ㄽࠉࠉᩥ

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀ㔝ࠉᮧࠉࠉ┈ࠉኵѽ㸦ྡྂᒇᏛ㝔኱Ꮫ⤒῭Ꮫ㒊ᩍᤵ㸧ᖹࠉ஭ࠉࠉ೺ࠉஅѽѽ㸦㤶ᕝ኱Ꮫ⤒῭Ꮫ㒊ᩍᤵ㸧㸯㸬ࡣࡌࡵ࡟
ࠉ㏆ᖺ㸪ྛᅜ࡟࠾ࡅࡿᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜ࡢᅉᯝ㛵ಀ࡟㛵ࡍࡿᐇド◊✲ࡀᩘከࡃᏑᅾࡍࡿࠋᨻᗓᨭฟ࡜
ᨻᗓ཰ධࡢᕪࡣ㸪㈈ᨻ㉥Ꮠ࡛࠶ࡿࠋᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢᅉᯝ㛵ಀ࡟㛵ࡍࡿᐇド◊✲࡛ࡣ㸪࢔࣓ࣜ࢝ྜ⾗ᅜࡢ᫬⣔ิࢹ࣮ࢱࢆ౑⏝ࡋࡓ◊✲ㄽᩥࡀከ࠸ࠋAnderson, Wallace and Warner㸦1986㸧
㸪Blackley㸦1986㸧
㸪Manage and Marlow㸦1986㸧
㸪von Furstenberg,Green and Jeong㸦1986㸧
㸪Ram㸦1988㸧➼ࡢ◊✲ࡣ㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢ᫬⣔ิࢹ࣮ࢱࡀᐃᖖ࡛࠶ࡿࡇ࡜ࢆ௬ᐃࡋ࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃࢆᐇ⾜ࡋ࡚࠸ࡿࠋ
ᚑࡗ࡚㸪ࡇࢀࡽࡢ◊✲࡛ࡣ㸪༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃࡢศᯒࡀ⾜ࢃࢀ࡞࠿ࡗࡓࠋࡑࡢᚋࡢ◊✲࡛ࡣ㸪
Miller and Russek㸦1990㸧
㸪Bohn㸦1991㸧
㸪Jones and Joulfaian㸦1991㸧
㸪Hoover and Sheffrin㸦1992㸧
㸪
Baghestani and McNown㸦1994㸧
㸪Payne㸦1998㸧➼ࡢࡼ࠺࡟㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡟㛵ࡍࡿ༢఩᰿᳨ᐃ
࡜ඹ࿴ศࡢ᳨ᐃࡀ⾜ࢃࢀ㸪ࡇࢀ࡟ᇶ࡙ࡁᅉᯝ㛵ಀࢆศᯒࡋ࡚࠸ࡿࠋࡲࡓ㸪≉࡟᭱㏆࡛ࡣ㸪࢔࣓ࣜ࢝ྜ⾗ᅜ௨እࡢ௚ࡢඛ㐍ㅖᅜࡸ㸪㈈ᨻ㉥Ꮠࡢၥ㢟ࢆᢪ࠼࡚࠸ࡿⓎᒎ㏵ୖᅜࡢࢹ࣮ࢱࢆ⏝࠸ࡓྠᵝࡢศᯒࡶᏑᅾࡍ
ࡿࠋࡋ࠿ࡋ㸪᪥ᮏ࡟࠾ࡅࡿᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢᅉᯝ㛵ಀ࡟㛵ࡍࡿᐇド◊✲ࡣ㸪Owoye㸦1995㸧ࡸChang, Liu and Caudill㸦2002㸧ࢆ㝖࠸࡚㸪㠀ᖖ࡟ᩘᑡ࡞࠸≧ែ࡛࠶ࡿࠋࠉNarayan and Narayan㸦2006㸧ࡣ㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢ2 ኚᩘ࡟GDPࢆຍ࠼࡚3 ኚᩘࡢศᯒࢆ⾜ࡗ࡚࠸ࡿࠋᨻᗓᨭฟ࡜GDPࡢ㛫ࡢᅉᯝ㛵ಀࡢศᯒࡶ㠀ᖖ࡟⭾኱࡞ᩘ࡟࡞ࡾ㸪࣡ࢢࢼ࣮㸦Wagner㸧ἲ๎ࡢศᯒ
࡜ࡋ࡚▱ࡽࢀ࡚࠸ࡿࠋHondroyiannis and Papapetrou㸦1995㸧ࡢཧ⪃ᩥ⊩ࡢࣜࢫࢺࢆཧ↷ࡉࢀࡓ࠸ࠋ୺࡞
ၥ㢟ࡣ㸪࣡ࢢࢼ࣮ἲ๎ࡢ௬ㄝ㸦GDP࠿ࡽᨻᗓᨭฟ࡬ࡢᅉᯝ㛵ಀ㸧࡜ࢣ࢖ࣥࢬ௬ㄝ㸦ᨻᗓᨭฟ࠿ࡽGDP࡬ࡢᅉᯝ㛵ಀ㸧ࡢ࠸ࡎࢀࡀᨭᣢࡉࢀࡿ࠿ࢆศᯒࡋ࡚࠸ࡿࠋ3 ኚᩘࡢࣔࢹࣝࡣ㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜ࡢᅉᯝ
㛵ಀ࡜㸪ᨻᗓᨭฟ࡜GDP࡜ࡢᅉᯝ㛵ಀࢆ⤫ྜࡋࡓᯟ⤌ࡳ࡛ศᯒ࡛ࡁࡿࠋ᪥ᮏ࡟࠾ࡅࡿ3 ኚᩘࡢࣔࢹ࡛ࣝ
ࡢᅉᯝ㛵ಀࡢศᯒࡣከࡃ࡞࠸ࠋ≉࡟㸪ୖグࡢᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜ࡢᅉᯝ㛵ಀ㸪࠾ࡼࡧ㸪ᨻᗓᨭฟ࡜
ѽ
1957 ᖺ⏕ࡲࢀࠋ⚄ᡞၟ⛉኱Ꮫ኱Ꮫ㝔⤒῭Ꮫ◊✲⛉༤ኈᚋᮇㄢ⛬༢఩ྲྀᚓ㏥Ꮫࠋ༤ኈ㸦⤒῭Ꮫ㸧ࠋ⚄ᡞၟ⛉኱Ꮫຓᡭ㸪㥴Ἑྎ኱Ꮫ⤒῭Ꮫ㒊ㅮᖌ࣭ຓᩍᤵ㸪ྡྂᒇᏛ㝔኱Ꮫ⤒῭Ꮫ㒊ຓᩍᤵࢆ⤒࡚㸪1999 ᖺ 4 ᭶ྡྂᒇᏛ㝔኱Ꮫ⤒῭Ꮫ㒊ᩍᤵࠋᑓᨷࡣ㸪ィ㔞⤒῭Ꮫ࣭㈈ᨻᏛࠋᡤᒓᏛ఍ࡣ㸪᪥ᮏ⤒῭Ꮫ఍㸪᪥ᮏ⤫ィᏛ఍㸪᪥ᮏ㈈ᨻᏛ఍ࠋ
ѽѽ
1961 ᖺ⏕ࡲࢀࠋ⚄ᡞၟ⛉኱Ꮫ኱Ꮫ㝔⤒῭Ꮫ◊✲⛉༤ኈᚋᮇㄢ⛬༢఩ྲྀᚓ㏥Ꮫࠋ1990 ᖺ⇃ᮏᏛᅬ኱Ꮫ⤒῭Ꮫ㒊ㅮᖌ㸪1996 ᖺ㤶ᕝ኱Ꮫ⤒῭Ꮫ㒊ຓᩍᤵ㸪2001 ᖺ㤶ᕝ኱Ꮫ⤒῭Ꮫ㒊ᩍᤵ㸪⌧ᅾ࡟⮳ࡿࠋᑓᨷࡣබඹ⤒῭ᏛࠋᡤᒓᏛ఍ࡣ㸪᪥ᮏ⤒῭Ꮫ఍㸪᪥ᮏ㈈ᨻᏛ఍㸪᪥ᮏᆅ᪉㈈ᨻᏛ఍ࠋ

̿ 13 ̿

఍ィ᳨ᰝ◊✲ࠉNo.44㸦2011.9㸧

GDP࡜ࡢᅉᯝ㛵ಀࡢᩥ⊩࡟ᇶ࡙ࡃ◊✲ࡣ࡯࡜ࢇ࡝࡞࠸≧ែ࡛࠶ࡿࠋ
ࠉᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜ᐇ㉁GDPࡢ3 ኚᩘ࡟ᑐࡋ࡚㸪᪥ᮏ࡟࠾ࡅࡿᅉᯝ㛵ಀࡢศᯒࢆ⾜ࡗࡓㄽᩥࡣᑡ࡞
࠸≧ែ࡛࠶ࡿࠋࡓࡔࡋ㸪Ώ㎶࣭⸭཭࣭ఀ⸨㸦2010㸧ࡣ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓ⛯཰㸪ᐇ㉁GDPࡢ3 ኚᩘ࡟㛵ࡍࡿ࣋ࢡࢺࣝ⮬ᕫᅇᖐ㸦VAR㸧ࣔࢹࣝࢆ㸪1965 ᖺ➨ 1 ᅄ༙ᮇ࠿ࡽ2004 ᖺ➨ 4 ᅄ༙ᮇࡲ࡛ࡢࢹ࣮
ࢱࢆ⏝࠸࡚ศᯒࡋ࡚࠸ࡿࠋΏ㎶࣭⸭཭࣭ఀ⸨ࡣ㸪ᅉᯝ㛵ಀࡸศᩓศゎࡢศᯒࢆ⾜ࢃࡎ㸪VARࢆ⏝࠸࡚࢖ࣥࣃࣝࢫ཯ᛂࢆศᯒࡋ࡚㈈ᨻ஌ᩘ࡟ࡘ࠸᳨࡚ウࡋ࡚࠸ࡿࠋࡲࡓ㸪㧗ᶫ㸦2010㸧ࡣ㸪1 ேᙜࡓࡾᐇ㉁ᨻᗓᨭ
ฟࡢᑐᩘ್㸪1 ேᙜࡓࡾᐇ㉁ᨻᗓ⣧཰ධࡢᑐᩘ್㸪1 ேᙜࡓࡾᐇ㉁GDPࡢᑐᩘ್㸪㛗ᮇ฼Ꮚ⋡ࡢࢹ࣮ࢱ࡟
ᑐࡋ࡚㸪༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃࢆ⾜ࡗ࡚㸪2 ಶࡢඹ࿴ศ㛵ಀࢆᚓ࡚࠸ࡿࠋࡇࢀࡽࡢ⤖ᯝ࡟ᇶ࡙࠸࡚࣋ࢡ
ࢺࣝㄗᕪಟṇ⮬ᕫᅇᖐࣔࢹࣝ㸦VECM㸧࡛࢖ࣥࣃࣝࢫ཯ᛂࢆィ ࡋ࡚㸪㈈ᨻ஌ᩘ࡟ࡘ࠸᳨࡚ウࡋ࡚࠸ࡿࠋ
㧗ᶫࡢศᯒᮇ㛫ࡣ㸪1990 ᖺ➨ 1 ᅄ༙ᮇ࠿ࡽ2008 ᖺ➨ 4 ᅄ༙ᮇࡲ࡛ࡢᮇ㛫࡛࠶ࡿࠋࠉᮏㄽᩥࡢ┠ⓗࡣ㸪᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜GDP࡟ࡼࡿ⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀࢆศᯒࡍࡿࡇ࡜࡛࠶ࡿࠋᅜ
ᐙ㈈ᨻࡣ㸪ᅜࡢ୍⯡఍ィண⟬ࡢỴ⟬್ࢆ⏝࠸࡚ィ⟬ࡉࢀࡓᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡛ᤊ࠼ࡿࠋᮏㄽᩥ࡛ࡣ㸪᪥ᮏᅜࡢ୍⯡఍ィண⟬࡟࠾ࡅࡿ1955 ᖺᗘ࠿ࡽ2008 ᖺᗘࡲ࡛ࢆศᯒᮇ㛫࡜ࡋ࡚㸪ᅜᐙ㈈ᨻ࡛ᤊ࠼ࡓᨻᗓᨭ
ฟ࡜ᨻᗓ཰ධ࠾ࡼࡧGDPࡢ࣋ࢡࢺࣝ⮬ᕫᅇᖐ㸦VAR㸧ࣔࢹࣝ࡟࠾࠸࡚㸪ࡇࡢ3 ኚᩘ࡟㛵ࡍࡿᅉᯝ㛵ಀࢆ
Grangerࡢᅉᯝ㛵ಀࢆ⏝࠸࡚ศᯒࢆ⾜࠺ࠋᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜GDPࡢ᫬⣔ิࢹ࣮ࢱ࡟ࡘ࠸࡚ࡑࢀࡒࢀ
༢఩᰿ࡢ᳨ᐃࢆ⾜࠸㸪ḟ࡟㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜GDPࡢ3 ኚᩘ࡟㛵ࡋ࡚Engle and Granger㸦1987㸧ࡢඹ࿴ศ᳨ᐃࢆ⾜࠺ࠋඹ࿴ศ᳨ᐃ࡟ࡣ㸪Johansen㸦1991㸧ࡢ᪉ἲࡶ࠶ࡿࠋZhou㸦2001㸧ࡣ㸪Engle andGranger᳨ᐃ࡜Johansen᳨ᐃࡢ᪉ἲࢆࣔࣥࢸ࣭࢝ࣝࣟᐇ㦂࡛ẚ㍑ࢆ⾜࠸㸪᳨ฟຊ࡜ࢧ࢖ࢬࢆᑻᗘ࡜ࡋ࡚⏝࠸࡚㸪ᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜ࡟ࡣEngle and Granger᳨ᐃࡢ᪉ἲࡀⰋ࠸࡜ࡋ࡚࠸ࡿࠋᮏㄽᩥࡢᖺḟࢹ࣮
ࢱᩘࡣ54 ಶ࡛࠶ࡿࡢ࡛㸪Engle and Grangerࡢ᪉ἲࢆ⏝࠸ࡿࠋࠉศᯒᑐ㇟ࡢ3 ኚᩘࡀ༢఩᰿ࢆᣢࡘሙྜ࡟ࡣ㸪Engle and Grangerࡢඹ࿴ศ᳨ᐃࢆ⏝࠸࡚ᨻᗓᨭฟ࡜ᨻᗓ
཰ධ࡜GDPࡀ㛗ᮇⓗ࡞ᆒ⾮㛵ಀ࡟࠶ࡿ࠿࡝࠺࠿ࢆศᯒࡍࡿࠋࡑࡋ࡚㸪ࡶࡋ3 ኚᩘ㛫࡛ඹ࿴ศࡢ㛵ಀࡀᏑᅾࡍࡿ࡞ࡽࡤ㸪ㄗᕪಟṇࣔࢹࣝࢆ᥎ᐃࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪㛗ᮇ࡟࠾ࡅࡿᨻᗓᨭฟ࡜ᨻᗓ཰ධ࡜ࡢᅉᯝ㛵ಀࢆศᯒࡍࡿࠋ3 ኚᩘ㛫࡛ඹ࿴ศࡢ㛵ಀࡀᏑᅾࡋ࡞࠸ሙྜ࡟ࡣ㸪ྛኚᩘ࡟ࡘ࠸࡚1 ᅇࡢ㝵ᕪࢆ࡜ࡾ㸪VARࣔࢹࣝࢆ᥎ᐃࡍࡿࡇ࡜࡟ࡼࡗ࡚Grangerࡢᅉᯝᛶ᳨ᐃࢆ⾜࠺ࠋࡇࢀ࡟ࡼࡾ㸪3 ኚᩘࡢ୰࠿ࡽ2 ኚᩘࢆ㑅ࢇ࡛▷ᮇࡢᅉᯝ㛵ಀࢆㄪ࡭ࡿࡇ࡜ࡀ࡛ࡁࡿࠋᚑ᮶ࡢ᪥ᮏㄒ࡛᭩࠿ࢀࡓᅉᯝ㛵ಀࡢ◊✲࡛ࡣ㸪㔠⼥⤒῭ࢆศᯒᑐ㇟࡜ࡋ࡚㸪ඹ࿴ศ᳨ᐃࢆ↓どࡋࡓศᯒࡶከ࠸ࠋ
ࠉᮏㄽᩥࡢᵓᡂࡣ㸪௨ୗࡢ㏻ࡾ࡛࠶ࡿࠋࡲࡎ➨ 2 ⠇㸦2.㸧࡛ࡣ㸪ศᯒ࡛⏝࠸ࡿ༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃ࡟
ࡘ࠸࡚ㄝ᫂ࡋ࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃࢆ⾜࠺ࡓࡵࡢkḟࡢ࣋ࢡࢺࣝ⮬ᕫᅇᖐࣔࢹࣝVAR㸦k㸧ࢆㄝ᫂ࡍࡿࠋ
ࡉࡽ࡟㸪౑⏝ࡍࡿࢹ࣮ࢱ࡟ࡘ࠸࡚ㄝ᫂ࡍࡿࠋࡑࡋ࡚➨ 3 ⠇㸦3.㸧࡟࠾࠸࡚㸪ᐇドศᯒࡢ⤖ᯝ࡟ࡘ࠸࡚㆟ㄽࡍࡿࠋ᭱ᚋ࡟㸪➨ 4 ⠇㸦4.㸧࡛⤖ㄽ࡜௒ᚋࡢㄢ㢟ࢆ㏙࡭ࡿࠋ㸰㸬ศᯒ᪉ἲ࡜ࢹ࣮ࢱ
2. 1 ࢹ࣮ࢱ࡜グྕࠉᨻᗓ཰ධ㸻ᅜࡢṓධѸබമ㔠཰ධ㸪ᨻᗓᨭฟ㸻ᅜࡢṓฟѸᅜമ㈝࡜ࡋ࡚㸪ࡑࢀࡒࢀGDPࢹࣇ࣮ࣞࢱ࣮࡛
ᐇ㉁໬ࢆ⾜࠺ࠋᨻᗓ཰ධ࡜ᨻᗓᨭฟࡢᐃ⩏ࡣ㸪ᇶ♏ⓗ㈈ᨻ཰ᨭࡢᐃ⩏ࢆ⪃៖ࡋ࡚࠸ࡿࠋᐇ㉁ࡢᨻᗓᨭฟ㸪
ᐇ㉁ࡢᨻᗓ཰ධ㸪ᐇ㉁GDPࡢࡑࢀࡒࢀࡢ⮬↛ᑐᩘࢆྲྀࡾ㸪ࡑࡢグྕࢆࡑࢀࡒࢀge㸪gr㸪gdp࡜ࡍࡿࠋࠉᮏㄽᩥࡢᐇドศᯒࡣ㸪ᨻᗓ㸦ᅜ㸧ࡢ୍⯡఍ィࢆศᯒᑐ㇟࡜ࡋ㸪1955 ᖺᗘ࠿ࡽ2008 ᖺᗘࡲ࡛ࡢᖺᗘࢹ࣮
ࢱࢆ౑⏝ࡍࡿࠋୖ㏙ࡢࡼ࠺࡟㸪ᨻᗓ཰ධࡣṓධ⥲㢠࠿ࡽබമ㔠཰ධࢆᕪࡋᘬ࠸ࡓࡶࡢ㸪ࡑࡋ࡚ᨻᗓᨭฟࡣ

