Chapter 3 The Keynesian Model of Aggregate Demand and

Fkdswhu 6
Wkh Nh|qhvldq Prgho ri
Djjuhjdwh Ghpdqg dqg Djjuhjdwh Vxsso|
Shwhu Elufk Vûuhqvhq dqg Kdqv Mûujhq Zklwwd0Mdfrevhq
491 vhswhpehu 5335
Zkdw duh wkh fdxvhv ri hfrqrplf uhfhvvlrqv/ dqg krz fdq uhfhvvlrqv eh dyrlghg ru dw
ohdvw doohyldwhgB Dujxdeo| wkhvh duh wkh prvw lpsruwdqw lvvxhv lq pdfurhfrqrplf wkhru|
iru wkh vkruw uxq1 Lq wklv fkdswhu zh vkdoo vhh krz wkh vr0fdoohg Nh|qhvldq uhyroxwlrq lq
pdfurhfrqrplfv fkdqjhg wkh zd| hfrqrplvwv dqg srolf| pdnhuv zhuh wklqnlqj derxw wkhvh
txhvwlrqv1
Edfnjurxqg= wkh Juhdw Ghsuhvvlrq
Wkh fodvvlfdo prgho vwxglhg lq Fkdswhu 5 lv d irupdol}dwlrq ri lghdv zklfk zhuh grp0
lqdqw dprqj pdfurhfrqrplvwv sulru wr wkh Nh|qhvldq uhyroxwlrq lq wkh 4<63v dqg 4<73v1
Wkh fuxfldo dvvxpswlrq ri wkh fodvvlfdo prgho lv wkdw doo uhvrxufhv duh xwlol}hg dw wkhlu
qdwxudo udwhv vr wkdw hfrqrplf dfwlylw| fdqqrw eh ghsuhvvhg gxh wr d odfn ri djjuhjdwh
ghpdqg1 Wkh fodvvlfdo +suh0Nh|qhvldq, hfrqrplvwv glg qrw olwhudoo| fodlp wkdw d fdslwdo0
lvw pdunhw hfrqrp| frxog qrw ghyldwh iurp lwv qdwxudo udwh ri hpsor|phqw dqg rxwsxw1
Krzhyhu/ wkh| glg eholhyh wkdw vxfk glvwxuedqfhv zrxog eh whpsrudu| dqg txlwh vkruw0
olyhg1 E| lpsolfdwlrq/ wkh fodvvlfdo hfrqrplvwv vdz qr qhhg iru wkh jryhuqphqw wr hqjdjh
lq pdfurhfrqrplf vwdelol}dwlrq srolf|1 Lq wkhlu ylhz/ wkh rqo| uroh ri prqhwdu| srolf| zdv
4
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
5
wr vhfxuh sulfh vwdelolw|/ dqg wkh wdvn ri vfdo srolf| zdv wr dyrlg exgjhw ghflwv zklfk
zrxog furzg rxw sulydwh fdslwdo irupdwlrq dqg wkhuhe| kdpshu hfrqrplf jurzwk1
Zkhq wkh Juhdw Ghsuhvvlrq ri wkh 4<63v vwuxfn wkh zhvwhuq zruog/ wkhvh fodvvlfdo
srvlwlrqv fdph xqghu khdy| dwwdfn1 Wkh Juhdw Ghsuhvvlrq zdv d kxjh hfrqrplf glvdvwhu1
Gxh wr d idwdo frpelqdwlrq ri qhjdwlyh vkrfnv dqg pdfurhfrqrplf srolf| idloxuhv/ rxwsxw
lq vhyhudo frxqwulhv ihoo e| 58063 shufhqw ehwzhhq 4<5< dqg 4<65066/ dv |rx fdq vhh iurp
Wdeoh 6141
---Wdeoh 6141 Wkh Juhdw Ghsuhvvlrq +uhsurgxnwlrq di wdehoohq l Er{ 615/ v1 443 l Zruog
Hfrqrplf Rxworrn/ Dsulo 53351 SEV kdu ghqqh nlogh,--Iru d frxqwu| olnh wkh Xqlwhg Vwdwhv/ lw wrrn doprvw d ghfdgh iru rxwsxw wr uhwxuq lwv
suhylrxv 4<5< shdn= d zkroh ghfdgh ri hfrqrplf jurzwk orvw$ Dqg zkloh d frxqwu| olnh wkh
Xqlwhg Nlqjgrp glg qrw vxhu d odujh gurs lq rxwsxw lq wkh hduo| 4<63v/ zkhq wkh frxqwu|
hqwhuhg wkh ghfdgh lw zdv douhdg| sodjxhg e| yhu| kljk dqg vwxeeruq xqhpsor|phqw
lqkhulwhg iurp wkh 4<53v1
Nh|qhv* dwwdfn rq wkh fodvvlfdo ruwkrgr{|
Djdlqvw wklv edfnjurxqg wkh Eulwlvk hfrqrplvw Mrkq Pd|qdug Nh|qhv dqg vhyhudo rwk0
huv dwwdfnhg wkh fodvvlfdo ylhz wkdw uhvrxufh xwlolwl}dwlrq dw qdwxudo udwhv lv wkh qrupdo
vwdwh ri ddluv1 Lqghhg/ Nh|qhv fkdoohqjhg wkh wlph0krqrxuhg ghqlwlrq ri hfrqrplfv dv
wkh vwxg| ri wkh doorfdwlrq ri vfdufh uhvrxufhv wr vdwlvi| frpshwlqj hqgv14 Nh|qhv* srlqw
zdv wkdw txlwh riwhq uhvrxufhv duh qrw vfdufh/ ehfdxvh wkh| duh xqghuxwlol}hg gxh wr d
odfn ri ghpdqg1 Lq vxfk flufxpvwdqfhv wkh jryhuqphqw kdg wkh delolw| dqg wkh gxw| wr
udlvh wrwdo hpsor|phqw dqg rxwsxw yld d vfdo ru prqhwdu| srolf| zklfk zrxog vwlpxodwh
djjuhjdwh ghpdqg1
Wklv sduwlfxodu irupxodwlrq lv gxh wr Qreho Sul}h odxuhdwh Jdu| Ehfnhu/ exw lw uh hfwv lghdv zklfk jr
edfn wr wkh qlqhwhhqwk fhqwxu| dqg zklfk zhuh hoderudwhg e| Olrqho Ureelqv lq 4<65 lq klv idprxv Dq
Hvvd| rq wkh Qdwxuh dqg Vljqlfdqfh ri Hfrqrplf Vflhqfh/ Orqgrq= Pdfploodq/ 5qg hglwlrq/ 4<681
4
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
6
Wkhvh lghdv zhuh odlg rxw lq 4<69 lq Nh|qhv* idprxv errn rq Wkh Jhqhudo Wkhru|
ri Hpsor|phqw/ Lqwhuhvw dqg Prqh|1 Wkdw errn lv riwhq frqvlghuhg wr pdun wkh eluwk
ri prghuq pdfurhfrqrplfv/ ehfdxvh lw uhyroxwlrql}hg wkh zd| hfrqrplvwv zhuh wklqnlqj
derxw wkh sureohp ri exvlqhvv f|fohv1
Rxu djhqgd
Lq wklv fkdswhu zh zloo uhvwdwh wkh vkruw uxq prgho ri Djjuhjdwh Vxsso| dqg Djjuhjdwh
Ghpdqg +wkh DV0DG prgho, zklfk judgxdoo| hphujhg dv wkh iroorzhuv ri Nh|qhv wulhg wr
foduli| dqg irupdol}h wkh hvvhqfh ri klv phvvdjh1 D zkroh dup| ri vfkroduv kdv ehhq ghedw0
lqj *zkdw Nh|qhv uhdoo| phdqw*1 Qrw doo ri wkhp djuhh wkdw wkh DV0DG prgho suhvhqwhg
ehorz dghtxdwho| uh hfwv wkh ruljlqdolw| ri Nh|qhv* wkrxjkw dqg wkh ixqgdphqwdo fkdudfwhu
ri klv euhdn zlwk wkh fodvvlfdo ruwkrgr{|15 Qhyhuwkhohvv/ vrph yhuvlrq ri wkh DV0DG prgho
kdv ehfrph wkh grplqdqw dqdo|wlfdo wrro e| zklfk prghuq pdfurhfrqrplvwv wu| wr xq0
ghuvwdqg vkruw uxq hfrqrplf xfwxdwlrqv1 Dqg dsduw iurp jlylqj dw ohdvw vrph lpsuhvvlrq
ri Nh|qhv* frqwulexwlrq wr hfrqrplfv/ d uhvwdwhphqw ri wkh wudglwlrqdo Nh|qhvldq DV0DG
prgho zloo kljkoljkw wkh uroh dqg lpsruwdqfh ri wkh ydulrxv fkdudfwhulvwlf dvvxpswlrqv
pdgh lq pdfurhfrqrplfv iru wkh vkruw uxq1
Lq wkh qh{w vhfwlrq zh vwduw e| uhiuhvklqj |rxu phpru| ri wkh DV0DG prgho1 Zh vhw
xs wkh prgho lq d pruh uljrurxv irup wkdq |rx kdyh suredeo| vhhq ehiruh1 E| grlqj vr
zh krsh wr lpsuryh |rxu xqghuvwdqglqj ri wkh prgho dqg wkh gulylqj dvvxpswlrqv ehklqg
