D Elyduldwh Lqwhjhu Ydoxhg Doorfdwlrq Prgho iru
Jxhvw Qljkwv lq Krwhov dqg Frwwdjhv
Nxuw Euçqqçv dqg Mrqdv Qrugvwuùp
Ghsduwphqw ri Hfrqrplfv/ Xphè Xqlyhuvlw|
VH0<34;: Xphè/ Vzhghq
Xphè Hfrqrplf Vwxglhv 87:/ 5333
Devwudfw
Wkh qxpehu ri Qruzhjldq jxhvw qljkwv lq Vzhglvk krwhov dqg frwwdjhv lv vwxg0
lhg1 Djjuhjdwlrq ri dq lqwhjhu0ydoxhg DU+4, prgho dqg d wzr0vwdjh ghpdqg
prgho xqghuolhv wkh hpslulfdo uhvxowv1 Wkh sdudphwhuv lq wkh prgho duh fkhfn0
rxw suredelolw|/ phdq fkhfn0lq dqg wkh suredelolw| ri vhohfwlqj wkh krwho do0
whuqdwlyh1 Wkhvh sdudphwhuv duh vshflhg wr ghshqg rq hfrqrplf yduldeohv
lpsolhg e| ghpdqg dqdo|vlv1 Yld wkh suredelolw| ri vhohfwlqj d krwho/ wkh
hpslulfdo uhvxowv lqglfdwh d vxevwlwxwlrq wrzdugv ohvv h{shqvlyh dffrpprgd0
wlrq dv wkh Vzhglvk sulfh ohyho lqfuhdvhv1 Iru wkh fkhfn0rxw suredelolw|/ dq
lqfuhdvh lq wkh frwwdjh sulfh uhgxfhv wkh suredelolw| iru vwd|lqj dqrwkhu qljkw
lq frwwdjh/ zkhuhdv dq lqfuhdvh lq wkh krwho sulfh lqglfdwhv d ghfuhdvh lq wkh
fkhfn0rxw suredelolw| iru krwho1
Nh|zrugv= Lqwhjhu0ydoxhg wlph vhulhv/ ghpdqg dqdo|vlv/ wrxulvp/ dffrprgd0
wlrq/ krwho/ frwwdjh1
MHO Fodvvlfdwlrq= F65/ F68/ F84/ G451
Wkh
qdqfldo vxssruw iurp wkh Zdoodqghu Irxqgdwlrq lv judwhixoo| dfnqrzohgjhg1
41
Lqwurgxfwlrq
Wklv sdshu prghov wkh qxpehu ri Qruzhjldq jxhvw qljkwv lq Vzhglvk krwhov dqg
frwwdjhv1 Zh dgrsw d prghoolqj vwudwhj| wkdw exlogv erwk rq krz wlph vhulhv dulvh
dqg rq ghpdqg dqdo|wlfdo uhvxowv iru wzr0vwdjh ghflvlrq pdnlqj1 E| ghsduwlqj iurp
d vlpsoh wlph vhulhv prgho iru gdlo| jxhvw qljkwv/ l1h1 iurp wkh plfur ohyho/ dqg
djjuhjdwlqj/ whpsrudoo| dv zhoo dv furvv0vhfwlrqdoo|/ zh rewdlq d vlpsoh dqg rshud0
wlrqdo wlph vhulhv prgho iru djjuhjdwh jxhvw qljkwv1 Wklv prghoolqj dssurdfk uhqghuv
sdudphwhuv wkdw duh hdv| wr lqwhusuhw1 Wkh sdudphwhuv duh phdq fkhfn0lq/ wkh gdlo|
fkhfn0rxw suredelolw|/ dqg wkh gdlo| suredelolw| ri vhohfwlqj krwho udwkhu wkdq frw0
wdjh1 Wkhvh sdudphwhuv duh qh{w vhw wr ghshqg rq hfrqrplf yduldeohv lpsolhg e|
ghpdqg dqdo|vlv1 Lq wklv dqdo|vlv/ srwhqwldo jxhvwv duh lq d uvw vwdjh dvvxphg wr
fkrrvh zklfk frxqwulhv wr ylvlw/ dqg wkhq frqglwlrqdoo| rq wkh uvw vwdjh doorfdwlrq
sureohp wkh| ghflgh rq wkh irup ri dffrpprgdwlrq1
Wkh dssurdfk uhvxowv lq d ghpdqg prgho wkdw lv qrqolqhdu lq hfrqrplf yduldeohv
dqg dovr g|qdplf1 Wklv eohqgv suhylrxv hfrqrplf dqg wlph vhulhv dssurdfkhv lq d
qhz zd|1 Suhylrxv vwxglhv rq lqwhuqdwlrqdo wrxulvp kdyh pdlqo| wulhg wr h{sodlq
wkh qxpehu ri duulylqj jxhvwv wr d frxqwu| ru wkh h{shqglwxuhv vshqw e| wkh wrxulvwv
+Furxfk/ 4<<7,1 E| xvlqj dffrpprgdwlrq vwdwlvwlfv zh fdq h{whqg wkh dqdo|vlv
dqg dovr dffrxqw iru wkh ohqjwk ri wkh vwd|1 Wkh dgrswhg wzr0vwdjh ghflvlrq sur0
fhvv dovr pdnhv lw srvvleoh wr lqfrusrudwh gdwd rq jxhvw qljkw qxpehuv dqg wrxulvp
h{shqglwxuhv zlwklq d frxqwu| lq wkh vdph doorfdwlrq prgho1 Dowkrxjk wkh vdph
h{sodqdwru| yduldeohv wkdw zh xvh kdyh dsshduhg lq vrph rwkhu vwxglhv/ wkh iru0
pdo ghulydwlrq ri wkh ghpdqg ixqfwlrqv kdyh vhogrp ehhq vkrzq1 Rwkhu vwxglhv
ri lqwhuqdwlrqdo wrxulvp edvhg rq hfrqrplf ghpdqg prghov duh/ h1j1/ Dgdprzlf}
+4<<7,/ Phohqehuj dqg ydq Vrhvw +4<<9,/ dqg Qrugvwuùp +4<<<,1 Vwxglhv hpsor|lqj
sxuh wlph vhulhv dqdo|wlfdo prghov duh/ h1j1/ Jdufld0Ihuuhu dqg Txhudow +4<<:, dqg
Jxvwdyvvrq dqg Qrugvwuùp +4<<<,/ zkloh vwxglhv xvlqj pl{hg hfrqrplf wlph vhulhv
dssurdfkhv glhuhqw iurp rxuv lqfoxgh Wxuqhu/ Nxohqgudq dqg Ihuqdqgr +4<<:,/ dqg
Zlww dqg Zlww +4<<8,1
Wkh xqghuo|lqj lqwhjhu0ydoxhg prgho iru wkh qxpehu ri jxhvw qljkwv lq d uhjlrq*v
4
krwhov ru frwwdjhv lv dq lqwhjhu0ydoxhg dxwruhjuhvvlyh +LQDU, prgho ri rughu rqh1
Wklv frxqw gdwd prgho ghfrpsrvhv wrgd|*v qxpehu ri jxhvw qljkwv lq krwhov dqg
frwwdjhv lqwr wkrvh wkdw vwd| ryhu iurp |hvwhugd| dqg wkrvh jxhvwv wkdw duulyh wr
wkh uhjlrq lq wkh lqwhuyhqlqj wlph1 Wkh LQDU prgho zdv lqwurgxfhg e| PfNhq}lh
+4<;8, dqg kdv odwhu ehhq hoderudwhg xsrq e| Do0Rvk dqg Do}dlg +4<;:,/ Euçqqçv
+4<<8, dqg rwkhuv1 Lq d suhylrxv sdshu/ Euçqqçv/ Khoovwuùp dqg Qrugvwuùp +4<<</
khuhdiwhu EKQ, frqvlghuhg wkh qdwlrqdo dqg prqwko| qxpehu ri jxhvw qljkwv lq
krwhov dqg ghprqvwudwhg wkdw wkh djjuhjdwlrq dssurdfk |lhogv dq lqwhjhu0ydoxhg
prylqj dyhudjh +LQPD, prgho ri rughu rqh1 EKQ dovr frqvlghuhg hvwlpdwlrq dqg
iruhfdvwlqj lvvxhv dqg jdyh d vxevwdqwldo dssolfdwlrq wr d vhulhv ri Qruzhjldq jxhvw
qljkwv lq Vzhglvk krwhov1 Wkh suhvhqw sdshu h{whqgv rq wkh zrun ri EKQ lq wkh
vhqvh ri vwxg|lqj wzr vhulhv mrlqwo| dv zhoo dv e| h{solflwo| irfxvlqj rq wkh doorfdwlrq
ehwzhhq wkh wzr w|shv ri dffrpprgdwlrq1
Lq Vhfwlrq 5 wkh edvlf vwrfkdvwlf dqg plfur ohyho prgho lv suhvhqwhg dorqj zlwk
wkh prgho iru d prqwko| wlph vhulhv dw wkh qdwlrqdo ohyho1 Dovr glvfxvvhg lv krz rqh
pd| lqfoxgh h{sodqdwru| yduldeohv lqwr wkh vwrfkdvwlf prgho1 Vhfwlrq 6 glvfxvvhv wkh
ghpdqg dqdo|wlf iudphzrun/ dqg Vhfwlrq 7 suhvhqwv wkh gdwd1 Hvwlpdwlrq lvvxhv duh
frqvlghuhg lq Vhfwlrq 81 Wkh hpslulfdo uhvxowv duh jlyhq lq Vhfwlrq 91 D frqfoxglqj
glvfxvvlrq qlvkhv wkh sdshu1
51
Prgho dqg Djjuhjdwlrq
Zh frqvlghu d prgho iru wkh qxpehu ri krwho E+M dqg frwwdjh E+ ylvlwruv iru d
uhjlrq dw d fhuwdlq gd| |=
+M| ' kM +M|
+| ' k +|
n q M "|
+4d,
n q "| +4e,
3
3
Wkh qxpehuv ri ylvlwruv lq hdfk fdwhjru| frqvlvw ri wkrvh vwd|lqj iurp wkh suhylrxv
gd| Ek +| c ' Mc / dqg wkrvh kdylqj d fkhfn0lq Eq "| / lq wkh shulrg E|c |1
3
Khuh/ wkh lqwhjhu0ydoxhg udqgrp yduldeoh "| lv wkh qxpehu ri duulylqj jxhvwv wr wkh
uhjlrq/ h1j1/ iurp vrph vshflf frxqwu|1 Wkh phdq qxpehu ri duulylqj jxhvwv dw
wlph | lv .E"| ' b 1 Wkh jxhvwv duh doorfdwhg wr hlwkhu ri wkh wzr w|shv ri gzhoolqj
5
e| wkh wklqqlqj rshudwlrq q M "| '
S"|
' 1 Wkh lqghshqghqw udqgrp yduldeohv wdnh wkh ydoxh ' li jxhvw / ri wrwdoo| "| qhz jxhvwv/ ghflghv wr vwd| lq d krwho
dqg ' f rwkhuzlvh1 Wkh ' f hyhqw wkhq fruuhvsrqgv wr d fkhfn0lq wr d frwwdjh1
Wkh suredelolw| iru ' lv q M / vr wkdw hE ' f ' q M ' q 1 Lq Dsshqgl{
D4 zh jlyh vrph ghwdlohg surshuwlhv ri wkh prgho1 Euçqqçv dqg Khoovwuùp +5333,
rewdlq uhodwhg surshuwlhv ri wkh prgho xqghu zhdnhu dvvxpswlrqv1
Judqjhu dqg Pruulv +4<:9, dqg rwkhuv kdyh hvwdeolvkhg wkdw furvv0vhfwlrqdo dj0
juhjdwlrq ryhu DU+4, prgho ohdgv wr dq dqdorjrxv prgho1 EKQ ghprqvwudwhg
d uhodwhg uhvxow iru wkh LQDU+4, prghov lq +4d,0+4e,1 Lw iroorzv gluhfwo| wkdw wkh
furvv0vhfwlrqdoo| djjuhjdwhg gd|0wr0gd| prgho lv elyduldwh LQDU+4,1 Lq wkh djjuh0
jdwh prgho 0| '
S
' "|/ zlwk phdq b ' b / uhsuhvhqwv wkh qxpehu ri duulylqj
jxhvwv dw wkh qdwlrqdo ohyho1 Wkh furvv0vhfwlrq/ djjuhjdwlrq vwhs frxog kdyh ehhq
dyrlghg e| gluhfwo| irfxvlqj dw qdwlrqdo gd|0wr0gd| jxhvw qljkwv1 Euhzhu +4<:6, dqg
rwkhuv/ dqg EKQ iru wkh LQDU prgho/ kdyh ghprqvwudwhg wkdw whpsrudo djjuhjd0
wlrq ri DU+4, dqg LQDU+4, prghov |lhog DUPD+4/4, dqg LQDUPD+4/4, prghov/
uhvshfwlyho|1 Lq dgglwlrq/ EKQ jdyh dujxphqwv vxjjhvwlqj wkdw wkh LQDUPD+4/4,
sudfwlfdoo| uhgxfhv wr dq LQPD+4, prgho dw wkh qhz wlph vfdoh li whpsrudo djjuh0
jdwlrq lv ryhu dv orqj d krul}rq dv d prqwk1 Dsso|lqj dq LQDU+4, prgho gluhfwo|
wr prqwko| jxhvw qljkw qxpehuv lv olnho| wr eh ri olwwoh lqwhuhvw dv prqwk0wr0prqwk
fkhfn0rxw suredelolwlhv E k fdq eh h{shfwhg wr eh htxdo wr rqh1 Lq wklv lqvwdqfh
wkh gd|0wr0gd| pryhphqwv duh wkrvh ri pdmru lqwhuhvw1
Whpsrudo djjuhjdwlrq +fi1 wkh Dsshqgl{, jlyhv xv d elyduldwh LQPD+4, prgho
dw wkh qdwlrqdo dqg prqwko| +| lv qrz dqg khuhdiwhu uhihuulqj wr prqwk, ohyho iru wkh
djjuhjdwh krwho E5M dqg frwwdjh E5 vhulhv=
+5d,
5| ' q 1 | n w q 1 | +5e,
5M| ' q M 1 | n wM q M 1 |
3
3
Khuh/ w k *E k c ' Mc / dqg .E1 | ' b ' b fruuhvsrqgv wr wkh qdwlrqdo
dqg prqwko| phdq qxpehu ri duulydov wr krwhov dqg frwwdjhv + lv wkh qxpehu
ri uhjlrqv/ lv wkh qxpehu ri gd|v lq wkh prqwk/ dqg b lv wkh uhjlrqdo phdq
duulydo,1 Wkh prgho lq +5d,0+5e, lv d vlpsolhg uhsuhvhqwdwlrq wkdw kdv wkh vdph
6
uvw prphqw surshuwlhv dv d wuxh whpsrudo djjuhjdwlrq prgho1 Wkh dgydqwdjh zlwk
+5d,0+5e, lv wkdw lw lv uhdglo| lqwhusuhwdeoh lq whupv ri wkh lqwhuhvwlqj sdudphwhuv k
+wkurxjk w ,/ q / dqg b1 Iru hvwlpdwlrq sxusrvhv zh qhhg wkh frqglwlrqdo h{shfwdwlrq
.E5| m3 c c 3| ' b q dE n w w o n w q 0| c c ' Mc / dqg zlwk 3| '
3
3
E5M| c 5| 1 Qhlwkhu vhfrqg rughu prphqwv qru d vshflf glvwulexwlrq zloo eh xvhg iru
hvwlpdwlrq1
Wkh LQPD+4, prgho lv rewdlqhg xqghu txlwh vwulqjhqw dvvxpswlrqv/ h1j1/ ri frq0
vwdqw sdudphwhuv1 Zkloh wklv wlph lqyduldqfh pd| eh d uhdvrqdeoh dssur{lpdwlrq
zlwklq wkh prqwk lw prvw olnho| lv wrr vlpsolhg ryhu wkh dqqxdo krul}rq1 Qrwdeo|/
wkhuh duh vwurqj vhdvrqdo sdwwhuqv lq jxhvw qljkw vhulhv/ vr wkdw dffrxqwlqj iru wklv
ihdwxuh e| glhuhqflqj dsshduv d uhdvrqdeoh dssurdfk1 Krzhyhu/ rxu pdlq lqwhuhvw
lv lq krz wkh phdq fkhfn0lq Eb/ wkh fkhfn0rxw Ek ru w dqg krwho Eq M suredelolwlhv
frxog eh uhodwhg wr hfrqrplf yduldeohv1 Vwxglhv edvhg rq ghpdqg dqdo|vlv vwurqjo|
vxjjhvw wkdw wkh lqfrph ohyho ri wkh frxqwu| ri ruljlq/ sulfhv dqg h{fkdqjh udwhv
duh lpsruwdqw ghwhuplqdqwv wr wkh phdq fkhfn0lq +h1j1/ Qrugvwuùp/ 4<<<,1 Qrwh
wkdw wkh sdudphwhuv ri wkh prgho duh wkhq wlph lqgh{hg lq fruuhvsrqghqfh zlwk wkh
dssursuldwh odj lq wkh i1 | j vhtxhqfh1 Lq dgglwlrq/ dv sdudphwhuv fkdudfwhul}h wkh
rffxuuhqfhv lq wlph lqwhuydov hqglqj dw wkh lqgh{hg wlph/ yduldeohv vkrxog eh odjjhg
