㸯㸬ࡣࡌࡵ
ࠉ㏆ᖺ㸪ྛᅜ࠾ࡅࡿᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀ㛵ࡍࡿᐇド◊✲ࡀᩘከࡃᏑᅾࡍࡿࠋᨻᗓᨭฟ ᨻᗓධࡢᕪࡣ㸪㈈ᨻ㉥Ꮠ࡛࠶ࡿࠋᨻᗓᨭฟᨻᗓධࡢᅉᯝ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ᨻ
ᗓᨭฟᨻᗓධࡢ⣔ิࢹ࣮ࢱࡀᐃᖖ࡛࠶ࡿࡇࢆ௬ᐃࡋ࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃࢆᐇ⾜ࡋ࡚࠸ࡿࠋ
ᚑࡗ࡚㸪ࡇࢀࡽࡢ◊✲࡛ࡣ㸪༢᰿᳨ᐃඹศ᳨ᐃࡢศᯒࡀ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ᨻᗓᨭฟᨻᗓධ㛵ࡍࡿ༢᰿᳨ᐃ ඹศࡢ᳨ᐃࡀ⾜ࢃࢀ㸪ࡇࢀᇶ࡙ࡁᅉᯝ㛵ಀࢆศᯒࡋ࡚࠸ࡿࠋࡲࡓ㸪≉᭱㏆࡛ࡣ㸪࣓ࣜ࢝ྜ⾗ᅜ ௨እࡢࡢඛ㐍ㅖᅜࡸ㸪㈈ᨻ㉥Ꮠࡢၥ㢟ࢆᢪ࠼࡚࠸ࡿⓎᒎ㏵ୖᅜࡢࢹ࣮ࢱࢆ⏝࠸ࡓྠᵝࡢศᯒࡶᏑᅾࡍ ࡿࠋࡋࡋ㸪᪥ᮏ࠾ࡅࡿᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀ㛵ࡍࡿᐇド◊✲ࡣ㸪Owoye㸦1995㸧ࡸ Chang, Liu and Caudill㸦2002㸧ࢆ㝖࠸࡚㸪㠀ᖖᩘᑡ࡞࠸≧ែ࡛࠶ࡿࠋ
ࠉNarayan and Narayan㸦2006㸧ࡣ㸪ᨻᗓᨭฟᨻᗓධࡢ2 ኚᩘGDPࢆຍ࠼࡚3 ኚᩘࡢศᯒࢆ⾜ࡗ࡚ ࠸ࡿࠋᨻᗓᨭฟGDPࡢ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GDPࡽᨻᗓᨭฟࡢᅉᯝ㛵ಀ㸧ࢣࣥࢬ௬ㄝ㸦ᨻᗓᨭฟࡽGDP ࡢᅉᯝ㛵ಀ㸧ࡢ࠸ࡎࢀࡀᨭᣢࡉࢀࡿࢆศᯒࡋ࡚࠸ࡿࠋ3 ኚᩘࡢࣔࢹࣝࡣ㸪ᨻᗓᨭฟᨻᗓධࡢᅉᯝ 㛵ಀ㸪ᨻᗓᨭฟGDPࡢᅉᯝ㛵ಀࢆ⤫ྜࡋࡓᯟ⤌ࡳ࡛ศᯒ࡛ࡁࡿࠋ᪥ᮏ࠾ࡅࡿ3 ኚᩘࡢࣔࢹ࡛ࣝ ࡢᅉᯝ㛵ಀࡢศᯒࡣከࡃ࡞࠸ࠋ≉㸪ୖグࡢᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀ㸪࠾ࡼࡧ㸪ᨻᗓᨭฟ
᪥ᮏ࠾ࡅࡿᅜᐙ㈈ᨻ⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀ
㔝ࠉᮧࠉࠉ┈ࠉኵ
ѽ㸦ྡྂᒇᏛ㝔Ꮫ⤒῭Ꮫ㒊ᩍᤵ㸧
ᖹࠉࠉࠉࠉஅ
ѽѽ㸦㤶ᕝᏛ⤒῭Ꮫ㒊ᩍᤵ㸧
ѽ 1957 ᖺ⏕ࡲࢀࠋ⚄ᡞၟ⛉ᏛᏛ㝔⤒῭Ꮫ◊✲⛉༤ኈᚋᮇㄢ⛬༢ྲྀᚓ㏥Ꮫࠋ༤ኈ㸦⤒῭Ꮫ㸧 ࠋ⚄ᡞၟ⛉Ꮫຓᡭ㸪㥴ἙྎᏛ⤒῭Ꮫ㒊ㅮ ᖌ࣭ຓᩍᤵ㸪ྡྂᒇᏛ㝔Ꮫ⤒῭Ꮫ㒊ຓᩍᤵࢆ⤒࡚㸪1999 ᖺ 4 ᭶ྡྂᒇᏛ㝔Ꮫ⤒῭Ꮫ㒊ᩍᤵࠋᑓᨷࡣ㸪ィ㔞⤒῭Ꮫ࣭㈈ᨻᏛࠋᡤᒓᏛࡣ㸪 ᪥ᮏ⤒῭Ꮫ㸪᪥ᮏ⤫ィᏛ㸪᪥ᮏ㈈ᨻᏛࠋ ѽѽ 1961 ᖺ⏕ࡲࢀࠋ⚄ᡞၟ⛉ᏛᏛ㝔⤒῭Ꮫ◊✲⛉༤ኈᚋᮇㄢ⛬༢ྲྀᚓ㏥Ꮫࠋ1990 ᖺ⇃ᮏᏛᅬᏛ⤒῭Ꮫ㒊ㅮᖌ㸪1996 ᖺ㤶ᕝᏛ⤒῭ Ꮫ㒊ຓᩍᤵ㸪2001 ᖺ㤶ᕝᏛ⤒῭Ꮫ㒊ᩍᤵ㸪⌧ᅾ⮳ࡿࠋᑓᨷࡣබඹ⤒῭ᏛࠋᡤᒓᏛࡣ㸪᪥ᮏ⤒῭Ꮫ㸪᪥ᮏ㈈ᨻᏛ㸪᪥ᮏᆅ᪉㈈ᨻᏛࠋGDPࡢᅉᯝ㛵ಀࡢᩥ⊩ᇶ࡙ࡃ◊✲ࡣࢇ࡞࠸≧ែ࡛࠶ࡿࠋ ࠉᨻᗓᨭฟᨻᗓධᐇ㉁GDPࡢ3 ኚᩘᑐࡋ࡚㸪᪥ᮏ࠾ࡅࡿᅉᯝ㛵ಀࡢศᯒࢆ⾜ࡗࡓㄽᩥࡣᑡ࡞ ࠸≧ែ࡛࠶ࡿࠋࡓࡔࡋ㸪Ώ㎶࣭⸭࣭ఀ⸨㸦2010㸧ࡣ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓ⛯㸪ᐇ㉁GDPࡢ3 ኚ ᩘ㛵ࡍࡿ࣋ࢡࢺࣝ⮬ᕫᅇᖐ㸦VAR㸧ࣔࢹࣝࢆ㸪1965 ᖺ➨ 1 ᅄ༙ᮇࡽ2004 ᖺ➨ 4 ᅄ༙ᮇࡲ࡛ࡢࢹ࣮ ࢱࢆ⏝࠸࡚ศᯒࡋ࡚࠸ࡿࠋΏ㎶࣭⸭࣭ఀ⸨ࡣ㸪ᅉᯝ㛵ಀࡸศᩓศゎࡢศᯒࢆ⾜ࢃࡎ㸪VARࢆ⏝࠸࡚ ࣥࣃࣝࢫᛂࢆศᯒࡋ࡚㈈ᨻᩘࡘ࠸᳨࡚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ᮇᏊ⋡ࡢࢹ࣮ࢱ ᑐࡋ࡚㸪༢᰿᳨ᐃඹศ᳨ᐃࢆ⾜ࡗ࡚㸪2 ಶࡢඹศ㛵ಀࢆᚓ࡚࠸ࡿࠋࡇࢀࡽࡢ⤖ᯝᇶ࡙࠸࡚࣋ࢡ ࢺࣝㄗᕪಟṇ⮬ᕫᅇᖐࣔࢹࣝ㸦VECM㸧࡛ࣥࣃࣝࢫᛂࢆィ ࡋ࡚㸪㈈ᨻᩘࡘ࠸᳨࡚ウࡋ࡚࠸ࡿࠋ 㧗ᶫࡢศᯒᮇ㛫ࡣ㸪1990 ᖺ➨ 1 ᅄ༙ᮇࡽ2008 ᖺ➨ 4 ᅄ༙ᮇࡲ࡛ࡢᮇ㛫࡛࠶ࡿࠋ ࠉᮏㄽᩥࡢ┠ⓗࡣ㸪᪥ᮏ࠾ࡅࡿᅜᐙ㈈ᨻGDPࡼࡿ⤒῭ᡂ㛗ࡢᅉᯝ㛵ಀࢆศᯒࡍࡿࡇ࡛࠶ࡿࠋᅜ ᐙ㈈ᨻࡣ㸪ᅜࡢ୍⯡ィண⟬ࡢỴ⟬್ࢆ⏝࠸࡚ィ⟬ࡉࢀࡓᨻᗓᨭฟᨻᗓධ࡛ᤊ࠼ࡿࠋᮏㄽᩥ࡛ࡣ㸪᪥ ᮏᅜࡢ୍⯡ィண⟬࠾ࡅࡿ1955 ᖺᗘࡽ2008 ᖺᗘࡲ࡛ࢆศᯒᮇ㛫ࡋ࡚㸪ᅜᐙ㈈ᨻ࡛ᤊ࠼ࡓᨻᗓᨭ ฟᨻᗓධ࠾ࡼࡧGDPࡢ࣋ࢡࢺࣝ⮬ᕫᅇᖐ㸦VAR㸧ࣔࢹࣝ࠾࠸࡚㸪ࡇࡢ3 ኚᩘ㛵ࡍࡿᅉᯝ㛵ಀࢆ Grangerࡢᅉᯝ㛵ಀࢆ⏝࠸࡚ศᯒࢆ⾜࠺ࠋᨻᗓᨭฟᨻᗓධGDPࡢ⣔ิࢹ࣮ࢱࡘ࠸࡚ࡑࢀࡒࢀ ༢᰿ࡢ᳨ᐃࢆ⾜࠸㸪ḟ㸪ᨻᗓᨭฟᨻᗓධGDPࡢ3 ኚᩘ㛵ࡋ࡚Engle and Granger㸦1987㸧ࡢ ඹศ᳨ᐃࢆ⾜࠺ࠋඹศ᳨ᐃࡣ㸪Johansen㸦1991㸧ࡢ᪉ἲࡶ࠶ࡿࠋZhou㸦2001㸧ࡣ㸪Engle and Granger᳨ᐃJohansen᳨ᐃࡢ᪉ἲࢆࣔࣥࢸ࣭࢝ࣝࣟᐇ㦂࡛ẚ㍑ࢆ⾜࠸㸪᳨ฟຊࢧࢬࢆᑻᗘࡋ࡚⏝ ࠸࡚㸪ᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜࡣEngle and Granger᳨ᐃࡢ᪉ἲࡀⰋ࠸ࡋ࡚࠸ࡿࠋᮏㄽᩥࡢᖺḟࢹ࣮ ࢱᩘࡣ54 ಶ࡛࠶ࡿࡢ࡛㸪Engle and Grangerࡢ᪉ἲࢆ⏝࠸ࡿࠋ