lw1 Lq wkh vxevhtxhqw sduw ri wkh fkdswhu zh looxvwudwh krz wkh prgho pd| khos wr h{sodlq
hfrqrplf uhfhvvlrqv/ xvlqj wkh Juhdw Ghsuhvvlrq dv d fdvh vwxg|1 Lq sduwlfxodu/ zh vkrz
Vrphwlphv hyhq Nh|qhv klpvhoi zdv qrw dozd|v vxuh zkdw kh phdqw1 D frqwhpsrudu| phpehu ri wkh
Eulwlvk Fdelqhw/ Huqhvw Ehylq/ rqfh mrnhg wkdw li |rx dvnhg Nh|qhv iru dgylfh rq dq hfrqrplf srolf| lvvxh/
|rx zrxog xvxdoo| jhw dw ohdvw wzr slhfhv ri dgylfh wr fkrrvh iurp$ Nh|qhv* fuhdwlyh plqg zdv dozd|v
ixoo ri lghdv/ dqg vrphwlphv wkhvh lghdv vhhphg wr frpshwh zlwk hdfk rwkhu1 Iru d jxlgh wr wkh glhuhqw
lqwhusuhwdwlrqv ri Nh|qhv/ |rx pd| frqvxow fkdswhuv 5/ 6 dqg : lq Euldq Vqrzgrq/ Krzdug Ydqh dqg Shwhu
Z|qduf}|n= D Prghuq Jxlgh wr Pdfurhfrqrplfv 0 Dq Lqwurgxfwlrq wr Frpshwlqj Vfkrrov ri Wkrxjkw/
Hgzdug Hojdu/ Fkhowhqkdp/ XN> Qruwkdpswrq/ PD/ XVD/ 4<<71
5
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
7
krz d plvjxlghg pdfurhfrqrplf srolf| pd| wxuq d uhfhvvlrq lqwr d ghsuhvvlrq/ dqg krz
d zhoo0lqiruphg srolf| pljkw khos wr doohyldwh uhfhvvlrqv1 Wkh qdo sduw ri wkh fkdswhu
vxpv xs dqg h{sodlqv krz Errn Wkuhh ri wklv wh{w zloo h{whqg dqg lpsuryh wkh Nh|qhvldq
iudphzrun iru dqdo|}lqj wkh hfrqrp| lq wkh vkruw uxq1
4
Ghyhorslqj wkh Nh|qhvldq prgho
Edvlf ihdwxuhv ri wkh Nh|qhvldq DV0DG prgho
Wkh wlph krul}rq ri wkh DV0DG prgho lv d vkruw shulrg/ vd|/ d |hdu1 Dv d uhdvrqdeoh
dssur{lpdwlrq/ wkh prgho wkhuhiruh wdnhv wkh hfrqrp|*v fdslwdo vwrfn dv jlyhq/ ehlqj
suhghwhuplqhg e| wkh fxpxodwhg qhw lqyhvwphqw xqghuwdnhq lq wkh sdvw1
Wkh prgho h{solflwo| frqvlghuv wkuhh pdunhwv= wkh jrrgv pdunhw/ wkh prqh| pdunhw dqg
wkh oderxu pdunhw1 Lpsolflw ehklqg wkh vfhqh lv d erqg pdunhw +d fdslwdo pdunhw,/ vlqfh
djhqwv kdyh wkh srvvlelolw| ri kroglqj lqwhuhvw0ehdulqj dvvhwv dv dq dowhuqdwlyh wr kroglqj
prqh|1
Wkh ehkdylrxu ri hfrqrplf djhqwv ghshqgv lqwhu dold rq h{shfwdwlrqv derxw wkh ixwxuh1
Wkhvh h{shfwdwlrqv zloo qrw qhfhvvdulo| eh fruuhfw1 Pruhryhu/ zkloh wkh jrrgv pdunhw lv
shuihfwo| frpshwlwlyh zlwk ixoo| h{leoh rxwsxw sulfhv/ wkh prqh| zdjh udwh lv suh0vhw dqg
khqfh uljlg gxulqj wkh shulrg frqvlghuhg1 Wkh uhdo zdjh lpsolhg e| wkh {hg qrplqdo zdjh
udwh lv vr kljk wkdw upv gr qrw qg lw surwdeoh wr hpsor| wkh hqwluh oderxu irufh1 Wkxv
wkhuh duh lqyroxqwdulo| xqhpsor|hg zrunhuv zkr fdq eh gudzq lqwr surgxfwlrq li upv
zdqw wr h{sdqg hpsor|phqw lq uhvsrqvh wr dq lqfuhdvh lq rxwsxw ghpdqg1
Dffruglqj wr wkh DV0DG prgho/ uhdo rxwsxw dqg wkh sulfh ohyho duh ghwhuplqhg lq
wkh lqwhuvhfwlrq srlqw ri dq djjuhjdwh vxsso| fxuyh +DV0fxuyh, dqg dq djjuhjdwh ghpdqg
fxuyh +DG0fxuyh,1 Wkh DG0fxuyh lv d qhjdwlyh uhodwlrqvkls ehwzhhq wkh sulfh ohyho dqg wkh
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
8
djjuhjdwh txdqwlw| ri rxwsxw ghpdqghg/ dulvlqj iurp wkh lqwhudfwlrq ri wkh jrrgv pdunhw
dqg wkh prqh| pdunhw1 Wkh djjuhjdwh vxsso| fxuyh lv d srvlwlyh uhodwlrqvkls ehwzhhq wkh
sulfh ohyho dqg wkh txdqwlw| ri rxwsxw vxssolhg e| surw0pd{lpl}lqj upv1
Zh zloo vwduw e| ghulylqj wkh DG0fxuyh1 Wklv zloo jlyh xv dq rssruwxqlw| wr uhylvlw
wkh Nh|qhvldq LV0OP prgho zklfk |rx kdyh hqfrxqwhuhg lq dq hduolhu pdfur frxuvh1 Wkhq
zh zloo ghulyh wkh DV0fxuyh dqg eulqj wkh DV0 dqg DG fxuyhv wrjhwkhu wr vwxg| wkh
pdfurhfrqrplf hhfwv ri ydulrxv vkrfnv/ lqfoxglqj vfdo dqg prqhwdu| srolf| fkdqjhv16
Dv idu dv srvvleoh/ rxu yhuvlrq ri wkh DV0DG prgho zloo exlog rq wkh vdph vshflfdwlrqv
zklfk zhuh xvhg lq rxu yhuvlrq ri wkh fodvvlfdo prgho lq Fkdswhu 5/ lq rughu wr looxvwudwh
wkh vlplodulwlhv dv zhoo dv wkh glhuhqfhv ehwzhhq wkh wzr prghov1
Ghulylqj wkh DG0fxuyh iurp wkh LV0OP prgho
Wkh DG0fxuyh hperglhv wkh frqglwlrqv iru htxloleulxp lq wkh pdunhwv iru jrrgv dqg
prqh|1 Lw lv wkhuhiruh edvhg rq wkh idploldu LV0OP prgho zklfk sruwud|v h{dfwo| wkrvh wzr
pdunhwv1
Frqvlghu wkh jrrgv pdunhw uvw1 Iru wklv pdunhw wr fohdu/ djjuhjdwh jurvv vdylqj +7,
pxvw htxdo djjuhjdwh jurvv lqyhvwphqw +U,/ 7 ' U1 Zh dvvxph wkdw jurvv lqyhvwphqw lv
jlyhq e|
U ' g _ g n Bgc
:f
+4,
Khuh lv d {hg sdudphwhu/ g lv wkh up*v fdslwdo vwrfn dw wkh ehjlqqlqj ri wkh shulrg/
6
Wkh LV0OP lqwhusuhwdwlrq ri Nh|qhv* wkhru| ri djjuhjdwh ghpdqg zdv ghyhorshg e| Mrkq U1 Klfnv/
Pu1 Nh|qhv dqg wkh Fodvvlfv> D Vxjjhvwhg Lqwhusuhwdwlrq/ Hfrqrphwulfd/ yro1 8/ Dsulo 4<6:/ ss1 47:0
48<1 Wkh uvw irupdo dffrxqw ri wkh ixoo Nh|qhvldq DV0DG v|vwhp zdv rhuhg e| Iudqfr Prgljoldql/
Oltxlglw| Suhihuhqfh dqg wkh Wkhru| ri Lqwhuhvw dqg Prqh|/ Hfrqrphwulfd/ yro1 45/ Mdqxdu| 4<77/ ss1
780;;1 Vwuhvvlqj wkh fuxfldo lpsruwdqfh ri h{shfwdwlrqv lq d zruog ri ixqgdphqwdo xqfhuwdlqw|/ wkh Pdvwhu
klpvhoi jdyh d yhuedo dqg vrphzkdw glhuhqw vxppdu| ri klv wkhru| lq Mrkq Pd|qdug Nh|qhv/ Wkh
Jhqhudo Wkhru| ri Hpsor|phqw/ Txduwhuo| Mrxuqdo ri Hfrqrplfv/ Iheuxdu| 4<6:1
Pdq| |hduv odwhu/ erwk Klfnv dqg Prgljoldql uhfhlyhg wkh Qreho Sul}h iru wkhlu pdq| frqwulexwlrqv wr
hfrqrplf vflhqfh1 Nh|qhv glhg lq 4<79/ orqj ehiruh wkh Qreho Sul}h lq Hfrqrplfv zdv lqvwlwxwhg1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
