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grjhqrxvo| rq prgho sdudphwhuv= erwk duh htxdo wr }re E n ? ! 1 Wdnlqj wr
eh d jlyhq whfkqlfdo sdudphwhu +qrw hdvlo| dhfwhg e| srolf|, wkh frqfoxvlrq iurp wklv
prgho*v vwhdg| vwdwh lv wkdw wr surprwh orqj uxq jurzwk lq JGS dqg frqvxpswlrq shu
shuvrq rqh vkrxog wu| wr surprwh srsxodwlrq jurzwk$ Wkhuh duh vwurqj hpslulfdo uhdvrqv
zk| rqh zrxog eh yhu| fdxwlrxv zlwk vxfk d srolf|1 Zh kdyh vhhq hduolhu wkdw wkhuh vhhpv
wr eh d vwurqj qhjdwlyh fruuhodwlrq ehwzhhq srsxodwlrq jurzwk udwhv dqg ohyhov ri JGS
shu zrunhu +dfurvv frxqwulhv,1 Wkh qh{w vxevhfwlrq zloo ghprqvwudwh dovr d whqghqf| wr
qhjdwlyh fruuhodwlrq ehwzhhq srsxodwlrq jurzwk udwhv dqg jurzwk lq JGS shu zrunhu ru
shu fdslwd1
Hpslulfv iru vhpl0hqgrjhqrxv jurzwk
Dv zh vdz deryh/ iru d jlyhq {hg srsxodwlrq jurzwk udwh wkdw frxog eh uhdvrqdeoh
H{whuqdolwlhv dqg Jurzwk
D Frxuvh lq Pdfur
49
iru pdq| zhvwhuq frxqwulhv dqg iru uhdolvwlf sdudphwhu ydoxhv wkh vwhdg| vwdwh jurzwk udwh
ri wkh vhpl0hqgrjhqrxv jurzwk prgho vhhpv sodxvleoh1 Krzhyhu/ lw lv dovr d ihdwxuh ri
wkh prgho*v vwhdg| vwdwh suhglfwlrq wkdw d kljkhu jurzwk udwh lq wkh oderu irufh/ ru wkh
srsxodwlrq/ vkrxog jlyh kljkhu jurzwk lq JGS shu fdslwd1 Rqh zd| wr whvw wklv suhglfwlrq
frxog eh wr sorw dyhudjh dqqxdo jurzwk udwhv lq JGS shu zrunhu ryhu vrph shulrg djdlqvw
dyhudjh dqqxdo srsxodwlrq jurzwk udwhv ryhu wkh vdph shulrg dfurvv frxqwulhv1 Iljxuh <15
grhv h{dfwo| wkdw1 Lw lv edvhg rq gdwd iurp wkh Shqq Zruog Wdeoh 9131 Vlqfh wkh vwhdg|
vwdwh suhglfwlrq zh duh whvwlqj frqfhuqv wkh orqj uxq zh kdyh fkrvhq wr kdyh d shulrg dv
orqj dv srvvleoh1 Iru wklv uhdvrq zh gr qrw wdnh gdwd iurp wdeoh D fryhulqj 4<93 wr 4<<;
iru d odujh qxpehu ri frxqwulhv/ exw suhihu wr frqvlghu 4<84 wr 4<<; dqg dffhsw wkdw zh
kdyh gdwd iru ihzhu frxqwulhv1 Vwloo xvlqj rxu dg krf fulwhulrq iru gdwd txdolw| +JGS shu
zrunhu dw ohdvw dw 43( wkh XV ohyho lq 4<93, zh fdq jhw jurzwk udwhv lq JGS shu zrunhu
+} , dqg lq srsxodwlrq +? , iru 84 frxqwulhv1 Dv vdlg/ Iljxuh <15 sorwv } djdlqvw ? 1
gi
0.070
0.060
0.050
0.040
0.030
0.020
0.010
ni
0.000
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-0.010
Iljxuh <15= Dyhudjh dqqxdo jurzwk udwh lq uhdo JGS shu zrunhu djdlqvw
dyhudjh dqqxdo jurzwk udwh lq srsxodwlrq 4<8404<<;/ 84 frxqwulhv
Qrwh= Wkh ghwdlov ri wkh hvwlp dwhg olqh duh= j @313603187q / wkh vwdqgdug ghyldwlrq ri wkh vorsh hvwlp dwh lv 314967/ dqg U 2 @314;1 W kh