ࠉศᯒᑐ㇟ࡢ3 ኚᩘࡀ༢᰿ࢆᣢࡘሙྜࡣ㸪Engle and Grangerࡢඹศ᳨ᐃࢆ⏝࠸࡚ᨻᗓᨭฟᨻᗓ ධGDPࡀ㛗ᮇⓗ࡞ᆒ⾮㛵ಀ࠶ࡿ࠺ࢆศᯒࡍࡿࠋࡑࡋ࡚㸪ࡶࡋ3 ኚᩘ㛫࡛ඹศࡢ㛵ಀࡀᏑ ᅾࡍࡿ࡞ࡽࡤ㸪ㄗᕪಟṇࣔࢹࣝࢆ᥎ᐃࡍࡿࡇࡼࡗ࡚㸪㛗ᮇ࠾ࡅࡿᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀ ࢆศᯒࡍࡿࠋ3 ኚᩘ㛫࡛ඹศࡢ㛵ಀࡀᏑᅾࡋ࡞࠸ሙྜࡣ㸪ྛኚᩘࡘ࠸࡚1 ᅇࡢ㝵ᕪࢆࡾ㸪VARࣔ ࢹࣝࢆ᥎ᐃࡍࡿࡇࡼࡗ࡚Grangerࡢᅉᯝᛶ᳨ᐃࢆ⾜࠺ࠋࡇࢀࡼࡾ㸪3 ኚᩘࡢ୰ࡽ2 ኚᩘࢆ㑅ࢇ࡛ ▷ᮇࡢᅉᯝ㛵ಀࢆㄪࡿࡇࡀ࡛ࡁࡿࠋᚑ᮶ࡢ᪥ᮏㄒ࡛᭩ࢀࡓᅉᯝ㛵ಀࡢ◊✲࡛ࡣ㸪㔠⼥⤒῭ࢆศᯒᑐ ㇟ࡋ࡚㸪ඹศ᳨ᐃࢆ↓どࡋࡓศᯒࡶከ࠸ࠋ ࠉᮏㄽᩥࡢᵓᡂࡣ㸪௨ୗࡢ㏻ࡾ࡛࠶ࡿࠋࡲࡎ➨2 ⠇㸦2.㸧࡛ࡣ㸪ศᯒ࡛⏝࠸ࡿ༢᰿᳨ᐃඹศ᳨ᐃ ࡘ࠸࡚ㄝ᫂ࡋ࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃࢆ⾜࠺ࡓࡵࡢkḟࡢ࣋ࢡࢺࣝ⮬ᕫᅇᖐࣔࢹࣝVAR㸦k㸧ࢆㄝ᫂ࡍࡿࠋ ࡉࡽ㸪⏝ࡍࡿࢹ࣮ࢱࡘ࠸࡚ㄝ᫂ࡍࡿࠋࡑࡋ࡚➨3 ⠇㸦3.㸧࠾࠸࡚㸪ᐇドศᯒࡢ⤖ᯝࡘ࠸࡚㆟ㄽ ࡍࡿࠋ᭱ᚋ㸪➨4 ⠇㸦4.㸧࡛⤖ㄽᚋࡢㄢ㢟ࢆ㏙ࡿࠋ
㸰
㸬ศᯒ᪉ἲࢹ࣮ࢱ
2. 1 ࢹ࣮ࢱグྕ ࠉᨻᗓධ㸻ᅜࡢṓධѸබമ㔠ධ㸪ᨻᗓᨭฟ㸻ᅜࡢṓฟѸᅜമ㈝ࡋ࡚㸪ࡑࢀࡒࢀGDPࢹࣇ࣮ࣞࢱ࣮࡛ ᐇ㉁ࢆ⾜࠺ࠋᨻᗓධᨻᗓᨭฟࡢᐃ⩏ࡣ㸪ᇶ♏ⓗ㈈ᨻᨭࡢᐃ⩏ࢆ⪃៖ࡋ࡚࠸ࡿࠋᐇ㉁ࡢᨻᗓᨭฟ㸪 ᐇ㉁ࡢᨻᗓධ㸪ᐇ㉁GDPࡢࡑࢀࡒࢀࡢ⮬↛ᑐᩘࢆྲྀࡾ㸪ࡑࡢグྕࢆࡑࢀࡒࢀge㸪gr㸪gdpࡍࡿࠋ ࠉᮏㄽᩥࡢᐇドศᯒࡣ㸪ᨻᗓ㸦ᅜ㸧ࡢ୍⯡ィࢆศᯒᑐ㇟ࡋ㸪1955 ᖺᗘࡽ2008 ᖺᗘࡲ࡛ࡢᖺᗘࢹ࣮ ࢱࢆ⏝ࡍࡿࠋୖ㏙ࡢࡼ࠺㸪ᨻᗓධࡣṓධ⥲㢠ࡽබമ㔠ධࢆᕪࡋᘬ࠸ࡓࡶࡢ㸪ࡑࡋ࡚ᨻᗓᨭฟࡣṓฟ⥲㢠ࡽᅜമ㈝ࢆᕪࡋᘬ࠸ࡓࡶࡢ࡛࠶ࡿࠋࡇࢀࡽࡢࢹ࣮ࢱ㸦ྡ┠್㸧ࡣࡍ࡚㸪㈈ົ┬ࡢࠗ㈈ᨻ⤫ィ࠘ ࡼࡾ㸪ᨻᗓ୍⯡ィࡢỴ⟬㢠ࡋ࡚ồࡵࡽࢀࡿࠋ࡞࠾㸪㏆ᖺࡢྠࢹ࣮ࢱࡘ࠸࡚ࡣ㸪㈈ົ┬ࡢ࣮࣒࣮࣍࣌ ࢪࡽධᡭ࡛ࡁࡿࠋࡲࡓ㸪ᨻᗓධᨻᗓᨭฟࡢኚᩘࢆᐇ㉁ࡍࡿࡓࡵࡢGDPࢹࣇ࣮ࣞࢱ࣮ࡣ㸪ࠗᅜẸ⤒ ῭ィ⟬ᖺሗ࠘㸦ෆ㛶ᗓ⤒῭♫⥲ྜ◊✲ᡤ㸧ࡽᚓࡽࢀࡿࠋࡉࡽ㸪ᐇ㉁GDPࡢࢹ࣮ࢱࡶࡲࡓ㸪ࠗᅜẸ⤒ ῭ィ⟬ᖺሗ࠘ࡼࡾᚓࡽࢀࡿࠋ ࠉࡇࡇ࡛㸪GDPࢹࣇ࣮ࣞࢱ࣮ᐇ㉁GDPࡢࢹ࣮ࢱࡘ࠸࡚㸪᭱㏆Ⅼࡲ࡛ࡢࢹ࣮ࢱࡣ1993 ᖺᨵゞࡢᅜ Ẹ⤒῭ィ⟬య⣔㸦93SNA㸧ࡼࡾồࡵࡽࢀࡿࠋࡇࢁࡀ㸪ࡇࡢ93SNAࡢࢹ࣮ࢱࡣ㐳ཬࡋ࡚1980 ᖺᗘࡲ࡛ ࡋබ⾲ࡉࢀ࡚࠸࡞࠸ࠋ୍᪉㸪ᅜẸ⤒῭ィ⟬࠾ࡅࡿ68SNA࡛ࡣ㸪1955 ᖺᗘࡼࡾ࠸ࡎࢀࡢࢹ࣮ࢱࡶධᡭ ࡍࡿࡇࡀྍ⬟࡛࠶ࡿࡀ㸪ࢹ࣮ࢱࡢ⤊ᮇࡣ1998 ᖺᗘ࡞ࡗ࡚࠸ࡿࠋࡇࢀࡼࡾ㸪93SNA࡛ࡣ68SNAࡢෆ ᐜࡀኚ᭦ࡉࢀ࡚࠸ࡿࡓࡵ㸪ࢹ࣮ࢱࡢ୍㈏ᛶၥ㢟ࡀ⏕ࡌࡿࡶࡢࡢ㸪㛗ᮇࢃࡓࡿࢹ࣮ࢱࢆ☜ಖࡍࡿࡓࡵ 㸪1955 ᖺᗘࡽ1998 ᖺᗘࡲ࡛ࡢᮇ㛫࠾࠸࡚ࡣ68SNAࡢࢹ࣮ࢱࢆ⏝ࡋ㸪1999 ᖺᗘ௨㝆ࡣ93SNA ࡢࢹ࣮ࢱࢆ⏝࠸ࡿࡇࡍࡿࠋࡑࡇ࡛㸪GDPࢹࣇ࣮ࣞࢱ࣮ᐇ㉁GDPࡘ࠸࡚ࡣࡑࢀࡒࢀ㸪68SNAࡢ 1990 ᬺᖺᇶ‽ࡢࢹ࣮ࢱᇶ࡙ࡁ㸪⏿㎰㸦2005㸧ྠᵝ㸪68SNA࠾ࡅࡿ1998 ᖺᗘࡢࢹ࣮ࢱࢆ93SNA ࡢᙜヱࢹ࣮ࢱࡢఙࡧ⋡࡛ᘏ㛗ࡋ࡚᥎ィࡍࡿࡇࡼࡾ㸪68SNA93SNAࡢࢹ࣮ࢱࢆ᥋⥆ࡍࡿࡇࡋࡓࠋ 2. 2 ༢᰿᳨ᐃඹศ᳨ᐃ
ࠉ༢᰿᳨ᐃࡣ㸪༢᰿ࢆᖐ↓௬ㄝࡍࡿADF᳨ᐃࢆ⏝࠸ࡿࠋHamori and Matsubayashi 㸦2001㸧 Li 㸦2001㸧ᚑࡗ࡚㸪ᐃᩘ㡯ࡢࡳࡢᅇᖐᘧ㸦ࣔࢹࣝC㸧㸪ᐃᩘ㡯ࢱ࣒࣭ࢺࣞࣥࢻࢆྵࡴᅇᖐᘧ㸦ࣔࢹ
ࣝC&T㸧ࢆ⏝࠸࡚㸪ADF᳨ᐃࢆ⾜࠺1㸧ࠋADF᳨ᐃ࡛ࡣ㸪ᖐ↓௬ㄝࡣ༢᰿ࢆᣢࡘ࠸࠺ࡇ࡛࠶ࡿࠋ
ADF᳨ᐃ࡛ࡣ㸪ᣑᙇ㡯ࡢࣛࢢᩘࡣ㸪㉥ụࡢሗ㔞ᇶ‽㸦Akaike Information Criterion, AIC㸧Schwarz ࡢሗ㔞ᇶ‽㸦Schwarz Information Criterion, SIC㸧ࢆ⏝࠸࡚㑅ᢥࡍࡿࠋ
ࠉᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ࡢᨻᗓᨭฟ㸦ge㸧㸪ᐇ㉁ࡢᨻᗓධ㸦gr㸧㸪ᐇ㉁GDP㸦gdp㸧ࡢ3 ኚᩘ㛵ࡋ࡚㸪௨ୗ
ࡢ⌮⏤࡛㸪Engle and Granger᳨ᐃࢆ⏝࠸࡚ඹศ᳨ᐃࢆ⾜࠺2㸧ࠋඹศ᳨ᐃࡣ㸪◊✲ㄽᩥ࡛㢖⦾
⏝ࡉࢀࡿ᳨ᐃࡋ࡚Engle and Granger㸦1987㸧ࡢ᪉ἲJohansen㸦1991㸧ࡢ᪉ἲࡀ࠶ࡿࠋZhou㸦2001㸧 ࡣ㸪ࣔࣥࢸ࣭࢝ࣝࣟᐇ㦂ࡼࡾEngle and Granger᳨ᐃJohansen᳨ᐃࢆ᳨ฟຊࡸࢧࢬࡢᑻᗘࢆ⏝࠸ ࡚ẚ㍑ࢆ⾜ࡗ࡚࠸ࡿࠋࡑࡢ⤖ᯝࡋ࡚㸪ᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜࡣEngle and Granger᳨ᐃࢆ⏝࠸ࡿ
ࡇࢆ⸀ࡵ࡚࠸ࡿࠋᑠᶆᮏࡢᖺḟࢹ࣮ࢱࡢሙྜ㸪Johansen᳨ᐃࡣ㸪Engle and Granger᳨ᐃẚ㍑ࡍࡿ㸪
