ㄽ ᩥ

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⤥ࢆᘬࡁ㉳ࡇࡍࡇ࡜ࢆ♧ࡋࡓ Zodrow and Mieszkowski㸦1986㸧
㸪Wilson㸦1986㸧ࡽࡢ㈨ᮏ⛯➇தࣔࢹࣝࡣ㸪⌮ㄽ࣭ᐇド୧㠃࠿ࡽᵝࠎ࡞᪉ྥ࡟ᣑᙇࡉࢀ࡚ࡁࡓࠋᑡᩘὴ࡞ࡀࡽ㸪ᨻᗓࡀ᧯సྍ⬟࡞ᨻ⟇ኚᩘ࡜ࡋ࡚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㉁ᑠᆅᇦ࠿ࡽ࡞ࡿᆅ᪉ᨻᗓ㛫ࡢỈᖹⓗ㈨ᮏ⛯➇தࣔࢹࣝࢆ㸪බമⓎ⾜ࢆ⤌ࡳධࢀࡓ 2 ᮇ㛫ࣔࢹࣝ࡟ᣑᙇࡋ㸪බമⓎ⾜ୗ࡛ࡢ㈨ᮏ⛯➇தࡢ⌮ㄽⓗᖐ⤖ࢆゎ᫂ࡋ࡚࠸ࡿࠋࡇࢀ࡟ࡼࡿ࡜㸪୧ᆅ᪉ᨻᗓࡢ཯ᛂ㛵ᩘࡢഴࡁࡀṇ࡛࠶ࢀࡤ㸪ᆅ᪉ᨻᗓࡣ㸦2 ᮇ┠ࡢ┦ᡭࡢ㈨ᮏ⛯⋡ࢆᘬࡁୖࡆࡿࡓࡵ࡟㸧
㸪㈈ᨻ㉥Ꮠࡢᣑ኱ࢆᚿྥࡍࡿࡇ࡜ࡀ♧ࡉࢀ࡚࠸ࡿࠋ
Matsumoto㸦2011㸧࡛ࡣ㸪Jensen and Toma㸦1991㸧࡜ྠࡌࡃබമⓎ⾜ࢆ⤌ࡳධࢀࡓ 2 ᮇ㛫ࣔࢹࣝࢆ᥇⏝ࡋࡘࡘࡶ㸪ᆅ᪉ᨻᗓྠኈ࡛ࡣ࡞ࡃ㸪୰ኸᨻᗓ࡜ᆅ᪉ᨻᗓ㛫ࡢᆶ┤ⓗ㈨ᮏ⛯➇தࣔࢹࣝࢆ⏝࠸࡚㸪බമⓎ⾜ୗ࡛ࡢ㈨ᮏ⛯➇த࡟ࡘ࠸࡚⌮ㄽศᯒࡋ࡚࠸ࡿࠋㄢ⛯࣮࣋ࢫࡀ㔜」ࡍࡿᆶ┤ⓗ㈨ᮏ⛯➇தࣔࢹ࡛ࣝࡣ㸪஫࠸࡟┦ᡭࡢ㈨ᮏ⛯⋡ᘬࡁୗࡆࢆ⏬⟇ࡍࡿ⤖ᯝ㸪୧ᆅ᪉ᨻᗓࡢ཯ᛂ㛵ᩘࡢഴࡁࡀṇ࡛࠶ࢀࡤ㸪୰ኸᨻᗓ࠾ࡼࡧᆅ
᪉ᨻᗓࡣ㸪㈈ᨻవ๫ࡢᣑ኱ࢆᚿྥࡍࡿ࡜ࡋ㸪Jensen and Toma㸦1991㸧࡜␗࡞ࡿ⌮ㄽⓗᖐ⤖ࢆᑟࡁฟࡋ࡚࠸ࡿࠋ㈈ᨻ➇தࣔࢹࣝࡢ⌧ᐇ㐺⏝ᛶࢆ㧗ࡵࡿୖ࡛㸪ྠ㉁ᆅᇦࡢ᝿ᐃࡸ㈨ᮏ౪⤥୍ᐃࡢ௬ᐃࢆ⦆ࡵࡿࡇ࡜࡟ຍ࠼
1㸧㸪බമⓎ⾜ࡢྍ⬟ᛶࢆ⪃៖ࡍࡿࡇ࡜ࡣ㸪㔜せ࡞どⅬ࡛࠶ࡿࠋࡋ࠿ࡋ࡞ࡀࡽ㸪ᆅᇦ㛫ࡢ㠀ᑐ⛠ᛶࡸ㈨ᮏ⵳

∗1967 ᖺ⏕ࡲࢀࠋ1998 ᖺ኱㜰኱Ꮫ኱Ꮫ㝔ᅜ㝿බඹᨻ⟇◊✲⛉༤ኈ๓ᮇㄢ⛬ಟ஢ࠋ2000 ᖺྠ◊✲⛉༤ኈᚋᮇㄢ⛬ಟ஢ࠋ༤ኈ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ᢥᏛ఍࡟ᡤᒓࠋE-Mail: hitanaka@mail.doshisha.ac.jp URL: http://www.cam.hi-ho.ne.jp/thiroki/1㸧౛࠼ࡤ㸪๓⪅ࢆᑐ㇟࡜ࡍࡿ௦⾲ⓗ࡞⌮ㄽศᯒ࡜ࡋ࡚㸪Bucovetsky㸦1991㸧ࡀ㸪ᚋ⪅ࢆᑐ㇟࡜ࡍࡿ௦⾲ⓗ࡞⌮ㄽศᯒ࡜ࡋ࡚㸪Batina㸦2009㸧ࡀ࠶ࡿࠋ㸫㸫

఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧✚ࢆ⪃៖ࡋࡓ㈨ᮏ⛯➇தࡢ◊✲࡟ẚ࡭ࡿ࡜㸪බമⓎ⾜ࢆ⤌ࡳධࢀࡓ◊✲ࡢ⵳✚ࡣஈࡋ࠸ࠋ୺࡟㸪཯ᛂ㛵ᩘࢆ᥎ᐃࡍࡿࡇ࡜࡛㸪㈨ᮏ⛯➇தࡢ᭷↓ࢆ᳨ドࡋࡓᐇドศᯒ࡟࠾࠸࡚ࡣ㸪බമⓎ⾜ࢆ๓ᥦ࡜ࡋ࡞࠸ Zodrow andMieszkowski㸦1986㸧
㸪Wilson㸦1986㸧ࡽࡢ⌮ㄽࣔࢹࣝࡀ᝿ᐃࡉࢀ࡚࠸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㉳ࡇࡍࡇ࡜ࢆ㸪EU ㅖᅜࡢࣃࢿࣝࢹ࣮ࢱ⏝࠸࡚㸪ᐇドⓗ࡟♧ࡋ࡚࠸ࡿࠋ᪥ᮏ࡟࠾࠸࡚㸪Ỉᖹⓗ⛒⛯➇தࢆᢅࡗࡓᐇド◊✲࡟ࡣ㸪኱ᓥ࣭ᅧᓮ࣭Ⳣཎ㸦2008㸧㸪῝⃝㸦2009㸧➼ࡀ࠶ࡿࡀ㸪බമⓎ⾜ࢆ๓ᥦ࡜ࡋࡓࣔࢹ࡛ࣝࡢ
⛒⛯➇தࡢ᳨ドࡲ࡛࡟ࡣ⮳ࡗ࡚࠸࡞࠸ࠋ
ᮏ✏࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢỈᖹⓗ㈈ᨻ➇த࡟╔┠ࡋ㸪බമ฼ᡶ࠸ࡢቑຍ࡜࡜ࡶ࡟ຍ㏿໬ࡀண᝿ࡉࢀࡿᆅ
᪉ᨻᗓࡢ㈈ᨻ෌ᘓ㸦ṓධቑ࣭ṓฟῶ㸧ࡢྲྀࡾ⤌ࡳࡀ㸪⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑ኱࡟ࡼࡗ࡚ᙳ㡪ࢆཷࡅࡓ࠿ྰ࠿ࢆ㸪᪥ᮏࡢ⮬἞యࡢࢹ࣮ࢱࢆࡶ࡜࡟ᐇドⓗᡭἲࢆ⏝࠸᳨࡚ドࡍࡿࠋලయⓗ࡟ࡣ㸪1975㹼2009 ᖺᗘ࡟࠾ࡅࡿ 47 㒔㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമ฼ᡶ࠸㈝࡜ἲே஦ᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧබമ฼ᡶ࠸㈝࡜
ᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧࡜ࡢ㛵ಀࡀ㸪Ẹ㛫㈨ᮏ⛣ືᣑ኱ࡢᙳ㡪ࢆཷࡅ࡚ኚ໬ࡍࡿ࠿ྰ࠿ࢆᐇドศᯒࡍࡿࠋ
ᮏ✏ࡢᵓᡂࡣ㸪௨ୗࡢ࡜࠾ࡾ࡛࠶ࡿࠋ➨ 2 ⠇࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢ㈈ᨻ➇தࣔࢹࣝࢆᵓ⠏ࡋ㸪
㸦㈨ᮏ⛣ື
ࢆㄏⓎࡍࡿ㸧㈈ᨻ➇தࡢᣑ኱࡟ࡼࡗ࡚㸪බമ฼ᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯⋡࠾ࡼࡧ㈈ᨻᨭฟ࡟୚࠼ࡿᙳ㡪࡟㐪࠸ࡀ⏕ࡌ࠺ࡿࡇ࡜ࢆ♧ࡍࠋ➨ 3 ⠇࡛ࡣ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝࢆ㋃ࡲ࠼㸪බമ㈝ඖ฼ൾ㑏㔠ࢆ㒔㐨ᗓ┴ࡢἲே஦ᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧࡟ᅇᖐࡉࡏࡿࡇ࡜࡛㸪㒔㐨ᗓ┴ࡢ㈈ᨻ෌ᘓࡢྲྀࡾ⤌ࡳ࡟ᑐ
ࡍࡿ㈈ᨻ➇தࡢᙳ㡪ࢆᐇドศᯒࡍࡿࠋ➨ 4 ⠇࡛ࡣ㸪ᮏ✏ࡢ⤖ㄽࢆせ⣙ࡋ㸪ṧࡉࢀࡓㄢ㢟ࢆᣦ᦬ࡍࡿࠋ

