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(1)

ㄽ ᩥ

࣐ࢿ࣮ࡢ୰❧ᛶ

̿᪥ᮏ࡟࠾ࡅࡿᐇド◊✲̿

᳃⏣ ὒ஧ࠊ ⃝⏣ ྜྷᏕࠊ ᐑᕝ 㔜⩏

ி㒔ඛ➃⛉Ꮫ኱Ꮫྡ㄃ᩍᤵி㒔ඛ➃⛉Ꮫ኱Ꮫ⤒῭⤒ႠᏛ㒊

Email:[email protected]

せ ᪨

ྡ┠࣐ࢿ࣮ࡀ㛗ᮇⓗ࡟ᐇ㉁GDP࡟ᙳ㡪ࢆཬࡰࡉ࡞࠸ࡇ࡜ࢆࠊ࣐ࢿ࣮ࡢ୰❧ᛶ࡜࠸࠺ࠋ

᪥ᮏ࡟࠾ࡅࡿ㛗ᮇ୰❧ᛶࢆᐇドศᯒࡍࡿࠋKing $ Watsonࡀ2ኚᩘࡢSVARࣔࢹ࡛ࣝศ ᯒࡋࡓࡢ࡜ྠࡌࣔࢹࣝࢆᢅ࠺ࠋKing & Watsonࡀ㛗ᮇ୰❧ᛶࡢᡂࡾ❧ࡘࣃ࣓࣮ࣛࢱ⠊ᅖ

ࢆ♧ࡍ࡟࡜࡝ࡲࡗࡓࡢ࡟ᑐࡋࠊᮏ◊✲࡛ࡣࠊSVARࣔࢹࣝࡢࣃ࣓࣮ࣛࢱࡢ┤᥋ࡢ᥎ᐃᡭ ἲࢆ㛤Ⓨࡋࠊ㛗ᮇ୰❧ᛶࡀᲠ༷ࡉࢀࡿ࠿ྰ࠿ࡢุᐃࢆලయⓗ࡟ୗࡍࡇ࡜ࢆྍ⬟࡜ࡋࡓࠋ ᐇ㉁GDP࡜M3ࢆᢅ࠸ࠊࢹ࣮ࢱ༊㛫(1980q1,2007q4)࡟࠾࠸࡚㛗ᮇ୰❧ᛶࡀᲠ༷ࡉࢀࡿ

ࡇ࡜ࢆ♧ࡋࡓࠋ

࣮࣮࢟࣡ࢻ: ࣐ࢿ࣮ࠊ㛗ᮇ୰❧ᛶࠊSVARࣔࢹࣝࠊ᭱ᑬ᥎ᐃࠊᶆ‽ㄗᕪ

㸯㸬ࡣࡌࡵ࡟

㛗ᮇ୰❧ᛶࡢ௬ㄝ࡜ࡣࠊ࣐ࢿ࣮ࢫࢺࢵࢡࢆᜏஂⓗ࡟ኚ໬ࡉࡏ࡚ࡶࠊᐇ㉁ࡢ⏘ฟࡢࣞ࣋ࣝࡣ㛗ᮇⓗ࡞ᙳ 㡪ࢆཷࡅ࡞࠸ࡇ࡜ࢆゝ࠺ࠋከࡃࡢ࣐ࢡ࢚ࣟࢥࣀ࣑ࢫࢺࡣࡇࡢ௬ㄝࢆཷࡅධࢀ࡚࠾ࡾࠊ࣐ࢿ࣮ࢫࢺࢵࢡࡢ ኚ໬࡟ᑐࡋ࡚ᙳ㡪ࢆཷࡅ࡞࠸ᐇ㉁⤒῭ኚᩘ࡜ࡋ࡚ࠊᐇ㉁⏘ฟࢆࡣࡌࡵࠊᐇ㉁ᾘ㈝ࠊᐇ㉁㈤㔠ࠊᐇ㉁㔠฼

࡞࡝ࡀࡇࡢ⠊␪࡟ධࡿ࡜ࡳ࡞ࡋ࡚࠸ࡿࠋKing & Watson (1997)[1] ࡣࠊ㛗ᮇ୰❧ᛶࡢ᳨ドࡢᇶᮏⓗ࡞ᯟ

⤌ࡳࢆ୚࠼ࡓࠋࡲࡎࠊ஦๓࡟‶ࡓࡍ࡭ࡁ2ࡘࡢ᮲௳ࢆタᐃࡋࡓࠋ(i) ሺlnሺݎ݈݁ܽܩܰܲሻ, lnሺ݉݋݊݁ݕሻሻࡀI(1)

࡟ᒓࡍࡿࡇ࡜ࠊࡍ࡞ࢃࡕࠊྛኚᩘࡢࣞ࣋ࣝࡀ㠀ᐃᖖ࡛ࠊ1㝵ࡢ㝵ᕪࡀᐃᖖ࡛࠶ࡿࡇ࡜ࠋ(ii)2ࡘࡢኚᩘ㛫

࡟ඹ࿴ศࡀᏑᅾࡋ࡞࠸ࡇ࡜ࠋࡇࢀࡽࡢ๓ᥦ᮲௳ࡢୗ࡛ࠊKing & Watsonࡣࠊ(1949q1,1990q4)ࡢᮇ㛫࡟

࠾ࡅࡿUSࢹ࣮ࢱࡣࠊࢩࢫࢸ࣒ࣃ࣓࣮ࣛࢱࡢᗈ࠸⠊ᅖ࡛࣐ࢿ࣮ࡢ୰❧ᛶࢆᲠ༷ࡋ࡞࠸ࡇ࡜ࢆ♧ࡋࡓࠋྠ

ࡌᡭἲࢆ㐺⏝ࡋ࡚ࠊSerletis & Koustas (1998)[2] ࡣࠊ࠸ࡃࡘ࠿ࡢᅜࠎ࡟࠾ࡅࡿ࣐ࢿ࣮ࡢ୰❧ᛶࢆ⪃ᐹ ࡋࡓࠋ኱஭ࠊⓑሯࠊ௦⏣ (2004)[3] ࡣࠊking & Watsonࡢᡭἲࢆ⏝࠸࡚ࠊ᪥ᮏࡢ㛗ᮇࢹ࣮ࢱ(1885,2003)

࡟࠾ࡅࡿ࣐ࢿ࣮ࡢ㛗ᮇ୰❧ᛶࡀᲠ༷࡛ࡁ࡞࠸ࡇ࡜ࢆ♧ࡋࡓࠋ

(2)

King & Watsonࡢᡭἲࡣࠊ୰❧ᛶࡀᲠ༷ࡉࢀࡿࠊ࠶ࡿ࠸ࡣᲠ༷ࡉࢀ࡞࠸ࡓࡵࡢࠊࢩࢫࢸ࣒ࣃ࣓࣮ࣛࢱ ࡢ⠊ᅖࢆᥦ౪ࡋ࡚ࡃࢀࡿࡀࠊᐇ㝿࡟ᡃࠎࡀᢅࡗ࡚࠸ࡿࢩࢫࢸ࣒㸦᪥ᮏ㸧ࡢࣃ࣓࣮ࣛࢱࡀ࡝ࡢ್ࢆྲྀࡗ࡚

࠸ࡿ࠿ࢆ♧ࡍࡶࡢ࡛ࡣ࡞࠸ࠋ୚࠼ࡽࢀࡓࢹ࣮ࢱᮇ㛫࡟ࡼࡗ࡚ࡣࠊKing & Watson࡟ࡼࡿࣃ࣓࣮ࣛࢱࡢ

⠊ᅖࡀࠊࠕ୰❧ᛶࢆᲠ༷࡛ࡁ࡞࠸ࠖ࡜࠸࠺ุᐃࢆୗࡍ࡟ࡣᅔ㞴࡛࠶ࡿࡼ࠺࡞≧ἣࡶ㉳ࡇࡾ࠺ࡿࠋᮏ◊✲

࡛ࡣࠊKing & Watson࡜ྠࡌࢩࢫࢸ࣒ࣔࢹࣝ࡟࠾࠸࡚ࠊᙼࡽࡢᡭἲࢆᣑᙇࡋ࡚ࠊᵓ㐀VARࡢᯟ⤌ࡳࡢ

୰࡛ࠊࢩࢫࢸ࣒ࣃ࣓࣮ࣛࢱࢆ᥎ᐃࡍࡿᡭἲࢆ㛤Ⓨࡋࡓࠋᡃࠎࡢ⪃ᐹ┠ⓗࡣࠊ᪥ᮏ࡟࠾ࡅࡿ࣐ࢿ࣮ࡢ୰❧

ᛶࡢ᳨ド࡛࠶ࡾࠊᑐ㇟࡜ࡍࡿኚᩘ࡜ࡋ࡚ࠊሺlnሺݎ݈݁ܽܩܦܲሻ, lnሺܯ3ሻሻࢆ᥇⏝ࡍࡿࠋM3ࡣ1980q1௨㝆࡟

㝈ᐃࡉࢀࡿࡇ࡜ࠊࡲࡓࠊྛኚᩘࡀ I(1)ࢆ‶ࡓࡉ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡇ࡜࡟ࡼࡾࠊ⪃ᐹࡢᮇ㛫ࡣ (1980q1,2007q4)࡜࠸࠺ẚ㍑ⓗ▷࠸ࡶࡢ࡜࡞ࡗ࡚࠸ࡿࠋࡇࡢᮇ㛫࡟࠾࠸࡚ࠊ࣐ࢿ࣮ࡢ୰❧ᛶࡀᲠ༷ࡉࢀ

ࡿࡇ࡜ࢆ♧ࡍࠋ

㸰㸬ࢹ࣮ࢱࡢᛶ㉁

ኚᩘ࡜グྕࡢㄝ᫂ࢆ⾜࠺ࠋ

ݕ_௧= 400כln (ݎ݈݁ܽ ܩܦܲ(ݐሻ)(1)

݉௧ = 400כln (ܯ3(ݐ)) (2)

ࡇࡇ࡛ࠊࢹ࣮ࢱࡣᅄ༙ᮇ࡛࠶ࡾࠊࢹ࣮ࢱᮇ㛫ࡣ(1980q1,2007q4)࡛࠶ࡿࠋฟ඾ࡣࠊFRED(Federal Reserve Economic Data, St.Louis,fed)࡟ࡼࡿࠋ

㸰㸫㸯㸬༢఩᰿ࢸࢫࢺ(unit root test)