frxqwulhv vhohfwhg duh frxqwulhv zlwk dydlodeoh gdwd zklfk kdg d J G S shu zrunhu ri dw ohdvw 43 shufhqw ri XV J G S shu zrunhu lq 4<931
Vrxufh= Shqq Zruog Wdeoh 913
H{whuqdolwlhv dqg Jurzwk
D Frxuvh lq Pdfur
4:
Wkh jxuh vkrzv d udwkhu fohdu qhjdwlyh uhodwlrqvkls ehwzhhq srsxodwlrq jurzwk dqg
hfrqrplf jurzwk dfurvv frxqwulhv lq wkh frqvlghuhg shulrg1 Wkh ROV0hvwlpdwhg vwudljkw
olqh kdv d vljqlfdqw qhjdwlyh vorsh +wkh ghwdlov ri wkh hvwlpdwlrq duh uhsruwhg lq wkh jxuh
ohjhqg,1 Wklv frqwudglfwv wkh vwhdg| vwdwh suhglfwlrq ri wkh frqvlghuhg prgho ri vhpl0
hqgrjhqrxv jurzwk1 Rqh fdq frqfoxgh wkdw wkh jurzwk shuirupdqfhv ri wkh frqvlghuhg
frxqwulhv ryhu wkh frqvlghuhg shulrg duh qrw uhsuhvhqwdeoh e| hdfk frxqwu| vhsdudwho|
ehlqj lq vwhdg| vwdwh ri wkh prgho ri vhpl0hqgrjhqrxv jurzwk1 Wklv grhv qrw qhfhvvdulo|
phdq wkdw rqh vkrxog glvsrvh ri wkh prgho/ krzhyhu1
Iluvw/ lw lv qrw fohdu h{dfwo| zkdw nlqg ri duhd wkh prgho fryhuv/ d uhjlrq/ d frxqwu|/ ru
shukdsv wkh +ghyhorshg, zruog1 Wkh Vrorz prghov frqvlghuhg vr idu kdyh/ iru wkh hpslulfdo
whvwv/ lpsolflwo| ehhq dvvxphg wr fryhu d frxqwu|1 Lw zdv wkxv wdflwo| dvvxphg wkdw hdfk
frxqwu| lv uhodwlyho| krprjhqhrxv zlwk uhvshfw wr wkh ehkdylrudo dvvxpswlrqv lq wkh Vrorz
prghov dqg wkdw wkh uhodwlrqv ehwzhhq frxqwulhv/ h1j1 ri wudgh dqg fdslwdo pryhphqwv/ gr
qrw vxevwdqwldoo| dhfw hdfk frxqwu|*v jurzwk shuirupdqfh1 Lq wkh suhvhqw prgho zh kdyh
dq dgglwlrqdo ihdwxuh/ wkh surgxfwlyh h{whuqdolw|/ dqg lw lv qrw hdv| wr whoo ryhu krz zlgh
duhdv wkh dvvxphg h{whuqdo hhfwv vkrxog eh h{shfwhg wr uhdfk1 Li wkh upv lq rqh frxqwu|
fdq orrn ryhu wkh vkrxoghuv ri upv lq rwkhu frxqwulhv wkhq shukdsv wkh prgho vkrxog
eh frqvlghuhg wr fryhu wkh zruog1 Li wkh h{whuqdo hhfwv duh pruh orfdo/ lw fryhuv shukdsv
d uhjlrq ru d vpdoohu frxqwu|1 Lw lv wkhuhiruh qrw fohdu hlwkhu li wkh nlqg ri furvv frxqwu|
hylghqfh uhsruwhg lq Iljxuh <15 lv wkh prvw uhohydqw hylghqfh1
Vhfrqg/ wkh prgho zh frqvlghu kdv d vwhdg| vwdwh dqg lw kdv frqyhujhqfh wr wkh vwhdg|
vwdwh lq wkh orqj uxq1 Gxulqj wkh frqyhujhqfh shulrg wkhuh zloo eh d wudqvlwru| jurzwk lq
dgglwlrq wr wkh xqghuo|lqj +hqgrjhqrxv, vwhdg| vwdwh jurzwk/ dqg wkh wudqvlwru| jurzwk
ghshqgv qhjdwlyho| rq srsxodwlrq jurzwk mxvw dv lq wkh Vrorz prghov/ dqg iru wkh vdph
uhdvrq= d ghfuhdvh lq wkh udwh ri srsxodwlrq jurzwk sxoov lq wkh gluhfwlrq ri d kljkhu dowlwxgh
