㸫㸫
බമⓎ⾜ୗࡢ㈈ᨻ➇த
㸫㈨ᮏ⛣ືࡀ㈈ᨻ࠼ࡿᙳ㡪㛵ࡍࡿᐇドศᯒ㸫
⏣ ୰ ᏹ ᶞ
∗㸦ྠᚿ♫Ꮫᨻ⟇Ꮫ㒊ᩍᤵ㸧
1㸬ࡣࡌࡵ
㈨ᮏ⛣ືୗ࠾ࡅࡿᆅ᪉ᨻᗓ㛫ࡢ➇தⓗࡘ㠀༠ຊⓗ࡞ᨻ⟇Ỵᐃࡀ㸪㐣ᑠㄢ⛯බඹ㈈ࡢ㐣ᑠ౪⤥ࢆᘬ ࡁ㉳ࡇࡍࡇࢆ♧ࡋࡓ Zodrow and Mieszkowski㸦1986㸧㸪Wilson㸦1986㸧ࡽࡢ㈨ᮏ⛯➇தࣔࢹࣝࡣ㸪⌮ㄽ࣭ ᐇド୧㠃ࡽᵝࠎ࡞᪉ྥᣑᙇࡉࢀ࡚ࡁࡓࠋᑡᩘὴ࡞ࡀࡽ㸪ᨻᗓࡀ᧯సྍ⬟࡞ᨻ⟇ኚᩘࡋ࡚㸪⛒⛯ࡢࡳ ࡞ࡽࡎ㸪බമⓎ⾜ࡶྵࡵࡓሙྜࡢ⛒⛯➇தࢆ⌮ㄽศᯒࡋࡓࡶࡢ㸪Jensen and Toma㸦1991㸧㸪Matsumoto㸦2011㸧 ࡽࡀ㸪ᐇドศᯒࢆヨࡳࡓࡶࡢ㸪Krogstrup㸦2002㸧ࡀ࠶ࡿࠋJensen and Toma㸦1991㸧ࡣ㸪Zodrow and Mieszkowski㸦1986㸧ࡢྠ㉁ᑠᆅᇦࡽ࡞ࡿᆅ᪉ᨻᗓ㛫ࡢỈᖹⓗ ㈨ᮏ⛯➇தࣔࢹࣝࢆ㸪බമⓎ⾜ࢆ⤌ࡳධࢀࡓ 2 ᮇ㛫ࣔࢹࣝᣑᙇࡋ㸪බമⓎ⾜ୗ࡛ࡢ㈨ᮏ⛯➇தࡢ⌮ㄽⓗ ᖐ⤖ࢆゎ᫂ࡋ࡚࠸ࡿࠋࡇࢀࡼࡿ㸪୧ᆅ᪉ᨻᗓࡢᛂ㛵ᩘࡢഴࡁࡀṇ࡛࠶ࢀࡤ㸪ᆅ᪉ᨻᗓࡣ㸦2 ᮇ┠ࡢ ┦ᡭࡢ㈨ᮏ⛯⋡ࢆᘬࡁୖࡆࡿࡓࡵ㸧㸪㈈ᨻ㉥Ꮠࡢᣑࢆᚿྥࡍࡿࡇࡀ♧ࡉࢀ࡚࠸ࡿࠋ
Matsumoto㸦2011㸧࡛ࡣ㸪Jensen and Toma㸦1991㸧ྠࡌࡃබമⓎ⾜ࢆ⤌ࡳධࢀࡓ 2 ᮇ㛫ࣔࢹࣝࢆ᥇⏝ࡋ ࡘࡘࡶ㸪ᆅ᪉ᨻᗓྠኈ࡛ࡣ࡞ࡃ㸪୰ኸᨻᗓᆅ᪉ᨻᗓ㛫ࡢᆶ┤ⓗ㈨ᮏ⛯➇தࣔࢹࣝࢆ⏝࠸࡚㸪බമⓎ⾜ୗ ࡛ࡢ㈨ᮏ⛯➇தࡘ࠸࡚⌮ㄽศᯒࡋ࡚࠸ࡿࠋㄢ⛯࣮࣋ࢫࡀ㔜」ࡍࡿᆶ┤ⓗ㈨ᮏ⛯➇தࣔࢹ࡛ࣝࡣ㸪࠸ ┦ᡭࡢ㈨ᮏ⛯⋡ᘬࡁୗࡆࢆ⏬⟇ࡍࡿ⤖ᯝ㸪୧ᆅ᪉ᨻᗓࡢᛂ㛵ᩘࡢഴࡁࡀṇ࡛࠶ࢀࡤ㸪୰ኸᨻᗓ࠾ࡼࡧᆅ ᪉ᨻᗓࡣ㸪㈈ᨻవࡢᣑࢆᚿྥࡍࡿࡋ㸪Jensen and Toma㸦1991㸧␗࡞ࡿ⌮ㄽⓗᖐ⤖ࢆᑟࡁฟࡋ࡚࠸ ࡿࠋ ㈈ᨻ➇தࣔࢹࣝࡢ⌧ᐇ㐺⏝ᛶࢆ㧗ࡵࡿୖ࡛㸪ྠ㉁ᆅᇦࡢᐃࡸ㈨ᮏ౪⤥୍ᐃࡢ௬ᐃࢆ⦆ࡵࡿࡇຍ࠼ 1㸧㸪බമⓎ⾜ࡢྍ⬟ᛶࢆ⪃៖ࡍࡿࡇࡣ㸪㔜せ࡞どⅬ࡛࠶ࡿࠋࡋࡋ࡞ࡀࡽ㸪ᆅᇦ㛫ࡢ㠀ᑐ⛠ᛶࡸ㈨ᮏ ∗ 1967 ᖺ⏕ࡲࢀࠋ1998 ᖺ㜰ᏛᏛ㝔ᅜ㝿බඹᨻ⟇◊✲⛉༤ኈ๓ᮇㄢ⛬ಟࠋ2000 ᖺྠ◊✲⛉༤ኈᚋᮇㄢ⛬ಟࠋ༤ኈ㸦ᅜ㝿බඹᨻ⟇㸧ࠋ ओPHP ⥲ྜ◊✲ᡤ௵◊✲ဨ㸪ෆ㛶ᗓ⤒῭♫⥲ྜ◊✲ᡤᐈဨ◊✲ဨ➼ࢆ⤒࡚㸪2004 ᖺࡼࡾ⌧⫋ࠋᑓ㛛ࡣ㈈ᨻᏛ㸪බඹ⤒῭Ꮫࠋ࡞⦅ⴭ ᭩㸪ࠗබⓗ㈨ᮏᙧᡂࡢᨻ⟇ホ౯࠘㸦PHP ◊✲ᡤ㸪2001 ᖺ㸧㸪᳨ࠗド ᱁ᕪᣑ♫࠘㸦᪥ᮏ⤒῭᪂⪺ฟ∧♫㸪2008 ᖺ㸧࡞ࠋ᪥ᮏ⤒῭ Ꮫ㸪᪥ᮏ㈈ᨻᏛ㸪බඹ㑅ᢥᏛᡤᒓࠋE-Mail: [email protected] URL: http://www.cam.hi-ho.ne.jp/thiroki/
1㸧 ࠼ࡤ㸪๓⪅ࢆᑐ㇟ࡍࡿ௦⾲ⓗ࡞⌮ㄽศᯒࡋ࡚㸪Bucovetsky㸦1991㸧ࡀ㸪ᚋ⪅ࢆᑐ㇟ࡍࡿ௦⾲ⓗ࡞⌮ㄽศᯒࡋ࡚㸪Batina㸦2009㸧
㸫㸫 ✚ࢆ⪃៖ࡋࡓ㈨ᮏ⛯➇தࡢ◊✲ẚࡿ㸪බമⓎ⾜ࢆ⤌ࡳධࢀࡓ◊✲ࡢ✚ࡣஈࡋ࠸ࠋ㸪ᛂ㛵ᩘ ࢆ᥎ᐃࡍࡿࡇ࡛㸪㈨ᮏ⛯➇தࡢ᭷↓ࢆ᳨ドࡋࡓᐇドศᯒ࠾࠸࡚ࡣ㸪බമⓎ⾜ࢆ๓ᥦࡋ࡞࠸Zodrow and Mieszkowski㸦1986㸧㸪Wilson㸦1986㸧ࡽࡢ⌮ㄽࣔࢹࣝࡀᐃࡉࢀ࡚࠸ࡿࠋ Krogstrup㸦2002㸧ࡣ㸪බമⓎ⾜ࢆ᫂♧ⓗᢅࡗࡓ⌮ㄽࣔࢹࣝࢆ࣮࣋ࢫ㸪㈨ᮏ⛣ືୗ࡛ࡢ㈈ᨻ➇தࡀ㸪 බⓗമົẚ⋡ࡢ㧗࠸ᅜ࠾࠸࡚㸪മົẚ⋡ࡢప࠸ᅜࡼࡾࡶ㸪㧗࠸ἲே⛯⋡ప࠸㈈ᨻᨭฟẚ⋡ࢆᘬࡁ㉳ࡇ ࡍࡇࢆ㸪EU ㅖᅜࡢࣃࢿࣝࢹ࣮ࢱ⏝࠸࡚㸪ᐇドⓗ♧ࡋ࡚࠸ࡿࠋ᪥ᮏ࠾࠸࡚㸪Ỉᖹⓗ⛒⛯➇தࢆᢅࡗ ࡓᐇド◊✲ࡣ㸪ᓥ࣭ᅧᓮ࣭Ⳣཎ㸦2008㸧㸪῝⃝㸦2009㸧➼ࡀ࠶ࡿࡀ㸪බമⓎ⾜ࢆ๓ᥦࡋࡓࣔࢹ࡛ࣝࡢ ⛒⛯➇தࡢ᳨ドࡲ࡛ࡣ⮳ࡗ࡚࠸࡞࠸ࠋ ᮏ✏࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢỈᖹⓗ㈈ᨻ➇த╔┠ࡋ㸪බമᡶ࠸ࡢቑຍࡶຍ㏿ࡀணࡉࢀࡿᆅ ᪉ᨻᗓࡢ㈈ᨻᘓ㸦ṓධቑ࣭ṓฟῶ㸧ࡢྲྀࡾ⤌ࡳࡀ㸪⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑࡼࡗ࡚ᙳ㡪ࢆཷࡅ ࡓྰࢆ㸪᪥ᮏࡢ⮬యࡢࢹ࣮ࢱࢆࡶᐇドⓗᡭἲࢆ⏝࠸᳨࡚ドࡍࡿࠋලయⓗࡣ㸪1975㹼2009 ᖺᗘ ࠾ࡅࡿ 47 㒔㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമᡶ࠸㈝ἲேᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧබമᡶ࠸㈝ ᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧ࡢ㛵ಀࡀ㸪Ẹ㛫㈨ᮏ⛣ືᣑࡢᙳ㡪ࢆཷࡅ࡚ኚࡍࡿྰࢆᐇドศᯒࡍࡿࠋ ᮏ✏ࡢᵓᡂࡣ㸪௨ୗࡢ࠾ࡾ࡛࠶ࡿࠋ➨ 2 ⠇࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢ㈈ᨻ➇தࣔࢹࣝࢆᵓ⠏ࡋ㸪㸦㈨ᮏ⛣ື ࢆㄏⓎࡍࡿ㸧㈈ᨻ➇தࡢᣑࡼࡗ࡚㸪බമᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯⋡࠾ࡼࡧ㈈ᨻᨭฟ࠼ࡿᙳ㡪㐪࠸ ࡀ⏕ࡌ࠺ࡿࡇࢆ♧ࡍࠋ➨ 3 ⠇࡛ࡣ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝࢆ㋃ࡲ࠼㸪බമ㈝ඖൾ㑏㔠ࢆ㒔㐨ᗓ┴ࡢἲே ᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧ᅇᖐࡉࡏࡿࡇ࡛㸪㒔㐨ᗓ┴ࡢ㈈ᨻᘓࡢྲྀࡾ⤌ࡳᑐ ࡍࡿ㈈ᨻ➇தࡢᙳ㡪ࢆᐇドศᯒࡍࡿࠋ➨ 4 ⠇࡛ࡣ㸪ᮏ✏ࡢ⤖ㄽࢆせ⣙ࡋ㸪ṧࡉࢀࡓㄢ㢟ࢆᣦࡍࡿࠋ
2㸬⌮ㄽࣔࢹࣝ
ࡇࡇ࡛ࡣ㸪Zodrow and Mieszkowski㸦1986㸧࠾ࡼࡧ Krogstrup㸦2002㸧ࢆ࣮࣋ࢫ㸪බമⓎ⾜ୗ࡛ࡢ⛒⛯ ➇தࣔࢹࣝࢆᵓ⠏ࡋ㸪㸦㈨ᮏ⛣ືࢆㄏⓎࡍࡿ㸧⛒⛯➇தࡢᣑࡼࡗ࡚㸪බമᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯⋡࠾ࡼ ࡧ㈈ᨻᨭฟ࠼ࡿᙳ㡪㐪࠸ࡀ⏕ࡌ࠺ࡿࡇࢆ♧ࡍࠋ ྠ㉁ N ᆅᇦࡽᵓᡂࡉࢀࡿ⤒῭ࢆᐃࡍࡿࠋྛᆅᇦࡢ௦⾲ⓗᴗࡣ㸪ᆅᇦ㛫࡛⛣ືྍ⬟ࡘ㠀ᙎຊⓗ ౪⤥ࡉࢀࡿປാ L ࠾ࡼࡧᆅᇦ㛫࡛⛣ືྍ⬟࡞Ẹ㛫㈨ᮏ K ࢆ⏕⏘せ⣲㸪୍ḟྠḟࡢ⏕⏘㛵ᩘ y=f(k) 㸦k=K⁄L㸧ࡢࡶ࡛㸪⚾ⓗ㈈ x ࢆ⏕⏘ࡍࡿࠋࡓࡔࡋ㸪 f(k) ࡣ㸪fk>0㸪fkk<0㸪fkkk=0 ࢆ‶ࡓࡍࡶࡢࡍࡿࠋ ྛᆅᇦࡢ௦⾲ⓗᐙィࡣ㸪⛯ᘬࡁᚋࡢ㈨ᮏ┈⋡ ρ ࢆ⪃៖ࡋ㸪⮬ࡽࡢ㈓ k ࢆ㸪⮬ᆅᇦࡢᢞ㈨ k ࠾ࡼࡧ ᆅᇦࡢᢞ㈨ kത㸫k ࡾྥࡅࡿࠋ⛯ᘬࡁᚋࡢ㈨ᮏ┈⋡ ρ ࡣ㸪㈨ᮏᕷሙ࠾ࡅࡿᐃࡢ⤖ᯝ㸪ࡍ࡚ࡢ ᆅᇦ୍࡛⮴ࡋ㸪
τ
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(1) ࢆ‶ࡓࡍỈ‽Ỵࡲࡿࠋࡓࡔࡋ㸪 τ ࡣᆅ᪉ᨻᗓࡀẸ㛫㈨ᮏㄢࡍ㈨ᮏ⛯⋡࡛࠶ࡿࠋ ᐙィࡣ㸪⚾ⓗ㈈ x ࠾ࡼࡧබඹ㈈ g ࡼࡾຠ⏝ࢆᚓࡿ௬ᐃࡍࡿࠋࡇࢀࡼࡾ㸪௦⾲ⓗᐙィࡢຠ⏝㛵ᩘࡣ㸪)