̿ 14 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀṓฟ⥲㢠࠿ࡽᅜമ㈝ࢆᕪࡋᘬ࠸ࡓࡶࡢ࡛࠶ࡿࠋࡇࢀࡽࡢࢹ࣮ࢱ㸦ྡ┠್㸧ࡣࡍ࡭࡚㸪㈈ົ┬ࡢࠗ㈈ᨻ⤫ィ࠘ࡼࡾ㸪ᨻᗓ୍⯡఍ィࡢỴ⟬㢠࡜ࡋ࡚ồࡵࡽࢀࡿࠋ࡞࠾㸪㏆ᖺࡢྠࢹ࣮ࢱ࡟ࡘ࠸࡚ࡣ㸪㈈ົ┬ࡢ࣮࣒࣮࣍࣌
ࢪ࠿ࡽධᡭ࡛ࡁࡿࠋࡲࡓ㸪ᨻᗓ཰ධ࡜ᨻᗓᨭฟࡢኚᩘࢆᐇ㉁໬ࡍࡿࡓࡵࡢGDPࢹࣇ࣮ࣞࢱ࣮ࡣ㸪ࠗᅜẸ⤒῭ィ⟬ᖺሗ࠘
㸦ෆ㛶ᗓ⤒῭♫఍⥲ྜ◊✲ᡤ㸧࠿ࡽᚓࡽࢀࡿࠋࡉࡽ࡟㸪ᐇ㉁GDPࡢࢹ࣮ࢱࡶࡲࡓ㸪ࠗᅜẸ⤒῭ィ⟬ᖺሗ࠘ࡼࡾᚓࡽࢀࡿࠋ
ࠉࡇࡇ࡛㸪GDPࢹࣇ࣮ࣞࢱ࣮࡜ᐇ㉁GDPࡢࢹ࣮ࢱ࡟ࡘ࠸࡚㸪᭱㏆᫬Ⅼࡲ࡛ࡢࢹ࣮ࢱࡣ1993 ᖺᨵゞࡢᅜẸ⤒῭ィ⟬య⣔㸦93SNA㸧ࡼࡾồࡵࡽࢀࡿࠋ࡜ࡇࢁࡀ㸪ࡇࡢ93SNAࡢࢹ࣮ࢱࡣ㐳ཬࡋ࡚1980 ᖺᗘࡲ࡛ࡋ࠿බ⾲ࡉࢀ࡚࠸࡞࠸ࠋ୍᪉㸪ᅜẸ⤒῭ィ⟬࡟࠾ࡅࡿ68SNA࡛ࡣ㸪1955 ᖺᗘࡼࡾ࠸ࡎࢀࡢࢹ࣮ࢱࡶධᡭ
ࡍࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿࡀ㸪ࢹ࣮ࢱࡢ⤊ᮇࡣ1998 ᖺᗘ࡜࡞ࡗ࡚࠸ࡿࠋࡇࢀࡼࡾ㸪93SNA࡛ࡣ68SNAࡢෆᐜࡀኚ᭦ࡉࢀ࡚࠸ࡿࡓࡵ㸪ࢹ࣮ࢱࡢ୍㈏ᛶ࡟ၥ㢟ࡀ⏕ࡌࡿࡶࡢࡢ㸪㛗ᮇ࡟ࢃࡓࡿࢹ࣮ࢱࢆ☜ಖࡍࡿࡓࡵ
࡟㸪1955 ᖺᗘ࠿ࡽ1998 ᖺᗘࡲ࡛ࡢᮇ㛫࡟࠾࠸࡚ࡣ68SNAࡢࢹ࣮ࢱࢆ౑⏝ࡋ㸪1999 ᖺᗘ௨㝆ࡣ93SNA
ࡢࢹ࣮ࢱࢆ⏝࠸ࡿࡇ࡜࡟ࡍࡿࠋࡑࡇ࡛㸪GDPࢹࣇ࣮ࣞࢱ࣮࡜ᐇ㉁GDP࡟ࡘ࠸࡚ࡣࡑࢀࡒࢀ㸪68SNAࡢ
1990 ᬺᖺᇶ‽ࡢࢹ࣮ࢱ࡟ᇶ࡙ࡁ㸪⏿㎰㸦2005㸧࡜ྠᵝ࡟㸪68SNA࡟࠾ࡅࡿ1998 ᖺᗘࡢࢹ࣮ࢱࢆ93SNA
ࡢᙜヱࢹ࣮ࢱࡢఙࡧ⋡࡛ᘏ㛗ࡋ࡚᥎ィࡍࡿࡇ࡜࡟ࡼࡾ㸪68SNA࡜93SNAࡢࢹ࣮ࢱࢆ᥋⥆ࡍࡿࡇ࡜࡜ࡋࡓࠋ
2. 2 ༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃ
ࠉ༢఩᰿᳨ᐃࡣ㸪୺࡟༢఩᰿ࢆᖐ↓௬ㄝ࡜ࡍࡿADF᳨ᐃࢆ⏝࠸ࡿࠋHamori and Matsubayashi㸦2001㸧࡜Li㸦2001㸧࡟ᚑࡗ࡚㸪ᐃᩘ㡯ࡢࡳࡢᅇᖐᘧ㸦ࣔࢹࣝC㸧㸪ᐃᩘ㡯࡜ࢱ࢖࣒࣭ࢺࣞࣥࢻࢆྵࡴᅇᖐᘧ㸦ࣔࢹ
ࣝC&T㸧ࢆ⏝࠸࡚㸪ADF᳨ᐃࢆ⾜࠺ 1㸧ࠋADF᳨ᐃ࡛ࡣ㸪ᖐ↓௬ㄝࡣ༢఩᰿ࢆᣢࡘ࡜࠸࠺ࡇ࡜࡛࠶ࡿࠋ
ADF᳨ᐃ࡛ࡣ㸪ᣑᙇ㡯ࡢࣛࢢᩘࡣ㸪㉥ụࡢ᝟ሗ㔞ᇶ‽㸦Akaike Information Criterion, AIC㸧࡜Schwarzࡢ᝟ሗ㔞ᇶ‽㸦Schwarz Information Criterion, SIC㸧ࢆ⏝࠸࡚㑅ᢥࡍࡿࠋࠉᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ࡢᨻᗓᨭฟ㸦ge㸧㸪ᐇ㉁ࡢᨻᗓ཰ධ㸦gr㸧
㸪ᐇ㉁GDP㸦gdp㸧ࡢ3 ኚᩘ࡟㛵ࡋ࡚㸪௨ୗࡢ⌮⏤࡛㸪Engle and Granger᳨ᐃࢆ⏝࠸࡚ඹ࿴ศ᳨ᐃࢆ⾜࠺ 2㸧ࠋඹ࿴ศ᳨ᐃ࡟ࡣ㸪◊✲ㄽᩥ࡛㢖⦾࡟฼⏝ࡉࢀࡿ᳨ᐃ࡜ࡋ࡚Engle and Granger㸦1987㸧ࡢ᪉ἲ࡜Johansen㸦1991㸧ࡢ᪉ἲࡀ࠶ࡿࠋZhou㸦2001㸧ࡣ㸪ࣔࣥࢸ࣭࢝ࣝࣟᐇ㦂࡟ࡼࡾEngle and Granger᳨ᐃ࡜Johansen᳨ᐃ࡜ࢆ᳨ฟຊࡸࢧ࢖ࢬࡢᑻᗘࢆ⏝࠸࡚ẚ㍑ࢆ⾜ࡗ࡚࠸ࡿࠋࡑࡢ⤖ᯝ࡜ࡋ࡚㸪ᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜ࡟ࡣEngle and Granger᳨ᐃࢆ⏝࠸ࡿࡇ࡜ࢆ⸀ࡵ࡚࠸ࡿࠋᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜ㸪Johansen᳨ᐃࡣ㸪Engle and Granger᳨ᐃ࡜ẚ㍑ࡍࡿ࡜㸪᳨ฟຊࡀపࡃ㸪ࢧ࢖ࢬࡢṍࡳࡀࡼࡾ኱ࡁ࠸ࠋᮏㄽᩥࡢࢹ࣮ࢱᩘࡣ54 ಶ࡛࠶ࡾ㸪ࡇࡢࢹ࣮ࢱ࠿ࡽᚓࡽࢀࡿ
ᶆᮏࡣ඾ᆺⓗ࡞ᑠᶆᮏ࡛࠶ࡿࠋ
ࠉ3 ኚᩘge㸪gr㸪gdp࡟㛵ࡍࡿEngle and Granger᳨ᐃ࡛ࡣ㸪ඹ࿴ศᅇᖐ࡟࠾࠸࡚㸪ge㸪gr㸪gdpࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿ3ࡘࡢᅇᖐᘧ࡟ࡘ࠸࡚ඹ࿴ศ᳨ᐃࢆ⾜࠺ࠋ1ࡘࡢᅇᖐᘧ㸦౛࠼ࡤ㸪⿕ㄝ᫂ኚᩘࡀge㸪ㄝ᫂ኚᩘ1㸧ᐃᩘ㡯ࢆྵࡴࣔࢹࣝC࡜ᐃᩘ㡯࣭ࢺࣞࣥࢻࢆྵࡴࣔࢹࣝC&Tࡣ㸪kį 0i ¨y t–i + u t 㸪ࣔࢹࣝ C㸸ࠉ¨y t =Į 0 +㸦Ȗ 0 – 1㸧y t–1 + Ȉ i=1k
į 0i ¨y t–i + u t 㸪ࣔࢹࣝC&T㸸¨y t =Į 0 + ȕ 0 t +㸦Ȗ 0 – 1㸧y t–1 + Ȉ i=1
㸦Ȗ 0 –1㸧㸪į 0i㸦i=1㸪2㸪͐, k㸧ࡣ࡛࠶ࡿࠋࡇࡇ࡛㸪¨ࡣ㝵ᕪ₇⟬Ꮚ࡛࠶ࡾ㸪y t ࡣ᫬Ⅼt࡛ࡢኚᩘ࡛࠶ࡾ㸪y t–1 ࡣ¨y t ࡢ i ᮇ๓ࡢࣛࢢኚᩘ࡛࠶ࡾ㸪Į 0㸪ȕ 0㸪ᅇᖐᘧ࡟࠾ࡅࡿಀᩘ㸪u t ࡣㄗᕪ㡯࡛࠶ࡿࠋ༢఩᰿᳨ᐃ࡛ࡣ㸪ᖐ↓௬ㄝ H 0㸸Ȗ 0 =1㸪ᑐ❧௬ㄝ H 1㸸Ȗ 0 <1࡛࠶ࡿࠋH 0㸸Ȗ 0 =1ࡣ H 0㸸Ȗ 0 –1=0 ࡟ྠ್࡛࠶ࡿ࠿ࡽ㸪ᖐ↓௬ㄝ H 0㸸Ȗ 0 Ѹ 1=0 ࡟ᑐࡍࡿADF᳨ᐃ⤫ィ㔞ࡢ್ࢆィ⟬ࡍࡿࠋMacKinnon㸦1996㸧ࡢ᪉ἲ࡟ࡼࡿADF᳨ᐃ⤫ィ㔞ࡢ⮫⏺್࡜pk
į 0i ¨y t–i ࡀ࡞࠸ሙྜࢆ♧ࡍࠋ್ࢆ⏝࠸࡚㸪᳨ᐃࢆ⾜࠺ࠋk=0 ࡣ㸪ᣑᙇ㡯 Ȉ i=1
2㸧
Engle and Granger ᳨ᐃࡣ㸪ඹ࿴ศᅇᖐᘧ x t =a+b y t +c z t +u t ࡟OLSࢆ㐺⏝ࡋ࡚㸪ṧᕪet ࢆồࡵࡿࠋࡇࡇ࡛㸪a㸪b㸪cࡣඹ࿴ศಀᩘࡲࡓࡣඹ࿴ศ
ࣃ࣓࣮ࣛࢱ࣮㸪u t ࡣㄗᕪ㡯㸪x t࡜ y t࡜z t ࡣࡑࢀࡒࢀI㸦1㸧ኚᩘ࡛࠶ࡿࠋࡇࡢṧᕪ et ࡟ᑐࡋ࡚㸪ADF᳨ᐃࢆ㐺⏝ࡍࡿࠋADF᳨ᐃࡢᅇᖐᘧࡣ㸪k¨et=ȡet–1 + Ȉ i=1
į i ¨et–i + u t 㸪࡛࠶ࡿࠋࣛࢢḟᩘࡢ㑅ᢥ࡟ࡘ࠸࡚ࡣ㸪AIC࡜SICࡢ୧᝟ሗ㔞ᇶ‽࡛⾜࠸㸪AIC࡜SIC࡟ᇶ࡙ࡃ⤖ᯝࢆ♧ࡍࠋADFࡢ᳨ᐃ⤫ィ㔞ࡢp ್ࡣ㸪
MacKinnon㸦1996㸧ࡢ᪉ἲ࡟ࡼࡿࠋADF᳨ᐃࢆ⾜࠺ሙྜࡣ㸪⮫⏺್࡜ࡋ࡚Engle and Yoo㸦1987㸧➼ࡢศᕸ⾲ࢆ⏝࠸ࡿࡇ࡜ࡶ࡛ࡁࡿࠋ