ri wkh vwhdg| vwdwh jurzwk sdwk/ exw d orzhu jurzwk udwh dorqj lw +vhh htxdwlrq +4<,,1
H{whuqdolwlhv dqg Jurzwk
D Frxuvh lq Pdfur
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Khqfh/ gxulqj wkh wudqvlwlrq wr wkh qhz vwhdg| vwdwh jurzwk sdwk wkhuh zloo iru vrph wlph
eh d srvlwlyh wudqvlwru| frqwulexwlrq wr jurzwk dulvlqj iurp wkh orzhu srsxodwlrq jurzwk1
Ixuwkhupruh/ frqyhujhqfh lq wkh prgho zh frqvlghu pd| eh txlwh vorz gxh wr wkh suhvhqfh
ri wkh surgxfwlyh h{whuqdolw|1 Dv frphv forvh wr rqh/ frqyhujhqfh zloo eh yhu| vorz1
+H{huflvhv 4 dqg 5 dw wkh hqg ri wkh fkdswhu zloo dvn |rx wr orrn pruh lqwr wkh frqyhujhqfh
surfhvv/ erwk qxphulfdoo| dqg dqdo|wlfdoo|,1 Zkdw zh kdyh irxqg lq Iljxuh <15 pd| eh
lqwhusuhwhg dv dq h{suhvvlrq ri d orqj odvwlqj wudqvlwru| jurzwk wkdw vkrxog lqghhg ghshqg
qhjdwlyho| rq srsxodwlrq jurzwk dffruglqj wr rxu prgho1 Wkhuhiruh wkh slfwxuh grhv qrw
qhfhvvdulo| frqwudglfw wkh prgho/ exw lw grhv frqwudglfw wkdw wkh frqvlghuhg frxqwulhv
vhsdudwho| vkrxog hyroyh dffruglqj wr wkh vwhdg| vwdwh ri wkh prgho1
Wkhvh uhpdunv vhhp wr fdoo iru orqjhu uxq hpslulfdo hylghqfh wkdw grhv qrw jr dfurvv
frxqwulhv1 Lq Wdeoh <14 wkh 453 |hduv iurp 4;:3 wr 4<<3 kdyh ehhq glylghg lqwr wkh wzr
vl{w| |hduv shulrgv iurp 4;:3 wr 4<63/ dqg iurp 4<63 wr 4<<3 uhvshfwlyho|1 Iru hdfk ri 4:
frxqwulhv +wkh frxqwulhv iru zklfk gdwd duh dydlodeoh, wkh wdeoh uhsruwv iru hdfk vxe0shulrg
wkh dyhudjh dqqxdo jurzwk udwh ri JGS shu fdslwd dqg wkh dyhudjh dqqxdo srsxodwlrq
jurzwk udwh1 Iru doo frxqwulhv hfrqrplf jurzwk lqfuhdvhg voljkwo| iurp wkh hduo| vxe0shulrg
wr wkh odwhu rqh/ zkloh iru doo frxqwulhv exw wzr srsxodwlrq jurzwk ghfuhdvhg1 Dovr li zh
frqvlghu udwkhu orqj shulrgv dqg vwd| zlwklq hdfk frxqwu| wkh hylghqfh vkrzv olwwoh vljq
wkdw jurzwk lq JGS shu shuvrq vkrxog eh d eorz xs ri srsxodwlrq jurzwk17
7
Wkhuh lv d frxqwhu dujxphqw wr wklv wkdw zh zloo srvwsrqh wr wkh qh{w fkdswhu zkhuh lw lv sduwlfxoduo|
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D Frxuvh lq Pdfur
Average annual
population growth rate
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Italy
Japan
Netherlands
New Zealand
Norway
Sweden
Switzerland
UK
USA
1870-1930
0.023
0.007
0.008
0.017
0.010
0.011
0.001
0.010
0.006
0.010
0.013
0.027
0.008
0.006
0.007
0.007
0.019
1930-1990
0.016
0.002
0.004
0.016
0.006
0.006
0.005
0.007
0.006
0.011
0.011
0.014
0.007
0.006
0.008
0.004
0.012
4<
Average annual growth
rate of GDP per capita
1870-1930
