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データ分析のための予備知識

 データ分析のための予備知識

2019年1月に実施した「高槻市データ利活用研修」における研修資料の抜粋版です。

Sayoko Shimoyama

January 15, 2019
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  1. ฏ੒೥౓
    ߴ௬ࢢσʔλར׆༻ݚम
    ʢ೔໨ʣ
    2019೥1݄15೔ʢՐʣ
    Ұൠࣾஂ๏ਓϦϯΫσʔλ ୅දཧࣄ Լࢁ ࣿ୅ࢠ

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  2. σʔλ෼ੳͷͨΊͷ
    ༧උ஌ࣝ
    4BZPLP4IJNPZBNB -JOL%BUB

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  3. σʔλ෼ੳʹඞཁͳͷ͸
    ʮαΠΤϯςΟετࢥߟʯ
    ೥ ϊʔϕϧҩֶੜཧֶ৆ ຊॸ༎ࢯ
    ʮڭՊॻΛ৴͡Δͳʯ
    ʮԿͰ΋ٙ͑ʯͱ͍͏Θ͚Ͱ͸ͳ͍
    ༩͑ΒΕͨ৘ใΛશͯӏವΈʹ͢ΔͷͰ͸ͳ͘ɺ
    ʮຊ౰ʹͦ͏ͳͷͩΖ͏͔ʁʯ
    ʮͳͥͦ͏ͳͷͩΖ͏͔ʁʯ
    ͱࣗ෼Ͱߟ͑Δ࢟੎ αΠΤϯςΟετࢥߟ ͕ॏཁ
    4BZPLP4IJNPZBNB -JOL%BUB

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  4. ҧ͍Λฉ͔ΕͨΒઆ໌Ͱ͖·͔͢ʁ
    σʔλ ৘ใ
    4BZPLP4IJNPZBNB -JOL%BUB

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  5. ʮσʔλʯͱ͸ʁ
    *40ٴͼ+*4ن֨ʹΑΔఆٛ
    "SFJOUFSQSFUBCMFSFQSFTFOUBUJPOPGJOGPSNBUJPOJOBGPSNBMJ[FENBOOFS
    TVJUBCMFGPSDPNNVOJDBUJPO JOUFSQSFUBUJPO PSQSPDFTTJOHz
    ৘ใͷදݱͰ͋ͬͯɺ
    ఻ୡɺղऍ·ͨ͸ॲཧʹద͢ΔΑ͏ʹܗࣜԽ͞Εɺ
    ࠶౓৘ใͱͯ͠ղऍͰ͖Δ΋ͷ
    *40 *&$ IUUQTX X X JTPPSHPCQVJJTPTUEJTPJFDFEFO
    ೔ ຊ ޻ ۀ ن ֨ ʮ 9৘ ใ ॲ ཧ ༻ ޠ ج ຊ ༻ ޠ ʯ IUUQLJLBLVSVJDPN Y9IUN M
    4BZPLP4IJNPZBNB -JOL%BUB

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  6. ʮ৘ใʯͱ͸ʁ
    *40ٴͼ+*4ن֨ʹΑΔఆٛ
    ,OPXMFEHFDPODFSOJOHPCKFDUT TVDIBTGBDUT FWFOUT UIJOHT QSPDFTTFT
    PSJEFBT JODMVEJOHDPODFQUT UIBUXJUIJOBDFSUBJODPOUFYUIBTBQBSUJDVMBS
    NFBOJOH
    ࣄ࣮ɼࣄ৅ɼࣄ෺ɼաఔɼண૝ͳͲͷ
    ର৅෺ʹؔͯ͠஌Γಘͨ͜ͱͰ͋ͬͯɼ
    ֓೦ΛؚΈɼҰఆͷจ຺தͰಛఆͷҙຯΛ΋ͭ΋ͷɻ
    *40 *&$ IUUQTX X X JTPPSHPCQVJJTPTUEJTPJFDFEFO
    ೔ ຊ ޻ ۀ ن ֨ ʮ 9৘ ใ ॲ ཧ ༻ ޠ ج ຊ ༻ ޠ ʯ IUUQLJLBLVSVJDPN Y9IUN M
    4BZPLP4IJNPZBNB -JOL%BUB

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  7. σʔλ͸ɺ৘ใΛܗࣜԽͨ͠΋ͷ
    σʔλ ৘ใ
    ࠶౓৘ใͱͯ͠ղऍͰ͖Δ΋ͷ
    4BZPLP4IJNPZBNB -JOL%BUB