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⛒⛯➇தࡢᣑ኱࡟ࡼࡗ࡚㸪බമ฼ᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯⋡࠾ࡼ
ࡧ㈈ᨻᨭฟ࡟୚࠼ࡿᙳ㡪࡟㐪࠸ࡀ⏕ࡌ࠺ࡿࡇ࡜ࢆ♧ࡍࠋ ྠ㉁ N ᆅᇦ࠿ࡽᵓᡂࡉࢀࡿ⤒῭ࢆ᝿ᐃࡍࡿࠋྛᆅᇦࡢ௦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ࡢࡶ࡜࡛㸪⚾ⓗ㈈ x ࢆ⏕⏘ࡍࡿࠋࡓࡔࡋ㸪 f(k) ࡣ㸪fk >0㸪fkk <0㸪fkkk =0 ࢆ‶ࡓࡍࡶࡢ࡜ࡍࡿࠋ ྛᆅᇦࡢ௦⾲ⓗᐙィࡣ㸪⛯ᘬࡁᚋࡢ㈨ᮏ཰┈⋡ ρ ࢆ⪃៖ࡋ㸪⮬ࡽࡢ㈓⵳ k ࢆ㸪⮬ᆅᇦ࡬ࡢᢞ㈨ k ࠾ࡼࡧ௚ᆅᇦ࡬ࡢᢞ㈨ kത㸫k ࡟᣺ࡾྥࡅࡿࠋ⛯ᘬࡁᚋࡢ㈨ᮏ཰┈⋡ ρ ࡣ㸪㈨ᮏᕷሙ࡟࠾ࡅࡿ⿢ᐃࡢ⤖ᯝ㸪ࡍ࡭࡚ࡢᆅᇦ୍࡛⮴ࡋ㸪ρ = fk − τ(1)ࢆ‶ࡓࡍỈ‽࡟Ỵࡲࡿࠋࡓࡔࡋ㸪 τ ࡣᆅ᪉ᨻᗓࡀẸ㛫㈨ᮏ࡟ㄢࡍ㈨ᮏ⛯⋡࡛࠶ࡿࠋᐙィࡣ㸪⚾ⓗ㈈ x ࠾ࡼࡧබඹ㈈ g ࡼࡾຠ⏝ࢆᚓࡿ࡜௬ᐃࡍࡿࠋࡇࢀࡼࡾ㸪௦⾲ⓗᐙィࡢຠ⏝㛵ᩘࡣ㸪

u = u (x, g )(2)࡛♧ࡉࢀࡿࠋࡓࡔࡋ㸪 u ࡣ㸪 ux 㸪ug >0㸪uxx 㸪ugg <0㸪uxg 㸪ugx =0 ࢆ‶ࡓࡍࡶࡢ࡜ࡍࡿࠋຍ࠼࡚㸪ᐙィࡣ㸪㸫㸫

බമⓎ⾜ୗࡢ㈈ᨻ➇த⮬ᆅᇦ㸪௚ᆅᇦࡑࢀࡒࢀࡢᢞ㈨࠿ࡽ཰┈ࢆᚓࡿࡢ࡛㸪ᐙィࡢண⟬ไ⣙ᘧࡣ㸪

x = f (k ) − f k k + ρk

(3)

࡜࡞ࡿࠋ
 ྛᆅᇦࡢᆅ᪉ᨻᗓࡣ㸪㈨ᮏ⛯⋡ τ ࡛Ẹ㛫㈨ᮏ࡟ㄢ⛯ࡋ㸪㐣ཤࡢබമ࡟ᑐࡍࡿ฼ᡶ࠸ ρd ࡜බඹ㈈ g ࡢᨭฟ࡟᣺ࡾྥࡅࡿࠋࡇࡢ᫬㸪ᆅ᪉ᨻᗓࡢண⟬ไ⣙ᘧࡣ㸪௨ୗ࡛♧ࡉࢀࡿࠋτk = g + ρ d(4) ᆅ᪉ᨻᗓࡣ㸪(3) ᘧ㸪(4) ᘧࢆไ⣙࡟㸪(2) ᘧࢆ᭱኱໬ࡍ࡭ࡃ㸪㈨ᮏ⛯⋡τ ࢆỴᐃࡍࡿࠋࡇࡢ᭱኱໬ၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡣ㸪௨ୗ࡛୚࠼ࡽࢀࡿࠋ

u g ( x, g )u x ( x, g )= mcpf > 1(5)

ࡇࡇ࡛㸪mcpf=1⁄(1㸫εk ) ࡣබⓗ㈨㔠ࡢ㝈⏺㈝⏝ࢆ㸪εk ࡣẸ㛫㈨ᮏ㟂せࡢ฼Ꮚᙎຊᛶࢆ⾲ࡍࠋ࠸ࡲ௬࡟㸪㈨ᮏ⛯⋡ࢆࡵࡄࡿᆅ᪉ᨻᗓ㛫࡛ࡢ➇தࡀ㸪Ẹ㛫㈨ᮏ⛣ືࢆᘬࡁ㉳ࡇࡉ࡞࠸㸦k=kത 㸧࡜ࡋࡓሙྜ㸪(1) ᘧࡼࡾ(3) ᘧࡣ௨ୗࡢࡼ࠺࡟᭩ࡁ᥮࠼ࡽࢀࡿࠋ

x = f (k ) − τk(3)’ ࡇࡢ᫬㸪ᆅ᪉ᨻᗓࡣ㸪(3)’ ᘧ㸪(4) ᘧࢆไ⣙࡟㸪(2) ᘧࢆ᭱኱໬ࡍࡿࡼ࠺㸪㈨ᮏ⛯⋡ τ ࢆỴᐃࡍࡿࠋࡇࡢ
᭱኱໬ၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡣ㸪௨ୗࡢ࡜࠾ࡾ࡜࡞ࡿࠋ

u g (x, g )u x ( x, g )= 1                  (6)1 㝵ࡢ᮲௳ࢆẚ㍑ࡍࡿࡇ࡜࡟ࡼࡾ㸪㈨ᮏ⛯➇த࡟ࡼࡾ㈨ᮏ⛣ືࡀㄏⓎࡉࢀࡿ≧ἣୗ࡛ࡣ㸪㈨ᮏ⛣ືࡀㄏ
Ⓨࡉࢀ࡞࠸≧ἣ࡟ẚ࡭࡚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Ⓨ⏕ࡍࡿࡇ࡜ࡀࢃ࠿ࡿࠋ බമ฼ᡶ࠸ࡢỈ‽ࡀ㈨ᮏ⛯཰࠾ࡼࡧ㈈ᨻᨭฟ࡟୚࠼ࡿᙳ㡪ࡣ㸪(5) ᘧ㸪(6) ᘧࢆࡑࢀࡒࢀ඲ᚤศࡍࡿࡇ࡜
࡛ồࡵࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡍ࡞ࢃࡕ㸪(5) ᘧࢆ඲ᚤศࡢୖ㸪ᘧࢆᩚ⌮ࡍࡿ࡜㸪௨ୗࡢ೫ᚤಀᩘࢆᚓࡿ2㸧ࠋ

ε gp
∂τ p
= p
>0
k (1 − ε kp )( ε xp + ε gp + ε mp )∂ρd2㸧ᑟฟࡣ㸪Appendix A ࢆཧ↷ࠋ㸫㸫   (7)఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧

ε gp
∂g p
=
−1< 0   ∂ ρ d (ε xp + ε gp + ε mp )pp

          (8)

p

p

p

p

ࡓࡔࡋ㸪 εx 㸪εg 㸪εm ࡣ㸪ࡑࢀࡒࢀ௨ୗ࡛♧ࡉࢀࡿ࡜࡜ࡶ࡟㸪ຠ⏝᭱኱໬ࡢ 2 㝵ࡢ᮲௳ࡼࡾ εx +εg +εm >0 ࡛
࠶ࡿࠋ

ε

p
x

ε

p
g

∂ u xp τ p
u xxp p p=
= − p k τ > 0                ∂ τ p u xp
ux=−

ε mp = −∂ u gp τ p∂ τ p u gp

=−

u ggp
u gp

k pτ p (1 − ε kp ) > 0            

(9)

(10)

f ⎤
∂ mcpf τ p
ε kp ⎡=
1 + ε kp + ε kp k p kkk ⎥ > 0      (11)p ⎢p
f kk ⎦∂τ1− εk ⎣mcpf

 ྠᵝ࡟㸪(6) ᘧࢆ඲ᚤศࡋ㸪ᘧࢆᩚ⌮ࡍࡿ࡜㸪௨ୗࡢ೫ᚤಀᩘࢆᚓࡿ3㸧ࠋ

ε gn
∂τ n
=
>0
k (ε xn + ε gn )
∂ρd

(12)

n

εg
∂g n
= n
−1 < 0   ∂ρd(ε x + ε gn )      (13)ࡓࡔࡋ㸪 εnx 㸪εng ࡣ㸪ࡑࢀࡒࢀ௨ୗ࡛♧ࡉࢀࡿࡶࡢ࡜ࡍࡿࠋ

ε xn =εng∂ u xn τ nu xxn n n=−
k τ >0∂ τ n u xn
u xn

=−

∂ u gn τ p
∂τ

n

u

n
g

=−

n
u gg

u

n
g

k nτ n > 0

(14)

(15)

 ࡇࡇ࡛㸪බമ฼ᡶ࠸ࡢỈ‽࡜㈨ᮏ⛯⋡࡜ࡢ㛵ಀ࡟ࡣ㸪(7) ᘧ㸪(12) ᘧࡼࡾṇࡢ㛵ಀࡀ㸪බമ฼ᡶ࠸࡜㈈ᨻᨭฟ࡜ࡢ㛵ಀ࡟ࡣ㸪(8) ᘧ㸪(13) ᘧࡼࡾ㈇ࡢ㛵ಀࡀ࠶ࡿࡇ࡜ࡀࢃ࠿ࡿࠋࡇࢀࡣ㸪ࡍ࡞ࢃࡕ㸪බമ฼ᡶ࠸
ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ᆅ᪉ᨻᗓࡣ㈨ᮏ⛯⋡ࡢୖ᪼ࡸ㈈ᨻᨭฟࡢῶᑡ࡟ࡼࡾ㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋ

3㸧

ᑟฟࡣ㸪Appendix B ࢆཧ↷ࠋ㸫㸫

බമⓎ⾜ୗࡢ㈈ᨻ➇த ࡛ࡣ㸪⛒⛯➇தୗ࡛ࡢබമ฼ᡶ࠸Ỉ‽࡜㈨ᮏ⛯⋡㸪࠾ࡼࡧ㈈ᨻᨭฟ࡜ࡢ㛵ಀࡣ㸪⛒⛯㠀➇தୗ࡛ࡢࡑࢀ
࡜࠸࠿࡞ࡿ㐪࠸ࡀ࠶ࡿࡔࢁ࠺࠿ࠋࡑࢀࡣ㸪(7) ᘧ࡜(12) ᘧࡢ኱ᑠ㛵ಀ㸪࠾ࡼࡧ (8) ᘧ࡜(13) ᘧࡢ኱ᑠ㛵ಀࢆẚ㍑ࡍࡿࡇ࡜࡛⪃ᐹྍ⬟࡛࠶ࡿࠋࡍ࡞ࢃࡕ㸪(7) ᘧ࡜(12) ᘧࡢ኱ᑠࢆẚ㍑ࡍࡿ࡜㸪∂τ p ∂τ n<∂ρ d ∂ρ dif ε xp + ε gp + ε mp > Φ (ε xn + ε gn ) and Φ =u ggp u gn τ p
nu gg
u gp τ n>1(16)ࡀᡂࡾ❧ࡘ4㸧ࠋࡲࡓ㸪(8) ᘧ࡜(13) ᘧࡢ኱ᑠ㛵ಀࢆẚ㍑ࡍࡿ࡜㸪

∂g n
∂g p
<
∂ρ d
∂ρ d

(17)