̿ 15 ̿

఍ィ᳨ᰝ◊✲ࠉNo.44㸦2011.9㸧

ࡀgr㸪gdpࡢඹ࿴ศᅇᖐᘧ㸧ࡢ⤖ᯝࡔࡅ࡛࡞ࡃ㸪⿕ㄝ᫂ኚᩘࢆධࢀ᭰࠼ࡿࡇ࡜࡟ࡼࡗ࡚⤖ᯝࡢ㡹೺ᛶࢆぢࡿࡇ࡜ࡀ࡛ࡁࡿࠋ
2. 3 Grangerࡢᅉᯝ㛵ಀࠉ࣋ࢡࢺࣝ⮬ᕫᅇᖐࣔࢹࣝ㸦VARࣔࢹࣝ㸧ࢆ⏝࠸࡚㸪Grangerࡢᅉᯝ㛵ಀࢆศᯒࡍࡿࠋHamilton㸦1994㸧
࡟ࡼࡿ࡜㸪3 ㏻ࡾࡢ᪉ἲࡀ࠶ࡿࠋ➨ 1ࡢ᪉ἲࡣ㸪Ỉ‽ኚᩘ㸦ࣞ࣋ࣝኚᩘ㸧ࢆ⏝࠸࡚VARࡢᅇᖐࢆ⾜࠺ࡇ࡜࡛࠶ࡾ㸪➨ 2ࡢ᪉ἲࡣ㸪Ỉ‽ኚᩘࡢ1 㝵ࡢ㝵ᕪࢆྲྀࡾVARࡢᅇᖐࢆ⾜࠺ࡇ࡜࡛࠶ࡿࠋ➨ 3ࡢ᪉ἲࡣ㸪ศᯒᑐ㇟ࡢࢹ࣮ࢱ࡟ᑐࡋ࡚༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃࢆ⾜࠸㸪ࡑࡢ⤖ᯝ࡟ᇶ࡙࠸࡚㐺ษ࡞VARࣔࢹࣝࢆ㑅ᢥࡋ࡚ᅇᖐࢆ⾜࠺ࡇ࡜࡛࠶ࡿࠋ
ࠉࡇࡢㄽᩥ࡛ࡣ㸪➨ 3ࡢ᪉ἲ࡟ᇶ࡙࠸࡚VARࡢᅇᖐࢆ⾜࠺ࠋ༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃࡢ⤖ᯝ࡟ࡼࡗ࡚㸪௨ୗࡢࡼ࠺࡟඾ᆺⓗ࡞ศᯒᡭ㡰࡜ࡋ࡚3 ㏻ࡾࡢሙྜࡀ࠶ࡾᚓࡿࠋࡓࡔࡋ㸪3 ㏻ࡾ௨እࡢ౛እⓗ࡞ሙྜࡶ࠶
ࡾᚓࡿࠋ➨ 1࡟㸪༢఩᰿᳨ᐃ࡟ࡼࡾศᯒࢹ࣮ࢱࡀ඲࡚I㸦0㸧ࡢᐃᖖኚᩘ࡛࠶ࡿሙྜ࡟ࡣ㸪Ỉ‽ኚᩘࡢࢹ࣮
ࢱࢆ⏝࠸࡚VARࣔࢹࣝࡢᅇᖐࢆ⾜࠺ࠋ➨ 2࡟㸪༢఩᰿᳨ᐃ࡟ࡼࡾศᯒࢹ࣮ࢱࡀ඲࡚I㸦1㸧࡛༢఩᰿ࢆᣢ
ࡘ㠀ᐃᖖኚᩘ࡛࠶ࡾ㸪࠿ࡘ3 ኚᩘ㛫࡟ඹ࿴ศࡀᏑᅾࡋ࡞࠸ሙྜ࡟ࡣ㸪1 㝵ࡢ㝵ᕪኚᩘࢆ⏝࠸࡚VARࣔࢹࣝࡢᅇᖐࢆ⾜࠺ࠋ➨ 3࡟㸪༢఩᰿᳨ᐃ࡟ࡼࡾศᯒࢹ࣮ࢱࡀ඲࡚I㸦1㸧࡛༢఩᰿ࢆᣢࡘ㠀ᐃᖖኚᩘ࡛࠶ࡾ㸪࠿ࡘ3 ኚᩘ㛫࡟ඹ࿴ศࡀᏑᅾࡍࡿሙྜ࡟ࡣ㸪1 㝵ࡢ㝵ᕪኚᩘ࡜ㄗᕪಟṇ㡯ࢆ⏝࠸࡚VARࣔࢹࣝ㸦VEC㸪
Vector Error Correction㸧ࡢᅇᖐࢆ⾜࠺ࠋVECࣔࢹ࡛ࣝࡣ㸪ㄗᕪಟṇ㡯ࡣEngle and Granger᳨ᐃ࡟࠾ࡅ
ࡿඹ࿴ศᅇᖐࡢṧᕪ࠿ࡽᚓࡿࡇ࡜ࡀ࡛ࡁࡿࠋ࡞࠾㸪➨ 1࡜➨ 2ࡢᡭ㡰ࡣ㸪๓㏙ࡢHamilton㸦1994㸧ࡢ➨ 1
࡜➨ 2ࡢ᪉ἲ࡟㢮ఝࡋ࡚࠸ࡿࠋ
ࠉ௨ୗࡢkḟࡢVAR㸦k㸧ࣔࢹࣝࢆ⪃ᐹࡍࡿࠋx㸪y㸪zࡢ3 ኚᩘ࡟ࡘ࠸࡚㸪kkk
ȕ 1i ¨x t + Ȉ i=1
Ȗ 1i ¨y t + Ȉ i=1
į 1i ¨z t + u 1t , 㸦1-1㸧
¨x t =Į 1 + Ȉ i=1kkkȕ 2i ¨x t + Ȉ i=1
Ȗ 2i ¨y t + Ȉ i=1
į 2i ¨z t + u 2t , 㸦1-2㸧
¨y t =Į 2 + Ȉ i=1kkkȕ 3i ¨x t + Ȉ i=1
Ȗ 3i ¨y t + Ȉ i=1
į 3i ¨z t + u 3t , 㸦1-3㸧
¨z t =Į 3 + Ȉ i=1ࡢᐃᩘ㡯㸦Į1㸪Į2㸪Į3㸧ࢆྵࡴVAR㸦k㸧ࢆ⪃࠼ࡿࠋୖグࡢᘧ㸦1-1㸧Ѹ㸦1-3㸧ࡢVAR㸦k㸧࡛㸪Tࢆᶆᮏ
ᩘ࡜ࡋ࡚t=1,2,͐T,࡜ࡍࡿࠋ୍⯡࡟㸪ᶆᮏᩘTࡣᮏㄽᩥ࡛ศᯒᑐ㇟࡜ࡍࡿࢹ࣮ࢱᩘ 54ࡼࡾᑠࡉ࠸ᩘᏐ࡛࠶
'ࡢ࣋ࢡࢺࣝࡣ㸪E
㸦ut 㸧=0㸪3 ⾜ 3 ิࡢศᩓ࣭ඹศᩓ⾜ิ V㸦ut 㸧=E㸦utut'㸧=Ȉ 㸪ࡿࠋㄗᕪ㡯ut=㸦u1t㸪u2t㸪u3t 㸧=0㸦s > 0 㸧ࡢ௬ᐃࢆ‶ࡓࡍࡶࡢ࡜ࡍࡿࠋ⾜ิȈࡣ㠀ᑐゅ⾜ิ࡛࠶ࡾ㸪ㄗᕪ㡯ࡣྠࡌ᫬Ⅼ t ࡛஫࠸E㸦utu't–s㸧࡟┦㛵ࢆᣢࡗ࡚࠸ࡿࠋࡇࡇ࡛㸪฼⏝ྍ⬟࡞ࢹ࣮ࢱᩘࡀ54 ಶ࡛࠶ࡿࡇ࡜ࢆ⪃៖ࡋ࡚㸪k ࡣ᭱኱ࡢࣛࢢḟᩘ
ࢆ5࡜ࡋ࡚k =1,2,͐,5 ࡜ࡍࡿࠋk =1,2,͐,5ࡢ್࡟ᑐࡋ࡚㸪
㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢVAR㸦k㸧࡟࠾ࡅࡿAIC࡜
SICࡢ᝟ሗ㔞ᇶ‽ࡢ⤫ィ㔞ࢆィ⟬ࡋ࡚㸪ࣛࢢḟᩘkࢆ㑅ᢥࡍࡿࠋ౛࠼ࡤ㸪x=ge㸪y=gr㸪z =gdp࡜ࡍࢀࡤⰋ࠸ࠋࠉ๓㏙ࡢࡼ࠺࡟㸪༢఩᰿᳨ᐃ࡜ඹ࿴ศ᳨ᐃࡢ⤖ᯝ࡟ࡼࡗ࡚㸪඾ᆺⓗ࡞ศᯒᡭ㡰ࡣ3 ㏻ࡾ࡛࠶ࡿࠋ➨ 1࡟㸪x㸪y㸪zࡢኚᩘࡀ༢఩᰿᳨ᐃ࡛඲࡚I㸦0㸧࡜ุ᩿ࡉࢀࡿ࡜ࡁ࡟ࡣ㸪ୖグࡢᘧ㸦1-1㸧Ѹ㸦1-3㸧࡛¨xt ࢆxt ࡟㸪¨ yt ࢆyt ࡟㸪¨ zt ࢆzt ࡟ࡑࢀࡒࢀ⨨ࡁ᥮࠼ࡓVAR㸦k㸧ࢆ⪃࠼ࡿࠋ➨ 2࡟㸪༢఩᰿᳨ᐃ࡟ࡼࡾx㸪y㸪zࡢኚᩘࡀ඲࡚I㸦1㸧࡛༢఩᰿ࢆᣢࡕ㸪࠿ࡘEngle and Granger᳨ᐃ࡟ࡼࡾ3 ኚᩘ㛫࡟ඹ࿴ศࡀᏑᅾࡋ࡞࠸ሙྜ
࡟ࡣ㸪ୖグࡢᘧࢆࡑࡢࡲࡲ⏝࠸ࡿࠋ➨ 3࡟㸪༢఩᰿᳨ᐃ࡟ࡼࡾx㸪y㸪zࡢኚᩘࡀ඲࡚I㸦1㸧࡛༢఩᰿ࢆᣢࡕ㸪࠿ࡘ Engle and Granger ᳨ᐃ࡟ࡼࡾ x ࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿඹ࿴ศᅇᖐ㸦xt= a + byt+ czt+ ut , a, b, c