2✀㢮ࡢ༢఩᰿ࢸࢫࢺࢆᐇ⾜ࡍࡿࠋERSࢸࢫࢺࡣᖐ↓௬ㄝࢆ༢఩᰿࠶ࡾ࡜タᐃࡍࡿࠋ୍᪉ࠊKPSSࢸ ࢫࢺࡣᐃᖖᛶ࠶ࡾ࡜࠸࠺ᖐ↓௬ㄝࢆタᐃࡍࡿࠋヲ⣽ࡣ௜㘓ࢆཧ↷ࠋࢸࢫࢺ⤖ᯝࡣࠊݕ௧࡜݉௧ࡢ࡝ࡕࡽࡶ༢

఩᰿ࢆ᭷ࡋࠊȟݕ௧࡜ȟ݉௧ࡢ࡝ࡕࡽࡶࡀᐃᖖ࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋࡇࡇ࡛ࠊȟݕ௧=ݕ௧െ ݕ௧ିଵ࡛࠶ࡿࠋ ࡋࡓࡀࡗ࡚ࠊݕ௧࡜݉௧ࡣI(1)࡟ᒓࡍࡿࡇ࡜ࡀ♧ࡉࢀࡓࠋ

㸰㸫㸰㸬ඹ࿴ศࢸࢫࢺ(cointegration test)

ݕ௧࡜݉௧ࡢ㛫࡟ඹ࿴ศࡀ࠶ࡿ࠿ྰ࠿ࢆࠊJohansen[4]ࡢඹ࿴ศࢸࢫࢺ࡟ࡼࡗ࡚ㄪ࡭ࡿࠋヲ⣽ࡣ௜㘓ཧ↷ࠋ ࢸࢫࢺ࡟ࡼࡗ࡚ࠊඹ࿴ศࡀ࡞࠸ࡇ࡜ࡀ♧ࡉࢀࡓࠋ

㸱㸬ࢲ࢖ࢼ࣑ࢵࢡ࡞㐃❧⣔ࣔࢹࣝ

㸱㸫㸯㸬ࢩࢫࢸ࣒ࣔࢹࣝ

King & Watson࡟ࡋࡓࡀࡗ࡚ࠊ௨ୗࡢ2ኚᩘSVAR(structural vector autoregressive)ࣔࢹࣝࢆᑟධ ࡍࡿࠋ

οݕ_௧=ߣ_௬௠ȟ݉_௧+σ^௣_௝ୀଵߙ_௝,௬௠ȟ݉_௧ି௝+σ^௣_௝ୀଵߙ_௝,௬௬ȟݕ_௧ି௝+߳_௧^K, (3) ο݉_௧ =ߣ_௠௬ȟݕ_௧+σ^௣_௝ୀଵߙ_௝,௠௠ȟ݉_௧ି௝+σ^௣_௝ୀଵߙ_௝,௠௬ȟݕ_௧ି௝+߳_௧^௠,(4)

(3)

ࡇࡇ࡛ࠊ߳_௧^௠ࡣࠊᖹᆒࢮ࡛ࣟ⊂❧࡞࣐ࢿ࣮ࢩࣙࢵࢡ⣔ิࢆ⾲ࡋࠊ߳_௧^Kࡣ࣐ࢿ࣮௨እ࡛οݕ_௧࡟ᙳ㡪ࢆཬࡰࡍࡶ

ࡢ࡛࠶ࡾࠊ࣐ࢿ࣮࡜ࡣ⊂❧࡞ᖹᆒࢮࣟࡢࢩࣙࢵࢡ⣔ิࢆ⾲ࡋ࡚࠸ࡿࠋࡲࡓࠊ݌ࡣ㐜ࢀḟᩘ࡛ࠊAICつ⠊

࡛ᐃࡵࡽࢀࡿࡶࡢ࡜ࡍࡿࠋ

ᐇ㝿ࡢࢩࢫࢸ࣒࡛ࡣࠊᘧ(3)࡜ᘧ(4)ࡢྑ㎶࡟ࠊܿ݋݊ݏݐ. +݈݅݊݁ܽݐ ݐݎ݁݊݀ ࡢ㡯ࡀධࡗ࡚ࡃࡿࠋࡑࡢ࡜ࡁࠊ ᘧ(3)ࡢ୧㎶࡟ᮇᚅ್ࢆ᥃ࡅ࡚ࠊᮇᚅ್࠿ࡽࡢ೫ᕪࢆᘧࡢ୧㎶࡛⪃࠼ࡿ࡜ࠊ೫ᕪ ݕ௧െ ܧ{ݕ௧}ࡣࠊᘧ(3)࡟

ᑟධࡉࢀࡓ ܿ݋݊ݏݐ. +݈݅݊݁ܽݐ ݐݎ݁݊݀ ࡢ㡯ࡢࡳࢆᡴࡕᾘࡋࠊඖࡢᘧ(3)࡜ྠࡌಀᩘࢆ᭷ࡍࡿࣔࢹࣝᘧ࡜࡞ࡿࠋ ᘧ(4)࡟㛵ࡋ࡚ࡶ ݉௧െ ܧ{݉ݕ௧} ࢆ⪃࠼ࢀࡤࠊྠࡌࡇ࡜࡟࡞ࡿࠋ⤖ᒁࠊᖹᆒ್࠿ࡽࡢ೫ᕪࡀ‶ࡓࡍ࡭ࡁࢩ ࢫࢸ࣒࡜ࡋ࡚ࠊᘧ(3)ࠊᘧ(4)ࢆᢅ࠺ࡇ࡜࡟ࡍࡿࠋ

࣐ࢿ࣮࠿ࡽ⏘ฟ࡬ࡢ㛗ᮇࡢᙎᛶ್ ߛ௬௠ ࡣࠊ௨ୗࡢࡼ࠺࡟ィ⟬ࡉࢀࡿࠋ

ߛ_௬௠ =^ఒ^೤೘^ାఈ^భ,೤೘^ାఈ^మ,೤೘^ାڮାఈ^೛,೤೘

ଵି(ఈభ,೤೤ାఈమ,೤೤ାڮାఈ೛,೤೤) (5)

ܺ௧= (ȟݕ௧,ȟ݉௧)^ᇱࠊ߳௧= (߳_௧^ఎ,߳௧௠)Ԣ࡜ᐃ⩏ࡋࠊࡉࡽ࡟

ܣ_଴=൬ 1 െߣ௬௠

െߣ௠௬ 1 ൰ (6)

࡜ᐃࡵࡿ࡜ࠊࢩࢫࢸ࣒ࣔࢹࣝ(1),(2)ࡣḟࡢࡼ࠺࡟グ㏙ࡉࢀࡿࠋ

ܣ଴ܺ௧=σ^௣_௝ୀଵߙ௝ܺ௧ି௝+ ߳௧ , (7)

߳௧ࡢඹศᩓ⾜ิࢆ

ȭఢ=൬ݏଵଶ 0

0 ݏଶଶ൰ (8)

࡜ᐃࡵ࡚ࠊᘧ(7)ࢆㄏᑟᆺ(reduced)VAR࡟᭩ࡁ┤ࡍࠋ

ܺ_௧=σ^௣_௜ୀଵȰ_௜ܺ_௧ି௜+ݑ_௧, (9) ࡇࡇ࡛

Ȱ௜=െܣ଴ିଵߙ௜, ݑ௧=ܣ଴ିଵ߳௧ . (10)

ṧᕪݑ௧= (ݑଵ௧,ݑଶ௧)Ԣࡣḟࡢ㛵ಀᘧࢆ‶ࡓࡍࠋ

(4)

ȭ௨=ܣ଴ିଵȭఢ(ܣ଴ିଵ)Ԣ(11) ࡇࡇ࡛ࠊȭ௨ࡣ ݑ௧ ࡢඹศᩓ⾜ิ࡛࠶ࡿࠋᘧ(11)ࡣ4ࡘࡢᮍ▱ኚᩘ(ߣ௬௠,ߣ௠௬,ݏଵ,ݏଶ) ࢆ᭷ࡍࡿࡀࠊᕥ㎶

ࡢ ȭ௨ ࡣᑐ⛠⾜ิ࡛࠶ࡿ࠿ࡽ㸱ࡘࡢ㛵ಀᘧࡋ࠿ᚓࡽࢀ࡞࠸ࠋࡇࡢࡲࡲ࡛ࡣࠊᘧ(11)ࡣゎࡅ࡞࠸ࡇ࡜࡟ὀ ពࡉࢀࡓ࠸ࠋᙜ↛ࡢࡇ࡜࡞ࡀࡽࠊᘧ(3)ࠊ(4)ࡶゎࡅ࡞࠸ࡇ࡜࡟࡞ࡿࠋ

㸱㸫㸰㸬ࢽ࢟࢓࡜ ಙ㢗༊㛫ࡢ᥎ᐃ.LQJ :DWVRQ

King & Watson ࡢᡭἲࢆ⏝࠸࡚ࠊᘧ(3)ࠊ(4)ࢆ⪃ᐹࡍࡿࠋᙼࡽࡣᵓ㐀VAR࡜ࡋ࡚ࢩࢫࢸ࣒ࢆ᥎ᐃࡍ

ࡿࡢ࡛࡞ࡃࠊIVἲ࡟ࡼࡿ᥎ᐃࢆ⾜ࡗࡓࠋ 㸱㸫㸰㸫㸯㸬ࣅ࢓࢟ࡢ㛵ᩘ࡜ࡋ࡚ࢽ࢟࢓ࡢ᥎ᐃ

ᘧ(4)࡟࠾࠸࡚ࠊߣ௠௬ ࢆ1ࡘࡢ್࡟ᅛᐃࡍࡿ࡜ࠊο݉௧െ ߣ௠௬ȟݕ௧ ࢆ {ȟ݉௧ି௝,ȟݕ௧ି௝, ݆= 1,2, … ,݌} ࡟

ࡼࡗ࡚ᅇᖐࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋOLS᥎ᐃࢆ⏝࠸ࡿࡇ࡜ࡀ࡛ࡁࡿࠋ ࡇࡇ࡛ᚓࡽࢀࡓṧᕪࢆIVኚᩘ࡜ࡋ