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(2) ࡛♧ࡉࢀࡿࠋࡓࡔࡋ㸪 u ࡣ㸪 ux㸪ug>0㸪uxx㸪ugg<0㸪uxg㸪ugx=0 ࢆ‶ࡓࡍࡶࡢࡍࡿࠋຍ࠼࡚㸪ᐙィࡣ㸪㸫㸫 ⮬ᆅᇦ㸪ᆅᇦࡑࢀࡒࢀࡢᢞ㈨ࡽ┈ࢆᚓࡿࡢ࡛㸪ᐙィࡢண⟬ไ⣙ᘧࡣ㸪
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(3) ࡞ࡿࠋ ྛᆅᇦࡢᆅ᪉ᨻᗓࡣ㸪㈨ᮏ⛯⋡ τ ࡛Ẹ㛫㈨ᮏㄢ⛯ࡋ㸪㐣ཤࡢබമᑐࡍࡿᡶ࠸ ρd බඹ㈈ g ࡢᨭฟ ࡾྥࡅࡿࠋࡇࡢ㸪ᆅ᪉ᨻᗓࡢண⟬ไ⣙ᘧࡣ㸪௨ୗ࡛♧ࡉࢀࡿࠋd
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(4) ᆅ᪉ᨻᗓࡣ㸪(3) ᘧ㸪(4) ᘧࢆไ⣙㸪(2) ᘧࢆ᭱ࡍࡃ㸪㈨ᮏ⛯⋡τ
ࢆỴᐃࡍࡿࠋࡇࡢ᭱ၥ㢟 ࡢ 1 㝵ࡢ᮲௳ࡣ㸪௨ୗ࡛࠼ࡽࢀࡿࠋ1
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(3)’ ࡇࡢ㸪ᆅ᪉ᨻᗓࡣ㸪(3)’ ᘧ㸪(4) ᘧࢆไ⣙㸪(2) ᘧࢆ᭱ࡍࡿࡼ࠺㸪㈨ᮏ⛯⋡ τ ࢆỴᐃࡍࡿࠋࡇࡢ ᭱ၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡣ㸪௨ୗࡢ࠾ࡾ࡞ࡿࠋ1
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x g (6) 1 㝵ࡢ᮲௳ࢆẚ㍑ࡍࡿࡇࡼࡾ㸪㈨ᮏ⛯➇தࡼࡾ㈨ᮏ⛣ືࡀㄏⓎࡉࢀࡿ≧ἣୗ࡛ࡣ㸪㈨ᮏ⛣ືࡀㄏ Ⓨࡉࢀ࡞࠸≧ἣẚ࡚㸪බⓗ㈨㔠ࡢ㝈⏺㈝⏝ࡀ㧗ࡃ࡞ࡿ㸦(5) ࡀ (6) ࢆୖᅇࡿ㸧ࡓࡵ㸪㐣ᑠㄢ⛯බඹ ㈈ࡢ㐣ᑠ౪⤥ࡀⓎ⏕ࡍࡿࡇࡀࢃࡿࠋ බമᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯࠾ࡼࡧ㈈ᨻᨭฟ࠼ࡿᙳ㡪ࡣ㸪(5) ᘧ㸪(6) ᘧࢆࡑࢀࡒࢀᚤศࡍࡿࡇ ࡛ồࡵࡿࡇࡀ࡛ࡁࡿࠋࡍ࡞ࢃࡕ㸪(5) ᘧࢆᚤศࡢୖ㸪ᘧࢆᩚ⌮ࡍࡿ㸪௨ୗࡢ೫ᚤಀᩘࢆᚓࡿ2㸧ࠋ0
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(7) 2㸧 ᑟฟࡣ㸪Appendix A ࢆཧ↷ࠋ㸫㸫
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(8) ࡓࡔࡋ㸪 εxp㸪εgp㸪εmp ࡣ㸪ࡑࢀࡒࢀ௨ୗ࡛♧ࡉࢀࡿࡶ㸪ຠ⏝᭱ࡢ 2 㝵ࡢ᮲௳ࡼࡾ εxp+εgp+εmp>0 ࡛ ࠶ࡿࠋ0
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+
+
−
=
∂
∂
−
=
kk kkk p p k p k p k p k p p p mmcpf
τ
mcpf
τ
ε
ε
ε
ε
k
f
f
ε
(11) ྠᵝ㸪(6) ᘧࢆᚤศࡋ㸪ᘧࢆᩚ⌮ࡍࡿ㸪௨ୗࡢ೫ᚤಀᩘࢆᚓࡿ3㸧ࠋ0
)
(
+
>
=
∂
∂
n g n x n g nk
d
ε
ε
ε
ρ
τ
(12)0
1
)
(
+
−
<
=
∂
∂
n g n x n g nd
g
ε
ε
ε
ρ
(13) ࡓࡔࡋ㸪 εxn㸪εgn ࡣ㸪ࡑࢀࡒࢀ௨ୗ࡛♧ࡉࢀࡿࡶࡢࡍࡿࠋ0
>
−
=
∂
∂
=
n n n x n xx n x n n n x n xτ
u
τ
u
u
u
k
τ
ε
(14)0
>
−
=
∂
∂
−
=
n n n g n gg n g p n n g n gk
u
u
u
u
τ
τ
τ
ε
(15) ࡇࡇ࡛㸪බമᡶ࠸ࡢỈ‽㈨ᮏ⛯⋡ࡢ㛵ಀࡣ㸪(7) ᘧ㸪(12) ᘧࡼࡾṇࡢ㛵ಀࡀ㸪බമᡶ࠸㈈ ᨻᨭฟࡢ㛵ಀࡣ㸪(8) ᘧ㸪(13) ᘧࡼࡾ㈇ࡢ㛵ಀࡀ࠶ࡿࡇࡀࢃࡿࠋࡇࢀࡣ㸪ࡍ࡞ࢃࡕ㸪බമᡶ࠸ ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ᆅ᪉ᨻᗓࡣ㈨ᮏ⛯⋡ࡢୖ᪼ࡸ㈈ᨻᨭฟࡢῶᑡࡼࡾ㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ື ࡍࡿࡇࢆ♧ࡋ࡚࠸ࡿࠋ 3㸧 ᑟฟࡣ㸪Appendix B ࢆཧ↷ࠋ㸫㸫 ࡛ࡣ㸪⛒⛯➇தୗ࡛ࡢබമᡶ࠸Ỉ‽㈨ᮏ⛯⋡㸪࠾ࡼࡧ㈈ᨻᨭฟࡢ㛵ಀࡣ㸪⛒⛯㠀➇தୗ࡛ࡢࡑࢀ ࠸࡞ࡿ㐪࠸ࡀ࠶ࡿࡔࢁ࠺ࠋࡑࢀࡣ㸪(7) ᘧ(12) ᘧࡢᑠ㛵ಀ㸪࠾ࡼࡧ (8) ᘧ(13) ᘧࡢᑠ㛵ಀ ࢆẚ㍑ࡍࡿࡇ࡛⪃ᐹྍ⬟࡛࠶ࡿࠋࡍ࡞ࢃࡕ㸪(7) ᘧ(12) ᘧࡢᑠࢆẚ㍑ࡍࡿ㸪
1
)
(
+
+
>
Φ
+
Φ
=
>
∂
∂
<
∂
∂
n p p g n g n gg p gg n g n x p m p g p x n pu
u
u
u
and
if
d
d
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τ
ε
ε
ε
ε
ε
ρ
τ
ρ
τ
(16) ࡀᡂࡾ❧ࡘ4㸧ࠋࡲࡓ㸪(8) ᘧ(13) ᘧࡢᑠ㛵ಀࢆẚ㍑ࡍࡿ㸪d
g
d
g
p nρ
ρ
∂
∂
<
∂
∂
(17) ࡀᡂࡾ❧ࡘࡇࡀࢃࡿࠋࡇࢀࡼࡾ㸪⛒⛯➇தࡢᣑࡼࡾᆅᇦ㛫ࡢ㈨ᮏ⛣ືࡀάⓎࡍࢀࡤ㸪ᆅ᪉ᨻᗓ ࡣ㈨ᮏ⛯⋡ᘬࡁୖࡆࡼࡿ㈨ᮏ㏨㑊ࢆᅇ㑊ࡋࡼ࠺ࡍࡿࡓࡵ㸪⛒⛯➇தࡀపㄪ࡞ሙྜẚ࡚㸪୍ᐃࡢ᮲ ௳ࡢࡶ࡛ࡣ㸪㈨ᮏ⛯⋡ࡢୖ᪼ᾘᴟⓗ࡞ࡿ୍᪉㸪㈈ᨻᨭฟࡢῶᑡ✚ᴟⓗ࡞ࡿุ᩿ࡉࢀࡿࠋࡍ࡞ ࢃࡕ㸪㈨ᮏ⛣ືୗࡢ⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡣ㸪ᡶ࠸Ỉ‽ࡢቑຍࡀ㈨ᮏ⛯⋡ࡢୖ᪼ࢆࡶࡓࡽࡍຠᯝࢆῶ ࡎࡿ᪉ྥ㸪ᡶ࠸Ỉ‽ࡢቑຍࡀ㈈ᨻᨭฟࡢῶᑡࢆࡶࡓࡽࡍຠᯝࢆቑࡍ᪉ྥ㸪ࡑࢀࡒࢀస⏝ࡍࡿ⪃࠼ ࡽࢀࡿࠋ3㸬ᐇドศᯒ
ࡇࡇ࡛ࡣ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝࢆ㋃ࡲ࠼㸪බമᡶ࠸㈝ἲேㄢ⛯㸪࠾ࡼࡧ㈈ᨻᨭฟࡢ㛵ಀࡀ㸪㈈ᨻ➇ தࡢᙳ㡪ࢆཷࡅࡿࡇ࡛ኚࡍࡿྰࢆᐇドศᯒࡍࡿࠋලయⓗࡣ 1975㹼2009 ᖺᗘ࠾ࡅࡿ 47 㒔㐨ᗓ ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമ㈝ඖൾ㑏㔠ࢆ㒔㐨ᗓ┴ࡢἲேᴗ⛯⋡ᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧 ᅇᖐࡉࡏࡿࡇ࡛㸪ࡑࡢᙳ㡪ࢆ᳨ドࡍࡿࠋ ௨ୗ㸪ࡲࡎ 3-1 ⠇࡛ࡣ㸪ᐇドศᯒ⏝࠸ࡿࣔࢹࣝࢆ≉ᐃࡍࡿࡶ㸪᥎ᐃ᪉ἲࡘ࠸࡚㏙ࡿࠋ3-2 ⠇࡛ࡣ㸪᥎ᐃ⏝࠸ࡓࢹ࣮ࢱࡘ࠸࡚㏙ࡿࠋ3-3 ⠇࡛ࡣ㸪᥎ィ⤖ᯝࢆ᳨ᐃࡢୖ㸪ࡑࡢ⤖ᯝࢆゎ㔘ࡋࡘࡘ㸪 ᑟࢀࡿᨻ⟇ⓗྵពࡘ࠸࡚ㄝ᫂ࡍࡿࠋ3-1 ᥎ᐃࣔࢹࣝࡢ≉ᐃ
㈈ᨻ➇தୗ࠾ࡅࡿබമ㈝ඖൾ㑏㔠ἲேㄢ⛯㸪࠾ࡼࡧᇶ♏ⓗṓฟࡢ㛵ಀࢆ᳨ドࡍࡿࡓࡵ㸪௨ୗࡢ ࡼ࠺࡞⥺ᙧᅇᖐࣔࢹࣝࢆᐃࡍࡿ5㸧ࠋ it i t k it k k it it it it itx