9
dqg g _ lv wkh ghvluhg fdslwdo vwrfn zklfk wkh up eholhyhv zloo pd{lpl}h lwv surw lq wkh
ixwxuh1 Lq wkh fodvvlfdo orqj uxq prgho zh dvvxphg wkdw wkh fdslwdo vwrfn kdg douhdg|
dgmxvwhg wr lwv ghvluhg ohyho vr wkdw g ' g _ 1 Khqfh wkh up rqo| qhhghg wr xqghuwdnh
uhsodfhphqw lqyhvwphqw Bg wr pdlqwdlq lwv ghvluhg fdslwdo vwrfn1 Exw lq wkh vkruw uxq
frqvlghuhg khuh/ wkh h{lvwlqj fdslwdo vwrfn pd| ghyldwh iurp lwv ghvluhg orqj uxq ohyho1 Li lw
grhv/ htxdwlrq +4, vd|v wkdw wkh up*v fxuuhqw lqyhvwphqw zloo dlp wr forvh wkh jds ehwzhhq
wkh h{lvwlqj dqg wkh ghvluhg fdslwdo vwrfn1 Li / wkh hqwluh jds zloo qrw eh ixoo| forvhg
lq wkh fxuuhqw shulrg/ uh hfwlqj wkdw wkh rughulqj/ gholyhu| dqg lqvwdoodwlrq ri qhz fdslwdo
jrrgv lv d wlph0frqvxplqj surfhvv1
Dv lq wkh fodvvlfdo prgho/ wkh up*v ghvluhg fdslwdo vwrfn lv wkh vwrfn zklfk lv h{shfwhg
wr htxdwh wkh pdujlqdo surgxfw ri fdslwdo wr wkh uhdo udwh ri lqwhuhvw1 Dvvxplqj d Free0
Grxjodv surgxfwlrq ixqfwlrq t ' g k uQ!k / zkhuh u lv oderxu lqsxw/ |rx pd| yhuli| wkdw
fdslwdo*v pdujlqdo surgxfw pd| eh zulwwhq dv 8g Yt *Yg ' k Et*g1 Lq olqh zlwk wklv/
wkh up h{shfwv wkdw wkh ixwxuh pdujlqdo surgxfwlylw| ri d fdslwdo vwrfn ri pdjqlwxgh g _
zloo eh htxdo wr k t e *g _ / zkhuh t e lv wkh up*v h{shfwhg ixwxuh yroxph ri rxwsxw dqg
vdohv1 Khqfh wkh up*v rswlpxp frqglwlrq wkdw wkh h{shfwhg ixwxuh pdujlqdo surgxfw ri
g _ pxvw htxdo wkh uhdo udwh ri lqwhuhvw o fdq eh zulwwhq dv k t e *g _ ' o1 Uhduudqjlqj
wklv/ zh jhw dq h{suhvvlrq iru wkh ghvluhg fdslwdo vwrfn/
g_ '
kt e
o
+5,
zklfk pd| eh lqvhuwhg lqwr +4, wr jlyh wkh lqyhvwphqw ixqfwlrq
U '
kt e
gJ n BgJ
o
+6,
Wkxv lqyhvwphqw ydulhv srvlwlyho| zlwk h{shfwhg ixwxuh vdohv/ t e / dqg qhjdwlyho| zlwk
wkh uhdo frvw ri qdqflqj lqyhvwphqw/ o1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
:
Zh duh qrz uhdg| wr ghulyh wkh LV0fxuyh1 Wklv fxuyh vkrzv wkh frpelqdwlrqv ri rxwsxw
dqg lqwhuhvw zklfk zloo hqvxuh htxdolw| ehwzhhq lqyhvwphqw dqg vdylqj1 Zh pdlqwdlq wkh
dvvxpswlrq iurp wkh fodvvlfdo prgho ri Fkdswhu 5 wkdw wrwdo vdylqj lv jlyhq e| rt / zkhuh
|rx uhfdoo wkdw r lv wkh h{rjhqrxv vdylqjv udwh1 Wkh whup Bg lq +6, lv mxvw d frqvwdqw zklfk
grhv qrw sod| dq| lqwhuhvwlqj uroh lq rxu vkruw uxq dqdo|vlv1 Iru vlpsolflw| zh wkhuhiruh
ljqruh lw e| vhwwlqj B ' f1 Rq wkh rwkhu kdqg/ wr eh deoh wr looxvwudwh wkh uroh ri wkh
h{shfwhg udwh ri lq dwlrq Ze / zh zloo xvh wkh ghqlwlrq ri wkh uhdo lqwhuhvw udwh o Z e /
zkhuh lv wkh qrplqdo lqwhuhvw udwh1 Lqvhuwlqj wklv lqwr +6, dorqj zlwk B ' f/ dqg htxdwlqj
vdylqj dqg lqyhvwphqw/ zh jhw
U
}
€
~
}€~
kt e
rt ' g
Ze
7
LV0fxuyh=
'
+,
kt e
n Ze
rt n g
+7,
Htxdwlrq +7, lv wkh htxdwlrq iru wkh LV0fxuyh/ vkrzlqj d qhjdwlyh uhodwlrqvkls ehwzhhq
fxuuhqw uhdo lqfrph t dqg wkh qrplqdo lqwhuhvw udwh 1 Li uhdo lqfrph jrhv xs/ wrwdo vdylqj
lqfuhdvhv1 Iru wklv wr wudqvodwh lqwr kljkhu lqyhvwphqw/ wkh uhdo lqwhuhvw udwh pxvw idoo1 Zlwk
d jlyhq udwh ri h{shfwhg lq dwlrq/ wklv lq wxuq uhtxluhv d idoo lq wkh qrplqdo lqwhuhvw udwh1
Qh{w frqvlghu wkh prqh| pdunhw1 Li  lv wkh qrplqdo prqh| vxsso| dqg lv wkh sulfh
ohyho/ wkh uhdo prqh| vxsso| lv * 1 Lq htxloleulxp wklv pxvw eh htxdo wr uhdo prqh|
ghpdqg Etc zklfk lv dq lqfuhdvlqj ixqfwlrq ri uhdo rxwsxw dqg d ghfuhdvlqj ixqfwlrq ri
wkh qrplqdo lqwhuhvw udwh/ dv zh h{sodlqhg lq Fkdswhu 51 Iru frqfuhwhqhvv/ ohw xv dvvxph
wkdw wkh uhdo prqh| ghpdqg ixqfwlrq kdv wkh irup Etc ' bt !0 / zkhuh b lv d srvlwlyh
sdudphwhu phdvxulqj wkh lqwhqvlw| ri wkh suhihuhqfh iru oltxlglw|1 Dv |rx fdq fkhfn iru
|rxuvhoi/ wklv vshflfdwlrq lpsolhv wkdw wkh lqfrph hodvwlflw| ri prqh| ghpdqg lv xqlw| +d
uhdvrqdeoh dssur{lpdwlrq dffruglqj wr hpslulfdo vwxglhv, dqg wkdw wkh qxphulfdo lqwhuhvw
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
;
hodvwlflw| ri prqh| ghpdqg lv jlyhq e| wkh sdudphwhu 07 1 Htxloleulxp lq wkh prqh| pdunhw
wkhq uhtxluhv

' bt !0
+,
#
OP0fxuyh=
'
bt
*
$ Q0
+8,
Htxdwlrq +8, jlyhv wkh OP0fxuyh vkrzlqj wkh frpelqdwlrqv ri uhdo lqfrph dqg wkh
qrplqdo lqwhuhvw udwh wkdw zloo fohdu wkh prqh| pdunhw1 Zkhq uhdo lqfrph jrhv xs/ wkh
wudqvdfwlrqv ghpdqg iru uhdo prqh| edodqfhv dovr lqfuhdvhv/ doo hovh htxdo1 Zlwk d jlyhq
uhdo prqh| vwrfn * / wkh lqwhuhvw udwh wkhuhiruh kdv wr ulvh wr lqgxfh djhqwv wr hfrqrpl}h
rq wkhlu kroglqjv ri prqh| vr wkdw d kljkhu yroxph ri rxwsxw fdq eh wudqvdfwhg zlwk dq
xqfkdqjhg wrwdo prqh| vwrfn1 Khqfh wkh OP0fxuyh lv xszdug0vorslqj lq Etc 0vsdfh1
Iljxuh 614 uhsurgxfhv wkh idploldu LV0OP gldjudp1 Vlpxowdqhrxv htxloleulxp lq wkh
pdunhwv iru prqh| dqg jrrgv lv dfklhyhg zkhuh wkh LV0fxuyh lqwhuvhfwv zlwk wkh OP0fxuyh1
Lpsruwdqwo|/ wkh OP0fxuyh lv gudzq iru d jlyhq sulfh ohyho1 Li wkh sulfh ohyho ulvhv iurp/ vd|/
J wr Q dqg wkh qrplqdo prqh| vxsso| lv nhsw frqvwdqw/ wkh uhdo prqh| vxsso| * jrhv
grzq1 Iru d jlyhq yroxph ri wudqvdfwlrqv ghwhuplqhg e| t / wklv phdqv wkdw wkh lqwhuhvw
udwh pxvw lqfuhdvh wr eulqj uhdo prqh| ghpdqg grzq lq olqh zlwk wkh orzhu uhdo vxsso|1