̿ 16 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀࡣඹ࿴ศಀᩘ࠶ࡿ࠸ࡣඹ࿴ศࣃ࣓࣮ࣛࢱ࣮㸪ut ࡣㄗᕪ㡯㸧ࢆ⏝࠸࡚3 ኚᩘ㛫࡟ඹ࿴ศࡀᏑᅾࡍࡿሙྜ࡟ࡣ㸪ࡇࡢඹ࿴ศᅇᖐ࡟㛵ࡋ࡚OLSࢆ⾜࠸ṧᕪet ࡢ1 ᮇ๓ࡢࣛࢢࢆྲྀࡗࡓet–1 ࢆ㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢࡑࢀࡒࢀ
࡟ຍ࠼࡚ᅉᯝ㛵ಀࢆศᯒࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋy࡜zࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿඹ࿴ศᅇᖐ࡟ࡘ࠸࡚ࡶྠᵝ࡞ࡇ࡜
ࢆ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿࠋ௨ୗ࡛ࡣ㸪ඹ࿴ศࡀᏑᅾࡍࡿሙྜ࡟ࡣ㸪x㸪y㸪zࡢ3 ኚᩘ࠿ࡽ1 ኚᩘࢆ㑅ᢥࡋ࡚⿕ㄝ᫂ኚᩘ࡜ࡋ࡚㸪ඹ࿴ศᅇᖐࡢṧᕪࡢ1 ᮇ๓ࡢࣛࢢࡢࡳࢆ㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢࡑࢀࡒࢀ࡟ຍ࠼ࡿࠋEngle
and Granger᳨ᐃࡢ1ࡘࡢḞⅬࡣ㸪࡝ࡢኚᩘࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿ࠿࡟㛵ࡋ࡚య⣔ⓗ࡞࣮ࣝࣝࡀ࡞࠸࡜࠸࠺
ࡇ࡜࡛࠶ࡿࠋEngle and Granger᳨ᐃࡢࡶ࠺1ࡘࡢḞⅬࡣ㸪
3 ኚᩘࡢሙྜ࡟ඹ࿴ศࢆ1 ಶࡢࡳⓎぢ࡛ࡁࡿࡀ㸪ඹ࿴ศࡀ2 ಶᏑᅾࡍࡿሙྜ࡟2 ಶⓎぢ࡛ࡁ࡞࠸ࡇ࡜࡛࠶ࡿࠋ࡞࠾㸪Johansen᳨ᐃࡣ㸪Engle and Granger
᳨ᐃࡢ2ࡘࡢḞⅬࢆゎỴ࡛ࡁࡿࠋࠉୖグࡢ㸦1-1㸧Ѹ㸦1-3㸧ᘧࢆ⏝࠸ࡓGrangerࡢᅉᯝ㛵ಀࡢ᳨ᐃ᪉ἲࢆㄝ᫂ࡍࡿࠋ
㸦1-1㸧ᘧࢆ⏝࠸࡚㸪Grangerࡢព࿡࡛¨ y࠿ࡽ¨x࡬ࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨ y Ж¨x㸧ࡇ࡜ࡢᚲせ༑ศ᮲௳ࡣ㸪Ȗ11 = Ȗ12 = ͐ = Ȗ1k = 0 ࡜࡞ࡿࡇ࡜࡛࠶ࡿࠋᅉᯝ㛵ಀࡢ᳨ᐃ᪉ἲ࡛ࡣ㸪ᖐ↓௬ㄝH0 ࡜ᑐ❧௬ㄝH1 ࡣ㸪
H0: Ȗ11 = Ȗ12 = ͐ = Ȗ1k = 0 ,H1: ࠸ࡎࢀ࠿ࡢi㸦i=1,2,͐,k）に関してȖi ӆ 0࡜࡞ࡿ࡛࠶ࡿࠋᖐ↓௬ㄝ H0 ࡢୗ࡛㸪᳨ᐃ⤫ィ㔞 F ࡜᳨ᐃ⤫ィ㔞 kF ࡀ฼⏝ྍ⬟࡛࠶ࡿࠋF ್ࡣ⮬⏤ᗘ㸦k,Tí3kí1㸧ࡢFศᕸࢆཧ↷ࡋ㸪kFࡢ್ࡣ⮬⏤ᗘkࡢ࢝࢖2 ஌ศᕸȤ㸦k㸧ࢆཧ↷ࡋ࡚㸪ࡑࢀࡒࢀ᳨ᐃࢆ
⾜࠺ࠋᮏㄽᩥ࡛ࡣ㸪௨ୗ࡛ㄝ᫂ࡍࡿࡼ࠺࡟kFࡢ್࡟ࡼࡿᅉᯝ㛵ಀࡢ⤖ᯝࡣF್ࡢሙྜ࡜ྠࡌ࡛࠶ࡿࡓࡵ㸪
Fศᕸࡢ್ࢆィ⟬ࡋ࡚ᅉᯝ㛵ಀࢆุ᩿ࡋࡓ⤖ᯝࢆ♧ࡍࠋF್ࡀ10%ࡢ᭷ពỈ‽࡛᭷ព࡛࠶ࢀࡤ㸪ᖐ↓௬ㄝ
H0 ࢆᲠ༷ࡋ࡚ᑐ❧௬ㄝH1 ࢆ᥇ᢥࡋ࡚㸪Grangerࡢព࿡࡛¨y࠿ࡽ¨x࡬ࡢᅉᯝ㛵ಀࡀ࠶ࡿ㸦¨yЍ¨x㸧࡜ุ᩿ࡍࡿࠋ
㸦1-1㸧ᘧࢆ⏝࠸࡚㸪Grangerࡢព࿡࡛¨z࠿ࡽ¨x࡬ࡢᅉᯝ㛵ಀ㸦¨zЍ¨x㸧ࢆ᳨ᐃࡍࡿሙྜࡣ㸪ᖐ
㸦1-2㸧ᘧࢆ⏝࠸࡚㸪ᅉᯝ㛵ಀ㸦¨xЍ¨y㸧࡜㸦¨zЍ↓௬ㄝࢆH0: į11=į12=͐=į1k=0࡜ࡍࢀࡤⰋ࠸ࠋྠᵝ࡟㸪¨y㸧ࡢ᳨ᐃ᪉ἲࢆᐃ⩏࡛ࡁ㸪
㸦1-3㸧ᘧࢆ⏝࠸࡚㸪ᅉᯝ㛵ಀ㸦¨xЍ¨z㸧࡜㸦¨yЍ¨z㸧ࡢ᳨ᐃ᪉ἲࢆᐃ⩏࡛ࡁࡿࠋ¨x࡜¨yࡢ཮᪉ྥࡢᅉᯝ㛵ಀࡀ࠶ࡿሙྜࡣ㸪¨x⇄¨yࡢグྕ࡛⾲ࡍࠋศᯒᑐ㇟ࡢx㸪y㸪zࡢ3 ኚᩘ㛫࡟ඹ࿴ศ㛵ಀࡀᏑᅾࡍࡿሙྜ࡟ࡣ㸪ㄗᕪಟṇ㡯ࢆྵࡵ࡚ᅉᯝ㛵ಀࢆศᯒࡍࡿࠋศᯒᑐ㇟ࡢx㸪y㸪zࡢ3ኚᩘࡀI㸦0㸧࡛࠶ࡿሙྜ࡟ࡣ㸪㸦xЍz㸧ࡢࡼ࠺࡟㸪㝵ᕪ₇⟬Ꮚ¨ࢆྲྀࡗࡓᙧ࡛ᅉᯝ㛵ಀࢆ⪃ᐹࡍࡿࠋࠉᮏㄽᩥ࡛ࡣ㸪ୖグ㸦1-1㸧Ѹ㸦1-3㸧࡟࠾࠸࡚x=ge㸪y=gr㸪z=gdpࢆ௦ධࡋ࡚㸪¨grЍ¨ge㸪¨gdpЍ¨ge㸪¨ geЍ¨ gr㸪¨ gdpЍ¨ gr㸪¨ geЍ¨ gdp㸪¨ grЍ¨ gdpࡢ6 ㏻ࡾࡢᅉᯝ㛵ಀࢆศᯒ┠ⓗ࡜ࡋ࡚࠸ࡿࠋ¨ ge࡜¨gr࡜¨gdpࡣࡑࢀࡒࢀศᯒኚᩘ࡟㛵ࡋ࡚⮬↛ᑐᩘࢆྲྀࡗࡓ್ࢆ⏝࠸࡚㝵ᕪࢆồࡵ࡚࠸ࡿࡢ࡛㸪¨geࡣᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡㸪¨grࡣᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡㸪¨gdpࡣᐇ㉁⤒῭ᡂ㛗⋡࡛࠶ࡿࠋᅉࡗ࡚㸪⪃ᐹࡍࡿ
Grangerࡢព࿡࡟ࡼࡿᅉᯝ㛵ಀࡣ㸪ᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡¨gr࠿ࡽᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨ge࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪ᐇ㉁⤒῭ᡂ㛗⋡¨gdp࠿ࡽᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨ge࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪
ᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨ge࠿ࡽᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡¨gr࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪ᐇ㉁⤒῭ᡂ㛗⋡¨gdp࠿ࡽᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡¨gr࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪ᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨ge࠿ࡽᐇ㉁⤒῭ᡂ㛗⋡¨gdp࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪ᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡¨gr࠿ࡽᐇ㉁⤒῭ᡂ㛗⋡¨gdp࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜㸪ࡢ6 ㏻ࡾ࡛࠶ࡿࠋ6 ㏻ࡾࡢᅉᯝ㛵ಀ࡟ࡘ࠸࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃ࡟ࡼࡗ࡚
࡝ࡢ㛵ಀࡀᏑᅾࡍࡿ࠿ࢆศᯒࡍࡿࠋ࡞࠾㸪௨ୗ࡛ࡣᅉᯝ㛵ಀࡢㄝ᫂ᩥ࡛ᡂ㛗⋡ࡢ⏝ㄒࢆ┬␎ࡋࡓ⾲⌧ࢆ⏝࠸ࡿሙྜࡶ࠶ࡿࠋ