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  8. ਺ࣈ


    4BZPLP4IJNPZBNB -JOL%BUB

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  9. ৘ใ
    ೥ʹ։࠵͞Εͨ
    ",#બൈ૯બڍʹ͓͚Δ
    ࢦݪᣦ೫ͷಘථ਺͸
    Ͱ͢ɻ
    4BZPLP4IJNPZBNB -JOL%BUB

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  10. σʔλ
    4BZPLP4IJNPZBNB -JOL%BUB
    ໊લ ",#બൈ૯બڍ
    ։࠵೥
    ಘථ਺
    ࢦݪᣦ೫

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  11. ৘ใ⁶σʔλ
    ૒ํ޲ʹม׵Մೳ
    ໊લ ",#
    બൈ૯બ
    ڍ։࠵೥
    ಘථ਺
    ࢦݪᣦ೫
    ೥ʹ։࠵͞Εͨ
    ",#બൈ૯બڍʹ͓͚Δ
    ࢦݪᣦ೫ͷಘථ਺͸
    Ͱ͢ɻ
    4BZPLP4IJNPZBNB -JOL%BUB

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  12. σʔλԽ͢Δ͜ͱͰ
    ৽͍͠ʮ৘ใʯ͕औΓग़ͤΔ
    ৽ͨͳʮ৘ใʯ͕ಘΒΕΔ
    ಘථ਺͸൪ଟ͔ͬͨ
    Ґͱൺ΂ͯഒ
    ಘථ਺͕ଟ͔ͬͨ
    4BZPLP4IJNPZBNB -JOL%BUB

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  13. ਺஋Խ͞ΕͨσʔλΛࣔ͢͜ͱͰ
    ղऍͷᴥᴪΛݮΒͤΔ
    σʔλΞΧσϛʔʹ͓͚Δ෼ੳ՝୊ͷྫɿ
    ʮٹٸୂһͷ࠷ద഑ஔ͕Ͱ͖͍ͯͳ͍ʯ






    4BZPLP4IJNPZBNB -JOL%BUB

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  14. ਺஋Խ͞ΕͨσʔλΛࣔ͢͜ͱͰ
    ղऍͷᴥᴪΛݮΒͤΔ
    ࢢ಺ͷ֤ୂͷୂһਓ͋ͨΓͷ
    ग़ಈ݅਺Λࢉग़ͯ͠ൺֱ
    ࠷େͰ
    ഒͷࠩ
    4BZPLP4IJNPZBNB -JOL%BUB
    n ਺ࣈ͸ݴ༿ΑΓ΋ղऍͷ෯͕ڱ͍
    n ղऍͷᴥᴪ͕ݴ༿ʹൺ΂ͯ
    ى͜Γʹ͍͘
    ग़ య ݩ ɿ σ ʔ λ Ξ Χ σ ϛ ʔ ʹ ͓ ͚ Δ ν ʔ Ϝ ͷ ౰ ೔ ൃ ද ࢿ ྉ

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  15. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  16. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  17. σʔλ͸ੑ࣭Ͱ
    େ͖ͭ͘ʹ෼͚ΒΕΔ
    ఆྔσʔλ
    n਺஋ͰେখΛද͢͜ͱ͕
    Ͱ͖Δσʔλ
    n٬؍ੑ͕ߴ͍ʢ୭͕ݟͯ΋
    େମಉ͡Α͏ʹղऍͰ͖Δʣ
    nϚΫϩͳࢹ఺Ͱͷ෼ੳʹ
    ༻͍Δʢௗͷ໨ʣ
    ఆੑσʔλ
    n਺஋ͰදݱͰ͖ͳ͍จষͳͲ
    ͷσʔλ
    nओ؍ੑ͕ߴ͍ʢղऍ͸ͦͷਓ
    ͷ࣋ͭई౓ʹҕͶΒΕΔʣ
    nϛΫϩͳࢹ఺Ͱͷ෼ੳʹ
    ༻͍Δʢ஬ͷ໨ʣ
    4BZPLP4IJNPZBNB -JOL%BUB

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  18. ఆྔσʔλͷྫɿ
    Ξϯέʔτͷબ୒߲໨
    ๭ࢢʹ͓͚Δߦ੓৬һ޲͚σʔλ׆༻ݚमͷΞϯέʔτΑΓ
    ͋ͳͨ͸ɺ೔ʑͷۀ຿ͷதͰɺσʔλΛ׆༻ग़དྷ͍ͯΔͱࢥ͍·͔͢ʁ
    ̍ɽे෼ʹग़དྷ͍ͯΔ
    ̎ɽग़དྷ͍ͯΔ
    ̏ɽ͋·Γग़དྷ͍ͯͳ͍
    ̐ɽ·ͬͨ͘ग़དྷ͍ͯͳ͍
    ̍ɽे෼ʹग़དྷ͍ͯΔ
    ̎ɽग़དྷ͍ͯΔ
    ̏ɽ͋·Γग़དྷ͍ͯͳ͍
    ̐ɽ·ͬͨ͘ग़དྷ͍ͯͳ͍
    ूܭͯ͠਺஋ԽͰ͖Δ ఆྔσʔλ
    4BZPLP4IJNPZBNB -JOL%BUB