m
x
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q
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y
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β
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∑
3=1γ
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λ
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(18) 4㸧 ୍⯡ⓗ‽⥺ᙧࡢຠ⏝㛵ᩘࢆ௬ᐃࡍࢀࡤ㸪(15) ᘧࡣ‶ࡓࡉࢀࡿࠋ 5㸧 බമ㈝ඖൾ㑏㔠ࡸ⛣㌿㈈※➼ࡣ㸪ண⟬⦅ᡂ㐣⛬࠾࠸࡚࡞ࡾࡢ⛬ᗘࡑࡢ㢠ࢆண ࡍࡿࡇࡀྍ⬟࡛࠶ࡿ⪃࠼ࡽࢀࡿࡇࡽ㸪௨ୗ ࡢ᥎ᐃ࡛ࡣྠ୍ᖺᗘࡢኚᩘྠኈࢆᅇᖐࡋ࡚࠸ࡿࠋ㸫㸫 ࡇࡇ࡛㸪 i ࡣᆅᇦ㸦i=1~47㸧ࢆ㸪t ࡣ㛫㸦t=1975~2009㸧ࢆ♧ࡍࠋ⿕ㄝ᫂ኚᩘ࡛࠶ࡿ yit ࡣ㸪㒔㐨ᗓ┴ࡢ ἲேᴗ⛯ᖹᆒ⛯⋡㸪࠾ࡼࡧᇶ♏ⓗṓฟࡢᑐ┴ෆ⥲⏕⏘ᑐࡍࡿẚ⋡ࢆ⾲ࡍࠋㄝ᫂ኚᩘ࡛࠶ࡿxit 㸪zit ࡣࡑ ࢀࡒࢀ㸪㒔㐨ᗓ┴ࡢබമ㈝ඖൾ㑏㔠㸪ᅜࡽࡢ⛣㌿㈈※ࡢᑐ┴ෆ⥲⏕⏘ẚ⋡ࢆ♧ࡍࠋ mit ࡣ㸪㒔㐨ᗓ┴ 㛫ࡢẸ㛫㈨ᮏ⛣ືࢆ⾲ࡍᣦᶆ࡛࠶ࡿࠋqitk ࡣ㸪ἲேᴗ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟᙳ㡪ࢆ࠼࠺ࡿࡑࡢࡢせ ᅉ࡛࠶ࡾ㸪ࡇࡇ࡛ࡣྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸪᭷ຠồேಸ⋡㸪⪁ᖺேཱྀẚ⋡ࡢ 3 ࡘࢆᐃࡍࡿࠋࡲࡓ㸪 2004㹼2006 ᖺᗘᐇࡉࢀࡓ୕୍యᨵ㠉ࡢຠᯝࢆ⧊ࡾ㎸ࡴࡓࡵ㸪ᕥグ 3 ࣧᖺᗘࢆ 1㸪ࡑࢀ௨እࡢᖺᗘࢆ 0ࡍࡿ㛫ࢲ࣑࣮ dt ࢆᐃࡍࡿࠋvi ࡣಶయຠᯝࢆ㸪εitࡣㄗᕪ㡯ࢆ⾲ࡋ㸪 εit~iid0㸪σε ࢆ‶ࡓࡍࡶࡢࡍ ࡿࠋ ᥎ᐃᮇ㛫ࡣ㸪1975㹼2009 ᖺᗘࡲ࡛ࡢ 35 ᖺ㛫࡛࠶ࡾ㸪㒔㐨ᗓ┴㛫ࡢ␗㉁ᛶࢆ⪃៖ࡋ࡚(18) ᘧࢆࣃࢿࣝศ ᯒࡼࡾ᥎ᐃࡍࡿࠋ㈈ᨻ➇தࡼࡾㄏⓎࡉࢀࡿẸ㛫㈨ᮏ⛣ືࡢ≧ἣࡢኚࢆ⧊ࡾ㎸ࡴࡓࡵ㸪ࢧࣥࣉࣝᮇ 㛫࡛ࡢ᥎ᐃຍ࠼㸪㈨ᮏ⛣ືࡀపㄪࡔࡗࡓ๓ᮇ㸦75㹼95 ᖺᗘ㸧㸪άⓎࡔࡗࡓᚋᮇ㸦96㹼09 ᖺᗘ㸧ࢧࣥ ࣉࣝࢆศࡋ㸪ࡑࢀࡒࢀࡢᮇ㛫࡛ࡢ᥎ᐃࡶ࠶ࢃࡏ࡚ᐇࡍࡿ6㸧ࠋ ⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢሙྜ㸪⌮ㄽࡼࡾ β1 ணࡉࢀࡿ➢ྕࡣṇ㸦㈇㸧࡛࠶ࡿࠋ୍᪉㸪 β2 ࡘ࠸࡚ࡣ㸪⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢሙྜ㸪㈇㸦㈇㸧࡞ࢀࡤ㸪⛒⛯➇தࡀබമࡢ ᡶ࠸㈝ቑຍࡼࡿ⛯⋡ୖ᪼ࡢពḧࢆῶࡎࡿ㸦ᇶ♏ⓗṓฟῶᑡࡢពḧࢆቑࡍ㸧᪉ྥస⏝ࡍࡿࡋࡓ 2 ⠇ࡢ ⌮ㄽࣔࢹࣝᩚྜⓗ࡞⤖ᯝࡀᚓࡽࢀࡓࡇ࡞ࡿࠋࡉࡽ࠸࠼ࡤ㸪ἲேᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢᅇᖐ࠾ ࠸࡚㸪ࢧࣥࣉࣝᚋᮇࡢ β1+β2ࡢ್ࡀࢧࣥࣉࣝ๓ᮇࡢ β1+β2ࡢ್ࢆ⤯ᑐ್࡛ୗᅇࡗࡓ㸦ୖᅇࡗࡓ㸧ሙྜ㸪⛒⛯ ➇தࡸᨭฟ➇தࡢᣑࡀ㸪⛯⋡ୖ᪼㸦ᨭฟῶ㸧ࢆ㏻ࡌࡓ㒔㐨ᗓ┴ࡢ㈈ᨻࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓ㸦ಁ ࡋࡓ㸧ゎ㔘࡛ࡁࡿࠋ
3-2 ࢹ࣮ࢱ
(18) ᘧࡢ᥎ᐃࡣ㸪1975㹼2009 ᖺᗘࡲ࡛ࡢ 47 㒔㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚⾜࡞࠺ࠋ௨ୗ㸪᥎ᐃ⏝ ࠸ࡓࢹ࣮ࢱࡘ࠸࡚㏙࡚࠸ࡇ࠺ࠋ ⿕ㄝ᫂ኚᩘ࡛࠶ࡿ㒔㐨ᗓ┴ࡢἲேᴗ⛯ᖹᆒ⛯⋡ࡣ㸪⥲ົ┬⮬⛯ົᒁࠕ㐨ᗓ┴⛯ᚩᐇ⦼ㄪࠖ࠶ࡿ ἲேᴗ⛯㢠㸦ἲே⌧ᖺㄢ⛯ศ㸧ࢆ㸪ෆ㛶ᗓ⤒῭♫⥲ྜ◊✲ᡤࡢࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖ㘓ࡉࢀ࡚࠸ ࡿ㒔㐨ᗓ┴ูࡢẸ㛫ἲேᴗᡤᚓ㸦ศ㓄ᡤᚓཷᡶᚋ㸧࡛㝖ࡍࡇ࡛ồࡵࡓ್࡛࠶ࡿࠋྠࡌࡃ⿕ㄝ᫂ኚᩘ࡛ ࠶ࡿᇶ♏ⓗṓฟࡢᑐ┴ෆ⥲⏕⏘ᑐࡍࡿẚ⋡ࡣ㸪⥲ົ┬⮬㈈ᨻᒁࡢࠕ㒔㐨ᗓ┴Ỵ⟬≧ἣㄪࠖ࠶ࡿᇶ♏ ⓗṓฟ㸦ṓฟ⥲㢠㸫බമ㈝㸧ࢆ㸪ࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖ㘓ࡉࢀ࡚࠸ࡿ㒔㐨ᗓ┴ูࡢྡ┠┴ෆ⥲⏕⏘࡛㝖 ࡋࡓ್࡛࠶ࡿࠋ ㄝ᫂ኚᩘ࡛࠶ࡿබമ㈝ඖൾ㑏㔠㸪୰ኸᨻᗓࡽࡢ⛣㌿㈈※ࡢᑐ┴ෆ⥲⏕⏘ẚ⋡ࡘ࠸࡚ࡣ㸪ࠕ㒔㐨ᗓ┴ Ỵ⟬≧ἣㄪࠖ࠶ࡿබമ㈝ඖൾ㑏㔠㸪ᅜᗜᨭฟ㔠ᆅ᪉⛯㔠ࡢྜィ್ࢆ㸪ࡑࢀࡒࢀࠕ┴Ẹ⤒῭ ィ⟬ᖺሗࠖ࠶ࡿ㒔㐨ᗓ┴ูྡ┠┴ෆ⥲⏕⏘ࡢ್࡛㝖ࡍࡇ࡛ồࡵࡓࠋࡲࡓ㸪බമ㈝ඖൾ㑏㈝ࡎࡿ 㒔㐨ᗓ┴㛫ࡢẸ㛫㈨ᮏ⛣ືࡢᣦᶆࡣ㸪῝ᑿ࣭ᓅ㸦2000㸧࡞ࡽ࠸㸪௨ୗࡢ᪉ἲࡼࡾẸ㛫㈨ᮏ⛣ື㢠ࢆ᥎ ィ7㸧ࡢୖ㸪ྡ┠┴ෆ⥲⏕⏘ࡢ್࡛㝖ࡍࡿࡇ࡛సᡂࡋࡓࠋ ᣦᶆసᡂᚲせ࡞Ẹ㛫㈨ᮏ⛣ື㢠ࡣ㸪Ẹ㛫㒊㛛ࡢ㈓ᢞ㈨ࡢᕪ㢠ࡋ࡚ồࡵࡽࢀࡿࠋࡑࡇ࡛㸪Ẹ㛫㒊 6㸧 ࢧࣥࣉࣝࡢศ࠶ࡓࡗ࡚ࡣ㸪Ẹ㛫㈨ᮏ⛣ືࡢ≧ἣຍ࠼㸪ࠕ┴Ẹ⤒῭ィ⟬ࠖࡢࢹ࣮ࢱࡘ࠸࡚㸪1975㹼1995 ᖺᗘࡲ࡛ࡣ 68SNA㸪1996 㹼2009 ᖺᗘࡲ࡛ࡣ 93SNA ࢆࡑࢀࡒࢀ⏝࠸ࡓࡇࢆ⪃៖ࡋࡓࠋ 7㸧 ῝ᑿ࣭ᓅࡼࡿࠕ᪥ᮏᗓ┴ࢹ࣮ࢱ࣮࣋ࢫࠖ㸦http://www.ier.hit-u.ac.jp/~fukao/japanese/data/index.html㸧ࡢせ⣲⛣ື㛵ࡍࡿࢹ࣮ࢱࢆ⏝࠸㸪᭱ ㏆ᖺࡘ࠸࡚ࡣ㸪῝ᑿ࣭ᓅ㸦2000㸧࡞ࡽࡗ࡚㸪ᘏ㛗᥎ィࢆ⾜࡞ࡗࡓࠋ㸫㸫 㛛ࡢ㈓㢠ࡣ㸪ᑐ㇟㒔㐨ᗓ┴ࡢྡ┠┴ෆ⥲⏕⏘┴እࡽࡢせ⣲ᡤᚓ㸦⣧㸧♫ಖ㞀࠾ࡅࡿẸ㛫㒊㛛 ࡢ⣧ཷྲྀࡢࡽᑐ㇟㒔㐨ᗓ┴ࡢẸ㛫᭱⤊ᾘ㈝ᨭฟ࠾ࡼࡧᅜ⛯ᆅ᪉⛯㸦㒔㐨ᗓ┴Ẹ⛯㸩ᕷ⏫ᮧ⛯㸧ࡢ ࢆᕪࡋᘬࡃࡇ࡛᥎ィࡋࡓࠋ୍᪉㸪Ẹ㛫㒊㛛ࡢᢞ㈨㢠ࡣ㸪Ẹ㛫⥲ᅛᐃ㈨ᮏᙧᡂẸ㛫ᅾᗜቑຍࡢࡋ࡚ ồࡵࡓࠋ ྡ┠┴ෆ⥲⏕⏘㸪┴እࡽࡢせ⣲ᡤᚓ㸦⣧㸧㸪Ẹ㛫᭱⤊ᾘ㈝ᨭฟ㸪Ẹ㛫⥲ᅛᐃ㈨ᮏᙧᡂ࠾ࡼࡧẸ㛫ᅾᗜቑ ຍࡘ࠸࡚ࡣ㸪ࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖࡢ್ࢆ⏝࠸ࡓ୍᪉㸪♫ಖ㞀࠾ࡅࡿẸ㛫㒊㛛ࡢ⣧ཷྲྀࡘ࠸࡚ࡣ㸪 㒔㐨ᗓ┴ูࡢ♫ಖ㞀㛵ಀࡢ⤫ィࡀ࡞࠸ࡓࡵ㸪ෆ㛶ᗓ⤒῭♫⥲ྜ◊✲ᡤࡢࠕᅜẸ⤒῭ィ⟬ᖺሗࠖ࠶ࡿ ࢹ࣮ࢱࢆࡶ♫ಖ㞀ࡢ⣧ཷྲྀ㢠ࡢᅜ್ࢆィ⟬ࡋ㸪ྛ㒔㐨ᗓ┴ࡢேཱྀẚࢆࡶᣨศࡍࡿࡇ࡛సᡂ ࡋࡓ8㸧ࠋ㒔㐨ᗓ┴ูࡢᅜ⛯࠾ࡼࡧᆅ᪉⛯㢠ࡣ㸪ᅜ⛯ࡘ࠸࡚ࡣᅜ⛯ᗇࡢࠕᅜ⛯ᗇ⤫ィᖺሗ᭩ࠖ࠶ࡿ㒔㐨 ᗓ┴ูࡢᅜ⛯ᚩ≧ἣࢆ㸪ᆅ᪉⛯ࡘ࠸࡚ࡣ⥲ົ┬⮬㈈ᨻᒁࡢࠕᆅ᪉㈈ᨻ⤫ィᖺሗࠖ࠶ࡿᅋయูࡢᆅ ᪉⛯㢠ࢆ⏝࠸࡚ィ⟬ࡋࡓࡶࡢ࡛࠶ࡿࠋ ṧࡿㄝ᫂ኚᩘ࡛࠶ࡿྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑຍ⋡㸪᭷ຠồேಸ⋡㸪࠾ࡼࡧ⪁ᖺேཱྀẚ⋡ࡘ࠸࡚ࡣ㸪௨ ୗࡢ㈨ᩱࡼࡾධᡭࡋࡓࠋࡲࡎ㸪ྡ┠┴ෆ⥲⏕⏘ࡣࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖࡼࡾධᡭࡋ㸪ᑐ๓ᖺࡢኚ⋡ࢆ ồࡵࡓࠋ᭷ຠồேಸ⋡ࡘ࠸࡚ࡣ㸪ཌ⏕ປാ┬⫋ᴗᏳᐃᒁࡢࠕ⫋ᴗᏳᐃᴗົ⤫ィࠖ㘓ࡉࢀ࡚࠸ࡿ㒔㐨 ᗓ┴ูࡢ᭷ຠồேಸ⋡ࡢᖺᗘᖹᆒࡢཎᩘ್ࢆ⏝࠸ࡓࠋ⪁ᖺேཱྀẚ⋡ࡘ࠸࡚ࡣ㸪⥲ົ┬⤫ィᒁࡢࠕᅜໃㄪ ᰝࠖ࠾ࡼࡧࠕ᥎ィேཱྀࠖࢆࡶ㸪65 ṓ௨ୖࡢேཱྀࢆேཱྀ࡛㝖ࡍࡿࡇ࡛ẚ⋡ࢆィ⟬ࡋࡓࠋ
