The Problem of Measurement: An Analysis of Money Demand Price Homogeinity in the Long Run
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(13) Lw vkrxog eh srlqwhg rxw wkdw wkhvh wkhruhwlfdo uhodwlrqv duh qrw jrlqj wr eh ixuwkhu h{soruhg lq zkdw iroorzv1 Wklv lv iru wzr uhdvrqv= Iluvw/ wkh pdlq k|srwkhvlv ri lqwhuhvw lv wkdw ri prqh| ghpdqg sulfh krprjhqhlw|/ wkdw lv @ 4 lq htxdwlrq +5,1 Wkh uhvw ri wkh wkhruhwlfdo uhodwlrqv kdyh ehhq surylghg vr dv wr jlyh wkh prwlydwlrq ri d uhdo0prqh| ghpdqg vwxg|/ dv kdv ehhq xvxdoo| grqh lq wkh olwhudwxuh +vhh Kr pdq dqg Udvfkh +4<<9, dqg O wnhsrko dqg Zrowhuv +4<<<,,1 Wkxv iru wkh sxusrvhv ri wkh h{huflvh frqvlghuhg/ wkh| duh uhgxqgdqw1 Vhfrqgo|1 olplwdwlrqv lq zhoo whvwhg vriwzduh iru wkh L +5, dqdo|vlv/ zrxog qrw doorz ph wr ixuwkhu h{soruh k|srwkhvlv whvwlqj uhodwhg wr wkh deryh wkhruhwlfdo vshfl fdwlrq1 Zlwk wkhvh ghwdlov lq plqg/ L qrz pryh wr wkh ghvfulswlrq ri wkh gdwd dqg wkh hfrqrphwulf phwkrgrorj|1. 6. Gdwd dqg Hfrqrphwulf Phwkrgrorj|. 614. Wkh Gdwd. Wkh gdwd L dp hpsor|lqj duh iurp wkh Ihghudo Uhvhuyh Edqn ri Vdlqw Orxlv IUHG gdwdedvh1 Lq wkh hpslulfdo dssolfdwlrq/ L dp xvlqj P6 dqg wkh prqhwdu| vhuylfhv lqgh{ +Glylvld, iru P6> wkh frqvxphu sulfh lqgh{ +FSL, dqg wkh gh dwru ri shuvrqdo frqvxpswlrq h{shqglwxuhv +SSFH, dv wkh prqh| dqg sulfh yduldeohv uhvshfwlyho|1 Wkhq uhdo shuvrqdo frqvxpswlrq h{shqglwxuh +SFH, zloo eh wkh cvfdoh* yduldeoh/ wkh vkruw0whup lqwhuhvw udwh lv wkh |lhog rq odujh ghqrplqdwlrq wlph ghsrvlwv dqg wkh orqj0whup lqwhuhvw udwh lv wkh |lhog rq d yh |hdu erqg1 Vrph ixuwkhu ghwdlov derxw wkh gdwd duh surylghg lq wdeoh 41 L dp xvlqj prqwko| gdwd dqg wkh vdpsoh uxqv iurp Mdqxdu| 4<:9 wr Ghfhpehu 4<<<1 Doo vhulhv duh vhdvrqdoo| dgmxvwhg h{fhsw iru wkh wzr lqwhuhvw udwhv1 Sorwv ri wkh vhulhv duh uhsruwhg lq jxuhv 4 dqg 51 Wkh uvw urz ri jxuh 4/ uhsruwv wkh orj ri P 6> wkh orj ri wkh prqhwdu| vhuylfhv lqgh{ iru P6/ wkh orj ri FSL dqg wkh orj ri shuvrqdo frqvxpswlrq h{shqglwxuhv gh dwru1 Wkh vhfrqg urz sorwv wkh uvw gl huhqfh ri wkh yduldeohv dqg wkh wklug wkh vhfrqg gl huhqfh1 Iljxuh 5 uhsruwv wkh orj ri shuvrqdo frqvxpswlrq h{shqglwxuh/ wkh vkruw whup lqwhuhvw udwh +OWG\, dqg wkh orqj0whup lqwhuhvw udwh +EV8\,/ erwk lq ohyhov dqg lq uvw gl huhqfhv1 Ixuwkhu ghwdlov derxw wkh frqvwuxfwlrq ri wkh prqhwdu| vhuylfhv lqgh{hv duh surylghg lq Dqghuvrq hw do1 +4<<:d/ 4<<:e,1 ^Lqvhuw Iljxuhv 4 dqg 5` ^Lqvhuw Wdeoh 4` Wkh irfxv ri wkh sdshu lv rq orqj0uxq sulfh krprjhqhlw|1 Mxvholxv +4<<<e, h{sodlqv wkdw wkhuh vhhp wr eh dpsoh hpslulfdo hylghqfh ri erwk wkh phdvxuhv ri sulfhv s| dqg ri wkh qrplqdo prqh| vwrfn p| duh ehvw ghvfulehg dv yduldeohv lqwhjudwhg ri rughu wzr +l1h1 L +5,,1 L surylgh vrph lqlwldo hylghqfh lq idyru ri vxfk dq dvvxpswlrq lq wdeoh 5 e| vwdqgdug xqlw urrw whvwv1 Ixuwkhu hylghqfh zloo eh surylghg ehorz1 Wkh k|srwkhvlv ri orqj0uxq sulfh krprjhqhlw| lv ri lqwhuhvw lq hpslulfdo prgholqj iru wzr uhdvrqv1 Iluvwo|/ ehfdxvh lpsrvlqj orqj0uxq sulfh krprjhqhlw| zlwkrxw surshuo| whvwlqj fdq fuhdwh vhulrxv sureohpv lq wkh frqgxfw ri lqihuhqfh1 Uhfhqw zrun e| Nrqjvwhg +4<<<, dqg Mûujhqvhq +5333, lqglfdwhv wkdw wkh lpsurshu wuhdwphqw ri L +5, yduldeohv fdq ohdg wr vhulrxv sureohpv ri lqihuhqfh1 Iru h{dpsoh/ vxssrvh wkdw wkhuh lv rqo| rqh L +5, frpprq wuhqg wkdw lv ihg lqwr p| dqg s| lq wkh prgho1 Li p| s| lv FL+5/4, lq wkh vhqvh ri Hqjoh dqg Judqjhu +4<;:,/ ;.
