wkdw pd| eh dvvrfldwhg zlwk shuirupdqfh/ glyhuvl�fdwlrq/ dqg lqfhqwlyhv lq d zd|
qrw vshfl�hg e| rxu prgho1 Wkh �{hg h�hfwv uhjuhvvlrq hvwdeolvkhv d uhodwlrqvkls ehwzhhq shu0
irupdqfh dqg lqfhqwlyhv dqg shuirupdqfh dqg glyhuvl�fdwlrq edvhg rqo| rq fkdqjhv zlwklq �upv
ryhu wlph1 Wkh ROV uhjuhvvlrq hvwdeolvkhv d uhodwlrqvkls ehwzhhq shuirupdqfh dqg lqfhqwlyhv
dqg shuirupdqfh dqg glyhuvl�fdwlrq edvhg rq frpsdulvrqv erwk zlwklq dqg dfurvv �upv1 Li �upv
duh qrw rwkhuzlvh lghqwlfdo/ wkh ROV uhjuhvvlrq zloo eh eldvhg e| xqrevhuyhg/ �up0vshfl�f idfwruv
zkhuhdv wkh �{hg h�hfw uhjuhvvlrq zloo qrw1 Frpsdulqj wkh U5 iurp wkh wzr uhjuhvvlrqv/ wkh lq0
foxvlrq ri wkh �{hg h�hfwv devruev d vxevwdqwldo dprxqw ri wkh yduldwlrq +lqfuhdvlqj wkh sursruwlrq
ri yduldqfh h{sodlqhg iurp 3=3987 wr 3=;944,/ exw wkh �{hg h�hfwv gr qrw fkdqjh wkh vljq ri wkh
suhglfwhg uhodwlrqvkls1 Zkhq zh lqfoxgh wkh rwkhu fryduldwhv lq wkh �{hg h�hfwv vshfl�fdwlrq/ zh
�qg wkdw wkh frh!flhqw rq wkh SSV whup ghfuhdvhv lq pdjqlwxgh exw lv vwloo vljql�fdqw zkloh wkh
frh!flhqw rq wkh glyhuvl�fdwlrq whup lv xqd�hfwhg1
Wkh �qglqjv lq Wdeohv 5 dqg 6 duh frqvlvwhqw zlwk wkh h{lvwlqj olwhudwxuh dqg rxu wkhruhwlfdo
prgho/ exw wkh| gr qrw surylgh d sduwlfxoduo| vwurqj whvw1 Lq wkh frqwh{w ri rxu prgho/ lw zrxog
qrw eh srvvleoh wr rewdlq d srvlwlyh frh!flhqw rq SSV li wkh rqo| vrxufh ri yduldwlrq zhuh e/
wkh pdqdjhu*v sulydwh ehqh�w iurp glyhuvl�fdwlrq1 Dv qrwhg deryh/ li zh revhuyh ydoxhv iru
shuirupdqfh/ lqfhqwlyhv/ dqg glyhuvl�fdwlrq wkdw duh htxloleulxp uhvsrqvhv iru gl�hulqj ohyhov ri
e/ wkhq Wrelq*v T dqg lqfhqwlyhv zloo eh qhjdwlyho| uhodwhg1 Wkxv/ zh fdq frqfoxgh wkdw vrph ri
wkh xqghuo|lqj yduldwlrq lv gxh wr vkliwv lq ulvn dyhuvlrq/ wkh yduldqfh ri vkrfnv/ dqg wkh glvxwlolw|
ri wkh dfwlrq fkrlfh1 Wkh �qglqj ri d qhjdwlyh frh!flhqw rq glyhuvl�fdwlrq lv dovr frqvlvwhqw
zlwk rxu prgho�lw zrxog qdwxudoo| eh lpsrvvleoh wr vxssruw d prgho lq zklfk pdqdjhuv kdyh d
4:
suhihuhqfh iru frvwo| glyhuvl�fdwlrq li kljkhu glyhuvl�fdwlrq zhuh qrw dvvrfldwhg zlwk orzhu �up
shuirupdqfh lq htxloleulxp1
Zh fdq surylgh d vwurqjhu whvw ri wkh wkhruhwlfdo prgho e| h{dplqlqj wkh uhodwlrqvkls ehwzhhq
glyhuvl�fdwlrq dqg lqfhqwlyhv gluhfwo|1 Zh hvwlpdwh dq dqdorjrxv uhjuhvvlrq iru glyhuvl�fdwlrq=
qlw @ �3. �
4SSVlw .
N[n@4
�n{n
lw.
<;[w@<7
�w . �l . %lw= +58,
Lq wklv htxdwlrq/ wkh ghshqghqw yduldeoh lv glyhuvl�fdwlrq dqg wkh �uvw lqghshqghqw yduldeoh lv
SSV1 Dv lq wkh T uhjuhvvlrq/ wkh rwkhu fryduldwhv duh ghqrwhg e| {nlw/ wkh |hdu h�hfwv duh
ghqrwhg e| �w/ dqg wkh �up ohyho �{hg h�hfwv duh �l1 Rxu wkhruhwlfdo iudphzrun fdq eh frqvlvwhqw
zlwk hlwkhu vljq iru �41 Li wkh xqghuo|lqj vrxufh ri yduldwlrq lv e/ wkh pdqdjhu*v sulydwh ehqh�w
iurp glyhuvl�fdwlrq/ wkhq glyhuvl�fdwlrq zloo eh srvlwlyho| uhodwhg wr lqfhqwlyhv lq htxloleulxp1
Wkh kljkhu lqfhqwlyhv duh dq lpshuihfw phdqv ri fxuwdlolqj wkh pdqdjhu*v kljkhu surshqvlw| wr
glyhuvli|1 Li wkh xqghuo|lqj vrxufh ri yduldwlrq lv ulvn dyhuvlrq/ yduldqfh ri vkrfnv/ ru glvxwlolw|
ri wkh dfwlrq fkrlfh/ wkhq glyhuvl�fdwlrq dqg lqfhqwlyhv zloo eh qhjdwlyho| uhodwhg1 Kljkhu ydoxhv
ri wkhvh sdudphwhuv zloo uhgxfh htxloleulxp lqfhqwlyhv/ wkhuhe| lqgxflqj pdqdjhuv wr lqfuhdvh
glyhuvl�fdwlrq1
Wdeohv 7 dqg 8 suhvhqw wkh uhvxowv ri wkh ROV dqg �{hg h�hfw hvwlpdwhv ri wkh frh!flhqwv lq
htxdwlrq +58, iru wkh wrs pdqdjhphqw whdp dqg FHRv1 Dv lq Wdeohv 5 dqg 6/ wkh �uvw froxpq ri
hdfk wdeoh suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv/ h{foxglqj wkh rwkhu fryduldwhv dqg wkh
�{hg h�hfwv1 Wkh vhfrqg froxpq lqfoxghv wkh �{hg h�hfwv exw qrw wkh rwkhu fryduldwhv1 Wkh wklug
froxpq suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv lqfoxglqj wkh rwkhu fryduldwhv exw qrw wkh
�{hg h�hfwv1 Wkh irxuwk froxpq lqfoxghv erwk wkh rwkhu fryduldwhv dqg wkh �{hg h�hfwv1 Rxu
lqlwldo uhjuhvvlrq lq Wdeoh 7 +wkh ROV vshfl�fdwlrq, lv vlplodu wr wkh uhjuhvvlrqv lq Ghqlv/ Ghqlv/
dqg Vdulq +4<<:, dqg Edwhv/ El}mdn/ dqg Ohpprq +4<<:,1 Frqvlvwhqw zlwk wkrvh sdshuv/ zh �qg
wkdw glyhuvl�fdwlrq lv qhjdwlyho| uhodwhg wr lqfhqwlyhv1 Wkh frh!flhqw rq wkh SSV whup lv 031349
dqg lv vwdwlvwlfdoo| vljql�fdqw1 Wklv frpsduhv wr d frh!flhqw rq rzqhuvkls ri 031346 lq Ghqlv/
Ghqlv/ dqg Vdulq*v +4<<:, �uvw furvv0vhfwlrqdo uhjuhvvlrq1 Uhjuhvvlrqv ri wklv irup duh wkh edvlv
iru wkh fodlp wkdw djhqf| sureohpv duh uhvsrqvleoh iru ydoxh0uhgxflqj glyhuvl�fdwlrq1
Wkh rwkhu uhjuhvvlrqv vkrz wkdw wklv uhvxow lv qrw urexvw wr wkh lqfoxvlrq ri rwkhu srwhqwldoo|
frqirxqglqj idfwruv1 Lq froxpq 5/ wkh lqfoxvlrq ri �{hg h�hfwv uhyhuvhv wkh vljq rq lqfhqwlyhv/
4;
pdnlqj lw srvlwlyh dqg vljql�fdqw1 Lq froxpq 6/ zh lqfoxgh dgglwlrqdo fryduldwhv wr frqwuro iru
�up0vshfl�f idfwruv exw rplw wkh �{hg h�hfwv1 Iru wklv vshfl�fdwlrq/ wkh frh!flhqw rq wkh SSV
whup lv hvwlpdwhg wr eh qhjdwlyh dqg lqvljql�fdqw/ exw vljql�fdqwo| kljkhu wkdq lq froxpq 4 zkhuh