3-3 ᥎ᐃ⤖ᯝ࠾ࡼࡧゎ㔘
ᮏ✏࡛ࡣ㸪ࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚࠸ࡿࡓࡵ㸪ᅇᖐศᯒࢆᐇࡍࡿ࠶ࡓࡾ㸪ࢹ࣮ࢱࡢᐃᖖᛶࡢࢳ࢙ࢵࢡ ࢆ⾜࡞࠺ᚲせࡀ࠶ࡿࠋᅗ⾲ 3-3-1 ࡣ㸪ᅇᖐศᯒ⏝࠸ࡓࢹ࣮ࢱࡘ࠸࡚ ADF ࢆ⏝࠸ࡓ༢᰿᳨ᐃࡢ⤖ᯝࢆ ♧ࡋࡓࡶࡢ࡛࠶ࡿࠋࡇࢀࡼࡿ㸪1975㹼2009 ᖺᗘࡲ࡛ࡢࢧࣥࣉࣝᮇ㛫࡛ࡣ㸪 xit×mit 㸦බമ㈝ඖൾ㑏 㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧ࢆ㝖ࡁ㸪༢᰿ࡀ࠶ࡿࡍࡿᖐ↓௬ㄝࡀᲠ༷ࡉࢀ࡚࠸ࡿࠋ 8㸧 ලయⓗࡣ㸪ࠕᅜẸ⤒῭ィ⟬ᖺሗࠖࡢࠕ୍⯡ᨻᗓࡽᐙィࡢ⛣㌿᫂⣽⾲㸦♫ಖ㞀㛵ಀ㸧ࠖ࠶ࡿࠕ⌧≀♫⛣㌿௨እࡢ♫⤥ࠖࡽ㸪 ࠕ♫ಖ㞀㈇ᢸࡢ᫂⣽⾲㸦♫ಖ㞀㛵ಀ㸧ࠖ࠶ࡿࠕ㞠⏝⪅ࡢ♫㈇ᢸࠖࢆᕪࡋᘬࡃࡇ࡛♫ಖ㞀ࡢ⣧ཷྲྀ㢠ࢆồࡵࡓࠋࡑࡢ⣧ཷྲྀ㢠ࢆࠕ┴ Ẹ⤒῭ィ⟬ᖺሗࠖ࠶ࡿ㒔㐨ᗓ┴ูࡢேཱྀẚ࡛ᣨศࡋࡓࡶࡢࢆ㸪㒔㐨ᗓ┴ูࡢ⣧ཷྲྀࡋ࡚࠸ࡿࠋ㸫㸫 ᅗ⾲ 3-3-1 ࣃࢿࣝ༢᰿᳨ᐃࡢ⤖ᯝ ኚᩘྡ (1) 75-09 (2) 75-95 (3) 96-09 it
y
㸦ἲேᴗ⛯ᖹᆒ⛯⋡㸧 259.4 *** 㸦0.000㸧 㸫 㸫 ity
㸦ᇶ♏ⓗṓฟ㸧 145.2 *** 㸦0.000㸧 㸫 㸫 itx
㸦බമ㈝ඖൾ㑏㔠ẚ⋡㸧 235.9 *** 㸦0.000㸧 㸫 㸫 it itm
x ∗
㸦බമ㈝ඖൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧 87.3 㸦0.673㸧 194.6 *** 㸦0.000㸧 129.1 *** 㸦0.000㸧 itz
㸦⛣㌿㈈※ẚ⋡㸧 216.2 *** 㸦0.000㸧 㸫 㸫 1 itq
㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧 690.4 *** 㸦0.000㸧 㸫 㸫 2 itq
㸦᭷ຠồேಸ⋡㸧 179.1 *** 㸦0.000㸧 㸫 㸫 㸦0.000㸧 3 itq
㸦⪁ᖺேཱྀẚ⋡㸧 172.3 *** 㸦0.000㸧 㸫 -0.178 *** 㸦0.000㸧 ὀ 1㸧ADF ࡼࡿ༢᰿᳨ᐃࡢ⤖ᯝࢆ♧ࡍࠋ ὀ 2㸧*** ࡣ୧ഃ 1㸣ࡢ᭷ពỈ‽㸪** ࡣ୧ഃ 5㸣ࡢ᭷ពỈ‽㸪* ࡣ୧ഃ 10㸣ࡢ᭷ពỈ‽࡛㸪ᖐ↓௬ㄝࡀᲠ༷࡛ࡁࡿ ࡇࢆ♧ࡍࠋ ὀ 3㸧ᣓᘼࡣ p ್ࢆ♧ࡍࠋ ຍ࠼࡚㸪xit×mit ࡘ࠸࡚ࡶ㸪ࢧࣥࣉࣝࢆ 1975㹼1995 ᖺᗘ 1996㹼2009 ᖺᗘࡢ 2 ᮇ㛫࡛ศࡋࡓሙྜ ࡣ㸪༢᰿ࡀ࠶ࡿࡍࡿᖐ↓௬ㄝࡀᲠ༷࡛ࡁࡿࡇࡀࢃࡿࠋPerron㸦1989㸧ࡣ㸪ࢧࣥࣉࣝࡀఱࡽࡢᵓ 㐀ኚࢆྵࡴሙྜ㸪༢᰿ࡀ࡞࠸ࢧࣥࣉࣝ࠾࠸࡚༢᰿ࡀ࠶ࡿ࠸࠺ㄗࡗࡓ᳨ᐃ⤖ᯝࡀᑟࢀࡸࡍ࠸ ࡋ㸪ࡑࡢᨵၿࢧࣥࣉࣝࢆศࡋࡓୖ࡛༢᰿᳨ᐃࢆᐇࡍࡿࡇࡀ᭷ຠ࡛࠶ࡿ㏙࡚࠸ࡿࠋᮏ✏࡛ࡶ ࡇࢀࢆ㋃くࡋ㸪⏝ࢧࣥࣉࣝ༢᰿ࡀ࡞࠸ุ᩿ࡋ㸪௨ୗ㸪ศᯒࢆ㐍ࡵࡿࡇࡍࡿࠋ (18) ᘧࢆᅇᖐศᯒࡋࡓ⤖ᯝࡀ㸪ᅗ⾲ 3-3-2 ࠾ࡼࡧᅗ⾲ 3-3-3 ୍ぴ࡛♧ࡉࢀ࡚࠸ࡿࠋࡇࡢ࠺ࡕ㸪๓⪅ࡀἲ ேᴗ⛯ᖹᆒ⛯⋡ࢆ⿕ㄝ᫂ኚᩘ㸪ᚋ⪅ࡀᇶ♏ⓗṓฟᑐྡ┠┴ෆ⥲⏕⏘ẚ⋡ࢆ⿕ㄝ᫂ኚᩘࡋࡓሙྜࡢ⤖ᯝ ࡛࠶ࡿࠋᅗ⾲୰ࡢ (1) ࡀ 75㹼09 ᖺᗘࡲ࡛ࡢࢧࣥࣉ࡛ࣝࡢ᥎ᐃ⤖ᯝࢆ㸪(2) ࡀ 75㹼95 ᖺᗘࡲ࡛ࡢ᥎ᐃ⤖ ᯝࢆ㸪(3) ࡀ 96㹼09 ᖺᗘࡲ࡛ࡢ᥎ᐃ⤖ᯝ࡛࠶ࡿࠋ௨ୗ㸪⤫ィⓗ᭷ពᛶࡢ᳨ᐃࢆ⾜࡞࠺ࡶ㸪⤖ᯝࡘ ࠸࡚ゎ㔘ࢆ⾜࡞ࡗ࡚࠸ࡇ࠺ࠋ㸫 㸫 ᅗ⾲ 3-3-2 ἲேᴗ⛯ᖹᆒ⛯⋡㛵ࡍࡿ᥎ᐃ⤖ᯝ ࣃ࣓࣮ࣛࢱ㸦ኚᩘྡ㸧 (1) 75-09 (2) 75-95 (3) 96-09 1
β
㸦බമ㈝ඖൾ㑏㔠ẚ⋡㸧 -0.323 㸦0.578㸧 -0.794 㸦0.430㸧 2.660 *** 㸦0.000㸧 2β
㸦බമ㈝ඖൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧 -0.131 *** 㸦0.000㸧 -0.312 *** 㸦0.000㸧 -0.129 *** 㸦0.000㸧 3β
㸦⛣㌿㈈※ẚ⋡㸧 -0.398 ** 㸦0.033㸧 0.789 ** 㸦0.002㸧 -0.376 *** 㸦0.001㸧 1γ
㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧 -0.194E-02 *** 㸦0.000㸧 -0.286 *** 㸦0.034㸧 -0.124E-02 *** 㸦0.000㸧 2γ
㸦᭷ຠồேಸ⋡㸧 0.394E-02 㸦0.401㸧 0.362E-03 㸦0.960㸧 0.019*** 㸦0.000㸧 3γ
㸦⪁ᖺேཱྀẚ⋡㸧 -0.368E-02 *** 㸦0.000㸧 0.538E-03 㸦0.719㸧 -0.178 *** 㸦0.000㸧λ
㸦ไᗘᨵ㠉ࢲ࣑࣮㸧 0.358E-02 㸦0.485㸧 㸫 -0.729E-02 *** 㸦0.000㸧 ࢧࣥࣉࣝᩘ 1645 987 658 F ್ 18.642 *** 㸦0.000㸧 18.189 *** 㸦0.000㸧 16.516 *** 㸦0.000㸧 Hausman 32.110 ***㸺6㸼 㸦0.000㸧 11.452 ***㸺6㸼 㸦0.075㸧 30.487 ***㸺6㸼 㸦0.000㸧 AdjR2 0.481 0.479 0.642ὀ 1 㸧᥎ᐃ⤖ᯝࡣ㸪ࣔࢹࣝࡢᐃᘧࡢㄗࡾᑐࡍࡿ᳨ᐃࡢ⤖ᯝ᥇ᢥࡉࢀࡓ fixed effects model ࡢ᥎ᐃ್࡛࠶ࡿࠋ ὀ 2 㸧*** ࡣ୧ഃ 1㸣ࡢ᭷ពỈ‽㸪** ࡣ୧ഃ 5㸣ࡢ᭷ពỈ‽㸪* ࡣ୧ഃ 10㸣ࡢ᭷ពỈ‽࡛࠶ࡿࡇࢆ♧ࡍࠋ
ὀ 3 㸧ࣃ࣓࣮ࣛࢱෆࡢᣓᘼࡣ p ್ࢆ♧ࡋ㸪AdjR2ࡣ⮬⏤ᗘಟṇ῭ࡳࡢỴᐃಀᩘࢆ♧ࡍࠋࡲࡓ㸪F ್ࡢᣓᘼ࠾ࡼࡧHausman ࡢᣓᘼࡣ p-value ࢆ♧ࡋ㸪Hausman ࡢ㸺 㸼ࡢᩘᏐࡣ⮬⏤ᗘࢆ♧ࡍࠋ