࡚ᘧ(3)࡟௦ධࡋࠊᘧ(3)ࡢಀᩘࢆ᥎ᐃࡍࡿࠋᚓࡽࢀࡓಀᩘࡢ್ࢆᘧ(5)࡟௦ධࡍࡿ࡜ࠊߛ௬௠ ࡢ᥎ᐃ್ࡀᚓ

ࡽࢀࡿࠋࡉࡽ࡟ࠊᘧ(3)ࡢಀᩘࡢඹศᩓ⾜ิࢆ⏝࠸࡚ࠊߛ௬௠ ࡢᶆ‽ㄗᕪ(standard error)ࢆィ⟬ࡍࡿࠋᘧ

(5)ࡢ ߛ௬௠ ࢆྛࣃ࣓࣮ࣛࢱ࡟㛵ࡋ࡚ࢸ࢖࣮ࣛᒎ㛤ࡋ࡚⥺ᙧ㡯ࡲ࡛ࢆᣠ࠼ࡤ㸦ࢹࣝࢱᡭἲ㸧ࠊᶆ‽ㄗᕪࡀ

ᚓࡽࢀࡿࠋ࡞࠾ࠊᘧ(3)ࠊ(4)࡛ࡣࠊ㐜ࢀḟᩘࡣAICつ⠊࡟ࡼࡾ݌= 3 ࡜Ỵᐃࡉࢀࡓࠋࡲࡓࠊ୧ᘧ࡜ࡶ࡟

ྑ㎶➨1㡯࡟ܿ݋݊ݏݐ. +݈݅݊݁ܽݐ ݐݎ݁݊݀ ࢆධࢀ࡚ࠊㄏᑟᆺࡢVARࡢಀᩘࢆ᥎ᐃࡋࡓࠋࢺࣞࣥࢻࢆ᭷ࡍࡿᖹ ᆒ್࠿ࡽࡢ೫ᕪࢆᨵࡵ࡚ࣔࢹࣝᘧࡢኚᩘ࡜ࡳ࡞ࡍ࡜ࠊࡑࢀࡽࡢᘧࡢಀᩘࡣࠊܿ݋݊ݏݐ. +݈݅݊݁ܽݐ ݐݎ݁݊݀ ࢆ ධࢀࡓࣔࢹࣝᘧࡢಀᩘ࡜ࠊܿ݋݊ݏݐ. +݈݅݊݁ܽݐ ݐݎ݁݊݀ ௨እࡣ᏶඲࡟୍⮴ࡍࡿࠋߛ௬௠ ࡢィ⟬࡟୙㒔ྜࡣ⏕ࡌ

࡞࠸ࠋ

ߣ௠௬ ࢆูࡢ್࡟ᅛᐃࡋ࡚ࠊୖグࡢ᥎ᐃᡭ㡰ࢆ⧞ࡾ㏉ࡍࡇ࡜࡟ࡼࡾࠊߣ௠௬ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ߛ௬௠ࡀ᥎ᐃࡉ

ࢀࠊ95% ᥎ᐃ༊㛫ࡀᚓࡽࢀࡿࠋ᥎ᐃ⤖ᯝࢆᅗ1࡟♧ࡍࠋߣ௠௬< 0.2 ࡢ⠊ᅖ࡛ࠊߛ௬௠ = 0 ࡀᲠ༷ࡉࢀࡿ

㸦୰❧ᛶࡀᲠ༷ࡉࢀࡿ㸧ࡇ࡜ࡀศ࠿ࡿࠋ

-0.8 -0.4 0.0 0.4 0.8 1.2

-.4 -.2 .0 .2 .4 .6

-0.8 -0.4 0.0 0.4 0.8 1.2

-2 -1 0 1 2

ᅗ1㸬ࣅ࢓࢟ࡢ㛵ᩘ࡜ࡋ࡚ࡢࢽ࢟࢓࡜ ಙ㢗 ᅗ2㸬ࣅ࢟࢓ࡢ㛵ᩘ࡜ࡋ࡚ࡢࢽ࢟࢓࡜ ಙ㢗

༊㛫㸦ߛ௬௠± 2כ ݏ.݁. )༊༊㛫㸦ߛ௬௠± 2כ ݏ.݁. )

(5)

㸱㸫㸰㸫㸰㸬ࣅ࢟࢓ࡢ㛵ᩘ࡜ࡋ࡚ࢽ࢟࢓ࡢ᥎ᐃ

ᘧ(3)࡟࠾࠸࡚ࠊߣ௬௠ ࢆᅛᐃࡍࡿ࡜ࠊοݕ௧െ ߣ௬௠ȟ݉௧ ࢆ{ȟ݉௧ି௝,ȟݕ௧ି௝, ݆= 1,2, … ,݌} ࡟ࡼࡗ࡚ᅇᖐ ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸦OLS᥎ᐃ㸧ࠋ๓⠇࡜ྠᵝ࡟ࠊߛ௬௠ ࡢ᥎ᐃ್࡜ࠊ95% ᥎ᐃᮇ㛫ࢆᚓࡿࠋߣ௬௠ ࢆูࡢ

್࡟ᅛᐃࡋ࡚᥎ᐃᡭ㡰ࢆ⧞ࡾ㏉ࡍ࡜ࠊߣ௬௠ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ߛ௬௠ࡀ᥎ᐃࡉࢀࠊ95% ᥎ᐃ༊㛫ࡀᚓࡽࢀࡿࠋ ᥎ᐃ⤖ᯝࢆᅗ2࡟♧ࡍࠋߣ௬௠>െ1.07 ࡢ⠊ᅖ࡟࠾࠸࡚ࠊߛ௬௠= 0 ࡀᲠ༷ࡉࢀࡿ㸦୰❧ᛶࡀᲠ༷ࡉࢀࡿ㸧 ࡇ࡜ࡀศ࠿ࡿࠋ

King & Watsonࡢ୺ᙇ࡛ࡣࠊߣ௠௬ ࡸ ߣ௬௠ ࡀ⤒῭Ꮫⓗ࡟ぢ࡚ྜ⌮ⓗ࡞⠊ᅖ࡟࠶ࡿ࡜ࡁ࡟ࡣࠊ୰❧ᛶ

(ߛ_௬௠= 0) ࡣᲠ༷ࡉࢀ࡞࠸࡜ࡋ࡚࠸ࡿࠋࡋ࠿ࡋ࡞ࡀࡽࠊᡃࠎࡢࢹ࣮ࢱ࡟࠾࠸࡚ࠊߛ௬௠= 0 ࡀᲠ༷ࡉࢀ

ࡿ⠊ᅖ (ߣ_௠௬< 0.2, ߣ௬௠>െ1.07) ࡀ⤒῭Ꮫⓗ࡟ྜ⌮ⓗ࡛࡞࠸࡜ุᐃࡍࡿ☜ᐇ࡞᰿ᣐࡶぢᙜࡓࡽ࡞࠸

ࡼ࠺࡛࠶ࡿࠋࡑࡇ࡛ࠊḟࡢ❶࡛ࡣࠊSVARࣔࢹࣝࡢᮍ▱ࣃ࣓࣮ࣛࢱ (ߣ௬௠,ߣ௠௬,ݏଵ,ݏଶ) ࡢ᥎ᐃࢆヨࡳࡿࠋ ලయⓗ࡟ ߣ௠௬ ࡸ ߣ௬௠ ࡢ್ࡀồࡲࢀࡤࠊߛ௬௠= 0 ࡀᲠ༷ࡉࢀ࡚࠸ࡿ࠿ྰ࠿ࡣࠊᅗ1ࠊ2ୖ࡛ࡍࡄ࡟ุ

ᐃ࡛ࡁࡿ࠿ࡽ࡛࠶ࡿࠋ

㸲㸬69$5 ࡟࠾ࡅࡿ(ૃ_ܡܕ,ૃ_ܕܡ,ܛ_૚,ܛ_૛)ࡢ᥎ᐃ

ᘧ(3)ࠊ(4)࡛⾲ࡉࢀࡿSVARࣔࢹࣝࡣࠊᘧ(11)࡟࠾࠸࡚ࠊ4ࡘࡢᮍ▱ᩘ (ɉ୷୫,ɉ୫୷, sଵ, sଶ) ࡜3ࡘࡢ᮲

௳࡜࠸࠺ไ⣙ࢆཷࡅ࡚࠸ࡿࠋࡑࢀࡺ࠼ࠊ1ࡘࡢᮍ▱ᩘ࡟ලయⓗ࡞್ࢆタᐃࡍࡿ࡜ࠊṧࡾ3ࡘࡢᮍ▱ᩘ

ࢆồࡵࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡇࡢᡭ㡰ࢆ౑ࡗ࡚ࠊ4ࡘࡢᮍ▱ᩘ┦஫㛫ࡢ㛵ಀࢆㄪ࡭ࡿࡇ࡜࡟ࡍࡿࠋ 㸲㸫㸯㸬(ૃܡܕ,ૃܕܡ,ܛ૚,ܛ૛)ࡢ┦஫㛵ಀ

㸲㸫㸯㸫㸯㸬(ૃܡܕ,ૃܕܡ)ࡢ㛵ಀ

ɉ_୷୫ ࡜ ɉ_୫୷ ࡢྛ್ࢆ㐺ᙜ࡟୚࠼࡚ࠊṧࡾ3ࡘࡢᮍ▱ᩘࢆồࡵࡿࠋࡇࡢ࡜ࡁࠊ(ɉ_୷୫,ɉ_୫୷)ࡢ㛵ಀࢆ

ᅗ♧ࡍࡿ࡜ࠊᅗ3ࡢ཮᭤⥺࡜࡞ࡿࠋ₞㏆⥺ࡣࠊɉ_୷୫؆ െ53, ɉ_୫୷؆ െ11 ࡛࠶ࡿࠋɉ_୷୫ ࡜ ɉ_୫୷ ࡣ஫࠸

࡟1౯㛵ᩘ࡛࠶ࡿࡇ࡜࡟ὀពࠋ࣐ࢿ࣮ࡢ୰❧ᛶࢆ⪃࠼ࡿ࡜ࡁࠊ൫ɉ୷୫,ɉ୫୷൯= (0,0) ㏆ഐࡀ㔜せ࡜࡞ࡿ

ࡢ࡛ࠊᅗ4࡛ (0,0) ㏆ഐࡢᣑ኱ᅗࢆ♧ࡍࠋᅗ㸲࡛ࡣࠊ࡯࡜ࢇ࡝ࡢሙྜࠊɉ_୷୫ ࡜ ɉ_୫୷ ࡀ஫࠸࡟␗➢ྕ

࡛࠶ࡿࡇ࡜࡟ὀពࠋ

-1,600 -1,200 -800 -400 0 400 800 1,200

-120 -100 -80 -60 -40 -20 0 20 40

-.6 -.4 -.2 .0 .2 .4 .6

-3 -2 -1 0 1 2 3

ᅗ3㸬൫ૃܡܕ,ૃܕܡ൯ࡢ㛵ಀ㸦኱ᇦⓗ㸧 ᅗ4㸬൫ૃܡܕ,ૃܕܡ൯ࡢ㛵ಀ(૙,૙)㏆ഐ㸧

(6)