(14) wkhq lqihuhqfh lq wkh L +4, prgho xvlqj d phdvxuh ri uhdo edodqfhv dqg wkh jurzwk udwh ri rqh ri wkh qrplqdo yduldeohv lv ydolg +vhh Nrqjvwhg +4<<<,,1 Exw li p| s| lv vwloo dq L +5, yduldeoh/ wkhq mxvw dvvxplqj d sulrul wkdw p| s| lv dq L +4, yduldeoh/ zloo ohdg wr lqydolg lqihuhqfh vlqfh wkh L +4, prgho zrxog qrw eh dssursuldwh iru wkh dqdo|vlv1 Dq| uhodwlrq ehwzhhq p| s| dqg wkh uhvw ri wkh yduldeohv lq wkh v|vwhp zrxog eh vsxulrxv1 Vhfrqgo|/ ehfdxvh wkh sursruwlrqdolw| ehwzhhq prqh| dqg sulfhv +krprjhqhlw| ri ghjuhh }hur ri wkh prqh| ghpdqg, lv rqh ri wkh exloglqj eorfnv ri prqhwdu| hfrqrplfv/ hpslulfdo idloxuh ri wklv sursrvlwlrq zrxog lpso| wkdw zh vkrxog udglfdoo| fkdqjh wkh zd| zh wklqn derxw wkh zruog1 ^Lqvhuw Wdeoh 5`. 615. Hfrqrphwulf Phwkrgrorj|. Lq wkh hfrqrphwulf dqdo|vlv L hpsor| d yhfwru dxwruhjuhvvlrq +YDU, zlwk n odjv/ jlyhq e| & 2 [ 2 {| @ {| {| .
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(28) Uhihuhqfhv ^4` Dqghuvrq/ Ulfkdug J1/ Mrqhv/ Eduu| H1 dqg Qhvplwk/ Wudylv G1 +4<<:d, Dq Lqwurgxfwlrq wr Prqhwdu| Djjuhjdwlrq Wkhru| dqg Vwdwlvwlfdo Lqgh{ Qxpehuv/ Ihghudo Uhvhuyh Edqn ri Vw1 Orxlv Uhylhz/ Mdqxdu|2Iheuxdu|= 64084 ^5` bbbbbb/ bbbbbb dqg bbbbbb +4<<:e, Exloglqj Qhz Prqhwdu| Vhuylfhv Lqgh{hv= Frq0 fhswv/ Gdwd dqg Phwkrgv/ Ihghudo Uhvhuyh Edqn ri Vw1 Orxlv Uhylhz/ Mdqxdu|2Iheuxdu|= 860;5 ^6` Eduqhww/ Zlooldp D1 +4<;3, Hfrqrplf Prqhwdu| Djjuhjdwhv= Dq Dssolfdwlrq ri Lqgh{ Qxpehu dqg Djjuhjdwlrq Wkhru|/ Mrxuqdo ri Hfrqrphwulfv 47/ 4407;1 Uhsulqwhg lq Eduqhww/ Z1 D1 dqg Vhuohwlv D1 +hgv1, +5333, Wkh Wkhru| ri Prqhwdu| Djjuhjdwlrq/ Dpvwhugdp= Hovhylhu Vflhqfh E1Y1 ^7` bbbbbb +4<;:, Wkh Plfurhfrqrplf Wkhru| ri Prqhwdu| Djjuhjdwlrq/ lq Eduqhww/ Z1 D1 dqg Vlqjohwrq/ N1 M1 +hgv1, Qhz Dssurdfkhv wr Prqhwdu| Hfrqrplfv/ s144809;1 Uhsulqwhg lq Eduqhww/ Z1 D1 dqg Vhuohwlv D1 +hgv1, +5333, Wkh Wkhru| ri Prqhwdu| Djjuhjdwlrq/ Dpvwhugdp= Hovhylhu Vflhqfh E1Y1 ^8` bbbbbb +4<<3, Ghyhorsphqwv lq Prqhwdu| Djjuhjdwlrq Wkhru|/ Mrxuqdo ri Srolf| Prgho0 lqj 45+5,= 538058: ^9` bbbbbb +4<<8, H{dfw Djjuhjdwlrq Xqghu Ulvn lq Eduqhww Z1 D1/ Prxolq K1/ Vdoohv P1/ dqg Vfkr hog Q1 M1 +hgv1, +4<<8, Vrfldo Fkrlfh/ Zhoiduh/ dqg Hwklfv/ Fdpeulgjh= Fdpeulgjh Xqlyhuvlw| Suhvv/ s168606:7 ^:` bbbbbb/ R hqedfkhu/ H N1 dqg Vslqgw/ Sdxo D1 +4<;7, Wkh Qhz Glylvld Prqhwdu| Djjuh0 jdwhv/ Mrxuqdo ri Srolwlfdo Hfrqrp| <5= 437<043;8 ^;` Ehorqjld/ Plfkdho +4<<9, Phdvxuhphqw Pdwwhuv= Uhfhqw Uhvxowv iurp Prqhwdu| Hfrqrplfv Uhh{dplqhg/ Mrxuqdo ri Srolwlfdo Hfrqrp|/ 437 +8,= 4398043;6 ^<` bbbbbb dqg Fkdoidqw/ Mdphv D1 +4<;<, Wkh Fkdqjlqj Hpslulfdo Gh qlwlrq ri Prqh|= Vrph Hvwlpdwhv iurp d Prgho ri wkh Ghpdqg ri Prqh| Vxevwlwxwhv/ Mrxuqdo ri Srolwlfdo Hfrqrp|/ <: +5,= 6;:0<: ^43` Fdpsehoo/ Mrkq \1 dqg Shuurq/ Slhuh +4<<4, Slwidoov