ὀ 4 㸧Hausman ࡣ㸪Hausman㸦1978㸧ࡼࡿࣔࢹࣝࡢᐃᘧࡢㄗࡾᑐࡍࡿ᳨ᐃ⤫ィ㔞࡛࠶ࡾ㸪random effects model ࠾ࡅࡿಶయຠᯝ㸦individual effect㸧ࢆ⪃៖ࡋࡓኚᩘㄝ᫂ኚᩘࡢ㛫┦㛵ࡀ࡞࠸࠸࠺ᖐ↓௬ ㄝࡢࡶ࡛㸪㏆ⓗ㸺 㸼ෆࡢᩘ್ࢆ⮬⏤ᗘࡍࡿ χ2ศᕸࡋࡓࡀ࠺ࠋ
㸫㸫 ᅗ⾲ 3-3-3 ᇶ♏ⓗṓฟ㛵ࡍࡿ᥎ᐃ⤖ᯝ ࣃ࣓࣮ࣛࢱ㸦ኚᩘྡ㸧 (1) 75-09 (2) 75-95 (3) 96-09 1
β
㸦බമ㈝ඖൾ㑏㔠ẚ⋡㸧 -1.620 *** 㸦0.000㸧 -2.041 *** 㸦0.000㸧 -0.860 *** 㸦0.000㸧 2β
㸦බമ㈝ඖൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧 0.120E-02 㸦0.626㸧 -0.441E-02 㸦0.442㸧 -0.013** 㸦0.037㸧 3β
㸦⛣㌿㈈※ẚ⋡㸧 1.301 *** 㸦0.000㸧 1.403 *** 㸦0.000㸧 1.139 *** 㸦0.000㸧 1γ
㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧 0.899E-03 *** 㸦0.000㸧 0.102E-02 *** 㸦0.000㸧 0.473E-03 *** 㸦0.000㸧 2γ
㸦᭷ຠồேಸ⋡㸧 0.401E-02 *** 㸦0.000㸧 -0.783E-05 㸦0.992㸧 0.011*** 㸦0.503㸧 3γ
㸦⪁ᖺேཱྀẚ⋡㸧 0.780E-03 *** 㸦0.000㸧 0.236E-02 *** 㸦0.000㸧 -0.772E-03 *** 㸦0.000㸧λ
㸦ไᗘᨵ㠉ࢲ࣑࣮㸧 -0.186 ** 㸦0.011㸧 㸫 -0.290 *** 㸦0.000㸧 ࢧࣥࣉࣝᩘ 1645 987 658 F ್ 29.828 *** 㸦0.000㸧 33.999 *** 㸦0.000㸧 16.184 *** 㸦0.000㸧 Hausman 41.962 ***㸺6㸼 㸦0.000㸧 31.015 ***㸺6㸼 㸦0.000㸧 60.243 ***㸺6㸼 㸦0.000㸧 AdjR2 0.954 0.985 0.935ὀ 1㸧 ᥎ᐃ⤖ᯝࡣ㸪ࣔࢹࣝࡢᐃᘧࡢㄗࡾᑐࡍࡿ᳨ᐃࡢ⤖ᯝ᥇ᢥࡉࢀࡓ fixed effects model ࡢ᥎ᐃ್࡛࠶ࡿࠋ ὀ 2㸧 *** ࡣ୧ഃ 1㸣ࡢ᭷ពỈ‽㸪** ࡣ୧ഃ 5㸣ࡢ᭷ពỈ‽㸪* ࡣ୧ഃ 10㸣ࡢ᭷ពỈ‽࡛࠶ࡿࡇࢆ♧ࡍࠋ
ὀ 3㸧 ࣃ࣓࣮ࣛࢱෆࡢᣓᘼࡣ p ್ࢆ♧ࡋ㸪AdjR2ࡣ⮬⏤ᗘಟṇ῭ࡳࡢỴᐃಀᩘࢆ♧ࡍࠋࡲࡓ㸪F ್ࡢᣓᘼ࠾ࡼࡧHausman ࡢᣓᘼࡣ p-value ࢆ♧ࡋ㸪Hausman ࡢ㸺 㸼ࡢᩘᏐࡣ⮬⏤ᗘࢆ♧ࡍࠋ
ὀ 4㸧 Hausman ࡣ㸪Hausman㸦1978㸧ࡼࡿࣔࢹࣝࡢᐃᘧࡢㄗࡾᑐࡍࡿ᳨ᐃ⤫ィ㔞࡛࠶ࡾ㸪random effects model ࠾ࡅࡿಶయຠᯝ㸦individual effect㸧ࢆ⪃៖ࡋࡓኚᩘㄝ᫂ኚᩘࡢ㛫┦㛵ࡀ࡞࠸࠸࠺ᖐ↓௬ ㄝࡢࡶ࡛㸪㏆ⓗ㸺 㸼ෆࡢᩘ್ࢆ⮬⏤ᗘࡍࡿ χ2ศᕸࡋࡓࡀ࠺ࠋ
ᅗ⾲ 3-3-2 ࠾ࡼࡧᅗ⾲ 3-3-3 ࡛ࡣ㸪fixed effects model ࡢࡳࡢ⤖ᯝࡀሗ࿌ࡉࢀ࡚࠸ࡿࠋࡇࢀࡣ㸪F ᳨ᐃࡼ ࡿ pool model fixed effects model ࡢ㑅ᢥ㸪Hausman ᳨ᐃࡼࡿ fixed effects model random effects model ࡢ㑅ᢥ࠾࠸࡚㸪fixed effects model ࡀ᥇ᢥࡉࢀࡓ⤖ᯝࢆ㋃ࡲ࠼ࡓࡶࡢ࡛࠶ࡿࠋ
ࣔࢹࣝࡢ≉ᐃᑐࡍࡿ᳨ᐃ⤖ᯝࢆ㋃ࡲ࠼㸪௨ୗ࡛ࡣ㸪ಀᩘࡢ⤫ィⓗ᭷ពᛶ࠾ࡼࡧ➢ྕ᮲௳ࡘ࠸᳨࡚ ウࡋ࡚࠸ࡃࡇࡋࡼ࠺ࠋࡲࡎ㸪⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯ᖹᆒ⛯⋡࡛࠶ࡿᅗ⾲ 3-3-2 ࡢ⤖ᯝࡽጞࡵࡿࠋ බമ㈝ඖൾ㑏㔠㸦β1㸧ࡘ࠸࡚ࡣ㸪(1)㸪(2) ࡀ⤫ィⓗ᭷ព࡛࡞ࡃ㸪(3) ࡣࣉࣛࢫ࡛᭷ព࡞ࡗ࡚࠸ࡿࠋ (1)㸪(2) ࡘ࠸࡚ࡣ➢ྕ᮲௳ࡶ‶ࡓࡋ࡚࠾ࡽࡎ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝᩚྜⓗ࡞⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿࡢࡣ㸪(3) ࡢࡳ࡛࠶ࡿࡇࡀࢃࡿࠋࡇࡢࡇࡽ㸪㒔㐨ᗓ┴ࡣ㐣ཤ࠾࠸࡚㸪බമᡶ࠸ࡢቑຍἲேᴗ⛯ࡢ⛯ ⋡ୖ࡛᪼ᑐᛂࡍࡿഴྥ࡞ࡗࡓࡀ㸪᭱㏆ᖺࡅ࡚ࡣබമᡶ࠸ࡢቑຍἲேᴗ⛯ࡢ⛯⋡ୖ࡛᪼ᑐᛂ
㸫㸫 ࡋࡣࡌࡵࡿࡼ࠺࡞ࡗࡓ⪃࠼ࡽࢀࡿࠋ බമ㈝ඖൾ㑏㔠Ẹ㛫㈨ᮏ⛣ືẚ⋡㸦β2㸧ࡘ࠸࡚ࡣ㸪(1)㸪(2)㸪(3) ࠸ࡎࢀࡶ࣐ࢼࢫ࡛᭷ព࡞ࡗ ࡚࠸ࡿࠋࡇࢀࡣ㸪⛒⛯➇தࡀබമࡢᡶ࠸㈝ቑຍࡼࡿ⛯⋡ୖ᪼ࡢຠᯝࢆῶࡎࡿ᪉ྥస⏝ࡍࡿࡋࡓ 2 ⠇ࡢ⌮ㄽࣔࢹࣝᩚྜⓗ࡞⤖ᯝ࡛࠶ࡿࠋࡇࡢ࠺ࡕ㸪(3) ࡘ࠸࡚ࡣ㸪β1ࡀࣉࣛࢫ࡛᭷ពࡘ β2ࡀ࣐ࢼࢫ ࡛᭷ព࡛࠶ࡿࡓࡵ㸪㏆ᖺ࠾࠸࡚ࡣ⛒⛯➇தࡢᣑࡀ㸪ἲேᴗ⛯⋡ࡢୖ᪼ࢆ㏻ࡌࡓ㒔㐨ᗓ┴ࡢ㈈ᨻ ࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓゎ㔘࡛ࡁࡿ୍᪉㸪(1)㸪(2) ࡘ࠸࡚ࡣ β1ࡀ᭷ព࡛࡞࠸ࡇࡽ㸪㐣ཤ࠾࠸࡚ ࡣ⛒⛯➇தࡢᣑ⛯⋡ୖ᪼ࡼࡿ㈈ᨻᘓࡢ㛫ᅉᯝ㛵ಀࢆぢฟࡍࡇࡣ࡛ࡁ࡞࠸⪃࠼ࡽࢀࡿࠋ ୍᪉㸪⿕ㄝ᫂ኚᩘࡀᇶ♏ⓗṓฟ࡛࠶ࡿᅗ⾲ 3-3-3 ࡢ⤖ᯝࢆࡳࡿ㸪බമ㈝ඖൾ㑏㔠㸦β1㸧ࡘ࠸࡚ࡣ㸪 (1)㸪(2)㸪(3) ࠸ࡎࢀࡢࢧࣥࣉࣝᮇ㛫࠾࠸࡚ࡶ࣐ࢼࢫ࡛᭷ព࡞ࡗ࡚࠾ࡾ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝᩚྜⓗ ࡞⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿࠋࢧࣥࣉࣝ (2) ࢧࣥࣉࣝ (3) ࢆẚ㍑ࡍࡿ㸪(2) ࡢ β1ࡀ (3) ࡢ β1ࢆୗᅇࡗ࡚ ࠸ࡿࡇࡀ☜ㄆࡉࢀࡿࠋࡇࢀࡼࡾ㸪බമᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪㒔㐨ᗓ┴ࡣᇶ♏ⓗṓฟࡢῶᑡࡼ ࡗ࡚㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࠶ࡾ㸪≉㸦㒔㐨ᗓ┴㛫ࡢ㈨ᮏ⛣ືࡀపㄪ࡛࠶ࡗࡓ㸧㐣ཤᮇ 㛫࠾࠸࡚㸪ࡑࡢഴྥࡀᙉࡗࡓ⪃࠼ࡽࢀࡿࠋ බമ㈝ඖൾ㑏㔠Ẹ㛫㈨ᮏ⛣ືẚ⋡㸦β2㸧ࡘ࠸࡚ࡳ࡚ࡳࡿ㸪(3) ࡢࡳࡀ࣐ࢼࢫ࡛᭷ព㸪(1)㸪(2) ࡶ᭷ព࡛࡞࠸ࡇࡀࢃࡿࠋβ1㸪β2ࡶ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝᩚྜⓗ࡞➢ྕ᮲௳ࡀ‶ࡓࡉࢀࡿࡢࡣ (3) ࡢࡳ࡛࠶ࡿࡇࡽ㸪᭱㏆ᖺ㛵ࡍࡿ㝈ࡾ㸪ᨭฟ➇தࡢᣑࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣᇶ♏ⓗṓฟࡢῶᑡ✚ ᴟⓗ࡞ࡿࡍࡿ⌮ㄽࣔࢹࣝࡢ⤖ᯝࡀ㸪ᐇドศᯒ࠾࠸࡚☜ㄆ࡛ࡁࡓ࠸࠼ࡿࠋ ࡑࡢࡢኚᩘࡘ࠸࡚ࡳ࡚ࡳࡿ㸪⛣㌿㈈※ẚ⋡㸦β3㸧ࡘ࠸࡚ࡣ㸪ἲேᴗᖹᆒ⛯⋡ࡀ⿕ㄝ᫂ኚᩘࡢ ሙྜࡣ࣐ࢼࢫ࡛᭷ព㸪ᇶ♏ⓗṓฟࡀ⿕ㄝ᫂ኚᩘࡢሙྜࡣࣉࣛࢫ࡛᭷ព࡞ࡗ࡚࠸ࡿࠋ⛣㌿㈈※ࡀ ከ࠸⮬యࡣ㸪ࡑࢀࢆᙜ࡚㎸ࢇ࡛⛯⋡ࢆᘬࡁୖࡆࡿᚲせᛶஈࡋࡃ㸪ࡲࡓṓฟつᶍࡶᣑࡋࡀࡕ࡛࠶ࡿࡇ ࡽ㸪࠸ࡎࢀࡢ⤖ᯝࡶ➢ྕ᮲௳ࢆ‶ࡓࡋ࡚࠸ࡿ⪃࠼ࡽࢀࡿࠋ ᆅᇦࡢ♫⤒῭≧ἣࢆ♧ࡍྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸦γ1㸧㸪᭷ຠồேಸ⋡㸦γ2㸧㸪⪁ᖺேཱྀẚ⋡㸦γ3㸧 ࡘ࠸࡚ࡣ㸪γ1ࢆ㝖ࡁ㸪⿕ㄝ᫂ኚᩘ࠾ࡼࡧࢧࣥࣉࣝᮇ㛫࡛ࡲࡕࡲࡕ࡞⤖ᯝ࡞ࡗ࡚࠸ࡿࠋγ1ࡘ࠸࡚ࡣ㸪 ⤒῭≧ἣࡀࡼ࠸ᆅᇦ࡛ࡣ㸪ῶ⛯వຊ࠾ࡼࡧṓฟᣑవຊࡀ㧗࠸ணࡉࢀࡿࡇࡽ㸪࠸ࡎࢀࡢ᥎ᐃ⤖ᯝ ࡶ➢ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯⋡ࡢሙྜࡣ࣐ࢼࢫ㸪ᇶ♏ⓗṓฟࡢሙྜࡣࣉࣛࢫ㸧ࡣ‶ࡓࡋ࡚࠸ࡿ ⪃࠼ࡽࢀࡿࠋ γ2ࡘ࠸࡚ணࡉࢀࡿ➢ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯⋡ࡢሙྜࡣ࣐ࢼࢫ㸪ᇶ♏ⓗṓฟࡢሙྜࡣࣉ ࣛࢫ㸧ࢆ‶ࡓࡍࡢࡣ㸪ᇶ♏ⓗṓฟࡢ (1) ࠾ࡼࡧ (3) ࡢ᥎ᐃ⤖ᯝࡢࡳ࡛࠶ࡿ୍᪉㸪γ3ࡘ࠸࡚ணࡉࢀࡿ➢ ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲேᴗ⛯⋡ࡢሙྜࡣ࣐ࢼࢫ㸪ᇶ♏ⓗṓฟࡢሙྜࡣࣉࣛࢫ㸧ࢆ‶ࡓࡍࡢࡣ㸪ἲே ᴗ⛯⋡ࡢ (1) (3) ࡢ᥎ᐃ⤖ᯝ㸪࠾ࡼࡧᇶ♏ⓗṓฟࡢ (1) (2) ࡢ᥎ᐃ⤖ᯝ࡛࠶ࡿࠋ ୕୍యᨵ㠉ࡢᙳ㡪ࢆࡽ࠼ࡓ
λ
ࡘ࠸࡚ࡣ㸪ἲேᴗ⛯⋡ࡀ⿕ㄝ᫂ኚᩘࡢሙྜࡣ (1) ࡀ᭷ព࡛࡞ࡃ㸪 (3) ࡀ࣐ࢼࢫ࡛᭷ព࡞ࡗ࡚࠸ࡿࠋ୍᪉㸪ᇶ♏ⓗṓฟࡀ⿕ㄝ᫂ኚᩘࡢሙྜࡣ㸪(1)㸪(3) ࡶ࣐ࢼࢫ ࡛᭷ព࡞ࡗ࡚࠸ࡿࠋ୕୍యᨵ㠉࡛ࡣ㸪ᅜᗜᨭฟ㔠ࡸᆅ᪉⛯ࡢῶ㢠ࡀ⛯※⛣ㆡ㢠ࢆୖᅇࡾ㸪⤖ᯝⓗ ㈈ᨻ≧ἣࡀⱞࡋࡃ࡞ࡗࡓ㒔㐨ᗓ┴ࡀከᩘ⏕ࡌࡓࡇࡽ㸪᥎ᐃ⤖ᯝࡣ㸦ṓฟ๐ῶ㏕ࡽࢀࡓ㸧㒔㐨ᗓ┴ ࡢ㈈ᨻᩚྜⓗ࡛࠶ࡿ⪃࠼ࡽࢀࡿࠋ ௨ୖ㸪ᅇᖐศᯒࡢ⤖ᯝࢆせ⣙ࡍࡿ㸪௨ୗࡢࡼ࠺࡞ࢁ࠺ࠋࡍ࡞ࢃࡕ㸪ἲேᴗ⛯ᖹᆒ⛯⋡ࡢ᥎ᐃ⤖ᯝ ࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡢᮇ㛫ࡢࡳ β1ࡀࣉࣛࢫ࡛᭷ព㸪ᇶ♏ⓗṓฟࡢ᥎ᐃ⤖ᯝ࠾࠸࡚㸪࡚ࡢࢧࣥࣉࣝ ᮇ㛫࡛ β1ࡀ࣐ࢼࢫ࡛᭷ព࡛࠶ࡿࡇࡽ㸪㒔㐨ᗓ┴ࡣබമᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ἲேᴗ⛯⋡ ࡢᘬࡁୖࡆࡼࡾࡣᇶ♏ⓗṓฟࡢῶᑡࡼࡗ࡚㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࠶ࡗࡓ⪃࠼ࡽࢀࡿࠋ㸫㸫 ἲேᴗ⛯ᖹᆒ⛯⋡ࡢ᥎ᐃ⤖ᯝ࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡛ࡣ β1ࡀࣉࣛࢫ࡛᭷ព㸪β2ࡀ࣐ࢼࢫ࡛᭷ព㸪 ᇶ♏ⓗṓฟࡢ᥎ᐃ⤖ᯝ࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡛ࡣ㸪β1㸪β2ࡶ࣐ࢼࢫ࡛᭷ព࡛࠶ࡿࡇࡽ㸪㈈ᨻ ➇தࡢᣑࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣ㏆ᖺ㸪ἲேᴗ⛯⋡ࡢୖ᪼ࡣᾘᴟⓗ࡞ࡿ୍᪉㸪ᇶ♏ⓗṓฟࡢῶᑡ ✚ᴟⓗ࡞ࡗ࡚࠸ࡿゎ㔘࡛ࡁࡿࠋ ୍㐃ࡢᐇドศᯒࡣ㸪Ẹ㛫㈨ᮏ⛣ືࡀάⓎࡋࡓ 1990 ᖺ௦ࡢ༙ࡤ௨㝆㸪㒔㐨ᗓ┴ࡣ⛒⛯➇தࡸᨭฟ➇தࡢ ᙳ㡪ᑐࡍࡿᠱᛕࡽ㸪⛯⋡ࡢᘬࡁୖࡆ㸦ṓฟ๐ῶ㸧ࢆ㏻ࡌࡓ㈈ᨻࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓ㸦άⓎ ࡉࡏࡓ㸧ྍ⬟ᛶࡀ࠶ࡿࡇࢆ♧၀ࡍࡿࡶࡢ࠸࠼ࡼ࠺ࠋ
4㸬࠾ࢃࡾ
ᮏ✏࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢỈᖹⓗ㈈ᨻ➇த╔┠ࡋ㸪බമᡶ࠸ࡢቑຍࡶຍ㏿ࡀணࡉࢀࡿᆅ ᪉ᨻᗓࡢ㈈ᨻᘓ㸦ṓධቑ࣭ṓฟῶ㸧ࡢྲྀࡾ⤌ࡳࡀ㸪㈈ᨻ➇தࡢᣑࡼࡗ࡚ᙳ㡪ࢆཷࡅࡓྰࢆ㸪᪥ ᮏࡢ⮬యࡢࢹ࣮ࢱࢆࡶᐇドⓗᡭἲࢆ⏝࠸᳨࡚ドࡋࡓࠋලయⓗࡣ㸪1975㹼2009 ᖺᗘ࠾ࡅࡿ 47 㒔 㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമᡶ࠸㈝ἲேᴗ⛯ᖹᆒ⛯⋡㸪࠾ࡼࡧᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧 ࡢ㛵ಀࡀ㸪㈨ᮏ⛣ືୗ࠾ࡅࡿ⛒⛯➇த࠾ࡼࡧᨭฟ➇தᣑࡢᙳ㡪ࢆཷࡅ࡚ኚࡍࡿྰࢆᐇドศᯒ ࡋࡓࠋ ᐇドศᯒࡽ㸪௨ୗࡢ 2 Ⅼࡀ᫂ࡽ࡞ࡗࡓࠋ➨ 1 㸪බമ㈝ඖൾ㑏㔠ࡢಀᩘࡀ㸪⿕ㄝ᫂ኚᩘࢆἲே ᴗ⛯ᖹᆒ⛯⋡ࡍࡿ᥎ᐃ⤖ᯝ࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡢᮇ㛫ࡢࡳࣉࣛࢫ࡛᭷ព㸪⿕ㄝ᫂ኚᩘࢆᇶ♏ⓗṓ ฟࡍࡿ᥎ᐃ⤖ᯝ࠾࠸࡚㸪ࡍ࡚ࡢࢧࣥࣉࣝᮇ㛫࡛࣐ࢼࢫ࡛᭷ព࡞ࡗࡓࡇࡽ㸪㒔㐨ᗓ┴ࡣබമ ᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ἲேᴗ⛯⋡ࡢᘬࡁୖࡆࡼࡾࡣᇶ♏ⓗṓฟࡢῶᑡࡼࡗ࡚㸪ண⟬ไ⣙ࢆ‶ ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࠶ࡾ㸪ࡑࡢഴྥࡣ㏆ᖺᙉࡲࡗ࡚࠸ࡿ࠸࠺ࡇ࡛࠶ࡿࠋ ➨ 2 㸪Ẹ㛫㈨ᮏ⛣ືࡀపㄪࡔࡗࡓ๓ᮇ㸦1975㹼1995 ᖺᗘ㸧άⓎࡔࡗࡓᚋᮇ㸦1996㹼2009 ᖺᗘ㸧࡛ࢧ ࣥࣉࣝࢆศࡋ㸪㈨ᮏ⛣ືୗࡢ⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑࡀ㸪㒔㐨ᗓ┴ࡢ㈈ᨻᘓ࠼ࡓᙳ㡪ࢆ᳨ ドࡋࡓࡇࢁ㸪ᚋᮇࡢࢧࣥࣉࣝᮇ㛫ࡘ࠸࡚ࡢࡳ㸪ἲேᴗ⛯ᖹᆒ⛯⋡ࢆ⿕ㄝ᫂ኚᩘࡍࡿሙྜࡣ㸪බ മ㈝ඖൾ㑏㔠ࡢಀᩘ㸦β1㸧ࡀࣉࣛࢫ㸪බമ㈝ඖൾ㑏㔠㈨ᮏ⛣ືᣦᶆࡢಀᩘ㸦β2㸧ࡀ࣐ࢼࢫ㸪ᇶ ♏ⓗṓฟࢆ⿕ㄝ᫂ኚᩘࡍࡿሙྜࡣ㸪බമ㈝ඖൾ㑏㔠ࡢಀᩘ㸦β1㸧㸪බമ㈝ඖൾ㑏㔠㈨ᮏ⛣ືᣦᶆ ࡢಀᩘ㸦β2㸧ࡀࡶ࣐ࢼࢫ࡞ࡗࡓࡇࡽ㸪⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣ ㏆ᖺ㸪ἲேᴗ⛯⋡ࡢᘬࡁୖࡆᾘᴟⓗ࡞ࡗࡓ㸦ᇶ♏ⓗṓฟࡢῶᑡ✚ᴟⓗ࡞ࡗࡓ㸧࠸࠺ࡇ࡛࠶ ࡿࠋ ୍㐃ࡢᐇドศᯒࡼࡗ࡚㸪⛒⛯➇தࡸᨭฟ➇தࡀබമࡢᡶ࠸㈝ቑຍࡼࡿ⛯ቑຍࡢຠᯝࢆῶࡌ㸪ᇶ ♏ⓗṓฟῶᑡࡢຠᯝࢆቑࡍࡋࡓ 2 ⠇ࡢ⌮ㄽⓗᖐ⤖ࡣ㸪᭱㏆ᖺ࠾࠸࡚ࡣᨭᣢࡉࢀࡿࡇࡀ᫂ࡽ࡞ࡗ ࡓࠋᮏ✏ࡢᐇドศᯒࡣ㸪Ẹ㛫㈨ᮏ⛣ືࡀάⓎࡋࡓ 1990 ᖺ௦ࡢ༙ࡤ௨㝆㸪㒔㐨ᗓ┴ࡣ⛒⛯➇தࡸᨭฟ➇த ࡢᙳ㡪ᑐࡍࡿᠱᛕࡽ㸪⛯⋡ࡢᘬࡁୖࡆࢆ㏻ࡌࡓ㈈ᨻࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓྍ⬟ᛶࡀ㧗࠸୍᪉㸪 