ࡀᡂࡾ❧ࡘࡇ࡜ࡀࢃ࠿ࡿࠋࡇࢀࡼࡾ㸪⛒⛯➇தࡢᣑ኱࡟ࡼࡾᆅᇦ㛫ࡢ㈨ᮏ⛣ືࡀάⓎ໬ࡍࢀࡤ㸪ᆅ᪉ᨻᗓ
ࡣ㈨ᮏ⛯⋡ᘬࡁୖࡆ࡟ࡼࡿ㈨ᮏ㏨㑊ࢆᅇ㑊ࡋࡼ࠺࡜ࡍࡿࡓࡵ㸪⛒⛯➇தࡀపㄪ࡞ሙྜ࡟ẚ࡭࡚㸪୍ᐃࡢ᮲௳ࡢࡶ࡜࡛ࡣ㸪㈨ᮏ⛯⋡ࡢୖ᪼࡟ᾘᴟⓗ࡜࡞ࡿ୍᪉㸪㈈ᨻᨭฟࡢῶᑡ࡟✚ᴟⓗ࡜࡞ࡿ࡜ุ᩿ࡉࢀࡿࠋࡍ࡞
ࢃࡕ㸪㈨ᮏ⛣ືୗࡢ⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡣ㸪฼ᡶ࠸Ỉ‽ࡢቑຍࡀ㈨ᮏ⛯⋡ࡢୖ᪼ࢆࡶࡓࡽࡍຠᯝࢆῶ
ࡎࡿ᪉ྥ࡟㸪฼ᡶ࠸Ỉ‽ࡢቑຍࡀ㈈ᨻᨭฟࡢῶᑡࢆࡶࡓࡽࡍຠᯝࢆቑࡍ᪉ྥ࡟㸪ࡑࢀࡒࢀస⏝ࡍࡿ࡜⪃࠼ࡽࢀࡿࠋ

3㸬ᐇドศᯒ
ࡇࡇ࡛ࡣ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝࢆ㋃ࡲ࠼㸪බമ฼ᡶ࠸㈝࡜ἲேㄢ⛯㸪࠾ࡼࡧ㈈ᨻᨭฟ࡜ࡢ㛵ಀࡀ㸪㈈ᨻ➇தࡢᙳ㡪ࢆཷࡅࡿࡇ࡜࡛ኚ໬ࡍࡿ࠿ྰ࠿ࢆᐇドศᯒࡍࡿࠋලయⓗ࡟ࡣ 1975㹼2009 ᖺᗘ࡟࠾ࡅࡿ 47 㒔㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമ㈝ඖ฼ൾ㑏㔠ࢆ㒔㐨ᗓ┴ࡢἲே஦ᴗ⛯⋡࡜ᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧࡟ᅇᖐࡉࡏࡿࡇ࡜࡛㸪ࡑࡢᙳ㡪ࢆ᳨ドࡍࡿࠋ௨ୗ㸪ࡲࡎ 3-1 ⠇࡛ࡣ㸪ᐇドศᯒ࡟⏝࠸ࡿࣔࢹࣝࢆ≉ᐃ໬ࡍࡿ࡜࡜ࡶ࡟㸪᥎ᐃ᪉ἲ࡟ࡘ࠸࡚㏙࡭ࡿࠋ3-2⠇࡛ࡣ㸪᥎ᐃ࡟⏝࠸ࡓࢹ࣮ࢱ࡟ࡘ࠸࡚㏙࡭ࡿࠋ3-3 ⠇࡛ࡣ㸪᥎ィ⤖ᯝࢆ᳨ᐃࡢୖ㸪ࡑࡢ⤖ᯝࢆゎ㔘ࡋࡘࡘ㸪ᑟ࠿ࢀࡿᨻ⟇ⓗྵព࡟ࡘ࠸࡚ㄝ᫂ࡍࡿࠋ

3-1 ᥎ᐃࣔࢹࣝࡢ≉ᐃ໬ ㈈ᨻ➇தୗ࡟࠾ࡅࡿබമ㈝ඖ฼ൾ㑏㔠࡜ἲேㄢ⛯㸪࠾ࡼࡧᇶ♏ⓗṓฟ࡜ࡢ㛵ಀࢆ᳨ドࡍࡿࡓࡵ㸪௨ୗࡢࡼ࠺࡞⥺ᙧᅇᖐࣔࢹࣝࢆ᝿ᐃࡍࡿ5㸧ࠋy it = β 1 x it + β 2 m it x it + β 3 z it + ∑ k =1 γ k q itk + λ d t + υ i + ε it
3

(18)

4㸧

୍⯡ⓗ࡟‽⥺ᙧࡢຠ⏝㛵ᩘࢆ௬ᐃࡍࢀࡤ㸪(15) ᘧࡣ‶ࡓࡉࢀࡿࠋ

5㸧

බമ㈝ඖ฼ൾ㑏㔠ࡸ⛣㌿㈈※➼ࡣ㸪ண⟬⦅ᡂ㐣⛬࡟࠾࠸࡚࠿࡞ࡾࡢ⛬ᗘࡑࡢ㢠ࢆண ࡍࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࡇ࡜࠿ࡽ㸪௨ୗࡢ᥎ᐃ࡛ࡣྠ୍ᖺᗘࡢኚᩘྠኈࢆᅇᖐࡋ࡚࠸ࡿࠋ

㸫㸫

఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧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┴ࡢἲே஦ᴗ⛯ᖹᆒ⛯⋡㸪࠾ࡼࡧᇶ♏ⓗṓฟࡢᑐ┴ෆ⥲⏕⏘࡟ᑐࡍࡿẚ⋡ࢆ⾲ࡍࠋㄝ᫂ኚᩘ࡛࠶ࡿxit 㸪zit ࡣࡑࢀࡒࢀ㸪㒔㐨ᗓ┴ࡢබമ㈝ඖ฼ൾ㑏㔠㸪ᅜ࠿ࡽࡢ⛣㌿㈈※ࡢᑐ┴ෆ⥲⏕⏘ẚ⋡ࢆ♧ࡍࠋ mit ࡣ㸪㒔㐨ᗓ┴㛫ࡢẸ㛫㈨ᮏ⛣ືࢆ⾲ࡍᣦᶆ࡛࠶ࡿࠋqkit ࡣ㸪ἲே஦ᴗ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟ࡟ᙳ㡪ࢆ୚࠼࠺ࡿࡑࡢ௚ࡢせᅉ࡛࠶ࡾ㸪ࡇࡇ࡛ࡣྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸪᭷ຠồேಸ⋡㸪⪁ᖺேཱྀẚ⋡ࡢ 3 ࡘࢆ᝿ᐃࡍࡿࠋࡲࡓ㸪
2004㹼2006 ᖺᗘ࡟ᐇ᪋ࡉࢀࡓ୕఩୍యᨵ㠉ࡢຠᯝࢆ⧊ࡾ㎸ࡴࡓࡵ㸪ᕥグ 3 ࣧᖺᗘࢆ 1㸪ࡑࢀ௨እࡢᖺᗘࢆ
0 ࡜ࡍࡿ᫬㛫ࢲ࣑࣮ dt ࢆ᝿ᐃࡍࡿࠋvi ࡣಶయຠᯝࢆ㸪εit ࡣㄗᕪ㡯ࢆ⾲ࡋ㸪 εit ~iid0㸪σε  ࢆ‶ࡓࡍࡶࡢ࡜ࡍ
ࡿࠋ᥎ᐃᮇ㛫ࡣ㸪1975㹼2009 ᖺᗘࡲ࡛ࡢ 35 ᖺ㛫࡛࠶ࡾ㸪㒔㐨ᗓ┴㛫ࡢ␗㉁ᛶࢆ⪃៖ࡋ࡚(18) ᘧࢆࣃࢿࣝศ
ᯒ࡟ࡼࡾ᥎ᐃࡍࡿࠋ㈈ᨻ➇த࡟ࡼࡾㄏⓎࡉࢀࡿẸ㛫㈨ᮏ⛣ືࡢ≧ἣࡢኚ໬ࢆ⧊ࡾ㎸ࡴࡓࡵ㸪඲ࢧࣥࣉࣝᮇ
㛫࡛ࡢ᥎ᐃ࡟ຍ࠼㸪㈨ᮏ⛣ືࡀపㄪࡔࡗࡓ๓ᮇ㸦75㹼95 ᖺᗘ㸧࡜㸪άⓎࡔࡗࡓᚋᮇ㸦96㹼09 ᖺᗘ㸧࡟ࢧࣥࣉࣝࢆศ๭ࡋ㸪ࡑࢀࡒࢀࡢᮇ㛫࡛ࡢ᥎ᐃࡶ࠶ࢃࡏ࡚ᐇ᪋ࡍࡿ6㸧ࠋ ⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢሙྜ㸪⌮ㄽࡼࡾ β1 ࡟ண᝿ࡉࢀࡿ➢ྕࡣṇ㸦㈇㸧࡛࠶ࡿࠋ୍᪉㸪β2 ࡟ࡘ࠸࡚ࡣ㸪⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢሙྜ㸪㈇㸦㈇㸧࡜࡞ࢀࡤ㸪⛒⛯➇தࡀබമࡢ฼
ᡶ࠸㈝ቑຍ࡟ࡼࡿ⛯⋡ୖ᪼ࡢពḧࢆῶࡎࡿ㸦ᇶ♏ⓗṓฟῶᑡࡢពḧࢆቑࡍ㸧᪉ྥ࡟స⏝ࡍࡿ࡜ࡋࡓ 2 ⠇ࡢ⌮ㄽࣔࢹࣝ࡜ᩚྜⓗ࡞⤖ᯝࡀᚓࡽࢀࡓࡇ࡜࡟࡞ࡿࠋࡉࡽ࡟࠸࠼ࡤ㸪ἲே஦ᴗ⛯⋡㸦㈈ᨻᨭฟ㸧ࡢᅇᖐ࡟࠾
࠸࡚㸪ࢧࣥࣉࣝᚋᮇࡢ β1 +β2 ࡢ್ࡀࢧࣥࣉࣝ๓ᮇࡢ β1 +β2 ࡢ್ࢆ⤯ᑐ್࡛ୗᅇࡗࡓ㸦ୖᅇࡗࡓ㸧ሙྜ㸪⛒⛯➇தࡸᨭฟ➇தࡢᣑ኱ࡀ㸪⛯⋡ୖ᪼㸦ᨭฟῶ㸧ࢆ㏻ࡌࡓ㒔㐨ᗓ┴ࡢ㈈ᨻ೺඲໬ࡢྲྀࡾ⤌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࡟⏝࠸ࡓࢹ࣮ࢱ࡟ࡘ࠸࡚㏙࡭࡚࠸ࡇ࠺ࠋ ⿕ㄝ᫂ኚᩘ࡛࠶ࡿ㒔㐨ᗓ┴ࡢἲே஦ᴗ⛯ᖹᆒ⛯⋡ࡣ㸪⥲ົ┬⮬἞⛯ົᒁࠕ㐨ᗓ┴⛯ᚩ཰ᐇ⦼ㄪࠖ࡟࠶ࡿ
ἲே஦ᴗ⛯㢠㸦ἲே⌧ᖺㄢ⛯ศ㸧ࢆ㸪ෆ㛶ᗓ⤒῭♫఍⥲ྜ◊✲ᡤࡢࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖ࡟཰㘓ࡉࢀ࡚࠸ࡿ㒔㐨ᗓ┴ูࡢẸ㛫ἲே௻ᴗᡤᚓ㸦ศ㓄ᡤᚓཷᡶᚋ㸧࡛㝖ࡍࡇ࡜࡛ồࡵࡓ್࡛࠶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࠶ࡿࠋࠕ㒔㐨ᗓ┴ ㄝ᫂ኚᩘ࡛࠶ࡿබമ㈝ඖ฼ൾ㑏㔠㸪୰ኸᨻᗓ࠿ࡽࡢ⛣㌿㈈※ࡢᑐ┴ෆ⥲⏕⏘ẚ⋡࡟ࡘ࠸࡚ࡣ㸪Ỵ⟬≧ἣㄪࠖ࡟࠶ࡿබമ㈝ඖ฼ൾ㑏㔠㸪ᅜᗜᨭฟ㔠࡜ᆅ᪉஺௜⛯஺௜㔠ࡢྜィ್ࢆ㸪ࡑࢀࡒࢀࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖ࡟࠶ࡿ㒔㐨ᗓ┴ูྡ┠┴ෆ⥲⏕⏘ࡢ್࡛㝖ࡍࡇ࡜࡛ồࡵࡓࠋࡲࡓ㸪බമ㈝ඖ฼ൾ㑏㈝࡟஌ࡎࡿ
㒔㐨ᗓ┴㛫ࡢẸ㛫㈨ᮏ⛣ືࡢᣦᶆࡣ㸪῝ᑿ࣭ᓅ㸦2000㸧࡟࡞ࡽ࠸㸪௨ୗࡢ᪉ἲ࡟ࡼࡾẸ㛫㈨ᮏ⛣ື㢠ࢆ᥎
ィ7㸧ࡢୖ㸪ྡ┠┴ෆ⥲⏕⏘ࡢ್࡛㝖ࡍࡿࡇ࡜࡛సᡂࡋࡓࠋ
ᣦᶆసᡂ࡟ᚲ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≧ἣ࡟ຍ࠼㸪ࠕ┴Ẹ⤒῭ィ⟬ࠖࡢࢹ࣮ࢱ࡟ࡘ࠸࡚㸪1975㹼1995 ᖺᗘࡲ࡛ࡣ 68SNA㸪1996

