その他のタイトル Experiments on Optimal Unemployment Insurance : Online Experiments with Real‑Effort Tasks through CrowdFlower

CrowdFlowerを用いた実作業オンライン予備実験

その他のタイトル Experiments on Optimal Unemployment Insurance : Online Experiments with Real‑Effort Tasks through CrowdFlower

著者 小林 創, 稲葉 大, 七條 達弘

雑誌名 關西大學經済論集

巻 67

号 4

ページ 789‑803

発行年 2018‑03‑10

URL http://hdl.handle.net/10112/16869

࠷దࣦۀอݥͷಋೖޮՌʹ͍ͭͯͷܦࡁ࣮ݧɿ CrowdFlower Λ༻͍࣮ͨ࡞ۀΦϯϥΠϯ༧උ࣮ݧ ^∗

খྛɹ૑ ^†

ؔ੢େֶ

Ҵ༿ɹେ ^‡

ؔ੢େֶ

ࣣᑍɹୡ߂ ^§

େࡕ෎ཱେֶ

ฏ੒ 30 ೥ 2 ݄ 23 ೔

֓ ཁ

ຊݚڀ͸ΦϯϥΠϯ࣮ݧΛ௨ͯ͡ Hopenhayn and Nicolini (1997) ʹΑΔ࠷దࣦ

ۀอݥͷԼͰͷݸਓͷ৬୳͠ߦಈ͕ࣦۀظؒʹԠͯ͡ͲͷΑ͏ʹมԽ͠ɺ Auturky ͱൺֱͯ͠Ͳͷఔ౓ͦͷڧ౓͕มԽ͢Δ͔ʹ͍ͭͯߟ࡯ͨ͠ɻಘΒΕͨ݁Ռͱͯ͠ɺ

ୈ̍ʹɺ࠷దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ

͸ҟͳΓɺඃݧऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳ௿Լ͍ͯ͠

͘͜ͱ͕෼͔ͬͨɻ͜Ε͸ɺඪ४తͳબ޷Ͱ͸ى͜Γ͑ͳ͍͜ͱͰɺݸਓ͕ԿΒ͔

ͷܗͰݱࡏόΠΞεΛ༗͍ͯ͠Δ͜ͱͷূࠨͰ͋Δ͜ͱ͕෼͔ͬͨɻୈ̎ʹɺ೚ҙ ͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗਫ४ͱ Auturky Ͱͷ౒ྗਫ४Λൺֱ

͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨɺ͜Ε͸౷ܭతʹ༗ҙͳࠩͰ͸ͳ͔ͬͨɻҎ্ͷ 2

ͭͷ݁ՌΛ૯߹తʹଊ͑Δͱɺݸਓ͕ݱࡏόΠΞεΛ༗͍ͯ͠ΔͨΊɺ Hopenhayn and Nicolini (1997) ʹΑͬͯ૝ఆ͞Ε͍ͯΔఔͷޮՌ͸ಘΒΕͳ͍͜ͱ͕֬ೝ͞Ε

ͨͱ͍͑Δɻ

∗

ຊݚڀ͸ɺฏ੒ 25 ೥౓ؔ੢େֶएखݚڀऀҭ੒ܦඅʹ͓͍ͯɺݚڀ՝୊ʮ࠷దࣦۀอݥͷޮ཰ੑͱϞ ϥϧɾϋβʔυʹ͍ͭͯͷܦࡁ࣮ݧʯͱͯ͠ݚڀඅΛड͚ɺͦͷ੒ՌΛެද͢Δ΋ͷͰ͋Δɻ·ͨɺຊݚڀ ʹ͓͍ͯ༻͍ΒΕͨΠϯετϥΫγϣϯɺਪఆίʔυ͸ಡऀ͔ΒͷٻΊ͕͋Γ࣍ୈஶऀ͔Β௚઀ख౉͢ܗ Ͱߦ͏ɻ

†

ؔ੢େֶܦࡁֶ෦; [email protected].