ṓฟῶࢆ㏻ࡌࡓ㈈ᨻࡢྲྀࡾ⤌ࡳࢆάⓎࡉࡏࡓྍ⬟ᛶࡀ㧗࠸ࡇࢆ♧၀ࡍࡿࡶࡢ࠸࠼ࡼ࠺ࠋ ᭱ᚋ㸪ᮏ✏ṧࡉࢀࡓㄢ㢟ࡘ࠸࡚㸪3 Ⅼᣦࡋ࡚࠾ࡁࡓ࠸ࠋ➨ 1 㸪ࣔࢹࣝࡢ๓ᥦࡘ࠸࡚࡛࠶ࡿࠋ ᮏ✏࡛ࡣ㸪Krogstrup㸦2002㸧ྠᵝ㸪⌮ㄽศᯒࡢ༢⣧ࡢࡓࡵ㸪ᐃᖖ≧ែ࠾࠸࡚ඛỴࡉࢀࡓබമỈ‽ ࢆ๓ᥦ㸪㈈ᨻ➇தࡢᙳ㡪ࡀ⪃ᐹࡉࢀ࡚࠸ࡿࠋࡋࡋඛ⾜ࡍࡿ⌮ㄽศᯒ࡛ࡣ㸪ᆅ᪉ᨻᗓࡀ㈨ᮏ⛯⋡බമ Ⓨ⾜࠸࠺ 2 ࡘࡢᨻ⟇ኚᩘࢆྠỴᐃࡍࡿࣔࢹࣝࡀ๓ᥦ࡞ࡗ࡚࠸ࡿࠋ⌧≧࡛ࡣ㸪බമⓎ⾜ࡽ㈨ᮏ⛯⋡ ࡸබඹ㈈౪⤥ࡢ୍᪉ྥࡢᙳ㡪ࡋ⪃៖ࡉࢀ࡚࠸࡞࠸ࠋࡇࡢⅬࡘ࠸࡚ࡣ㸪ࡉࡽ࡞ࡿᨵၿࢆᶍ⣴ࡋࡓ࠸ࠋ㸫㸫 ➨ 2 㸪ࣛࢢࡁෆ⏕ኚᩘࢆྵࡴ᥎ᐃࣔࢹࣝࡢᣑᙇࡘ࠸࡚࡛࠶ࡿࠋ⿕ㄝ᫂ኚᩘ࡞ࡗ࡚࠸ࡿἲே ᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟࡣ㸪ㄝ᫂ኚᩘࡋ࡚ᐃࡋࡓࡶࡢ௨እ㸪๓ᮇࡢࡑࢀ⮬㌟ࡢ್ࡽࡶᙳ㡪 ࢆཷࡅࡿྍ⬟ᛶࡀ࠶ࡿ⪃࠼ࡽࢀࡿࠋ≉㸪ᇶ♏ⓗṓฟࡘ࠸࡚ࡣ㸪ண⟬࠾ࡅࡿቑศ⩏ࡢᙳ㡪ࢆཷࡅ ࡸࡍ࠸⪃࠼ࡽࢀ㸪Arellano-Bond ࡢ 2 ẁ㝵᧯సኚᩘἲࡸ Blundell-Bond ࡢࢩࢫࢸ࣒ GMM ➼ࡢࢲࢼ࣑ࢵ ࢡ࣭ࣃࢿ࡛ࣝࡢ᥎ᐃࢆヨࡳࡿᚲせࡀ࠶ࡿࠋࡇࡢⅬࡘ࠸࡚ࡣ㸪ᚋࡢㄢ㢟ࡋ࡚ྲྀࡾ⤌ࡳࡓ࠸ࠋ ➨ 3 㸪ᅇᖐศᯒ࠾ࡅࡿከ㔜ඹ⥺ᛶࡢၥ㢟ࡘ࠸࡚࡛࠶ࡿࠋㄝ᫂ኚᩘ࠶ࡆࡽࢀ࡚࠸ࡿኚᩘࡣ㸪࠸ࡎ ࢀࡶṓධ࣭ṓฟ㛵㐃ࡋࡓࢹ࣮ࢱ࡛࠶ࡾ㸪ኚᩘ㛫࡛ከ㔜ඹ⥺ᛶࡢⓎ⏕ࡀᠱᛕࡉࢀࡿࠋ௬ㄝࡢ᳨ド࠾࠸࡚㸪 ࡸࡴࢆᚓ࡞࠸ᐃᘧ࡛ࡣ࠶ࡿࡀ㸪ከ㔜ඹ⥺ᛶࡢࢳ࢙ࢵࢡ㸪ࡑࢀࡢ⤫ィⓗᑐฎࡼࡗ࡚㸪᥎ᐃ⤖ᯝࡢ㡹 ᙉᛶࢆ☜ㄆࡍࡿᚲせࡀ࠶ࡿࠋࡇࡢⅬࡘ࠸࡚ࡶ㸪ࡉࡽ࡞ࡿᨵၿࢆ┠ᣦࡋ࡚ྲྀࡾ⤌ࡳࡓ࠸ࠋ Appendix A ㈨ᮏ⛣ືୗ࡛ࡢ
,
d
pρ
τ
∂
∂
d
g
pρ
∂
∂
ࡢᑟฟ (3) ᘧ㸪(4) ᘧࢆไ⣙㸪(2) ᘧࢆ᭱ࡍࡿၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡼࡾ㸪௨ୗࢆᚓࡿࠋ)
,
(
)
,
(
)
1
(
p p p x p p p g p ku
x
g
=
u
x
g
− ε
㸦A-1㸧 㸦A-1㸧ᘧࢆᚤศࡍࡿ㸪௨ୗࢆᚓࡿࠋ p p p p p x p p p p p p p p x p p p p p g p p p p p p p p g p k p g p p p k p kd
x
x
u
d
d
d
g
d
g
g
u
d
x
x
u
d
d
d
g
d
g
g
u
u
d
τ
τ
ρ
ρ
τ
τ
τ
τ
ρ
ρ
τ
τ
ε
τ
τ
ε
ε
∂
∂
∂
∂
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
∂
∂
+
∂
∂
∂
∂
=
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
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∂
∂
∂
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
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1
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0 㸦A-2㸧=
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∂
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p p g p p xx
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1
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p pd
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p p pk
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∂
τ
ࡼࡾ㸪㸦A-2㸧ࡣ௨ୗࡢࡼ࠺ᩚ⌮ࡉࢀࡿࠋ p p gg p k p p g p p k p k p p xx p k kk p p p gg p ku
k
u
d
u
d
d
f
k
u
τ
ε
ρ
τ
ε
ε
ε
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1 1=
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⎩
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⎧
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∂
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+
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+
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⎞
⎜⎜⎝
⎛
+
−
− − 㸦A-3㸧 (9)㸪(10)㸪(11) ᘧࢆ⏝࠸࡚㸪㸦A-3㸧ࢆᩚ⌮ࡍࡿ㸪௨ୗࢆᚓࡿࠋ㸫㸫
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1 p m p g p x p k p p g p g p p m p k p k p p xx p k p p k p gg p k p gg p k p pk
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k
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⎭
⎬
⎫
⎩
⎨
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⎞
⎜⎜⎝
⎛ −
−
−
+
−
+
−
−
−
=
− 㸦A-4㸧 (4) ᘧࡼࡾ㸪−
1
∂
∂
⎟⎟⎠
⎞
⎜⎜⎝
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∂
+
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=
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∂
p p p kk p p p p p p p p pd