Khqfh wkh OP0fxuyh vkliwv xs/ dv looxvwudwhg lq Iljxuh 614 +|rx fdq yhuli| iurp +8, wkdw dq
lqfuhdvh lq pxvw lqghhg fdxvh wr ulvh iru dq| jlyhq ydoxh ri t ,1 Wkxv zh vhh iurp wkh
jxuh wkdw d kljkhu sulfh ohyho zloo ohdg wr d orzhu ghpdqg iru uhdo rxwsxw1
Dv |rx uhfdoo/ wkh lqfrph hodvwlflw| ri prqh| ghpdqg lv ghqhg dv wkh shufhqwdjh lqfuhdvh lq prqh|
Cc \ 1 E| dqdorj|/
ghpdqg jhqhudwhg e| d rqh shufhqw lqfuhdvh lq lqfrph1 Lq irupdo whupv/ wklv lv htxdo wr C\
c
l
wkh lqwhuhvw hodvwlflw| ri prqh| ghpdqg lv jlyhq e| Cc
Cl c 1
7
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
<
i
LM(P1)
LM(P0)
i1
i0
IS
Y1
Y0
Y
Iljxuh 614= Wkh hhfw ri dq lqfuhdvh lq wkh sulfh ohyho lq wkh LV0OP prgho
Li zh xvh rxu LV0OP gldjudp wr wudfh wkh hhfw rq t ri ydu|lqj dqg sorw wkh
fruuhvsrqglqj tc 0sdluv lq d Etc gldjudp/ zh jhw wkh djjuhjdwh ghpdqg fxuyh +DG0
fxuyh, vkrzq lq Iljxuh 6151 Wkh DG0fxuyh vorshv grzq ehfdxvh wkh hurvlrq ri wkh uhdo
prqh| vxsso| fdxvhg e| kljkhu sulfhv gulyhv xs wkh qrplqdo dqg uhdo lqwhuhvw udwh/ wkxv
uhgxflqj lqyhvwphqw ghpdqg1 Wklv phfkdqlvp lv vrphwlphv uhihuuhg wr dv wkh Nh|qhv hhfw
ehfdxvh lw zdv ghvfulehg lq Nh|qhv* Jhqhudo Wkhru|1 Qrwh wkdw wkh Nh|qhv hhfw uholhv rq
wkh frqvwdqf| ri wkh qrplqdo prqh| vxsso|1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
43
P
AD
Y
Iljxuh 615= Wkh djjuhjdwh ghpdqg fxuyh
Wr pdnh h{solflw krz wkh srvlwlrq ri wkh DG0fxuyh ghshqgv rq wkh h{rjhqrxv yduldeohv
dqg sdudphwhuv ri wkh prgho/ zh fdq htxdwh wkh uljkw0kdqg vlghv ri +7, dqg +8, wr jhw
#
b t

DG0fxuyh=
$ Q0
'
kt e
n Ze
rt n g

'
bt
#
+,
kt e
n Ze
rt n g
$0
+9,
Wklv htxdwlrq vkrzv gluhfwo| wkdw d kljkhu ohyho ri pxvw eh dvvrfldwhg zlwk d orzhu
ohyho ri t dorqj wkh DG0fxuyh1 Htxdwlrq +9, zloo eh xvhixo odwhu rq zkhq zh glvfxvv krz
ydulrxv vkrfnv zloo dhfw djjuhjdwh ghpdqg1
Wkh oderxu pdunhw dqg wkh DV0fxuyh
Zh wxuq qrz wr wkh hfrqrp|*v vxsso| vlgh1 Dw wkh ehjlqqlqj ri wkh fxuuhqw shulrg
wkh qrplqdo zdjh udwh ` kdv douhdg| ehhq vhw/ vd|/ lq d surfhvv ri edujdlqlqj ehwzhhq
upv dqg zrunhuv1 Vxssrvh wkdw wkh prqh| zdjh udwh lv vhw zlwk wkh dlp ri dwwdlqlqj d
fhuwdlq uhdo zdjh // edvhg rq wkh sulfh ohyho e zklfk lv h{shfwhg wr suhydlo lq wkh fxuuhqw
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
44
shulrg/ exw zklfk lv qrw nqrzq zlwk fhuwdlqw| zkhq prqh| zdjhv duh vhw1 Wkhq zh kdyh
` ' / e 1 E| ghqlwlrq/ e E n Ze !Q / zkhuh !Q lv wkh dfwxdo sulfh ohyho revhuyhg
lq wkh suhylrxv shulrg zkhq zdjhv zhuh qhjrwldwhg/ dqg Z e lv wkh h{shfwhg udwh ri lq dwlrq
ehwzhhq wkh suhylrxv dqg wkh fxuuhqw shulrg1 Zh pd| wkhuhiruh zulwh
` ' / E n Ze !Q
+:,
Zh dvvxph wkdw/ gxh wr wudgh xqlrq srzhu ru rwkhu lpshuihfwlrqv lq wkh oderxu pdunhw/
wkh dfwxdo fxuuhqw uhdo zdjh `* lpsolhg e| wkh prqh| zdjh vshflhg lq +:, lv vr kljk
wkdw vrph zrunhuv jr xqhpsor|hg1 Wkhvh lgoh oderxu uhvrxufhv hqvxuh wkdw upv zloo eh
deoh wr h{sdqg wrwdo hpsor|phqw dqg rxwsxw li wkh| duh idfhg zlwk dq lqfuhdvh lq ghpdqg1
Htxdwlrq +:, fkdudfwhul}hv wkh vxsso| vlgh ri wkh oderxu pdunhw1 Wkh ghpdqg vlgh lv
ghvfulehg lq ruwkrgr{ fodvvlfdo whupv= surw0pd{lpl}lqj upv zloo kluh oderxu xs wr wkh
srlqw zkhuh lwv pdujlqdo surgxfw htxdov wkh uhdo zdjh/ 8u ' `* 1 Iurp wkh Free0Grxjodv
surgxfwlrq ixqfwlrq t ' g k uQ!k |rx fdq fkhfn wkdw 8u Yt *Yu ' E k Et *u1
Khqfh wkh upv* oderxu ghpdqg lv jlyhq e|
}
8u
€ ~
t
`
E k
'
u
+,
'
`
k
u
t
+;,
Iurp wkh surgxfwlrq ixqfwlrq zh kdyh
k Q!k
t ' g u
+,
t
u'
g k
Q!Q k
+<,
Vxevwlwxwlqj +<, lqwr +;,/ zh hqg xs zlwk wkh htxdwlrq iru wkh djjuhjdwh vxsso| fxuyh/
DV0fxuyh=
Q!kk
Q
`
t
'
k!Q
k
gk
+43,
Dv lqglfdwhg e| +43, dqg looxvwudwhg lq Iljxuh 616/ wkh DV0fxuyh lv xszdug0vorslqj= wr eh
deoh wr vxsso| dgglwlrqdo rxwsxw/ upv pxvw kluh pruh oderxu/ exw ehfdxvh ri glplqlvklqj
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
45
pdujlqdo surgxfwlylw| ri oderxu lw zloo rqo| eh surwdeoh iru upv wr h{sdqg hpsor|phqw
li wkh uhdo zdjh lv gulyhq grzq yld d ulvh lq wkh sulfh ohyho zklfk hurghv wkh uhdo ydoxh ri
wkh suh0vhw qrplqdo zdjh udwh1
P
AS
Y
Iljxuh 616= Wkh djjuhjdwh vxsso| fxuyh
Vxppdul}lqj wkh DV0DG prgho
Wklv frpsohwhv wkh frqvwuxfwlrq ri rxu DV0DG prgho1 Lq h{whqvlyh irup/ wkh prgho lv
jlyhq e| wkh iroorzlqj htxdwlrqv=
Zdjh vhwwlqj=
LV0fxuyh=
` ' / E n Z e !Q
+:,
kt e
n Ze
rt n g
+7,
'
#
OP0fxuyh=
'
bt
*
$ Q0
+8,
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
t ' g k uQ!k
+44,
`
t
E k
'
u
+;,
Surgxfwlrq ixqfwlrq=
Oderxu ghpdqg=
46
Lq wklv v|vwhp ri yh htxdwlrqv wkh yh hqgrjhqrxv yduldeohv duh ` / t / / dqg u/
zkloh wkh h{rjhqrxv yduldeohv dqg sdudphwhuv duh // Ze / !Q / / k/ t e / r/ b/ 0/ / gJ / dqg
1 Dw uvw/ zh pd| xvh htxdwlrq +:, wr ghwhuplqh ` / jlyhq // Z e / dqg !Q 1 Htxdwlrqv
+7,/ +8,/ +44, dqg +;, wkhq vlpxowdqhrxvo| ghwhuplqh t / / dqg u8 1
Lq lwv frpsdfw irup/ wkh DV0DG prgho lv jlyhq e| htxdwlrq +:, soxv wkh wzr htxdwlrqv
iru wkh DG0 dqg DV0fxuyhv zklfk zh kdyh douhdg| ghulyhg=
DG0fxuyh=
DV0fxuyh=

'
bt
#
kt e
n Ze
rt n g
$0
k
Q
`
t Q!k
k
!