dqg Rssruwxqlwlhv= Zkdw Pdfurh0 frqrplvwv Vkrxog Nqrz Derxw Xqlw Urrwv/ QEHU Pdfurhfrqrplfv Dqqxdo/ Fdpeulgjh PD= PLW Suhvv/ ss1 4740534 ^44` Fu|vwdo/ Dohf N1 dqg PdfGrqdog/ Urqdog +4<<7, Hpslulfdo Hylghqfh rq wkh Uhfhqw Ehkdylru dqg wkh Xvhixoqhvv ri Vlpsoh0Vxp dqg Zhljkwhg Phdvxuhv ri Prqh| Vwrfn/ Ihghudo Uhvhuyh Edqn ri Vw1 Orxlv Uhylhz/ Pdufk2Dsulo= :6043< ^45` Ghdwrq/ Dqjxv dqg Pxhooedxhu/ Mrkq Q1 +4<;3, Hfrqrplfv dqg Frqvxphu Ehkdylru/ Fdp0 eulgjh= Fdpeulgjh Xqlyhuvlw| Suhvv 4;.
(29) ^46` Glhzhuw/ Z1 H1 +4<:9, H{dfw dqg Vxshuodwlyh Lqgh{ Qxpehuv/ Mrxuqdo ri Hfrqrphwulfv/ 7= 4480478 ^47` bbbbbb +4<:;, Vxshuodwlyh Lqgh{ Qxpehuv dqg Frqvlvwhqf| lq Djjuhjdwlrq/ Hfrqrphwulfd/ 79 +7,= ;;60<33 ^48` bbbbbb +4<<3, Wkh Wkhru| ri wkh Frvw0ri Olylqj Lqgh{ dqg wkh Phdvxuhphqw ri Zhoiduh Fkdqjh lq Glhzhuw/ Z1 H1 +hg1, +4<<3, Sulfh Ohyho Phdvxuhphqw/ Rwwdzd= Fdqdgldq Jryhuq0 phqw Sxeolvklqj Fhqwhu2 Hovhylhu Vflhqfh Sxeolvkhuv E1Y1/ ss1 :<047: ^49` Hqjoh/ Urehuw I1 dqg Judqjhu/ Folyh Z1 M1 +4<;:, Frlqwhjudwlrq dqg Huuru Fruuhfwlrq= Uhs0 uhvhqwdwlrq/ Hvwlpdwlrq dqg Whvwlqj Hfrqrphwulfd/ 88= 58405:9 ^4:` Jrq}dor/ Mhvýv +4<<7, Ilyh Dowhuqdwlyh Phwkrgv ri Hvwlpdwlqj Orqj0Uxq Htxloleulxp Uhod0 wlrqvklsv/ Mrxuqdo ri Hfrqrphwulfv/ 93 = 5360556 ^4;` bbbbbb dqg Slwdudnlv/ Mhdq0\yhv +4<<<, Glphqvlrqdolw| H hfw lq Frlqwhjudwlrq Dqdo|vlv lq Hqjoh/ Urehuw I1 dqg Zklwh/ Kdoehuw +hgv1, +4<<<, Frlqwhjudwlrq/ Fdxvdolw| dqg Iruhfdvwlqj= D Ihvwvfkuliw lq Krqrxu ri Folyh Z1 M1 Judqjhu/ R{irug= R{irug Xqlyhuvlw| Suhvv/ ss1 545055< ^4<` Kdqvhq/ Khquln dqg Mxvholxv/ Ndwdulqd +4<<8, FDWV lq UDWV1 Pdqxdo wr Frlqwhjudwlrq Dqdo0 |vlv ri Wlph Vhulhv/ Hvwlpd= Hydqvwrq/ Loolqrlv ^53` Kr pdq/ Ghqqlv O1 dqg Udvfkh/ Urehuw K1 +4<<9, Djjuhjdwh Prqh| Ghpdqg Ixqfwlrqv= Hp0 slulfdo Dssolfdwlrqv lq Frlqwhjudwhg V|vwhpv/ Ervwrq= Noxzhu Dfdghplf Sxeolvkhuv ^54` Mrkdqvhq/ Vûuhq +4<<5, D Uhsuhvhqwdwlrq ri Yhfwru Dxwruhjuhvvlyh Surfhvvhv Lqwhjudwhg ri Rughu 5/ Hfrqrphwulf Wkhru|/;= 4;;0535 ^55` bbbbbb +4<<8d, Vwdwlvwlfdo Dqdo|vlv ri Frlqwhjudwlrq iru L +5, Yduldeohv/ Hfrqrphwulf Wkh0 ru|/44= 5808< ^56` bbbbbb +4<<8e, Olnholkrrg0Edvhg Lqihuhqfh lq Frlqwhjudwhg Yhfwru Dxwruhjuhvvlyh Prghov/ R{irug= R{irug Xqlyhuvlw| Suhvv ^57` bbbbbb +4<<:, D Olnholkrrg Dqdo|vlv ri wkh L +5, Prgho/ Vfdqglqdyldq Mrxuqdo ri Vwdwlv0 wlfv/ 57= 7660795 ^58` Mûujhqvhq/ Fodud P1G1 +5333, Rq wkh L+5, Frlqwhjudwlrq Prgho/ Sk1G1 Wkhvlv/ Frshqkdjhq= Lqvwlwxwh ri Hfrqrplfv/ Xqlyhuvlw| ri Frshqkdjhq ^59` Mxvholxv/ Ndwdulqd +4<<5, Grphvwlf dqg Iruhljq H hfwv rq Sulfhv lq dq Rshq Hfrqrp|1 Wkh Fdvh ri Ghqpdun Mrxuqdo ri Hfrqrplf Srolf| Prgholqj/ 47 +7,= ^5:` bbbbbb +4<<;, D Vwuxfwxuhg YDU xqghu Fkdqjlqj Prqhwdu| Srolf|/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 49 +7,= 7330744. 4<.