᳨ฟຊࡀపࡃ㸪ࢧࢬࡢṍࡳࡀࡼࡾࡁ࠸ࠋᮏㄽᩥࡢࢹ࣮ࢱᩘࡣ54 ಶ࡛࠶ࡾ㸪ࡇࡢࢹ࣮ࢱࡽᚓࡽࢀࡿ ᶆᮏࡣᆺⓗ࡞ᑠᶆᮏ࡛࠶ࡿࠋ
ࠉ3 ኚᩘge㸪gr㸪gdp㛵ࡍࡿEngle and Granger᳨ᐃ࡛ࡣ㸪ඹศᅇᖐ࠾࠸࡚㸪ge㸪gr㸪gdpࢆ⿕ㄝ᫂ ኚᩘࡍࡿ3ࡘࡢᅇᖐᘧࡘ࠸࡚ඹศ᳨ᐃࢆ⾜࠺ࠋ1ࡘࡢᅇᖐᘧ㸦࠼ࡤ㸪⿕ㄝ᫂ኚᩘࡀge㸪ㄝ᫂ኚᩘ
1㸧ᐃᩘ㡯ࢆྵࡴࣔࢹࣝCᐃᩘ㡯࣭ࢺࣞࣥࢻࢆྵࡴࣔࢹࣝC&Tࡣ㸪
ࣔࢹࣝC㸸ࠉ¨yt=Į0 +㸦Ȗ0 – 1㸧yt–1 + Ȉki=1 į0i ¨yt–i + ut 㸪
ࣔࢹࣝC&T㸸¨yt=Į0 + ȕ0t +㸦Ȗ0 – 1㸧yt–1 + Ȉki=1 į0i ¨yt–i + ut 㸪
࡛࠶ࡿࠋࡇࡇ࡛㸪¨ࡣ㝵ᕪ₇⟬Ꮚ࡛࠶ࡾ㸪ytࡣⅬt࡛ࡢኚᩘ࡛࠶ࡾ㸪yt–1ࡣ¨ytࡢi ᮇ๓ࡢࣛࢢኚᩘ࡛࠶ࡾ㸪Į0㸪ȕ0㸪㸦Ȗ0–1㸧㸪į0i 㸦i=1㸪2㸪͐, k㸧ࡣ ᅇᖐᘧ࠾ࡅࡿಀᩘ㸪utࡣㄗᕪ㡯࡛࠶ࡿࠋ༢᰿᳨ᐃ࡛ࡣ㸪ᖐ↓௬ㄝH0㸸Ȗ0=1㸪ᑐ❧௬ㄝ H1㸸Ȗ0<1࡛࠶ࡿࠋH0㸸Ȗ0=1ࡣ H0㸸Ȗ0–1=0ྠ್ ࡛࠶ࡿࡽ㸪ᖐ↓௬ㄝH0㸸Ȗ0Ѹ1=0ᑐࡍࡿADF᳨ᐃ⤫ィ㔞ࡢ್ࢆィ⟬ࡍࡿࠋMacKinnon 㸦1996㸧ࡢ᪉ἲࡼࡿADF᳨ᐃ⤫ィ㔞ࡢ⮫⏺್p ್ࢆ⏝࠸࡚㸪᳨ᐃࢆ⾜࠺ࠋk=0ࡣ㸪ᣑᙇ㡯 Ȉk
i=1 į0i ¨yt–iࡀ࡞࠸ሙྜࢆ♧ࡍࠋ
2㸧Engle and Granger᳨ᐃࡣ㸪ඹศᅇᖐᘧ x
t=a+b yt+czt+utOLSࢆ㐺⏝ࡋ࡚㸪ṧᕪetࢆồࡵࡿࠋࡇࡇ࡛㸪a㸪b㸪cࡣඹศಀᩘࡲࡓࡣඹศ
ࣃ࣓࣮ࣛࢱ࣮㸪utࡣㄗᕪ㡯㸪xtytztࡣࡑࢀࡒࢀI㸦1㸧 ኚᩘ࡛࠶ࡿࠋࡇࡢṧᕪ etᑐࡋ࡚㸪ADF᳨ᐃࢆ㐺⏝ࡍࡿࠋADF᳨ᐃࡢᅇᖐᘧࡣ㸪
¨et=ȡet–1 + Ȉki=1 įi ¨et–i + ut 㸪
࡛࠶ࡿࠋࣛࢢḟᩘࡢ㑅ᢥࡘ࠸࡚ࡣ㸪AICSICࡢ୧ሗ㔞ᇶ‽࡛⾜࠸㸪AICSICᇶ࡙ࡃ⤖ᯝࢆ♧ࡍࠋADFࡢ᳨ᐃ⤫ィ㔞ࡢp ್ࡣ㸪 MacKinnon 㸦1996㸧ࡢ᪉ἲࡼࡿࠋADF᳨ᐃࢆ⾜࠺ሙྜࡣ㸪⮫⏺್ࡋ࡚Engle and Yoo 㸦1987㸧➼ࡢศᕸ⾲ࢆ⏝࠸ࡿࡇࡶ࡛ࡁࡿࠋ
ࡀgr㸪gdpࡢඹศᅇᖐᘧ㸧ࡢ⤖ᯝࡔࡅ࡛࡞ࡃ㸪⿕ㄝ᫂ኚᩘࢆධࢀ᭰࠼ࡿࡇࡼࡗ࡚⤖ᯝࡢ㡹ᛶࢆぢ ࡿࡇࡀ࡛ࡁࡿࠋ 2. 3 Grangerࡢᅉᯝ㛵ಀ ࠉ࣋ࢡࢺࣝ⮬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࠺ࡇ࡛࠶ࡿࠋ➨ 3ࡢ᪉ἲࡣ㸪 ศᯒᑐ㇟ࡢࢹ࣮ࢱᑐࡋ࡚༢᰿᳨ᐃඹศ᳨ᐃࢆ⾜࠸㸪ࡑࡢ⤖ᯝᇶ࡙࠸࡚㐺ษ࡞VARࣔࢹࣝࢆ㑅 ᢥࡋ࡚ᅇᖐࢆ⾜࠺ࡇ࡛࠶ࡿࠋ ࠉࡇࡢㄽᩥ࡛ࡣ㸪➨3ࡢ᪉ἲᇶ࡙࠸࡚VARࡢᅇᖐࢆ⾜࠺ࠋ༢᰿᳨ᐃඹศ᳨ᐃࡢ⤖ᯝࡼࡗ࡚㸪 ௨ୗࡢࡼ࠺ᆺⓗ࡞ศᯒᡭ㡰ࡋ࡚3 ㏻ࡾࡢሙྜࡀ࠶ࡾᚓࡿࠋࡓࡔࡋ㸪3 ㏻ࡾ௨እࡢእⓗ࡞ሙྜࡶ࠶ ࡾᚓࡿࠋ➨1㸪༢᰿᳨ᐃࡼࡾศᯒࢹ࣮ࢱࡀ࡚I㸦0㸧ࡢᐃᖖኚᩘ࡛࠶ࡿሙྜࡣ㸪Ỉ‽ኚᩘࡢࢹ࣮ ࢱࢆ⏝࠸࡚VARࣔࢹࣝࡢᅇᖐࢆ⾜࠺ࠋ➨ 2㸪༢᰿᳨ᐃࡼࡾศᯒࢹ࣮ࢱࡀ࡚I㸦1㸧࡛༢᰿ࢆᣢ ࡘ㠀ᐃᖖኚᩘ࡛࠶ࡾ㸪ࡘ3 ኚᩘ㛫ඹศࡀᏑᅾࡋ࡞࠸ሙྜࡣ㸪1 㝵ࡢ㝵ᕪኚᩘࢆ⏝࠸࡚VARࣔࢹ ࣝࡢᅇᖐࢆ⾜࠺ࠋ➨3㸪༢᰿᳨ᐃࡼࡾศᯒࢹ࣮ࢱࡀ࡚I㸦1㸧࡛༢᰿ࢆᣢࡘ㠀ᐃᖖኚᩘ࡛࠶ࡾ㸪 ࡘ3 ኚᩘ㛫ඹศࡀᏑᅾࡍࡿሙྜࡣ㸪1 㝵ࡢ㝵ᕪኚᩘㄗᕪಟṇ㡯ࢆ⏝࠸࡚VARࣔࢹࣝ㸦VEC㸪 Vector Error Correction㸧ࡢᅇᖐࢆ⾜࠺ࠋVECࣔࢹ࡛ࣝࡣ㸪ㄗᕪಟṇ㡯ࡣEngle and Granger᳨ᐃ࠾ࡅ
ࡿඹศᅇᖐࡢṧᕪࡽᚓࡿࡇࡀ࡛ࡁࡿࠋ࡞࠾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 ኚᩘࡘ࠸࡚㸪 ¨xt=Į1 + Ȉk i=1 ȕ1i ¨xt + Ȉ k i=1Ȗ1i¨yt+ Ȉ k i=1į1i¨zt + u1t , 㸦1-1㸧 ¨yt=Į2 + Ȉk i=1 ȕ2i ¨xt + Ȉ k i=1Ȗ2i¨yt+ Ȉ k i=1į2i¨zt + u2t , 㸦1-2㸧 ¨zt=Į3 + Ȉk i=1 ȕ3i ¨xt + Ȉ k i=1Ȗ3i¨yt+ Ȉ k i=1į3i¨zt + u3t , 㸦1-3㸧 ࡢᐃᩘ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࠶
ࡿࠋㄗᕪ㡯ut=㸦u1t㸪u2t㸪u3t㸧'ࡢ࣋ࢡࢺࣝࡣ㸪E㸦ut㸧=0㸪3 ⾜ 3 ิࡢศᩓ࣭ඹศᩓ⾜ิ V㸦ut㸧=E 㸦utut'㸧=Ȉ 㸪
E 㸦utu't–s㸧=0 㸦s > 0 㸧ࡢ௬ᐃࢆ‶ࡓࡍࡶࡢࡍࡿࠋ⾜ิȈࡣ㠀ᑐゅ⾜ิ࡛࠶ࡾ㸪ㄗᕪ㡯ࡣྠࡌⅬ t ࡛࠸ ┦㛵ࢆᣢࡗ࡚࠸ࡿࠋࡇࡇ࡛㸪⏝ྍ⬟࡞ࢹ࣮ࢱᩘࡀ54 ಶ࡛࠶ࡿࡇࢆ⪃៖ࡋ࡚㸪k ࡣ᭱ࡢࣛࢢḟᩘ ࢆ5ࡋ࡚k =1,2,͐,5 ࡍࡿࠋk =1,2,͐,5ࡢ್ᑐࡋ࡚㸪㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢVAR㸦k㸧࠾ࡅࡿAIC SICࡢሗ㔞ᇶ‽ࡢ⤫ィ㔞ࢆィ⟬ࡋ࡚㸪ࣛࢢḟᩘkࢆ㑅ᢥࡍࡿࠋ࠼ࡤ㸪x=ge㸪y=gr㸪z=gdpࡍࢀࡤ Ⰻ࠸ࠋ ࠉ๓㏙ࡢࡼ࠺㸪༢᰿᳨ᐃඹศ᳨ᐃࡢ⤖ᯝࡼࡗ࡚㸪ᆺⓗ࡞ศᯒᡭ㡰ࡣ3 ㏻ࡾ࡛࠶ࡿࠋ➨ 1㸪 x㸪y㸪zࡢኚᩘࡀ༢᰿᳨ᐃ࡛࡚I㸦0㸧ุ᩿ࡉࢀࡿࡁࡣ㸪ୖグࡢᘧ㸦1-1㸧Ѹ㸦1-3㸧࡛¨xtࢆxt㸪