Q
'
k
gk
+9,
+43,
Lq wkh frpsdfw prgho yhuvlrq/ wkh zdjh htxdwlrq +:, vwloo ghwhuplqhv wkh prqh| zdjh/
dqg wkhq +9, dqg +43, vlpxowdqhrxvo| ghwhuplqh rxwsxw dqg wkh sulfh ohyho1 Dv looxvwudwhg
lq Iljxuh 617/ t dqg duh irxqg lq wkh srlqw ri lqwhuvhfwlrq ehwzhhq wkh DV0fxuyh dqg
wkh DG0fxuyh1
Qrwh wkdw lq rxu fodvvlfdo prgho lq Fkdswhu 5/ zdjh h{lelolw| hqvxuhv wkdw hpsor|phqw O zdv dozd|v
htxdo wr wkh h{rjhqrxv oderxu irufh1 Khqfh zh wuhdwhg O dv dq h{rjhqrxv yduldeoh lq wkh fodvvlfdo prgho1
Lq wkh Nh|qhvldq prgho/ hpsor|phqw O lv hqgrjhqrxv dqg ohvv wkdq wkh wrwdo oderxu irufh1
8
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
47
P
AS
AD
Y
Iljxuh 617= Ghwhuplqlqj rxwsxw dqg sulfhv lq wkh DV0DG prgho
5
Xqghuvwdqglqj uhfhvvlrqv
Wkh uroh ri djjuhjdwh ghpdqg vkrfnv lq wkh Juhdw Ghsuhvvlrq
Wr looxvwudwh krz wkh DV0DG prgho khosv xv wr wklqn derxw wkh fdxvhv ri hfrqrplf
uhfhvvlrqv/ zh pd| xvh wkh prgho wr kljkoljkw d qxpehu ri k|srwkhvhv zklfk kdyh ehhq
rhuhg wr h{sodlq wkh Juhdw Ghsuhvvlrq lq wkh Xqlwhg Vwdwhv lq wkh 4<63v19
Lq Rfwrehu 4<5< wkh X1V1 vwrfn pdunhw lq Zdoo Vwuhhw h{shulhqfhg zkdw kdv frph wr
eh nqrzq dv wkh Juhdw Fudvk/ zlwk vwrfn sulfhv wxpeolqj gudpdwlfdoo| iurp wkh yhu| kljk
ohyho uhdfkhg gxulqj wkh *urdulqj wzhqwlhv*1 Lq wkh frxuvh ri d ihz zhhnv/ kxjh dprxqwv
ri qdqfldo zhdowk zhuh ghvwur|hg/ dqg pdq| lqyhvwruv dqg wkh edqnv wkdw kdg qdqfhg
wkhp zhqw edqnuxsw1 Hyhq wkrxjk vwrfn rzqhuvkls zdv qrw dv zlghvsuhdg dprqj ruglqdu|
Dphulfdqv dv lw lv wrgd|/ wkhvh hyhqwv pdgh pdq| frqvxphuv qhuyrxv derxw wkh ixwxuh
Zh gr qrw grfxphqw wkh hpslulfdo edvlv iru wkhvh frpshwlqj k|srwkhvhv ru wu| wr hydoxdwh wkhlu uhodwlyh
lpsruwdqfh> zh mxvw eulh | uhsruw wkhp wr looxvwudwh wkh dqdo|wlfdo xvhixoqhvv ri wkh DV0DG iudphzrun1
9
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
48
hfrqrplf survshfwv/ dqg edqnv dovr ehfdph ohvv hdjhu wr ohqg1 Dv d uhvxow/ frqvxphuv fxw
edfn rq wkhlu vshqglqj dqg lqfuhdvhg wkhlu suhfdxwlrqdu| vdylqj iru ixwxuh *udlq| gd|v*1 Lq
whupv ri rxu DV0DG prgho/ wkh vdylqjv udwh r lqfuhdvhg/ fdxvlqj d grzqzdug vkliw lq wkh
LV0 dqg DG0fxuyhv/ dffruglqj wr +7, dqg +9,1
Vhyhudo rwkhu hyhqwv lq wkh 4<5<04<65 shulrg dpsolhg wklv qhjdwlyh ghpdqg vkrfn1 Dv
idoolqj hfrqrplf dfwlylw| uhgxfhg ihghudo wd{ uhyhqxhv yld d vkulqnlqj wd{ edvh/ wkh X1V1
Frqjuhvv uhdfwhg wr wkh ulvlqj exgjhw ghflw e| hqdfwlqj vxevwdqwldo wd{ lqfuhdvhv lq 4<65/
lq ixoo dffrugdqfh zlwk wkh suhydlolqj fodvvlfdo ruwkrgr{| zklfk vdz exgjhw ghflwv dv d
pdmru hylo1 Dv wkh sxeolf vhfwru uhgxfhg lwv glvvdylqj lq wklv zd|/ wkh qdwlrqdo vdylqjv
udwh r lqfuhdvhg hyhq pruh/ frqwulexwlqj ixuwkhu wr wkh grzqzdug vkliw lq wkh LV0 dqg
DG0fxuyhv1 Dqg dowkrxjk lw lv kdug wr yhuli|/ wkhuh lv kdugo| dq| grxew wkdw wkh idoolqj
hfrqrplf dfwlylw| pdgh exvlqhvv upv pruh jorrp| derxw wkh ixwxuh/ fdxvlqj wkhp wr
uhylvh wkhlu h{shfwhg ixwxuh vdohv t e grzqzdugv1 Pruhryhu/ wkh revhuydwlrq ri d gudvwlf
idoo lq wkh sulfh ohyho lq wkh hduo| 4<63v pxvw vxuho| kdyh lqgxfhg lqyhvwruv wr uhgxfh wkhlu
h{shfwdwlrqv ri lq dwlrq/ Ze 1 Dffruglqj wr +7, dqg +9,/ d idoo lq t e dqg Ze zloo sxvk wkh
LV0 dqg DG0fxuyhv grzq +d fkdqjh lq Ze zloo dovr dhfw wkh DV0fxuyh/ exw zh zloo frph
edfn wr wkdw odwhu,1
Wkh idfwruv glvfxvvhg vr idu doo uhodwh wr wkh LV0fxuyh1 Exw frqwudfwlrqdu| irufhv dovr hp0
dqdwhg iurp wkh prqhwdu| vhfwru/ zrunlqj yld wkh OP0fxuyh1 Vhyhudo revhuyhuv +lqfoxglqj
Nh|qhv, kdyh dujxhg wkdw wkh shufhlyhg lqfuhdvh lq xqfhuwdlqw| derxw wkh ixwxuh fdxvhg dq
lqfuhdvh lq wkh ghpdqg iru oltxlg dvvhwv olnh prqh| dw wkh h{shqvh ri wkh ghpdqg iru ulvnlhu
dvvhwv olnh vwrfnv dqg orqj whup erqgv1 Lq wkh qrwdwlrq ri rxu prgho/ wkh oltxlglw| suhihu0
hqfh sdudphwhu b vkrw xs/ vkliwlqj xs wkh OP0fxuyh +8, dqg sxvklqj grzq wkh DG0fxuyh
+9,1 Ixuwkhupruh/ dv wkh fulvlv vsuhdg dfurvv wkh Dwodqwlf/ lqfuhdvlqj wkh qhhg iru oltxlglw|
lq Hxursh/ pdq| Hxurshdq lqyhvwruv vwduwhg wr uhsdwuldwh wkh qdqfldo lqyhvwphqwv wkh|
kdg pdgh lq wkh X1V1/ fdxvlqj dq rxw rz ri fdslwdo iurp Dphulfd1 Ehfdxvh wkh X1V1 kdg
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
49
d {hg h{fkdqjh udwh v|vwhp xqghu wkh wkhq suhydlolqj jrog vwdqgdug/ wkh X1V1 Ihghudo
Uhvhuyh Edqn ihow reoljhg wr ghihqg wkh h{fkdqjh udwh e| wljkwhqlqj prqhwdu| srolf| lq
rughu wr vwhp wkh fdslwdo rxw rz1 Lq rxu prgho/ wklv zrxog eh uh hfwhg lq d idoo lq /
frqwulexwlqj ixuwkhu wr wkh xszdug vkliw lq wkh OP0fxuyh dqg wkh grzqzdug vkliw lq wkh
DG0fxuyh1
Odvw/ exw qrw ohdvw/ wkh idloxuh ri vrph edqnv lq wkh hduo| vwdjh ri wkh uhfhvvlrq fuhdwhg
d uxq rq pdq| rwkhu edqnv/ dv ghsrvlwruv vwdpshghg wr zlwkgudz wkhlu prqh| iurp edqnv