wr phdvxuh ohyhov dw wkh lqlwldo wlph srlqw1 Wklv kdv wkh dgghg dgydqwdjh ri dyrlglqj
srwhqwldo hqgrjhqhlw| sureohpv1
Iru vx!flhqwo| odujh 5M| dqg 5| ydoxhv wkh b| zloo eh idu dzd| iurp }hur vr
| : f1 Zkhq wklv lv wkh fdvh zh pd| suhihu wr xvh d olqhdu
wkdw hpslulfdoo| b
irup b| ' | lqvwhdg ri dq h{srqhqwldo rqh1 Wkh olqhdu irup fdq eh h{shfwhg wr
vlpsoli| hvwlpdwlrq1 Wkrxjk | lv lqgh{hg e| | lw vkrxog frqwdlq odjjhg ydoxhv rq
h{sodqdwru| yduldeohv dv b| +dqg wkh rwkhu sdudphwhuv, fkdudfwhul}h hyhqwv lq wkh
wlph lqwhuydo E| c |1 Vlqfh k| ' w| *E n w| 5 dfc oc w| fc ' Mc c dqg dq
h{srqhqwldo uhsuhvhqwdwlrq w| ' i TE| lv wkhq dssursuldwh1 Qrwh wkdw wklv uhvxowv
lq d orjlvwlf glvwulexwlrq ixqfwlrq k| ' *d n i TE| o +fi1 Euçqqçv/ 4<<8,1 Iru
q M| zh pd| xvh d uhodwhg orjlvwlf glvwulexwlrq ixqfwlrq/ l1h1 q M| ' *d n i TE | o
iru hdfk prqwk |1 Zklfk hfrqrplf yduldeohv wr lqfoxgh lq wkh | c | dqg | yhfwruv lv
glvfxvvhg lq wkh qh{w vhfwlrq1 Hdfk yhfwru frxog dovr lqfoxgh qrq0hfrqrplf yduldeohv/
7
vxfk dv prqwko| gxpp| yduldeohv1 Wkh sdudphwhu yhfwru lv xqnqrzq dv lv dqg
' E M c 1
61
Ghpdqg Dqdo|vlv
Lq wklv vhfwlrq zh frqvlghu ghpdqg ixqfwlrqv iru jxhvw0qljkwv lq krwhov dqg frwwdjhv
dw wkh qdwlrqdo ohyho dqg wkh suhihuhqfhv wkdw pd| kdyh jhqhudwhg wkhp1 Vlqfh zh
odwhu zloo frqvlghu wkh Qruzhjldq wrxulvp ghpdqg lq Vzhghq/ zh xvh d wkhruhwlfdo
iudphzrun wkdw lv dssursuldwh iru lqwhuqdwlrqdo wrxulvp1 Iurp pdunhw vxuyh|v zh
nqrz wkdw lqwhuqdwlrqdo wrxulvwv riwhq pdnh rqh orqjhu wuls dqg vhyhudo vkruwhu
wulsv1 Wklv pdnhv xv eholhyh wkdw wrxulvwv kdyh d suhihuhqfh vwuxfwxuh dvvrfldwhg
zlwk surgxfw glhuhqwldwlrq1 Wkdw lv/ wkh| olnh wr ylvlw pdq| glhuhqw sodfhv/ hdfk
srvvhvvlqj vrph xqltxh surshuwlhv wkdw glvwlqjxlvkhv lw iurp rwkhu ghvwlqdwlrqv/ h1j1/
zlwk uhvshfw wr wkh vxsso| ri uhfuhdwlrq idflolwlhv/ wkh zhdwkhu/ ru wkh glvwdqfh wkh
ylvlwru kdv wr wudyho wr uhdfk lw1
Ehjlqqlqj zlwk wkh zrun ri Vshqfh +4<:9, dqg Gl{lw dqg Vwljolw} +4<::, vxfk
suhihuhqfhv fdq eh uhsuhvhqwhg e| d wzr0ohyho xwlolw| ixqfwlrq
L E^ ' 8 d8 E^ c c 8 6 E^6 o
+7,
Khuh/ wkh vxexwlolw| ixqfwlrq 8 E^ frqvlvwv ri jrrgv dqg vhuylfhv +vxfk dv jxhvw
qljkwv lq krwhov dqg frwwdjhv, frqvxphg lq wkh wk frxqwu| +rxw ri 6 frxqwulhv,1
Dowkrxjk wkh suhihuhqfh vwuxfwxuh lv edvhg rq wkh dvvxpswlrq ri wdvwh iru ydulhw|/
wklv grhv qrw phdq wkdw wkh lqglylgxdo wrxulvw qhfhvvdulo| zrxog olnh wr vwd| lq erwk
krwhov dqg frwwdjhv gxulqj wkhlu vwd| lq Vzhghq1 Doo zh uhtxluh lv wkdw wkh srsxodwlrq
lv frpsrvhg ri wrxulvwv zlwk glhuhqw suhihuhqfhv iru vwd|lqj lq krwhov dqg frwwdjhv/
l1h1 wkdw wkhuh h{lvw d wdvwh iru ydulhw| lq djjuhjdwh ghpdqg1
Wr uhsuhvhqw wkh suhihuhqfh rughulqj iru wkh vxexwlolw| zh hpsor| wkh Vwrqh0Jhdu|
xwlolw| ixqfwlrq
8 E^ '
?
T
E^ V ) c
'
^ : V / : ) : f/
?
[
'
) ' c
zkhuh ^ c ' Mc c uhsuhvhqwv wkh qxpehu +vlqfh wrxulvp frqvxpswlrq vsuhdgv ryhu
d odujh qxpehu ri jrrgv dqg vhuylfhv ? lv jhqhudoo| odujhu wkdq 2, ri jxhvw qljkwv
8
lq krwhov dqg frwwdjhv lq d vshflf frxqwu|/ dqg V lv d sdudphwhu1 Wkh uhdvrq iru
fkrrvlqj d txdvl krprwkhwlf xwlolw| ixqfwlrq lv sulpdulo| gxh wr wkh idfw wkdw prvw
vwxglhv rq lqwhuqdwlrqdo wrxulvp ghpdqg qg dq lqfrph ru h{shqglwxuh hodvwlflw|
odujhu wkdq rqh1 E| dsso|lqj wklv vshflfdwlrq wkh hodvwlflwlhv duh doorzhg wr eh
odujhu wkdq rqh/ exw zloo whqg wr xqlw| dv wkh lqfrph ru h{shqglwxuhv lqfuhdvh1
Wkh suhihuhqfhv iru wkh uvw vwdjh doorfdwlrq sureohp/ l1h1 wkh ghflvlrq iru zklfk
frxqwu| wr ylvlw fdq wkhq eh uhsuhvhqwhg e| d Free0Grxjodv djjuhjdwru xwlolw| ixqf0
wlrq/ vxfk wkdw wkh xwlolw| ixqfwlrq +7, fdq eh zulwwhq dv
L E^ '
6
T
?
T
E^ V )
' '
c
: : fc
6
[
'
'
Wkh djjuhjdwru xwlolw| ixqfwlrq wudqvodwhv doo vxexwlolw| ohyhov/ l1h1 wrxulvp lq glhu0
hqw frxqwulhv/ wr dq ryhudoo xwlolw| ru zhoiduh ohyho1 E| ghqlqj dssursuldwh txdqwlw|/
^ / dqg sulfh/ R / lqglfhv +Dqghuvrq/ 4<:<, iru wkh jrrgv dqg vhuylfhv lq hdfk frxqwu|
zh fdq vroyh wkh uvw vwdjh doorfdwlrq sureohp/ l1h1 iru wkh ghpdqg ri wrxulvp lq
hdfk frxqwu|/ e| pd{lpl}lqj 8 E^ '
T6
'E^ V / vxemhfw wr '
S6
' R ^ /
zkhuh lv wrwdo h{shqglwxuhv rq rxwerxqg wrxulvp14 Wklv uhvxowv lq wkh iroorzlqj
ghpdqg htxdwlrqv
^ ' V n
6
[
R& V& n
R &'
c
R
' c c 6
+8,
dqg fruuhvsrqgv wr wkh yduldeohv lq wkh b ixqfwlrq15
Frqglwlrqdo rq wkh doorfdwlrq lq wkh uvw vwdjh zh fdq vroyh wkh vhfrqg vwdjh
doorfdwlrq sureohp/ l1h1 wkh ghpdqg iru hdfk frpprglw| zlwklq d frxqwu|/ e| pd{0
T?
)
'E^ V vxemhfw wr wkh h{shqglwxuhv wkdw kdyh ehhq
S
doorfdwhg wr ydfdwlrq lq frxqwu| / l1h1 ' ' ?' R ^ +Sroodn/ 4<:4,1 Wkh
lpl}lqj 8 E^ '
uhvxowlqj ghpdqg htxdwlrq lv jlyhq e|
^ ' V n
4
?
) [
)
R, V, n c
R ,'
R
' c c ?