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d
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τ
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τ
࡛࠶ࡿࡇࡽ㸪1
)
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1
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1
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−
+
+
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⎞
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+
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p m p g p x p g p m p g p x p k p p g p kk p p pk
k
f
d
d
dg
ε
ε
ε
ε
ε
ε
ε
ε
ε
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㸦A-5㸧 ࡞ࡿࠋ Appendix B ㈨ᮏ㠀⛣ືୗ࡛ࡢ,
d
nρ
τ
∂
∂
d
g
nρ
∂
∂
ࡢᑟฟ (3)’ ᘧ㸪(4) ᘧࢆไ⣙㸪(2) ᘧࢆ᭱ࡍࡿၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡼࡾ㸪௨ୗࢆᚓࡿࠋ)
,
(
)
,
(
n n n x n n n gx
g
u
x
g
u
=
㸦B-1㸧 㸦B-1㸧ᘧࢆᚤศࡍࡿ㸪௨ୗࢆᚓࡿࠋ n n n n n x n n n n n n n n x n n n n n g n n n n n n n n gd
x
x
u
d
d
d
g
d
g
g
u
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x
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d
d
d
g
d
g
g
u
τ
τ
ρ
ρ
τ
τ
τ
τ
ρ
ρ
τ
τ
∂
∂
∂
∂
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
∂
∂
+
∂
∂
∂
∂
=
∂
∂
∂
∂
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
∂
∂
+
∂
∂
∂
∂
㸦B-2㸧,
0
=
∂
∂
=
∂
∂
n n g n n xx
u
g
u
,
n n nk
g
=
∂
∂
τ
∂
=
−
1
,
∂
n nd
g
ρ
n n nk
x
=
−
∂
∂
τ
ࡼࡾ㸪㸦B-2㸧ࡣ௨ୗࡢࡼ࠺࡞ࡿࠋ n n gg p n n xx n n ggk
u
k
d
u
d
d
u
+
)
τ =
ρ
(
㸦B-3㸧 (14)㸪(15) ᘧࢆ⏝࠸࡚㸪㸦B-3㸧ࢆᩚ⌮ࡍࡿ㸪௨ୗࢆᚓࡿࠋ㸫㸫
)
(
n g n x n n g n n xx n n gg n gg p pk
k
u
k
u
u
d
d
d
ε
ε
ε
ρ
τ
+
=
+
=
㸦B-4㸧 (4) ᘧ࠾ࡼࡧ㸦B-4㸧ᘧࡼࡾ㸪1
1
−
+
=
−
∂
∂
=
∂
∂
+
∂
∂
∂
∂
=
∂
∂
n g n x n g p p n n n n n n n n nd
k
d
g
d
g
g
ε
ε
ε
ρ
τ
ρ
ρ
τ
τ
τ
㸦B-5㸧 ࡞ࡿࠋ㸫㸫
ཧ⪃ᩥ⊩
Batina, R.G.㸦2009㸧“Local capital tax competition and coordinated tax reform in an overlapping generations economy,” Regional Science and Urban Economics, Vol.39, pp.472-478.
Bucovetsky, S.㸦1991㸧“Asymmetric tax competition,” Journal of Urban Economics, Vol.30, pp.167-181.
Jensen, R. and E. F. Toma.㸦1991㸧“Debt in a model of tax competition,” Regional Science and Urban Economics, Vol.21, pp.371-391.
Krogstrup, S.㸦2002㸧“Public debt asymmetries : The effect on taxes and spending in the European Union,” European Central Bank, Working paper No.162.
Matsumoto, M.㸦2011㸧“Strategic debt/surplus policy under vertical fiscal competition, ” The Ritsumeikan Economic Review, Vol.59, No.6, pp.665-682.
Perron, P.㸦1989㸧“The great crash, the oil price shock and the unit hypothesis,”Econometrica No.57, pp.1361-1401. Wilson, J.D.㸦1986㸧“A theory of inter-regional tax competition,” Journal of Urban Economics, Vol.19, pp.296-315. Zodrow, R.G. and P. Mieszkowski.㸦1986㸧“Pigou, tiebout, property taxation, and the underprovision of local public
goods, ”Journal of Urban Economics, Vol.19, pp.356-370.
ᓥ⪃࣭ᅧᓮ⛱࣭Ⳣཎᏹኴ㸦2008㸧ࠕᅛᐃ㈨⏘⛯ࡢᅵᆅホ౯࠾ࡅࡿ⮬య㛫┦౫Ꮡࡢᐇドศᯒࠖ㸪ࠗឡ ▱Ꮫ⤒῭ㄽ㞟࠘No.176㸪pp.1-19. ῝ᑿிྖ࣭ᓅᕼ᫂㸦2000㸧ࠕᡓᚋ᪥ᮏᅜෆ࠾ࡅࡿ⤒῭᮰⏕⏘せ⣲ᢞධ㸫ࢯ࣮ࣟᡂ㛗ࣔࢹࣝࡣ㐺⏝࡛ࡁ ࡿ㸫ࠖ㸪ࠗ⤒῭◊✲࠘Vol.51㸪No.2㸪pp.136-151. ῝⃝ᫎྖ㸦2009㸧ࠕᡃࡀᅜࡢᆅ᪉ἲேㄢ⛯ࢆࡵࡄࡿ⛒⛯➇த㸫ἲேᴗ⛯ࢆᑐ㇟ࡋࡓ⌧≧ศᯒ㸫ࠖ㸪ࠗࣞࣇ ࣞࣥࢫ࠘No.703㸪pp.55-75.