㹼2009 ᖺᗘࡲ࡛ࡣ 93SNA ࢆࡑࢀࡒࢀ⏝࠸ࡓࡇ࡜ࢆ⪃៖ࡋࡓࠋ7㸧

῝ᑿ࣭ᓅ࡟ࡼࡿࠕ᪥ᮏᗓ┴ࢹ࣮ࢱ࣮࣋ࢫࠖ
㸦http://www.ier.hit-u.ac.jp/~fukao/japanese/data/index.html㸧ࡢせ⣲⛣ື࡟㛵ࡍࡿࢹ࣮ࢱࢆ⏝࠸㸪᭱㏆ᖺ࡟ࡘ࠸࡚ࡣ㸪῝ᑿ࣭ᓅ㸦2000㸧࡟࡞ࡽࡗ࡚㸪ᘏ㛗᥎ィࢆ⾜࡞ࡗࡓࠋ㸫㸫

බമⓎ⾜ୗࡢ㈈ᨻ➇த㛛ࡢ㈓⵳㢠ࡣ㸪ᑐ㇟㒔㐨ᗓ┴ࡢྡ┠┴ෆ⥲⏕⏘࡜┴እ࠿ࡽࡢせ⣲ᡤᚓ㸦⣧㸧࡜♫఍ಖ㞀࡟࠾ࡅࡿẸ㛫㒊㛛ࡢ⣧ཷྲྀࡢ࿴࠿ࡽᑐ㇟㒔㐨ᗓ┴ࡢẸ㛫᭱⤊ᾘ㈝ᨭฟ࠾ࡼࡧᅜ⛯࡜ᆅ᪉⛯㸦㒔㐨ᗓ┴Ẹ⛯㸩ᕷ⏫ᮧ⛯㸧ࡢ࿴ࢆᕪࡋᘬࡃࡇ࡜࡛᥎ィࡋࡓࠋ୍᪉㸪Ẹ㛫㒊㛛ࡢᢞ㈨㢠ࡣ㸪Ẹ㛫⥲ᅛᐃ㈨ᮏᙧᡂ࡜Ẹ㛫ᅾᗜቑຍࡢ࿴࡜ࡋ࡚ồࡵࡓࠋ ྡ┠┴ෆ⥲⏕⏘㸪┴እ࠿ࡽࡢせ⣲ᡤᚓ㸦⣧㸧㸪Ẹ㛫᭱⤊ᾘ㈝ᨭฟ㸪Ẹ㛫⥲ᅛᐃ㈨ᮏᙧᡂ࠾ࡼࡧẸ㛫ᅾᗜቑຍ࡟ࡘ࠸࡚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ࡢ඲ᅜ್ࢆィ⟬ࡋ㸪ྛ㒔㐨ᗓ┴ࡢேཱྀẚࢆࡶ࡜࡟ᣨศࡍࡿࡇ࡜࡛సᡂ
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ᑐ๓ᖺ࡜ࡢኚ໬⋡ࢆồࡵࡓࠋ᭷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 ṓ௨ୖࡢேཱྀࢆ඲ேཱྀ࡛㝖ࡍࡿࡇ࡜࡛ẚ⋡ࢆィ⟬ࡋࡓࠋ

3-3 ᥎ᐃ⤖ᯝ࠾ࡼࡧゎ㔘 ᮏ✏࡛ࡣ㸪ࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚࠸ࡿࡓࡵ㸪ᅇᖐศᯒࢆᐇ᪋ࡍࡿ࡟࠶ࡓࡾ㸪ࢹ࣮ࢱࡢᐃᖖᛶࡢࢳ࢙ࢵࢡ
ࢆ⾜࡞࠺ᚲせࡀ࠶ࡿࠋᅗ⾲ 3-3-1 ࡣ㸪ᅇᖐศᯒ࡟⏝࠸ࡓࢹ࣮ࢱ࡟ࡘ࠸࡚ ADF ࢆ⏝࠸ࡓ༢఩᰿᳨ᐃࡢ⤖ᯝࢆ♧ࡋࡓࡶࡢ࡛࠶ࡿࠋࡇࢀ࡟ࡼࡿ࡜㸪1975㹼2009 ᖺᗘࡲ࡛ࡢ඲ࢧࣥࣉࣝᮇ㛫࡛ࡣ㸪 xit ×mit 㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧ࢆ㝖ࡁ㸪༢఩᰿ࡀ࠶ࡿ࡜ࡍࡿᖐ↓௬ㄝࡀᲠ༷ࡉࢀ࡚࠸ࡿࠋ

8㸧ලయⓗ࡟ࡣ㸪
ࠕᅜẸ⤒῭ィ⟬ᖺሗࠖࡢࠕ୍⯡ᨻᗓ࠿ࡽᐙ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♫఍㈇ᢸࠖࢆᕪࡋᘬࡃࡇ࡜࡛♫఍ಖ㞀ࡢ⣧ཷྲྀ㢠ࢆồࡵࡓࠋࡑࡢ⣧ཷྲྀ㢠ࢆࠕ┴Ẹ⤒῭ィ⟬ᖺሗࠖ࡟࠶ࡿ㒔㐨ᗓ┴ูࡢேཱྀẚ࡛ᣨศࡋࡓࡶࡢࢆ㸪㒔㐨ᗓ┴ูࡢ⣧ཷྲྀ࡜ࡋ࡚࠸ࡿࠋ

㸫㸫

఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧ᅗ⾲ 3-3-1 ࣃࢿࣝ༢఩᰿᳨ᐃࡢ⤖ᯝ
ኚᩘྡ

(1)

(2)

(3)

75-09

75-95

96-09

㸫

㸫

㸫

㸫

㸫

㸫

259.4

yit 㸦ἲே஦ᴗ⛯ᖹᆒ⛯⋡㸧***

㸦0.000㸧
145.2

yit 㸦ᇶ♏ⓗṓฟ㸧***㸦0.000㸧
235.9

xit 㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡㸧***㸦0.000㸧

xit ∗ mit㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧

87.3

194.6

㸦0.673㸧
216.2

zit 㸦⛣㌿㈈※ẚ⋡㸧

***

129.1

***

㸦0.000㸧㸦0.000㸧

㸫

㸫

㸫

㸫

***

㸦0.000㸧
***

q

690.4

1
it 㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧qq

㸦0.000㸧
179.1

2
it 㸦᭷ຠồேಸ⋡㸧***

㸦0.000㸧
172.3

3
it 㸦⪁ᖺேཱྀẚ⋡㸧㸫***

㸦0.000㸧㸫㸫㸦0.000㸧-0.178 ***㸦0.000㸧ὀ 1㸧ADF ࡟ࡼࡿ༢఩᰿᳨ᐃࡢ⤖ᯝࢆ♧ࡍࠋὀ 2㸧*** ࡣ୧ഃ 1㸣ࡢ᭷ពỈ‽㸪** ࡣ୧ഃ 5㸣ࡢ᭷ពỈ‽㸪* ࡣ୧ഃ 10㸣ࡢ᭷ពỈ‽࡛㸪ᖐ↓௬ㄝࡀᲠ༷࡛ࡁࡿ
ࡇ࡜ࢆ♧ࡍࠋ
ὀ 3㸧ᣓᘼࡣ p ್ࢆ♧ࡍࠋຍ࠼࡚㸪xit ×mit ࡟ࡘ࠸࡚ࡶ㸪ࢧࣥࣉࣝࢆ 1975㹼1995 ᖺᗘ࡜ 1996㹼2009 ᖺᗘࡢ 2 ᮇ㛫࡛ศ๭ࡋࡓሙྜ࡟
ࡣ㸪༢఩᰿ࡀ࠶ࡿ࡜ࡍࡿᖐ↓௬ㄝࡀᲠ༷࡛ࡁࡿࡇ࡜ࡀࢃ࠿ࡿࠋPerron㸦1989㸧ࡣ㸪ࢧࣥࣉࣝࡀఱࡽ࠿ࡢᵓ
㐀ኚ໬ࢆྵࡴሙྜ㸪༢఩᰿ࡀ࡞࠸ࢧࣥࣉࣝ࡟࠾࠸࡚༢఩᰿ࡀ࠶ࡿ࡜࠸࠺ㄗࡗࡓ᳨ᐃ⤖ᯝࡀᑟ࠿ࢀࡸࡍ࠸࡜
ࡋ㸪ࡑࡢᨵၿ࡟ࢧࣥࣉࣝࢆศ๭ࡋࡓୖ࡛༢఩᰿᳨ᐃࢆᐇ᪋ࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ࡜㏙࡭࡚࠸ࡿࠋᮏ✏࡛ࡶ
ࡇࢀࢆ㋃くࡋ㸪౑⏝ࢧࣥࣉࣝ࡟༢఩᰿ࡀ࡞࠸࡜ุ᩿ࡋ㸪௨ୗ㸪ศᯒࢆ㐍ࡵࡿࡇ࡜࡟ࡍࡿࠋ
 (18) ᘧࢆᅇᖐศᯒࡋࡓ⤖ᯝࡀ㸪ᅗ⾲ 3-3-2 ࠾ࡼࡧᅗ⾲ 3-3-3 ࡟୍ぴ࡛♧ࡉࢀ࡚࠸ࡿࠋࡇࡢ࠺ࡕ㸪๓⪅ࡀἲே஦ᴗ⛯ᖹᆒ⛯⋡ࢆ⿕ㄝ᫂ኚᩘ㸪ᚋ⪅ࡀᇶ♏ⓗṓฟᑐྡ┠┴ෆ⥲⏕⏘ẚ⋡ࢆ⿕ㄝ᫂ኚᩘ࡜ࡋࡓሙྜࡢ⤖ᯝ࡛࠶ࡿࠋᅗ⾲୰ࡢ (1) ࡀ 75㹼09 ᖺᗘࡲ࡛ࡢ඲ࢧࣥࣉ࡛ࣝࡢ᥎ᐃ⤖ᯝࢆ㸪(2) ࡀ 75㹼95 ᖺᗘࡲ࡛ࡢ᥎ᐃ⤖ᯝࢆ㸪(3) ࡀ 96㹼09 ᖺᗘࡲ࡛ࡢ᥎ᐃ⤖ᯝ࡛࠶ࡿࠋ௨ୗ㸪⤫ィⓗ᭷ពᛶࡢ᳨ᐃࢆ⾜࡞࠺࡜࡜ࡶ࡟㸪⤖ᯝ࡟ࡘ࠸࡚ゎ㔘ࢆ⾜࡞ࡗ࡚࠸ࡇ࠺ࠋ