wkh fryduldwhv duh h{foxghg1 Lq froxpq 7/ zh lqfoxgh wkh dgglwlrqdo fryduldwhv dqg wkh �{hg
h�hfwv dqg �qg wkdw wkh frh!flhqw rq wkh SSV whup lv hvwlpdwhg wr eh srvlwlyh dqg vljql�fdqw
dqg odujhu lq pdjqlwxgh wkdq lq wkh �{hg h�hfwv vshfl�fdwlrq zlwkrxw dgglwlrqdo fryduldwhv lq
froxpq 51 Wdeoh 8 suhvhqwv uhvxowv iru FHRv1 Wkh vljqv dqg vwdwlvwlfdo vljql�fdqfh ri wkh
hvwlpdwhg frh!flhqwv rq wkh SSV whupv h{dfwo| pdwfk wkrvh iru wkh wrs pdqdjhphqw whdp lq
Wdeoh 71 Zlwkrxw �{hg h�hfwv/ d kljkhu SSV lv dvvrfldwhg zlwk orzhu glyhuvl�fdwlrq1 Krzhyhu/
zkhq �{hg h�hfwv duh lqfoxghg/ wkh uhodwlrqvkls ehwzhhq SSV dqg glyhuvl�fdwlrq lv srvlwlyh1
Wklv sdwwhuq lq wkh frh!flhqwv vwurqjo| vxjjhvwv wkdw wkh �qglqjv lq wkh h{lvwlqj olwhudwxuh lq
zklfk d kljkhu SSV lv dvvrfldwhg zlwk ohvv glyhuv�fldwlrq duh gulyhq e| rplwwhg ghwhuplqdqwv ri
glyhuvl�fdwlrq wkdw duh qrw h{solflwo| uhodwhg wr pdqdjhuldo lqfhqwlyhv1 Dgglqj lq rwkhu fryduldwhv
lqfuhdvhv wkh frh!flhqw rq SSV wrzdug }hur1 Pdq| ri wkhvh yduldeohv duh uhodwhg wr wkh �up*v vl}h
dqg lqgxvwu|/ dqg khqfh wkh �up*v surshqvlw| wr glyhuvli|1 Lqfoxglqj �{hg h�hfwv/ zklfk frqwuro
iru wkh �up0vshfl�f dyhudjh ydoxh ri hyhu| xqrevhuyhg idfwru/ pdnh wkh uhodwlrqvkls srvlwlyh dqg
vljql�fdqw1 Wkh �{hg h�hfwv h{sodlq derxw :3 shufhqw ri wkh yduldwlrq lq wkh qxpehu ri vhjphqwv/
lqfuhdvlqj wkh U5 iurp 3=4:; wr 3=;:8 lq wkh uhjuhvvlrqv lqfoxglqj wkh rwkhu fryduldwhv lq Wdeoh 71
Wklv glyhujhqfh ehwzhhq rxu uhvxowv dqg wkrvh ri Ghqlv/ Ghqlv/ dqg Vdulq +4<<:, fdq eh h{sodlqhg
e| wkh idfw wkdw wkh| kdyh d vlqjoh furvv0vhfwlrq ri �upv lq 4<;8 zkhuhdv zh duh deoh wr h{sorlw
wkh sdqho qdwxuh ri rxu gdwd wr frqwuro iru rplwwhg �up0vshfl�f idfwruv1
Wkh srvlwlyh hvwlpdwhg uhodwlrqvkls ehwzhhq glyhuvl�fdwlrq dqg lqfhqwlyhv lqglfdwhv wkdw wkhuh
pxvw eh zlwklq0�up yduldwlrq lq wkh pdqdjhu*v ohyho ri sulydwh ehqh�wv wkhpvhoyhv1 Frpelqhg
zlwk wkh uhvxowv iurp Wdeohv 5 dqg 6 uhjduglqj wkh srvlwlyh uhodwlrqvkls ehwzhhq shuirupdqfh dqg
lqfhqwlyhv +frqwuroolqj iru glyhuvl�fdwlrq,/ wklv uhodwlrqvkls vkrzv wkdw erwk vrxufhv ri yduldwlrq lq
rxu wkhruhwlfdo iudphzrun�iurp e dqg iurp dq| ri u/ �5/ ru n�duh qhfhvvdu| wr h{sodlq wkh gdwd1
Wkh frxqwhuydlolqj h�hfwv ri vkliwv lq wkh odwwhu vhw ri sdudphwhuv jlyhv dq lqglfdwlrq ri zk| wkh
hvwlpdwhg frh!flhqwv lq Wdeohv 7 dqg 8 duh vpdoo1 Dv qrwhg deryh/ dq lqfuhdvh lq dq| ri wkhvh
sdudphwhuv fdxvhv d uhgxfwlrq lq lqfhqwlyhv dqg dq lqfuhdvh lq glyhuvl�fdwlrq1 Iru h{dpsoh/ wkh
4<
frh!flhqw ri 3133:3 rq lqfhqwlyhv lq Wdeoh 7 vxjjhvwv wkdw dq lqfuhdvh lq pdqdjhuldo lqfhqwlyhv
iurp 3 wr 43 shufhqw rzqhuvkls zrxog eh dvvrfldwhg zlwk dq lqfuhdvh lq wkh qxpehu ri vhjphqwv
ri rqo| 313:1 Wklv lv qrw wkh fkdqjh lq rxwfrphv wkdw zrxog uhvxow iurp d fkdqjh lq e dorqh/ exw
wkh qhw h�hfw ri wkh fkdqjhv lq doo sdudphwhuv dv wkh| rffxu zlwklq �upv lq wkh gdwd1 Wkh rqo|
frqfoxvlrq wkdw fdq eh uhdfkhg lv wkdw/ ehfdxvh wkh frh!flhqw lv srvlwlyh dqg vljql�fdqw/ wkhuh lv
hylghqfh wkdw e lv ydu|lqj zlwklq �upv dovr1
Wkh nqrzohgjh wkdw wkhuh lv zlwklq0�up yduldwlrq lq wkh sulydwh ehqh�wv ri glyhuvl�fdwlrq
doorzv xv wr uhylvlw wkh Wrelq*v T uhjuhvvlrqv wr surylgh d ixuwkhu whvw ri wkh frqvlvwhqf| ri rxu
wkhruhwlfdo prgho1 Dqrwkhu zd| wr lqihu wkh xqghuo|lqj vrxufh ri yduldwlrq wkdw jhqhudwhv fkdqjhv
lq glyhuvl�fdwlrq lv wr hvwlpdwh wkh iroorzlqj uhjuhvvlrq=
Tlw @ �3. �
4SSVlw . �
5+SSVlw ��lw, . �
6�lw . �
7qlw .
N[n@4
�n{n
lw.
<;[w@<7
�w . �l . %lw= +59,
Wklv htxdwlrq lv wkh vdph dv htxdwlrq +57,/ zlwk wkh dgglwlrq ri wzr yduldeohv edvhg rq �/
zklfk lv d gxpp| yduldeoh iru zkhwkhu ru qrw wkh �up kdv h{shulhqfhg d fkdqjh lq wkh ohyho ri
glyhuvl�fdwlrq vlqfh wkh sulru vdpsoh |hdu1 Lq wklv htxdwlrq/ wkh ghshqghqw yduldeoh lv Wrelq*v T1
Wkh nh| lqghshqghqw yduldeohv duh SSV +lqfhqwlyhv, dqg SSV lqwhudfwhg zlwk�1 Wkh frh!flhqw
rq wkh lqwhudfwlrq ri SSV dqg � lv wkh gl�huhqfh lq wkh h�hfw ri wkh SSV rq T iru �upv wkdw
frqwhpsrudqhrxvo| h{shulhqfh d fkdqjh lq glyhuvl�fdwlrq uhodwlyh wr wkh h�hfw ri SSV rq T iru
�upv wkdw gr qrw fkdqjh wkhlu ohyho ri glyhuvl�fdwlrq1 Wkh vljq ri �5lghqwl�hv wkh xqghuo|lqj
vrxufh ri yduldwlrq wkdw fdxvhv fkdqjhv lq glyhuvl�fdwlrq144
Wkh lqwxlwlrq iru wklv uhjuhvvlrq lv wkdw/ dffruglqj wr wkh wkhru|/ fkdqjhv lq glyhuvl�fdwlrq
pxvw eh fdxvhg e| fkdqjhv lq wkh xqghuo|lqj sdudphwhuv/ u> �5> n> dqg e1 Wkhuhiruh/ zh xvh
fkdqjhv lq glyhuvl�fdwlrq wr sur{| iru d fkdqjh lq wkhvh sdudphwhuv1 Dffruglqj wr htxdwlrq
+53,/ wkh frh!flhqw rq wkh lqwhudfwlrq ri wkh SSV whup zlwk wkh gxpp| yduldeoh iru d fkdqjh
lq glyhuvl�fdwlrq �5vkrxog eh srvlwlyh li wkh fkdqjh lq glyhuvl�fdwlrq lv fdxvhg e| d fkdqjh lq
u> �5> ru n= �5vkrxog eh qhjdwlyh li wkh fkdqjh lq glyhuvl�fdwlrq lv fdxvhg e| d fkdqjh lq e1 Dq
dowhuqdwlyh zd| ri vwdwlqj wklv srlqw lv wkdw/ li wkh xqghuo|lqj vrxufh ri yduldwlrq lv ulvn dyhuvlrq/
wkh yduldqfh ri vkrfnv/ ru wkh glvxwlolw| ri wkh dfwlrq fkrlfh/ wkhq �upv h{shulhqflqj fkdqjhv lq