¨ytࢆyt㸪¨ztࢆztࡑࢀࡒࢀ⨨ࡁ࠼ࡓVAR㸦k㸧ࢆ⪃࠼ࡿࠋ➨ 2㸪༢᰿᳨ᐃࡼࡾx㸪y㸪zࡢኚ
ᩘࡀ࡚I㸦1㸧࡛༢᰿ࢆᣢࡕ㸪ࡘEngle and Granger᳨ᐃࡼࡾ3 ኚᩘ㛫ඹศࡀᏑᅾࡋ࡞࠸ሙྜ
ࡣ㸪ୖグࡢᘧࢆࡑࡢࡲࡲ⏝࠸ࡿࠋ➨3㸪༢᰿᳨ᐃࡼࡾx㸪y㸪zࡢኚᩘࡀ࡚I㸦1㸧࡛༢᰿ࢆᣢࡕ㸪
ࡣඹศಀᩘ࠶ࡿ࠸ࡣඹศࣃ࣓࣮ࣛࢱ࣮㸪utࡣㄗᕪ㡯㸧ࢆ⏝࠸࡚3 ኚᩘ㛫ඹศࡀᏑᅾࡍࡿሙྜࡣ㸪 ࡇࡢඹศᅇᖐ㛵ࡋ࡚OLSࢆ⾜࠸ṧᕪetࡢ1 ᮇ๓ࡢࣛࢢࢆྲྀࡗࡓet–1ࢆ㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢࡑࢀࡒࢀ ຍ࠼࡚ᅉᯝ㛵ಀࢆศᯒࡍࡿࡇࡀ࡛ࡁࡿࠋyzࢆ⿕ㄝ᫂ኚᩘࡍࡿඹศᅇᖐࡘ࠸࡚ࡶྠᵝ࡞ࡇ ࢆ⾜࠺ࡇࡀ࡛ࡁࡿࠋ௨ୗ࡛ࡣ㸪ඹศࡀᏑᅾࡍࡿሙྜࡣ㸪x㸪y㸪zࡢ3 ኚᩘࡽ1 ኚᩘࢆ㑅ᢥࡋ࡚⿕ ㄝ᫂ኚᩘࡋ࡚㸪ඹศᅇᖐࡢṧᕪࡢ1 ᮇ๓ࡢࣛࢢࡢࡳࢆ㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢࡑࢀࡒࢀຍ࠼ࡿࠋEngle and Granger᳨ᐃࡢ1ࡘࡢḞⅬࡣ㸪ࡢኚᩘࢆ⿕ㄝ᫂ኚᩘࡍࡿ㛵ࡋ࡚య⣔ⓗ࡞࣮ࣝࣝࡀ࡞࠸࠸࠺
ࡇ࡛࠶ࡿࠋEngle and Granger᳨ᐃࡢࡶ࠺1ࡘࡢḞⅬࡣ㸪3 ኚᩘࡢሙྜඹศࢆ1 ಶࡢࡳⓎぢ࡛ࡁࡿࡀ㸪
ඹศࡀ2 ಶᏑᅾࡍࡿሙྜ2 ಶⓎぢ࡛ࡁ࡞࠸ࡇ࡛࠶ࡿࠋ࡞࠾㸪Johansen᳨ᐃࡣ㸪Engle and Granger ᳨ᐃࡢ2ࡘࡢḞⅬࢆゎỴ࡛ࡁࡿࠋ ࠉୖグࡢ㸦1-1㸧Ѹ㸦1-3㸧ᘧࢆ⏝࠸ࡓGrangerࡢᅉᯝ㛵ಀࡢ᳨ᐃ᪉ἲࢆㄝ᫂ࡍࡿࠋ㸦1-1㸧ᘧࢆ⏝࠸࡚㸪Granger ࡢព࡛¨yࡽ¨xࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨y Ж¨x㸧ࡇࡢᚲせ༑ศ᮲௳ࡣ㸪Ȗ11 = Ȗ12 = ͐ = Ȗ1k = 0 ࡞ࡿࡇ ࡛࠶ࡿࠋᅉᯝ㛵ಀࡢ᳨ᐃ᪉ἲ࡛ࡣ㸪ᖐ↓௬ㄝH0ᑐ❧௬ㄝH1ࡣ㸪 H0: Ȗ11 = Ȗ12 = ͐ = Ȗ1k = 0 , H1: ࠸ࡎࢀࡢi㸦i=1,2,͐,k）に関してȖiӆ0࡞ࡿ ࡛࠶ࡿࠋᖐ↓௬ㄝH0ࡢୗ࡛㸪᳨ᐃ⤫ィ㔞F ᳨ᐃ⤫ィ㔞 kF ࡀ⏝ྍ⬟࡛࠶ࡿࠋF ್ࡣ⮬⏤ᗘ 㸦k,Tí3kí1㸧ࡢFศᕸࢆཧ↷ࡋ㸪kFࡢ್ࡣ⮬⏤ᗘkࡢ࢝2 ศᕸȤ㸦k㸧ࢆཧ↷ࡋ࡚㸪ࡑࢀࡒࢀ᳨ᐃࢆ ⾜࠺ࠋᮏㄽᩥ࡛ࡣ㸪௨ୗ࡛ㄝ᫂ࡍࡿࡼ࠺kFࡢ್ࡼࡿᅉᯝ㛵ಀࡢ⤖ᯝࡣF್ࡢሙྜྠࡌ࡛࠶ࡿࡓࡵ㸪 Fศᕸࡢ್ࢆィ⟬ࡋ࡚ᅉᯝ㛵ಀࢆุ᩿ࡋࡓ⤖ᯝࢆ♧ࡍࠋF್ࡀ10%ࡢ᭷ពỈ‽࡛᭷ព࡛࠶ࢀࡤ㸪ᖐ↓௬ㄝ H0ࢆᲠ༷ࡋ࡚ᑐ❧௬ㄝH1ࢆ᥇ᢥࡋ࡚㸪Grangerࡢព࡛¨yࡽ¨xࡢᅉᯝ㛵ಀࡀ࠶ࡿ㸦¨yЍ¨x㸧ุ ᩿ࡍࡿࠋ㸦1-1㸧ᘧࢆ⏝࠸࡚㸪Grangerࡢព࡛¨zࡽ¨xࡢᅉᯝ㛵ಀ㸦¨zЍ¨x㸧ࢆ᳨ᐃࡍࡿሙྜࡣ㸪ᖐ ↓௬ㄝࢆH0: į11=į12=͐=į1k=0ࡍࢀࡤⰋ࠸ࠋྠᵝ㸪㸦1-2㸧ᘧࢆ⏝࠸࡚㸪ᅉᯝ㛵ಀ㸦¨xЍ¨y㸧㸦¨zЍ ¨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¨yࡢ᪉ྥࡢᅉᯝ㛵ಀࡀ࠶ࡿሙྜࡣ㸪¨x⇄¨yࡢグྕ࡛⾲ࡍࠋศᯒᑐ㇟ࡢx㸪y㸪zࡢ3 ኚᩘ 㛫ඹศ㛵ಀࡀᏑᅾࡍࡿሙྜࡣ㸪ㄗᕪಟṇ㡯ࢆྵࡵ࡚ᅉᯝ㛵ಀࢆศᯒࡍࡿࠋศᯒᑐ㇟ࡢx㸪y㸪zࡢ3 ኚᩘࡀI㸦0㸧࡛࠶ࡿሙྜࡣ㸪㸦xЍz㸧ࡢࡼ࠺㸪㝵ᕪ₇⟬Ꮚ¨ࢆྲྀࡗࡓᙧ࡛ᅉᯝ㛵ಀࢆ⪃ᐹࡍࡿࠋ
ࠉᮏㄽᩥ࡛ࡣ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㉁ᨻᗓධࡢᡂ㛗⋡㸪¨gdpࡣᐇ㉁⤒῭ᡂ㛗⋡࡛࠶ࡿࠋᅉࡗ࡚㸪⪃ᐹࡍࡿ Grangerࡢពࡼࡿᅉᯝ㛵ಀࡣ㸪ᐇ㉁ᨻᗓධࡢᡂ㛗⋡¨grࡽᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨geࡢᅉᯝ㛵 ಀࡀᏑᅾࡍࡿࡇ㸪ᐇ㉁⤒῭ᡂ㛗⋡¨gdpࡽᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨geࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ㸪 ᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨geࡽᐇ㉁ᨻᗓධࡢᡂ㛗⋡¨grࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ㸪ᐇ㉁⤒῭ᡂ㛗⋡ ¨gdpࡽᐇ㉁ᨻᗓධࡢᡂ㛗⋡¨grࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ㸪ᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡¨geࡽᐇ㉁ ⤒῭ᡂ㛗⋡¨gdpࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ㸪ᐇ㉁ᨻᗓධࡢᡂ㛗⋡¨grࡽᐇ㉁⤒῭ᡂ㛗⋡¨gdpࡢ ᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇ㸪ࡢ6 ㏻ࡾ࡛࠶ࡿࠋ6 ㏻ࡾࡢᅉᯝ㛵ಀࡘ࠸࡚㸪Grangerࡢᅉᯝᛶ᳨ᐃࡼࡗ࡚ ࡢ㛵ಀࡀᏑᅾࡍࡿࢆศᯒࡍࡿࠋ࡞࠾㸪௨ୗ࡛ࡣᅉᯝ㛵ಀࡢㄝ᫂ᩥ࡛ᡂ㛗⋡ࡢ⏝ㄒࢆ┬␎ࡋࡓ⾲⌧ࢆ⏝ ࠸ࡿሙྜࡶ࠶ࡿࠋ