̿ 17 ̿

఍ィ᳨ᰝ◊✲ࠉNo.44㸦2011.9㸧

ࠉᨻᗓ཰ධ㸦ࡲࡓࡣ⛯཰㸧࡜ᨻᗓᨭฟࡢᅉᯝ㛵ಀࡢ◊✲ࡣ㸪ࡑࡢከࡃࡀ2 ኚᩘge࡜grࡢࡳࢆศᯒᑐ㇟࡜ࡋ࡚㸪¨ grЍ¨ ge࡜¨ geЍ¨ grࡢᅉᯝ㛵ಀࢆศᯒࡋ࡚࠸ࡿࠋࡲࡓ㸪࣡ࢢࢼ࣮௬ㄝࡢ◊✲ࡣ㸪2 ኚᩘge
࡜gdpࡢࡳࢆศᯒᑐ㇟࡜ࡋ࡚㸪࣡ࢢࢼ࣮௬ㄝࡢᅉᯝ㛵ಀ㸦¨gdpЍ¨ge㸧࡜ࢣ࢖ࣥࢬ௬ㄝࡢᅉᯝ㛵ಀ㸦¨geЍ¨ gdp㸧ࢆศᯒࡋ࡚࠸ࡿࠋ¨ gr Ѝ¨ gdp ࡜¨ gdp Ѝ¨ gr ࡢᅇᖐศᯒࡸ࢖ࣥࣃࣝࢫ཯ᛂ࡟ࡘ࠸࡚ࡶ㸪
Mamatzakis㸦2005㸧➼࡟ࡳࡽࢀࡿࡼ࠺࡟◊✲ࡀᏑᅾࡍࡿࠋ¨gdpЍ¨grࡢᅉᯝ㛵ಀࡀ࠶ࢀࡤ㸪⤒῭ᡂ㛗ࡀᨻᗓ཰ධࢆቑຍࡉࡏࡿ࡜࠸࠺Thorn㸦1967㸧ࡢ⪃࠼᪉ࡀጇᙜࡍࡿྍ⬟ᛶࡀ࠶ࡿࠋ¨grЍ¨gdpࡢᅉᯝ㛵ಀࡀ࠶ࢀࡤ㸪ῶ⛯ࢆ⾜࠼ࡤᐇ㉁GDPࡀቑຍࡍࡿ࡜࠸࠺ࢣ࢖ࣥࢬࡢῶ⛯ࡢ⌮ㄽࡣጇᙜࡍࡿྍ⬟ᛶࡀ࠶ࡿࠋᨻ
ᗓ཰ධ㸦ࡲࡓࡣ⛯཰㸧࡜ᨻᗓᨭฟࡢᅉᯝ㛵ಀࡢ◊✲ࡸ࣡ࢢࢼ࣮௬ㄝࡢ◊✲ࡣ㸪ศᯒᑐ㇟ࡀ2 ኚᩘࡢሙྜࡀ
㠀ᖖ࡟ከࡃ㸪ኚᩘࢆ1ࡘⴠ࡜ࡍࡇ࡜࡟ࡼࡿᐃᘧ໬ࡢㄗࡾࡢྍ⬟ᛶࡀ࠶ࡿࠋ㸱㸬Grangerࡢᅉᯝ㛵ಀࡢศᯒ⤖ᯝࠉ༢఩᰿᳨ᐃ㸪ඹ࿴ศ᳨ᐃ㸪ᅉᯝ㛵ಀࡢ᳨ᐃ࡛ࡣ㸪᭷ពỈ‽࡜ࡋ࡚10%ࢆ⏝࠸ࡿࡇ࡜࡟ࡍࡿࠋศᯒ⤖ᯝ࡛ࡣ㸪1%㸪5%㸪10%ࡢ᭷ពỈ‽ุ࡛᩿࡛ࡁࡿࡼ࠺࡟⾲グࡋ࡚࠸ࡿࠋ
3. 1 ༢఩᰿᳨ᐃࡢ⤖ᯝ
ࠉᐇ㉁ᨻᗓᨭฟ㸦ge㸧㸪ᐇ㉁ᨻᗓ཰ධ㸦gr㸧
㸪ᐇ㉁GDP㸦gdp㸧ࡢADF᳨ᐃ࡟ࡼࡿ༢఩᰿᳨ᐃࡢ⤖ᯝࡀ⾲ 1࡟♧ࡉࢀ࡚࠸ࡿࠋࣔࢹࣝC࡜C&Tࡢࣛࢢᩘkࡣ㸪ᣑᙇ㡯ࡀ࡞࠸k = 0࡜k = 1,2,͐,5ࡢ್࡟ᑐࡋ࡚AIC࡜
SICࡢ⤫ィ㔞ࢆィ⟬ࡋ㸪AIC࡜SICࡢ୧᝟ሗሗ㔞ᇶ‽࡟ᇶ࡙࠸࡚㑅ᢥࡉࢀ࡚࠸ࡿࠋ

䛣䛣䛷䠈 ¨ 䛿 1 㝵䛾㝵ᕪ₇⟬Ꮚ䛷䛒䜛䚹 䝰䝕䝹䛾グྕ䛿䠈 ⬮ὀ 1䠅 䛾䝰䝕䝹䛷ῧ䛘Ꮠ 0 䜢ྲྀ䜚䠈 䛥䜙䛻䃒㻜 䌦 1 䠙䃒䛸䛧䛶䛔䜛䚹 ᳨ᐃᘧ䛻䛚䛡䜛ᣑᙇ㡯䛾䝷䜾䛾ḟᩘ k䛿䠈 ᭱኱ḟᩘ䜢 5 䛸䛧䛶㻭㻵㻯䛸 㻿㻵㻯䛻ᇶ䛵䛝㑅ᢥ䛥䜜䜛䚹 㻭㻵㻯 䠄k䠅 䛸 㻿㻵㻯 䠄k䠅䛿䠈 䛭䜜䛮䜜 㻭㻵㻯 䛸 㻿㻵㻯 䛻ᇶ䛵䛔䛶㑅ᢥ䛥䜜䛯ḟᩘ k 䜢♧䛧䛶䛔䜛䚹 㻭㻰㻲 ᳨ᐃ䛻䛚䛡䜛⮫⏺್䛸 㼜 ್䛿䠈 ᫂♧䛧䛶䛔䛺䛔䛜䠈 㻹㼍㼏㻷㼕㼚㼚㼛㼚 䠄1996䠅 䜘䜚ᚓ䜙䜜䜛䚹 ᫍ༳䛷䛿䠈 㻖㻖㻖 䛿 1䠂Ỉ‽䛷᭷ព䠈 㻖㻖 䛿 5䠂Ỉ‽䛷᭷ព䠈 㻖 䛿 10䠂Ỉ‽䛷᭷ព䛷䛒䜛䛣䛸䜢♧䛩䚹

̿ 18 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀࠉࣔࢹࣝCࡢ⤖ᯝࡣ㸪௨ୗࡢ㏻ࡾ࡛࠶ࡿࠋgeࡣ㸪SIC࡛㑅ࢇࡔࣛࢢḟᩘk=0ࡀAICࡢ⤖ᯝ࡟୍⮴ࡋ㸪Ỉ‽ኚᩘࡢ᳨ᐃ⤫ィ್Ѹ 5.059228ࡀ1%ࡢ᭷ពỈ‽࡛᭷ព࡛࠶ࡾ㸪ᐃᖖࡢI㸦0㸧࡛࠶ࡿ࡜ุ᩿࡛ࡁࡿࠋgrࡣ㸪Ỉ‽ኚᩘࡢSIC࡟ᇶ࡙ࡃ᳨ᐃ⤫ィ್Ѹ 2.949526ࡀ5%ࡢ᭷ពỈ‽࡛᭷ព࡛࠶ࡾ㸪ᐃᖖࡢI㸦0㸧࡛࠶ࡿࠋࡉ
ࡽ࡟㸪grࡢAICᇶ‽࡟ᇶ࡙ࡃ⤖ᯝ࡛ࡣ㸪Ỉ‽ኚᩘࡢ᳨ᐃ⤫ィ್Ѹ 2.713566ࡀ10%Ỉ‽࡛᭷ព࡛࠶ࡾ㸪gr
ࡣᐃᖖࡢI㸦0㸧࡛࠶ࡿࠋAIC࡜SICࡢ୧ᇶ‽ࡢ⤖ᯝࡼࡾ㸪grࡢỈ‽ኚᩘࡣI㸦0㸧࡛࠶ࡿࠋྠᵝ࡟ࡋ࡚㸪
gdpࡢỈ‽ኚᩘࡣSIC࡛㑅ࢇࡔࣛࢢḟᩘk=0ࡀAICࡢ⤖ᯝ࡟୍⮴ࡋ㸪ࡑࡢỈ‽ኚᩘࡣI㸦0㸧࡛࠶ࡿࠋAIC
࡜SICࡢ୧ᇶ‽࡛ࣛࢢḟᩘkࢆ㑅ࢇࡔ⤖ᯝ࡛ࡣ㸪ge࡜gr࡜gdpࡢỈ‽ኚᩘࡣࡑࢀࡒࢀI㸦0㸧࡜ุ᩿࡛ࡁࡿࠋࠉࣔࢹࣝC&Tࡢሙྜ࡟ࡣ㸪ḟࡢ㏻ࡾ࡛࠶ࡿࠋgeࡣ㸪Ỉ‽ኚᩘ࡜➨ 1 㝵ᕪኚᩘ࡟ᑐࡋ࡚SIC࡛㑅ࢇࡔࣛࢢḟᩘk=0ࡀAICࡢ⤖ᯝ࡟୍⮴ࡋ㸪Ỉ‽ኚᩘࡢ᳨ᐃ⤫ィ್Ѹ 0.474629ࡀ10%ࡢ᭷ពỈ‽࡛᭷ព࡛ࡣ࡞ࡃ㸪➨ 1 㝵ᕪኚᩘࡢ᳨ᐃ⤫ィ್Ѹ 5.636290ࡀ1%Ỉ‽࡛᭷ព࡛࠶ࡿࠋᚑࡗ࡚㸪geࡣ༢఩᰿ࢆᣢࡘI㸦1㸧ࡢኚᩘ࡛࠶ࡿ࡜ุ᩿࡛ࡁࡿࠋ2 ኚᩘgr࡜gdp࡟ࡘ࠸࡚ࡶྠᵝ࡞᳨ᐃࢆᐇ⾜ࡋ࡚㸪2 ኚᩘ࡜ࡶI㸦1㸧࡜ุ᩿࡛ࡁࡿࠋ
AIC࡜SICࡢ୧ᇶ‽ࢆ⏝࠸ࡿ࡜㸪ge࡜gr࡜gdpࡢỈ‽ኚᩘࡣࡑࢀࡒࢀI㸦1㸧࡜ุ᩿࡛ࡁࡓࠋࠉࣔࢹࣝC࡜C&Tࡢ⤖ᯝࡣ኱ࡁࡃ␗࡞ࡗ࡚࠸ࡿࡀ㸪௨ୗ࡛ࡣࣔࢹࣝC&Tࡢ⤖ᯝ࡟ᇶ࡙࠸࡚㸪ge࡜gr࡜
gdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦1㸧࡜ุ᩿ࡋ࡚ศᯒࢆ⾜࠺ࠋKwiatkowski, Phillips, Schmidt and Shin㸦1992㸧
ࡣ㸪ᐃᖖᛶࢆᖐ↓௬ㄝ㸪༢఩᰿ࢆᣢࡘࡇ࡜ࢆᑐ❧௬ㄝ࡜ࡍࡿKPSS᳨ᐃࢆᥦ᱌ࡋ࡚࠸ࡿࡀ㸪ࡇࡢ᳨ᐃࡀከ
ࡃࡢ◊✲ㄽᩥ࡛฼⏝ࡉࢀ࡚࠸ࡿࠋ౛࠼ࡤ㸪Narayan and Narayan㸦2006㸧ࡣ㸪KPSS᳨ᐃ⤫ィ㔞ࡢィ⟬ᡭ⥆ࡁࡢせ⣙ࢆ⾜࠸㸪ࡇࡢ⤫ィ㔞ࢆ⏝࠸࡚ࢹ࣮ࢱࡢศᯒࢆ⾜ࡗ࡚࠸ࡿࠋศᯒ⤖ᯝࡢᥦ♧ࡣ┬␎ࡍࡿࡀ㸪
KPSS᳨ᐃࡢ⤖ᯝࡣ㸪ᐃᩘ㡯࡜ࢺࣞࣥࢻࢆྵࡴࣔࢹࣝࢆ⏝࠸ࡓሙྜ࡟ࡣ㸪ge࡜gr࡜gdpࡀࡑࢀࡒࢀI㸦1㸧
࡜ุ᩿࡛ࡁࡿࠋ

3. 2 ඹ࿴ศ᳨ᐃࡢ⤖ᯝࠉge㸪gr㸪gdpࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿ3ࡘࡢᅇᖐᘧ࡟ࡘ࠸࡚Engle and Grangerࡢඹ࿴ศ᳨ᐃࡢ⤖ᯝࡀ⾲ 2࡟♧ࡉࢀ࡚࠸ࡿࠋ⿕ㄝ᫂ኚᩘࢆge࡜ࡍࡿඹ࿴ศᅇᖐᘧࡣ㸪ㄝ᫂ኚᩘࡀgr࡜gdp࡛࠶ࡿࠋᙜ↛㸪ࡇࡢඹ࿴ศ
ᅇᖐᘧ࡛ㄝ᫂ኚᩘࡢgr࡜gdpࡢ㡰␒ࢆධࢀ᭰࠼࡚ࡶྠࡌ࡛࠶ࡿࠋᣑᙇ㡯ࡢࣛࢢḟᩘࡣ㸪ᣑᙇ㡯ࡀ࡞࠸k=0࡜k= 1,2,͐,5ࡢ್࡟ᑐࡋ࡚㸪ඹ࿴ศᅇᖐ࡟࠾ࡅࡿAIC࡜SICࡢ᝟ሗ㔞ᇶ‽ࡢ⤫ィ㔞ࢆィ⟬ࡋ࡚㑅ᢥࡉࢀ࡚࠸ࡿࠋ⾲ 2࡛ࡣ㸪Engle and Granger᳨ᐃ࡛⏝࠸ࡽࢀࡿADF᳨ᐃ⤫ィ㔞㸪p್㸪AIC࡜SICࡢ᝟ሗ㔞ᇶ‽ࢆ⏝࠸࡚㑅ᢥࡉࢀࡓࣛࢢḟᩘࡀ♧ࡉࢀ࡚࠸ࡿࠋㄝ᫂ኚᩘࢆge࡜ࡍࡿඹ࿴ศᅇᖐᘧࡣ㸪AIC࡜SICࡢ୧ᇶ‽࡟ࡼࡾADF᳨ᐃ⤫ィ㔞ࡢ್㸦Ѹ 2.349696࡜Ѹ 2.091621㸧ࡀ10%ࡢ᭷ពỈ‽࡛᭷ព࡛࡞࠸ࡢ࡛㸪ඹ࿴ศ㛵ಀࡀᏑᅾࡋ࡞࠸ࠋ๓㏙ࡢ⤖ᯝࡢ㡹೺ᛶࢆぢࡿࡓࡵ࡟㸪ṧࡾ2ࡘࡢඹ࿴ศᅇᖐᘧ࡟ࡘ࠸࡚ࡶ᳨ᐃࢆ⾜࠺ࠋ⿕ㄝ᫂ኚᩘࢆgr࡜gdp࡜ࡍࡿඹ࿴ศᅇᖐᘧ࡟ࡘ࠸ࡣ㸪ྠᵝ࡟ࡋ࡚㸪ඹ࿴ศ㛵ಀࡀᏑᅾࡋ࡞࠸ࠋge㸪gr㸪
gdpࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿ3ࡘࡢᅇᖐᘧ࡟ࡘ࠸࡚㸪࠸ࡎࢀࡶඹ࿴ศ㛵ಀࡀᏑᅾࡋ࡞࠸࡜࠸࠺⤖ᯝࢆᚓࡓࠋ