㸲㸫㸯㸫㸰㸬(ૃ_ܡܕ,ૃ_ܕܡ)࡜࢙_૚ࡢ㛵ಀ

ݏଵ ࡢ್ࢆ㐺ᙜ࡟タᐃࡋ࡚ࠊṧࡾ3ࡘࡢᮍ▱ᩘࢆồࡵࡿࠋࡑࡢ࡜ࡁࡢ൫ɉ୷୫,ɉ୫୷൯= (0,0) ㏆ഐࡢ್

ࢆᅗ5࡟♧ࡍࠋݏଵ= 2.85 ࡜ᐃࡵࡿ࡜ࠊ൫ɉ୷୫,ɉ୫୷൯= (െ0.092, 0) ࡢ1Ⅼࡀᐃࡲࡿࠋݏଵ ࡢタᐃ್ࢆࡇ

ࢀࡼࡾ኱ࡁࡃࡋ࡚࠸ࡃ࡜ࠊ㸯ࡘࡢ ݏଵ ࡟ᑐࡋ࡚ࠊ2⤌ࡢ ൫ɉ୷୫,ɉ୫୷൯ ࡀᐃࡲࡗ࡚ࡃࡿࠋࡍ࡞ࢃࡕࠊݏଵ

ࡣ2౯㛵ᩘ࡛࠶ࡿࠋ

-.4 -.3 -.2 -.1 .0 .1 .2 .3 .4

-2 -1 0 1 2

s1=2.9 to 3.5 s1=3.5 s1=3.2 s1=2.9 s1=2.85

ᅗ5㸬࢙૚ ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ൫ૃܡܕ,ૃܕܡ൯ ࡢ್

㸲㸫㸯㸫㸱㸬(ૃܡܕ,ૃܕܡ)࡜࢙૛ࡢ㛵ಀ

ݏଶ ࡢ್ࢆ㐺ᙜ࡟タᐃࡋ࡚ࠊṧࡾ3ࡘࡢᮍ▱ᩘࢆồࡵࡿࠋࡑࡢ࡜ࡁࡢ൫ɉ୷୫,ɉ୫୷൯= (0,0) ㏆ഐࡢ್

ࢆᅗ6࡟♧ࡍࠋݏଶ= 1.29 ࡜ᐃࡵࡿ࡜ࠊ൫ɉ୷୫,ɉ୫୷൯= (0,െ0.0187) ࡢ1Ⅼࡀᐃࡲࡿࠋݏଶ ࡢタᐃ್ࢆ

ࡇࢀࡼࡾ኱ࡁࡃࡋ࡚࠸ࡃ࡜ࠊ1ࡘࡢݏଶ ࡟ᑐࡋ࡚ࠊ㸰⤌ࡢ൫ɉ୷୫,ɉ୫୷൯ ࡀᐃࡲࡗ࡚ࡃࡿࠋࡍ࡞ࢃࡕࠊݏଶ

ࡣ2౯㛵ᩘ࡛࠶ࡿࠋ

ݏଵ= 65.7, ݏଶ= 1100 ࡜ࡋ࡚ݏଵ,ݏଶ ࡟ࡑࢀࡒࢀࡢ್ࢆタᐃࡋࡓ࡜ࡁࠊྛ2⤌ࡢ൫ɉ୷୫,ɉ୫୷൯ ࡀᐃࡲ

ࡿࠋ኱ᇦⓗ࡞ ൫ɉ୷୫,ɉ୫୷൯ ୖ࡛ࡢ ݏଵ,ݏଶ ࡢ2౯㛵ᩘࡢᵝᏊࢆᅗ㸵࡟♧ࡍࠋ௨ୖࡼࡾࠊ

ݏଵ ࡣࠊO_௬௠=െ0.092 ࡢⅬࢆ୰ᚰ࡜ࡋx㍈᪉ྥ࡟ᑐ⛠࡞ⅬࢆⓎ⏕ࡉࡏࡿ2౯㛵ᩘ࡜ゝ࠼ࡿࠋ ݏଶ ࡣࠊO_௠௬=െ0.0187 ࡢⅬࢆ୰ᚰ࡜ࡋy㍈᪉ྥ࡟ᑐ⛠࡞ⅬࢆⓎ⏕ࡉࡏࡿ2౯㛵ᩘ࡜ゝ࠼ࡿࠋ

(7)

-.3 -.2 -.1 .0 .1 .2 .3

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

s2=1.30,1.32,...,1.50 s2=1.5

s2=1.4 s2=1.3 s2=1.29

ᅗ6㸬࢙૛ࡢ㛵ᩘ࡜ࡋ࡚ࡢ൫ૃܡܕ,ૃܕܡ൯ࡢ್

-1,600 -1,200 -800 -400 0 400 800 1,200

-120 -80 -40 0 40 80

(l_ym, l_my) s1=65.7 s2=1100

ᅗ7㸬࢙૚, ࢙૛ࡢ㛵ᩘ࡜ࡋ࡚ࡢ൫ૃܡܕ,ૃܕܡ൯ࡢ್㸦኱ᇦⓗ㸧

(8)

㸲㸫㸰㸬ᶆ‽ㄗᕪࡢゎᯒ࡟ࡼࡿ(ૃܡܕ,ૃܕܡ,ܛ૚,ܛ૛)ࡢ᥎ᐃ

sଵ ࡢ್㸦ࡲࡓࡣ sଶ ࡢ್㸧ࢆタᐃࡍࢀࡤࠊṧࡾࡢ㸱ࡘࡢᮍ▱ᩘ (ɉ୷୫,ɉ୫୷, sଵ) 㸦ࡲࡓࡣ

(ɉ୷୫,ɉ୫୷, sଶ)㸧ࡣ᭱ᑬἲ࡛Ỵᐃࡉࢀࡿࠋ᥎ᐃࡉࢀࡓᮍ▱ᩘࡢᶆ‽ㄗᕪࡣsଵ㸦ࡲࡓࡣsଶ 㸧ࡢ㛵ᩘ࡛࠶

ࡿࡺ࠼ࠊタᐃࡋࡓsଵ㸦ࡲࡓࡣsଶ 㸧ࡀ┿್࡛࠶ࡿሙྜࡣࠊ᥎ᐃࡉࢀࡓṧࡾ3ࡘࡢᮍ▱ᩘࡢᶆ‽ㄗᕪࡀ᭱

ᑠ࡟࡞ࡗ࡚࠸ࡿ࡜ᮇᚅ࡛ࡁࡿࠋs_ଵ㸦ࡲࡓࡣs_ଶ 㸧ࡣ㸰್㛵ᩘ࡛࠶ࡿ࠿ࡽࠊᅗ5ࠊ6࡟ᑐᛂࡋ࡚᥎ᐃ್ࡢ

⤌ࢆ4ࡘ࡟ศ㢮ࡍࡿࠋݏଵ ՜(ɉ୷୫,ɉ୫୷, sଶ) ࡢሙྜศࡅࠊݏଶ ՜(ɉ୷୫,ɉ୫୷, sଵ) ࡢሙྜศࡅࢆ⪃࠼ࡿࠋ

(case-i) ݏଵ ՜(ɉ୷୫>െ0.09, ɉ୫୷< 0, sଶ) (case-ii) ݏ_ଵ ՜(ɉ୷୫<െ0.09, ɉ୫୷> 0, sଶ) (case-iii) ݏ_ଶ ՜(ɉ୷୫>െ0.09, ɉ୫୷< 0, sଵ) (case-iv) ݏ_ଶ ՜(ɉ୷୫<െ0.09, ɉ୫୷> 0, sଵ)

sଵ ࢆ୚࠼ࡓ᫬ࡢ(case-i) ࡜(case-ii) ࡟࠾ࡅࡿ᥎ᐃ್ࢆᅗ8࡟ࠊsଶ ࢆ୚࠼ࡓ᫬ࡢ(case-iii) ࡜(case-iv) ࡟

࠾ࡅࡿ᥎ᐃ್ࢆᅗ9࡟♧ࡍࠋ

-2 -1 0 1 2 3 4

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 s1, (case-i) and (case-ii)

ym_i ym_ii

my_i my_ii

s2_i s2_ii

-2 -1 0 1 2 3 4

1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 s2, (case-iii) and (case-iv)

ym_iii ym_iv

my_iii my_iv

s1_iii s1_iv

ᅗ8㸬࢙_૚ ࡢ㛵ᩘ࡜ࡋ࡚ࡢ (ૃ_ܡܕ,ૃ_ܕܡ,ܛ_૛)ࠊ ᅗ9㸬࢙_૛ ࡢ㛵ᩘ࡜ࡋ࡚ࡢ (ૃ_ܡܕ,ૃ_ܕܡ,ܛ_૚)ࠊ (case-i)࠾ࡼࡧ(case-ii) (case-iii)࠾ࡼࡧ(case-iv)

㸲㸫㸰㸫㸯㸬(ૃܡܕ>െ૙.૙ૢ, ૃܕܡ<૙)࡟࠾ࡅࡿᶆ‽ㄗᕪࠊ(case-i)࡜(case-iii)

(case-i) ݏ݁_ݕ݉,ݏ݁_݉ݕ,ݏ݁_ݏ2 ࢆࠊྛࠎ ߣ௬௠,ߣ௠௬,ݏଶ ࡢᶆ‽ㄗᕪ࡜ࡍࡿࠋݏଵ ࢆ㐺ᙜ࡞ศ๭ᖜ࡛୚࠼

ࡿࡇ࡜࡟ࡍࡿࠋݏଵ ࡣ2౯㛵ᩘ࡛࠶ࡿ࠿ࡽࠊߣ௬௠>െ0.09, ߣ௠௬< 0 ࡢ㡿ᇦ࡛ィ⟬ࡉࢀࡓ3ኚᩘࡢᶆ‽

ㄗᕪࡢྛࠎࢆࠊݏଵ ࡢ㛵ᩘ࡜ࡋ࡚ᅗ10࡟♧ࡍࠋ

(9)

ᅗ10㸬࢙૚ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૛ࠊFDVHL ࣅ࢟࢓>െ૙.૙ૢ, ࣅ࢓࢟<૙