zklfk zhuh eholhyhg wr eh lq gdqjhu ri idlolqj1 Dw wklv fuxfldo prphqw/ pdq| ri wkh edqnv
pljkw kdyh ehhq deoh wr vxuylyh li wkh| frxog kdyh rewdlqhg vx!flhqw vkruw whup fuhglw
iurp wkh Ihghudo Uhvhuyh V|vwhp1 Exw wkh Ihg idlohg wr dghtxdwho| ixoo lwv uroh dv d ohqghu
ri odvw uhvruw/ dqg wkh hqg uhvxow ri wkh sdqlf zdv d zdyh ri edqn idloxuhv zklfk ghvwur|hg
d orw ri ghsrvlwv/ fdxvlqj wkh qrplqdo prqh| vwrfn +zklfk lqfoxghv ghpdqg ghsrvlwv, wr
idoo e| d fdwdvwursklf 58 shufhqw ehwzhhq 4<5< dqg 4<661 Reylrxvo| wklv idoo lq  lpsolhg
d vwurqj xszdug suhvvxuh rq wkh OP0fxuyh1
Wkh idfwruv phqwlrqhg khuh duh doo h{dpsohv ri qhjdwlyh ghpdqg vkrfnv= wkh| doo whqg
wr vkliw wkh DG0fxuyh grzqzdugv/ fdxvlqj d idoo lq rxwsxw dqg sulfhv/ dv looxvwudwhg lq
Iljxuh 618/ dqg dv revhuyhg lq wkh X1V1 lq wkh hduo| 4<63v1 Uhvhdufkhuv duh vwloo ghedwlqj
zklfk ri wkh ydulrxv qhjdwlyh ghpdqg vkrfnv glvfxvvhg deryh zhuh wkh prvw lpsruwdqw
rqhv> suhvxpdeo| wkh| doo sod|hg vrph uroh1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
4:
P
AS
P0
P1
AD0
AD1
Y1
Y0
Y
Iljxuh 618= Wkh vkruw uxq hhfwv ri d qhjdwlyh ghpdqg vkrfn
Zh pd| gudz wzr lpsruwdqw ohvvrqv iurp rxu dqdo|vlv ri vkrfnv wr wkh DG0fxuyh1
Iluvw ri doo/ shvvlplvwlf h{shfwdwlrqv kdyh d qdvw| zd| ri ehlqj vhoi0ixooolqj= li +vrph,
frqvxphuv lqfuhdvh wkhlu vdylqjv udwh dqg wkhlu suhihuhqfh iru oltxlglw| iru ihdu wkdw wkh|
pd| eh derxw wr orvh wkhlu mrev/ ru li exvlqhvv pdqdjhuv uhgxfh wkhlu h{shfwdwlrqv ri ixwxuh
vdohv/ wkh uhvxowlqj grzqzdug vkliw lq wkh DG0fxuyh phdqv wkdw rxwsxw dqg hpsor|phqw
zloo lqghhg idoo/ wkhuhe| xowlpdwho| ydolgdwlqj wkh jorrp| h{shfwdwlrqv zklfk jhqhudwhg
wklv rxwfrph lq wkh uvw sodfh1 X1V1 Suhvlghqw Iudqnolq G1 Urrvhyhow pxvw kdyh kdg dq
lqwxlwlyh xqghuvwdqglqj ri wklv zkhq kh vdlg lq d 4<66 udglr vshhfk rq wkh vwdwh ri wkh
hfrqrp| wkdw wkh rqo| wklqj zh kdyh wr ihdu lv ihdu lwvhoi1
Vhfrqg/ zh vdz wkdw wkh idloxuh wr uhfrjql}h wkh qhhg wr vxssruw djjuhjdwh ghpdqg
ohg wr vhulrxv prqhwdu| dqg vfdo srolf| plvwdnhv lq wkh hduo| 4<63v zklfk frqwulexwhg
vljqlfdqwo| wr wkh vhyhulw| ri wkh Juhdw Ghsuhvvlrq1 Iurp wklv |rx fdq vxuho| vhh wkh
lpsruwdqfh ri xqghuvwdqglqj krz wkh pdfur hfrqrp| zrunv$
Glg djjuhjdwh vxsso| vkrfnv sod| d uroh lq wkh Juhdw GhsuhvvlrqB
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
4;
Dv d ixuwkhu looxvwudwlrq ri wkh zrunlqjv ri wkh DV0DG prgho/ ohw xv glvfxvv wkh uroh ri
wkh djjuhjdwh vxsso| vlgh lq wkh Juhdw Ghsuhvvlrq1 Zh qrwhg deryh wkdw wkh h{shulhqfh ri
idoolqj sulfhv suredeo| ohg wr d idoo lq wkh h{shfwhg lq dwlrq udwh +suhvxpdeo| Ze ehfdph
qhjdwlyh,1 Dffruglqj wr +:, wklv vkrxog fdxvh wkh prqh| zdjh udwh ` wr idoo/ dqg iurp
+43, zh zrxog wkhq h{shfw wr vhh d grzqzdug vkliw lq wkh djjuhjdwh vxsso| fxuyh1
Exw wkhuh zdv dq rvhwwlqj lq xhqfh rq wkh DV0fxuyh lq wkh X1V1 gxulqj wkh 4<63v=
Urrvhyhow*v *Qhz Ghdo* srolflhv lqwurgxfhg xqhpsor|phqw ehqhwv dqg sxeolf zrunv sur0
judpphv iru wkh xqhpsor|hg dqg hqfrxudjhg zrunhuv wr irup wudgh xqlrqv1 Dv d uhvxow/
wkh edujdlqlqj srzhu ri zrunhuv zdv vwuhqjwkhqhg/ dqg wklv suredeo| ohg wr vrph lqfuhdvh
lq wkhlu uhdo zdjh wdujhwv1 Lq whupv ri rxu prgho/ wkh sdudphwhu / zhqw xs/ fdxvlqj dq
xszdug vkliw lq wkh DV0fxuyh/ dv vkrzq e| htxdwlrq +43,1 Iurp Iljxuh 619 zh vhh wkdw vxfk
d qhjdwlyh vxsso| vkrfn zloo jhqhudwh dq lqfuhdvh lq sulfhv dqg d gurs lq uhdo rxwsxw/ doo
hovh htxdo1
AS1
P
AS0
P1
P0
AD
Y1
Y0
Y
Iljxuh 619= Wkh vkruw uxq hhfwv ri d qhjdwlyh vxsso| vkrfn
Wklv dqdo|vlv khosv xv xqghuvwdqg zk| vrph fulwlfv dujxhg dw wkh wlph +dqg zk| vrph
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
4<
vwloo gr, wkdw wkh Qhz Ghdo srolflhv iurp 4<66 zhuh uhvsrqvleoh iru wkh yhu| vorz uhfryhu|
iurp wkh Juhdw Ghsuhvvlrq +uhdo JGS glg qrw uhdfk lwv suhylrxv 4<5< shdn xqwlo wkh odwh
4<63v,1
Lq frqwudvw/ ghihqghuv ri wkh Qhz Ghdo dujxhg wkdw/ dsduw iurp doohyldwlqj wkh kxpdq
plvhu| dqg lqmxvwlfh fdxvhg e| xqhpsor|phqw dqg sryhuw|/ wkhvh srolflhv khoshg wr vwrs
wkh sulfh ohyho iurp idoolqj/ wkhuhe| holplqdwlqj d vhulrxv uhvwudlqw rq ghpdqg1 Zh fdq
dssuhfldwh wklv dujxphqw e| qrwlqj wkdw li wkh hqglqj ri gh dwlrq khoshg wr lqfuhdvh Ze
+zklfk lw suredeo| glg,/ wklv zrxog whqg wr uhgxfh wkh uhdo lqwhuhvw udwh dqg vkliw wkh LV0
dqg DG0fxuyhv xs/ dv lpsolhg e| +7, dqg +9,1 Lqwxlwlyho|/ wkh Urrvhyhow dgplqlvwudwlrq ihow
wkdw idoolqj sulfhv dqg wkh dvvrfldwhg h{shfwdwlrqv ri gh dwlrq zdv d gdqjhurxv frqwudf0
wlrqdu| irufh/ hyhq li lw zhuh dffrpsdqlhg e| idoolqj prqh| zdjhv1 Lq wklv ylhz wkh X1V1
dgplqlvwudwlrq zdv vxssruwhg e| Nh|qhv zkr vdlg diwhu d phhwlqj zlwk wkh X1V1 suhvlghqw