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pk

3. 3 ᅉᯝ㛵ಀࡢศᯒ⤖ᯝ
ࠉADF᳨ᐃ➼ࢆ⏝࠸ࡓ༢఩᰿᳨ᐃࡢ⤖ᯝࡼࡾ㸪ge࡜gr࡜gdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦1㸧࡛࠶ࡿ࡜ุ᩿
ࡋࡓࠋEngle and Grangerࡢඹ࿴ศ᳨ᐃࡢ⤖ᯝࡼࡾ㸪ge࡜gr࡜gdpࡢ3 ኚᩘ࡟㛵ࡍࡿඹ࿴ศ㛵ಀࡣᏑᅾࡋ
࡞࠸ࠋVAR㸦k㸧࡛ࡣ㸪ge࡜gr࡜gdpࡢ➨ 1 㝵ᕪኚᩘࢆ⏝࠸ࡿࡀ㸪Engle and Granger᳨ᐃ࡟࠾ࡅࡿඹ࿴
ศᅇᖐࡢṧᕪ࠿ࡽᚓࡿㄗᕪಟṇ㡯ࢆྵࡵ࡞࠸ࠋᚑࡗ࡚㸪ge㸪gr㸪gdpࡢ➨ 1 㝵ᕪኚᩘࢆ⏝࠸ࡿ㸦1-1㸧Ѹ㸦1-3㸧
ࡢVAR㸦k㸧ࡣ㸪ㄗᕪಟṇ㡯ࢆྵࡵ࡞࠸࡛ศᯒࡍࡿࠋᚑࡗ࡚㸪
㸦1-1㸧Ѹ㸦1-3㸧ࡢVAR㸦k㸧࡛ࡣ㸪¨ ge㸪¨gr㸪¨gdpࢆ⏝࠸࡚ศᯒࡍࡿࠋ
ࠉᮏከ㸦1998㸧࡟ぢࡽࢀࡿࡼ࠺࡟㸪VAR㸦k㸧ࡢࣛࢢḟᩘࡣAIC࡜SICࡢ୧᝟ሗ㔞ᇶ‽ࢆ⏝࠸࡚Ỵᐃࡍࡿࠋ⾲ 3࡛ࡣ㸪
㸦1-1㸧Ѹ㸦1-3㸧ࡢVAR㸦k㸧ࢆ⏝࠸࡚㸪k = 0࡜k = 1,2,͐,5ࡢ್࡟ᑐࡋ࡚AIC࡜SICࡢ⤫ィ್ࡀィ⟬ࡉࢀ࡚࠸ࡿࠋk = 0ࡢ࡜ࡁࡣ㸪
㸦1-1㸧Ѹ㸦1-3㸧ࡢྑ㎶ࡣᐃᩘ㡯ࡢࡳࡢࣔࢹࣝ࡟࡞ࡿࠋAICᇶ‽ࡣ,ࣛࢢḟᩘk =2ࡀ㑅ᢥࡉࢀࡿࠋSICᇶ‽ࡣ㸪ࣛࢢḟᩘk =1ࡀ㑅ᢥࡉࢀࡿࠋkࠉᘧ㸦1-1㸧ࢆ⏝࠸ࡿ࡜㸪Grangerࡢព࿡࡛¨y࠿ࡽ¨x࡬ࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨y Ж¨x㸧ࡇ࡜ࡢᚲせ༑ศ᮲௳ࡣ㸪Ȗ11= Ȗ12=͐= Ȗ1k=0 ࡜࡞ࡿࡇ࡜࡛࠶ࡿࠋ⾲ 4࡛ࡣ㸪Grangerࡢព࿡࡛¨y࠿ࡽ¨x ࡬ࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨y Ж¨x㸧࡜࠸࠺ᖐ↓௬ㄝ㸪᳨ᐃ⤫ィ㔞ࡢF್㸪Fศᕸࢆ⏝࠸࡚ィ⟬ࡉࢀࡓp್ࡀ♧ࡉࢀ࡚࠸ࡿࠋ⾲ 4࡛ࡣ㸪¨ge㸪¨gr㸪¨gdpࡢ3 ኚᩘ࠿ࡽᚓࡽࢀࡿ6 ಶࡢ⤌ࡳྜࢃࡏࡢᖐ↓௬ㄝ࡜㸪AIC࡜SICࡢ୧ᇶ‽࡛㑅ᢥ̿ 20 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀࡉࢀࡓḟᩘk = 1,2ࡢ್࡟ᑐࡋ࡚㸪F್࡜p್ࡀ♧ࡉࢀ࡚࠸ࡿࠋ
ࠉge࡜gr࡜gdpࡢ➨ 1 㝵ᕪኚᩘࢆ⏝࠸࡚ศᯒࡉࢀࡓ⾲ 4ࡢ⤖ᯝࢆㄝ᫂ࡍࡿࠋ⾲ 4࡛ࡣ㸪¨ ge࡜¨ gr࡜
¨gdpࢆ⏝࠸࡚࠸ࡿࡢ࡛㸪¨geࡣᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡㸪¨grࡣᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡㸪¨gdpࡣᐇ㉁⤒῭ᡂ㛗⋡࡛࠶ࡿࠋSICᇶ‽࡟ࡼࡿk = 1ࡢሙྜ㸪Grangerࡢព࿡࡛¨gr࠿ࡽ¨ge࡬ࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨gr Ж¨ge㸧࡜࠸࠺ᖐ↓௬ㄝࡢ᳨ᐃࡣ㸪F್ 0.650823ࡀ10㸣ࡢ᭷ពỈ‽࡛᭷ព࡛࡞࠸ࡢ࡛㸪㸦¨gr Ж¨ge㸧࡜࠸࠺ᖐ↓௬ㄝࢆᲠ༷࡛ࡁ࡞࠸ࠋᚑࡗ࡚㸪¨gr Ж¨ge࡜࠸࠺⤖ᯝࢆᚓࡿࠋGrangerࡢព࿡࡛¨gdp ࠿ࡽ¨ge࡬ࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨gdp Ж¨ge㸧࡜࠸࠺ᖐ↓௬ㄝࡢ᳨ᐃࡣ㸪F್ 8.550285ࡀ1㸣ࡢ᭷ពỈ‽࡛᭷ព࡛࠶
ࡿࡢ࡛㸪㸦¨gdp Ж¨ge㸧࡜࠸࠺ᖐ↓௬ㄝࢆᲠ༷࡛ࡁࡿࠋGrangerࡢព࿡࡛¨gdp࠿ࡽ¨ge࡬ࡢᅉᯝ㛵ಀࡀ࠶ࡿ㸦¨gdpЍ¨ge㸧࡜࠸࠺⤖ᯝࢆᚓࡿࠋྠᵝ࡟ࡋ࡚㸪¨ge Ж¨gr㸪¨gdpЍ¨gr㸪¨geЍ¨gdp㸪¨grЍ¨gdp
ࡢ⤖ᯝࢆᚓࡿࠋAICᇶ‽࡟ࡼࡿk =2ࡢሙྜ㸪¨gr Ж¨ge㸪¨gdpЍ¨ge㸪¨ge Ж¨gr㸪¨gdpЍ¨gr㸪¨geЍ¨gdp㸪¨grЍ¨gdpࡢ⤖ᯝࢆᚓࡿࠋࡇࢀࡽࡢ⤖ᯝࡣ㸪SICᇶ‽࡟ࡼࡿk = 1ࡢሙྜ࡜඲ࡃྠࡌ࡛࠶ࡿࠋ

p

k
k㸻1

ǻgr Ж ǻgeǻgdp Ж ǻgeǻge Ж ǻgrǻgdp Ж ǻgrǻge Ж ǻgdpǻgr Ж ǻgdpk㸻2

ǻgr Ж ǻgeǻgdp Ж ǻgeǻge Ж ǻgrǻgdp Ж ǻgrǻge Ж ǻgdpǻgr Ж ǻgdpࠉ⾲ 4ࡢF್࡟ࣛࢢḟᩘkࢆ᥃ࡅ࡚kFࡢ್ࢆồࡵ࡚㸪࢝࢖2 ஌᳨ᐃࢆ⏝࠸࡚ࡶF್࡜ྠࡌ⤖ᯝࢆᚓࡿࠋkF
ࡢ್ࡣᥦ♧ࡋ࡞࠸ࡀ㸪ࣛࢢḟᩘ k = 1,2࡟࠾ࡅࡿ 4ࡘࡢᖐ↓௬ㄝ¨gdp Ж¨ge㸪¨gdp Ж¨gr㸪¨ge Ж¨gdp㸪
¨ge Ж¨gdp࡟ᑐࡋ࡚㸪kF್ࡣࣛࢢḟᩘk =2ࡢ¨gr Ж¨gdpࡢሙྜࢆ㝖࠸࡚F್࡜ྠࡌ᭷ពỈ‽࡛᭷ព࡛࠶ࡿࠋk =2ࡢᖐ↓௬ㄝ¨gr Ж¨gdp࡟ᑐࡋ࡚ࡣ㸪F್ࡣ10%࡛᭷ព࡛࠶ࡿࡀ㸪kFࡢ್ࡣ5%Ỉ‽࡛᭷ព࡟࡞ࡿࠋࣛࢢḟᩘk =1,2࡟࠾ࡅࡿ 2ࡘࡢᖐ↓௬ㄝ ¨gr Ж¨ge࡜¨ge Ж¨gr࡟ᑐࡋ࡚ࡣ㸪kF್ࡣF್࡜ྠࡌࡼ
࠺࡟10%Ỉ‽࡛᭷ព࡛࡞࠸ࠋ
ࠉAIC࡜SICࡢ୧ᇶ‽࡟ࡼࡿGrangerࡢᅉᯝ㛵ಀࡢ⤖ᯝࡣ㸪ᅗ 1࡟ᅗ♧ࡉࢀ࡚࠸ࡿࠋᅜᐙ㈈ᨻ࡟࠾ࡅࡿᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡㸦¨ge㸧࡜ᐇ㉁ᨻᗓ཰ධࡢᡂ㛗⋡㸦¨gr㸧࡟㛵ࡋ࡚㸪Grangerࡢព࿡࡛ᅉᯝ㛵ಀࡀ࡞࠸࡜࠸࠺⤖ᯝࡣ㸪ᚑ᮶ࡢ᪥ᮏ࡟࠾ࡅࡿศᯒ⤖ᯝ࡜኱ࡁࡃ␗࡞ࡾ㸪⯆࿡῝࠸ࠋChang㸪
Liu and Caudill
㸦2002㸧ࡣ㸪ྎ‴ࡢᩍ⫱┬㸦Taiwan Ministry of Education㸧ࡢAREMOSࢹ࣮ࢱ࠿ࡽ᪥ᮏࡢࢹ࣮ࢱࢆᚓ࡚㸪⛯཰Ѹ

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ᨭฟ௬ㄝ㸦ᨻᗓ཰ධѸᨻᗓᨭฟ௬ㄝ㸪¨ grЍ¨ ge㸧ࢆᨭᣢࡍࡿ⤖ᯝࢆᚓࡓࠋOwoye㸦1995㸧ࡣ㸪IMFࡢ
ࠗInternational Financial Statistics Yearbook࠘ࡢ᪥ᮏࡢࢹ࣮ࢱࢆ⏝࠸࡚㸪⛯཰࡜ᨭฟࡢᅉᯝ㛵ಀࢆぢฟࡋ࡚࠸ࡿࠋChang㸪Liu and Caudill㸦2002㸧࡜Owoye㸦1995㸧ࡣ㸪ඹ࡟⛯཰࡜ᨻᗓᨭฟࡢ2 ኚᩘࡢࣔࢹࣝ
ࢆศᯒࡋ࡚࠸ࡿࡋ㸪ࡇࡢㄽᩥ࡜␗࡞ࡿࢹ࣮ࢱࢆศᯒࡋ࡚࠸ࡿࠋᅜࡢ୍⯡఍ィண⟬࡛ࡣ㸪ᐇ㉁ࡢᨻᗓᨭฟࡢ
୰㌟࡟♫఍ಖ㞀㛵ಀ㈝ࡢᨭฟࢆྵࢇ࡛࠸ࡿࡀ㸪ᐇ㉁ࡢᨻᗓ཰ධࡢ୰㌟࡟ᨭฟࡢ♫఍ಖ㞀㛵ಀ㈝࡟ᑐᛂࡍࡿ
཰ධࡀ᏶඲࡟ධࡗ࡚࠸࡞࠸ࡇ࡜ࡀཎᅉࡢ1ࡘ࡛ࡣ࡞࠸࠿࡜⪃࠼ࡿࠋᆅ᪉஺௜⛯஺௜㔠➼ࡢᆅ᪉⛣㌿ࡶᙳ㡪ࡋ࡚࠸ࡿྍ⬟ᛶࡀ࠶ࡿࠋ
ᅗ 1ࠉGrangerࡢᅉᯝ㛵ಀ

ge

gr

gdp

㸦ฟ඾㸧➹⪅సᡂࠉᅗ 1ࡼࡾ㸪ᅜᐙ㈈ᨻ㸦¨ge࡜¨gr࡛ᤊ࠼ࡓ㸧࡜ᐇ㉁⤒῭ᡂ㛗⋡㸦¨gdp㸧ࡢᅉᯝ㛵ಀࢆせ⣙ࡍࡿࠋᅜᐙ㈈ᨻ࡛ࡣ㸪ᐇ㉁ࡢᨻᗓᨭฟ㸦ge㸧࡜ᐇ㉁GDP㸦gdp㸧࡟㛵ࡋ࡚ࡣ㸪཮᪉ྥࡢᅉᯝ㛵ಀ¨ge⇄¨gdpࢆ☜ㄆࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋ࣡ࢢࢼ࣮௬ㄝ㸦¨gdpЍ¨ge㸧࡜ࢣ࢖ࣥࢬ௬ㄝ㸦¨geЍ¨gdp㸧ࡢᅉᯝ㛵ಀࢆⓎぢ࡛ࡁࡓࠋᐇ㉁ࡢᨻᗓ཰ධ㸦gr㸧࡜ᐇ㉁GDP㸦gdp㸧࡟㛵ࡋ࡚ࡣ㸪཮᪉ྥࡢᅉᯝ㛵ಀ¨ge⇄¨gdpࢆ☜ㄆࡍࡿࡇ࡜ࡀ
࡛ࡁࡓࠋThorn㸦1967㸧ࡢࢡࣟࢫ࣭ࢭࢡࢩࣙࣥࢹ࣮ࢱࡢศᯒ࡛ぢࡽࢀࡿࡼ࠺࡟㸪⤒῭ᡂ㛗ࡀᨻᗓ཰ධࡢᡂ
㛗ࢆቑຍࡉࡏࡿ௬ㄝ㸦¨gdpЍ¨ge㸧ࡢྍ⬟ᛶࢆⓎぢ࡛ࡁࡓࠋࢣ࢖ࣥࢬࡢῶ⛯⌮ㄽ࡟ぢࡽࢀࡿࡼ࠺࡟㸪ᨻᗓ཰ධࡢᡂ㛗⋡ࡀ⤒῭ᡂ㛗⋡ࢆῶᑡࡉࡏࡿ௬ㄝ㸦¨grЍ¨gdp㸧ࡢྍ⬟ᛶࢆⓎぢࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋ࡞࠾㸪ᨻᗓ཰ධࡢᡂ㛗⋡ࡀ⤒῭ᡂ㛗⋡ࢆῶᑡࡉࡏ࡞࠸ྍ⬟ᛶࡶ࠶ࡾᚓࡿࠋ