ᅗ10࡛ࡣࠊ௨ୗࡢ3ࡘࡢ᭱ᑠ್ࢆぢࡿࡇ࡜ࡀ࡛ࡁࡿࠋ

z ݏ݁_݉ݕ ࡣ ݏଵ= 3.44 ࡛᭱ᑠ್ࢆྲྀࡿ㸦3.2 <ݏଵ< 3.8 ࡢ㛫࡛ࡣࠊ0.04้ࡳ࡛ݏଵࢆື࠿ࡍ㸧ࠋ z ݏ݁_ݕ݉ ࡣ ݏଵ= 4.10 ࡛᭱ᑠ್ࢆྲྀࡿࠋ

z ݏ݁_ݏ2 ࡣ ݏଵ= 2.875 ࡛᭱ᑠ್ࢆྲྀࡿࠋ

ᶆ‽ㄗᕪࢆ᭱ᑠ࡟ࡍࡿ ݏଵ ࡢ୰࡛ࠊݏ݁_݉ݕ ࢆ᭱ᑠ࡟ࡍࡿ ݏଵ ࡀ┿್ࡢ᥎ᐃ್࡛࠶ࡿࡇ࡜ࢆᡃࠎࡣ୺ᙇ ࡍࡿࠋ➨㸳❶ࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟࠾࠸࡚ࠊ┿್ࡀศ࠿ࡗ࡚࠸ࡿࢩࢫࢸ࣒࡛ࢹ࣮ࢱࢆⓎ⏕ࡉࡏࠊᶆ‽ㄗ ᕪ᭱ᑠࡢつ⠊࡛᥎ᐃࡍࡿ࡜ࠊୖグࡢ⤖ㄽࠕ ݏ݁_݉ݕ ࢆ ݏଵ ࡟㛵ࡋ࡚᭱ᑠ໬ࡍࡿሙྜࡀ┿ࡢ ݏଵ ࢆ᥎ᐃࠖ

ࢆᚓࡿࠋ➨5❶ࢆཧ↷ࡉࢀࡓ࠸ࠋ

(case-iii) ݏ_ଶ ࢆ㐺ᙜ࡟୚࠼ࡓ᫬ࠊߣ_௬௠,ߣ_௠௬,ݏ_ଵ ࡀィ⟬ࡉࢀࠊᑐᛂࡍࡿᶆ‽೫ᕪࢆ ݏ݁_ݕ݉,ݏ݁_݉ݕ,ݏ݁_ݏ1

࡜ࡍࡿࠋ (case-i)࡜ྠࡌኚᩘྡ ݏ݁_ݕ݉,ݏ݁_݉ݕ ࢆ౑ࡗ࡚࠸ࡿࡀࠊ(case-i)࡛ࡣྛᶆ‽೫ᕪࡣݏଵ ࡢ㛵ᩘࠊ

(case-iii)࡛ࡣ ݏଶ ࡢ㛵ᩘ࡛࠶ࡿࡇ࡜࡟ὀពࠋݏଶ ࡢ୚࠼᪉ࡣ௨ୗࡢࡼ࠺࡟⾜࠺ࡶࡢ࡜ࡍࡿࠋ(case-i)࡛

ݏଵ=ݏ_ଵ^(ଵ),ݏ_ଵ^(ଶ),ڮ,ݏ_ଵ^(௞) ࡢࡼ࠺࡟ k ㏻ࡾࡢ್ࢆタᐃࡋࡓ࡜ࡍࡿࠋࡑࡢ࡜ࡁࠊ᥎ᐃ್࡜ࡋ࡚ࠊݏଶ= ݏ_ଶ^(ଵ),ݏ_ଶ^(ଶ),ڮ,ݏ_ଶ^(௞) ࡀ ᚓ ࡽ ࢀ ࡓ ࡶ ࡢ ࡜ ࡍ ࡿ ࠋ(case-iii)࡛ ࡢ ݏଶ ࡣ ࠊ(case-i)࡛ ᚓ ࡽ ࢀ ࡓ ݏଶ= ݏ_ଶ^(ଵ),ݏ_ଶ^(ଶ),ڮ,ݏ_ଶ^(௞) ࢆ☜ᐃ್࡜ࡋ࡚୚࠼ࡿࡇ࡜࡟ࡍࡿࠋ㸰౯㛵ᩘ࡛࠶ࡿ࠿ࡽࠊߣ_௬௠>െ0.09, ߣ_௠௬ < 0 ࡢ 㡿ᇦ࡛ィ⟬ࡍࡿࡀࠊࡇࡢ⠊ᅖ࡛ࡣࠊ᥎ᐃ್ߣ௬௠,ߣ௠௬,ݏଵ ࡣ(case-i)࡜ࡲࡗࡓࡃྠࡌ್ࡀᚓࡽࢀࠊᶆ‽೫ ᕪࡢࡳࡀ᪂ࡋࡃィ⟬ࡉࢀࡓࡶࡢ࡜࡞ࡗ࡚࠸ࡿࠋ㸱ኚᩘࡢᶆ‽ㄗᕪࡢྛࠎࢆࠊݏଶ ࡢ㛵ᩘ࡜ࡋ࡚ᅗ11࡟

♧ࡍࠋ

OQVHB\POQVHBP\OQVHBV DVDIXQFWLRQRIVFDVHL

OQVHB\P OQVHBP\ OQVHBV PLQ

(10)

ᅗ11㸬࢙૛ࡢ㛵ᩘ࡜ࡋ࡚ࡢ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૚ࠊFDVHLLL ࣅ࢟࢓>െ૙.૙ૢ, ࣅ࢓࢟<૙

ᅗ11࡛ࡣࠊ௨ୗࡢ3ࡘࡢ᭱ᑠ್ࢆぢࡿࡇ࡜ࡀ࡛ࡁࡿࠋ z ݏ݁_݉ݕ ࡣ ݏଶ= 1.84 ࡛᭱ᑠ್ࢆྲྀࡿࠋ

z ݏ݁_ݕ݉ ࡣ ݏଶ= 1.509516 ࡛᭱ᑠ್ࢆྲྀࡿ (ݏ_ଵ^(௜)= 3.44՞ ݏ_ଶ^(௜)= 1.509516)ࠋ z ݏ݁_ݏ2 ࡣ ݏଶ= 1.32 ࡛᭱ᑠ್ࢆྲྀࡿࠋ

ݏ݁_ݕ݉ ࢆ᭱ᑠ࡟ࡍࡿ ݏଶ ࡢ್ࡀ┿ࡢ᥎ᐃ್࡜࡞ࡿࠋ➨5❶ࡢࢩ࣑࣮ࣗࣞࢩࣙࣥࢆཧ↷ࡉࢀࡓ࠸ࠋ

[(case-i)࡜(case-iii)ࡢ⤖ᯝ] ݏ݁_݉ݕ ࢆ ݏଵ ࡟㛵ࡋ࡚᭱ᑠ໬ࡍࡿࡇ࡜ࠊݏ݁_ݕ݉ ࢆ ݏଶ ࡟㛵ࡋ࡚᭱ᑠ

໬ࡍࡿࡇ࡜ࠊ࡝ࡕࡽ࡟ࡼࡗ࡚ࡶ┿ࡢ᥎ᐃ್ࢆᚓࡿࠋཝᐦ࡟ࡣ୧⪅ࡢ᥎ᐃ್ࡣఝ㏻ࡗ࡚ࡃࡿࡀࠊ୍⮴ࡣࡋ

࡞࠸ࠋ௒ࡢሙྜࡣࠊݏଵ ࡢ್ࡢタᐃࡢ௙᪉ࢆࠊᑡࡋᗈࡵ࡟࡜ࡿࡇ࡜ࠊ࠾ࡼࡧࠊݏଵ ࡟ࡼࡿ᥎ᐃ್ݏଶ ࢆࠊ ݏଶ ࡢタᐃ್࡜ࡋ࡚෌฼⏝ࡋࡓࡇ࡜࡟ࡼࡾࠊ(case-i)࡜(case-iii)ࡢ᥎ᐃᡭἲࡀࠊྠࡌ᥎ᐃ⤖ᯝࢆᑟฟࡋࡓࠋ

൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (1.368308,െ0.28889, 3.44, 1.509516) (12) 㸲㸫㸰㸫㸰㸬(ૃܡܕ<െ૙.૙ૢ, ૃܕܡ>૙)࡟࠾ࡅࡿᶆ‽ㄗᕪࠊFDVHLL࡜FDVHLY

(case-ii) ݏଵ ࡢ್ࢆࠊ๓⠇㸲㸫㸰㸫㸯ࡢሙྜ࡜ྠࡌ್ (ݏ_ଵ=ݏ_ଵ^(ଵ),ݏ_ଵ^(ଶ),ڮ,ݏ_ଵ^(௞) )࡟タᐃࡍࡿࠋݏଵ ࡣ2 ౯㛵ᩘ࡛࠶ࡿ࠿ࡽࠊ(ɉ୷୫<െ0.09, ɉ୫୷> 0) ࡢ㡿ᇦ࡛ࠊṧࡾࡢ3ኚᩘ(ɉ୷୫,ɉ୫୷, sଶ) ࡢ᥎ᐃ್࡜ᶆ

‽೫ᕪࢆồࡵࡿࠋݏଵ ࡢ್ࡢࡳ๓⠇࡜ྠࡌ࡛࠶ࡿࡀࠊṧࡾ3ኚᩘࡢ᥎ᐃ್࡜ᶆ‽ㄗᕪࡣࠊ࡝ࢀࡶ๓⠇࡜

ࡣ␗࡞ࡗ࡚࠸ࡿࠋᚓࡽࢀࡓᶆ‽೫ᕪࢆ ݏଵ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᅗ12࡟♧ࡍࠋ௨ୗࡢ3Ⅼࡀㄞࡳྲྀࢀࡿࠋ z ݏ݁_݉ݕࡣݏଵ= 3.36࡛᭱ᑠ್ࢆྲྀࡿࠋ

z ݏ݁_ݕ݉ࡣݏଵ= 4.10࡛᭱ᑠ್ࢆྲྀࡿࠋ z ݏ݁_ݏ2ࡣݏଵ= 2.92࡛᭱ᑠ್ࢆྲྀࡿࠋ

OQVHB\POQVHBP\OQVHBV DVDIXQFWLRQRIV FDVHLLL

(11)

๓⠇࡜ྠࡌ᥎ㄽ࡟ࡼࡗ࡚ࠊ3ࡘࡢ᭱ᑠ໬ࡢ୰࡛ࠊݏ݁_݉ݕ ࢆ ݏ_ଵ ࡟㛵ࡋ࡚᭱ᑠ໬ࡍࡿሙྜࡀ┿ࡢݏ_ଵ ࢆ ᥎ᐃࡋ࡚࠸ࡿ࡜⤖ㄽ௜ࡅࡿࠋ

ᅗ12㸬࢙૚ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૛ࠊFDVHLL ࣅ࢟࢓<െ૙.૙ૢ, ࣅ࢓࢟>૙