44Zh dovr lqfoxgh { lq wkh uhjuhvvlrq qrq0lqwhudfwhg lq rughu wr doorz iru wkh srvvlelolw| wkdw �upv wkdw fkdqjh
wkhlu qxpehu ri vhjphqwv kdyh v|vwhpdwlfdoo| gl�huhqw dyhudjh ydoxhv ri Wrelq*v T frpsduhg wr �upv wkdw gr qrw
fkdqjh wkhlu qxpehu ri vhjphqwv1
53
glyhuvl�fdwlrq vkrxog kdyh juhdwhu uhvsrqvhv ri shuirupdqfh wr lqfhqwlyhv wkdq vkrxog �upv wkdw
gr qrw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq1 Pdwkhpdwlfdoo|/ �4. �
5vkrxog eh juhdwhu wkdq �
4=
Frqyhuvho|/ li wkh xqghuo|lqj vrxufh ri yduldwlrq lv wkh sulydwh ehqh�w dvvrfldwhg zlwk glyhuvl�fdwlrq
+wkh pdujlqdo xwlolw| ri glyhuvl�fdwlrq,/ wkhq �upv h{shulhqflqj fkdqjhv lq glyhuvl�fdwlrq vkrxog
kdyh zhdnhu uhvsrqvhv ri shuirupdqfh wr lqfhqwlyhv wkdq vkrxog �upv wkdw gr qrw h{shulhqfh
fkdqjhv lq glyhuvl�fdwlrq1 Pdwkhpdwlfdoo|/ �4. �
5vkrxog eh ohvv wkdq �
4=
Wdeohv 9 dqg : suhvhqw wkh hfrqrphwulf hvwlpdwhv ri wkh sdudphwhuv lq htxdwlrq +59,1 Wdeoh
9 suhvhqwv uhvxowv iru wkh wrs pdqdjhphqw whdp dqg Wdeoh : suhvhqwv uhvxowv iru FHRv1 Dv lq
wkh hduolhu wdeohv/ wkh �uvw froxpq lq hdfk wdeoh suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv/
h{foxglqj wkh rwkhu fryduldwhv dqg wkh �{hg h�hfwv1 Wkh vhfrqg froxpq lqfoxghv wkh �{hg h�hfwv
exw qrw wkh rwkhu fryduldwhv1 Wkh wklug froxpq suhvhqwv wkh ROV hvwlpdwhv ri wkh frh!flhqwv
lqfoxglqj wkh rwkhu fryduldwhv exw qrw wkh �{hg h�hfwv1 Wkh irxuwk froxpq lqfoxghv erwk wkh
rwkhu fryduldwhv dqg wkh �{hg h�hfwv1
Wdeoh 9 vkrzv wkdw wkh frh!flhqw rq wkh lqwhudfwlrq ri wkhSSV whup zlwk wkh gxpp| yduldeoh
iru d fkdqjh lq glyhuvl�fdwlrq �5lv hvwlpdwhg wr eh qhjdwlyh dqg vljql�fdqw lq doo irxu uhjuhvvlrqv1
Wklv lv frqvlvwhqw zlwk wkh sulydwh ehqh�wv dvvrfldwhg zlwk glyhuvl�fdwlrq ehlqj wkh xqghuo|lqj
vrxufh ri yduldwlrq iru �upv wkdw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq1 Wkh erwwrp sdqho ri
Wdeoh 9 suhvhqwv wkh hvwlpdwhg frh!flhqw rq lqfhqwlyhv iru �upv wkdw h{shulhqfh d fkdqjh lq
glyhuvl�fdwlrq/ �4.�
51 Wklv frh!flhqw lv�3=3383 iru wkh ROV vshfl�fdwlrq1 Ehorz wkh frh!flhqw
lv wkh s0ydoxh iru wkh whvw wkdw �4. �
5@ 31 Wklv whvw grhv qrw uhmhfw wkh qxoo�wkh frh!flhqw rq
lqfhqwlyhv iru �upv wkdw h{shulhqfh d fkdqjh lq glyhuvl�fdwlrq lv qrw hvwlpdwhg wr eh vljql�fdqwo|
gl�huhqw iurp }hur1 Wkh vdph lv wuxh ri wkh ROV vshfl�fdwlrq lqfoxglqj wkh dgglwlrqdo fryduldwhv
lq froxpq 61 Iru wkh �{hg h�hfwv vshfl�fdwlrq lqfoxglqj wkh dgglwlrqdo fryduldwhv lq froxpq 7/
�4lv srvlwlyh dqg vljql�fdqw/ �
5lv qhjdwlyh dqg vljql�fdqw/ dqg �
4.�
5lv srvlwlyh exw vljql�fdqw
rqo| dw wkh < shufhqw ohyho1 Wkh uhvxowv lq Wdeoh : iru FHRv duh vlplodu wr wkrvh lq Wdeoh 9 iru wkh
wrs pdqdjhphqw whdp1 Lq doo vshfl�fdwlrqv/ �4lv srvlwlyh dqg �
5lv qhjdwlyh1 Wkh| duh kljko|
vljql�fdqw lq doo vshfl�fdwlrqv h{fhsw �{hg h�hfwv zlwk fryduldwhv lq froxpq 71 Wkh vxp ri wkh
frh!flhqwv/ �4. �
5/ lv lqvljql�fdqw lq wkh vshfl�fdwlrqv wkdw lqfoxgh �{hg h�hfwv1
Wkh uhvxowv lq Wdeohv 9 dqg : surylgh d whvw ri wkh prgho ehfdxvh wkh| surylgh dqrwkhu slhfh
54
ri hylghqfh uhjduglqj wkh vrxufh ri glyhuvl�fdwlrq fkdqjhv1 Ilupv wkdw h{shulhqfh glyhuvl�fdwlrq
fkdqjhv fdq kdyh d ohvv srvlwlyh uhodwlrqvkls ehwzhhq SSV dqg Wrelq*v T rqo| li glyhuvl�fdwlrq
fkdqjhv duh fdxvhg e| fkdqjhv lq e1 Rxu prgho zrxog eh idovl�hg li wkh vrxufh ri yduldwlrq iru
glyhuvl�fdwlrq fkdqjhv lq wkh uhjuhvvlrqv ri glyhuvl�fdwlrq rq lqfhqwlyhv +Wdeohv 7 dqg 8, zhuh
gl�huhqw iurp wkh vrxufh ri yduldwlrq lghqwl�hg e| wkh uhjuhvvlrqv ri Wrelq*v T rq lqfhqwlyhv/ frq0
wuroolqj iru glyhuvl�fdwlrq dqg glyhuvl�fdwlrq fkdqjhv +Wdeohv 9 dqg :,1 Wkh htxloleulxp rxwfrphv
iru �upv wkdw gr qrw fkdqjh wkhlu ohyho ri glyhuvl�fdwlrq duh wkh uhvxow ri xqghuo|lqj yduldwlrq
lq u> �5> ru n= Dv d uhvxow/ �up shuirupdqfh dqg pdqdjhuldo lqfhqwlyhv duh srvlwlyho| uhodwhg1
Iru �upv wkdw gr fkdqjh wkhlu ohyho ri glyhuvl�fdwlrq/ wkhuh pxvw eh dgglwlrqdo yduldwlrq gxh wr
e1 E| lwvhoi/ wklv yduldwlrq zrxog jhqhudwh d qhjdwlyh uhodwlrqvkls ehwzhhq �up shuirupdqfh dqg
lqfhqwlyhv1 Wrjhwkhu zlwk wkh rwkhu vrxufhv ri yduldwlrq/ lw vhuyhv wr uhgxfh wkh fruuhodwlrq iurp
d srvlwlyh dqg vljql�fdqw qxpehu wr d qxpehu jhqhudoo| qrw glvwlqjxlvkdeoh iurp }hur1
Wkhvh uhvxowv surylgh dq lpsruwdqw frpsohphqw wr hduolhu zrun lq Djjduzdo dqg Vdpzlfn
+4<<<f,1 Lq wkdw sdshu/ zh dujxh wkdw pdqdjhuv gr qrw ryhulqyhvw lq surshuw|/ sodqw/ dqg htxls0
phqw dv d uhvxow ri sulydwh ehqh�wv dvvrfldwhg zlwk �{hg lqyhvwphqw1 Lqvwhdg/ wkh uhvxowv vkrz
wkdw pdqdjhuv xqghulqyhvw ehfdxvh lqyhvwlqj lpsrvhv sulydwh frvwv rq wkhp1 Wkhuh lv qr hylghqfh
wkdw sulydwh ehqh�wv ri wkdw w|sh ri lqyhvwphqw gulyh wkh htxloleulxp rxwfrphv iru �up shuiru0
pdqfh/ wkh ohyho ri lqyhvwphqw/ dqg pdqdjhuldo lqfhqwlyhv1 Wkh uhvxowv lq wklv sdshu vkrz wkdw
glyhuvl�fdwlrq ghflvlrqv duh ixqgdphqwdoo| gl�huhqw iurp lqyhvwphqw ghflvlrqv1 Hyhu| |hdu/ �upv
hqjdjh lq pdq| lqyhvwphqw surmhfwv ri ydu|lqj vl}hv dqg vljql�fdqfh1 Glyhuvl�fdwlrq ghflvlrqv