‡

ؔ੢େֶܦࡁֶ෦; [email protected].

§

େࡕ෎ཱେֶେֶӃܦࡁֶݚڀՊ; [email protected].

1

࠷దࣦۀอݥͷಋೖޮՌʹ͍ͭͯͷܦࡁ࣮ݧɿ CrowdFlower Λ༻͍࣮ͨ࡞ۀΦϯϥΠϯ༧උ࣮ݧ ^∗

খྛɹ૑ ^†

ؔ੢େֶ

Ҵ༿ɹେ ^‡

ؔ੢େֶ

ࣣᑍɹୡ߂ ^§

େࡕ෎ཱେֶ

ฏ੒ 30 ೥ 2 ݄ 23 ೔

֓ ཁ

ຊݚڀ͸ΦϯϥΠϯ࣮ݧΛ௨ͯ͡ Hopenhayn and Nicolini (1997) ʹΑΔ࠷దࣦ

ۀอݥͷԼͰͷݸਓͷ৬୳͠ߦಈ͕ࣦۀظؒʹԠͯ͡ͲͷΑ͏ʹมԽ͠ɺ Auturky ͱൺֱͯ͠Ͳͷఔ౓ͦͷڧ౓͕มԽ͢Δ͔ʹ͍ͭͯߟ࡯ͨ͠ɻಘΒΕͨ݁Ռͱͯ͠ɺ

ୈ̍ʹɺ࠷దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ

͸ҟͳΓɺඃݧऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳ௿Լ͍ͯ͠

͘͜ͱ͕෼͔ͬͨɻ͜Ε͸ɺඪ४తͳબ޷Ͱ͸ى͜Γ͑ͳ͍͜ͱͰɺݸਓ͕ԿΒ͔

ͷܗͰݱࡏόΠΞεΛ༗͍ͯ͠Δ͜ͱͷূࠨͰ͋Δ͜ͱ͕෼͔ͬͨɻୈ̎ʹɺ೚ҙ ͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗਫ४ͱ Auturky Ͱͷ౒ྗਫ४Λൺֱ

͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨɺ͜Ε͸౷ܭతʹ༗ҙͳࠩͰ͸ͳ͔ͬͨɻҎ্ͷ 2

ͭͷ݁ՌΛ૯߹తʹଊ͑Δͱɺݸਓ͕ݱࡏόΠΞεΛ༗͍ͯ͠ΔͨΊɺ Hopenhayn and Nicolini (1997) ʹΑͬͯ૝ఆ͞Ε͍ͯΔఔͷޮՌ͸ಘΒΕͳ͍͜ͱ͕֬ೝ͞Ε

ͨͱ͍͑Δɻ

∗

ຊݚڀ͸ɺฏ੒ 25 ೥౓ؔ੢େֶएखݚڀऀҭ੒ܦඅʹ͓͍ͯɺݚڀ՝୊ʮ࠷దࣦۀอݥͷޮ཰ੑͱϞ ϥϧɾϋβʔυʹ͍ͭͯͷܦࡁ࣮ݧʯͱͯ͠ݚڀඅΛड͚ɺͦͷ੒ՌΛެද͢Δ΋ͷͰ͋Δɻ·ͨɺຊݚڀ ʹ͓͍ͯ༻͍ΒΕͨΠϯετϥΫγϣϯɺਪఆίʔυ͸ಡऀ͔ΒͷٻΊ͕͋Γ࣍ୈஶऀ͔Β௚઀ख౉͢ܗ Ͱߦ͏ɻ

†

ؔ੢େֶܦࡁֶ෦; [email protected].

‡

ؔ੢େֶܦࡁֶ෦; [email protected].

§

େࡕ෎ཱେֶେֶӃܦࡁֶݚڀՊ; [email protected].