㸫㸫

බമⓎ⾜ୗࡢ㈈ᨻ➇தᅗ⾲ 3-3-2 ἲே஦ᴗ⛯ᖹᆒ⛯⋡࡟㛵ࡍࡿ᥎ᐃ⤖ᯝࣃ࣓࣮ࣛࢱ㸦ኚᩘྡ㸧β 1 㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡㸧
β 2㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧
β 3 㸦⛣㌿㈈※ẚ⋡㸧

γ 1 㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧
γ 2 㸦᭷ຠồேಸ⋡㸧

(1)

(2)

(3)

75-09

75-95

96-09

-0.323-0.7942.660 ***

㸦0.578㸧㸦0.430㸧㸦0.000㸧-0.131***-0.312 ***-0.129 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧-0.398 **0.789 **

-0.376 ***㸦0.033㸧㸦0.002㸧

㸦0.001㸧

-0.194E-02 ***-0.286 ***-0.124E-02 ***㸦0.000㸧㸦0.034㸧

㸦0.000㸧

0.394E-02

0.362E-03

0.019***

㸦0.401㸧

㸦0.960㸧㸦0.000㸧

0.538E-03-0.178 ***㸦0.719㸧

㸦0.000㸧***γ 3 㸦⪁ᖺேཱྀẚ⋡㸧-0.368E-02

λ 㸦ไᗘᨵ㠉ࢲ࣑࣮㸧

0.358E-02

ࢧࣥࣉࣝᩘ

1645

F್

HausmanAdjR2

㸦0.000㸧㸦0.485㸧

-0.729E-02 ***㸫㸦0.000㸧

987

658
***

16.516 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧

32.110 ***㸺6㸼

11.452 ***㸺6㸼

30.487 ***㸺6㸼㸦0.000㸧㸦0.075㸧

㸦0.000㸧

0.481

0.479

0.642

18.642***18.189ὀ 1 㸧᥎ᐃ⤖ᯝࡣ㸪ࣔࢹࣝࡢᐃᘧ໬ࡢㄗࡾ࡟ᑐࡍࡿ᳨ᐃࡢ⤖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‽࡛࠶ࡿࡇ࡜ࢆ♧ࡍࠋ
ὀ 3 㸧ࣃ࣓࣮ࣛࢱෆࡢᣓᘼࡣ p ್ࢆ♧ࡋ㸪AdjR2 ࡣ⮬⏤ᗘಟṇ῭ࡳࡢỴᐃಀᩘࢆ♧ࡍࠋࡲࡓ㸪F ್ࡢᣓᘼ࠾ࡼࡧ Hausmanࡢᣓᘼࡣ p-value ࢆ♧ࡋ㸪Hausman ࡢ㸺 㸼ࡢᩘᏐࡣ⮬⏤ᗘࢆ♧ࡍࠋ
ὀ 4 㸧Hausman ࡣ㸪Hausman㸦1978㸧࡟ࡼࡿࣔࢹࣝࡢᐃᘧ໬ࡢㄗࡾ࡟ᑐࡍࡿ᳨ᐃ⤫ィ㔞࡛࠶ࡾ㸪random effects
model ࡟࠾ࡅࡿಶయຠᯝ㸦individual effect㸧ࢆ⪃៖ࡋࡓኚᩘ࡜ㄝ᫂ኚᩘ࡜ࡢ㛫࡟┦㛵ࡀ࡞࠸࡜࠸࠺ᖐ↓௬
2ㄝࡢࡶ࡜࡛㸪₞㏆ⓗ࡟㸺 㸼ෆࡢᩘ್ࢆ⮬⏤ᗘ࡜ࡍࡿ χ ศᕸ࡟ࡋࡓࡀ࠺ࠋ

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఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧ᅗ⾲ 3-3-3 ᇶ♏ⓗṓฟ࡟㛵ࡍࡿ᥎ᐃ⤖ᯝࣃ࣓࣮ࣛࢱ㸦ኚᩘྡ㸧β 1 㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡㸧
β 2㸦බമ㈝ඖ฼ൾ㑏㔠ẚ⋡Ẹ㛫㈨ᮏ⛣ື㸧
β 3 㸦⛣㌿㈈※ẚ⋡㸧

γ 1 㸦ྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸧
γ 2 㸦᭷ຠồேಸ⋡㸧
γ 3 㸦⪁ᖺேཱྀẚ⋡㸧λ 㸦ไᗘᨵ㠉ࢲ࣑࣮㸧
ࢧࣥࣉࣝᩘ
F್

Hausman
AdjR2

(1)

(2)

(3)

75-09

75-95

96-09

-1.620 ***-2.041 ***-0.860 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧

0.120E-02-0.441E-02-0.013**

㸦0.626㸧㸦0.442㸧

㸦0.037㸧 1.301 *** 1.403 *** 1.139 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧

0.899E-03 ***0.102E-02 ***0.473E-03 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧-0.783E-05

0.011***

㸦0.992㸧㸦0.503㸧

0.401E-02***

㸦0.000㸧
0.780E-03***

㸦0.000㸧-0.186

0.236E-02***

㸦0.000㸧**㸦0.011㸧
1645

㸦0.000㸧-0.290 ***㸫㸦0.000㸧

987

658
***

16.184 ***㸦0.000㸧㸦0.000㸧㸦0.000㸧

41.962 ***㸺6㸼

31.015 ***㸺6㸼

60.243 ***㸺6㸼㸦0.000㸧㸦0.000㸧㸦0.000㸧

0.954

0.985

0.935

29.828***-0.772E-03 ***33.999ὀ 1㸧 ᥎ᐃ⤖ᯝࡣ㸪ࣔࢹࣝࡢᐃᘧ໬ࡢㄗࡾ࡟ᑐࡍࡿ᳨ᐃࡢ⤖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‽࡛࠶ࡿࡇ࡜ࢆ♧ࡍࠋ
ὀ 3㸧 ࣃ࣓࣮ࣛࢱෆࡢᣓᘼࡣ p ್ࢆ♧ࡋ㸪AdjR2 ࡣ⮬⏤ᗘಟṇ῭ࡳࡢỴᐃಀᩘࢆ♧ࡍࠋࡲࡓ㸪F ್ࡢᣓᘼ࠾ࡼࡧ Hausmanࡢᣓᘼࡣ p-value ࢆ♧ࡋ㸪Hausman ࡢ㸺 㸼ࡢᩘᏐࡣ⮬⏤ᗘࢆ♧ࡍࠋ
ὀ 4㸧 Hausman ࡣ㸪Hausman㸦1978㸧࡟ࡼࡿࣔࢹࣝࡢᐃᘧ໬ࡢㄗࡾ࡟ᑐࡍࡿ᳨ᐃ⤫ィ㔞࡛࠶ࡾ㸪random effects
model ࡟࠾ࡅࡿಶయຠᯝ㸦individual effect㸧ࢆ⪃៖ࡋࡓኚᩘ࡜ㄝ᫂ኚᩘ࡜ࡢ㛫࡟┦㛵ࡀ࡞࠸࡜࠸࠺ᖐ↓௬
2ㄝࡢࡶ࡜࡛㸪₞㏆ⓗ࡟㸺 㸼ෆࡢᩘ್ࢆ⮬⏤ᗘ࡜ࡍࡿ χ ศᕸ࡟ࡋࡓࡀ࠺ࠋ

ᅗ⾲ 3-3-2 ࠾ࡼࡧᅗ⾲ 3-3-3 ࡛ࡣ㸪fixed effects model ࡢࡳࡢ⤖ᯝࡀሗ࿌ࡉࢀ࡚࠸ࡿࠋࡇࢀࡣ㸪F ᳨ᐃ࡟ࡼࡿ pool model ࠿ fixed effects model ࠿ࡢ㑅ᢥ㸪Hausman ᳨ᐃ࡟ࡼࡿ fixed effects model ࠿ random effects model࠿ࡢ㑅ᢥ࡟࠾࠸࡚㸪fixed effects model ࡀ᥇ᢥࡉࢀࡓ⤖ᯝࢆ㋃ࡲ࠼ࡓࡶࡢ࡛࠶ࡿࠋ
ࣔࢹࣝࡢ≉ᐃ໬࡟ᑐࡍࡿ᳨ᐃ⤖ᯝࢆ㋃ࡲ࠼㸪௨ୗ࡛ࡣ㸪ಀᩘࡢ⤫ィⓗ᭷ពᛶ࠾ࡼࡧ➢ྕ᮲௳࡟ࡘ࠸᳨࡚ウࡋ࡚࠸ࡃࡇ࡜࡟ࡋࡼ࠺ࠋࡲࡎ㸪⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯ᖹᆒ⛯⋡࡛࠶ࡿᅗ⾲ 3-3-2 ࡢ⤖ᯝ࠿ࡽጞࡵࡿࠋ
බമ㈝ඖ฼ൾ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⌮ㄽࣔࢹࣝ࡜ᩚྜⓗ࡞⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿࡢࡣ㸪(3)ࡢࡳ࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡿࠋࡇࡢࡇ࡜࠿ࡽ㸪㒔㐨ᗓ┴ࡣ㐣ཤ࡟࠾࠸࡚㸪බമ฼ᡶ࠸ࡢቑຍ࡟ἲே஦ᴗ⛯ࡢ⛯⋡ୖ࡛᪼ᑐᛂࡍࡿഴྥ࡟࡞࠿ࡗࡓࡀ㸪᭱㏆ᖺ࡟࠿ࡅ࡚ࡣබമ฼ᡶ࠸ࡢቑຍ࡟ἲே஦ᴗ⛯ࡢ⛯⋡ୖ࡛᪼ᑐᛂ