wkdw Suhvlghqw Urrvhyhow lv uljkw1
Wkh fkdudfwhulvwlf dvvxpswlrqv ri vkruw uxq pdfurhfrqrplfv
Dv wklv fdvh vwxg| vkrxog kdyh pdgh fohdu/ wkh Nh|qhvldq DV0DG prgho rhuv d ulfk
rujdql}lqj iudphzrun iru wklqnlqj derxw vkruw uxq xfwxdwlrqv/ fdsdeoh ri dffrpprgdwlqj
pdq| glhuhqw k|srwkhvhv derxw wkh fdxvhv ri uhfhvvlrqv dqg errpv1 Qrwlfh krz wkh prgho
uholhv fuxfldoo| rq doo ri wkh wkuhh ghqlqj fkdudfwhulvwlfv ri pdfurhfrqrplf wkhru| iru wkh
vkruw uxq phqwlrqhg lq Fkdswhu 41 Iluvw ri doo/ xfwxdwlrqv duh lqlwldwhg e| h{rjhqrxv
vkrfnv wr ghpdqg ru vxsso|1 Vhfrqg/ wkhuh lv qrplqdo +zdjh, uljlglw| fdxvlqj wkh vkrfnv
wr eh wudqvplwwhg lqwr fkdqjhv lq wkh ohyho ri hpsor|phqw dqg rxwsxw1 Wklug/ wkhuh duh
h{shfwdwlrqdo huuruvG wkh h{shfwhg ydoxhv ri hfrqrplf yduldeohv qhhg qrw frlqflgh zlwk wkhlu
uhdol}hg ydoxhv1
Ohw xv qrz vxp xs zkdw zh kdyh ohduqhg lq wklv fkdswhu1
Wkh Nh|qhvldq Prgho
6
Jurzwk dqg Exvlqhvv F|fohv
53
Vxpplqj xs dqg orrnlqj dkhdg
Surshuwlhv ri wkh DV0DG prgho= d vxppdu|
4, Wkh Nh|qhvldq DV0DG prgho lv d vkruw uxq prgho zklfk wdnhv wkh fdslwdo vwrfn
dv jlyhq1 Wkh fdslwdo vwrfn lv qrw qhfhvvdulo| ixoo| dgmxvwhg wr lwv ghvluhg orqj uxq ohyho1
5, Wkhuh lv qrplqdo zdjh uljlglw| jhqhudwlqj lqyroxqwdu| xqhpsor|phqw1 6, Hfrqrplf
xfwxdwlrqv duh gulyhq e| h{rjhqrxv vkrfnv wr ghpdqg dqg vxsso|1 7, Wkh ehkdylrxu ri
hfrqrplf djhqwv lv edvhg rq h{shfwdwlrqv zklfk zloo jhqhudoo| wxuq rxw wr eh zurqj zkhq
wkh hfrqrp| lv klw e| d vkrfn1 Dw wkh vdph wlph dq h{rjhqrxv vkliw lq h{shfwdwlrqv whqgv
wr vhoi0ixooolqj1 8, Ehfdxvh ri qrplqdo uljlglw|/ wkhuh lv qr glfkrwrp| ehwzhhq wkh uhdo
dqg wkh prqhwdu| vhfwru1 Khqfh prqh| lv qrq0qhxwudo= dq lqfuhdvh lq wkh qrplqdo prqh|
vxsso| zloo lqfuhdvh uhdo rxwsxw dv zhoo dv wkh sulfh ohyho1 9, H{sdqvlrqdu| vfdo srolf|
fdq eh xvhg wr vwlpxodwh uhdo dfwlylw|/ hyhq li lw wdnhv wkh irup ri d ixoo| wd{0qdqfhg
lqfuhdvh lq sxeolf vshqglqj1 Khqfh wkhuh lv ohvv wkdq ixoo furzglqj rxw ri sulydwh e| sxeolf
vshqglqj1:
Reylrxvo| wkhvh surshuwlhv ri wkh DV0DG prgho vwdqg lq vkdus frqwudvw wr wkh surshu0
wlhv ri wkh fodvvlfdo prgho ghvfulehg lq Fkdswhu 51 Wklv looxvwudwhv wkh lpsruwdqfh ri wkh
glhuhqw dvvxpswlrqv pdgh lq pdfurhfrqrplfv iru wkh vkruw uxq dqg lq pdfur iru wkh orqj
uxq1
Pdfurhfrqrplfv iru wkh vkruw uxq= zkdw lv rxu djhqgdB
Dowkrxjk wkh Nh|qhvldq DV0DG prgho lv khosixo lq pdq| uhvshfwv/ lw dovr kdv vhyhudo
xquhdolvwlf ihdwxuhv1 Wkh djhqgd iru Errn Wkuhh ri wklv wh{w lv wr judgxdoo| h{whqg wkh
DV0DG iudphzrun wr pdnh lw pruh uhdolvwlf dqg xs wr gdwh1 Lq sduwlfxodu/ zh zloo vhhn wr
:
Lq H{huflvh 615 |rx duh dvnhg wr ghprqvwudwh dqg h{sodlq wklv uhvxow zklfk frqwudvwv zlwk wkh fodvvlfdo
prgho zkhuh d wd{0qdqfhg ulvh lq sxeolf vshqglqj zdv irxqg wr uhgxfh uhdo dfwlylw| dqg wr lpso| pruh
wkdq ixoo furzglqj rxw1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
54
lpsuryh wkh Nh|qhvldq prgho lq wkh iroorzlqj glphqvlrqv=
Wkh ghwhuplqdqwv ri djjuhjdwh ghpdqg1 Wkh wkhru| ri frqvxpswlrq dqg lqyhvwphqw
xqghuo|lqj wkh DV0DG prgho deryh lv udwkhu uxglphqwdu| dqg dg krf1 Lq fkdswhuv 4; dqg
4< zh zloo vwxg| pruh fduhixoo| wkh ghwhuplqdqwv ri frqvxpswlrq dqg lqyhvwphqw1 Wklv
zloo lpsuryh rxu xqghuvwdqglqj ri wkh olqnv ehwzhhq wkh vwrfn pdunhw/ wkh erqg pdunhw/
wkh krxvlqj pdunhw/ dqg djjuhjdwh ghpdqg1
Wkh irupdwlrq ri zdjhv dqg sulfhv1 Lq Fkdswhu 53 zh zloo dqdo|}h wkh ghwhuplqdwlrq
ri zdjhv dqg sulfhv lq pruh ghwdlo1 Lq vr grlqj/ zh zloo uhsodfh wkh xquhdolvwlf dvvxpswlrq
ri shuihfw jrrgv pdunhw frpshwlwlrq zlwk wkh pruh uhdolvwlf dvvxpswlrq ri prqrsrolvwlf
frpshwlwlrq1 Zh zloo dovr dqdo|}h wkh olqn ehwzhhq lq dwlrq dqg xqhpsor|phqw dqg vkrz
wkh frqqhfwlrq ehwzhhq rxu vkruw uxq wkhru| ri zdjh dqg sulfh vhwwlqj dqg rxu wkhru| ri
orqj uxq vwuxfwxudo xqhpsor|phqw lq Errn Wzr1 Ilqdoo|/ zh zloo vkrz krz htxloleulxp
lq wkh oderxu pdunhw lv ixoo| frpsdwleoh zlwk shupdqhqw lq dwlrq/ dv revhuyhg lq wkh uhdo
zruog1
Wkh frqgxfw ri prqhwdu| srolf|1 Wkh Nh|qhvldq DV0DG prgho dvvxphv wkdw prqhwdu|
srolf| fkdqjhv wdnh wkh irup ri h{rjhqrxv fkdqjhv lq wkh qrplqdo prqh| vxsso|1 Lq sudfwlfh
prqhwdu| srolf| lv frqgxfwhg e| fkdqjlqj wkh vkruw whup lqwhuhvw udwh frqwuroohg e| wkh
fhqwudo edqn1 H{shulhqfh vkrzv wkdw fhqwudo edqnv whqg wr fkdqjh wkh vkruw whup lqwhuhvw
udwh lq d v|vwhpdwlf zd| lq uhvsrqvh wr fkdqjhv lq wkh vwdwh ri wkh hfrqrp|1 Lq Fkdswhu
54 zh zloo prgli| rxu DV0DG prgho wr dffrxqw iru wklv dqg dqdo|}h lwv lpsolfdwlrqv iru
wkh ghwhuplqdwlrq ri djjuhjdwh ghpdqg1
Wkh dgmxvwphqw iurp vkruw uxq wr orqj uxq htxloleulxp1 Wkh Nh|qhvldq DV0DG prgho
surylghv d rqh0vkrw slfwxuh ri wkh hfrqrp| lq d vlqjoh shulrg/ exw lw grhv qrw looxvwudwh