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  19. ఆྔσʔλͷ࢖͍Ͳ͜Ζ͸
    ʮ၆ᛌʯ
    n਺஋Ͱൺֱ͢Δ͜ͱͰɺঢ়ଶΛ၆ᛌతʹ೺ѲͰ͖Δ
    n౷Ұ͞Εͨج४ͰൺֱͰ͖Δ
    શडߨऀͷ
    ͕೔ৗͷ
    ۀ຿ͰσʔλΛ׆༻Ͱ͖͍ͯΔ
    2 ͋ ͳ ͨ ͸ ɺ ೔ ʑ ͷ ۀ ຿ ͷ த Ͱ ɺ
    σ ʔ λ Λ ׆ ༻ ग़ དྷ ͯ ͍ Δ ͱ ࢥ ͍ · ͢ ͔ ʁ
    ݚमͷ
    ࣮ࢪ
    ݚम࣮ࢪલ
    શडߨऀͷ
    ͕೔ৗͷ
    ۀ຿ͰσʔλΛ׆༻Ͱ͖͍ͯΔ
    ݚम࣮ࢪ೥ޙ
    2 ͋ ͳ ͨ ͸ ɺ ೔ ʑ ͷ ۀ ຿ ͷ த Ͱ ɺ
    σ ʔ λ Λ ׆ ༻ ग़ དྷ ͯ ͍ Δ ͱ ࢥ ͍ · ͢ ͔ ʁ
    4BZPLP4IJNPZBNB -JOL%BUB

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  20. ఆੑσʔλͷྫɿ
    Ξϯέʔτͷࣗ༝هड़߲໨
    ๭ࢢʹ͓͚Δߦ੓৬һ޲͚σʔλ׆༻ݚमͷΞϯέʔτΑΓ
    σʔλ׆༻ʹ͍ͭͯɺ՝୊౳͕͋Ε͹ڭ͍͑ͯͩ͘͞ɻʢࣗ༝هड़ʣ
    ਺஋ԽͰ͖ͳ͍
    ʹఆੑσʔλ
    σʔλऩूɺ׆༻ɺఏڙͷϊ΢ϋ΢ෆ଍
    ݱࡏͷۀ຿಺༰্ɺ͋·Γଟ͘ͷσʔλΛѻΘͳ͍ͨΊɺ׆༻ํ๏ʹ೰ΜͰ͍Δ
    Φʔϓϯσʔλͷ֓೦͕શ͘ਁಁ͍ͯ͠ͳ͍ɺ࢓ࣄ΋σʔλ΋λςׂΓ
    ̥̘౳ɺϋʔυɾιϑτ؀ڥ͕ෆ଍͍ͯ͠Δʢॲཧೳྗ౳ʣ
    ීஈͷۀ຿͔Β׆༻ͨ͠ޙͷΠϝʔδ͕Θ͔Βͳ͍
    σʔλΛݟͯԿ͔Λײ͡ͱΔɺ೺Ѳ͢Δ͜ͱʹۤखҙ͕ࣝ͋Γ׆༻·ͰࢸΒͳ͍ɺηϯεʁ׳Εʁ
    ະ஌ͷ༗ޮ׆༻͞Ε͍ͯͳ͍ி಺σʔλ͕ଘࡏ͢ΔͱࢥΘΕΔ
    ɾɾɾ
    4BZPLP4IJNPZBNB -JOL%BUB