1

343

論　　文

1 ং࿦

೔ຊΛؚΉઌਐࠃͷଟ͘ʹ͓͚Δࣦۀอݥ੍౓͸ɺࣦۀޙͷ༗ݶͷҰఆظؒʹҰఆۚ

ֹͷڅ෇Λड͚Δͱ͍͏΋ͷͰ͋Δɻ͜ͷ࢓૊Έͷ໰୊఺ͷҰͭ͸ɺ৬୳͠ͷ౒ྗͷఔ

౓ʹ͔͔ΘΒͣɺܾΊΒΕͨڅ෇ֹ͕ड͚औΕΔͱ͜Ζʹ͋Δɻ΋ͪΖΜɺͨͱ͑͹೔

ຊͰ͸ɺϋϩʔϫʔΫ΁ͷ௨ॴͷٛ຿͕՝͞Ε͍ͯΔ͕ɺͦΕ͕౰֘ݸਓ͕අ΍͢ʹ;

͞Θ͍͠౒ྗਫ४͔͸ٙΘ͍͠ɻͭ·Γɺ৬୳͠ʹ͍ͭͯͷϞϥϧϋβʔυ͕ൃੜ͢Δ

͓ͦΕ͕͋Δɻ

͜ͷΑ͏ͳ؍఺͔Βɺ Hopenhayn and Nicolini (1997) ͸ɺࣦۀऀͷࣦۀظؒͷ௕͞

ʹԠͯ͡ɺద੾ͳਫ४ͷ౒ྗΛඅ΍͢ΠϯηϯςΟϒΛݸਓʹ༩͑ΔΑ͏ͳࣦۀอݥ੍

౓ͷ͋ΓํΛߟ࡯ͨ͠ ¹ ɻ൴Β͸ɺ࠷దͳࣦۀอݥͷಛ௃ͱͯ͠ɺࣦۀͯ͠΋ࣦۀظؒʹ Ԡࣦͯ͡ۀอݥͷڅ෇ֹ͕ঃʑʹݮֹ͞Ε͍ͯ͘ܗͷࣦۀอݥ͕࠷దʹͳΔ͜ͱΛࣔ͠

ͨɻ·ͨɺ͜ͷΑ͏ͳࣦۀอݥΛ࠾༻͢Δ͜ͱͰɺ੓෎ʹͱͬͯݱߦ੍౓ͷΑ͏ͳࣦۀ อݥʹൺ΂ͯɺ࣮ࢪඅ༻͕཈͑ΒΕΔ͜ͱΛ਺஋ܭࢉʹΑ͍ͬͯࣔͯ͠Δɻ

͜ͷ Hopenhayn and Nicolini (1997) ʹΑΔݚڀ͸ɺ੓෎ͷࡒ੓ͷޮ཰తͳӡӦͱٻ ৬ऀͷ৬୳͠ΠϯηϯςΟϒΛಉ࣌ʹ΋ͨΒ͢޼ົͳ࢓૊ΈͷΑ͏ʹΈ͑Δ͕ɺͦΕ͕