krz wkh hfrqrp| pryhv iurp wkh Nh|qhvldq vkruw uxq htxloleulxp wr wkh fodvvlfdo orqj uxq
htxloleulxp1 Lq Fkdswhu 54 zh zloo dqdo|}h wklv dgmxvwphqw surfhvv lq d g|qdplf DV0DG
prgho ri rxwsxw dqg lq dwlrq1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
55
Wkh f|folfdo ehkdylrxu ri rxwsxw dqg lq dwlrq1 Wkh Nh|qhvldq prgho lv vwdwlf dqg khqfh
fdqqrw h{sodlq zk| hfrqrplf dfwlylw| whqgv wr pryh lq d f|folfdo +dowkrxjk luuhjxodu,
idvklrq ryhu wlph1 Lq Fkdswhu 55 zh vkrz krz rxu g|qdplf DV0DG prgho lv fdsdeoh ri
uhsurgxflqj wkh edvlf vw|ol}hg idfwv ri wkh exvlqhvv f|foh li rqh dvvxphv wkdw wkh hfrqrp|
lv uhshdwhgo| klw e| vwrfkdvwlf ghpdqg dqg vxsso| vkrfnv1
Wkh irupdwlrq ri h{shfwdwlrqv1 Wkh Nh|qhvldq prgho wdnhv h{shfwdwlrqv ri wkh ixwxuh wr
eh h{rjhqrxv1 Lq uhdolw|/ h{shfwdwlrqv duh olnho| wr lqwhudfw zlwk wkh hqgrjhqrxv yduldeohv
zklfk wkh| khos wr ghwhuplqh1 Lq fkdswhuv 53 dqg 58 zh glvfxvv lq ghwdlo krz rqh pljkw
uhdvrqdeo| hqgrjhql}h wkh irupdwlrq ri h{shfwdwlrqv/ dqg zh vwxg| wkh lpsolfdwlrqv ri
dowhuqdwlyh wkhrulhv ri h{shfwdwlrqv irupdwlrq1
Wkh rshq hfrqrp|1 Wkh Nh|qhvldq DV0DG prgho vhw xs deryh ghvfulehv d forvhg hfrq0
rp|/ exw uhdo0zruog hfrqrplhv duh rshq wr wudgh lq jrrgv dqg fdslwdo1 Fkdswhuv 5: wkurxjk
63 vkrz krz rxu DV0DG iudphzrun fdq eh prglhg wr dffrxqw iru wkh rshqqhvv ri wkh
hfrqrp|/ dqg krz wkh fkrlfh ri h{fkdqjh udwh uhjlphv dhfwv wkh zd| wkh hfrqrp| uhdfwv
wr vkrfnv lq wkh vkruw uxq1
Ilqdoo|/ d pdmru prwlydwlrq iru vwxg|lqj exvlqhvv f|fohv lv wkdw vxfk d vwxg| pd|
lpsuryh rxu xqghuvwdqglqj ri wkh qhhg iru dqg wkh surshu ghvljq ri pdfurhfrqrplf vwd0
elol}dwlrq srolf|1 Lq vhyhudo fkdswhuv lq Errn Wkuhh zh zloo dgguhvv wklv edvlf lvvxh lq
pdfurhfrqrplfv1
Wkh Nh|qhvldq Prgho
7
Jurzwk dqg Exvlqhvv F|fohv
56
H{huflvhv
H{huflvh 41 H{sodlq wkh dvvxpswlrqv xqghuo|lqj wkh Nh|qhvldq DV0DG prgho dqg wkh
glhuhqfhv dv zhoo wkh vlplodulwlhv ehwzhhq wkh surshuwlhv ri wkh Nh|qhvldq dqg wkh fodvvlfdo
prgho1 H{sodlq wkh hfrqrplf phfkdqlvpv xqghuo|lqj wkh qhjdwlyh vorsh ri wkh DG0fxuyh
dqg wkh srvlwlyh vorsh ri wkh DV0fxuyh1
H{huflvh 51 Wklv h{huflvh dvnv |rx wr ghulyh wkh qdwlrqdo vdylqjv udwh dqg wr dqdo|}h
wkh hhfwv ri vfdo srolf| lq wkh DV0DG prgho1 Uhfdoo iurp Fkdswhu 5 wkdw uhdo qdwlrqdo
vdylqj lv ghqhg dv
7 ' t R C
+4,
zkhuh zh kdyh xvhg rxu suhylrxv qrwdwlrq1 Sulydwh frqvxpswlrq lv dvvxphg wr eh sursru0
wlrqdo wr glvsrvdeoh lqfrph E t / zkhuh lv dq h{rjhqrxv lqfrph wd{ udwh1 Li wkh
surshqvlw| wr frqvxph lv SR / zh wkxv kdyh
' SR E tc
f SR c
f 
+5,
Wkh jryhuqphqw frqvxphv d frqvwdqw iudfwlrq S} ri JGS vr wkdw
C ' S} tc
f S} 
+6,
Lq wkh fodvvlfdo orqj uxq htxloleulxp zlwkrxw jurzwk/ lw zdv qhfhvvdu| iru wkh jryhuq0
phqw wr edodqfh lwv exgjhw wr pdnh vxuh wkdw sxeolf ghew vwd|hg frqvwdqw1 Krzhyhu/ lq wkh
vkruw uxq wkh exgjhw qhhg qrw eh lq edodqfh/ vr wkh wzr vfdo srolf| lqvwuxphqwv S} dqg gr qrw kdyh wr wdnh wkh vdph ydoxh1
41 Xvh htxdwlrqv +4, wkurxjk +6, wr ghulyh dq h{suhvvlrq iru wkh qdwlrqdo vdylqjv udwh
r/ ghqhg dv wkh sursruwlrq ri JGS zklfk zloo eh vdyhg1
Wkh Nh|qhvldq Prgho
Jurzwk dqg Exvlqhvv F|fohv
57
51 Xvh |rxu uhvxow lq Txhvwlrq 4 dv zhoo dv wkh DV0DG prgho wr looxvwudwh krz wkh wd{
lqfuhdvhv hqdfwhg e| wkh X1V1 Frqjuhvv lq 4<65 pxvw kdyh dhfwhg wkh X1V1 hfrqrp| +wudfh
wkh hhfwv iurp wkh LV0OP gldjudp wr wkh DV0DG gldjudp,1 H{sodlq |rxu uhvxowv1 Glvfxvv
zkdw pljkw kdyh prwlydwhg X1V1 srolf| pdnhuv lq 4<65 wr lqfuhdvh wd{hv lq wkdw |hduB
61 Xvh |rxu uhvxow lq Txhvwlrq 4 dv zhoo dv wkh DV0DG prgho wr looxvwudwh dqg h{sodlq
wkh hhfwv ri dq lqfuhdvh lq wkh sxeolf frqvxpswlrq vkduh ri JGS1
71 Dvvxph qrz wkdw lv hqgrjhqrxv dqg dozd|v nhsw htxdo wr wkh h{rjhqrxv srolf|
yduldeoh S} wr hqvxuh wkdw wkh sxeolf exgjhw lv frqwlqxdoo| edodqfhg1 Xvh wkh DV0DG prgho
wr looxvwudwh wkh hhfwv ri d ixoo| wd{0qdqfhg lqfuhdvh lq sxeolf frqvxpswlrq +klqw= fkhfn
krz r lv dhfwhg e| dq lqfuhdvh lq S} zkhq ' S} ,1 H{sodlq wkh hfrqrplf phfkdqlvpv
xqghuo|lqj |rxu uhvxow1
H{huflvh 61 Glvfxvv wkh idfwruv zklfk pljkw fdxvh d srvlwlyh vxsso| vkrfn wr wkh
hfrqrp| dqg xvh wkh DV0DG prgho wr looxvwudwh dqg h{sodlq wkh hhfwv ri d vxfk d vkrfn1
H{huflvh 71 Lq uhfhqw |hduv Mdsdq kdv h{shulhqfhg gh dwlrq/ wkdw lv/ d frqwlqxlqj
idoo lq wkh sulfh ohyho1 Suhvxpdeo| Mdsdqhvh frqvxphuv dqg upv duh wkhuhiruh h{shfwlqj
ixuwkhu gh dwlrq grzq wkh urdg1 Xvh wkh DV0DG prgho dv d iudphzrun iru glvfxvvlqj krz
wklv lv olnho| wr dhfw wkh vkruw whup survshfwv iru wkh Mdsdqhvh hfrqrp|1
H{huflvh 81 Frxog dq hfrqrplf ghsuhvvlrq olnh wkh Juhdw Ghsuhvvlrq ri wkh 4<63v
kdsshq djdlqB Glvfxvv1