0.004
0.011
0.010
0.017
0.016
0.014
0.015
0.012
0.011
0.015
0.012
0.012
0.016
0.014
0.017
0.008
0.015
1930-1990
0.020
0.026
0.021
0.024
0.021
0.031
0.023
0.025
0.029
0.039
0.018
0.016
0.027
0.025
0.021
0.019
0.021
Wdeoh <14= Dyhudjh dqqxdo jurzwk udwhv lq srsxodwlrq dqg uhdo JGS shu
zrunhu lq 4: lqgxvwuldol}hg frxqwulhv/ 4;:404<<3
Vrxufh= Dqjxv P dgglvrq/ P rqlwrulqj wkh zruog hfrqrp| 4;5304<<5/ Sdulv = R HFG/ 4<<81
Vwloo zh fdqqrw frqfoxgh wkdw wkh prgho lv zurqj1 Lw frxog eh wkdw frqyhujhqfh dffruglqj
wr lw lv vr vorz wkdw lw wdnhv sodfh ryhu vxevhtxhqw vl{w| |hduv shulrgv vr wkdw wkh jhqhudo
slfwxuh irxqg lq Wdeoh <14 lv frpsdwleoh zlwk wudqvlwru| jurzwk1 Krzhyhu/ li frqyhujhqfh wr
vwhdg| vwdwh lv wkdw vorz wkhq wkh prgho*v vwhdg| vwdwh lv qrw yhu| ghvfulswlyh vr shukdsv
zh vkrxog frqvlghu wkh frqyhujhqfh surfhvv rxwvlgh vwhdg| vwdwh dv wkh prgho*v pdlq
suhglfwlrq1 Wklv lv h{dfwo| wkh shuvshfwlyh wdnhq lq wkh qh{w vhfwlrq1 Zh zloo pdnh dq
dvvxpswlrq wkdw pdnhv wkh frqyhujhqfh shulrg qrw mxvw yhu| orqj/ exw hwhuqdo1 Zh zloo
wkhq xvh wkh prgho*v hyhu odvwlqj/ rxwvlgh vwhdg| vwdwh ehkdylru dv dq dssur{lpdwlrq ri d
mxvw yhu| orqj odvwlqj frqyhujhqfh1
6
Hqgrjhqrxv Jurzwk
Lq wkh lpsruwdqw H{huflvh 5 |rx duh dvnhg wr qg dq dqdo|wlfdo h{suhvvlrq iru wkh udwh ri
frqyhujhqfh iru +| dffruglqj wr wkh deryh frqvlghuhg prgho zlwk 1 Iru wkh fdvh zkhuh
H{whuqdolwlhv dqg Jurzwk
D Frxuvh lq Pdfur
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srsxodwlrq jurzwk lv yhu| vpdoo/ ? ' f/ wkh udwh lv b ' E kE B1 Wklv yhulhv wkh
deryh fodlp wkdw d odujh +ehorz rqh, lpsolhv yhu| vorz frqyhujhqfh1 Ehorz zh zloo vhw
? ' f/ vlqfh zh qrz wdnh wkh ylhz wkdw ryhu shulrgv ri lqwhuhvw/ olnh fhqwxulhv/ srsxodwlrq
jurzwk lv qrw wkh idfwru wkdw fdxvhv hfrqrplf jurzwk1 Wkh vl}h ri wkh oderu irufh lv wkhq
frqvwdqw/ htxdo wr u vd|1 Wkh lghd lv wr frqvlghu wkh jurzwk prgho ri wklv fkdswhu zlwk
' 1 Wklv jlyhv d }hur udwh ri frqyhujhqfh dqg dq hyhuodvwlqj frqyhujhqfh surfhvv1 Zh
frqvlghu wkh hfrqrplf hyroxwlrq wkdw uhvxowv wr eh ri lqwhuhvw ehfdxvh lw dssur{lpdwhv wkh
hyroxwlrq wkdw zrxog uhvxow iurp d odujh/ exw ohvv wkdq xqlw|/ 1 Wkh g|qdplfv ri wkh
frqvlghuhg prgho zlwk '  lv wkxv ri lqwhuhvw ehfdxvh lw lv forvh wr/ dqg uhdvrqdeo|
uhsuhvhqwdwlyh iru/ wkh g|qdplfv wkdw zrxog dulvh zlwk d odujh ehorz rqh zklfk zrxog
jlyh d yhu| orqj odvwlqj frqyhujhqfh/ exw qrw dq hyhuodvwlqj rqh18