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  21. ఆੑσʔλͷ࢖͍Ͳ͜Ζ͸
    ʮਂ۷Γʯ
    nఆྔσʔλΑΓ΋৘ใྔ͸ଟ͍ͨΊɺݸʑͷঢ়ଶΛΑΓਂ۷Γ
    ͯ͠೺ѲͰ͖Δ
    n࣍ͷΞΫγϣϯΛݕ౼͢Δ্Ͱͷ͕ࣔࠦಘΒΕΔ
    σʔλऩूɺ׆༻ɺఏڙͷϊ΢ϋ΢ෆ଍
    ݱࡏͷۀ຿಺༰্ɺ͋·Γଟ͘ͷσʔλΛѻΘͳ͍
    ͨΊɺ׆༻ํ๏ʹ೰ΜͰ͍Δ
    Φʔϓϯσʔλͷ֓೦͕શ͘ਁಁ͍ͯ͠ͳ͍ɺ࢓ࣄ
    ΋σʔλ΋λςׂΓ
    ̥̘౳ɺϋʔυɾιϑτ؀ڥ͕ෆ଍͍ͯ͠Δʢॲཧ
    ೳྗ౳ʣ
    ීஈͷۀ຿͔Β׆༻ͨ͠ޙͷΠϝʔδ͕Θ͔Βͳ͍
    σʔλΛݟͯԿ͔Λײ͡ͱΔɺ೺Ѳ͢Δ͜ͱʹۤख
    ҙ͕ࣝ͋Γ׆༻·ͰࢸΒͳ͍ɺηϯεʁ׳Εʁ
    ະ஌ͷ༗ޮ׆༻͞Ε͍ͯͳ͍ி಺σʔλ͕ଘࡏ͢Δ
    ͱࢥΘΕΔ
    ɾɾɾ
    2σʔλ׆༻ʹ͍ͭͯɺ՝୊౳͕͋Ε͹ڭ͍͑ͯͩ͘͞ɻ
    ෼ྨɾ
    ੔ཧ
    σʔλΛࣗ༝ʹ࢖͑Δ؀ڥ͕
    ੔͍ͬͯͳ͍
    ࣗ෼ͷۀ຿ͱ݁ͼ෇͚ͯ
    ߟ͑Δ͜ͱ͕ࠔ೉
    σʔλΛ࢖͏͜ͱʹର͢Δ
    യવͱͨۤ͠खײ͕֮͋Δ
    ݸผͷΠϯλϏϡʔ౳ͰΑΓঢ়گ
    Λਂ͘೺Ѳ
    ϐοΫΞοϓ
    4BZPLP4IJNPZBNB -JOL%BUB

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  22. ఆྔσʔλɾఆੑσʔλ͸
    ͏·͘૊Έ߹Θͤͯ࢖͏ඞཁ͕͋Δ
    ࢪࡦཱҊ ࢪࡦ࣮ࢪ ࢪࡦධՁ
    ՝୊ઃఆ
    ݱঢ়ͷ՝୊Λ೺Ѳ
    ͢Δ
    ࢪࡦ࣮ࢪʹΑΔ
    ໨ඪΛઃఆ͠
    ܭըΛཱͯΔ
    ໰୊ͳ͘ࢪࡦΛ
    ࣮ࢪͰ͖͍ͯΔ͔
    ֬ೝ͢Δ
    ࢪࡦΛ࣮ࢪͨ͠
    ͜ͱʹΑΔޮՌ΍
    ӨڹΛධՁ͢Δ
    • ౷ܭௐࠪσʔλ
    • Ξϯέʔτ
    • ΠϯλϏϡʔ
    • ౷ܭௐࠪσʔλ
    • ྨࣅࣄྫͷධՁ
    σʔλ
    • ఆ఺؍ଌσʔλ
    • ࣮ࢪه࿥
    • ηϯαʔػث౳
    ͷϩά
    • ఆ఺؍ଌͷ
    ൺֱσʔλ
    • Ξϯέʔτ
    • ΠϯλϏϡʔ
    4BZPLP4IJNPZBNB -JOL%BUB

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  23. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ˠఆྔσʔλͱఆੑσʔλ͸͏·͘࢖͍෼͚Δ
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  24. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ˠఆྔσʔλͱఆੑσʔλ͸͏·͘࢖͍෼͚Δ
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  25. ૬ؔͱ͸
    ೋͭͷࣄ৅͕ີ઀ʹ͔͔ΘΓ߹͍ɺҰํ͕มԽ͢Ε͹ଞํ΋มԽ
    ͢ΔΑ͏ͳؔ܎ɻ
    ෛͷ૬ؔ
    ਖ਼ͷ૬ؔ
    Ұํͷ஋͕େ͖͘ͳΔͱɺ
    ΋͏Ұํͷ஋΋େ͖͘ͳΔ
    Ұํͷ஋͕େ͖͘ͳΔͱɺ
    ΋͏Ұํͷ஋͸খ͘͞ͳΔ
    4BZPLP4IJNPZBNB -JOL%BUB