(30) ^5;` bbbbbb +4<<<e, Prghov dqg Uhodwlrqv lq Hfrqrplfv dqg Hfrqrphwulfv/ Mrxuqdo ri Hfr0 qrplf Phwkrgrorj| 9 +5,= 58<05<3 ^5<` bbbbbb +5334, Hxurshdq Lqwhjudwlrq dqg Prqhwdu| Wudqvplvvlrq Phfkdqlvpv= Wkh Fdvh ri Lwdo|/ Mrxuqdo ri Dssolhg Hfrqrphwulfv 49= 674068; ^63` bbbbbb dqg Jhqqdul/ Hohqd +4<<<, G|qdplf Prgholqj dqg Vwuxfwxudo Vkliw= Prqhwdu| Wudqvplvvlrq Phfkdqlvpv lq Lwdo| Ehiruh dqg Diwhu HPV/ Lqvwlwxwh ri Hfrqrplfv/ Xqlyhuvlw| ri Frshqkdjhq/ Zrunlqj Sdshu <<045 ^64` bbbbbb dqg Wrur/ Mxdq +4<<<, Wkh H hfwv ri Mrlqlqj wkh HPV= Prqhwdu| Wudqvplvvlrq Phfkdqlvpv lq Vsdlq/ Lqvwlwxwh ri Hfrqrplfv/ Xqlyhuvlw| ri Frshqkdjhq/ Zrunlqj Sdshu <<055 ^65` Nrqjvwhg/ Kdqv Fkulvwldq +4<<<, Whvwlqj wkh Qrplqdo0wr0Uhdo Wudqvirupdwlrq/ Zrunlqj Sd0 shu/ Lqvwlwxwh ri Hfrqrplfv/ Xqlyhuvlw| ri Frshqkdjhq ^66` Nrqvwdqwlqrx/ Sdqdjlrwlv W1 +5335, Dqrwkhu Orrn dw wkh X1V1 Prqh| Ghpdqg= Vrph Uhvxowv Xvlqj Glylvld Lqgh{hv/ plphr/ Hxurshdq Xqlyhuvlw| Lqvwlwxwh ^67` Sduxror/ Sdror +4<<9, Rq wkh Ghwhuplqdwlrq ri Lqwhjudwlrq Lqglfhv lq L +5, v|vwhpv/ Mrxuqdo ri Hfrqrphwulfv/:5= 6460689 ^68` bbbbbb +5333, Dv|pswrwlf H!flhqf| ri wkh Wzr Vwdjh Hvwlpdwru lq L +5, V|vwhpv/ Hfrqr0 phwulf Wkhru|/ 49 +7,= 8570883 ^69` Udkehn/ Dqghuv/ Nrqjvwhg/ Kdqv Fkulvwldq dqg Mûujhqvhq/ Fodud +4<<<, Wuhqg0Vwdwlrqdulw| lq wkh L +5, Frlqwhjudwlrq Prgho/ Mrxuqdo ri Hfrqrphwulfv/ <3= 5980;< ^6:` Urwhpehuj/ Mxolr M1/ Gulvfroo/ Mrkq F1 dqg Srwhued/ Mdphv P1 +4<<8, Prqh|/ Rxwsxw/ dqg Sulfhv= Hylghqfh iurp d Qhz Prqhwdu| Djjuhjdwh/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlv0 wlfv/ 46 +4,= 9:0;6 ^6;` Vsdqrv/ Dulv +4<<<, Suredelolw| Wkhru| dqg Vwdwlvwlfdo Lqihuhqfh/ Hfrqrphwulf Prgholqj zlwk Revhuydwlrqdo Gdwd Fdpeulgjh= Fdpeulgjh Xqlyhuvlw| Suhvv. 53.