+9,
Lw lv e| qr phdqv reylrxv wkdw wkh ghpdqg iru rxwerxqg wrxulvp vkrxog vroho| eh h{sodlqhg
e| wkh sulfhv dqg h{shqglwxuhv rq rxwerxqg wrxulvp1 Ghshqglqj rq wkh sxusrvh ri wkh dqdo|vlv/
rqh frxog dovr lqfoxgh sulfhv dqg h{shqglwxuhv rq grphvwlf wrxulvp ru uhfuhdwlrq lq wkh ghpdqg
iru rxwerxqg wulsv1
5
Wkh hvwlpdwhg prgho lv dfwxdoo| d wkuhh0vwdjh/ ru kljkhu/ doorfdwlrq prgho/ zkhuh wkh doorfdwlrq
ri wrwdo h{shqglwxuhv rq doo jrrgv dqg vhuylfhv lv qrw hvwlpdwhg1
9
Wklv ghshqgv rqo| rq wkh sulfhv ri wkh jrrgv dqg vhuylfhv zlwklq wkh frxqwu| dqg
wrwdo h{shqglwxuh doorfdwhg wr lw/ dqg fruuhvsrqgv wr wkh h{sodqdwru| yduldeohv lq
wkh q ixqfwlrq1 Khqfh/ wkh frqvxpswlrq ri jxhvw qljkwv lq krwhov dqg frwwdjhv lq rqh
frxqwu| lv lq xhqfhg e| wkh sulfhv ri wrxulvp lq wkh rwkhu frxqwulhv rqo| wkurxjk
wkhlu hhfwv rq frxqwu| h{shqglwxuh1
Frqglwlrqdo rq wkh uvw0vwdjh doorfdwlrq sureohp/ zh fdq dovr ghulyh wkh yduldeohv
wkdw hqwhu wkh k0ixqfwlrqv1 Vlqfh wklv lv wkh vdph pd{lpl}dwlrq sureohp dv wkh
vhfrqg vwdjh doorfdwlrq sureohp vkrzq deryh/ wkh vdph yduldeohv zloo hqwhu erwk
wkh q dqg k ixqfwlrqv1 Wkh dyhudjh gxudwlrq d*E k o/ ' Mc / ri vwd| lv wkxv
ghwhuplqhg e| wkh h{shqglwxuhv doorfdwhg wr wrxulvp lq frxqwu| / / dqg wkh
sulfhv lq frxqwu| / R, / , ' c c ?/ dv vkrzq lq +9,1 Wkxv wkh suredelolw| ri vwd|lqj
dqrwkhu qljkw lq d krwho/ kM / ghshqgv qrw rqo| rq wkh krwho sulfh/ exw rq doo sulfhv
iru wrxulvp jrrgv zlwklq wkh frxqwu|1
Dv wkh h{shfwhg gxudwlrq ri vwd| lv *E k / wkh ghpdqg iru jxhvw qljkwv lq kr0
whov dqg frwwdjhv fruuhvsrqgv wr ^ ' q *E k c ' Mc 1 Pdujlqdo hhfwv fdq eh
rewdlqhg e| fdofxodwlqj Y^ *Y%& iru glhuhqw fkrlfhv ri %& 1 Jlyhq wkh vshflfdwlrq
glvfxvvhg lq wkh suhylrxv vhfwlrq/ q M *E k ' d n i TE o*d n i TE o '
d n w o*d n i TE o/ iru ' Mc / lw dsshduv uhdvrqdeoh wr vhw '
1 Wkh
ixqfwlrqdo irup vxjjhvwv wkdw lw pd| eh gl!fxow wr hvwlpdwh wkh sdudphwhu yhfwruv
dqg vhsdudwho|1
71
Gdwd
Wkh wzr vhulhv iru Qruzhjldq jxhvwv lq Vzhglvk krwhov dqg frwwdjhv/ 4<;9=44<<<=</
duh suhvhqwhg judsklfdoo| lq Iljxuh 41 Dv lv reylrxv wkhuh duh vwurqj vhdvrqdo sdw0
whuqv lq erwk vhulhv/ erwk kdyh pdmru shdnv lq Mxo| dqg wkhlu wurxjkv duh lq wkh
idoo0zlqwhu shulrg1 Wkh qxpehuv ri jxhvwv duh pxfk orzhu lq wkh hduo| 4<<3v wkdq lq
wkh odwh 4<;3v dqg 4<<3v/ dqg wkh gluhfw fruuhodwlrq ehwzhhq wkh wzr vhulhv lv 31<61
Wkh qxpehu ri frwwdjh jxhvwv duh pxfk vpdoohu wkurxjkrxw wkh shulrg/ fi1 Iljxuh 5/
dqg wkhuh lv d vwurqj vhdvrqdo sdwwhuq dovr lq wkh shufhqw wkdw vwd| lq frwwdjhv1 Wkh
vhulhv vxjjhvwv wkdw ohlvxuh wudyho lv pruh iuhtxhqw lq wkh w|slfdo ydfdwlrq zhhnv lq
:
wkh vxpphu dqg lq wkh vsulqj1 Wkh odwwhu shulrg fruuhvsrqgv wr wkh vnllqj shulrgv
lq wkh prxqwdlqv1
Qrugvwuùp +4<<9, qgv wkdw wrxulvp frqvxpswlrq vsuhdgv ryhu d odujh qxpehu ri
jrrgv dqg vhuylfhv1 Zh wkhuhiruh wdnh wkh frqvxphu sulfh lqglfhv +FSL, dv sur{lhv
iru wrxulvp sulfhv lq hdfk frxqwu|1 Dv wkh sxufkdvlqj srzhu ri wkh ylvlwruv iurp
Qruzd|/ lv dhfwhg e| wkh h{fkdqjh udwh/ zh dgmxvw wkh FSL ri frxqwu| & zlwk wkh
h{fkdqjh udwh +HU& , ehwzhhq wkh Qruzhjldq nurqd +QRN, dqg wkh fxuuhqf| ri
frxqwu| &/ vxfk wkdw
R& ' FSL& *HU& c
& ' c c 6
+:,
Iurp RHFG vwdwlvwlfv +4<<5, rqh fdq vhh wkdw Qruzhjldqv kdyh pdlqo| doorfdwhg
wkhlu jxhvw qljkwv wr wkh rwkhu Vfdqglqdyldq frxqwulhv dqg wr Jhupdq|1 Wkhuhiruh/
zh lqfoxgh wkh sulfhv ri wrxulvp lq Ghqpdun/ Ilqodqg dqg Jhupdq|/ lq dgglwlrq wr
wkh Vzhglvk wrxulvp sulfh lq htxdwlrq +8,1 Vlqfh gdwd iru Qruzhjldq*v h{shqglwxuh
rq rxwerxqg wudyho lv qrw dydlodeoh/ zh kdyh xvhg Qruzhjldq jurvv grphvwlf surgxfw
+JGS, dv d sur{|1 Rq d |hduo| edvlv wkh Qruzhjldq JGS dqg jurvv grphvwlf lqfrph/
zklfk fdq eh vhhq dv wkh wrwdo h{shqglwxuh doorfdwhg ehwzhhq doo jrrgv lq d uvw vwhs
+fi1 irrwqrwh 5, kdyh d fruuhodwlrq ri 41331 Wkh JGS yduldeoh lv h{suhvvhg lq uhdo
ydoxhv dqg edvhg rq txduwhuo| revhuydwlrqv1
Wkh yduldeohv wkdw kdyh ehhq lqfoxghg lq wkh q dqg k ixqfwlrqv duh wkh uhdo sulfh
ri jxhvw qljkwv lq krwhov dqg frwwdjhv/6 fi1 Iljxuh 4/ wkh Vzhglvk FSL wr dffrxqw iru
doo rwkhu jrrgv dqg vhuylfhv wkh wrxulvw frqvxphv/ dqg uhdo Qruzhjldq h{shqglwxuhv
rq wrxulvp lq Vzhghq iurp wkh edodqfh ri sd|phqwv1 Frqvhtxhqwo|/ wkh '
yduldeoh lq +9, zloo eh phdvxuhg fruuhfwo| dowkrxjk zh kdyh qrw ehhq deoh wr xvh
wkh wuxh yduldeoh iru lq +8,1 Doo yduldeohv kdyh ehhq dgmxvwhg zlwk wkh h{fkdqjh
udwh EHU7 ehwzhhq wkh Vzhglvk nurqd +VHN, dqg QRN/ l1h1 wkh yduldeohv duh
h{suhvvhg lq QRN/ dv lq +:,1 Dv Iljxuh 4 uhyhdov/ wkhuh lv d vwurqj vhdvrqdo sdwwhuq
lq erwk wkh frwwdjh dqg krwho sulfhv vhulhv/ zlwk shdnv lq Iheuxdu|/ Pdufk dqg Mxo|
6
Wkh frwwdjh sulfh lqgh{ uhsruwhg e| Vwdwlvwlfv Vzhghq +xsgdwhg dqqxdoo|, kdyh ehhq dgmxvwhg
e| dq dgglwlyh vhdvrqdo sdwwhuq edvhg rq h{shqglwxuhv iru qljkwv vshqw lq frwwdjhv1 Vrxufh= wkh
Wrxulvw dqg Wudyho Gdwd Edvh +WGE, 4<<3=4 0 4<<9=<1
;
Guest Nights in Hotels and Cottages (10000)
25
20
15
10
5
0
86