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බമⓎ⾜ୗࡢ㈈ᨻ➇தࡋࡣࡌࡵࡿࡼ࠺࡟࡞ࡗࡓ࡜⪃࠼ࡽࢀࡿࠋ
බമ㈝ඖ฼ൾ㑏㔠Ẹ㛫㈨ᮏ⛣ືẚ⋡㸦β2㸧࡟ࡘ࠸࡚ࡣ㸪(1)㸪(2)㸪(3) ࠸ࡎࢀࡶ࣐࢖ࢼࢫ࡛᭷ព࡜࡞ࡗ
࡚࠸ࡿࠋࡇࢀࡣ㸪⛒⛯➇தࡀබമࡢ฼ᡶ࠸㈝ቑຍ࡟ࡼࡿ⛯⋡ୖ᪼ࡢຠᯝࢆῶࡎࡿ᪉ྥ࡟స⏝ࡍࡿ࡜ࡋࡓ 2⠇ࡢ⌮ㄽࣔࢹࣝ࡜ᩚྜⓗ࡞⤖ᯝ࡛࠶ࡿࠋࡇࡢ࠺ࡕ㸪(3) ࡟ࡘ࠸࡚ࡣ㸪β1 ࡀࣉࣛࢫ࡛᭷ព࠿ࡘ β2 ࡀ࣐࢖ࢼࢫ
࡛᭷ព࡛࠶ࡿࡓࡵ㸪㏆ᖺ࡟࠾࠸࡚ࡣ⛒⛯➇தࡢᣑ኱ࡀ㸪ἲே஦ᴗ⛯⋡ࡢୖ᪼ࢆ㏻ࡌࡓ㒔㐨ᗓ┴ࡢ㈈ᨻ೺඲
໬ࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓ࡜ゎ㔘࡛ࡁࡿ୍᪉㸪(1)㸪(2) ࡟ࡘ࠸࡚ࡣ β1 ࡀ᭷ព࡛࡞࠸ࡇ࡜࠿ࡽ㸪㐣ཤ࡟࠾࠸࡚
ࡣ⛒⛯➇தࡢᣑ኱࡜⛯⋡ୖ᪼࡟ࡼࡿ㈈ᨻ෌ᘓ࡜ࡢ㛫࡟ᅉᯝ㛵ಀࢆぢฟࡍࡇ࡜ࡣ࡛ࡁ࡞࠸࡜⪃࠼ࡽࢀࡿࠋ
୍᪉㸪⿕ㄝ᫂ኚᩘࡀᇶ♏ⓗṓฟ࡛࠶ࡿᅗ⾲ 3-3-3 ࡢ⤖ᯝࢆࡳࡿ࡜㸪බമ㈝ඖ฼ൾ㑏㔠㸦β1㸧࡟ࡘ࠸࡚ࡣ㸪(1)㸪(2)㸪(3) ࠸ࡎࢀࡢࢧࣥࣉࣝᮇ㛫࡟࠾࠸࡚ࡶ࣐࢖ࢼࢫ࡛᭷ព࡜࡞ࡗ࡚࠾ࡾ㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝ࡜ᩚྜⓗ࡞⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿࠋࢧࣥࣉࣝ (2) ࡜ࢧࣥࣉࣝ (3) ࡜ࢆẚ㍑ࡍࡿ࡜㸪(2) ࡢ β1 ࡀ (3) ࡢ β1 ࢆୗᅇࡗ࡚
࠸ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡿࠋࡇࢀࡼࡾ㸪බമ฼ᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪㒔㐨ᗓ┴ࡣᇶ♏ⓗṓฟࡢῶᑡ࡟ࡼ
ࡗ࡚㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࡟࠶ࡾ㸪≉࡟㸦㒔㐨ᗓ┴㛫ࡢ㈨ᮏ⛣ືࡀపㄪ࡛࠶ࡗࡓ㸧㐣ཤᮇ㛫࡟࠾࠸࡚㸪ࡑࡢഴྥࡀᙉ࠿ࡗࡓ࡜⪃࠼ࡽࢀࡿࠋ
බമ㈝ඖ฼ൾ㑏㔠Ẹ㛫㈨ᮏ⛣ືẚ⋡㸦β2㸧࡟ࡘ࠸࡚ࡳ࡚ࡳࡿ࡜㸪(3) ࡢࡳࡀ࣐࢖ࢼࢫ࡛᭷ព㸪(1)㸪(2)࡜ࡶ࡟᭷ព࡛࡞࠸ࡇ࡜ࡀࢃ࠿ࡿࠋβ1㸪β2 ࡜ࡶ࡟㸪2 ⠇ࡢ⌮ㄽࣔࢹࣝ࡜ᩚྜⓗ࡞➢ྕ᮲௳ࡀ‶ࡓࡉࢀࡿࡢࡣ (3)ࡢࡳ࡛࠶ࡿࡇ࡜࠿ࡽ㸪᭱㏆ᖺ࡟㛵ࡍࡿ㝈ࡾ㸪ᨭฟ➇தࡢᣑ኱࡟ࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣᇶ♏ⓗṓฟࡢῶᑡ࡟✚ᴟⓗ࡟࡞ࡿ࡜ࡍࡿ⌮ㄽࣔࢹࣝࡢ⤖ᯝࡀ㸪ᐇドศᯒ࡟࠾࠸࡚☜ㄆ࡛ࡁࡓ࡜࠸࠼ࡿࠋ
ࡑࡢ௚ࡢኚᩘ࡟ࡘ࠸࡚ࡳ࡚ࡳࡿ࡜㸪⛣㌿㈈※ẚ⋡㸦β3㸧࡟ࡘ࠸࡚ࡣ㸪ἲே஦ᴗᖹᆒ⛯⋡ࡀ⿕ㄝ᫂ኚᩘࡢ
ሙྜ࡟ࡣ࣐࢖ࢼࢫ࡛᭷ព࡟㸪ᇶ♏ⓗṓฟࡀ⿕ㄝ᫂ኚᩘࡢሙྜ࡟ࡣࣉࣛࢫ࡛᭷ព࡜࡞ࡗ࡚࠸ࡿࠋ⛣㌿㈈※ࡀከ࠸⮬἞యࡣ㸪ࡑࢀࢆᙜ࡚㎸ࢇ࡛⛯⋡ࢆᘬࡁୖࡆࡿᚲせᛶ࡟ஈࡋࡃ㸪ࡲࡓṓฟつᶍࡶᣑ኱ࡋࡀࡕ࡛࠶ࡿࡇ
࡜࠿ࡽ㸪࠸ࡎࢀࡢ⤖ᯝࡶ➢ྕ᮲௳ࢆ‶ࡓࡋ࡚࠸ࡿ࡜⪃࠼ࡽࢀࡿࠋ
㸪᭷ຠồேಸ⋡㸦γ2㸧㸪⪁ᖺேཱྀẚ⋡㸦γ3㸧ᆅᇦࡢ♫఍⤒῭≧ἣࢆ♧ࡍྡ┠┴ෆ⥲⏕⏘ᑐ๓ᖺቑῶ⋡㸦γ1㸧࡟ࡘ࠸࡚ࡣ㸪γ1 ࢆ㝖ࡁ㸪⿕ㄝ᫂ኚᩘ࠾ࡼࡧࢧࣥࣉࣝᮇ㛫࡛ࡲࡕࡲࡕ࡞⤖ᯝ࡜࡞ࡗ࡚࠸ࡿࠋγ1 ࡟ࡘ࠸࡚ࡣ㸪⤒῭≧ἣࡀࡼ࠸ᆅᇦ࡛ࡣ㸪ῶ⛯వຊ࠾ࡼࡧṓฟᣑ኱వຊࡀ㧗࠸࡜ண᝿ࡉࢀࡿࡇ࡜࠿ࡽ㸪࠸ࡎࢀࡢ᥎ᐃ⤖ᯝࡶ➢ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯⋡ࡢሙྜࡣ࣐࢖ࢼࢫ㸪ᇶ♏ⓗṓฟࡢሙྜࡣࣉࣛࢫ㸧ࡣ‶ࡓࡋ࡚࠸ࡿ
࡜⪃࠼ࡽࢀࡿࠋ
γ2 ࡟ࡘ࠸࡚ண᝿ࡉࢀࡿ➢ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯⋡ࡢሙྜࡣ࣐࢖ࢼࢫ㸪ᇶ♏ⓗṓฟࡢሙྜࡣࣉ
ࣛࢫ㸧ࢆ‶ࡓࡍࡢࡣ㸪ᇶ♏ⓗṓฟࡢ (1) ࠾ࡼࡧ (3) ࡢ᥎ᐃ⤖ᯝࡢࡳ࡛࠶ࡿ୍᪉㸪γ3 ࡟ࡘ࠸࡚ண᝿ࡉࢀࡿ➢ྕ᮲௳㸦⿕ㄝ᫂ኚᩘࡀἲே஦ᴗ⛯⋡ࡢሙྜࡣ࣐࢖ࢼࢫ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ࢆ࡜ࡽ࠼ࡓ λ ࡟ࡘ࠸࡚ࡣ㸪ἲே஦ᴗ⛯⋡ࡀ⿕ㄝ᫂ኚᩘࡢሙྜ࡟ࡣ (1) ࡀ᭷ព࡛࡞ࡃ㸪(3) ࡀ࣐࢖ࢼࢫ࡛᭷ព࡜࡞ࡗ࡚࠸ࡿࠋ୍᪉㸪ᇶ♏ⓗṓฟࡀ⿕ㄝ᫂ኚᩘࡢሙྜ࡟ࡣ㸪(1)㸪(3) ࡜ࡶ࡟࣐࢖ࢼࢫ
࡛᭷ព࡟࡞ࡗ࡚࠸ࡿࠋ୕఩୍యᨵ㠉࡛ࡣ㸪ᅜᗜᨭฟ㔠ࡸᆅ᪉஺௜⛯ࡢῶ㢠ࡀ⛯※⛣ㆡ㢠ࢆୖᅇࡾ㸪⤖ᯝⓗ࡟㈈ᨻ≧ἣࡀⱞࡋࡃ࡞ࡗࡓ㒔㐨ᗓ┴ࡀከᩘ⏕ࡌࡓࡇ࡜࠿ࡽ㸪᥎ᐃ⤖ᯝࡣ㸦ṓฟ๐ῶ࡟㏕ࡽࢀࡓ㸧㒔㐨ᗓ┴
ࡢ㈈ᨻ஦᝟࡜ᩚྜⓗ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
௨ୖ㸪ᅇᖐศᯒࡢ⤖ᯝࢆせ⣙ࡍࡿ࡜㸪௨ୗࡢࡼ࠺࡟࡞ࢁ࠺ࠋࡍ࡞ࢃࡕ㸪ἲே஦ᴗ⛯ᖹᆒ⛯⋡ࡢ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡢᮇ㛫ࡢࡳ β1 ࡀࣉࣛࢫ࡛᭷ព㸪ᇶ♏ⓗṓฟࡢ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪඲࡚ࡢࢧࣥࣉࣝ
ᮇ㛫࡛ β1 ࡀ࣐࢖ࢼࢫ࡛᭷ព࡛࠶ࡿࡇ࡜࠿ࡽ㸪㒔㐨ᗓ┴ࡣබമ฼ᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ἲே஦ᴗ⛯⋡ࡢᘬࡁୖࡆࡼࡾࡣᇶ♏ⓗṓฟࡢῶᑡ࡟ࡼࡗ࡚㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࡟࠶ࡗࡓ࡜⪃࠼ࡽࢀࡿࠋ