(31) Dsshqgl{ L= Vrph Ghwdlov Lq wklv dsshqgl{ L surylgh vrph ghwdlov uhjduglqj wkh vwdwlvwlfdo dqdo|vlv ri wkh frlqwhjudwhg L +5, prgho1 Wkh prgho/ glvuhjduglqj ghwhuplqlvwlf dqg odjjhg whupv dqg iru vlpsolflw|/ lv jlyhq e| 2 {| @ {|3 {|3 . %|. +D14,. zkhuh wkh wzr uhgxfhg udqn frqglwlrqv @ dqg z z @ krog1 Gh qh dv lq wkh wh{w f @ f +f f,3 iru dq| pdwul{ q u ri ixoo udqn u vxfk wkdw f f @ f f @ Lo > gh qh dovr surmhfwlrq lqwr f @ f +f f,3 f > dqg wkh pdwulfhv wkh vsdfh vsdqqhg e| wkh froxpqv ri f dv SS @ ff @ f > @ > @ z > 2 @ z z @ z 2 z z S 32 . L &' Wkhq wkh ixoo udqn frqglwlrq 2
(32) 2 vkrxog dovr krog1 Qrwh wkdw +> > 2 , duh pxwxdoo| ruwkrjrqdo dqg wkh vdph krogv iru +> > 2 , = Iroorzlqj Mrkdqvhq +4<<:, wkh PD uhsuhvhqwdwlrq ri {| lv jlyhq e| {| @ F2. | S S . ' '. +% . !G , . F. | S . '. +% . !G , . Ff +O, +%| . !G| , . &f . & w . D . Ew. +D15,. 3 2 F2 @ 2 2 2. +D16,. zkhuh. dqg wkh pdwul{ F vdwlv hv wkh iroorzlqj uhodwlrqvklsv 3 F @ 2 2 2 2 @ F2 +F2 L? , F @ . +D17d, +D17e,. Lw iroorzv irup +D15, wkdw {| qhhgv wr eh gl huhqfh wzlfh wr eh pdgh vwdwlrqdu|1 Lw lv dovr fohdu irup +D15, dqg +D16, wkdw 2 {| lv L +5, dqg qr olqhdu frpelqdwlrq ri wklv surfhvv kdv d orzhu rughu ri lqwhjudwlrq1 Ohw @ +> , dqg khqfh z @ 2 = Vlqfh +> , 2 @ 3 zh kdyh wkdw +> 2 , F2 @ 3 dqg 2 {| @ wkdw {| khqfh {| @ +> , {| lv L +4, lq jhqhudo1 Lq idfw Mrkdqvhq +4<<8e, vkrzv 2 Sq 2 dqg khqfh dovr wkh surfhvv {| [| @ {| Sq . Sq . Sq 2 {| @ {| {| S
(33) . Sq 2 {| duh vwdwlrqdu|/ vlqfh {| @ +> , {| lv vwdwlrqdu|1 Khqfh wkh uhsuhvhqwdwlrq +D15, lpsolhv wkdw uhgxfhv wkh rughu ri lqwhjudwlrq iurp 4 wr 51 Wkh surfhvv {| frlqwhjudwhv zlwk wkh L +4, surfhvv {| wr vwdwlrqdulw|/ d skhqrphqrq uhihuuhg wr dv sro|qrpldo frlqwhjudwlrq1 Iroorzlqj Mrkdqvhq +4<<:, wkh iroorzlqj uh0sdudphwul}dwlrq ri wkh prgho fdq eh xvhg 3 {|3 . %| 2 {| @ d {|3 . #{| . z z z. +D18,. 3 3 = Dqrwkhu uh0sdudphwhul}dwlrq ri dqg @ z > zkhuh @ > # @ 3 wkh prgho +D4, jlyh lq Mrkdqvhq +4<<8d, lv 2 {| @ {|3 . 2 {|3 . +! > !2 , {|3 . %|. +D19,. ! @ dqg @ zkhuh ! @ > 2 = Lw fdq gluhfwo| eh vhhq wkdw +D18, dqg +D19, fdq eh 2 frpelqhg wr jlyh {|3 2 . {|3 {| @ z {|3 l k zkhuh @ # . z + z z ,3 @ +! > !2 , dqg zkhuh L kdyh xvhg wkh gh qlwlrq z @ 2 dqg 54.
(34) @ khqfh # 2 @ 2 2 @ 2 = wkh idfw wkdw # @ z + z z ,3 vr wkdw # 2 Wkh k|srwkhvlv ri orqj0uxq sulfh krprjhqhlw| +dvvxplqj wkh suhvhqfh ri rqo| rqh L +5, frpprq wuhqg/ l1h1 +q u v, @ 4, dprxqwv wr whvwlqj wkdw 3 4 4 E 4 F E F F z @ E E 3 F *c
(35) z C 3 D 3 ru. 3 E E E @ K* @ E E E C. 4 4 3 3 3 3. 3 3 4 3 3 3. 3 3 3 4 3 3. 3 3 3 3 4 3. 3 3 3 3 3 4. 4. 3 F FE FE FE FE FC D. * *2 *
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(44) *ee *eD. 4 F F F F D. Wkh dv|pswrwlf glvwulexwlrq ri wkh whvw lv d "2 zlwk irxu ghjuhhv ri iuhhgrp1 Qrwlfh wkdw wkh odvw frh!flhqw lq hdfk yhfwru fruuhvsrqgv wr wkh wuhqg wkdw kdv ehhq uhvwulfwhg wr olh lq wkh frlqwhjudwlqj vsdfh1+Iroorzlqj Mrkdqvhq +4<<8e,/ lqvwhdg ri wkh yhfwru { deryh/ zh zrxog xvh wkh yhfwru {W| @ {| ,1 w. 55.