ࠉᨻᗓධ㸦ࡲࡓࡣ⛯㸧ᨻᗓᨭฟࡢᅉᯝ㛵ಀࡢ◊✲ࡣ㸪ࡑࡢከࡃࡀ2 ኚᩘgegrࡢࡳࢆศᯒᑐ㇟ 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ࢣࣥࢬ௬ㄝࡢᅉᯝ㛵ಀ㸦¨ge Ѝ¨ gdp㸧ࢆศᯒࡋ࡚࠸ࡿࠋ¨ gr Ѝ¨ gdp ¨ gdp Ѝ¨ gr ࡢᅇᖐศᯒࡸࣥࣃࣝࢫᛂࡘ࠸࡚ࡶ㸪 Mamatzakis㸦2005㸧➼ࡳࡽࢀࡿࡼ࠺◊✲ࡀᏑᅾࡍࡿࠋ¨gdpЍ¨grࡢᅉᯝ㛵ಀࡀ࠶ࢀࡤ㸪⤒῭ᡂ㛗ࡀ ᨻᗓධࢆቑຍࡉࡏࡿ࠸࠺Thorn㸦1967㸧ࡢ⪃࠼᪉ࡀጇᙜࡍࡿྍ⬟ᛶࡀ࠶ࡿࠋ¨grЍ¨gdpࡢᅉᯝ㛵ಀ ࡀ࠶ࢀࡤ㸪ῶ⛯ࢆ⾜࠼ࡤᐇ㉁GDPࡀቑຍࡍࡿ࠸࠺ࢣࣥࢬࡢῶ⛯ࡢ⌮ㄽࡣጇᙜࡍࡿྍ⬟ᛶࡀ࠶ࡿࠋᨻ ᗓධ㸦ࡲࡓࡣ⛯㸧ᨻᗓᨭฟࡢᅉᯝ㛵ಀࡢ◊✲ࡸ࣡ࢢࢼ࣮௬ㄝࡢ◊✲ࡣ㸪ศᯒᑐ㇟ࡀ2 ኚᩘࡢሙྜࡀ 㠀ᖖከࡃ㸪ኚᩘࢆ1ࡘⴠࡍࡇࡼࡿᐃᘧࡢㄗࡾࡢྍ⬟ᛶࡀ࠶ࡿࠋ
㸱
㸬Grangerࡢᅉᯝ㛵ಀࡢศᯒ⤖ᯝ
ࠉ༢᰿᳨ᐃ㸪ඹศ᳨ᐃ㸪ᅉᯝ㛵ಀࡢ᳨ᐃ࡛ࡣ㸪᭷ពỈ‽ࡋ࡚10%ࢆ⏝࠸ࡿࡇࡍࡿࠋศᯒ⤖ᯝ ࡛ࡣ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㉁ᨻᗓධ㸦gr㸧㸪ᐇ㉁GDP㸦gdp㸧ࡢADF᳨ᐃࡼࡿ༢᰿᳨ᐃࡢ⤖ᯝࡀ⾲ 1 ♧ࡉࢀ࡚࠸ࡿࠋࣔࢹࣝCC&Tࡢࣛࢢᩘkࡣ㸪ᣑᙇ㡯ࡀ࡞࠸k = 0k = 1,2,͐,5ࡢ್ᑐࡋ࡚AIC SICࡢ⤫ィ㔞ࢆィ⟬ࡋ㸪AICSICࡢ୧ሗሗ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 ⬮ὀ1䠅 䛾䝰䝕䝹䛷ῧ䛘Ꮠ0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ḟᩘk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ḟᩘk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ࠉࣔࢹࣝCࡢ⤖ᯝࡣ㸪௨ୗࡢ㏻ࡾ࡛࠶ࡿࠋgeࡣ㸪SIC࡛㑅ࢇࡔࣛࢢḟᩘk=0ࡀAICࡢ⤖ᯝ୍⮴ࡋ㸪Ỉ‽ ኚᩘࡢ᳨ᐃ⤫ィ್Ѹ5.059228ࡀ1%ࡢ᭷ពỈ‽࡛᭷ព࡛࠶ࡾ㸪ᐃᖖࡢI㸦0㸧࡛࠶ࡿุ᩿࡛ࡁࡿࠋgrࡣ㸪 Ỉ‽ኚᩘࡢSICᇶ࡙ࡃ᳨ᐃ⤫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㸧࡛࠶ࡿࠋAICSICࡢ୧ᇶ‽ࡢ⤖ᯝࡼࡾ㸪grࡢỈ‽ኚᩘࡣI㸦0㸧࡛࠶ࡿࠋྠᵝࡋ࡚㸪 gdpࡢỈ‽ኚᩘࡣSIC࡛㑅ࢇࡔࣛࢢḟᩘk=0ࡀAICࡢ⤖ᯝ୍⮴ࡋ㸪ࡑࡢỈ‽ኚᩘࡣI㸦0㸧࡛࠶ࡿࠋAIC SICࡢ୧ᇶ‽࡛ࣛࢢḟᩘkࢆ㑅ࢇࡔ⤖ᯝ࡛ࡣ㸪gegrgdpࡢỈ‽ኚᩘࡣࡑࢀࡒࢀI㸦0㸧ุ᩿࡛ࡁࡿࠋ ࠉࣔࢹࣝC&Tࡢሙྜࡣ㸪ḟࡢ㏻ࡾ࡛࠶ࡿࠋgeࡣ㸪Ỉ‽ኚᩘ➨ 1 㝵ᕪኚᩘᑐࡋ࡚SIC࡛㑅ࢇࡔࣛࢢ ḟᩘk=0ࡀAICࡢ⤖ᯝ୍⮴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ࡢኚᩘ ࡛࠶ࡿุ᩿࡛ࡁࡿࠋ2 ኚᩘgrgdpࡘ࠸࡚ࡶྠᵝ࡞᳨ᐃࢆᐇ⾜ࡋ࡚㸪2 ኚᩘࡶI㸦1㸧ุ᩿࡛ࡁࡿࠋ AICSICࡢ୧ᇶ‽ࢆ⏝࠸ࡿ㸪gegrgdpࡢỈ‽ኚᩘࡣࡑࢀࡒࢀI㸦1㸧ุ᩿࡛ࡁࡓࠋ ࠉࣔࢹࣝCC&Tࡢ⤖ᯝࡣࡁࡃ␗࡞ࡗ࡚࠸ࡿࡀ㸪௨ୗ࡛ࡣࣔࢹࣝC&Tࡢ⤖ᯝᇶ࡙࠸࡚㸪gegr
gdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦1㸧ุ᩿ࡋ࡚ศᯒࢆ⾜࠺ࠋKwiatkowski, Phillips, Schmidt and Shin㸦1992㸧
ࡣ㸪ᐃᖖᛶࢆᖐ↓௬ㄝ㸪༢᰿ࢆᣢࡘࡇࢆᑐ❧௬ㄝࡍࡿKPSS᳨ᐃࢆᥦࡋ࡚࠸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⏝࠸ࡓሙྜࡣ㸪gegrgdpࡀࡑࢀࡒࢀI㸦1㸧 ุ᩿࡛ࡁࡿࠋ
3. 2 ඹศ᳨ᐃࡢ⤖ᯝ
ࠉge㸪gr㸪gdpࢆ⿕ㄝ᫂ኚᩘࡍࡿ3ࡘࡢᅇᖐᘧࡘ࠸࡚Engle and Grangerࡢඹศ᳨ᐃࡢ⤖ᯝࡀ⾲ 2
♧ࡉࢀ࡚࠸ࡿࠋ⿕ㄝ᫂ኚᩘࢆgeࡍࡿඹศᅇᖐᘧࡣ㸪ㄝ᫂ኚᩘࡀgrgdp࡛࠶ࡿࠋᙜ↛㸪ࡇࡢඹศ
ᅇᖐᘧ࡛ㄝ᫂ኚᩘࡢgrgdpࡢ㡰␒ࢆධࢀ᭰࠼࡚ࡶྠࡌ࡛࠶ࡿࠋᣑᙇ㡯ࡢࣛࢢḟᩘࡣ㸪ᣑᙇ㡯ࡀ࡞࠸k=
0k= 1,2,͐,5ࡢ್ᑐࡋ࡚㸪ඹศᅇᖐ࠾ࡅࡿAICSICࡢሗ㔞ᇶ‽ࡢ⤫ィ㔞ࢆィ⟬ࡋ࡚㑅ᢥࡉࢀ
࡚࠸ࡿࠋ⾲2࡛ࡣ㸪Engle and Granger᳨ᐃ࡛⏝࠸ࡽࢀࡿADF᳨ᐃ⤫ィ㔞㸪p್㸪AICSICࡢሗ㔞ᇶ
‽ࢆ⏝࠸࡚㑅ᢥࡉࢀࡓࣛࢢḟᩘࡀ♧ࡉࢀ࡚࠸ࡿࠋㄝ᫂ኚᩘࢆgeࡍࡿඹศᅇᖐᘧࡣ㸪AICSICࡢ୧
ᇶ‽ࡼࡾADF᳨ᐃ⤫ィ㔞ࡢ್㸦Ѹ 2.349696Ѹ 2.091621㸧ࡀ10%ࡢ᭷ពỈ‽࡛᭷ព࡛࡞࠸ࡢ࡛㸪ඹ ศ㛵ಀࡀᏑᅾࡋ࡞࠸ࠋ๓㏙ࡢ⤖ᯝࡢ㡹ᛶࢆぢࡿࡓࡵ㸪ṧࡾ2ࡘࡢඹศᅇᖐᘧࡘ࠸࡚ࡶ᳨ᐃࢆ⾜࠺ࠋ