rffxu lqiuhtxhqwo| dqg duh yhu| odujh0vfdoh ghflvlrqv1 Wkh irufhv gulylqj glyhuvl�fdwlrq ghflvlrqv
duh qdwxudoo| yhu| gl�huhqw iurp wkrvh wkdw gulyh lqyhvwphqw ghflvlrqv1 Rxu uhvxowv vxjjhvw wkdw
glyhuvl�fdwlrq ghflvlrqv duh gulyhq e| wkh pdujlqdo xwlolw| pdqdjhuv uhfhlyh iurp juhdwhu glyhuvl0
�fdwlrq1
81 Frqfoxvlrq
Zh h{dplqh krz wkh vhsdudwlrq ri rzqhuvkls dqg frqwuro d�hfwv glyhuvl�fdwlrq dqg �up shu0
irupdqfh1 Wkh h{lvwlqj olwhudwxuh lv edvhg rq wzr �qglqjv= �up shuirupdqfh lv ghfuhdvlqj lq
glyhuvl�fdwlrq +Vhuydhv +4<<9,/ Ehujhu dqg Rihn +4<<8,/ Frpphqw dqg Mduuhoo +4<<8,/ dqg Odqj
dqg Vwxo} +4<<7,, dqg glyhuvl�fdwlrq lv ghfuhdvlqj lq lqfhqwlyhv +Ghqlv/ Ghqlv/ dqg Vdulq +4<<:,
55
dqg Edwhv/ El}mdn/ dqg Ohpprq +4<<:,,1 Wkhvh wzr �qglqjv vxjjhvw wkdw �upv zlwk zruvh lq0
fhqwlyh vwuxfwxuhv duh pruh glyhuvl�hg dqg shuirup zruvh wkdq gr �upv zlwk ehwwhu lqfhqwlyh
vwuxfwxuhv1 Wklv zrxog vhhp wr lpso| wkdw glyhuvl�fdwlrq lv dq djhqf| sureohp1
Wkh sureohp zlwk wklv lqwhusuhwdwlrq lv wkdw lw lv qrw dq htxloleulxp vwru|1 Li glyhuvl�fd0
wlrq lv gxh wr djhqf| sureohpv/ zk| gr �upv qrw lpsuryh wkh lqfhqwlyhv wkdw wkh| surylgh wr
pdqdjhuv/ wkhuhe| uhgxflqj glyhuvl�fdwlrq dqg lpsurylqj �up shuirupdqfhB Wkh lqwhusuhwdwlrq
deryh lpsolflwo| dvvxphv wkdw lqfhqwlyhv duh vhw h{rjhqrxvo|/ vr wkdw yduldwlrq lq lqfhqwlyhv rf0
fxuv iru hqwluho| h{rjhqrxv uhdvrqv1 Rxu srlqw lv vlpso| wkdw lqfhqwlyhv duh vhw hqgrjhqrxvo| wr
lq xhqfh wzr w|shv ri dfwlrqv wkdw wkh pdqdjhu pljkw wdnh= �uvw/ d jhqhulf dfwlrq wkdw lqfuhdvhv
�up shuirupdqfh vxfk dv h�ruw surylvlrq ru lqyhvwphqw ghflvlrqv/ dqg vhfrqg/ wkh glyhuvl�fdwlrq
ghflvlrq1 Yduldwlrq lq lqfhqwlyhv lv gulyhq e| pxfk pruh sodxvleo| h{rjhqrxv sdudphwhuv= ulvn
dyhuvlrq/ wkh yduldqfh ri vkrfnv wr �up shuirupdqfh/ wkh pdqdjhu*v glvxwlolw| ri wdnlqj dfwlrqv/ ru
wkh sulydwh ehqh�wv pdqdjhuv uhfhlyh iurp glyhuvli|lqj1
Zh whvw rxu prgho lq zklfk lqfhqwlyhv duh hqgrjhqrxv1 Frqvlvwhqw zlwk suhylrxv vwxglhv/ zh
�qg wkdw �up shuirupdqfh lv lqfuhdvlqj lq lqfhqwlyhv dqg ghfuhdvlqj lq glyhuvl�fdwlrq1 Krzhyhu/
e| fduhixoo| frqwuroolqj iru �up0vshfl�f idfwruv wkdw lq xhqfh glyhuvl�fdwlrq/ zh �qg hylghqfh
wkdw glyhuvl�fdwlrq lv srvlwlyho| uhodwhg wr lqfhqwlyhv1 Wklv lv lq vkdus frqwudvw wr wkh qhjdwlyh
uhodwlrqvkls wkdw kdv ehhq irxqg e| suhylrxv vwxglhv1 Wklv �qglqj lv qrw lqfrqvlvwhqw zlwk rxu
djhqf| prgho1 Lw vxjjhvwv wkdw zkhq pdqdjhuv* sulydwh ehqh�wv iurp glyhuvl�fdwlrq lqfuhdvh/
pdqdjhuv zloo eh jlyhq pruh lqfhqwlyhv wr frxqwhudfw wkhlu surshqvlw| wr glyhuvli|1 Ehfdxvh
lqfhqwlyhv gr qrw ixoo| r�vhw wkh surshqvlw| wr glyhuvli|/ glyhuvl�fdwlrq zloo dovr lqfuhdvh1 Lq
htxloleulxp/ erwk lqfhqwlyhv dqg glyhuvl�fdwlrq lqfuhdvh1
Lq dgglwlrq/ zh �qg wkdw/ lq d vhw ri �upv lq zklfk lw lv sodxvleoh wr eholhyh wkdw wkh| kdyh
h{shulhqfhg odujh fkdqjhv lq h{rjhqrxv sdudphwhuv/ wkh olqn ehwzhhq lqfhqwlyhv dqg �up shuiru0
pdqfh lv zhdnhu1 Dffruglqj wr rxu wkhru|/ �upv wkdw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq gr
vr ehfdxvh ri vkliwv lq wkh h{rjhqrxv sdudphwhuv1 Rxu wkhru| wkhq suhglfwv wkdw �upv lq zklfk
pdqdjhuv h{shulhqfh vkliwv lq sulydwh ehqh�wv zloo kdyh zhdnhu uhvsrqvhv ri shuirupdqfh wr lqfhq0
wlyhv1 Zkhq zh h{dplqh �upv wkdw h{shulhqfh fkdqjhv lq glyhuvl�fdwlrq dv rxu sur{| iru fkdqjhv
lq h{rjhqrxv sdudphwhuv/ zh �qg wkdw wkhvh �upv kdyh hvvhqwldoo| qr uhvsrqvh ri shuirupdqfh wr
56
lqfhqwlyhv1 Wklv �qglqj lv frqvlvwhqw zlwk wkh srvlwlyh uhodwlrqvkls ehwzhhq glyhuvl�fdwlrq dqg
lqfhqwlyhv qrwhg deryh1 Erwk duh fdxvhg e| h{rjhqrxv vkliwv lq wkh sulydwh ehqh�wv dvvrfldwhg
zlwk glyhuvl�fdwlrq1
Rxu uhvxowv vxjjhvw wkdw glyhuvl�fdwlrq lv lqghhg uhodwhg wr djhqf| sureohpv/ exw lq d pxfk
gl�huhqw zd| wkdq kdv ehhq h{soruhg lq wkh olwhudwxuh1 Lq htxloleulxp/ �upv lq zklfk pdqdjhuv
h{shulhqfh dq lqfuhdvh lq sulydwh ehqh�wv dvvrfldwhg zlwk glyhuvl�fdwlrq zloo kdyh pdqdjhuv zlwk
juhdwhu lqfhqwlyhv/ zloo glyhuvli| pruh/ dqg zloo vkrz zhdnhu uhvsrqvhv ri shuirupdqfh wr lqfhqwlyhv1
Dv d uhvxow/ zh eholhyh wkh djhqf| h{sodqdwlrq ri glyhuvl�fdwlrq kdv d pruh vrolg irxqgdwlrq1
57
Dsshqgl{Lq wklv Dsshqgl{/ zh h{whqg wkh sulqflsdo0djhqw prgho lq Vhfwlrq 5 wr doorz djhqwv wr kdyh
pruh jhqhudo sulydwh ehqh�wv ixqfwlrqv1 Ilup ydoxh lv vwloo jlyhq e|
� @ {� q. % +15:,
dqg wkh djhqw vwloo uhfhlyhv d olqhdu frpshqvdwlrq frqwudfw
z @ z3 . ��= +15;,
Wkh djhqw*v fhuwdlqw| htxlydohqw lv=
x @ � +{� q, . }e+q,� n
5{5 � u
5�5�5= +15<,
Zh dvvxph wkdw n lv qrw wrr forvh wr }hur vr wkdw wkh djhqw*v dfwlrq { uhpdlqv erxqghg1 Zh dvvxph
wkdw wkh djhqw jhqhudwhv sulydwh ehqh�wv ri wkh irup }e +q, iurp juhdwhu glyhuvl�fdwlrq/ zkhuh
} A 3 lqgh{hv wkh ehqh�wv wkh djhqw ghulyhv iurp glyhuvl�fdwlrq1 Wkh sulydwh ehqh�wv ixqfwlrq
e+q, dvvrfldwhg zlwk glyhuvl�fdwlrq lv frqfdyh/ e3 A 3> e33 ? 3>;q A 3 vr wkdw wkhuh lv glplqlvklqj
pdujlqdo xwlolw| iru wkh djhqw iurp glyhuvl�fdwlrq1 Zh lpsrvh wkh iroorzlqj dvvxpswlrq rq wkh