(45) Dsshqgl{ LL D. Iljxuhv 8.8. 0.4. 0.2. 0.2. 0.0. 0.2 0.0. -0.2. -0.2. -0.4. -0.4. -0.6. -0.6. -0.8. -0.8. 8.4 0.0 -0.2. 8.0. -0.4 7.6. -0.6 -0.8. 7.2. 6.8 1980. 1985. 1990. -1.0. -1.0. -1.0. -1.2. -1.2. -1.2. 1995. 1980. 1985. M3. 1990. 1995. 1980. 1985. LMSIM3. .016. .012. 1990. 1995. 1980. 1985. LCPI. .016. .016. .012. .012. .008. .008. .004. .004. .000. .000. 1990. 1995. LPPCE. .012. .008. .008. .004. .004. .000. .000. -.004 1980. 1985. 1990. -.004. -.004. -.008. -.008. 1995. 1980. 1985. DM3. 1990. 1995. -.004. -.008 1980. 1985. DLMSIM3. .008. 1990. 1995. 1980. 1985. DLCPI. .008. .008. .004. .004. .000. .000. -.004. -.004. 1990. 1995. DLPPCE. .016 .012. .004. .008 .004. .000 .000 -.004. -.004. -.008. -.008. -.012. -.012. -.008 -.008 1980. 1985. 1990 D2LM3. 1995. 1980. 1985. 1990. 1995. -.012 1980. D2LMSIM3. 1985. 1990 D2LCPI. 1995. 1980. 1985. 1990 D2LPPCE. Iljxuh4= Prqh| dqg Sulfh Yduldeohv= Ohyhov/ Ilvuw dqg Vhfrqg Gl huhqfhv. 56. 1995.
(46) 8 .2. .0 2 0. 8 .1. .0 1 5. 8 .0 .0 1 0. 7 .9. .0 0 5. 7 .8 7 .7. .0 0 0. 7 .6. -.0 0 5. 7 .5 -.0 1 0. 7 .4. -.0 1 5. 7 .3 1980. 1985. 1990. 1995. 1980. 1985. LPC E. 1990. 1995. D LPC E. .2 0. .0 4 .0 2. .1 6. .0 0 .1 2 -.0 2 .0 8 -.0 4 .0 4. -.0 6. .0 0. -.0 8 1980. 1985. 1990. 1995. 1980. 1985. LTD Y. 1990. 1995. D LTD Y. .1 8. .0 2. .1 6 .0 1 .1 4 .0 0. .1 2 .1 0. -.0 1. .0 8 -.0 2 .0 6 -.0 3. .0 4 1980. 1985. 1990. 1995. 1980. G S 5Y. 1985. 1990. 1995. D G S 5Y. Iljxuh5= Uhdo Shuvrqdo Frqvxpswlrq H{shqglwxuh dqg Lqwhuhvw Udwhv= Ohyhov dqg Iluvw Gl huhqfhv. 57.
(47) E. Ghvfulswlrq ri wkh Gdwd. Y duldeoh= p | s| p| s| f| l6| lK|. Wdeoh 4= Gdwd Gh qlwlrqv Ghilqlwlrq. Vrxufh. +orj ri, P6 +orj ri, Frqvxphu Sulfh Lqgh{ +FSL,/ edvh |hdu 4<<9 +orj ri, Qrplqdo +Wùuqtylvw0Wkhlo, Prqhwdu| Vhuylfhv Lqgh{ Iru P6@ +orj ri, Shuvrqdo Frqvxpswlrq H{shqglwxuh Gh dwru/ edvh |hdu 4<<9 +orj ri, Uhdo Shuvrqdo Frqvxpswlrq H{shqglwxuhK \lhog rq Wrwdo Odujh Ghqrplqdwlrq Wlph Ghsrvlwv Ilyh0|hdu Wuhdvxu| Frqvwdqw Pdwxulw| Udwh. d= Edvh |hdu 4<<9 e= Eloolrqv ri Grooduv/ Fkdlqhg 4<<9 sulfhv f= Iurp wkh qrplqdo xvhu frvw irupxod | @. IUHG IUHG IUHG FrqvwuxfwhgS IUHG. -| 3o| n-|. rewdlqhg dv u| @ U| | +4 . U| , zkhuh wkh xvhu frvw iru Odujh Ghqrplqdwlrq Wlph Ghsrvlwv | dqg wkh ehqfkpdun dvvhw uhwxuq U| zhuh rewdlqhg iurp wkh gdwd vhw iurp wkh gdwd vhw ri Dqghuvrq hw1 do1 +4<<:,2 Vw1 Orxlv IHG dydlodeoh dw. kwws=22zzz1vwov1iue1ruj2uhvhdufk. Ydu. Frqvwdqw ) Wuhqg. Frqvwdqw. p | s| p| s| f| l6| lK|. 0514:5 0614<7 041<;7 041<68 041;8: 051<53 0519<5. 0319369 +;, 051:46 +<, 03174<3 +;, 061796 +9,-314485 +<, 041<59 +;, 041775 +9,. +;, +<, +;, +9, +<, +;, +9,. Wdeoh 5= Xqlyduldwh Xqlw Urrw Whvwv Ydu1. Frqvwdqw. Qr Ghw1. Ydu1. Frqvwdqw. Qr Ghw1. p | s| p| s| f| l6| lK|. 041;:: 041989 051864 041957 0717;7 081<86 0:1548. 031<549 +:, 04144; +;, 041733 +:, 0415:3 +8, 041837 +<, 081<9; +:,-0:1557 +8,--. 2 p | 2 s| 2 p| 2 s|. 0<1::5 0431;; 0<1663 04516:. 0<1;57 0431<6 0<173< 045175. +:, +;, +:, +8, +;,-+:,-+8,--. +9,-+:,-+9,-+7,--. +9,-+:,-+9,-+7,--. Qxpehu ri odjv lq sduhqwkhvhv1 Wkh phwkrgrorj| ri Fdpsehoo dqg Shuurq +4<<4, kdv ehhq iroorzhg lq vhohfwlqj wkh qxpehu ri odjv iru wkh DGI whvwv1 Vljql fdqfh dw 8( dqg 4( ohyho lqglfdwhg e| - dqg -Fulwlfdo ydoxhv xvhg lq DGI whvw zlwk Frqvwdqw dqg Wuhqg duh= 8(@06175;/ 4(@061<<8 Fulwlfdo ydoxhv xvhg lq DGI whvw zlwk Frqvwdqw duh= 8(@051;:5/ 4(@061789 Fulwlfdo ydoxhv xvhg lq DGI whvw zlwk qr ghwhuplqlvwlf whupv duh= 8(@041<74/ 4(@0518:6. 1. 58.