88
90
92
94
96
98
2000
86
88
90
92
94
96
98
2000
Hotel and Cottage Price Indices
2.0
1.5
1.0
0.5
Year
Iljxuh 4= Qruzhjldq qxpehuv +lq 43 333, ri jxhvwv lq Vzhglvk krwhov +grw0gdvk olqh,
dqg frwwdjhv +vrolg olqh, ^wrs`/ krwho sulfh lqgh{ lq QRN +vrolg olqh, dqg frwwdjh
sulfh lqgh{ lq QRN +grw0gdvk olqh, ^erwwrp`/ 4<;9=4 0 4<<<=<1
<
Percent in Cottages
Month
60
12
11
10
9
8
7
6
5
4
3
2
1
45
30
15
0
0
10
20
30
86
40
88
90
92
94
96
98 2000
Year
Percent in Cottages
Iljxuh 5= Wkh shufhqw ri Qruzhjldq jxhvwv lq Vzhglvk frwwdjhv +phdq @ 3149/
vwdqgdug ghyldwlrq @ 313;,1 Wkh ohiw sdqho jlyhv dyhudjhv ryhu wkh hqwluh shulrg1
iru wkh frwwdjh sulfhv dqg wurxjkv lq Mxo| iru wkh krwho sulfh vhulhv1 Lq Vhswhpehu
4<<< wkh sulfh zdv <93 VHN shu qljkw lq d grxeoh urrp1 Iru frwwdjhv wkh dyhudjh
sulfh lq 4<<< zdv 798 VHN shu qljkw17
81
Hvwlpdwlrq
Wr hvwlpdwh wkh sdudphwhuv ri wkh elyduldwh LQPD+4, prgho/ d qrqolqhdu/ frqglwlrqdo
ohdvw vtxduhv hvwlpdwru edvhg rq suhglfwlrq huuruv zloo eh hpsor|hg1 E| wklv wkhuh
lv qr qhhg wr pdnh h{solflw glvwulexwlrqdo dvvxpswlrqv1 Lw vkrxog eh uhpdunhg wkdw
qdwlrqdo dqg prqwko| jxhvw qljkw qxpehuv duh xvxdoo| odujh/ vr wkdw pdlqwdlqlqj
d frxqw gdwd lqwhusuhwdwlrq lv ri olwwoh sudfwlfdo lqwhuhvw iru hvwlpdwlrq1 Wkh frxqw
gdwd vhwwlqj kdv d nh| uroh rqo| iru surylglqj wkh lqwhusuhwdwlrqdo dvshfwv ri wkh
7
Gdwd vrxufhv= Dffrpprgdwlrq vwdwlvwlfv dqg dffrpprgdwlrq sulfhv iru krwho dqg frwwdjhv
+Vwdwlvwlfv Vzhghq,1 Frqvxphu sulfh lqglfhv +RHFG/ Pdlq Hfrqrplf Lqglfdwruv,1 H{fkdqjh udwhv/
ghqhg dv prqwko| dyhudjhv ri wkh pdunhw udwhv/ dqg Qruzhjldq wrxulvp h{shqglwxuhv lq Vzhghq
+wkh Vzhglvk Fhqwudo Edqn,1 Qruzhjldq JGS +Lqwhuqdwlrqdo Ilqdqfldo Vwdwlvwlfv/ Lqwhuqdwlrqdo
Prqhwdu| Ixqg,1 Qruzhjldq jurvv grphvwlf lqfrph +Vwdwlvwlfv Qruzd|,1
43
prgho sdudphwhuv1 Wkhvh lqwhusuhwdwlrqv duh qrw dhfwhg e| wkh vl}hv ri jxhvw qljkw
qxpehuv1
Iluvw/ zh glvfxvv wkh fdvh zlwk h{sodqdwru| yduldeohv lq wkh ohyhov prgho/ dqg odwhu
zh surfhhg wr jlyh vrph uhpdunv rq frqvwdqw sdudphwhu prghov1 Wkh ohdvw vtxduhv
hvwlpdwru iru wkh prgho lq ohyhov/ l1h1 5| ' q | 1 | n w| q |
3
fulwhulrq ixqfwlrq
3
1 | / plqlpl}hv wkh
3
A
[
7'
e2M| n e2| c
|'2
zkhuh wkh suhglfwlrq huuruv duh e| ' 5| .E5| m3 c c 3| ' 5| q | b| 3
w| q |
3
3
E b|3 w|3 q |3 0|3
Ec ' Mc 1 Wklv lv d vwudljkwiruzdug ds0
surdfk lq doo uhvshfwv exw iru krz wr ghwhuplqh wkh i0| j vhtxhqfh1 Li 0| lv ghwhuplqhg
iurp hdfk htxdwlrq vhsdudwho| wkhuh zrxog xqiruwxqdwho| eh wzr glhuhqw vhtxhqfhv1
Lqvwhdg/ zulwh wkh ohyhov prgho rq wkh dowhuqdwlyh irup q | 1 | ' 5| w | q |
vr wkdw 1 | '
3
S2
1 |3 /
' .Eq | 1 | m1 |c 1 | ' E5M| n 5| dwM| q M| n w| E q | o1 | c
3
3
3
3
vlqfh q M| n q | ' c iru doo |1 Wklv h{suhvvlrq lq 1 | fdq eh xvhg wr uhfxuvlyho| fdo0
fxodwh wkh hqwluh vhtxhqfh1 Wkh 1 | h{suhvvlrq lv dovr zkdw rqh jhwv iru d frqwlqxrxv
yduldeoh prgho/ iru zklfk qr h{shfwdwlrq rshudwlrqv duh uhtxluhg +vhh dovr Euçqqçv
dqg Kdoo/ 4<<;,1 Xvlqj wkh ghqlwlrq ri 1 | dqg uhsodflqj 0| & c & : f/ zlwk h{shfwhg
3
ydoxhv b| / jlyhv
0| ' E5M| n 5| dwM| q M|
3
3
n w| E q M| oE0|
3
3
3
n E b| Qrwh wkdw wkh 5| duh frqglwlrqdoo| dv zhoo dv xqfrqglwlrqdoo| khwhurvnhgdvwlf1 Lq
dgglwlrq/ vrph ri wkh vshflfdwlrqv pd| eh vxemhfw wr uhpdlqlqj vhuldo fruuhodwlrq1
Dv zh gr qrw zlvk wr xqqhfhvvdulo| hpedun rq d ixoo vshflfdwlrq ri wkh ghshqghqfh
vwuxfwxuh +fi1 Euçqqçv dqg Khoovwuùp/ 5333, d zhljkwhg frqglwlrqdo ohdvw vtxduhv
hvwlpdwru lv qrw ihdvleoh1 Iru lqihuhqfh sxusrvhv zh/ krzhyhu/ uhfrpphqg dffrxqwlqj
iru khwhurvnhgdvwlflw| dqg vhuldo fruuhodwlrq e| xvlqj d urexvw vdqgzlfk hvwlpdwru ri
wkh fryduldqfh pdwul{ +h1j1/ EKQ,1
Iru d frqvwdqw sdudphwhu prgho qhlwkhu q M qru q fdq eh hvwlpdwhg gluhfwo|1
Dv wkh suhglfwlrq huuru wkhq frqwdlqv d ohdglqj whup b ' q b zh pd| hvwlpdwh q *Eb
M n b
dqg b e| b
M n b
rqfh ohdvw vtxduhv hvwlpdwhv ri bM dqg b duh
e| b
44
dydlodeoh1 Dv zh fdq qrw hqirufh wkh sdudphwhu uhvwulfwlrqv dfurvv htxdwlrqv/ wkh
wzr htxdwlrqv fdq eh hvwlpdwhg vhsdudwho| e| vwdqgdug vriwzduh1
91
Uhvxowv
Wkh hvwlpdwlrq uhvxowv duh suhvhqwhg Wdeoh 41 Wkh prghov duh hvwlpdwhg mrlqwo|
e| wkh frqglwlrqdo ohdvw vtxduhv hvwlpdwru/ zlwk vhdvrqdo gxpp| yduldeohv lqfoxghg
lq wkh olqhduo| vshflhg b ixqfwlrq1 Wkh ixoo| sdudphwhul}hg prgho lq wkh uvw
froxpq jlyhv k ydoxhv wkdw dsshdu wrr vpdoo/ lq prvw lqvwdqfhv htxdo wr }hur iru k 1
Wkhuhiruh/ d ohvv sdudphwhul}hg prgho lv suhvhqwhg lq wkh vhfrqg froxpq ri Wdeoh 41
Frpsdulqj wkh wzr prghov zh vhh wkdw wkh hvwlpdwhg sdudphwhuv lq wkh b ixqf0
wlrq iru wkh ixoo| sdudphwhul}hg prgho duh odujhu dqg kdyh vpdoohu vwdqgdug huuruv1
Wxuqlqj wr wkh srlqw hvwlpdwhv/ Wdeoh 4 uhyhdov wkdw lqfuhdvhv lq wkh Jhupdq ERC /
Ilqqlvk ER8 dqg Vzhglvk ER7 sulfh ohyhov zloo uhgxfh wkh qxpehu ri krwho dqg frw0
wdjh jxhvw qljkwv1 Wkh qhjdwlyh hhfwv ri wkh Jhupdq dqg Ilqqlvk sulfh ohyhov duh
vxusulvlqj/ exw fdq eh d uhvxow ri ihzhu wudqvlw ylvlwruv lq Vzhghq1 Derxw rqh iwk