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  26. ૬ؔ㱠ҼՌؔ܎
    ྫʣΞΠεΫϦʔϜͷചΓ্͛ͱనࢮऀͷ਺ʹ૬͕ؔ͋ͬͨ
    ΞΠε͕ചΕΔͱ
    నࢮऀ͕૿͑Δ
    ؾԹͷ্ঢ
    4BZPLP4IJNPZBNB -JOL%BUB

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  27. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶃɿ
    ڞ௨ͷཁҼ͕͋Δʢަབྷʣ
    n$͕"ͱ#ʹӨڹΛ༩͍͑ͯΔঢ়ଶ
    n"ͱ#ͷؒʹ௚઀తͳؔ܎ੑ͸ͳ͍
    A B
    C
    4BZPLP4IJNPZBNB -JOL%BUB

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  28. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶃɿ
    ڞ௨ͷཁҼ͕͋Δʢަབྷʣ
    nྫʣʮίʔώʔΛҿΉྔʯͱʮ৺ےߎ࠹ͷൃ঱཰ʯʹ
    ਖ਼ͷ૬͕ؔ͋ͬͨ






    4BZPLP4IJNPZBNB -JOL%BUB
    ίʔώʔΛΑ͘ҿΉਓͰ
    λόίΛٵ͏ਓ͕ଟ͔ͬͨ
    ٤Ԏ͕৺ےߎ࠹ൃ঱ͷ
    ཁҼʹͳ͍ͬͯͨ

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  29. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶄɿ
    ҼՌؔ܎ͷํ޲͕ٯ
    n"ʹΑͬͯ#͕Ҿ͖ى͜͞ΕͨͷͰ͸ͳ͘ɺ#ʹΑͬͯ"͕Ҿ͖ى
    ͜͞Εͨ
    n૬ؔ෼ੳͰ͸࣌ؒతͳલޙؔ܎͕ݟ͑ͳ͍ͨΊɺؾ͖ͮʹ͍͘
    A B
    4BZPLP4IJNPZBNB -JOL%BUB

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  30. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶄɿ
    ҼՌؔ܎ͷํ޲͕ٯ
    nྫʣʮࣄނͷൃੜ݅਺ʯͱʮ஫ҙשىͷ؃൘ͷઃஔ਺ʯʹ
    ਖ਼ͷ૬͕ؔ͋ͬͨ




    4BZPLP4IJNPZBNB -JOL%BUB

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  31. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶅɿ
    બ୒όΠΞε
    n"ͱ#ͷ෼ੳର৅σʔλ͕ҼՌͷ߹ྲྀ఺$ʹ͓͍ͯɺબൈʗ૚ผ
    ʗௐ੔͞Εͯ͠·͍ͬͯΔӨڹͰɺҼՌؔ܎͕ͳ͍ͷʹ૬͕ؔ
    ੜͯ͡͠·͏έʔε
    A B
    C
    4BZPLP4IJNPZBNB -JOL%BUB

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  32. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶅɿ
    બ୒όΠΞε
    nྫʣ࣮ٕࢼݧͷ఺਺ͱֶྗࢼݧͷ఺਺ͷ߹ܭ఺Ͱ߹൱͕ܾ·Δ
    ࢼݧʹ͓͍ͯɺ߹֨ऀͷʮ࣮ٕࢼݧͷ఺਺ʯͱʮֶྗࢼݧͷ఺
    ਺ʯʹෛͷ૬͕ؔ͋ͬͨ








    4BZPLP4IJNPZBNB -JOL%BUB

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  33. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶆɿ
    શ͘ͷۮવ
    nશ͘Կͷؔ܎΋ͳ͍"ͱ#Ͱ͋ͬͯ΋ɺۮવ૬͕ؔੜͯ͡͠·͏
    έʔε
    A B
    4BZPLP4IJNPZBNB -JOL%BUB

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  34. ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍έʔεᶆɿ
    શ͘ͷۮવ
    nྫʣʮϓʔϧʹ͓͚Δనࢮऀ਺ʯͱʮχίϥεɾέΠδͷөը
    ग़ԋ਺ʯʹਖ਼ͷ૬͕ؔ͋ͬͨ
    4BZPLP4IJNPZBNB -JOL%BUB
    http://www.tylervigen.com/spurious-correlations

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  35. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ˠఆྔσʔλͱఆੑσʔλ͸͏·͘࢖͍෼͚Δ
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ˠ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍৔߹͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  36. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ˠఆྔσʔλͱఆੑσʔλ͸͏·͘࢖͍෼͚Δ
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ˠ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍৔߹͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    4BZPLP4IJNPZBNB -JOL%BUB