⿕ㄝ᫂ኚᩘࢆgrgdpࡍࡿඹศᅇᖐᘧࡘ࠸ࡣ㸪ྠᵝࡋ࡚㸪ඹศ㛵ಀࡀᏑᅾࡋ࡞࠸ࠋge㸪gr㸪
k
p
3. 3 ᅉᯝ㛵ಀࡢศᯒ⤖ᯝ
ࠉADF᳨ᐃ➼ࢆ⏝࠸ࡓ༢᰿᳨ᐃࡢ⤖ᯝࡼࡾ㸪gegrgdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦1㸧࡛࠶ࡿุ᩿ ࡋࡓࠋEngle and Grangerࡢඹศ᳨ᐃࡢ⤖ᯝࡼࡾ㸪gegrgdpࡢ3 ኚᩘ㛵ࡍࡿඹศ㛵ಀࡣᏑᅾࡋ ࡞࠸ࠋVAR㸦k㸧࡛ࡣ㸪gegrgdpࡢ➨ 1 㝵ᕪኚᩘࢆ⏝࠸ࡿࡀ㸪Engle and Granger᳨ᐃ࠾ࡅࡿඹ
ศᅇᖐࡢṧᕪࡽᚓࡿㄗᕪಟṇ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ࡢࣛࢢḟᩘࡣAICSICࡢ୧ሗ㔞ᇶ‽ࢆ⏝࠸࡚Ỵᐃࡍࡿࠋ ⾲3࡛ࡣ㸪㸦1-1㸧Ѹ㸦1-3㸧ࡢVAR㸦k㸧ࢆ⏝࠸࡚㸪k = 0k = 1,2,͐,5ࡢ್ᑐࡋ࡚AICSICࡢ⤫ィ್ ࡀィ⟬ࡉࢀ࡚࠸ࡿࠋk = 0ࡢࡁࡣ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ᢥࡉࢀࡿࠋ k ࠉᘧ㸦1-1㸧ࢆ⏝࠸ࡿ㸪Grangerࡢព࡛¨yࡽ¨xࡢᅉᯝ㛵ಀࡀ࡞࠸㸦¨y Ж¨x㸧ࡇࡢᚲせ༑ศ᮲ ௳ࡣ㸪Ȗ11=Ȗ12=͐= Ȗ1k=0 ࡞ࡿࡇ࡛࠶ࡿࠋ⾲ 4࡛ࡣ㸪Grangerࡢព࡛¨yࡽ¨x ࡢᅉᯝ㛵ಀࡀ࡞࠸ 㸦¨y Ж¨x㸧࠸࠺ᖐ↓௬ㄝ㸪᳨ᐃ⤫ィ㔞ࡢF್㸪Fศᕸࢆ⏝࠸࡚ィ⟬ࡉࢀࡓp್ࡀ♧ࡉࢀ࡚࠸ࡿࠋ⾲ 4࡛ ࡣ㸪¨ge㸪¨gr㸪¨gdpࡢ3 ኚᩘࡽᚓࡽࢀࡿ6 ಶࡢ⤌ࡳྜࢃࡏࡢᖐ↓௬ㄝ㸪AICSICࡢ୧ᇶ‽࡛㑅ᢥ
ࡉࢀࡓḟᩘk = 1,2ࡢ್ᑐࡋ࡚㸪F್p್ࡀ♧ࡉࢀ࡚࠸ࡿࠋ ࠉgegrgdpࡢ➨ 1 㝵ᕪኚᩘࢆ⏝࠸࡚ศᯒࡉࢀࡓ⾲ 4ࡢ⤖ᯝࢆㄝ᫂ࡍࡿࠋ⾲ 4࡛ࡣ㸪¨ ge¨ gr ¨gdpࢆ⏝࠸࡚࠸ࡿࡢ࡛㸪¨geࡣᐇ㉁ᨻᗓᨭฟࡢᡂ㛗⋡㸪¨grࡣᐇ㉁ᨻᗓධࡢᡂ㛗⋡㸪¨gdpࡣᐇ㉁⤒῭ ᡂ㛗⋡࡛࠶ࡿࠋSICᇶ‽ࡼࡿk = 1ࡢሙྜ㸪Grangerࡢព࡛¨grࡽ¨geࡢᅉᯝ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࠸࠺⤖ᯝࢆᚓࡿࠋGrangerࡢព࡛¨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↓௬ㄝࢆᲠ༷࡛ࡁࡿࠋGrangerࡢព࡛¨gdpࡽ¨geࡢᅉᯝ㛵ಀࡀ࠶ ࡿ㸦¨gdpЍ¨ge㸧࠸࠺⤖ᯝࢆᚓࡿࠋྠᵝࡋ࡚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 = 1ࡢሙྜࡃྠࡌ࡛࠶ࡿࠋ ǻgr Ж ǻge ǻgdp Ж ǻge ǻge Ж ǻgr ǻgdp Ж ǻgr ǻge Ж ǻgdp ǻgr Ж ǻgdp k㸻1 k p k㸻2 ǻgr Ж ǻge ǻgdp Ж ǻge ǻge Ж ǻgr ǻgdp Ж ǻgr ǻge Ж ǻgdp ǻgr Ж ǻgdp ࠉ⾲4ࡢF್ࣛࢢḟᩘkࢆࡅ࡚kFࡢ್ࢆồࡵ࡚㸪࢝2 ᳨ᐃࢆ⏝࠸࡚ࡶF್ྠࡌ⤖ᯝࢆᚓࡿࠋkF ࡢ್ࡣᥦ♧ࡋ࡞࠸ࡀ㸪ࣛࢢḟᩘk = 1,2࠾ࡅࡿ 4ࡘࡢᖐ↓௬ㄝ¨gdp Ж¨ge㸪¨gdp Ж¨gr㸪¨ge Ж¨gdp㸪 ¨ge Ж¨gdpᑐࡋ࡚㸪kF್ࡣࣛࢢḟᩘk =2ࡢ¨gr Ж¨gdpࡢሙྜࢆ㝖࠸࡚F್ྠࡌ᭷ពỈ‽࡛᭷ព࡛ ࠶ࡿࠋk =2ࡢᖐ↓௬ㄝ¨gr Ж¨gdpᑐࡋ࡚ࡣ㸪F್ࡣ10%࡛᭷ព࡛࠶ࡿࡀ㸪kFࡢ್ࡣ5%Ỉ‽࡛᭷ព ࡞ࡿࠋࣛࢢḟᩘk =1,2࠾ࡅࡿ 2ࡘࡢᖐ↓௬ㄝ ¨gr Ж¨ge¨ge Ж¨grᑐࡋ࡚ࡣ㸪kF್ࡣF್ྠࡌࡼ ࠺10%Ỉ‽࡛᭷ព࡛࡞࠸ࠋ ࠉAICSICࡢ୧ᇶ‽ࡼࡿGrangerࡢᅉᯝ㛵ಀࡢ⤖ᯝࡣ㸪ᅗ 1ᅗ♧ࡉࢀ࡚࠸ࡿࠋᅜᐙ㈈ᨻ࠾ࡅࡿᐇ ㉁ᨻᗓᨭฟࡢᡂ㛗⋡㸦¨ge㸧ᐇ㉁ᨻᗓධࡢᡂ㛗⋡㸦¨gr㸧㛵ࡋ࡚㸪Grangerࡢព࡛ᅉᯝ㛵ಀࡀ࡞
࠸࠸࠺⤖ᯝࡣ㸪ᚑ᮶ࡢ᪥ᮏ࠾ࡅࡿศᯒ⤖ᯝࡁࡃ␗࡞ࡾ㸪⯆῝࠸ࠋChang㸪Liu and Caudill㸦2002㸧
ᨭฟ௬ㄝ㸦ᨻᗓධѸᨻᗓᨭฟ௬ㄝ㸪¨grЍ¨ge㸧ࢆᨭᣢࡍࡿ⤖ᯝࢆᚓࡓࠋOwoye 㸦1995㸧ࡣ㸪IMFࡢ
ࠗInternational Financial Statistics Yearbook࠘ࡢ᪥ᮏࡢࢹ࣮ࢱࢆ⏝࠸࡚㸪⛯ᨭฟࡢᅉᯝ㛵ಀࢆぢฟࡋ
࡚࠸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㉁ࡢᨻᗓධࡢ୰㌟ᨭฟࡢ♫ಖ㞀㛵ಀ㈝ᑐᛂࡍࡿ ධࡀධࡗ࡚࠸࡞࠸ࡇࡀཎᅉࡢ1ࡘ࡛ࡣ࡞࠸⪃࠼ࡿࠋᆅ᪉⛯㔠➼ࡢᆅ᪉⛣㌿ࡶᙳ㡪 ࡋ࡚࠸ࡿྍ⬟ᛶࡀ࠶ࡿࠋ ᅗ1ࠉGrangerࡢᅉᯝ㛵ಀ
ge
gdp
gr
㸦ฟ㸧➹⪅సᡂ ࠉᅗ1ࡼࡾ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☜ㄆࡍ ࡿࡇࡀ࡛ࡁࡓࠋ࣡ࢢࢼ࣮௬ㄝ㸦¨gdpЍ¨ge㸧ࢣࣥࢬ௬ㄝ㸦¨geЍ¨gdp㸧ࡢᅉᯝ㛵ಀࢆⓎぢ࡛ࡁࡓࠋ ᐇ㉁ࡢᨻᗓධ㸦gr㸧ᐇ㉁GDP㸦gdp㸧㛵ࡋ࡚ࡣ㸪᪉ྥࡢᅉᯝ㛵ಀ¨ge⇄¨gdpࢆ☜ㄆࡍࡿࡇࡀ ࡛ࡁࡓࠋThorn㸦1967㸧ࡢࢡࣟࢫ࣭ࢭࢡࢩࣙࣥࢹ࣮ࢱࡢศᯒ࡛ぢࡽࢀࡿࡼ࠺㸪⤒῭ᡂ㛗ࡀᨻᗓධࡢᡂ 㛗ࢆቑຍࡉࡏࡿ௬ㄝ㸦¨gdpЍ¨ge㸧ࡢྍ⬟ᛶࢆⓎぢ࡛ࡁࡓࠋࢣࣥࢬࡢῶ⛯⌮ㄽぢࡽࢀࡿࡼ࠺㸪ᨻ ᗓධࡢᡂ㛗⋡ࡀ⤒῭ᡂ㛗⋡ࢆῶᑡࡉࡏࡿ௬ㄝ㸦¨grЍ¨gdp㸧ࡢྍ⬟ᛶࢆⓎぢࡍࡿࡇࡀ࡛ࡁࡓࠋ࡞࠾㸪 ᨻᗓධࡢᡂ㛗⋡ࡀ⤒῭ᡂ㛗⋡ࢆῶᑡࡉࡏ࡞࠸ྍ⬟ᛶࡶ࠶ࡾᚓࡿࠋ㸲