ri wkh Qruzhjldq ylvlwruv sdvv wkurxjk Vzhghq wr uhdfk wkhlu pdlq ghvwlqdwlrqv1
Qrwh/ krzhyhu/ wkdw wkh Ilqqlvk sulfh hhfw lv qrw vljqlfdqw1 Wkh qhjdwlyh hhfw ri
wkh Vzhglvk sulfh ohyho lv wkh h{shfwhg rqh1 Dv lpsolhg e| wkh hfrqrplf prgho wkh
hvwlpdwhg frh!flhqw iru wkh lqfrph yduldeoh E lv srvlwlyh1
Frqwlqxlqj zlwk wkh hvwlpdwhv ri wkh q ixqfwlrq/ l1h1 wkh suredelolw| ri vhohfwlqj
wkh krwho dowhuqdwlyh/ zh qg wkdw wkh sulfh hhfwv iurp krwhov ERM dqg frwwdjhv
ER duh srvlwlyh1 Zkloh wkh srvlwlyh hhfw iurp dq lqfuhdvh lq wkh frwwdjh sulfh lv
h{shfwhg/ wkh srvlwlyh rzq sulfh hhfw lv qrw1 Dgglwlrqdoo|/ d kljkhu sulfh ohyho lq
Vzhghq uhgxfhv wkh suredelolw| ri fkrrvlqj wkh krwho dowhuqdwlyh/ zkhuhdv d kljkhu
h{shqglwxuh ohyho E7 c dffruglqj wr wkh ixoo| sdudphwhul}hg prgho/ zloo lqfuhdvh
wkh suredelolw| ri fkrrvlqj d krwho1 Frpsduhg wr wkh sulfh hhfwv wkh h{shqglwxuh
hhfw lv vpdoo1
Irfxvlqj qh{w rq wkh hvwlpdwlrq uhvxowv iru wkh h{sodqdwru| yduldeohv lq wkh wM
dqg w ixqfwlrqv/ zh qg wkdw dq lqfuhdvh lq krwho sulfh lqfuhdvhv wM dqg wkhq dovr
45
Wdeoh 4= Hvwlpdwlrq uhvxowv iru Qruzhljdq jxhvw qljkw vhulhv +ohyho, +M lqglfdwhv
krwho dqg frwwdjh,1 Vhdvrqdo gxpplhv lqfoxghg lq wkh b ixqfwlrq duh qrw uhsruwhg1
Hvw1
v1h1
Hvw1
v1h1
b ixqfwlrq
Sulfh lqgh{ ERC 031443 31338
031389 3134:
Sulfh lqgh{ ER8 03133< 31339
031355 31355
Sulfh lqgh{ ER( 31775 3135<
314<: 313;<
Sulfh lqgh{ ER7 031535 3133<
031448 3136;
Lqfrph E 31388 31337
3137< 31347
q M ixqfwlrq
Krwho sulfh ERM 41453 31394
61365 31977
Frwwdjh sulfh ER 31:93 31384
413;< 413:5
Sulfh lqgh{ ER7 061:69 3147<
0:156< 51674
H{shqglwxwh E7 31334 31333
0313337 31334
Frqvwdqw
613;; 313<5
71;44 41537
wM ixqfwlrq
Krwho sulfh ERM 0;14;: 31<4<
31:4< 314:7
Frwwdjh sulfh ER 0461;67 31588
0
Sulfh lqgh{ ER7 471647 31;73
041;39 3189<
H{shqglwxuh E7 031335 31333
0
Frqvwdqw
51965 3175:
031698 318<9
w ixqfwlrq
0:1745 31943
0
Frwwdjh sulfh ER 0551;33 317;9
0541954 4148:
Sulfh lqgh{ ER7 591977 319;6
4:17;6 51<<7
H{shqglwxuh E7 31334 31333
0
Frqvwdqw
051898 3158<
0413;; 51373
Krwho sulfh ERM OE+45/ Krwho,
:91<
861;
OE+45/ Frwwdjh,
<<1<
;:13
-2 +Krwho,
31<9
31<8
-2 +Frwwdjh,
31;7
31;5
46
0.5
0.9
0.0
Marginal Cottage Effect
Marginal Hotel Effect
1.0
0.8
0.7
0.6
0.5
0.4
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0.50
0.75
1.00
1.25
1.50
0.50
Hotel Price
0.75
1.00
1.25
1.50
1.75
Cottage Price
Iljxuh 6= Pdujlqdo hhfwv ri krwho sulfh +uljkw, dqg frwwdjh sulfh +ohiw, rq ^| '
q | *E k| iru krwhov dqg frwwdjhv1 Edvhg rq doo revhuydwlrqv dqg wkh prgho lq
froxpq wzr ri Wdeoh 41
wkh suredelolw| ri uhpdlqlqj dqrwkhu qljkw lq d krwho EkM 18 Wklv xqh{shfwhg hhfw
lv rqo| suhvhqw lq wkh ohvv sdudphwhul}hg prgho1 Dq lqfuhdvh lq frwwdjh sulfh kdv dq
h{shfwhg qhjdwlyh hhfw lq wkh w ixqfwlrqv1 Wkh Vzhglvk sulfh ohyho kdv d qhjdwlyh
hhfw rq wkh suredelolw| ri vwd|lqj dqrwkhu qljkw lq d krwho iru wkh ohvv sdudphwhul}hg
prgho/ dqg d srvlwlyh hhfw rq wkh w ixqfwlrq1 Iru wkh ohvv sdudphwhul}hg prgho wkh
phdq ydoxhv k
7/ k
7 M dqg q7 ryhu wkh wrwdo vdpsoh duh ffS/ fH dqg f.H/ uhvshfwlyho|1
Dv Iljxuh 5 vkrz/ wkh phdq ri q lv 31;71 Iru erwk prghov wkhuh lv vxevwdqwldo exw
udwkhu vlploduo| vkdshg uhpdlqlqj dxwrfruuhodwlrq/ zlwk d odujh srvlwlyh shdn dw odj
451 E| dsso|lqj wkh ohvv sdudphwhul}hg vshflfdwlrq wkh dxwrfruuhodwlrq lv voljkwo|
uhgxfhg/ wr wkh frvw ri d pdujlqdoo| orzhu h{sodqdwru| srzhu iru wkh frwwdjh vhulhv1
Klwkhuwr zh kdyh irfxvhg rq wkh gluhfw hhfwv zlwklq hdfk ixqfwlrq1 Lq Iljxuh
6 wkh pdujlqdo hhfwv ri krwho dqg frwwdjh sulfhv rq ^ ' q *E k iru krwhov
dqg frwwdjhv lv vkrzq1 Iurp wkh jxuh zh vhh wkdw wkh pdujlqdo hhfw ydulhv pruh
iru frwwdjhv gxh wr d fkdqjh lq wkh rzq sulfh1 Krzhyhu/ prvw ri wkh hhfwv olh
ehwzhhq f dqg fD zlwk d phdq ydoxh ri f2 dv wkh er{ sorw lq Iljxuh 7
8
Qrwh wkdw wkh vljq lqwhusuhwdwlrqv iru wkh dqg ixqfwlrqv duh wkh vdph1
47
Cottage/MNS
Cottage/pS
Cottage/pC
Cottage/pH
Hotel/MNS
Hotel/pS
Hotel/pC
Hotel/pH
-3
-2
-1
0
1
2
3
Marginal Effect
Iljxuh 7= Er{ sorw ri pdujlqdo hhfwv ri krwho sulfh/ frwwdjh sulfh/ Vzhglvk sulfh
ohyho/ dqg h{shqglwxuh rq ^| ' q | *E k| iru krwhov dqg frwwdjhv1 Edvhg rq doo
revhuydwlrqv dqg wkh prgho lq froxpq wzr ri Wdeoh 41 Rxwo|lqj pdunhuv fruuhvsrqg
wr wkh 8wk dqg <8wk shufhqwlohv1
uhyhdov1 Iljxuh 6 dovr lqglfdwhv wkdw wkh pdujlqdo hhfw iurp dq lqfuhdvhg frwwdjh
sulfh lv odujhu zkhq wkh frwwdjh sulfh lv orz/ l1h1 lq r shdn shulrgv zkhq wkh frwwdjh
ghpdqg lv orz1 Iru krwhov qr vxfk fohdu sdwwhuq lv pdqlihvw1
Iljxuh 7 suhvhqwv wkh pdujlqdo hhfwv rq ^ ' q *E k iru krwhov dqg frwwdjhv
iru hdfk ri wkh h{sodqdwru| yduldeohv lq wkh k dqg q ixqfwlrqv1 Wkh pdujlqdo hhfw
ri h{shqglwxuh +Frwwdjh2 7 dqg Krwho2 7 , lv vpdoo1 Zklfk lqglfdwh wkdw wkh
Qruzhjldqv whqg wr lqfuhdvh wkhlu ghpdqg iru rwkhu jrrgv/ wkdq jxhvw qljkwv lq
krwhov dqg frwwdjhv/ dv wkh| doorfdwh pruh prqh| wr wulsv wr Vzhghq1 Wkh Vzhglvk