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  37. #FGPSF"GUFSσʔλ͚ͩͰ
    ҼՌؔ܎Λಛఆ͢Δͷ͸ࠔ೉
    n࣮ݧࣨ಺ͳΒӨڹΛٴ΅͢Մೳੑͷ͋ΔཁૉΛഉআ͢ΔΑ͏ʹ
    ৚݅ΛίϯτϩʔϧͰ͖Δ
    n͔࣮ࣾ͠͠ձͰ͸ಛఆͷཁૉΛഉআ͢Δ͜ͱ͸ࠔ೉
    nେྔͷσʔλ΍ߴ౓ͳ౷ܭϞσϧ͕͋ͬͨΒղܾՄೳʁ
    ˠ೉͍͠ͱݴΘΕ͍ͯΔ
    n͕ͨͬͯ͠#FGPSF"GUFSͷσʔλ͚ͩͰ͸ɺࢪࡦʹΑͬͯ՝୊
    ͕վળ͞Ε͔ͨ͸෼͔Βͳ͍ʢଞͷཁҼͷՄೳੑΛഉআͰ͖ͳ͍ʣ
    ࢪࡦ࣮ࢪલ ࢪࡦ࣮ࢪޙ
    ࢪࡦͷ
    ࣮ࢪ
    ՝୊ͷ
    վળ
    ʁ
    4BZPLP4IJNPZBNB -JOL%BUB

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  38. ϥϯμϜԽൺֱࢼݧ
    3BOEPNJ[FE $POUSPMMFE 5SJBM3$5

    nର৅ΛϥϯμϜʹάϧʔϓ෼͚ͯ͠ࢦඪΛܭଌ͠ൺֱ
    ࢪࡦΛ࣮ࢪ͢Δάϧʔϓʢॲஔ܈ʣ
    ࢪࡦΛ࣮ࢪ͠ͳ͍άϧʔϓʢରর܈ʣ
    nϥϯμϜɾάϧʔϐϯάʹΑͬͯଞͷཁҼʹΑΔӨڹΛഉআ
    ର৅
    ॲஔ܈
    ରর܈
    ࢦඪΛܭଌ
    ࢦඪΛܭଌ
    ࢪࡦޮՌ
    ࠩΛൺֱ
    ϥϯμϜʢແ࡞ҝʣ
    ʹάϧʔϐϯά
    4BZPLP4IJNPZBNB -JOL%BUB

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  39. ϥϯμϜԽൺֱࢼݧʹ
    ඞཁͳཁૉ
    ΤϯυϙΠϯτ
    ࢪࡦͷޮՌΛܭΔͨΊͷ٬؍తͳई౓
    ൺֱରর
    ࢪࡦΛ࣮ࢪ͢Δ܈ʢॲஔ܈ʣʹର͠ɺࢪࡦΛ࣮ࢪ͠ͳ͍܈ʢରর܈ʣ
    ϥϯμϜԽ
    ࣮ࢪͨ͠ࢪࡦҎ֎ͷ৚݅ʹภΓΛੜͤ͡͞ͳ͍Α͏ʹɺ
    ॲஔ܈ͱରর܈ͷϥϯμϜͳৼΓ෼͚Λߦ͏
    ໡ݕԽ
    ܭଌ͢Δਓʹɺॲஔ܈ͱରর܈͕ͲͪΒͰ͋Δ͔෼͔Βͳ͍Α͏ʹ
    ͢Δʢܭଌʹओ؍͕ೖΒͳ͍Α͏ʹ͢ΔͨΊʣ
    4BZPLP4IJNPZBNB -JOL%BUB

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  40. ΤϏσϯεͷڧ͞ͷ֊૚
    nʮΤϏσϯεʹجͮ͘ҩྍ &WJEFODF#BTFE .FEJDJOF
    ʯʹ
    ୺Λൃͨ͠ΤϏσϯεͷ֊૚ Ϩϕϧ
    ͕ࣾձՊֶʹ΋Ԡ༻͞Ε͍ͯΔ
    nϨϕϧ্͕͕Δ΄ͲΑΓਖ਼֬ʹҼՌؔ܎ΛਪఆͰ͖Δͱݟͳ͞ΕΔ
    ग़యɿਖ਼໦๎໵ɺ௡୩تҰ࿠ʢʣʮΤϏσϯεʹجͮ͘ҩྍʢ&.#ͷܥේͱํ޲ੑɿอ݈
    ҩྍධՁʹՌͨ͢ίΫϥϯڞಉܭըͷ໾ׂͱະདྷʣʯʰ೔ຊධՁݚڀ ୈרୈ߸ʱQQ
    4

    b
    a
    1b
    1a ෳ਺ͷϥϯμϜԽൺֱࢼݧͷϝλɾΞφϦγε
    গͳ͘ͱ΋̍ͭͷϥϯμϜԽൺֱࢼݧ
    গͳ͘ͱ΋̍ͭͷඇϥϯμϜԽൺֱࢼݧ
    গͳ͘ͱ΋̍ͭͷ४࣮ݧతݚڀ
    ඇ࣮ݧతݚڀɺهड़తݚڀ
    ઐ໳Ոͷใࠂ΍ҙݟɺݖҖऀͷܦݧ
    4BZPLP4IJNPZBNB -JOL%BUB