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dovr lq vrph ghqrplqdwruv/ dqg vhyhudo h{suhvvlrqv zhuh phdqlqjohvv iru ' 1 Khqfh zh
fdqqrw uhxvh wkh deryh dqdo|vlv1 Iru zkdw zh glg lq Vhfwlrq 4/ rq wkh rwkhu kdqg/ wkh
dvvxpswlrq rq zdv qrw lpsruwdqw/ vr wkh h{suhvvlrqv iru wkh uhqwdo udwhv zh irxqg wkhuh
dqg wkh dvvrfldwhg wkhru| ri wkh lqfrph glvwulexwlrq duh dovr uhohydqw zkhq ' 1 Zlwk
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wkdw ( " lv ri lqwhuhvw1 Wkhuh lv qr uhdvrq wr
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iurp +6,/ zlwk ' / zkloh wkh vhfrqg htxdwlrq lv wkh xvxdo fdslwdo dffxpxodwlrq htxdwlrq
uhvxowlqj iurp +;, dqg +<,1 Wkh prgho*v odvw htxdwlrq +43, kdv ehhq uhsodfhg e| u| ' u1
Qrwh wkdw lq +54, zh kdyh xvhg wkh ghqlwlrq u3k 1 Wklv lv d elw ri dq dexvh ri
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Zh dsso| wklv qrwdwlrq ehfdxvh wkh prgho zh frqvlghu lv vr riwhq uhihuuhg wr dv wkh DN0
prgho wkdw lw zrxog eh d slw| qrw wr kdyh dq DN0h{suhvvlrq iru wkh djjuhjdwh surgxfwlrq
ixqfwlrq1 D EN0prgho zrxog qrw eh wkh vdph1
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yduldeohv lqwr shu zrunhu whupv/ jlyhv +| ' &| 1 Glylglqj dovr rq erwk vlghv ri wkh fdslwdo
dffxpxodwlrq htxdwlrq +55, e| u/ dqg lqvhuwlqj iru +| / wkhq jlyhv wkh wudqvlwlrq htxdwlrq=
&|n ' Er n  B &| +56,
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shu zrunhu &| / dqg khqfh lq fdslwdo g| 1 Vlqfh +| lv d frqvwdqw wlphv &| / dovr wkh jurzwk
H{whuqdolwlhv dqg Jurzwk
D Frxuvh lq Pdfur
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wkh yduldeohv zh duh lqwhuhvwhg lq1 Lq fdvh r B : f/ dv zh xvxdoo| wklqn ri/ wkh jurzwk
udwh }e lv srvlwlyh1 Wkh pdlq frqfoxvlrq iurp wkh prgho/ dqg rqh wkdw kdv wkh reylrxv
lpsolfdwlrqv iru hfrqrplf srolf|/ lv wkdw d kljkhu vdylqjv +lqyhvwphqw, udwh r jlyhv ulvh wr
dq hyhuodvwlqj kljkhu jurzwk udwh lq JGS dqg frqvxpswlrq shu shuvrq1 Wkh glhuhqfh wr
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odujh vpdoohu wkdq rqh/ zh vkrxog uhphpehu wkdw vwulfwo| vshdnlqj wkh fruuhfw vwdwhphqw
lv wkdw dq lqfuhdvh lq r jlyhv d yhu| orqj odvwlqj wudqvlwru| jurzwk lq JGS shu shuvrq1
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ohdg wr d orzhu udwh ri ghsuhfldwlrq/ dqg d orzhu udwh ri ghsuhfldwlrq ohdgv/ lq wkh prgho
ri hqgrjhqrxv jurzwk/ wr d shupdqhqwo| kljkhu jurzwk udwh lq JGS shu zrunhu +uhdoo| wr
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