sulfh ohyho kdv d qhjdwlyh pdujlqdo hhfw rq krwho +Krwho2 R7 , dqg d srvlwlyh hhfw
rq frwwdjh +Frwwdjh2 R7 , jxhvw qljkwv1 Wkxv/ frqglwlrqdo rq wkh ghflvlrq wr wudyho
wr Vzhghq/ wkh Qruzhjldqv zloo lqfuhdvh wkhlu vwd| lq fkhdshu dffrpprgdwlrq +frw0
wdjhv, dv wkh Vzhglvk sulfh ohyho lqfuhdvhv1 Dv uhyhdohg hduolhu lq Iljxuh 6/ wkh
pdujlqdo rzq sulfh hhfw rq frwwdjh +Frwwdjh2 R , lv qhjdwlyh1 Wkh pdujlqdo hhfw
ri dq lqfuhdvh lq wkh krwho sulfh rq frwwdjhv lv dovr qhjdwlyh/ vlqfh wkh suredelolw| ri
48
fkrrvlqj wkh krwho dowhuqdwlyh lqfuhdvhv dv wkh krwho sulfh lqfuhdvhv1
Iru krwhov/ zh qg d srvlwlyh pdujlqdo hhfw iurp erwk frwwdjh dqg krwho sulfhv1
Zkloh wkh srvlwlyh pdujlqdo hhfw iurp wkh frwwdjh sulfh +Krwho2 R , lv h{shfwhg/
wkh srvlwlyh rzq sulfh hhfw +Krwho2 RM , lv qrw1 Wklv pd| eh d uhvxow ri rplwwhg
h{sodqdwru| yduldeohv/ vlqfh pdq| ri wkh krwho jxhvwv duh exvlqhvv ylvlwruv1
:1
Frqfoxvlrq
Wkh sdshu kdv dgrswhg d qryho vwudwhj| ri uvw rewdlqlqj d g|qdplf dqg vwrfkdvwlf
prgho vwuxfwxuh e| djjuhjdwlrq iurp d vlpsoh krwho ru frwwdjh vshflf prgho +d
phdvxuhphqw prgho,/ dqg vhfrqg xvhg vwdqgdug ghpdqg dqdo|wlfdo uhvxowv wr h{sodlq
vrph ri wkh sdudphwhuv ri wkh vwrfkdvwlf prgho +wkh vwuxfwxudo sduw,1 Wkh rewdlqhg
prgho dqg wkh hvwlpdwlrq uhvxowv surylgh d ulfkhu slfwxuh ri lqwhuqdwlrqdo jxhvw
qljkwv wkdq suhylrxvo| xvhg prgho dssurdfkhv1
Wkh ghulyhg sdudphwhuv lq wkh djjuhjdwhg phdvxuhphqw prgho duh wkh prqwko|
phdq fkhfn0lq/ wkh suredelolw| ri vhohfwlqj krwho udwkhu wkdq frwwdjh dqg wkh gdlo|
fkhfn0rxw suredelolw|1 Lq wkh dqdo|vlv/ wkh ylvlwruv zhuh uvw dvvxphg wr ghflgh xsrq
zklfk frxqwu| wr ylvlw/ dqg wkhq lq d vhfrqg vwdjh ghflgh wkh irup ri dffrpprgdwlrq1
Wr hvwlpdwh wkh sdudphwhuv/ d qrqolqhdu/ frqglwlrqdo ohdvw vtxduh hvwlpdwru edvhg
rq suhglfwlrq huuruv zdv hpsor|hg1 Wkh hvwlpdwlrq uhvxowv lqglfdwh wkdw prvw ri wkh
h{sodqdwru| yduldeohv duh vljqlfdqw1 Wkh hvwlpdwlrq dovr lqglfdwhv wkdw wkh uhvxowv
duh urexvw/ zlwk wkh h{fhswlrq ri wkh sdudphwhuv lq wkh krwho fkhfn0rxw suredelolw|1
Lq wkh ghflvlrq surfhvv iru zklfk frxqwu| wr ylvlw wkh rzq sulfh kdv d vwurqjo|
qhjdwlyh dqg vljqlfdqw hhfw1 Wkh sulfh ohyho lq wkh ghvwlqdwlrq frxqwu| fdq wkxv
eh frqvlghuhg dv rqh ri wkh pruh lpsruwdqw idfwruv lq wkh ghflvlrq surfhvv iru zklfk
frxqwu| wr ylvlw1
Frqglwlrqdo rq wkh ghflvlrq wr ylvlw Vzhghq/ wkh odujhvw pdujlqdo hhfw rq wkh
ghpdqg iru krwho dqg frwwdjh jxhvw qljkwv frphv iurp wkh ryhudoo sulfh ohyho zlwklq
Vzhghq/ zlwk d srvlwlyh hhfw rq frwwdjhv dqg d qhjdwlyh hhfw rq krwhov1 Wkh vpdoo
pdujlqdo hhfw iurp wkh h{shqglwxuh yduldeoh lqglfdwhv wkdw wkh Qruzhjldqv whqg
wr lqfuhdvh wkhlu frqvxpswlrq ri rwkhu jrrgv/ wkdq jxhvw qljkwv/ dv wkh| doorfdwh
49
pruh prqh| iru wulsv wr Vzhghq1 Krzhyhu/ wkh h{shqglwxuh yduldeoh dovr lqfoxghv
h{shqglwxuhv iurp vdph gd| ylvlwruv dqg erughu wudgh/ zklfk fdq kdyh lqfuhdvhg
uhodwlyh wr h{shqglwxuhv iurp ryhu qljkw ylvlwruv gxulqj wkh vdpsoh shulrg1
Wkh pdujlqdo hhfw iurp dq lqfuhdvh lq wkh rzq sulfh lv qhjdwlyh iru frwwdjh dqg
srvlwlyh iru krwho1 Zkloh wkh qhjdwlyh hhfw rq frwwdjh lv h{shfwhg wkh srvlwlyh hhfw
rq krwho lv qrw/ dqg pd| eh d uhvxow ri rplwwhg h{sodqdwru| yduldeohv1 D odujh sduw
ri wkh krwho ylvlwruv gxulqj wkh idoo/ zlqwhu dqg vsulqj duh exvlqhvv ylvlwruv1 Iurp
wkh wlph vhulhv sorw ri wkh krwho sulfh/ rqh fdq dvvxph d kljk srvlwlyh fruuhodwlrq
ehwzhhq wkh sulfh iru krwho dffrpprgdwlrq dqg wkh exvlqhvv wuhqg lq Vzhghq1
Dowkrxjk wkh dgrswhg whfkqltxh kdv ehhq dssolhg wr wkh doorfdwlrq sureohp iru
glhuhqw vruwv ri dffrpprgdwlrq/ wkhuh duh d qxpehu ri rwkhu duhdv zkhuh wklv prg0
hoolqj dssurdfk fdq eh ri lqwhuhvw1 Iru h{dpsoh/ wkh surfhgxuh fdq eh dssolhg wr d
qxpehu ri glhuhqw vwrfn0nhhslqj sureohpv/ dqg wr prghoolqj wkh qxpehu ri vwxghqwv
rq glhuhqw frxuvhv dw d xqlyhuvlw|1 Wkh hpslulfdo looxvwudwlrq dovr lqglfdwhv wkdw
wkh phdvxuhphqw prgho fdq hdvlo| eh h{whqghg zlwk d odujh qxpehu ri h{sodqdwru|
yduldeohv1
4:
Dsshqgl{ D4= Elyduldwh LQDU+4, Prgho Surshuwlhv
Iru wkh LQDU+4, prgho ri Vhfwlrq 5/ ohw .E"| ' bc T E"| ' B dqg .E"| "r ' b2 c | 9'
r1 Wkhq wkh iroorzlqj surshuwlhv krog= .Eq "| ' qb/ T Eq "| ' qB n qE qb dqg .Eq "| q "r ' q 2 b2 c | 9' r Wkh wklqqlqj rshudwlrqv lqyroylqj k c '
c 2c duh dqdorjrxvo| ghqhg1 Iru wkh prgho dw wkh gdlo| dqg uhjlrqdo ohyho zh fdq
ghprqvwudwh wkh iroorzlqj surshuwlhv=
.E+| ' q b*E k T E+| ' Ek q b n B*E k2 JE+|c +2| ' q q 2 B*E k k2 f
JooE+| c +| & ' k& fc
3
' c 2c
&f
JE+| c +2| & ' k& JE+|c +2| fc
&f
JE+| & c +2| ' k&2 JE+|c +2| fc
&f
3
3
Khqfh/ wkhuh lv erwk vhuldo dv zhoo dv furvv fruuhodwlrq lq wkh gd|0wr0gd| vhulhv1
Dsshqgl{ D5= Whpsrudo Djjuhjdwlrq
Frqvlghu djjuhjdwlrq ryhu wkuhh wlph srlqwv dqg irfxv rqo| rq wkh PD0sduw1 Diwhu
wklv lqgxfwlrq frxog eh xvhg/ exw zh devwdlq iurp jlylqj d ixoo dffrxqw1 Wkh uhvxow
lv edvhg rq dq xqghuo|lqj Srlvvrq l1l1g1 dvvxpswlrq iru i0| j1 Zh pd| zulwh
D | ' 0| n 0|