㸲㸬⤖ࡧࠉᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓ཰ධ㸪ᐇ㉁GDPࡢ3 ኚᩘࡢࣔࢹ࡛ࣝ㸪ᅜᐙ㈈ᨻ࡟࠾ࡅࡿᐇ㉁ᨻ
ᗓᨭฟ࡜ᐇ㉁ᨻᗓ཰ධࡢᅉᯝ㛵ಀࢆⓎぢ࡛ࡁ࡞࠿ࡗࡓࠋᐇ㉁ᨻᗓᨭฟ࡜ᐇ㉁ᨻᗓ཰ධ࡛ᤊ࠼ࡓᅜᐙ㈈ᨻ࡜
ᐇ㉁GDP࡛ィ⟬ࡉࢀࡓ⤒῭ᡂ㛗࡜ࡢ㛫࡟ࡣ㸪Grangerࡢព࿡࡛ᅉᯝ㛵ಀࡀᏑᅾࡋࡓࠋᚑࡗ࡚㸪ᅜᐙ㈈ᨻ
࡟࠾ࡅࡿᐇ㉁ᨻᗓᨭฟ࡜ᐇ㉁ᨻᗓ཰ධࡢᕪ࡜ࡋ࡚ࡢ㈈ᨻ㉥Ꮠࡢၥ㢟࡛ࡣ㸪⤒῭ᡂ㛗࠿ࡽࡢどⅬࡀ㔜せ࡛࠶ࡿࠋᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ኚᩘࢆศᯒᑐ㇟࡜ࡋ࡚࠸ࡿࡓࡵ㸪࢖ࣥࣇ࣮ࣞࢩࣙࣥࡸࢹࣇ࣮ࣞࢩࣙࣥࢆ⪃៖ࡋ࡚࠸࡞࠸ࠋࠉᇶ♏ⓗ㈈ᨻ཰ᨭ࡟╔┠ࡍࡿ࡜㸪㈈ᨻ㉥Ꮠࢆῶࡽࡍ࡟ࡣ㸪ᨻᗓᨭฟࢆῶࡽࡍ᪉ἲ࡜ቑ⛯࡟ࡼࡾᨻᗓ཰ධ
㸦⛯཰➼㸧ࢆቑࡸࡍ᪉ἲࡀ⪃࠼ࡽࢀࡿࠋࡇࡇ࡛ࡣᅜᐙࡢ㈈ᨻ㉥Ꮠࢆᇶ♏ⓗ㈈ᨻ཰ᨭ࡛ᤊ࠼࡚࠸ࡿࠋᮏㄽᩥ
࡛ࡣ㸪ᐇ㉁್࡛ぢࡓᇶ♏ⓗ㈈ᨻ཰ᨭࡣᐇ㉁ᨻᗓ཰ධ࠿ࡽᐇ㉁ᨻᗓᨭฟࢆᕪࡋᘬ࠸ࡓᩘ್࡛࠶ࡿࠋᨻᗓᨭฟ
ࡢቑῶࡸቑῶ⛯ࡢ⤒῭ᡂ㛗࡬ࡢᙳ㡪ࡣࢣ࢖ࣥࢬຠᯝ࡛ᢕᥱ࡛ࡁࡿሙྜࡶ࠶ࡿࠋ㏻ᖖࡢ࣐ࢡࣟ⤒῭Ꮫࡢᩍ⛉̿ 22 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀ᭩࡛ㄝ᫂ࡉࢀ࡚࠸ࡿෆᐜࢆ㋃ࡲ࠼࡚㸪ࢣ࢖ࣥࢬຠᯝࡣ㸪ᨻᗓᨭฟࡢቑຍࡸῶ⛯ࡀ஌ᩘຠᯝࢆ㏻ࡋ࡚GDP࡟୚࠼ࡿࣉࣛࢫࡢᙳ㡪࡛࠶ࡾ㸪ᨻᗓᨭฟࡢῶᑡࡸቑ⛯ࡀGDP࡟୚࠼ࡿ࣐࢖ࢼࢫࡢᙳ㡪࡛࠶ࡿࠋ㠀ࢣ࢖ࣥࢬຠᯝࡣ㸪ᨻᗓᨭฟࡢῶᑡࡸቑ⛯➼ࡢ⥭⦰㈈ᨻࡀGDP࡟୚࠼ࡿࣉࣛࢫࡢᙳ㡪➼ࡢࡇ࡜࡛࠶ࡿࠋ⏣୰࣭໭
㔝㸦2002㸧ࡣ㸪㠀ࢣ࢖ࣥࢬຠᯝࡢඛ⾜◊✲࡟ࡘ࠸࡚⡆₩࡞ᒎᮃࢆ⾜ࡗ࡚࠸ࡿࠋ⏣୰࣭໭㔝ࡣ㸪OECD21࠿ᅜࡢࣉ࣮ࣝࡋࡓࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪ᨻᗓᨭฟ๐ῶࡸቑ⛯࡟౫Ꮡࡋࡓ㈈ᨻ෌ᘓࡀᖖ࡟⤒῭ᡂ㛗ࡢపୗࢆࡶࡓࡽࡍࡶࡢ࡛࡞࠸࡜࠸࠺ศᯒ⤖ᯝࢆᚓ࡚࠸ࡿࠋ
ࠉ㈈ᨻ㉥Ꮠࢆῶࡽࡍࡓࡵࡢᨻᗓᨭฟࡢ๐ῶ࡟ࡘ࠸᳨࡚ウࡍࡿࠋ௨ୗ࡛ࡣ㸪ᅉᯝ㛵ಀࡢᩥ❶⾲⌧࡛ࡣᡂ㛗⋡ࡢ⏝ㄒࢆ┬␎ࡋ࡚࠸ࡿࠋGrangerࡢព࿡࡛ᐇ㉁ᨻᗓᨭฟ࠿ࡽᐇ㉁ᨻᗓ཰ධ࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁ࡞࠿ࡗࡓࡓࡵ㸪ᐇ㉁ᨻᗓᨭฟࡢ๐ῶࡀᐇ㉁ᨻᗓ཰ධ࡬୚࠼ࡿຠᯝࡣ኱ࡁࡃ࡞࠸࡜ุ᩿࡛ࡁࡿࠋ
Grangerࡢព࿡࡛ᐇ㉁ᨻᗓᨭฟ࠿ࡽᐇ㉁GDP࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁࡓࡢ࡛㸪ᐇ㉁ᨻᗓ
ᨭฟࡢ๐ῶ࡟ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࡜࠸࠺ࢣ࢖ࣥࢬຠᯝࡀᶵ⬟ࡍࡿሙྜ࡟ࡣ㸪࠶ࡿ఍ィᖺᗘ࡟࠾ࡅࡿᐇ㉁ᨻᗓᨭฟࡢ๐ῶࡣḟ఍ィᖺᗘ௨㝆ࡢᐇ㉁GDP࡬ࡢ࣐࢖ࢼࢫࡢຠᯝࢆᣢࡘࡇ࡜ࡀண᝿ࡉࢀࡿࠋ࡞࠾㸪Grangerࡢព࿡࡛ᐇ㉁ᨻᗓᨭฟ࠿ࡽᐇ㉁GDP࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࡣ㸪
㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢVARࣔࢹ࡛ࣝ㐣ཤࡢᐇ㉁ᨻᗓᨭฟ㸦ࣛࢢ௜ኚᩘ㸧ࡀᐇ㉁GDPࡢኚື࡟ࡘ࠸࡚ㄝ᫂ຊࢆᣢࡘࡇ࡜࡛࠶ࡿࠋᐇ㉁ᨻᗓᨭฟࡢ๐ῶ࡟ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࡜࠸࠺ࢣ࢖ࣥࢬຠᯝࡀᶵ⬟ࡋ࡞࠸ሙྜ࡟ࡣ㸪㠀ࢣ࢖ࣥࢬຠᯝ࡟
ࡼࡾ㸪ᐇ㉁ᨻᗓᨭฟࡢ๐ῶ࡟ࡼࡿᐇ㉁GDP࡬ࡢࣉࣛࢫࡢຠᯝࡀᏑᅾࡍࡿྍ⬟ᛶࡣ࠶ࡾᚓࡿࠋ
ࠉ㈈ᨻ㉥Ꮠࢆῶࡽࡍࡓࡵࡢቑ⛯࡟ࡘ࠸᳨࡚ウࡍࡿࠋGrangerࡢព࿡࡛ᐇ㉁ᨻᗓ཰ධ࠿ࡽᐇ㉁ᨻᗓᨭฟ࡬ࡢ
ᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁ࡞࠿ࡗࡓࡓࡵ㸪ቑ⛯࡟ࡼࡿᐇ㉁ᨻᗓ཰ධࡢቑຍࡀᐇ㉁ᨻᗓᨭฟ࡬୚࠼
ࡿຠᯝࡣ኱ࡁࡃ࡞࠸࡜ᮇᚅ࡛ࡁࡿࠋGrangerࡢព࿡࡛ᐇ㉁ᨻᗓ཰ධ࠿ࡽᐇ㉁GDP࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁࡓࡢ࡛㸪ቑ⛯࡟ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࡜࠸࠺ࢣ࢖ࣥࢬຠᯝࡀᶵ⬟ࡍࡿሙྜ࡟ࡣ㸪࠶ࡿ఍ィᖺᗘ࡟࠾ࡅࡿቑ⛯࡟ࡼࡿᐇ㉁ᨻᗓ཰ධࡢቑຍࡀḟ఍ィᖺᗘ௨㝆ࡢᐇ㉁GDP࡬୚࠼ࡿ࣐࢖ࢼࢫࡢຠᯝ
ࡣᏑᅾࡍࡿࡇ࡜ࢆᮇᚅ࡛ࡁࡿࠋቑ⛯࡟ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࡜࠸࠺ࢣ࢖ࣥࢬຠᯝࡀᶵ⬟ࡋ࡞࠸ሙྜ࡟ࡣ㸪㠀ࢣ࢖ࣥࢬຠᯝ࡟ࡼࡾ㸪ቑ⛯࡟ࡼࡿᐇ㉁GDP࡬ࡢࣉࣛࢫࡢຠᯝࡀᏑᅾࡍࡿྍ⬟ᛶࡣ࠶ࡾᚓࡿࠋࠉ⤒῭ᡂ㛗ࡀᅜᐙ㈈ᨻ࡟࠾ࡅࡿ㈈ᨻ㉥Ꮠ࡟୚࠼ࡿຠᯝࢆ᳨ウࡍࡿࠋඛࡎ㸪Grangerࡢព࿡࡛ᐇ㉁GDP࠿ࡽᐇ㉁ᨻᗓ཰ධ࡬ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁࡓࡢ࡛㸪Thorn㸦1967㸧࡟ぢࡽࢀࡿࡼ࠺࡟ᐇ㉁⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓ཰ධ࡬ࣉࣛࢫࡢຠᯝࢆᣢࡘࡢ࡛࠶ࢀࡤ㸪࠶ࡿ఍ィᖺᗘ࡟࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡣḟ఍ィᖺᗘ௨㝆ࡢᐇ㉁ᨻᗓ཰ධ࡬୚࠼ࡿࣉࣛࢫࡢຠᯝࢆᣢࡘࡇ࡜ࡀᮇᚅࡉࢀࡿࠋᮏㄽᩥࡢVARࣔࢹ࡛ࣝᤊ࠼ࡿࡇ
࡜ࡣ࡛ࡁ࡞࠸ࡀ㸪࠶ࡿ఍ィᖺᗘ࡟࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡀᙜヱᖺᗘ࡟࠾ࡅࡿᐇ㉁ᨻᗓ཰ධ࡬୚࠼ࡿࣉࣛࢫࡢ
ຠᯝࡣᐇ㝿࡟ࡋࡤࡋࡤぢࡽࢀࡿࡇ࡜࡛࠶ࡿࠋࡲࡓ㸪ᐇ㉁⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓ཰ධ࡬࣐࢖ࢼࢫࡢຠᯝࢆᣢࡘ
ሙྜࡣ㸪ᐇドⓗ࡟࠶ࡲࡾព࿡ࡢ࡞࠸ࡶࡢ࡛࠶ࡿࠋḟ࡟㸪Grangerࡢព࿡࡛ᐇ㉁GDP࠿ࡽᐇ㉁ᨻᗓᨭฟ࡬
ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ࡜ࢆⓎぢ࡛ࡁࡓࡢ࡛㸪࣡ࢢࢼ࣮ἲ๎࡟ぢࡽࢀࡿࡼ࠺࡟ᐇ㉁GDPࡢቑຍ࡟ࡼࡿ⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓᨭฟ࡬ࣉࣛࢫࡢຠᯝࢆᣢࡘࡢ࡛࠶ࢀࡤ㸪࠶ࡿ఍ィᖺᗘ࡟࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡣḟ఍ィᖺᗘ௨㝆ࡢᐇ㉁ᨻᗓᨭฟ࡬୚࠼ࡿࣉࣛࢫࡢຠᯝࢆᣢࡘࡇ࡜ࡀᮇᚅࡉࢀࡿࠋᚑࡗ࡚㸪⤒῭ࡀᡂ㛗ࡍࡿ࡜ࡁ࡟
ࡣ㸪┦ᑐⓗ࡟ᐇ㉁ᨻᗓ཰ධࡀᐇ㉁ᨻᗓᨭฟ࡟ẚࡋ࡚ቑຍࡍࢀࡤ㸪㈈ᨻ㉥Ꮠࢆ๐ῶ࡛ࡁࡿࡇ࡜࡟࡞ࡿࠋᐇ㉁GDPࡢቑຍ࡟ࡼࡿ⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓᨭฟ࡬ࣉࣛࢫࡢຠᯝࢆᣢࡘࡀࡑࡢຠᯝࡀᑠࡉ࠸ࡢ࡛࠶ࢀࡤ㸪㈈ᨻ
㉥Ꮠࡣᨵၿࡍࡿࡇ࡜ࡀᮇᚅࡉࢀࡿࠋ௨ୖࡼࡾ㸪ᐇ㉁⤒῭ᡂ㛗ࡀಁ㐍ࡉࢀ࡚ᐇ㉁ᨻᗓ཰ධ࡟ẚࡋ࡚ᐇ㉁ᨻᗓ
ᨭฟࡢቑຍࢆᢚไ࡛ࡁࡿሙྜ࡟ࡣ㸪㈈ᨻ㉥Ꮠࡀᨵၿࡍࡿࡇ࡜ࢆᮇᚅ࡛ࡁࡿࠋ
ࠉ㈈ᨻ㉥Ꮠࢆᨵၿࡋࡓ࠸ሙྜ࡟ࡣ㸪ᨻᗓᨭฟࡢ๐ῶࡸቑ⛯ࡶ኱஦࡛࠶ࡿࡀ㸪⤒῭ᡂ㛗࠿ࡽࡢどⅬࡣᴟࡵ࡚㔜せ࡜⪃࠼ࡿࠋቑ⛯ࡸᨻᗓᨭฟࡢ๐ῶࡣ㸪ࢣ࢖ࣥࢬຠᯝࡀ᪥ᮏ⤒῭࡟ᶵ⬟ࡋ࡚࠸ࡿሙྜ࡟ࡣ㸪ᐇ㉁⤒῭ᡂ