sulydwh ehqh�wv ixqfwlrq=C�
e
3
e
33
�Cq
@ f3> +163,
zkhuh f3 lv d frqvwdqw dqg f3 9@ 31 Wklv dvvxpswlrq lv vdwlv�hg e| d zlgh ydulhw| ri ixqfwlrqv/
lqfoxglqj wkh orjdulwkplf dqg srzhu ixqfwlrqv +ri wkh irup e+q, @ �qw iru � A 3 dqg 3 ? w ? 4/ ru
� ? 3 dqg w ? 3,1 Wkh iroorzlqj ohppd zloo eh xvhixo1
Ohppd 4 f3 ? 3 dqg e333 A 3=
Surri1 Lqwhjudwlqj +63, |lhogv e
3
e
33@ f3q. f4 zkhuh f4 lv wkh frqvwdqw ri lqwhjudwlrq1 Frqfdylw|
ri e+q, lpsolhv wkdw f3q. f4 ? 3>;q A 3 zklfk lpsolhv wkdw erwk f3 ? 3 dqg f4 � 3= Vlqfh f3 ? 3/C
�e3
e33
�
Cq
@+e33,5�e
3e
333
+e33,5? 3/ lpsolhv wkdw e333 A 31
Wkh djhqw*v sureohp lv=
pd{{>q
� +{� q, . }e+q,� n
5{5 � u
5�5�5=
58
Wkh �uvw dqg vhfrqg rughu frqglwlrqv iru glyhuvl�fdwlrq q duh=
��. }e3+q, @ 3 IRF +164,
}e33+q, ? 3 VRF
Qrwh wkdw zh fdq zulwh wkh �uvw rughu frqglwlrq dv=
e3+q�, @�
}+165,
dqg e| wkh lpsolflw ixqfwlrq wkhruhp=
Cq�
C�@
4
}e33+q�,? 3 +166,
Cq�
C}
�����@
b
�
@�e3+q�,
}e33+q�,A 3= +167,
Htxdwlrqv +66, dqg +67, ghvfuleh pryhphqwv dorqj wkh djhqw*v �uvw0rughu frqglwlrq/ iru dq| ydoxh
ri � fkrvhq e| wkh sulqflsdo1 Li wkh sulqflsdo surylghv pruh lqfhqwlyhv/ wkhq wkh djhqw fkrrvhv
ohvv glyhuvl�fdwlrq1 Dw d jlyhq ohyho ri lqfhqwlyhv +ghqrwhg e|b
� lq htxdwlrq +67,,/ juhdwhu sulydwh
ehqh�wv ohdg wr pruh glyhuvl�fdwlrq1 Zkhq zh wxuq wr wkh sulqflsdo*v sureohp ri rswlpdoo|
fkrrvlqj lqfhqwlyhv ehorz/ zh vkdoo fdofxodwh krz glyhuvl�fdwlrq dqg lqfhqwlyhv frydu| zkhq erwk
duh hqgrjhqrxvo| ghwhuplqhg1
Iru wkh djhqw*v dfwlrq fkrlfh {/ wkh �uvw dqg vhfrqg rughu frqglwlrqv duh=
�� n{ @ 3 IRF +168,
�n ? 3 VRF
Wkh �uvw rughu frqglwlrq jlyhv xv {� dv d ixqfwlrq ri �=
{� @�
n= +169,
H{shfwhg �up ydoxh qhw ri frpshqvdwlrq iru wkh djhqw lv=
H^�`�z @ {� � q� . }e+q�,� n
5+{�,5 � u
5�5�5 +16:,
Vxevwlwxwlqj wkh djhqw*v fkrlfh ri dfwlrq dqg glyhuvl�fdwlrq lqwr wkh �up ydoxh htxdwlrq deryh
dqg pd{lpl}lqj zlwk uhvshfw wr � |lhogv wkh sulqflsdo*v sureohp=
pd{�
�
n� q�+�> }, . }e+q�+�> },,� �5
5n� u
5�5�5 +16;,
59
Wkh �uvw rughu frqglwlrq lv=
4� �
n� +4� }e3+q�+�> },,,
Cq�
C�� u��5 @ 3= +16<,
Zh fdq uhzulwh wkh �uvw rughu frqglwlrq xvlqj +65, dqg +66, dv=
+4� �,
�4
n� 4
}e33+q�,
�� u��5 @ 3> +173,
zkhuh zh kdyh vxssuhvvhg wkh ghshqghqfh ri q� rq � dqg } +l1h1/ q�+�> },,1 Wklv uhsuhvhqwdwlrq
zloo eh yhu| xvhixo odwhu rq1 Wkh vhfrqg rughu frqglwlrq lv=
�4
n.
4
}e33+q�,. +4� �,
e333+q�,
}5 +e33+q�,,6� u�5> +174,
zkhuh zh kdyh xvhg htxdwlrq +66, wr vlpsoli| wkh h{suhvvlrq1 Lw lv vwudljkwiruzdug wr yhuli| wkdw
wkhuh h{lvwv d xqltxh �� 5 +3> 4, dqg wkdw wkh vhfrqg rughu frqglwlrq lv qhjdwlyh iru doo � 5 +3> 4,1
Zh kdyh wkh iroorzlqj frpsdudwlyh vwdwlfv iru ���u> �5> n> }
�=
C��
Cu@
���5
� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
? 3 +175,
C��
C�5@
u��
� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
? 3 +176,
C��
Cn@
+4� ��, @n5
� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
? 3 +177,
C��
C}@
� 4���
}5+e
33+q
�,,5
�e33+q�, . }e333+q�,
�Cq
�
C}
����@
b
�
��� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
+178,
@� 4��
�
}5e33+q
�,
+e33+q�
,,5�e3+q�
,e333
+q�
,
+e33+q
�,,5
� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
@� 4��
�
}5e33+q
�,f3
� 4
n. 4
}e33+q
�,. +4� ��, e
333+q
�,
}5+e
33+q
�,,6 � u�5
A 3
zkhuh f3? 3 e| wkh Ohppd1
Iru wkh djhqw*v glyhuvl�fdwlrq fkrlfh q�/ zh vxevwlwxwh ���u> �5> n> }
�lqwr htxdwlrq +64,=
��� �u> �5> n> }�. }e3+q�, @ 3= +179,
Zh �uvw wdnh wkh ghulydwlyh ri q� zlwk uhvshfw wr wkh h{rjhqrxv sdudphwhuv dqg wkhq fdofxodwh
krz q� ydulhv zlwk �� jlyhq d fkdqjh lq wkh h{rjhqrxv sdudphwhu1 Wkh frpsdudwlyh vwdwlfv zlwk
5:
uhvshfw wr wkh h{rjhqrxv sdudphwhuv duh=
Cq�
Cu@
4
}e33+q�,
C��
CuA 3 +17:,
Cq�
C�5@
4
}e33+q�,
C��
C�5A 3
Cq�
Cn@
4
}e33+q�,
C��
CnA 3
Cq�
C}
������@�
�+u>�
5>n>},
@C�
�
C}
� e3+q�,
}e33+q�,
@4
}e33+q�,
3EC � 4��
�
}
5e
33+q
�,
+e33+q�
,,5�e3+q�
,e333
+q�
,
+e33+q
�,,5
� 4
n
. 4
}e
33+q
�,. +4� ��, e
333+q
�,
}
5+e
33+q
�,,6 � u�5
� e3+q�,
4FD
@ � 4
}e33+q�,
3C 4��
�
}
5e
33+q
�,. e3+q�,
�� 4
n
. 4
}e
33+q
�,� u�5
�� 4
n
. 4
}e
33+q
�,. +4� ��, e
333+q
�,
}
5+e
33+q
�,,6 � u�5
4D A 3=
Wklv h{suhvvlrq iru Cq
�
C}
gl�huv iurp wkdw lq htxdwlrq +67, lq wkdw lw uhfrjql}hv wkdw �� ydulhv zlwk
} dv zhoo1
Wr vhh krz q� ydulhv zlwk �� lq htxloleulxp jlyhq d fkdqjh lq dq h{rjhqrxv sdudphwhu/ zh
kdyh=
Cq�
C��
����Cu
@Cq�
Cu!C��
Cu? 3 +17;,
Cq�
C��
����C�
5
@Cq�
C�5!C��
C�5? 3
Cq�
C��
����Cn
@Cq�
Cn!C��
Cn? 3
Cq�
C��
����C}
@Cq�
C}
�����
�@�
�+u>�
5>n>},
!C��
C}A 3=
Qrz zh wxuq wr �up ydoxh1 H{shfwhg �up ydoxh ydulhv zlwk wkh h{rjhqrxv sdudphwhuv lq wkh
iroorzlqj zd|/ zkhuh lw lv xqghuvwrrg wkdw doo ghulydwlyhv ri e duh hydoxdwhg dw q�=
CH+�,
Cu@
4
n
C��
Cu� Cq�
Cu? 3 +17<,
CH+�,
C�5@
4
n
C��
C�5� Cq�
C�5? 3
CH+�,
Cn@ ��
�
n5.
4
n
C��
Cn� Cq�
Cn? 3
CH+�,
C}@
4
n
C��
C}� Cq�
C}
@� 4��
�
}
5e
33n
f3. 4��
�
}
6+e
33,5 .
e
3
}e
33
�� 4
n
. 4
}e
33� u�5
�� 4
n
. 4
}e
33. +4� ��, e
333
}
5+e
33,6 � u�5
5;
@� 4��
�
}5e33nf3 .