' 1 ||
3
2
3
n 0|
n k 1 ||
2
3
3
3
n k E0|
n k2 1 ||
3
3
3
n 0|
3
2
n 0| n k2 E0|
3
3
2
n 0|
3
n 0| e 3
e
2
Khuh/ .E1 || r ' T E1 || r ' b dqg khqfh .ED | ' bE n k n k2 1 Wkh frqglwlrqdo
3
3
h{shfwdwlrq lv .ED | m5 c c 5| ' b n 2kbE n k n kE n k0| 1 Lq wklv zh kdyh
3
vhw .E0| e m5 c c 5| ' b dv 0|
3
3
3
3
e
lv ehwzhhq wlph srlqwv dw wkh qhz wlph vfdoh1
Vwulfwo|/ lw lv/ krzhyhu/ lq wkh lqirupdwlrq vhw1 Iru wkh yduldqfh zh qhhg
JE1 || 2 1 || ' 2bc JE1 || 2 1 || e2 ' bc
3
3
3
3
3
3
JE1 || 1 || e2 ' 2bc T Ek& 1 ' k2& T E1 n k& E k& .E1
3
3
3
3
Wkhq T ED | ' bd n .k n Dk2 n ek o1 Zulwlqj lqvwhdg rq wkh qhz wlph vfdoh /| '
1| n k 1|
3
nk
2
1|
3
jlyhv wkh vdph uvw frqglwlrqdo dqg xqfrqglwlrqdo prphqwv/
4;
exw qrw wkh vdph vhfrqg rughu prphqwv1 Wkh glhuhqfh lv gxh wr wkh yduldeoh
ghshqghqfh ehwzhhq wkh 1 frpsrqhqwv lq wkh ruljlqdo prgho qrz ehlqj irufhg wr
eh frqvwdqw1 Wklv yduldwlrq lq ghshqghqfh zloo uhpdlq iru doo djjuhjdwlrq ryhu pruh
wkdq wzr wlph shulrgv1
4<
Uhihuhqfhv
Dgdprzlf}/ Z1O1 +4<<7,1 Kdelw Irupdwlrq dqg Ydulhw| Vhhnlqj lq d Glvfuhwh Fkrlfh
Prgho ri Uhfuhdwlrq Ghpdqg1 Mrxuqdo ri Djulfxowxudo dqg Uhvrxufh Hfr0
qrplfv 4</ 4<0641
Do0Rvk/ P1D1 dqg Do}dlg/ D1D1 +4<;:,1 Iluvw0Rughu Lqwhjhu Ydoxhg Dxwruhjuhvvlyh
+LQDU +4,, Surfhvv1 Mrxuqdo ri Wlph Vhulhv Dqdo|vlv ;/ 59405:81
Do}dlg/ D1D1 dqg Do0Rvk/ P1D1 +4<;;,1 Iluvw Rughu Lqwhjhu Ydoxhg Dxwruhjuhv0
vlyh +LQDU+4,, Surfhvv= Glvwulexwlrqdo dqg Uhjuhvvlrq Surshuwlhv1 Vwdwlvwlfd
Qhhuodqglfd 75/ 860941
Dqghuvrq/ U1D1 +4<:<,1 Shuihfw Sulfh Djjuhjdwlrq dqg Hpslulfdo Ghpdqg Dqdo|vlv/
Hfrqrphwulfd 7:/ 453<045631
Eoxqghoo/ U1/ Jul!wk/ U1 dqg Zlqgphlmhu/ I1 +4<<<,1 Lqglylgxdo Hhfwv dqg G|qdp0
lfv lq Frxqw Gdwd Prghov1 Zrunlqj Sdshu Z<<26/ Lqvwlwxwh ri Ilvfdo Vwxglhv/
Orqgrq1
Euhzhu/ N1U1Z1 +4<:6,1 Vrph Frqvhtxhqfhv ri Whpsrudo Djjuhjdwlrq dqg V|vwhp0
dwlf Vdpsolqj iru DUPD dqg DUPD[ Prghov1 Mrxuqdo ri Hfrqrphwulfv 4/
46604871
Euçqqçv/ N1 +4<<8,1 H{sodqdwru| Yduldeohv lq wkh DU+4, Frxqw Gdwd Prgho1 Xphè
Hfrqrplf Vwxglhv 6;41
Euçqqçv/ N1 dqg Kdoo/ D1 +4<<;,1 Hvwlpdwlrq lq Lqwhjhu0Ydoxhg Prylqj Dyhudjh
Prghov1 Xphè Hfrqrplf Vwxglhv 7::1
Euçqqçv/ N1 dqg Khoovwuùp/ M1 +5333,1 Jhqhudol}hg Lqwhjhu0Ydoxhg Dxwruhjuhvvlrq1
Wr dsshdu lq Hfrqrphwulf Uhylhzv1
Euçqqçv/ N1/ Khoovwuùp/ M1 dqg Qrugvwuùp/ M1 +4<<<,1 D Qhz Dssurdfk wr Prghoolqj
dqg Iruhfdvwlqj Prqwko| Jxhvw Qljkwv lq Krwhov1 Xphè Hfrqrplf Vwxglhv 836
+uhylvhg,1
Furxfk/ J1L1 +4<<7,1 Wkh Vwxg| ri Lqwhuqdwlrqdo Wrxulvp Ghpdqg= D Vxuyh| ri
Sudfwlfh1 Mrxuqdo ri Wudyho Uhvhdufk/ Vsulqj/ 740881
Gl{lw/ D1 dqg Vwljolw}/ M1H1 +4<::,1 Prqrsrolvwlf Frpshwlwlrq dqg Rswlpxp Surgxfw
Glyhuvlw|1 Dphulfdq Hfrqrplf Uhylhz 9:/ 5<:063;1
53
Jdufld0Ihuuhu/ D1 dqg Txhudow/ U1D1 +4<<:,1 D Qrwh rq Iruhfdvwlqj Lqwhuqdwlrqdo
Wrxulvp Ghpdqg lq Vsdlq1 Lqwhuqdwlrqdo Mrxuqdo ri Iruhfdvwlqj 46/ 86<087<1
Judqjhu/ F1Z1M1 dqg Pruulv/ P1M1 +4<:9,1 Wlph Vhulhv Prghoolqj dqg Lqwhusuhwdwlrq1
Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw| D46</ 579058:1
Jxvwdyvvrq/ S1 dqg Qrugvwuùp/ M1 +4<<<,1 Wkh Lpsdfw ri Vhdvrqdo Xqlw Urrwv
dqg Yhfwru DUPD Prgholqj rq Iruhfdvwlqj Prqwko| Wrxulvp Iorzv1 Xphè
Hfrqrplf Vwxglhv 7<91
Kduyh|/ D1F1 +4<;4,1 Wlph Vhulhv Dqdo|vlv1 Sklols Doodq/ R{irug1
PfNhq}lh/ H1 +4<;8,1 Vrph Vlpsoh Prghov iru Glvfuhwh Yduldwh Wlph Vhulhv1 Zdwhu
Uhvrxufhv Exoohwlq 54/ 97809831
PfNhq}lh/ H1 +4<;9,1 Dxwruhjuhvvlyh Prylqj0Dyhudjh Surfhvvhv zlwk Qhjdwlyh0
Elqrpldo dqg Jhrphwulf Pdujlqdo Glvwulexwlrqv1 Dgydqfhv lq Dssolhg Sured0
elolw| 4;/ 9:<0:381
Phohqehuj/ E1 dqg ydq Vrhvw/ D1 +4<<9,1 Sdudphwulf dqg Vhpl0Sdudphwulf Prghoolqj
ri Ydfdwlrq H{shqglwxuhv1 Mrxuqdo ri Dssolhg Hfrqrphwulfv 44/ 8<0:91
Qrugvwuùp/ M1 +4<<<,1 Xqrevhuyhg Frpsrqhqwv lq Lqwhuqdwlrqdo Wrxulvp Ghpdqg1
Xphè Hfrqrplf Vwxglhv 8351
Qrugvwuùp/ M1 +4<<9,1 Wrxulvp Vdwhoolwh Dffrxqwv iru Vzhghq 4<<50<61 Wrxulvp
Hfrqrplfv 5/ 460751
RHFG1 +4<<5,1 Wrxulvp Srolf| dqg Lqwhuqdwlrqdo Wrxulvp lq RHFG Phpehu Frxq0
wulhv1 Sdulv1
Suhvv/ Z1K1/ Iodqqhu|/ E1S1/ Whxnrovn|/ V1D1 dqg Yhwwhuolqj/ Z1W1 +4<;:,1 Qxphu0
lfdo Uhflshv1 Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh1
Sroodn/ U1D1 +4<:4,1 Frqglwlrqdo Ghpdqg Ixqfwlrqv dqg wkh Lpsolfdwlrqv ri Vhsd0
udeoh Xwlolw|1 Vrxwkhuq Hfrqrplf Mrxuqdo 6:/ 75607661
Sroodn/ U1D1 dqg Zdohv/ W1M1 +4<<5,1 Ghpdqg V|vwhp Vshflfdwlrq dqg Hvwlpdwlrq1
R{irug Xqlyhuvlw| Suhvv/ R{irug1
Vshqfh/ P1H1 +4<:9,1 Surgxfw Vhohfwlrq/ Il{hg Frvwv/ dqg Prqrsrolvwlf Frpshwl0
wlrq/ Uhylhz ri Hfrqrplf Vwxglhv 76/ 54:05691
Vyhuljhv Wxulvwuèg1 +4<<5,1 Ghq xwoçqgvnd wxulvphq l Vyhuljh1 Udssruw 4<<5=6
+LVVQ 443403:87,/ Vwrfnkrop1
54
Wxuqhu/ O1Z1/ Nxohqgudq/ Q1 dqg Ihuqdqgr/ K1 +4<<:,1 Wkh Xvh ri Frpsrvlwh
Qdwlrqdo Lqglfdwruv iru Wrxulvp Iruhfdvwlqj/ Wrxulvp Hfrqrplfv 6/ 63<064:1
Zlww/ V1I1 dqg Zlww/ F1D1 +4<<8,1 Iruhfdvwlqj Wrxulvp Ghpdqg= D Uhylhz ri
Hpslulfdo Uhvhdufk1 Lqwhuqdwlrqdo Mrxuqdo ri Iruhfdvwlqj 44/ 77:07:81
55
© Copyright 2026 Paperzz