㸫㸫

఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧ἲே஦ᴗ⛯ᖹᆒ⛯⋡ࡢ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡛ࡣ β1 ࡀࣉࣛࢫ࡛᭷ព㸪β2 ࡀ࣐࢖ࢼࢫ࡛᭷ព࡟㸪ᇶ♏ⓗṓฟࡢ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡛ࡣ㸪β1㸪β2 ࡜ࡶ࡟࣐࢖ࢼࢫ࡛᭷ព࡛࠶ࡿࡇ࡜࠿ࡽ㸪㈈ᨻ
➇தࡢᣑ኱࡟ࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣ㏆ᖺ㸪ἲே஦ᴗ⛯⋡ࡢୖ᪼࡟ࡣᾘᴟⓗ࡟࡞ࡿ୍᪉㸪ᇶ♏ⓗṓฟࡢῶᑡ࡟
✚ᴟⓗ࡟࡞ࡗ࡚࠸ࡿ࡜ゎ㔘࡛ࡁࡿࠋ୍㐃ࡢᐇドศᯒࡣ㸪Ẹ㛫㈨ᮏ⛣ືࡀάⓎ໬ࡋࡓ 1990 ᖺ௦ࡢ༙ࡤ௨㝆㸪㒔㐨ᗓ┴ࡣ⛒⛯➇தࡸᨭฟ➇தࡢᙳ㡪࡟ᑐࡍࡿᠱᛕ࠿ࡽ㸪⛯⋡ࡢᘬࡁୖࡆ㸦ṓฟ๐ῶ㸧ࢆ㏻ࡌࡓ㈈ᨻ೺඲໬ࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓ㸦άⓎ໬ࡉࡏࡓ㸧ྍ⬟ᛶࡀ࠶ࡿࡇ࡜ࢆ♧၀ࡍࡿࡶࡢ࡜࠸࠼ࡼ࠺ࠋ

4㸬࠾ࢃࡾ࡟
ᮏ✏࡛ࡣ㸪බമⓎ⾜ୗ࡛ࡢỈᖹⓗ㈈ᨻ➇த࡟╔┠ࡋ㸪බമ฼ᡶ࠸ࡢቑຍ࡜࡜ࡶ࡟ຍ㏿໬ࡀண᝿ࡉࢀࡿᆅ
᪉ᨻᗓࡢ㈈ᨻ෌ᘓ㸦ṓධቑ࣭ṓฟῶ㸧ࡢྲྀࡾ⤌ࡳࡀ㸪㈈ᨻ➇தࡢᣑ኱࡟ࡼࡗ࡚ᙳ㡪ࢆཷࡅࡓ࠿ྰ࠿ࢆ㸪᪥ᮏࡢ⮬἞యࡢࢹ࣮ࢱࢆࡶ࡜࡟ᐇドⓗᡭἲࢆ⏝࠸᳨࡚ドࡋࡓࠋලయⓗ࡟ࡣ㸪1975㹼2009 ᖺᗘ࡟࠾ࡅࡿ 47 㒔㐨ᗓ┴ࡢࣃࢿࣝࢹ࣮ࢱࢆ⏝࠸࡚㸪බമ฼ᡶ࠸㈝࡜ἲே஦ᴗ⛯ᖹᆒ⛯⋡㸪࠾ࡼࡧᇶ♏ⓗṓฟ㸦㝖ࡃබമ㈝㸧
࡜ࡢ㛵ಀࡀ㸪㈨ᮏ⛣ືୗ࡟࠾ࡅࡿ⛒⛯➇த࠾ࡼࡧᨭฟ➇தᣑ኱ࡢᙳ㡪ࢆཷࡅ࡚ኚ໬ࡍࡿ࠿ྰ࠿ࢆᐇドศᯒࡋࡓࠋᐇドศᯒ࠿ࡽ㸪௨ୗࡢ 2 Ⅼࡀ᫂ࡽ࠿࡜࡞ࡗࡓࠋ➨ 1 ࡟㸪බമ㈝ඖ฼ൾ㑏㔠ࡢಀᩘࡀ㸪⿕ㄝ᫂ኚᩘࢆἲே
஦ᴗ⛯ᖹᆒ⛯⋡࡜ࡍࡿ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪ࢧࣥࣉࣝ (3) ࡢᮇ㛫ࡢࡳࣉࣛࢫ࡛᭷ព㸪⿕ㄝ᫂ኚᩘࢆᇶ♏ⓗṓฟ࡜ࡍࡿ᥎ᐃ⤖ᯝ࡟࠾࠸࡚㸪ࡍ࡭࡚ࡢࢧࣥࣉࣝᮇ㛫࡛࣐࢖ࢼࢫ࡛᭷ព࡜࡞ࡗࡓࡇ࡜࠿ࡽ㸪㒔㐨ᗓ┴ࡣබമ฼ᡶ࠸ࡀ✚ࡳ㔜࡞ࡗ࡚ࡃࢀࡤ㸪ἲே஦ᴗ⛯⋡ࡢᘬࡁୖࡆࡼࡾࡣᇶ♏ⓗṓฟࡢῶᑡ࡟ࡼࡗ࡚㸪ண⟬ไ⣙ࢆ‶ࡓࡍࡼ࠺⾜ືࡍࡿഴྥ࡟࠶ࡾ㸪ࡑࡢഴྥࡣ㏆ᖺᙉࡲࡗ࡚࠸ࡿ࡜࠸࠺ࡇ࡜࡛࠶ࡿࠋ
➨ 2 ࡟㸪Ẹ㛫㈨ᮏ⛣ືࡀపㄪࡔࡗࡓ๓ᮇ㸦1975㹼1995 ᖺᗘ㸧࡜άⓎࡔࡗࡓᚋᮇ㸦1996㹼2009 ᖺᗘ㸧࡛ࢧࣥࣉࣝࢆ஧ศࡋ㸪㈨ᮏ⛣ືୗࡢ⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑ኱ࡀ㸪㒔㐨ᗓ┴ࡢ㈈ᨻ෌ᘓ࡟୚࠼ࡓᙳ㡪ࢆ᳨ドࡋࡓ࡜ࡇࢁ㸪ᚋᮇࡢࢧࣥࣉࣝᮇ㛫࡟ࡘ࠸࡚ࡢࡳ㸪ἲே஦ᴗ⛯ᖹᆒ⛯⋡ࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿሙྜ࡟ࡣ㸪බ
മ㈝ඖ฼ൾ㑏㔠ࡢಀᩘ㸦β1㸧ࡀࣉࣛࢫ㸪බമ㈝ඖ฼ൾ㑏㔠㈨ᮏ⛣ືᣦᶆࡢಀᩘ㸦β2㸧ࡀ࣐࢖ࢼࢫ࡟㸪ᇶ㸪බമ㈝ඖ฼ൾ㑏㔠㈨ᮏ⛣ືᣦᶆ♏ⓗṓฟࢆ⿕ㄝ᫂ኚᩘ࡜ࡍࡿሙྜ࡟ࡣ㸪බമ㈝ඖ฼ൾ㑏㔠ࡢಀᩘ㸦β1㸧
ࡢಀᩘ㸦β2㸧ࡀ࡜ࡶ࡟࣐࢖ࢼࢫ࡜࡞ࡗࡓࡇ࡜࠿ࡽ㸪⛒⛯➇த࠾ࡼࡧᨭฟ➇தࡢᣑ኱࡟ࡼࡗ࡚㸪㒔㐨ᗓ┴ࡣ㏆ᖺ㸪ἲே஦ᴗ⛯⋡ࡢᘬࡁୖࡆ࡟ᾘᴟⓗ࡟࡞ࡗࡓ㸦ᇶ♏ⓗṓฟࡢῶᑡ࡟✚ᴟⓗ࡟࡞ࡗࡓ㸧࡜࠸࠺ࡇ࡜࡛࠶ࡿࠋ୍㐃ࡢᐇドศᯒ࡟ࡼࡗ࡚㸪⛒⛯➇தࡸᨭฟ➇தࡀබമࡢ฼ᡶ࠸㈝ቑຍ࡟ࡼࡿ⛯཰ቑຍࡢຠᯝࢆῶࡌ㸪ᇶ♏ⓗṓฟῶᑡࡢຠᯝࢆቑࡍ࡜ࡋࡓ 2 ⠇ࡢ⌮ㄽⓗᖐ⤖ࡣ㸪᭱㏆ᖺ࡟࠾࠸࡚ࡣᨭᣢࡉࢀࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗ
ࡓࠋᮏ✏ࡢᐇドศᯒࡣ㸪Ẹ㛫㈨ᮏ⛣ືࡀάⓎ໬ࡋࡓ 1990 ᖺ௦ࡢ༙ࡤ௨㝆㸪㒔㐨ᗓ┴ࡣ⛒⛯➇தࡸᨭฟ➇தࡢᙳ㡪࡟ᑐࡍࡿᠱᛕ࠿ࡽ㸪⛯⋡ࡢᘬࡁୖࡆࢆ㏻ࡌࡓ㈈ᨻ೺඲໬ࡢྲྀࡾ⤌ࡳࢆ㕌ࡽࡏࡓྍ⬟ᛶࡀ㧗࠸୍᪉㸪ṓฟῶࢆ㏻ࡌࡓ㈈ᨻ೺඲໬ࡢྲྀࡾ⤌ࡳࢆάⓎ໬ࡉࡏࡓྍ⬟ᛶࡀ㧗࠸ࡇ࡜ࢆ♧၀ࡍࡿࡶࡢ࡜࠸࠼ࡼ࠺ࠋ ᭱ᚋ࡟㸪ᮏ✏࡟ṧࡉࢀࡓㄢ㢟࡟ࡘ࠸࡚㸪3 Ⅼᣦ᦬ࡋ࡚࠾ࡁࡓ࠸ࠋ➨ 1 ࡟㸪ࣔࢹࣝࡢ๓ᥦ࡟ࡘ࠸࡚࡛࠶ࡿࠋ
ᮏ✏࡛ࡣ㸪Krogstrup㸦2002㸧࡜ྠᵝ࡟㸪⌮ㄽศᯒࡢ༢⣧໬ࡢࡓࡵ㸪ᐃᖖ≧ែ࡟࠾࠸࡚ඛỴࡉࢀࡓබമỈ‽ࢆ๓ᥦ࡟㸪㈈ᨻ➇தࡢᙳ㡪ࡀ⪃ᐹࡉࢀ࡚࠸ࡿࠋࡋ࠿ࡋඛ⾜ࡍࡿ⌮ㄽศᯒ࡛ࡣ㸪ᆅ᪉ᨻᗓࡀ㈨ᮏ⛯⋡࡜බമⓎ⾜࡜࠸࠺ 2 ࡘࡢᨻ⟇ኚᩘࢆྠ᫬Ỵᐃࡍࡿࣔࢹࣝࡀ๓ᥦ࡜࡞ࡗ࡚࠸ࡿࠋ⌧≧࡛ࡣ㸪බമⓎ⾜࠿ࡽ㈨ᮏ⛯⋡ࡇࡢⅬ࡟ࡘ࠸࡚ࡣ㸪ࡉࡽ࡞ࡿᨵၿࢆᶍ⣴ࡋࡓ࠸ࠋ
ࡸබඹ㈈౪⤥࡬ࡢ୍᪉ྥ࡬ࡢᙳ㡪ࡋ࠿⪃៖ࡉࢀ࡚࠸࡞࠸ࠋ