(case-iv) (case-ii)࡟࠾࠸࡚ ݏଵ ࡢ್ࢆݏଵ=ݏ_ଵ^(ଵ),ݏ_ଵ^(ଶ),ڮ,ݏ_ଵ^(௞) ࡜タᐃࡋࡓ࡜ࡁࠊݏଵ ࡣ2౯㛵ᩘ࡛࠶ࡿ

࠿ࡽࠊ(ɉ୷୫<െ0.09, ɉ୫୷> 0) ࡢ㡿ᇦ࡛sଶ ࡢ್ࡀࠊ ݏଶ=ݏ_ଶ^(ଵ),ݏ_ଶ^(ଶ),ڮ,ݏ_ଶ^(௞) ࡜᥎ᐃࡉࢀࡓࡶࡢ࡜

ࡍࡿࠋ(case-iv)࡛ࡣࠊࡇࢀࡽࡢ ݏ_ଶ ࡢ್ࢆࠊ☜ᐃ್࡜ࡋ࡚タᐃࡋ࡚ࠊṧࡾ3ኚᩘ(ɉ_୷୫,ɉ_୫୷, s_ଵ) ࡢ᥎ ᐃ್࡜ᶆ‽೫ᕪࢆồࡵࡿࠋݏଶ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᶆ‽ㄗᕪࡢ್ࢆᅗ13࡟♧ࡍࠋ

ᅗ13㸬࢙૛ࡢ㛵ᩘ࡜ࡋ࡚ࡢ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૚ࠊFDVHLY ࣅ࢟࢓<െ૙.૙ૢ, ࣅ࢓࢟>૙

OQVHB\POQVHBP\OQVHBV DVDIXQFRIVFDVHLL

OQ\P OQP\ OQV PLQ

OQVHB\POQVHBP\OQVHBV DVDIXQFRIVFDVHLY

(12)

ᅗ13࡛ࡣࠊ௨ୗࡢ3Ⅼࡢ᭱ᑠ್ࢆ☜ㄆࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋ z ݏ݁_݉ݕ ࡣ ݏ_ଶ= 1.8277 ࡛᭱ᑠ್ࢆྲྀࡿࠋ

z ݏ݁_ݕ݉ ࡣ ݏ_ଶ= 1.5537 ࡛᭱ᑠ್ࢆྲྀࡿࠋ z ݏ݁_ݏ1 ࡣ ݏଶ= 1.295 ࡛᭱ᑠ್ࢆྲྀࡿࠋ ݏ݁_ݕ݉ ࢆ᭱ᑠ࡟ࡍࡿ ݏ_ଶ ࡢ್ࡀồࡵࡿ᥎ᐃ್࡛࠶ࡿࠋ

[(case-ii)࡜(case-iv)ࡢ⤖ᯝ] (ɉ୷୫<െ0.09, ɉ୫୷> 0) ࡢ㡿ᇦ࡛ࠊݏଵ ࡜ ݏଶ ࢆື࠿ࡋࡓ⤖ᯝࠊ ݏ݁_݉ݕ ࢆ ݏଵ ࡟㛵ࡋ࡚᭱ᑠ໬ࡍࡿࡇ࡜ࠊݏ݁_ݕ݉ ࢆ ݏଶ ࡟㛵ࡋ࡚᭱ᑠ໬ࡍࡿࡇ࡜ࠊ࡝ࡕࡽ࡟ࡼࡗ࡚ࡶ┿

ࡢ᥎ᐃ್ࢆᚓࡿࠋݏଵ ࡢ್ࡢタᐃࡢ௙᪉ࢆࠊᑡࡋᗈࡵ࡟࡜ࡿࡇ࡜ࠊ࠾ࡼࡧࠊݏଵ ࡟ࡼࡿ᥎ᐃ್ ݏଶ ࢆࠊݏଶ

ࡢタᐃ್࡜ࡋ࡚෌฼⏝ࡋࡓࡇ࡜࡟ࡼࡾࠊ(case-ii)࡜(case-iv)ࡢ᥎ᐃᡭἲࡀࠊྠࡌ᥎ᐃ⤖ᯝࢆᑟฟࡋࡓࠋ

൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (െ1.43686, 0.280348, 3.36, 1.553799) (13)

4ࡘࡢᮍ▱ᩘࡢ᥎ᐃ್ࡢೃ⿵ࡣࠊᘧ(12)࡜ᘧ(13)࡛♧ࡉࢀࡓ࡜࠾ࡾ࡛࠶ࡿࠋ࡝ࡕࡽࡀ⤒῭Ꮫⓗ࡟ྜ⌮ⓗ

࡛࠶ࡿ࠿࡟ࡼࡗ࡚ࠊ᭱⤊ุ᩿ࢆୗࡍࠋࣂࣈࣝ⤒῭ࡢ᫬௦ࢆྵࡴࢹ࣮ࢱ࡛࠶ࡿ࠿ࡽࠊɉ୷୫> 0 ࡀ㐺ษ࡛

࠶ࡿࠋࡋࡓࡀࡗ࡚ࠊᘧ(12)ࢆ᥎ᐃ್࡜ࡋ࡚᥇⏝ࡍࡿࠋɉ୫୷ ࡢ್ࢆᅗ㸯࡟௦ධࠊࡲࡓࡣࠊɉ୷୫ ࡢ್ࢆᅗ 2࡟௦ධࡍࡿ࡜ࠊ࡝ࡕࡽࡢᅗ࡟࠾࠸࡚ࡶࠊ୰❧ᛶࡢ௬ㄝ [ߛ_௬௠= 0] ࡣᲠ༷ࡉࢀࡿࠋ࡞࠾ࠊɉ୷୫ ࡜ ɉ୫୷

ࡣࠊ୍᪉ࢆᐃࡵࡿ࡜ࠊ௚᪉ࡣ୍ពⓗ࡟ᐃࡲࡿࡢ࡛ࠊᅗ1࡜ᅗ2ࡣ࡝ࡕࡽ࠿1ࡘ࡛ࡼ࠸ࠋɉ୷୫ ࡢ࡯࠺ࡀ ߛ௬௠ ࡢィ⟬ࡀᐜ࡛᫆࠶ࡿࡇ࡜ࢆ⪃៖ࡍࡿ࡜ࠊᅗ1ࡣ୙せ࡛࠶ࡾࠊᅗ2ࡔࡅ࡛ࡼ࠸ࠋ

ᅗ10࡜ᅗ12࡟࠾࠸࡚ࠊỈᖹ㍈ࢆ ݏ_ଵ ࠿ࡽɉ_୷୫ ࡟ኚ᥮ࡋࠊ୧᪉ࡢᅗࢆࡲ࡜ࡵ࡚ࠊᅗ14࡟♧ࡍࠋ

ᅗ14㸬࢙૚ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૛ࠊỈᖹ㍈࢙૚ࢆ ࣅ࢟࢓࡟ኚ᥮

OQVHB\POQVHBP\OQVHBVDVDIXQF RIVZWKVUHSODFHGE\ λ

\P

FDVHLLL

OQ\P OQP\ OQV PLQFDVHLL PLQFDVHL

(13)

ᅗ11࡜ᅗ13࡟࠾࠸࡚ࠊỈᖹ㍈ࢆݏଶ ࠿ࡽɉ୷୫ ࡟ኚ᥮ࡋ࡚ࠊ୧᪉ࡢᅗࢆࡲ࡜ࡵࡓࡶࡢࢆࠊḟࡢᅗ 15࡟⾲♧ࡍࡿࠋ

ᅗ15㸬࢙૛ࡢ㛵ᩘ࡜ࡋ࡚ࡢ ࢙ࢋ_࢟࢓,࢙ࢋ_࢓࢟,࢙ࢋ_࢙૚ࠊỈᖹ㍈࢙૛ࢆ ࣅ࢟࢓࡟ኚ᥮

㸳㸬ࢩ࣑࣮ࣗࣞࢩࣙࣥ

ᘧ(7)࡜ᘧ(9)ࢆࠊㄗᕪ㡯࡟╔┠ࡋࠊࡉࡽ࡟const.+trend 㡯ࢆ௜ࡅ࡚᭩ࡁ┤ࡍࠋ

ܣ଴ܺ௧=ܿ଴+ܿଵכ ݐݎ݁݊݀+σ ߙ௝ܺ௧ି௝+൬ݏଵ 0 0 ݏଶ൰ ൬߳_௧^ఎ

߳௧௠൰

௣

௝ୀଵ (14)

ܺ௧=ܿഥ଴+ܿഥ כ ݐݎ݁݊݀ଵ +σ ߙഥ ܺఫ ௧ି௝+ܣ_଴^ିଵ൬ݏଵ 0 0 ݏଶ൰ ൬߳_௧^ఎ

߳௧௠൰

௣

௝ୀଵ (15)

ᘧ(14)ࠊ(15)ࡢ୧㎶࡟ᮇᚅ್ࢆ᥃ࡅࠊඖࡢᘧ࠿ࡽᮇᚅ್ࡢᘧࢆᘬࡁ⟬ࡍࡿࠋܺ෪௧=ܺ௧െ ܧ{ܺ௧} ࡜ᐃ⩏ࡍ

ࡿ࡜ࠊܺ෪௧ ࡣᘧ(14)ࠊ(15)࡟࠾࠸࡚ࠊconst.+trend 㡯ࡢࡳࢆᾘཤࡋࠊࡑࢀ௨እࡢಀᩘࡢ್ࢆࡑࡢࡲࡲ⥔

ᣢࡋࡓᘧ࡟ኚ᭦ࡉࢀࡿࠋࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ௨ୗࡢᡭ㡰࡛ᐇ⾜ࡍࡿࠋ z ᮍ▱ࣃ࣓࣮ࣛࢱࡢ┿್ࢆ௨ୗࡢࡼ࠺࡟௬ᐃࡍࡿࠋ