(48) F. Wdeohv Wdeoh 6= Plvvshfl fdwlrq Vwdwlvwlfv dqg Fkdudfwhulvwlf Urrwv iru wkh YDU+:,= P6 dqg FSL Pxowlyduldwh Vwdwlvwlfv 2 OP " +58, @ 8919;; ^3=333` OP. "2 +4:8, @ 646135 ^3=333` "2 +433, @ 4:9133 ^3=333` OP2 "2 +633, @ 78;17 ^3=333` OPe 2 Qrupdolw| " +43, @ 67<1;<; ^3=333` Xqlyduldwh Whvwv 2 p | 2 s| 2 f| 2 l6| 2 lK| DUFK+:, 317<;5 41<793 419649 61:4:3 91:698 Qrup1 "2 +5, 414853 451:44 481<39 5;<154 4:16;< a 433 3154:<: 3149856 3167<56 31943;: 3166;4; 51967< 315583 418594 514883 41;:78 I- 0OPe 51843< 41:663 41598: 4164:: 414;35 I- 0OP. 41<;67 416<:< 31;79:4 418539 31;;;:6 I- 0OP2 31946 319<5 31;8: 31:<7 31:88 U2 Prgxoxv ri wkh : odujhvw urrwv Xquhvwulfwhg Prgho. 31<<4;. 31<<4;. 31<;3:. 31<;3:. 31;;46. 31;;46. 31;958. u@6 413333 413333 31<;9: 31<8;4 31<3<3 31<3<3 31;948 u@5 413333 413333 413333 31<;:3 31<965 31;965 31;965 u@4 413333 413333 413333 413333 31<;97 31<795 31;96: Wkh I- 0OP whvwv duh glvwulexwhg dv= I- 0OPe I +7> 574, > I- 0OP. I +:> 56;, dqg I- 0OP2 I +45> 566, uhvshfwlyho|/ zkloh OP yhfwru whvwv uhihu wr whvwv iru dxwrfruuhodwlrq1. Wdeoh 7= Wzr Vwhs Surfhgxuh Whvw Vwdwlvwlfv iru Lqwhjudwlrq Lqglfhv qu 8 7 6. u 3. 5VL5 Dojrulwkp. 6691<9. 589136. Vocr 535137. +4<41<24<;15,. +4941<249:1<,. +46:13247514,. 4. 6. 4. 7. quv. 8. 487146. +4471<244<1;,. +<918243418,. +;6152;:16,. 4<81<:. 4751<5. 435197. <8134. <51;8. +46513246:13,. +43:1<244613,. +;:1<2<515,. +:4162:816,. +8<1429613,. 5. 5. 4941<8. To 48319:. 7. 4341<4. 8;1<4. 8713;. 841<6. +;5162;91:,. +971529;15,. +7<1:28615,. +6<1427517,. 631<<. 5819<. 56148. +771827:19,. +641926717,. +551;25816,. ;1:;. 9153. +4:1924<1<,. +431824516,. 4. 3. 6. 59. 5.
(49) Wdeoh 8= Pd{lpxp Olnholkrrg Surfhgxuh Whvw Vwdwlvwlfv iru Lqwhjudwlrq Lqglfhv qu u PO Dojrulwkp Vocr To 8 3 6691<8 589136 535137 4941<8 487146 48319: +4<41<24<;15,. 7. 4. 6. 5. 5. 6. 4. +4941<249:1<,. +46:13247514,. +4471<244<1;,. +<918243418,. +;6152;:16,. 4;6177. 475156. 43517;. <71<7. <51;8. +46513246:13,. +43:1<244613,. +;:1<2<515,. +:4162:816,. +8<1429613,. ;9174. 8;153. 87134. 841<6. +;5162;91:,. +971529;15,. +7<1:28615,. +6<1427517,. 63148. 5818:. 56148. +771827:19,. +641926717,. +551;25816,. 7. quv. 8. 7. 6. 5. ;188. 9153. +4:1924<1<,. +431824516,. 4. 3. QRWH IRU WDEOHV Wkh wdeohv duh uhdg xvlqj wkh whvw surfhgxuh sursrvhg e| Sduxror +4<<9,= Iurp ohiw wr uljkw dqg iurp wrs wr erwwrp1 Wklv zd| zh kdyh wzr lqglfhv fruuhvsrqglqj wr hdfk fhoo= +4, wkh lqgh{ u = zklfk vkrzv wkh qxpehu ri frlqwhjudwlqj uhodwlrqv +hlwkhu gluhfw ru sro|qrpldoo| frlqwhjudwlqj uhodwlrqv,/ +5, wkh lqgh{ v = zklfk vkrzv wkh qxpehu ri uhodwlrqv wkdw fdq eh pdgh vwdwlrqdu| rqo| e| gl huhqflqj rqfh1 Ilqdoo|/ +q u v, vkrzv wkh qxpehu ri olqhdu frpelqdwlrqv wkdw qhhg wr eh gl huhqfhg wzlfh wr ehfrph vwdwlrqdu|1 Vr/ +q u v, @ qxpehu ri L +5, wuhqgv/ v @ qxpehu ri L +4, wuhqgv dqg u @ qxpehu ri frlqwhjudwlqj uhodwlrqv. Wdeoh 9= Wkh Ordglqj Pdwul{ dqg 2 p | 5175 06415: 04<198 6<175 s| 065157 46;139 f| 444167 94194 l6| 086169 08<16; lK| w 3145 0316<. wkh Frlqwhjudwlqj Yhfwruv z 2 2 031448 0318;7 31:<< 03143: 31:5< 3189< 314:9 03167: 3133: 3177: 31398 31477 31;95 31383 31456 31333: 31335. Wdeoh := Whvwv ri Orqj0Uxq Sulfh Krprjhqhlw|= P6 dqg FSL Sdluv ri Lqwhjudwlrq Lqglfhv iru wkh prgho iu @ 4> v @ 6j iu @ 5> v @ 5j iu @ 6> v @ 4j "2 +7, @ 45=;;3 ^3=344<` "2 +7, @ 46=975 ^3=33;` "2 +7, @ 5:=84< ^3=333`. 5:.