㸫㸫

බമⓎ⾜ୗࡢ㈈ᨻ➇த ➨ 2 ࡟㸪ࣛࢢ௜ࡁෆ⏕ኚᩘࢆྵࡴ᥎ᐃࣔࢹࣝ࡬ࡢᣑᙇ࡟ࡘ࠸࡚࡛࠶ࡿࠋ⿕ㄝ᫂ኚᩘ࡜࡞ࡗ࡚࠸ࡿἲே஦
ᴗ⛯ᖹᆒ⛯⋡࠾ࡼࡧᇶ♏ⓗṓฟࡣ㸪ㄝ᫂ኚᩘ࡜ࡋ࡚᝿ᐃࡋࡓࡶࡢ௨እ࡟㸪๓ᮇࡢࡑࢀ⮬㌟ࡢ್࠿ࡽࡶᙳ㡪ࢆཷࡅࡿྍ⬟ᛶࡀ࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ≉࡟㸪ᇶ♏ⓗṓฟ࡟ࡘ࠸࡚ࡣ㸪ண⟬࡟࠾ࡅࡿቑศ୺⩏ࡢᙳ㡪ࢆཷࡅࡸࡍ࠸࡜⪃࠼ࡽࢀ㸪Arellano-Bond ࡢ 2 ẁ㝵᧯సኚᩘἲࡸ Blundell-Bond ࡢࢩࢫࢸ࣒ GMM ➼ࡢࢲ࢖ࢼ࣑ࢵ
ࢡ࣭ࣃࢿ࡛ࣝࡢ᥎ᐃࢆヨࡳࡿᚲせࡀ࠶ࡿࠋࡇࡢⅬ࡟ࡘ࠸࡚ࡣ㸪௒ᚋࡢㄢ㢟࡜ࡋ࡚ྲྀࡾ⤌ࡳࡓ࠸ࠋ ➨ 3 ࡟㸪ᅇᖐศᯒ࡟࠾ࡅࡿከ㔜ඹ⥺ᛶࡢၥ㢟࡟ࡘ࠸࡚࡛࠶ࡿࠋㄝ᫂ኚᩘ࡟࠶ࡆࡽࢀ࡚࠸ࡿኚᩘࡣ㸪࠸ࡎࢀࡶṓධ࣭ṓฟ࡟㛵㐃ࡋࡓࢹ࣮ࢱ࡛࠶ࡾ㸪ኚᩘ㛫࡛ከ㔜ඹ⥺ᛶࡢⓎ⏕ࡀᠱᛕࡉࢀࡿࠋ௬ㄝࡢ᳨ド࡟࠾࠸࡚㸪ࡸࡴࢆᚓ࡞࠸ᐃᘧ໬࡛ࡣ࠶ࡿࡀ㸪ከ㔜ඹ⥺ᛶࡢࢳ࢙ࢵࢡ࡜㸪ࡑࢀ࡬ࡢ⤫ィⓗᑐฎ࡟ࡼࡗ࡚㸪᥎ᐃ⤖ᯝࡢ㡹ᙉᛶࢆ☜ㄆࡍࡿᚲせࡀ࠶ࡿࠋࡇࡢⅬ࡟ࡘ࠸࡚ࡶ㸪ࡉࡽ࡞ࡿᨵၿࢆ┠ᣦࡋ࡚ྲྀࡾ⤌ࡳࡓ࠸ࠋ

∂g p
∂τ p
ࡢᑟฟ
Appendix A ㈨ᮏ⛣ືୗ࡛ࡢ,∂ρ d ∂ρ d
 (3) ᘧ㸪(4) ᘧࢆไ⣙࡟㸪(2) ᘧࢆ᭱኱໬ࡍࡿၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡼࡾ㸪௨ୗࢆᚓࡿࠋ

(1 − ε kp ) u gp ( x p , g p ) = u xp ( x p , g p )



㸦A-1㸧

 㸦A-1㸧ᘧࢆ඲ᚤศࡍࡿ࡜㸪௨ୗࢆᚓࡿࠋ

(1−εkp )0⎧∂ugp ⎛ ∂g p p ∂g p
∂ugp ∂x p p ⎫⎪∂εkp p p
p ⎪
p⎞
⎟
⎜
(
1
)
d
τ
u
ε
d
τ
d
ρ
d
+
+
−
+
g
k ⎨
p
p
⎟ ∂x p ∂τ p dτ ⎬⎪
∂τ p
∂ρd p
⎪⎩∂g ⎜⎝ ∂τ⎠⎭pp∂u p ⎛ ∂g p
∂g p
p ⎞ ∂ux ∂x
⎟
d
d
dτ p
ρ
+
= xp ⎜⎜ p dτ p +
p
p
p
⎟
∂ρd
∂g ⎝ ∂τ⎠ ∂x ∂τ  㸦A-2㸧

p∂u xp ∂u g
∂g p τ p
∂g p
∂x p
p
=
+
k
,
=
−
1
,
=
0
,
=
= − k p ࡼࡾ㸪㸦A-2㸧ࡣ௨ୗࡢࡼ࠺࡟ᩚ⌮ࡉࢀࡿࠋ
p
p
p
p
p
∂τ
f kk
∂ρd
∂x
∂g
∂τ

⎧ ⎛
∂ε p ⎫
τp ⎞(1− ε kp )⎨uggp ⎜⎜ k p + ⎟⎟ + (1− ε kp )−1uxxp k p + (1− ε kp )−1 kp ugp ⎬dτ p = (1− ε kp )uggp dρd p
fkk ⎠
∂τ
⎩ ⎝
⎭
 (9)㸪(10)㸪(11) ᘧࢆ⏝࠸࡚㸪
㸦A-3㸧ࢆᩚ⌮ࡍࡿ࡜㸪௨ୗࢆᚓࡿࠋ

㸫㸫



㸦A-3㸧

఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧

dτ p
=
dρd p

εgp

p
(1−εkp )ugg

=
㸦A-4㸧
p p
⎧p
⎫ k p (1−εkp )(εxp +εgp +εmp )p pp −1 p pp ⎛ (1−εk )εm ⎞ p⎟⎟ug ⎬(1−ε )⎨ugg(1−εk )k +(1−εk ) uxxk +(1−εk )⎜⎜−
p
τ
⎝
⎠ ⎭
⎩
  

 (4) ᘧࡼࡾ㸪pkp
∂g p ∂g p ∂τ p
∂g p ⎛ τ p
p ⎞ ∂τ
⎜
⎟
=
+
=
+
k
⎟ ∂ρd p − 1 ࡛࠶ࡿࡇ࡜࠿ࡽ㸪∂τ p ∂τ p ∂ρd p ∂ρd p ⎜⎝ f kk
⎠

ε gp
ε gp
dg p ⎛ τ pp⎞= ⎜ + k ⎟⎟ p
−1 = p p p −1pppp(ε x + ε g + ε m )dρd p ⎜⎝ fkk⎠ k (1− ε k )(ε x + ε g + ε m )   㸦A-5㸧     

㸦B-1㸧

࡜࡞ࡿࠋ

∂g n
∂τ n
ࡢᑟฟ
Appendix B ㈨ᮏ㠀⛣ືୗ࡛ࡢ,∂ρ d ∂ρ d(3)’ ᘧ㸪(4) ᘧࢆไ⣙࡟㸪(2) ᘧࢆ᭱኱໬ࡍࡿၥ㢟ࡢ 1 㝵ࡢ᮲௳ࡼࡾ㸪௨ୗࢆᚓࡿࠋ

u gn ( x n , g n ) = u xn ( x n , g n )  㸦B-1㸧ᘧࢆ඲ᚤศࡍࡿ࡜㸪௨ୗࢆᚓࡿࠋ

nn∂ugn ∂xn n ∂uxn ⎛ ∂gn n ∂gn∂ugn ⎛ ∂gn n ∂gnn⎞n ⎞ ∂ux ∂x
⎟
⎟
⎜
⎜
d
d
d
+
=
d
d
+
dτ n     㸦B-2㸧
d
d
+
τ
ρ
τ
τ
+
ρ
n⎜
n
n
n
n
n⎜
n
n
n
n
⎟
⎟
∂g ⎝ ∂τ∂ρd∂g ⎝ ∂τ∂ρd⎠ ∂x ∂τ⎠ ∂x ∂τn∂g n∂u xn ∂u g
∂g n
∂x n
n
= −1, n = − k n ࡼࡾ㸪㸦B-2㸧ࡣ௨ୗࡢࡼ࠺࡟࡞ࡿࠋ
= n = 0,
=k ,
n
n
n
∂ρd
∂g
∂x
∂τ
∂τ

n
n
( u ggk n + u xxn k n ) d τ p = u ggdρd n(14)㸪(15) ᘧࢆ⏝࠸࡚㸪
㸦B-3㸧ࢆᩚ⌮ࡍࡿ࡜㸪௨ୗࢆᚓࡿࠋ

㸫㸫   㸦B-3㸧බമⓎ⾜ୗࡢ㈈ᨻ➇த

n
ugg
ε gn
dτ p
= n n n n= n n ndρd p ugg
k + uxxkk (ε x + ε g )      㸦B-4㸧(4) ᘧ࠾ࡼࡧ㸦B-4㸧ᘧࡼࡾ㸪p
ε gn∂g n ∂g n ∂τ n
∂g n
n ∂τ
k
=
+
=
−
1
=
−1
ε xn + ε gn
∂τ n ∂τ n ∂ρd n ∂ρd n
∂ρd p

࡜࡞ࡿࠋ

㸫㸫     㸦B-5㸧఍ィ᳨ᰝ◊✲ No.47㸦2013.3㸧ཧ⪃ᩥ⊩
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኱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
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῝⃝ᫎྖ㸦2009㸧ࠕᡃࡀᅜࡢᆅ᪉ἲேㄢ⛯ࢆࡵࡄࡿ⛒⛯➇த㸫ἲே஦ᴗ⛯ࢆᑐ㇟࡜ࡋࡓ⌧≧ศᯒ㸫ࠖ㸪ࠗࣞࣇ࢓ࣞࣥࢫ࠘No.703㸪pp.55-75.

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