4���
}6+e33,
5 � ��
}5e33n. e
3
}e33
��4��
�
��n
. 4
}e33��
�� 4
n. 4
}e33. +4� ��, e
333
}5+e33,
6 � u�5
@� 4
}5e33n
k+4� ��, f3 � +5��
�
,n
}e33
. 4l
� 4
n. 4
}e33. +4� ��, e
333
}5+e33,
6 � u�5
@� 4
}5e33n
k+4� ��, f3 � +5��
�
,n
��
e3
e33. 4
l� 4
n. 4
}e33. +4� ��, e
333
}5+e33,
6 � u�5
@� 4
}5e33n
k+4� ��, f3 � +5��
�
,n
��
+f3q� . f4, . 4l
� 4
n. 4
}e33. +4� ��, e
333
}5+e33,
6 � u�5
? 3>
zklfk iroorzv iurp wkh ohppd/ dqg ehfdxvh �� 5 +3> 4,/ n lv erxqghg dzd| iurp 3> dqg q� � 41
Zh kdyh xvhg htxdwlrq +73, dqg wkh Ohppd wr vlpsoli| wkh h{suhvvlrq iru C�
C}1 Qrwh wkdw wkh
dvvxpswlrq wkdwC
�e3
e33
�
Cq@ f3 lv vx!flhqw/ exw qrw qhfhvvdu| iru wklv uhvxow1 Dq dowhuqdwlyh
frqglwlrq wkdw lv dovr vdwlv�hg lq pdq| fdvhv lv wkdw +e33+q�
,,5�e3+q�
,e333
+q�
,
+e33+q�,,5 5 ^�4> 3`= Wkh vdph
frpsdudwlyh vwdwlfv duh wkhq jhqhudwhg zlwkrxw uhtxlulqj wkdwC
�e3
e33
�
Cqeh frqvwdqw1
Doo ri wkh uhvw ri rxu uhvxowv lq Vhfwlrq 5 wkhq iroorz e| wkh vdph dujxphqwv jlyhq wkhuh1
5<
UHIHUHQFHV
Djjduzdo/ Udmhvk N1 dqg Dqguhz D1 Vdpzlfn +4<<<d,1 �Wkh Rwkhu Vlgh ri wkh Wudghr�= WkhLpsdfw ri Ulvn rq H{hfxwlyh Frpshqvdwlrq1� Mrxuqdo ri Srolwlfdo Hfrqrp|1 43:= 9804381
Djjduzdo/ Udmhvk N1 dqg Dqguhz D1 Vdpzlfn +4<<<e,1 �Shuirupdqfh Lqfhqwlyhv ZlwklqIlupv= Wkh H�hfw ri Pdqdjhuldo Uhvsrqvlelolw|1� QEHU Zrunlqj Sdshu Qr1 :6671
Djjduzdo/ Udmhvk N1 dqg Dqguhz D1 Vdpzlfn +4<<<f,1 �Hpsluh0Exloghuv dqg Vklunhuv= Lq0yhvwphqw/ Ilup Shuirupdqfh/ dqg Pdqdjhuldo Lqfhqwlyhv1� QEHU Zrunlqj Sdshu Qr1 :6681
Dplkxg/ \dnry dqg Eduxfk Ohy +4<;4,1 �Ulvn Uhgxfwlrq dv d Pdqdjhuldo Prwlyh iru Frq0jorphudwh Phujhuv1� Ehoo Mrxuqdo ri Hfrqrplfv1 45=93804:
Edwhv/ Wkrpdv Z1/ Mrkq P1 El}mdn/ dqg Plfkdho O1 Ohpprq +4<<:,1 �Sd|0iru Shuirupdqfhdqg Ilup Glyhuvl�fdwlrq1� Dul}rqd Vwdwh Xqlyhuvlw| Zrunlqj Sdshu1
Ehujhu/ Sklols J1 dqg Hol Rihn +4<<8,1 �Glyhuvl�fdwlrq*v H�hfw rq Ilup Ydoxh1� Mrxuqdo riIlqdqfldo Hfrqrplfv1 6:= 6<0981
Ehuwudqg/ Pduldqqh dqg Vhqgklo Pxoodlqdwkdq +4<<<,1 �Duh FHRv Uhzdughg iru OxfnB�PLW dqg Sulqfhwrq Zrunlqj Sdshu1
Fkdqj/ Fkxq +4<<6,1 �Sd|rxw Srolf|/ Fdslwdo Vwuxfwxuh/ dqg Frpshqvdwlrq Frqwudfwv zkhqPdqdjhuv Ydoxh Frqwuro1� Uhylhz ri Ilqdqfldo Vwxglhv1 9= <440661
Frpphqw/ Urehuw dqg Juhj D1 Mduuhoo +4<<8,1 �Frusrudwh Irfxv dqg Vwrfn Uhwxuqv1�Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 6:= 9:0;:1
Ghqlv/ Gdylg/ Gldqh Ghqlv dqg Dwxo|d Vdulq +4<<:,1 �Djhqf| Sureohpv/ Htxlw| Rzqhuvkls/dqg Frusrudwh Glyhuvl�fdwlrq1� Mrxuqdo ri Ilqdqfh1 85= 4680931
Id}}dul Vwhyhq P1/ U1 Johqq Kxeedug/ dqg Euxfh F1 Shwhuvhq +4<;;,1 �Ilqdqflqj Frq0vwudlqwv dqg Frusrudwh Lqyhvwphqw1� Eurrnlqjv Sdshuv rq Hfrqrplf Dfwlylw|1 4<;;= 4=47404<81
Kduw/ Rolyhu dqg Mrkq Prruh +4<<8,1 �Ghew dqg Vhqlrulw|= Dq Dqdo|vlv ri wkh Uroh ri KdugFodlpv lq Frqvwudlqlqj Pdqdjhphqw1� Dphulfdq Hfrqrplf Uhylhz1 ;8= 89:0;81
Klpphoehuj/ Fkduohv/ U1 Johqq Kxeedug/ dqg Gdulxv Sdold +4<<<,1 �Xqghuvwdqglqj wkhGhwhuplqdqwv ri Pdqdjhuldo Rzqhuvkls dqg wkh Olqn Ehwzhhq Rzqhuvkls dqg Shuirupdqfh1�Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 86= 6860;71
Kropvwurp/ Ehqjw +4<:<,1 �Prudo Kd}dug dqg Revhuydelolw|1� Ehoo Mrxuqdo ri Hfrqrplfv143= :70<41
Kropvwurp/ Ehqjw dqg Sdxo Plojurp +4<;:,1 �Djjuhjdwlrq dqg Olqhdulw| lq wkh Surylvlrqri Lqwhuwhpsrudo Lqfhqwlyhv1� Hfrqrphwulfd1 88= 63605;1
Kxeedug/ U1 Johqq dqg Gdulxv Sdold +4<<<,1 �D Uhh{dplqdwlrq ri wkh Frqjorphudwh PhujhuZdyh lq wkh 4<93v= Dq Lqwhuqdo Fdslwdo Pdunhwv Ylhz1� Mrxuqdo ri Ilqdqfh1 87= 4464044851
Mhqvhq/ Plfkdho F1 +4<;9,1 �Djhqf| Frvwv ri Iuhh Fdvk Iorz/ Frusrudwh Ilqdqfh/ dqgWdnhryhuv1� Dphulfdq Hfrqrplf Uhylhz1 :9= 656065<1
Mhqvhq/ Plfkdho F1 +4<<6,1 �Wkh Prghuq Lqgxvwuldo Uhyrxwlrq/ H{lw/ dqg wkh Idloxuh riLqwhuqdo Frqwuro V|vwhpv1� Mrxuqdo ri Ilqdqfh1 7;= ;640;;31
63
Mhqvhq/ Plfkdho F1 dqg Zlooldp K1 Phfnolqj +4<:9,1 �Wkhru| ri wkh Ilup= PdqdjhuldoEhkdylru/ Djhqf| Frvwv dqg Rzqhuvkls Vwuxfwxuh1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 6=6380931
Mhqvhq/ Plfkdho F1 dqg Nhylq M1 Pxusk| +4<<3,1 �Shuirupdqfh Sd| dqg Wrs PdqdjhphqwLqfhqwlyhv1� Mrxuqdo ri Srolwlfdo Hfrqrp|1 <;= 5580971
Mrkq/ Nrvh dqg Hol Rihn +4<<8,1 �Dvvhw Vdohv dqg Lqfuhdvh lq Irfxv1� Mrxuqdo ri IlqdqfldoHfrqrplfv1 6:= 4380591
Ndsodq/ Vwhyhq +4<;<,1 �Wkh H�hfwv ri Pdqdjhphqw Ex|rxwv rq Rshudwlqj Shuirupdqfhdqg Ydoxh1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 57= 54:05871
Odqj/ Oduu| K1 S1 dqg Uhqh P1 Vwxo} +4<<7,1 �Wrelq*v t/ Frusrudwh Glyhuvl�fdwlrq/ dqgIlup Shuirupdqfh1� Mrxuqdo ri Srolwlfdo Hfrqrp|1 435= 457;0;31
Pd|/ Grq R1 +4<<8,1 �Gr Pdqdjhuldo Prwlyhv Lq xhqfh Ilup Ulvn0Uhgxfwlrq VwudwhjlhvB�Mrxuqdo ri Ilqdqfh1 83= 45<40463;1
PfFrqqhoo/ Mrkq M1 dqg Fkulv M1 Pxvfduhood +4<;8,1 �Frusrudwh Fdslwdo H{shqglwxuh Ghfl0vlrqv dqg wkh Pdunhw Ydoxh ri wkh Ilup1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 47= 6<<07551
PfFrqqhoo/ Mrkq M1 dqg Khqul Vhuydhv +4<<3,1 �Dgglwlrqdo Hylghqfh rq Htxlw| Rzqhuvklsdqg Frusrudwh Ydoxh1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 5:= 8<809451
Prufn/ Udqgdoo/ Dqguhl Vkohlihu/ dqg Urehuw Ylvkq| +4<;;,1 �Pdqdjhphqw Rzqhuvkls dqgPdunhw Ydoxdwlrq�Dq Hpslulfdo Dqdo|vlv1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 53= 5<606481
Pxusk|/ Nhylq M1 +4<<<,1 �H{hfxwlyh Frpshqvdwlrq/� lq Ruoh| Dvkhqihowhu dqg Gdylg Fdug+hgv1, Kdqgerrn ri Oderu Hfrqrplfv Yro1 6/ Qruwk Kroodqg1
Udmdq/ Udjkxudp J1/ Khqul Vhuydhv/ dqg Oxljl ]lqjdohv +5333,1 �Wkh Frvw ri Glyhuvlw|=Wkh Glyhuvl�fdwlrq Glvfrxqw dqg Lqh!flhqw Lqyhvwphqw1� Mrxuqdo ri Ilqdqfh/ iruwkfrplqj1
Vhuydhv/ Khqul +4<<9,1 �Wkh Ydoxh ri Glyhuvl�fdwlrq Gxulqj wkh Frqjorphudwh PhujhuZdyh1� Mrxuqdo ri Ilqdqfh1 84= 4534045581