൫ɉ_୷୫,ɉ_୫୷, s_ଵ, s_ଶ൯= (1.4,െ0.3, 3.5, 1.5)

z ᐇࢹ࣮ࢱ࠿ࡽࠊᘧ(15)ࡢㄏᑟᆺVARࣔࢹࣝࢆࠊܿഥ଴+ܿഥ כ ݐݎ݁݊݀ ଵ ࡢ㡯ࢆྵࡵ࡚ィ⟬ࡋࠊಀᩘߙഥఫ ࢆ ධᡭࡍࡿࠋ

z N(0,1) ࡜࡞ࡿ஫࠸࡟⊂❧࡞ṇつ஘ᩘิ߳_௧^K,߳_௧^௠^{ࢆⓎ⏕ࡉࡏࡿࠋ}

z ௬ᐃࡉࢀࡓࣃ࣓࣮ࣛࢱࡢ┿್ࢆ⏝࠸࡚ࠊᘧ(15)ࡢྑ㎶᭱⤊㡯ࡢࣀ࢖ࢬᡂศࢆィ⟬ࡍࡿࠋ

OQVHB\POQVHBP\OQVHBVDVDIXQF RIVZLWKVUHSODFHGE\ λ

\P

FDVHLLLLY

OQVHB\P OQVHBP\ OQVHBV PLQFDVHLY PLQFDVHLLL

(14)

z ᐇࢹ࣮ࢱ࠿ࡽᚓࡽࢀࡓಀᩘࡢ᥎ᐃ್ߙഥఫ ࢆ⏝࠸࡚ࠊୖࡢᡭ㡰࡛Ⓨ⏕ࡋࡓࣀ࢖ࢬ㡯࡛㥑ືࡉࢀࡿࢩ ࢫࢸ࣒㸦ᘧ(15)㸧ࡢࢹ࣮ࢱ ܺ_௧ ࢆⓎ⏕ࡉࡏࡿࠋࢧࣥࣉࣝࢧ࢖ࢬࢆ500࡜ࡍࡿࠋࡓࡔࡋࠊܿഥ_଴+ܿഥ כ_ଵ ݐݎ݁݊݀ ࡢ㡯ࡣຍ࠼࡞࠸ࠋܺ_௧ ࢆᖹᆒ್࠿ࡽࡢ೫ᕪ࡜ࡳ࡞ࡋ࡚࠸ࡿࠋ

z ᚓࡽࢀࡓࢹ࣮ࢱࢆࡶ࡜࡟ ݏ݁_݉ݕ ࢆ ݏଵ ࡟㛵ࡋ࡚᭱ᑠ໬ࡋ࡚ࠊ᥎ᐃ್ࢆồࡵࡿࠋྠᵝ࡟ࠊݏ݁_ݕ݉

ࢆ ݏ_ଶ ࡟㛵ࡋ࡚᭱ᑠ໬ࡋ࡚ࠊ᥎ᐃ್ࢆồࡵࡿࠋ

߳_௧^ఎ ࡜ ߳௧௠ ࡢඹศᩓ⾜ิࡀ௨ୗࡢࡼ࠺࡟࡞ࡗࡓ஘ᩘࢆ౑⏝ࡋࡓࠋ cov.( ߳_௧^ఎ, ߳௧௠)=ቀ1.00000045 0.0000365

0.0000365 1.00000045ቁ

㸳㸫㸯㸬☜ᐃⓗ࡟ ࣅ࢟࢓ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܕܡ,ܛ૚,ܛ૛൯ ࡢ᥎ᐃ

☜ᐃⓗ࡟ ߣ௬௠ ࢆ୚࠼ࡓ᫬ࡢ ൫ɉ୫୷, sଵ, sଶ൯ ࡢ᥎ᐃ್ࢆߣ௬௠ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᅗ16࡟♧ࡍࠋ

ᅗ16㸬☜ᐃⓗ࡟ ࣅ࢟࢓ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܕܡ,ܛ૚,ܛ૛൯ ࡢ᥎ᐃ್

ߣ௬௠=െ0.15169 (ɉ୫୷= 0) ࡢ᫬࡟ sଵ ࡀ᭱ᑠ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋࡲࡓࠊsଶ ࡢ᭱ᑠ್ࡣ ߣ௬௠= 0 ࡢ᫬࡟ᐇ⌧ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ

൫ɉ୫୷, s_ଵ, s_ଶ൯ ࡢᶆ‽ㄗᕪࢆ ߣ_௬௠ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᅗ17࡟♧ࡍࠋݏ݁_ݏ1 ࡢ᭱ᑠ್ࡣࠊߣ_௬௠=

െ0.15169 (ɉ୫୷= 0) ࡢ᫬࡟ᐇ⌧ࡋ࡚࠾ࡾࠊݏ݁_ݏ2 ࡜ݏ݁_݉ݕ ࡣࠊ࡝ࡕࡽࡶߣ௬௠= 0 ࡢ᫬࡟᭱ᑠ࡜

࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋࡋࡓࡀࡗ࡚ࠊߣ௬௠ ࢆ☜ᐃⓗ࡟୚࠼ࡓ᫬ࠊṧࡾ3ኚᩘࡢᶆ‽ㄗᕪࡣࠊᮍ▱ࣃ

࣓࣮ࣛࢱࡢ┿್࡟ࡣ㛵୚ࡋ࡚࠸࡞࠸ࠋ

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(15)

ᅗ17㸬☜ᐃⓗ࡟ ࣅ࢟࢓ ࢆ୚࠼ࡓ᫬ࡢ(ܛ܍_ܕܡ, ܛ܍_ܛ૚,ܛ܍_ܛ૛)

㸳㸫㸰㸬☜ᐃⓗ࡟ ࣅ࢓࢟ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܡܕ,ܛ૚,ܛ૛൯ ࡢ᥎ᐃ

☜ᐃⓗ࡟ ߣ௠௬ ࢆ୚࠼ࡓ᫬ࡢ ൫ɉ୷୫, sଵ, sଶ൯ ࡢ᥎ᐃ್ࢆߣ௠௬ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᅗ18࡟♧ࡍࠋɉ୫୷= 0 (ߣ௬௠=െ0.15169) ࡢ᫬࡟sଵ ࡀ᭱ᑠ࡟࡞ࡗ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋࡲࡓࠊsଶ ࡢ᭱ᑠ್ࡣߣ௠௬=

െ0.03027 (ߣ௬௠= 0)ࡢ᫬࡟ᐇ⌧ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ

ᅗ18㸬☜ᐃⓗ࡟ࣅ࢓࢟ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܡܕ,ܛ૚,ܛ૛൯ ࡢ᥎ᐃ್

൫ɉ୷୫, sଵ, sଶ൯ ࡢᶆ‽ㄗᕪࢆ ߣ௠௬ ࡢ㛵ᩘ࡜ࡋ࡚ࠊᅗ19࡟♧ࡍࠋݏ݁_ݏ2 ࡢ᭱ᑠ್ࡣࠊߣ௠௬=

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(16)

െ0.03207 (ɉ୷୫= 0) ࡢ᫬࡟ᐇ⌧ࡋ࡚࠾ࡾࠊݏ݁_ݏ1 ࡜ݏ݁_ݕ݉ ࡣࠊ࡝ࡕࡽࡶߣ௬௠=െ0.15169 ࡢ᫬

࡟᭱ᑠ࡜࡞ࡗ࡚࠸ࡿࠋߣ௠௬ ࢆ☜ᐃⓗ࡟୚࠼ࡓ᫬ࠊṧࡾ3ኚᩘࡢᶆ‽ㄗᕪࡣࠊ┿್࡟ࡣ㛵୚ࡋ࡞࠸ࠋ

ᅗ19㸬λ^myࢆ୚࠼ࡓ᫬ࡢࠊse_ym, se_s1, se_s2ࡢ್

㸳㸫㸱㸬☜ᐃⓗ࡟ ࢙૚ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܡܕ,ࣅ࢓࢟, ܛ૛൯ ࡢ᥎ᐃ

ݏଵ ࡣ2౯㛵ᩘ࡛࠶ࡿࡀࠊᡃࠎࡢ㛵ᚰࡢ࠶ࡿࡢࡣ (case-i) (λ^ym >-0.15169, λ^my<0) ࡛࠶ࡿࠋ(case-ii)ࡢ ᥎ᐃࡣ┬␎ࡍࡿࠋ☜ᐃⓗ࡟ ݏଵ ࢆ୚࠼ࡓ᫬ࡢᶆ‽ㄗᕪ (se_ym, se_my, se_s2) ࢆᅗ20࡟♧ࡍࠋ

ᅗ20㸬࢙૚ࢆ୚࠼ࡓ᫬ࡢࠊVHB\PVHBP\VHBV ࡢ್

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(17)

ᅗ20ࡣ3ࡘࡢ᭱ᑠ್ࢆ᭷ࡋ࡚࠸ࡿࠋ

z se_s2 ^ࡣࠊݏଵ= 2.897 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯=

(0,െ0.0303, 2.897, 1.291) ࡛࠶ࡿࠋ୍᪉ࠊᅗ17ࡼࡾࠊɉ୷୫= 0 ࡜୚࠼ࡓ᫬࡟ࠊse_s2 ^ࡣ᭱

ᑠ್ࢆ᭷ࡋ࡚࠸ࡓࡢ࡛ࠊᅗ21࡟࠾ࡅࡿse_s2ࡢ᭱ᑠ್ࢆㄝ᫂ࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋࡲࡓࠊse_s2 ࡢ᭱ᑠ್ࡣࠊࣃ࣓࣮ࣛࢱࡢ┿್࡟㛵ࡍࡿ᝟ሗࢆ୚࠼࡞࠸ࡇ࡜ࡀศ࠿ࡿࠋ

z se_my ^ࡣࠊݏଵ= 3.474 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ᥎ᐃ್ࡣࠊ൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (1.336,െ0.285, 3.474, 1.5) ࡛࠶ࡿࠋ┿್(1.4,െ0.3, 3.5, 1.5) ࡣࠊݏଵ ࡟ࡼࡿse_my ࡢ᭱ᑠ

໬࡟ࡼࡗ࡚᥎ᐃࡉࢀ࡚࠸ࡿ࡜⤖ㄽ௜ࡅࡿࠋ

z se_ym ^ࡣࠊݏଵ= 4.06 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ᥎ᐃ್ࡣࠊ൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (2.066,െ0.4229, 4.06, 1.7199) ࡛࠶ࡿࠋݏଵ ࡟ࡼࡿse_ym ࡢ᭱ᑠ໬ࡣࠊ┿್࡟㛵ࡍࡿ᝟ሗࢆ

ྵࡲ࡞࠸ࠋ

㸳㸫㸲㸬☜ᐃⓗ࡟ ࢙૛ ࢆ୚࠼ࡓ᫬ࡢ൫ૃܡܕ,ࣅ࢓࢟, ܛ૚൯ ࡢ᥎ᐃ

ݏଶ ࡣ2౯㛵ᩘ࡛࠶ࡿࡀࠊᡃࠎࡢ㛵ᚰࡢ࠶ࡿࡢࡣ (case-iii) (λ^ym >-0.15169, λ^my^<0)^࡛࠶ࡿࠋ^(case-iv) ࡢ᥎ᐃࡣ┬␎ࡍࡿࠋ☜ᐃⓗ࡟ݏଶ ࢆ୚࠼ࡓ᫬ࡢᶆ‽ㄗᕪ (se_ym, se_my, se_s1) ࢆᅗ21࡟♧ࡍࠋ