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  41. ࣄྫɿਆಸ઒ݝ༿ࢁொͷ
    ์ஔ͝Έ࡟ݮࢪࡦͷޮՌݕূ
    n༿ࢁொ͸೥ʹ೔ຊͰ൪໨ʹʮθϩɾ΢ΣΠετʯ੓ࡦʢ͝Έͷపఈతͳ
    ࢿݯԽɾݮྔԽʣͷಋೖΛද໌
    nࢿݯ͝Έͷऩूڌ఺Ͱ͋Δࢿݯεςʔγϣϯͷ؅ཧ͸ɺθϩɾ΢ΣΠετͷ
    ୡ੒ʹ޲͚ͨॏཁࢪࡦ
    nࢿݯεςʔγϣϯͰͷ์ஔ͝Έ͕ݮΒͳ͍͜ͱʹொɾॅຽ͕಄Λ೰·͍ͤͯͨ
    ˠࢪࡦ࣮ݧΛ࣮ࢪ
    ϞχλϦϯάର৅
    εςʔγϣϯ

    ରࡦɿνϥγ഑෍

    ରࡦɿ؃൘ܝࡌ

    ରࡦͳ͠

    ࣄલϞχλϦϯά
    ʹج͖ͮϥϯμϜ
    ʹάϧʔϓԽ
    ࠩ͸ແ͔ͬͨ
    ʢޮՌͳ͠ʣ
    ଟ͘
    ࡟ݮͰ͖ͨ
    ʢ࡟ݮޮՌ͋Γʣ
    ϞχλϦϯά
    Λ࣮ࢪ͠ɺ
    ݁ՌΛൺֱ
    ग़యɿ੓ࡦͷޮՌΛͲ͏ଌఆ͢Δ͔ʁɿւ֎ʹ͓͚ΔʮΤϏσϯεʹجͮ͘੓ࡦʯͷ࠷৽ಈ޲
    IUUQTXXXSJFUJHPKQKQFWFOUTCCMIUNM
    શொల։
    4BZPLP4IJNPZBNB -JOL%BUB

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  42. ࠷ऴతʹධՁʹඞཁͱͳΔσʔλΛ
    ֤ϓϩηεʹ͓͍ͯऔಘ
    ࢪࡦཱҊ ࢪࡦ࣮ࢪ ࢪࡦධՁ
    ՝୊ઃఆ
    ݱঢ়ͷ՝୊Λ೺Ѳ
    ͢Δ
    ࢪࡦ࣮ࢪʹΑΔ
    ໨ඪΛઃఆ͠
    ܭըΛཱͯΔ
    ໰୊ͳ͘ࢪࡦΛ
    ࣮ࢪͰ͖͍ͯΔ͔
    ֬ೝ͢Δ
    ࢪࡦΛ࣮ࢪͨ͠
    ͜ͱʹΑΔޮՌ΍
    ӨڹΛධՁ͢Δ
    • ֤ࢿݯεςʔ
    γϣϯͷ์ஔ
    ΰϛൃੜ཰
    ʢࣄલϞχλ
    Ϧϯάʣ
    • ொ಺ձͰͷ
    ϞχλϦϯά
    ڠྗొ࿥σʔλ
    • ֤ࢿݯεςʔ
    γϣϯͷ์ஔ
    ΰϛൃੜ཰
    ʢఆ఺؍ଌʣ
    • ࢪࡦผͷ์ஔ
    ΰϛൃੜ཰
    ൺֱσʔλ
    • ࢀՃऀ΁ͷ
    Ξϯέʔτ
    4BZPLP4IJNPZBNB -JOL%BUB