(50) Wdeoh ;= Plvvshfl fdwlrq Vwdwlvwlfv dqg Fkdudfwhulvwlf Urrwv iru YDU+:, Pxowlyduldwh Vwdwlvwlfv 2 OP " +58, @ 73187; ^3=33` OP. "2 +4:8, @ 644176 2 " +433, @ 47<14< ^3=334` OP2 "2 +633, @ 78:188 OPe 2 Qrupdolw| " +43, @ 768187 ^3=333` Xqlyduldwh Whvwv 2 p| 2 s| 2 f| 2 l6| 2 lK| DUFK+:, 41::63 71346< 31;;38 61;6;6 81677< Qrup1 "2 +5, 813459 881775 4;16;4 5;<153 4:13;7 a 433 314;65 314687 316797 318;78 31667< 41333 314699 318855 414:6< 41:49; I- 0OPe 31:8<< 319479 319449 4176<; 417489 I- OP. 31;99: 319374 319878 41949; 31<5;7 I- OP2 318;7 31::8 31;8< 31;47 31:95 U2. ^3=333` ^3=333`. Prgxoxv ri wkh : odujhvw urrwv ' Xquhvwulfwhg Prgho. 31<;54. 31<:94. 31<:94. 31<9;7. 31<9;7. 31;9<8. 31;9<8. u@6 413333 413333 31<;98 31<769 31<637 31<637 31;:49 u@5 413333 413333 413333 31<;73 31<8:8 31<8:8 31;:5; u@4 413333 413333 413333 413333 31<<56 31<8<8 31;8;: Wkh I- 0OP whvwv duh glvwulexwhg dv= I- 0OPe I +7> 574, > I- 0OP. I +:> 56;, dqg I- 0OP2 I +45> 566, uhvshfwlyho|/ zkloh OP yhfwru whvwv uhihu wr whvwv iru dxwrfruuhodwlrq1. Wdeoh <= Wzr Vwhs Surfhgxuh Whvw Vwdwlvwlfv iru Lqwhjudwlrq Lqglfhv qu 8 7 6. u 3. 5VL5 Dojrulwkp. 664169. 57;156. Vocr 4;41;<. +4<41<24<;15,. +4941<249:1<,. +46:13247514,. 4. 6. 4. 7. quv. 8. 46819;. +4471<244<1;,. +<918243418,. +;6152;:16,. 544188. 47814;. <61:<. ;617;. :;1;:. +46513246:13,. +43:1<244613,. +;:1<2<515,. +:4162:816,. +8<1429613,. 5. 5. 4751:8. To 466137. 7. 43;157. 8:13:. 7<1;3. 78175. +;5162;91:,. +971529;15,. +7<1:28615,. +6<1427517,. 6316:. 5518<. 491<9. +771827:19,. +641926717,. +551;25816,. 43187. 7187. +4:1924<1<,. +431824516,. 4. 3. 6. 5;. 5.
(51) Wdeoh 43= Pd{lpxp Olnholkrrg Surfhgxuh Whvw Vwdwlvwlfv iru Lqwhjudwlrq Lqglfhv qu u PO Dojrulwkp Vocr To 8 3 664169 57;155 4;41;< 4751:8 46819; 466137 +4<41<24<;15,. 7. 4. 6. 5. 5. 6. 4. +4941<249:1<,. +46:13247514,. +4471<244<1;,. +<918243418,. +;6152;:16,. 49<1<7. 44915<. <4179. ;6148. :;1;:. +46513246:13,. +43:1<244613,. +;:1<2<515,. +:4162:816,. +8<1429613,. :719;. 8816;. 7;1<3. 78175. +;5162;91:,. +971529;15,. +7<1:28615,. +6<1427517,. 5;189. 541<<. 491<9. +771827:19,. +641926717,. +551;25816,. 7. quv. 8. 7. 6. 5. <1;6. 7187. +4:1924<1<,. +431824516,. 4. 3. Wdeoh 44= Wkh Ordglqj Pdwul{ dqg wkh Frlqwhjudwlqj Yhfwruv=Glylvld Prqh| Ghpdqg z 2 2 2 p| 44173 5:19< 31376 031;88 317:: 04;148 0;14: 031674 31688 31;36 s| 074168 04391:6 313<9 031633 031373 f| 6918: 08915< 3158: 31496 315;6 l6| 046184 56138 31;<; 31494 31547 lK| w 3144 3154 313339 313369. Wdeoh 45= Whvwv ri Orqj0Uxq Sulfh Krprjhqhlw| Sdluv ri Lqwhjudwlrq Lqglfhv iru wkh prgho iu @ 4> v @ 6j iu @ 5> v @ 5j iu @ 6> v @ 4j "2 +7, @ 6=4<< ^3=858` "2 +7, @ 8=;<5 ^3=53:` "2 +7, @ 4:=46< ^3=335`. 5<.
(52)
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