㸬⤖ࡧ
ࠉᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓධ㸪ᐇ㉁GDPࡢ3 ኚᩘࡢࣔࢹ࡛ࣝ㸪ᅜᐙ㈈ᨻ࠾ࡅࡿᐇ㉁ᨻ ᗓᨭฟᐇ㉁ᨻᗓධࡢᅉᯝ㛵ಀࢆⓎぢ࡛ࡁ࡞ࡗࡓࠋᐇ㉁ᨻᗓᨭฟᐇ㉁ᨻᗓධ࡛ᤊ࠼ࡓᅜᐙ㈈ᨻ ᐇ㉁GDP࡛ィ⟬ࡉࢀࡓ⤒῭ᡂ㛗ࡢ㛫ࡣ㸪Grangerࡢព࡛ᅉᯝ㛵ಀࡀᏑᅾࡋࡓࠋᚑࡗ࡚㸪ᅜᐙ㈈ᨻ ࠾ࡅࡿᐇ㉁ᨻᗓᨭฟᐇ㉁ᨻᗓධࡢᕪࡋ࡚ࡢ㈈ᨻ㉥Ꮠࡢၥ㢟࡛ࡣ㸪⤒῭ᡂ㛗ࡽࡢどⅬࡀ㔜せ࡛࠶ ࡿࠋᮏㄽᩥ࡛ࡣ㸪ᐇ㉁ኚᩘࢆศᯒᑐ㇟ࡋ࡚࠸ࡿࡓࡵ㸪ࣥࣇ࣮ࣞࢩࣙࣥࡸࢹࣇ࣮ࣞࢩࣙࣥࢆ⪃៖ࡋ࡚࠸ ࡞࠸ࠋ ࠉᇶ♏ⓗ㈈ᨻᨭ╔┠ࡍࡿ㸪㈈ᨻ㉥Ꮠࢆῶࡽࡍࡣ㸪ᨻᗓᨭฟࢆῶࡽࡍ᪉ἲቑ⛯ࡼࡾᨻᗓධ 㸦⛯➼㸧ࢆቑࡸࡍ᪉ἲࡀ⪃࠼ࡽࢀࡿࠋࡇࡇ࡛ࡣᅜᐙࡢ㈈ᨻ㉥Ꮠࢆᇶ♏ⓗ㈈ᨻᨭ࡛ᤊ࠼࡚࠸ࡿࠋᮏㄽᩥ ࡛ࡣ㸪ᐇ㉁್࡛ぢࡓᇶ♏ⓗ㈈ᨻᨭࡣᐇ㉁ᨻᗓධࡽᐇ㉁ᨻᗓᨭฟࢆᕪࡋᘬ࠸ࡓᩘ್࡛࠶ࡿࠋᨻᗓᨭฟ ࡢቑῶࡸቑῶ⛯ࡢ⤒῭ᡂ㛗ࡢᙳ㡪ࡣࢣࣥࢬຠᯝ࡛ᢕᥱ࡛ࡁࡿሙྜࡶ࠶ࡿࠋ㏻ᖖࡢ࣐ࢡࣟ⤒῭Ꮫࡢᩍ⛉᭩࡛ㄝ᫂ࡉࢀ࡚࠸ࡿෆᐜࢆ㋃ࡲ࠼࡚㸪ࢣࣥࢬຠᯝࡣ㸪ᨻᗓᨭฟࡢቑຍࡸῶ⛯ࡀᩘຠᯝࢆ㏻ࡋ࡚GDP ࠼ࡿࣉࣛࢫࡢᙳ㡪࡛࠶ࡾ㸪ᨻᗓᨭฟࡢῶᑡࡸቑ⛯ࡀGDP࠼ࡿ࣐ࢼࢫࡢᙳ㡪࡛࠶ࡿࠋ㠀ࢣࣥ ࢬຠᯝࡣ㸪ᨻᗓᨭฟࡢῶᑡࡸቑ⛯➼ࡢ⥭⦰㈈ᨻࡀGDP࠼ࡿࣉࣛࢫࡢᙳ㡪➼ࡢࡇ࡛࠶ࡿࠋ⏣୰࣭ 㔝㸦2002㸧ࡣ㸪㠀ࢣࣥࢬຠᯝࡢඛ⾜◊✲ࡘ࠸࡚⡆₩࡞ᒎᮃࢆ⾜ࡗ࡚࠸ࡿࠋ⏣୰࣭㔝ࡣ㸪OECD21 ᅜࡢࣉ࣮ࣝࡋࡓࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪ᨻᗓᨭฟ๐ῶࡸቑ⛯౫Ꮡࡋࡓ㈈ᨻᘓࡀᖖ⤒῭ᡂ㛗ࡢపୗ ࢆࡶࡓࡽࡍࡶࡢ࡛࡞࠸࠸࠺ศᯒ⤖ᯝࢆᚓ࡚࠸ࡿࠋ ࠉ㈈ᨻ㉥Ꮠࢆῶࡽࡍࡓࡵࡢᨻᗓᨭฟࡢ๐ῶࡘ࠸᳨࡚ウࡍࡿࠋ௨ୗ࡛ࡣ㸪ᅉᯝ㛵ಀࡢᩥ❶⾲⌧࡛ࡣᡂ㛗⋡ ࡢ⏝ㄒࢆ┬␎ࡋ࡚࠸ࡿࠋGrangerࡢព࡛ᐇ㉁ᨻᗓᨭฟࡽᐇ㉁ᨻᗓධࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࢆ Ⓨぢ࡛ࡁ࡞ࡗࡓࡓࡵ㸪ᐇ㉁ᨻᗓᨭฟࡢ๐ῶࡀᐇ㉁ᨻᗓධ࠼ࡿຠᯝࡣࡁࡃ࡞࠸ุ᩿࡛ࡁࡿࠋ Grangerࡢព࡛ᐇ㉁ᨻᗓᨭฟࡽᐇ㉁GDPࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࢆⓎぢ࡛ࡁࡓࡢ࡛㸪ᐇ㉁ᨻᗓ ᨭฟࡢ๐ῶࡼࡾᐇ㉁GDPࢆῶࡽࡍ࠸࠺ࢣࣥࢬຠᯝࡀᶵ⬟ࡍࡿሙྜࡣ㸪࠶ࡿィᖺᗘ࠾ࡅࡿᐇ ㉁ᨻᗓᨭฟࡢ๐ῶࡣḟィᖺᗘ௨㝆ࡢᐇ㉁GDPࡢ࣐ࢼࢫࡢຠᯝࢆᣢࡘࡇࡀணࡉࢀࡿࠋ࡞࠾㸪 Grangerࡢព࡛ᐇ㉁ᨻᗓᨭฟࡽᐇ㉁GDPࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࡣ㸪㸦1-1㸧Ѹ㸦1-3㸧ᘧࡢVAR ࣔࢹ࡛ࣝ㐣ཤࡢᐇ㉁ᨻᗓᨭฟ㸦ࣛࢢኚᩘ㸧ࡀᐇ㉁GDPࡢኚືࡘ࠸࡚ㄝ᫂ຊࢆᣢࡘࡇ࡛࠶ࡿࠋᐇ㉁ ᨻᗓᨭฟࡢ๐ῶࡼࡾᐇ㉁GDPࢆῶࡽࡍ࠸࠺ࢣࣥࢬຠᯝࡀᶵ⬟ࡋ࡞࠸ሙྜࡣ㸪㠀ࢣࣥࢬຠᯝ ࡼࡾ㸪ᐇ㉁ᨻᗓᨭฟࡢ๐ῶࡼࡿᐇ㉁GDPࡢࣉࣛࢫࡢຠᯝࡀᏑᅾࡍࡿྍ⬟ᛶࡣ࠶ࡾᚓࡿࠋ ࠉ㈈ᨻ㉥Ꮠࢆῶࡽࡍࡓࡵࡢቑ⛯ࡘ࠸᳨࡚ウࡍࡿࠋGrangerࡢព࡛ᐇ㉁ᨻᗓධࡽᐇ㉁ᨻᗓᨭฟࡢ ᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࢆⓎぢ࡛ࡁ࡞ࡗࡓࡓࡵ㸪ቑ⛯ࡼࡿᐇ㉁ᨻᗓධࡢቑຍࡀᐇ㉁ᨻᗓᨭฟ࠼ ࡿຠᯝࡣࡁࡃ࡞࠸ᮇᚅ࡛ࡁࡿࠋGrangerࡢព࡛ᐇ㉁ᨻᗓධࡽᐇ㉁GDPࡢᅉᯝ㛵ಀࡀᏑᅾࡍ ࡿࡇࢆⓎぢ࡛ࡁࡓࡢ࡛㸪ቑ⛯ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࠸࠺ࢣࣥࢬຠᯝࡀᶵ⬟ࡍࡿሙྜࡣ㸪࠶ࡿ ィᖺᗘ࠾ࡅࡿቑ⛯ࡼࡿᐇ㉁ᨻᗓධࡢቑຍࡀḟィᖺᗘ௨㝆ࡢᐇ㉁GDP࠼ࡿ࣐ࢼࢫࡢຠᯝ ࡣᏑᅾࡍࡿࡇࢆᮇᚅ࡛ࡁࡿࠋቑ⛯ࡼࡾᐇ㉁GDPࢆῶࡽࡍ࠸࠺ࢣࣥࢬຠᯝࡀᶵ⬟ࡋ࡞࠸ሙྜࡣ㸪 㠀ࢣࣥࢬຠᯝࡼࡾ㸪ቑ⛯ࡼࡿᐇ㉁GDPࡢࣉࣛࢫࡢຠᯝࡀᏑᅾࡍࡿྍ⬟ᛶࡣ࠶ࡾᚓࡿࠋ ࠉ⤒῭ᡂ㛗ࡀᅜᐙ㈈ᨻ࠾ࡅࡿ㈈ᨻ㉥Ꮠ࠼ࡿຠᯝࢆ᳨ウࡍࡿࠋඛࡎ㸪Grangerࡢព࡛ᐇ㉁GDP ࡽᐇ㉁ᨻᗓධࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࢆⓎぢ࡛ࡁࡓࡢ࡛㸪Thorn㸦1967㸧ぢࡽࢀࡿࡼ࠺ᐇ㉁⤒ ῭ᡂ㛗ࡀᐇ㉁ᨻᗓධࣉࣛࢫࡢຠᯝࢆᣢࡘࡢ࡛࠶ࢀࡤ㸪࠶ࡿィᖺᗘ࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡣḟィᖺ ᗘ௨㝆ࡢᐇ㉁ᨻᗓධ࠼ࡿࣉࣛࢫࡢຠᯝࢆᣢࡘࡇࡀᮇᚅࡉࢀࡿࠋᮏㄽᩥࡢVARࣔࢹ࡛ࣝᤊ࠼ࡿࡇ ࡣ࡛ࡁ࡞࠸ࡀ㸪࠶ࡿィᖺᗘ࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡀᙜヱᖺᗘ࠾ࡅࡿᐇ㉁ᨻᗓධ࠼ࡿࣉࣛࢫࡢ ຠᯝࡣᐇ㝿ࡋࡤࡋࡤぢࡽࢀࡿࡇ࡛࠶ࡿࠋࡲࡓ㸪ᐇ㉁⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓධ࣐ࢼࢫࡢຠᯝࢆᣢࡘ ሙྜࡣ㸪ᐇドⓗ࠶ࡲࡾពࡢ࡞࠸ࡶࡢ࡛࠶ࡿࠋḟ㸪Grangerࡢព࡛ᐇ㉁GDPࡽᐇ㉁ᨻᗓᨭฟ ࡢᅉᯝ㛵ಀࡀᏑᅾࡍࡿࡇࢆⓎぢ࡛ࡁࡓࡢ࡛㸪࣡ࢢࢼ࣮ἲ๎ぢࡽࢀࡿࡼ࠺ᐇ㉁GDPࡢቑຍࡼࡿ⤒ ῭ᡂ㛗ࡀᐇ㉁ᨻᗓᨭฟࣉࣛࢫࡢຠᯝࢆᣢࡘࡢ࡛࠶ࢀࡤ㸪࠶ࡿィᖺᗘ࠾ࡅࡿᐇ㉁⤒῭ᡂ㛗ࡣḟィᖺ ᗘ௨㝆ࡢᐇ㉁ᨻᗓᨭฟ࠼ࡿࣉࣛࢫࡢຠᯝࢆᣢࡘࡇࡀᮇᚅࡉࢀࡿࠋᚑࡗ࡚㸪⤒῭ࡀᡂ㛗ࡍࡿࡁ ࡣ㸪┦ᑐⓗᐇ㉁ᨻᗓධࡀᐇ㉁ᨻᗓᨭฟẚࡋ࡚ቑຍࡍࢀࡤ㸪㈈ᨻ㉥Ꮠࢆ๐ῶ࡛ࡁࡿࡇ࡞ࡿࠋᐇ㉁ GDPࡢቑຍࡼࡿ⤒῭ᡂ㛗ࡀᐇ㉁ᨻᗓᨭฟࣉࣛࢫࡢຠᯝࢆᣢࡘࡀࡑࡢຠᯝࡀᑠࡉ࠸ࡢ࡛࠶ࢀࡤ㸪㈈ᨻ ㉥Ꮠࡣᨵၿࡍࡿࡇࡀᮇᚅࡉࢀࡿࠋ௨ୖࡼࡾ㸪ᐇ㉁⤒῭ᡂ㛗ࡀಁ㐍ࡉࢀ࡚ᐇ㉁ᨻᗓධẚࡋ࡚ᐇ㉁ᨻᗓ ᨭฟࡢቑຍࢆᢚไ࡛ࡁࡿሙྜࡣ㸪㈈ᨻ㉥Ꮠࡀᨵၿࡍࡿࡇࢆᮇᚅ࡛ࡁࡿࠋ ࠉ㈈ᨻ㉥Ꮠࢆᨵၿࡋࡓ࠸ሙྜࡣ㸪ᨻᗓᨭฟࡢ๐ῶࡸቑ⛯ࡶ࡛࠶ࡿࡀ㸪⤒῭ᡂ㛗ࡽࡢどⅬࡣᴟࡵ࡚ 㔜せ⪃࠼ࡿࠋቑ⛯ࡸᨻᗓᨭฟࡢ๐ῶࡣ㸪ࢣࣥࢬຠᯝࡀ᪥ᮏ⤒῭ᶵ⬟ࡋ࡚࠸ࡿሙྜࡣ㸪ᐇ㉁⤒῭ᡂ
㛗࣐ࢼࢫ࡛࠶ࡾ㸪㠀ࢣࣥࢬຠᯝࡀᶵ⬟ࡋ࡚࠸ࡿሙྜࡣ㸪ᐇ㉁⤒῭ᡂ㛗ࣉࣛࢫ࡞ࡾᚓࡿࠋቑ⛯ ࡸᨻᗓᨭฟࡢ๐ῶࡼࡿ㈈ᨻ㉥Ꮠࡢ๐ῶࢆ⾜࠺ࡢ࡛࠶ࢀࡤ㸪ࢣࣥࢬຠᯝࡀᏑᅾࡋ࡞࠸࠶ࡿ࠸ࡣᏑᅾࡋ ࡚ࡶࡑࡢຠᯝࡀᑠࡉ࠸ุ᩿ࡉࢀࡿሙྜ࡛࠶ࡿࠋᐇ㉁⤒῭ᡂ㛗ࡣ㸪ᐇ㉁ᨻᗓධẚ㍑ࡋ࡚ᐇ㉁ᨻᗓᨭฟ ࡢቑຍࢆᢚไ࡛ࡁࡿሙྜࡣ㸪㈈ᨻ㉥Ꮠࢆᨵၿࡍࡿࡇࡀᮇᚅࡉࢀࡿࠋࡇࡢࡼ࠺࡞ព࡛ࡣ㸪ᮏㄽᩥ࡛ࡣ 㔠⼥ኚᩘࢆศᯒᑐ㇟ࡋ࡚࠸࡞࠸ࡀ㸪㔠⼥ᨻ⟇ࡼࡿ⤒῭ࡢ่⃭⟇ࡀ㈈ᨻ㉥Ꮠ๐ῶࡗ࡚㔜せ࡛࠶ࡿྍ ⬟ᛶࡣศ࠶ࡾᚓࡿࠋ ࠉᮏㄽᩥ࡛ࡣ㸪4 ኚᩘࢆศᯒᑐ㇟ࡍࡿ㧗ᶫ㸦2010㸧␗࡞ࡾ㸪ᐇ㉁ᨻᗓᨭฟ㸪ᐇ㉁ᨻᗓධ㸪ᐇ㉁ GDPࡢ3 ኚᩘ㛫࡛ࡣඹศࢆⓎぢࡍࡿࡇࡀ࡛ࡁ࡞ࡗࡓࠋᮏㄽᩥࡣ㸪Ώ㎶࣭⸭࣭ఀ⸨㸦2010㸧㧗 ᶫ㸦2010㸧␗࡞ࡾ㸪ࡼࡾศᯒᮇ㛫ࡢ㛗࠸ᖺḟࢹ࣮ࢱࡀ⏝ࡉࢀ㸪ᨻᗓධᨻᗓᨭฟࡢᅉᯝ㛵ಀ࣡ ࢢࢼ࣮௬ㄝࡢ◊✲ᇶ࡙࠸࡚࠸ࡿࠋ ࠉᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀࡢ◊✲࡛ࡣ㸪ࣥࣃࣝࢫᛂศᩓศゎࢆศᯒࡋࡓ◊✲ࡣഹᑡ࡛࠶ࡿࠋ Carneiro㸦2007㸧ࡣ㸪ᨻᗓᨭฟᨻᗓධࡢᅉᯝ㛵ಀࡢᯟ⤌ࡳ࡛㸪ᨻᗓᨭฟ㸪▼Ἔ⛯ࡢධ㸪ᐇ㉁GDP ࡢ3 ኚᩘ㛫ࡢࣥࣃࣝࢫᛂศᩓศゎࡢศᯒࢆࣥࢦࣛᑐࡋ࡚⾜ࡗ࡚࠸ࡿࠋGiorgioni and Holden 㸦2003㸧ࡣ㸪GDP㸪Ẹ㛫ᾘ㈝㸪ᨻᗓᨭฟ㸪ᨻᗓධ㸪ᰴᘧᕷሙࡢᣦᶆࡢ5 ኚᩘ㛵ࡋ࡚㸪ࣥࣃࣝࢫ ᛂࢆศᯒࡋࡓࠋ
ࠉᚋࡢㄢ㢟ࡣ㸪ࣥࣃࣝࢫᛂศᩓศゎࡢศᯒ࡛࠶ࡿࠋᐇ㉁ᨻᗓᨭฟ㸦ge㸧ᐇ㉁GDP㸦gdp㸧㛵
ࡋ࡚ࡣ㸪᪉ྥࡢᅉᯝ㛵ಀ㸦¨ge⇄¨gdp）ࢆ☜ㄆࡍࡿࡇࡀ࡛ࡁࡓࠋࡉࡽ㸪ᐇ㉁ᨻᗓධ㸦gr㸧ᐇ
㉁GDP㸦gdp㸧㛵ࡋ࡚ࡣ㸪᪉ྥࡢᅉᯝ㛵ಀ㸦¨ge⇄¨gdp㸧ࢆ☜ㄆࡍࡿࡇࡀ࡛ࡁࡓࠋḟࡢ4ࡘࡢᅉᯝ
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࠸ࡣ࣐ࢼࢫࡢຠᯝࢆᣢࡘࡢࢆศᯒࡍࡿࡇࡣ㸪⯆῝࠸ࠋࡇࡢࡼ࠺࡞ศᯒࡣ㸪ࣥࣃ ࣝࢫᛂࢆศᯒࡍࡿࡇ࡛᫂ࡽ࡞ࡿྍ⬟ᛶࡀ࠶ࡿࠋ ࠉࡲࡓ㸪gegrgdpࡢỈ‽ኚᩘࢆ⏝࠸ࡓᅉᯝ㛵ಀࡢศᯒࡣ㸪ヨࡳࡿࡁㄢ㢟࡛࠶ࡿࠋࣔࢹࣝC࠾ࡅ ࡿADF᳨ᐃࡼࡿ༢᰿᳨ᐃࡢ⤖ᯝࡣ㸪AICSICࡢ୧ᇶ‽࡛ࣛࢢḟᩘkࢆ㑅ࢇࡔࡁ㸪gegr gdpࡢỈ‽ኚᩘࡀࡑࢀࡒࢀI㸦0㸧ุ᩿࡛ࡁࡓࠋࡉࡽ㸪VARࣔࢹࣝࢆ⏝࠸࡚Grangerࡢᅉᯝ㛵ಀࢆศᯒ ࡍࡿሙྜ㸪Hamilton㸦1994㸧ࡢ➨ 1ࡢ᪉ἲࡣ㸪Ỉ‽ኚᩘ㸦ࣞ࣋ࣝኚᩘ㸧⏝࠸࡚VARࡢᅇᖐࢆ⾜࠺ࡇ࡛ ࠶ࡿࠋ
ཧ⪃ᩥ⊩
⏣୰⚽࣭᫂㔝♸୍㑻㸦2002㸧ࠕḢ⡿ㅖᅜ࠾ࡅࡿ㈈ᨻᨻ⟇ࡢ࣐ࢡࣟ⤒῭ⓗຠᯝࠖࠉࠗࣇࢼࣥࢩ࣭ࣕࣝࣞ ࣅ࣮ࣗ࠘➨63 ྕ㸪pp.114-159㸦㈈ົ⥲ྜᨻ⟇◊✲ᡤࡢࣇࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗࡢ࣮࣒࣮࣍࣌ࢪࡼ ࡿ࣮࣌ࢪᩘ㸧㸬 㧗ᶫ㟷ኳ㸦2010㸧ࠕ᪥ᮏ࠾ࡅࡿࣂࣈࣝᔂቯᚋࡢ㈈ᨻᨻ⟇ࡢຠᯝ-ඹศศᯒࡼࡿィ ࠖࠉ㈈ᨻᏛ⦅㞟 ࠗࢣࣥࢬࡣ⏛ࡗࡓ࠘㈈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⪃࠼ࡿ࠘ᮾிᏛฟ∧ࠉ➨2 ❶ࠉpp.53 Ѹ 81㸬 ᮏከభ୕㸦1998㸧ࠕࢣࣥࢬ⌧௦⤒῭:ࠉ㈨⏘౯᱁ࡢどⅬࡽࡢᒎᮃࠖࠉࠗࣇࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗ࠘ࠉ ➨45 ྕ㸪pp.1-22㸦㈈ົ⥲ྜᨻ⟇◊✲ᡤࡢࣇࢼࣥࢩ࣭ࣕࣝࣞࣅ࣮ࣗࡢ࣮࣒࣮࣍࣌ࢪࡼࡿ࣮࣌ࢪᩘ㸧㸬 Ώ㎶ດ࣭⸭Ⰻ࣭ఀ⸨᪂㸦2010㸧ࠕไᗘሗࢆ⏝࠸ࡓ㈈ᨻᩘࡢィ ࠖࠉᇼᏹ⦅㞟ࠗ㈈ᨻᨻ⟇♫ ಖ㞀࠘᠕⩏ሿᏛฟ∧ 㸬Anderson,W., Wallace M.S. and J.T. Warner(1986), ͆Government Spending and Taxation: What Causes What? ͇, Southern Economic Journal, Vol.52, pp.630-639.
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