Vkohlihu/ Dqguhl dqg Urehuw Ylvkq| +4<;<,1 �Pdqdjhphqw Hqwuhqfkphqw�Wkh Fdvh riPdqdjhu0Vshfl�f Lqyhvwphqwv1� Mrxuqdo ri Ilqdqfldo Hfrqrplfv1 58= 456046<1
Vkohlihu/ Dqguhl dqg Urehuw Ylvkq| +4<<:,1 �D Vxuyh| ri Frusrudwh Jryhuqdqfh1� Mrxuqdori Ilqdqfh1 85= :6:0;61
Vwxo}/ Uhqh P1 +4<<3,1 �Pdqdjhuldo Glvfuhwlrq dqg Rswlpdo Ilqdqflqj Srolflhv1� Mrxuqdori Ilqdqfldo Hfrqrplfv1 59= 605:1
Vwdqgdug dqg Srru*v +4<<8,1 V)S Frpsxvwdw H{hfxFrps= Wkh H{hfxwlyh FrpshqvdwlrqGdwdedvh1 Hqjohzrrg/ FR= PfJudz0Kloo/ Qryhpehu1
Vwhlq/ Mhuhp| F1 +4<<:,1 �Lqwhuqdo Fdslwdo Pdunhwv dqg wkh Frpshwlwlrq iru FrusrudwhUhvrxufhv1� Mrxuqdo ri Ilqdqfh1 85= 44404661
64
32
Table 1Descriptive Statistics for Variables Used in Econometric Analyses
VariableNumber of
Observations MeanStandardDeviation
10th
Percentile25th
Percentile Median75th
Percentile90th
Percentile
Team PPS 7045 7.1269 10.7508 0.4491 1.1308 3.1259 7.1269 19.4998 CEO PPS 7045 4.1565 7.3757 0.1550 0.4583 1.3371 3.9261 11.8047Tobin’s Q 7045 2.1397 2.1263 1.0666 1.2479 1.6002 2.3375 3.6263No. of Segments 7045 2.1796 1.8230 1.0000 1.0000 1.0000 3.0000 4.0000No. of 4-digit SICs 7045 1.7918 1.2110 1.0000 1.0000 1.0000 2.0000 3.0000No. of 2-digit SICs 7045 1.5517 0.9517 1.0000 1.0000 1.0000 2.0000 3.0000Investment/Capital 7045 0.2543 0.1731 0.0845 0.1377 0.2106 0.3308 0.4815Dividend Yield 7045 1.4928 2.1584 0.0000 0.0000 0.8700 2.3500 4.0200Ln(sales) 7045 7.0342 1.5832 5.1308 6.0369 6.9847 8.0879 9.0983Capital/Sales 7045 0.5385 0.8911 0.0703 0.1318 0.2573 0.5576 1.4390Cash Flow/Capital 7045 0.8628 2.7421 0.1471 0.2461 0.4941 0.9321 1.8251Debt/Assets 7015 0.2338 0.1818 0.0033 0.0828 0.2236 0.3472 0.4461Std Dev of Returns 6814 669.65 1491.69 61.70 106.20 235.82 601.38 1393.56R & D/Capital 3815 0.3989 1.3003 0.0000 0.0120 0.0935 0.3647 0.9758Advertising/Capital 1567 0.3216 0.8444 0.0226 0.0498 0.1219 0.3226 0.6579
Notes:1) Pay-performance sensitivities (PPS) represent incentives provided by direct ownership of stock and stock options for each top
management team or chief executive officer (CEO). They are expressed as percentages of the firm, from 0 to 100.2) Pay-performance sensitivities are calculated from ExecuComp. The standard deviation of monthly returns is based on dollar
returns calculated from CRSP, expressed in millions. All other variables are calculated from Compustat.3) The PPS for the top management team includes the PPS for the CEO plus four times the average PPS for all other executives for
whom data are available.4) All dollar values are in millions of constant 1997 dollars.5) The sample is comprised of 1602 firms observed in any year from 1993 to 1998.
33
Table 2Regressions of Tobin’s Q on Top Management Incentives and Diversification
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.2090
(0.1719)2.1427
(0.0575)5.2739
(0.8673)5.1538
(1.2811)No. of 4-digit SICs -0.2022
(0.0211)-0.0446(0.0177)
-0.0641(0.0125)
-0.0680(0.0196)
PPS 0.0384(0.0196)
0.0193(0.0041)
0.0288(0.0201)
0.0143(0.0035)
Investment 2.3904(0.4431)
0.9827(0.1768)
Dividend Yield 0.0330(0.0223)
-0.0227(0.0169)
Ln(sales) -0.9811(0.2226)
-0.9344(0.3319)
Ln(sales)2 0.0391(0.0145)
0.0806(0.0227)
Capital/Sales -0.1930(0.0529)
-0.2897(0.0694)
(Capital/Sales)2 -0.0008(0.0025)
0.0047(0.0024)
Cash Flow/Capital 0.0191(0.0215)
0.0729(0.0225)
Debt/Assets -0.8397(0.1645)
-0.9099(0.1753)
Missing D/A 0.7094(0.4301)
-0.6667(0.4954)
CDF of Std Dev 2.6836(0.2119)
-0.9533(0.2812)
Missing Std Dev 1.9313(0.4918)
-0.3441(0.2993)
R & D/Capital -0.0065(0.0632)
0.0418(0.0343)
Missing R&D/K -0.1534(0.0523)
0.0551(0.0904)
Advertising/Capital 0.0956(0.1698)
-0.2123(0.0763)
Missing Adv/K -0.1173(0.0569)
-0.0170(0.0587)
Year = 1994 -0.2382(0.0601)
-0.1837(0.0380)
-0.2223(0.0525)
-0.1786(0.0379)
Year = 1995 -0.1236(0.0622)
-0.0886(0.0371)
-0.0982(0.0540)
-0.0781(0.0413)
Year = 1996 -0.0650(0.0632)
-0.0702(0.0375)
-0.0538(0.0552)
-0.0497(0.0449)
Year = 1997 0.1564(0.0748)
-0.0078(0.0406)
0.1114(0.0664)
0.0254(0.0558)
Year = 1998 0.2976(0.0957)
-0.0166(0.0473)
0.1640(0.0960)
0.0676(0.0527)
R-squared 0.0654 0.8611 0.2322 0.8689Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.
34
Table 3Regressions of Tobin’s Q on CEO Incentives and Diversification
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.3856
(0.0654)2.2385
(0.0515)5.7443
(0.8573)5.4209
(1.2894)No. of 4-digit SICs -0.2252
(0.0128)-0.0411(0.0177)
-0.0656(0.0116)
-0.0645(0.0196)
PPS 0.0332(0.0091)
0.0115(0.0045)
0.0180(0.0072)
0.0058(0.0043)
Investment 2.4840(0.5156)
1.0061(0.1783)
Dividend Yield 0.0244(0.0150)
-0.0236(0.0173)
Ln(sales) -1.0341(0.2393)
-0.9704(0.3339)
Ln(sales)2 0.0409(0.0150)
0.0818(0.0228)
Capital/Sales -0.2342(0.0363)
-0.3016(0.0698)
(Capital/Sales)2 0.0003(0.0021)
0.0050(0.0024)
Cash Flow/Capital 0.0139(0.0247)
0.0724(0.0229)
Debt/Assets -0.8806(0.1595)
-0.9048(0.1748)
Missing D/A 0.7006(0.4439)
-0.6687(0.4931)
CDF of Std Dev 2.6208(0.1785)
-0.9701(0.2830)
Missing Std Dev 1.9073(0.4933)
-0.3499(0.3028)
R & D/Capital -0.0268(0.0718)
0.0411(0.0347)
Missing R&D/K -0.1170(0.0362)
0.0640(0.0909)
Advertising/Capital 0.1464(0.2041)
-0.2038(0.0771)
Missing Adv/K -0.1316(0.0532)
-0.0159(0.0590)
Year = 1994 -0.2372(0.0596)
-0.1902(0.0385)
-0.2266(0.0518)
-0.1818(0.0381)
Year = 1995 -0.1219(0.0621)
-0.0975(0.0377)
-0.1011(0.0533)
-0.0818(0.0415)
Year = 1996 -0.0683(0.0632)
-0.0827(0.0382)
-0.0593(0.0543)
-0.0547(0.0451)
Year = 1997 0.1537(0.0748)
-0.0240(0.0414)
0.1054(0.0655)
0.0188(0.0560)
Year = 1998 0.3025(0.1025)
-0.0404(0.0486)
0.1642(0.0997)
0.0566(0.0530)
R-squared 0.0415 0.8605 0.2178 0.8685Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.
35
Table 4Regressions of Diversification on Top Management Incentives
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.0796
(0.0494)1.7676
(0.0271)1.6475
(0.2015)1.6629
(0.3203)PPS -0.0160
(0.0015)0.0050
(0.0018)-0.0014(0.0013)
0.0070(0.0019)
Investment -0.4973(0.1261)
0.0014(0.0879)
Dividend Yield 0.0749(0.0253)
0.0020(0.0045)
Ln(sales) -0.2301(0.0609)
-0.3017(0.1036)
Ln(sales)2 0.0349(0.0046)
0.0488(0.0094)
Capital/Sales -0.0659(0.0329)
-0.1232(0.0451)
(Capital/Sales)2 0.0012(0.0012)
0.0032(0.0013)
Cash Flow/Capital -0.0259(0.0054)
-0.0187(0.0062)
Debt/Assets 0.1424(0.0857)
0.1556(0.0830)
Missing D/A -0.3185(0.1134)
0.1496(0.0868)
CDF of Std Dev -0.2586(0.0777)
-0.4174(0.1186)
Missing Std Dev -0.1024(0.0877)
-0.1919(0.1080)
R & D/Capital -0.0396(0.0122)
-0.0286(0.0156)
Missing R&D/K 0.0334(0.0307)
0.0052(0.0898)
Advertising/Capital 0.1496(0.0339)
0.0466(0.0275)
Missing Adv/K 0.3204(0.0328)
-0.0115(0.0296)
Year = 1994 -0.1191(0.0608)
-0.0123(0.0250)
-0.0929(0.0564)
-0.0278(0.0255)
Year = 1995 -0.1814(0.0594)
-0.0408(0.0240)
-0.1624(0.0560)
-0.0838(0.0267)
Year = 1996 -0.2416(0.0581)
-0.0691(0.0245)
-0.2092(0.0561)
-0.1329(0.0284)
Year = 1997 -0.3232(0.0567)
-0.0850(0.0260)
-0.2479(0.0553)
-0.1719(0.0319)
Year = 1998 -0.1108(0.0571)
0.1261(0.0329)
-0.0333(0.0546)
0.0234(0.0408)
R-squared 0.0270 0.8696 0.1780 0.8749Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.
36
Table 5Regressions of Diversification on CEO Incentives
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.0508
(0.0489)1.8009
(0.0242)1.6447
(0.2016)1.7632
(0.3187)PPS -0.0208
(0.0018)0.0016
(0.0020)-0.0026(0.0018)
0.0046(0.0020)
Investment -0.4987(0.1262)
0.0115(0.0883)
Dividend Yield 0.0746(0.0252)
0.0014(0.0043)
Ln(sales) -0.2285(0.0610)
-0.3135(0.1037)
Ln(sales)2 0.0347(0.0046)
0.0491(0.0095)
Capital/Sales -0.0659(0.0329)
-0.1279(0.0451)
(Capital/Sales)2 0.0012(0.0012)
0.0034(0.0013)
Cash Flow/Capital -0.0260(0.0054)
-0.0191(0.0061)
Debt/Assets 0.1422(0.0857)
0.1595(0.0831)
Missing D/A -0.3155(0.1136)
0.1488(0.0872)
CDF of Std Dev -0.2573(0.0774)
-0.4227(0.1188)
Missing Std Dev -0.1011(0.0876)
-0.1928(0.1081)
R & D/Capital -0.0397(0.0122)
-0.0289(0.0157)
Missing R&D/K 0.0332(0.0306)
0.0085(0.0898)
Advertising/Capital 0.1494(0.0338)
0.0516(0.0261)
Missing Adv/K 0.3196(0.0329)
-0.0113(0.0296)
Year = 1994 -0.1171(0.0610)
-0.0141(0.0250)
-0.0923(0.0564)
-0.0290(0.0255)
Year = 1995 -0.1815(0.0594)
-0.0436(0.0240)
-0.1621(0.0560)
-0.0853(0.0267)
Year = 1996 -0.2396(0.0582)
-0.0731(0.0243)
-0.2088(0.0560)
-0.1350(0.0283)
Year = 1997 -0.3210(0.0568)
-0.0903(0.0258)
-0.2474(0.0552)
-0.1749(0.0319)
Year = 1998 -0.1112(0.0572)
0.1170(0.0325)
-0.0344(0.0546)
0.0174(0.0407)
R-squared 0.0228 0.8696 0.1779 0.8747Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.
37
Table 6Regressions of Tobin’s Q on Top Mgmt. Incentives Controlling for Changes in Diversification
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.1609
(0.1765)2.1308
(0.0552)5.2414
(0.8674)5.1524
(1.2796)β1 PPS 0.0410
(0.0208)0.0201
(0.0041)0.0311
(0.0212)0.0150
(0.0036)β2 PPS x ∆ -0.0460
(0.0209)-0.0098(0.0026)
-0.0419(0.0202)
-0.0079(0.0027)
∆ (Change in SICs) -0.0371(0.1148)
-0.0047(0.0337)
-0.0318(0.1062)
-0.0205(0.0317)
No. of 4-digit SICs -0.1866(0.0197)
-0.0422(0.0177)
-0.0512(0.0122)
-0.0645(0.0197)
Investment 2.3743(0.4386)
0.9829(0.1776)
Dividend Yield 0.0328(0.0220)
-0.0228(0.0168)
Ln(sales) -0.9842(0.2219)
-0.9349(0.3316)
Ln(sales)2 0.0391(0.0144)
0.0804(0.0227)
Capital/Sales -0.2019(0.0507)
-0.2926(0.0694)
(Capital/Sales)2 -0.0004(0.0025)
0.0048(0.0024)
Cash Flow/Capital 0.0178(0.0218)
0.0716(0.0226)
Debt/Assets -0.8103(0.1663)
-0.9107(0.1752)
Missing D/A 0.6971(0.4301)
-0.6668(0.4959)
CDF of Std Dev 2.6996(0.2143)
-0.9527(0.2814)
Missing Std Dev 1.9460(0.4935)
-0.3415(0.2998)
R & D/Capital -0.0068(0.0626)
0.0409(0.0342)
Missing R&D/K -0.1414(0.0492)
0.0521(0.0907)
Advertising/Capital 0.1052(0.1726)
-0.2040(0.0761)
Missing Adv/K -0.1121(0.0579)
-0.0137(0.0587)
R-squared 0.0698 0.8612 0.2355 0.8690Coefficient on Incentives (∆=1), p-value in [.]
β1 + β2
H0: = 0-0.0050[0.214]
0.0103[0.019]
-0.0091[0.076]
0.0071[0.090]
Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.4) Year effects are included in all regressions but not reported.5) ∆=1 if No. of 4-digit SICs has changed this year, ∆=0 otherwise.
38
Table 7Regressions of Tobin’s Q on CEO Incentives Controlling for Changes in Diversification
Variable OLS Fixed Effect OLS w/Controls FE w/ControlsIntercept 2.3414
(0.0676)2.2317
(0.0521)5.7221
(0.8551)5.4267
(1.2878)β1 PPS 0.0352
(0.0096)0.0119
(0.0045)0.0194
(0.0076)0.0061
(0.0043)β2 PPS x ∆ -0.0460
(0.0107)-0.0118(0.0047)
-0.0328(0.0096)
-0.0092(0.0047)
∆ (Change in SICs) -0.1644(0.0536)
-0.0387(0.0178)
-0.1569(0.0502)
-0.0276(0.0314)
No. of 4-digit SICs -0.2065(0.0125)
-0.0387(0.0178)
-0.0502(0.0123)
-0.0608(0.0197)
Investment 2.4659(0.5127)
1.0045(0.1789)
Dividend Yield 0.0244(0.0149)
-0.0237(0.0172)
Ln(sales) -1.0386(0.2390)
-0.9712(0.3336)
Ln(sales)2 0.0410(0.0150)
0.0817(0.0228)
Capital/Sales -0.2404(0.0362)
-0.3041(0.0698)
(Capital/Sales)2 0.0005(0.0021)
0.0051(0.0024)
Cash Flow/Capital 0.0134(0.0248)
0.0718(0.0230)
Debt/Assets -0.8612(0.1591)
-0.9082(0.1747)
Missing D/A 0.6892(0.4440)
-0.6692(0.4935)
CDF of Std Dev 2.6326(0.1794)
-0.9702(0.2832)
Missing Std Dev 1.9129(0.4933)
-0.3490(0.3033)
R & D/Capital -0.0265(0.0712)
0.0406(0.0346)
Missing R&D/K -0.1093(0.0359)
0.0614(0.0912)
Advertising/Capital 0.1499(0.2046)
-0.1989(0.0772)
Missing Adv/K -0.1287(0.0532)
-0.0136(0.0590)
R-squared 0.0442 0.8606 0.2195 0.8686Coefficient on Incentives (∆=1), p-value in [.]
β1 + β2
H0: = 0-0.0108[0.017]
0.0001[0.987]
-0.0134[0.016]
-0.0031[0.619]
Notes:1) Each regression pertains to our sample of 1602 firms and 7045 firm-years.2) The Fixed Effects specification includes a dummy variable for each sample firm.3) Heteroskedasticity-robust standard errors are reported in parentheses beneath each coefficient.4) Year effects are included in all regressions but not reported.5) ∆=1 if No. of 4-digit SICs has changed this year, ∆=0 otherwise.