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  43. 3$5͕࣮ࢪͰ͖ͳ͍৔߹ɺ࣭ͷߴ͍
    ΤϏσϯεΛಘΔ͜ͱ͸ෆՄೳʁ
    n౴͑͸ʮ/Pʯ
    nϥϯμϜԽൺֱࢼݧ 3$5
    Λߦͳͬͨͷͱಉ༷ͷ
    ঢ়گͷσʔλ͕ೖखͰ͖Ε͹Մೳ
    nطଘͷߦ੓σʔλ͕࢖͑Δ৔߹͕͋Δ
    4BZPLP4IJNPZBNB -JOL%BUB

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  44. ྫʣΧϦϑΥϧχΞभʹ͓͚Δ
    ిྗফඅྔͷ෼ੳ
    ग़యɿ੓ࡦͷޮՌΛͲ͏ଌఆ͢Δ͔ʁɿւ֎ʹ͓͚ΔʮΤϏσϯεʹجͮ͘੓ࡦʯͷ࠷৽ಈ޲
    IUUQTXXXSJFUJHPKQKQFWFOUTCCMIUNM
    n෼ੳͷ໨తɿ
    ʮిྗͷྉۚΛ্͛Δͱɺফඅऀ͕Ͳͷ͘Β͍ͷྔΛઅి͢Δͷ͔
    ஌Γ͍ͨ ʯ
    n෼ੳ࣮ࢪऀɿγΧΰେֶެڞ੓ࡦେֶӃ ҏ౻ެҰ࿕ࢯ
    nڠྗػؔɿ $B*JGPSOJB &OFSHZ $PNNJTTJPO ੓෎

    4$& 4%(& ిྗձࣾ

    nར༻σʔλɿੈଳ͝ͱͷ݄ؒిྗফඅσʔλ೥෼
    pΧϦϑΥϧχΞभͷ͋Δ౎ࢢͰ͸ೆ๺Ͱ
    ిྗձ͕ࣾҟͳΔ
    p྆ํͷిྗձࣾͷిྗྉ͕ۚಉ༷ʹ
    มԽ͍ͯͨ࣌͠ظͱɺೆ෦͚ͩ
    ిྗྉ্͕͕ۚͬͨ࣌ظ͕͋Δ
    4BZPLP4IJNPZBNB -JOL%BUB

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  45. ྫʣΧϦϑΥϧχΞभʹ͓͚Δ
    ిྗফඅྔͷ෼ੳ
    ྆ํͷిྗձࣾͷిྗྉ͕ۚಉ༷ʹมԽ͍ͯͨ࣌͠ظͱൺֱ͢Δͱɺ
    ೆ෦Ͱిྗྉ্͕͕ۚͬͨ࣌ظͷిྗফඅྔ͸ݮগ͍ͯͨ͠
    ˠిྗྉ্͕͕ۚΔͱফඅऀ͸અి͢Δ
    ྆஍ҬͰྉ͕ۚಉ༷ͩͬͨ࣌ظ ೆ෦͚ͩྉ্͕͕ۚͬͨ࣌ظ
    ๺෦ ೆ෦ ๺෦ ೆ෦
    KoichiroIto, AmericanEconomicReview2014, 104(2): 537–563
    http://dx.doi.org/10.1257/aer.104.2.537
    4BZPLP4IJNPZBNB -JOL%BUB

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  46. σʔλ׆༻ʹ͓͚Δ
    Α͋͘Δצҧ͍
    ఆੑσʔλ͸໾ʹཱͨͳ͍
    ˠఆྔσʔλͱఆੑσʔλ͸͏·͘࢖͍෼͚Δ
    ૬͕ؔ͋Ε͹ඞͣҼՌؔ܎͕͋Δ
    ˠ૬͕ؔ͋ͬͯ΋ҼՌؔ܎͕ͳ͍৔߹͕͋Δ
    ΤϏσϯεΛٻΊΒΕͨ࣌͸ɺ
    σʔλΛࣔͤ͹0,ʂ
    ˠΤϏσϯεʹ΋࣭ͷϨϕϧ͕ଘࡏ͢ΔͨΊɺ
    ͨͩσʔλΛ͚ࣔͩ͢Ͱ͸Պֶతࠜڌͱͯ͠ऑ͍৔߹͕
    ͋Δ
    4BZPLP4IJNPZBNB -JOL%BUB

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  47. Ұൠࣾஂ๏ਓϦϯΫσʔλ ୅දཧࣄ
    Լࢁ ࣿ୅ࢠ
    Email: [email protected]
    ຊࢿྉʹؔ͢Δ࣭͝໰ɾ͝ҙݟ΍ɺ
    σʔλ׆༻ʹؔ͢Δ͝૬ஊ͸ͪ͜Β΁͓د͍ͤͩ͘͞ɻ
    4BZPLP4IJNPZBNB -JOL%BUB

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