̿ 23 ̿

఍ィ᳨ᰝ◊✲ࠉNo.44㸦2011.9㸧

㛗࡟࣐࢖ࢼࢫ࡛࠶ࡾ㸪㠀ࢣ࢖ࣥࢬຠᯝࡀᶵ⬟ࡋ࡚࠸ࡿሙྜ࡟ࡣ㸪ᐇ㉁⤒῭ᡂ㛗࡟ࣉࣛࢫ࡟࡞ࡾᚓࡿࠋቑ⛯ࡸᨻᗓᨭฟࡢ๐ῶ࡟ࡼࡿ㈈ᨻ㉥Ꮠࡢ๐ῶࢆ⾜࠺ࡢ࡛࠶ࢀࡤ㸪ࢣ࢖ࣥࢬຠᯝࡀᏑᅾࡋ࡞࠸࠿࠶ࡿ࠸ࡣᏑᅾࡋ
࡚ࡶࡑࡢຠᯝࡀᑠࡉ࠸࡜ุ᩿ࡉࢀࡿሙྜ࡛࠶ࡿࠋᐇ㉁⤒῭ᡂ㛗ࡣ㸪ᐇ㉁ᨻᗓ཰ධ࡟ẚ㍑ࡋ࡚ᐇ㉁ᨻᗓᨭฟ
ࡢቑຍࢆᢚไ࡛ࡁࡿሙྜ࡟ࡣ㸪㈈ᨻ㉥Ꮠࢆᨵၿࡍࡿࡇ࡜ࡀᮇᚅࡉࢀࡿࠋࡇࡢࡼ࠺࡞ព࿡࡛ࡣ㸪ᮏㄽᩥ࡛ࡣ
㔠⼥ኚᩘࢆศᯒᑐ㇟࡜ࡋ࡚࠸࡞࠸ࡀ㸪㔠⼥ᨻ⟇࡟ࡼࡿ⤒῭ࡢ่⃭⟇ࡀ㈈ᨻ㉥Ꮠ๐ῶ࡟࡜ࡗ࡚㔜せ࡛࠶ࡿྍ⬟ᛶࡣ඘ศ࡟࠶ࡾᚓࡿࠋ
ࠉᮏㄽᩥ࡛ࡣ㸪4 ኚᩘࢆศᯒᑐ㇟࡜ࡍࡿ㧗ᶫ㸦2010㸧࡜␗࡞ࡾ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓ཰ධ㸪ᐇ㉁GDPࡢ3 ኚᩘ㛫࡛ࡣඹ࿴ศࢆⓎぢࡍࡿࡇ࡜ࡀ࡛ࡁ࡞࠿ࡗࡓࠋᮏㄽᩥࡣ㸪Ώ㎶࣭⸭཭࣭ఀ⸨㸦2010㸧࡜㧗ᶫ㸦2010㸧࡜␗࡞ࡾ㸪ࡼࡾศᯒᮇ㛫ࡢ㛗࠸ᖺḟࢹ࣮ࢱࡀ฼⏝ࡉࢀ㸪ᨻᗓ཰ධ࡜ᨻᗓᨭฟࡢᅉᯝ㛵ಀ࡜࣡ࢢࢼ࣮௬ㄝࡢ◊✲࡟ᇶ࡙࠸࡚࠸ࡿࠋ
ࠉᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢᅉᯝ㛵ಀࡢ◊✲࡛ࡣ㸪࢖ࣥࣃࣝࢫ཯ᛂ࡜ศᩓศゎࢆศᯒࡋࡓ◊✲ࡣഹᑡ࡛࠶ࡿࠋ
Carneiro㸦2007㸧ࡣ㸪ᨻᗓᨭฟ࡜ᨻᗓ཰ධࡢᅉᯝ㛵ಀࡢᯟ⤌ࡳ࡛㸪ᨻᗓᨭฟ㸪▼Ἔ⛯ࡢ཰ධ㸪ᐇ㉁GDP
ࡢ3 ኚᩘ㛫ࡢ࢖ࣥࣃࣝࢫ཯ᛂ࡜ศᩓศゎࡢศᯒࢆ࢔ࣥࢦࣛ࡟ᑐࡋ࡚⾜ࡗ࡚࠸ࡿࠋGiorgioni and Holden
㸦2003㸧ࡣ㸪GDP㸪Ẹ㛫ᾘ㈝㸪ᨻᗓᨭฟ㸪ᨻᗓ཰ධ㸪ᰴᘧᕷሙࡢᣦᶆࡢ5 ኚᩘ࡟㛵ࡋ࡚㸪࢖ࣥࣃࣝࢫ཯
ᛂࢆศᯒࡋࡓࠋ
ࠉ௒ᚋࡢㄢ㢟ࡣ㸪࢖ࣥࣃࣝࢫ཯ᛂ࡜ศᩓศゎࡢศᯒ࡛࠶ࡿࠋᐇ㉁ᨻᗓᨭฟ㸦ge㸧࡜ᐇ㉁GDP㸦gdp㸧࡟㛵ࡋ࡚ࡣ㸪཮᪉ྥࡢᅉᯝ㛵ಀ㸦¨ge⇄¨gdp）ࢆ☜ㄆࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋࡉࡽ࡟㸪ᐇ㉁ᨻᗓ཰ධ㸦gr㸧࡜ᐇ㉁GDP㸦gdp㸧࡟㛵ࡋ࡚ࡣ㸪཮᪉ྥࡢᅉᯝ㛵ಀ㸦¨ge⇄¨gdp㸧ࢆ☜ㄆࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋḟࡢ4ࡘࡢᅉᯝ㛵ಀ㸦¨gdpЍ¨ge㸧㸪㸦¨geЍ¨gdp㸧
㸪㸦¨gdpЍ¨ge㸧㸪㸦¨grЍ¨gdp㸧࡟㛵ࡋ࡚㸪ᅉᯝ㛵ಀࡀࣉࣛࢫࡢຠᯝ
ࢆᣢࡘࡢ࠿࠶ࡿ࠸ࡣ࣐࢖ࢼࢫࡢຠᯝࢆᣢࡘࡢ࠿ࢆศᯒࡍࡿࡇ࡜ࡣ㸪⯆࿡῝࠸ࠋࡇࡢࡼ࠺࡞ศᯒࡣ㸪࢖ࣥࣃࣝࢫ཯ᛂࢆศᯒࡍࡿࡇ࡜࡛᫂ࡽ࠿࡟࡞ࡿྍ⬟ᛶࡀ࠶ࡿࠋ
ࠉࡲࡓ㸪ge࡜gr࡜gdpࡢỈ‽ኚᩘࢆ⏝࠸ࡓᅉᯝ㛵ಀࡢศᯒࡣ㸪ヨࡳࡿ࡭ࡁㄢ㢟࡛࠶ࡿࠋࣔࢹࣝC࡟࠾ࡅࡿADF᳨ᐃ࡟ࡼࡿ༢఩᰿᳨ᐃࡢ⤖ᯝࡣ㸪AIC࡜SICࡢ୧ᇶ‽࡛ࣛࢢḟᩘkࢆ㑅ࢇࡔ࡜ࡁ࡟㸪ge࡜gr࡜
gdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦0㸧࡜ุ᩿࡛ࡁࡓࠋࡉࡽ࡟㸪VARࣔࢹࣝࢆ⏝࠸࡚Grangerࡢᅉᯝ㛵ಀࢆศᯒࡍࡿሙྜ㸪Hamilton㸦1994㸧ࡢ➨ 1ࡢ᪉ἲࡣ㸪Ỉ‽ኚᩘ㸦ࣞ࣋ࣝኚᩘ㸧⏝࠸࡚VARࡢᅇᖐࢆ⾜࠺ࡇ࡜࡛࠶ࡿࠋ̿ 24 ̿

᪥ᮏ࡟࠾ࡅࡿᅜᐙ㈈ᨻ࡜⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀཧ⪃ᩥ⊩⏣୰⚽࣭᫂໭㔝♸୍㑻㸦2002㸧
ࠕḢ⡿ㅖᅜ࡟࠾ࡅࡿ㈈ᨻᨻ⟇ࡢ࣐ࢡࣟ⤒῭ⓗຠᯝࠖࠉࠗࣇ࢕ࢼࣥࢩ࣭ࣕࣝࣞ
ࣅ࣮ࣗ࠘➨ 63 ྕ㸪pp.114-159㸦㈈ົ⥲ྜᨻ⟇◊✲ᡤࡢࣇ࢕ࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗࡢ࣮࣒࣮࣍࣌ࢪࡼ
ࡿ࣮࣌ࢪᩘ㸧
㸬㧗ᶫ㟷ኳ㸦2010㸧ࠕ᪥ᮏ࡟࠾ࡅࡿࣂࣈࣝᔂቯᚋࡢ㈈ᨻᨻ⟇ࡢຠᯝ-ඹ࿴ศศᯒ࡟ࡼࡿィ ࠖ
ࠉ㈈ᨻᏛ఍⦅㞟ࠗࢣ࢖ࣥࢬࡣ⏛ࡗࡓ࠿࠘㈈ᨻ◊✲➨ 6 ᕳࠉ᭷ᩫ㛶㸬⏿㎰㗦▮㸦2005㸧
ࠕ␗᫬Ⅼ㛫ࡢㄢ⛯ཎ⌮࡜㈈ᨻ㉥ᏐѸㄢ⛯ᖹ‽໬࡜⥲㟂せᖹ‽໬ࠖࠉ㔝ཱྀᝆ⣖㞝⦅ࠗබඹᨻ
⟇ࡢ᪂ࡓ࡞ᒎ㛤ࠉ㌿᥮ᮇࡢ㈈ᨻ㐠Ⴀࢆ⪃࠼ࡿ࠘ᮾி኱Ꮫฟ∧఍ࠉ➨ 2 ❶ࠉpp.53 Ѹ 81㸬ᮏከభ୕㸦1998㸧ࠕࢣ࢖ࣥࢬ࡜⌧௦⤒῭:ࠉ㈨⏘౯᱁ࡢどⅬ࠿ࡽࡢᒎᮃࠖ
ࠉࠗࣇ࢕ࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗ࠘
ࠉ➨ 45 ྕ㸪pp.1-22㸦㈈ົ⥲ྜᨻ⟇◊✲ᡤࡢࣇ࢕ࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗࡢ࣮࣒࣮࣍࣌ࢪࡼࡿ࣮࣌ࢪᩘ㸧㸬Ώ㎶ດ࣭⸭཭Ⰻ࣭ఀ⸨᪂㸦2010㸧ࠕไᗘ᝟ሗࢆ⏝࠸ࡓ㈈ᨻ஌ᩘࡢィ ࠖࠉ஭ᇼ฼ᏹ⦅㞟ࠗ㈈ᨻᨻ⟇࡜♫఍ಖ㞀࠘៞᠕⩏ሿ኱Ꮫฟ∧఍ 㸬
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