ᅗ21㸬࢙૛ࢆ୚࠼ࡓ᫬ࡢࠊVHB\PVHBP\VHBV ࡢ್

ᅗ21࡛ࡣࠊ3ࡘࡢ᭱ᑠ್ࡀᏑᅾࡍࡿࠋ

z se_s1 ࡣࠊݏ_ଶ= 1.3281 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ൫ɉ_୷୫,ɉ_୫୷, s_ଵ, s_ଶ൯= (0.5194,

െ0.1330, 3.0, 1.3281) ࡛࠶ࡿࠋ୍᪉࡛ࠊᅗ17ࡼࡾࠊɉ୷୫=െ0.15169 (ɉ୫୷=0) ࡜୚࠼ࡓ᫬

࡟ࠊse_s1 ࡣ᭱ᑠ್ࢆ᭷ࡋ࡚࠸ࡓࡇ࡜ࢆ⪃࠼ࡿ࡜ࠊᩚྜⓗ࡛࡞࠸ࠋࡇࡢ⌮⏤࡜ࡋ࡚ࠊᅗ17࡛

ࡣࠊɉ୷୫ ࢆ☜ᐃⓗ࡟୚࠼ࡿࡢ࡟ᑐࡋࠊᅗ21࡛ ɉ୷୫=െ0.15169 ࢆ୚࠼ࡿݏଶ ࡟࠾࠸࡚ࠊᑐᛂ

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(18)

ࡍࡿse_ym ࡢ್ࡣ1000ࢆ㉺࠼࡚࠸ࡿࠋࡇࡢࡼ࠺࡞se_ym ࡢ኱ࡁ࡞್࡟ᘬࡁࡎࡽࢀ࡚ࠊse_s1 ࡢ᭱ᑠ್ࡀࣂ࢖࢔ࢫࢆཷࡅࡓࡶࡢ࡜⪃࠼ࡿࠋ

z se_ym ^ࡣࠊݏଶ= 1.496 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ᥎ᐃ್ࡣࠊ൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (1.363,െ0.290, 3.492, 1.496) ࡛࠶ࡿࠋ┿್(1.4,െ0.3, 3.5, 1.5) ࡣࠊݏଶ ࡟ࡼࡿse_ym ࡢ᭱ᑠ

໬࡟ࡼࡗ࡚᥎ᐃࡉࢀ࡚࠸ࡿ࡜⤖ㄽ௜ࡅࡿࠋ

z se_my ^ࡣࠊݏଶ= 1.846 ࡟࠾࠸࡚᭱ᑠ್ࢆᣢࡘࠋࡇࡢ࡜ࡁࠊ᥎ᐃ್ࡣࠊ൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (2.423,െ0.4865, 4.4, 1.846) ࡛࠶ࡿࠋݏଶ ࡟ࡼࡿse_my ࡢ᭱ᑠ໬ࡣࠊ┿್࡟㛵ࡍࡿ᝟ሗࢆྵࡲ

࡞࠸ࠋ

ࢩ࣑࣮ࣗࣞࢩࣙࣥࡢ⤖ᯝࢆࡲ࡜ࡵࡿ࡜ࠊ ݏଵ ࡟㛵ࡍࡿse_my^{ࡢ᭱ᑠ໬࡜ࡋ࡚ࠊ}

൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (1.336,െ0.285, 3.474, 1.5) (16) ݏଶ ࡟㛵ࡍࡿse_ym ^{ࡢ᭱ᑠ໬࡜ࡋ࡚ࠊ}

൫ɉ୷୫,ɉ୫୷, sଵ, sଶ൯= (1.363,െ0.290,3.492,1.496) (17)

ࢆᚓࡿࠋ࡝ࡕࡽࡢ᥎ᐃࡶࠊ┿್(1.4,െ0.3,3.5,1.5) ࢆࡼࡃ᥎ᐃࡋ࡚࠸ࡿ࡜ゝ࠼ࡿࠋ4❶ࡢ᥎ᐃᡭἲࡢ

᭷ຠᛶࡀ♧ࡉࢀࡓࠋ

㸴㸬⤖ ㄽ

᪥ᮏ࡟࠾ࡅࡿ࣐ࢿ࣮ࡢ㛗ᮇ୰❧ᛶࢆ⪃ᐹࡋࡓࠋKing & Watsonࡢ᪉ἲࢆᣑᙇࡋ࡚ࠊ2ኚᩘ

ࡢSVARࢩࢫࢸ࣒࡟࠾࠸࡚ࠊᮍ▱ᩘ4ࡘࠊㄗᕪඹศᩓࡢ㛵ಀᘧ3ࡘࡢၥ㢟ࢆゎࡃࡇ࡜࡟ᡂຌ

ࡋࡓࠋࡇࢀ࡟ࡼࡗ࡚ࠊKing & Watsonࡢᡭἲ࡛ࡣࠊ୰❧ᛶࡀᡂࡾ❧ࡘࡓࡵࡢࣃ࣓࣮ࣛࢱࡢ⠊

ᅖࢆ♧ࡍ࡟࡜࡝ࡲࡗ࡚࠸ࡓࡶࡢࡀࠊᐇ㝿࡟୚࠼ࡽࢀࡓ࣐ࢿ࣮ࢩࢫࢸ࣒࡟࠾࠸࡚ࠊලయⓗ࡞ࢩ ࢫࢸ࣒ࣃ࣓࣮ࣛࢱࡢ್ࢆ᥎ᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡓࡢ࡛ࠊ㛗ᮇ୰❧ᛶࢆᲠ༷࡛ࡁࡿ࠿࡛ࡁ࡞࠸࠿

ࡢุᐃࢆୗࡍࡇ࡜ࢆྍ⬟࡟ࡋࡓࠋ(1980q1,2007q4)࡟࠾࠸࡚ࠊ᪥ᮏࡢ࣐ࢿ࣮ࢩࢫࢸ࣒ࢆࠊ(real GDP, M3)࡟ࡼࡗ࡚⪃ᐹࡋࠊ࣐ࢿ࣮ࡢ㛗ᮇ୰❧ᛶࡀᲠ༷ࡉࢀࡿࡇ࡜ࢆ♧ࡋࡓࠋ

ᡃࠎࡢᡭἲࢆUSAࡢࢹ࣮ࢱ࡟㐺⏝ࡋࠊ(1960q1,2019q1)࡟࠾ࡅࡿUSAࡢ࣐ࢿ࣮ࢩࢫࢸ࣒

(real GDP, M3)࡛ࡶࠊ࣐ࢿ࣮ࡢ㛗ᮇ୰❧ᛶࡀᲠ༷ࡉࢀࡿࡇ࡜ࢆ☜ㄆࡋ࡚࠸ࡿ㸦Ⓨ⾲‽ഛ୰㸧ࠋ

୰❧ᛶ࡟㛵ࡍࡿ㛵㐃ࡋࡓヰ㢟㸦Fisher ຠᯝࠊPhillips ᭤⥺㸧࡟㛵ࡍࡿศᯒ⤖ᯝࡶᚓ࡚࠾ࡾࠊ

Ⓨ⾲ࡢணᐃ࡛࠶ࡿࠋ

௜ 㘓

༢఩᰿ࢸࢫࢺ㸦⾲1㸧࡛ࡣࠊ2✀㢮ࡢࢸࢫࢺࢆ⾜࠺ࠋERSࢸࢫࢺࡣࠕ༢఩᰿࠶ࡾࠖࡢᖐ↓௬ㄝࢆタ ᐃࡋࠊKPSSࢸࢫࢺࡣᐃᖖᛶࡢᖐ↓௬ㄝࢆ⨨ࡃࡶࡢ࡛࠶ࡿࠋ

ඹ࿴ศࢸࢫࢺ㸦⾲2㸧࡛ࡣࠊ2ḟࡢ☜ᐃࢺࣞࣥࢻࢆࣞ࣋ࣝኚᩘࡀ᭷ࡋ࡚࠸ࡿ࡜௬ᐃࡋࡓࠋᶭy࡜ᶭm ࡢunit root test࡟࠾࠸࡚ࠊ୧⪅࡜ࡶ࡟c+trend ࡢ㡯ࡀ᳨ฟࡉࢀࡓ࠿ࡽ࡛࠶ࡿࠋ

(19)

⾲1㸬༢఩᰿ࢸࢫࢺ

vrbls ERS(t-stat.) KPSS(LM-stat.) c, trend

y 0.775851 1.123203*** c

ᶭy -2.947952* 0.111096 c+trend

m -0.037738 1.121261*** c

ᶭm -2.9497* 0.074206 c+trend

*, **, *** means “rejection of null hypothesis” with 10%, 5%, 1% significance level respectively.

⾲2㸬Cointegration test (Johansen) Trace test

Hypo. No. of CEs Eigenvalue Trace stat. 0.05 crit. value Prob.*

None 0.0515 8.6177 18.3977 0.619

At most 1 0.0265 2.9058 3.8415 0.088

Maximum Eigenvalue test

Hypo. No. of CEs Eigenvalue Max-Eigen stat. 0.05 crit. value Prob.*

None 0.0515 5.7112 17.1477 0.8436

At most 1 0.0265 2.9058 3.8415 0.088

*MacKinnon-Hayg-Michelis [5] p-value

ཧ⪃ᩥ⊩

[1] King, Robert G., and Mark W. Watson (1997), ‘’Testing Long Run Neutrality,”

Economic Quarterly, 83 (2), Federal Reserve Bank of Richmond, pp. 69-101.

[2] Serletis, Apostolos, and Zisimos Koustas (1998), ‘’International Evidence on the Neutrality of Money,” Journal of Money, Credit, and Banking, 30 (1), pp. 1-25.

[3] ኱஭༤அࠊⓑሯ㔜඾ࠊ௦⏣㇏୍㑻 (2004) ࠕᡃࡀᅜ࡟࠾ࡅࡿ㈌ᖯࡢ㛗ᮇ୰❧ᛶ࡟ࡘ࠸࡚ࠖ

ࠗ㔠⼥◊✲࠘᪥ᮏ㖟⾜㔠⼥◊✲ᡤ, pp.121-160.

[4] Johansen, Søren (1991), ‘’Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models,” Econometrica, 59, pp. 1551-1580.

[5] MacKinnon, James G., Alfred A. Haug, and Leo Michelis (1999), ‘’Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration,” Journal of Applied Econometrics, 14, pp. 563-577.

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