ຊ౰ʹཧ࿦͕૝ఆ͢ΔΑ͏ʹػೳ͢Δ͔ʹ͍࣮ͭͯࡍʹσʔλΛ༻͍ͯݕূ͢Δඞཁ͕

͋Δɻ͔͠͠ͳ͕Βɺ࣮ࡍʹ͜ͷ࠷దࣦۀอݥΛಋೖ͢Δࣄྫ͸ͳ͘ɺ࣮ࡍͷܦࡁσʔ λΛ༻͍ͨݕূ͸೉͍͠ɻͦ͜Ͱɺຊݚڀ͸ɺۙ೥੝Μʹݚڀ͕͓͜ͳΘΕ͍ͯΔܦࡁ

࣮ݧΛ༻͍ͯɺ্ड़ͷ࠷దࣦۀอݥ͕ཧ࿦͕૝ఆͨ͠Α͏ʹػೳ͢Δ͔Λݕূ͢Δ͜ͱ Λ໨తͱ͢Δɻ

۩ମతʹ͸ҎԼͷखॱʹΑ࣮ͬͯݧΛ࣮ࢪͨ͠ɻ·ͣɺඃݧऀΛΦϯϥΠϯͰืू͠ɺ

࠷దࣦۀอݥΛઃܭ͢Δ্ͰඞཁͱͳΔجૅతͳύϥϝʔλͱͯ͠ɺϦεΫճආ౓ͱ৬

୳͠ͷ౒ྗඅ༻ؔ਺ͷύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࣍ʹɺͦ͜ͰಘΒΕͨ

ύϥϝʔλΛ Hopenhayn and Nicolini (1997) ͷϞσϧʹ౰ͯ͸Ίͯɺ࠷దࣦۀอݥΛ ܭࢉͨ͠ɻͦͯ͠ɺ͜ͷ࠷దࣦۀอݥͷ΋ͱͰɺͲͷΑ͏ͳਫ४ͷ৬୳͠Λඃݧऀ͕࣮

ࢪ͢Δ͔ΛݟΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࠷ޙʹɺ౷੍܈ͱͯ͠ɺࣦۀอݥ͕ଘࡏ͠ͳ͍

Auturky ʹ͓͚Δඃݧऀͷ৬୳͠ߦಈΛௐ΂ͨɻ͜ͷ 2 ͭͷτϦʔτϝϯτΛൺֱ͢Δ

͜ͱͰɺ࠷దࣦۀอݥಋೖͷޮՌΛݕূ͢Δɻ

͜ͷΑ͏ʹઃܭ͞ΕͨΦϯϥΠϯ࣮ݧͰಘΒΕͨ݁Ռ͸࣍ͷ௨ΓͰ͋Δɻୈ̍ʹɺ࠷

దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ͸ҟͳΓɺඃݧ

ऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳɺ௿Լ͍ͯ͘͜͠ͱ͕෼͔ͬͨɻ

ୈ̎ʹɺ೚ҙͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗਫ४ͱ Auturky Ͱͷ౒ྗਫ ४Λൺֱ͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨ౷ܭతʹ༗ҙͳࠩͰ͸ͳ͔ͬͨɻ

·ͣɺୈ̍ͷ݁Ռʹ͍ͭͯ͸ɺ Hopenhayn and Nicolini (1997) Ͱ͸ى͜Γ͑ͳ͍ύ λʔϯΛ༗͍ͯ͠Δɻཧ࿦తʹ͸ɺࣦۀظ͕ؒ௕͘ͳΔͱͦͷঢ়ଶͰͷظ଴૯རಘ͕௿

Լ͍ͯ͘͠ͷͰɺফඅͷฏ४ԽʹΑͬͯࣗΒͷޮ༻্͕ঢ͢Δ͜ͱΛߟ͑Δͱɺ৬Λͳ Δ΂͘ಘΒΕΔΑ͏ʹ౒ྗਫ४Λ্ঢͤ͞Δ͔ͩΒͰ͋Δɻͭ·Γɺ͜ͷ݁Ռ͕ҙຯ͢

1

Pavoni (2007) ͸ɺ௨ৗݸਓ͸࠷௿ݶͷޮ༻ਫ४Λอো͢Δٛ຿͕੓෎ʹ͋Δ͜ͱΛߟྀ͠ɺ Hopenhayn and Nicolini (1997) ʹ௥Ճతͳ੍໿Λ՝ͨ͠ϞσϧΛߟ࡯͍ͯ͠Δɻ͞ΒʹɺHopenhayn and Nicolini

(2009) ͸ɺब৬ޙʹ࠶౓ࣦۀ͢ΔՄೳੑ͕͋Δ৔߹ͷ࠷దࣦۀอݥʹ͍ͭͯ࿦͍ͯ͡Δɻ

Δ͜ͱ͸ɺඃݧऀ͸ඪ४తͳબ޷Λ༗͓ͯ͠ΒͣɺԿΒ͔ͷܗͰݱࡏʹ͓͚Δޮ༻Λۃ

୺ʹॏࢹ͓ͯ͠Γɺͦͷ݁Ռͱͯ͠৬୳͠ͷ౒ྗΛඅ΍͢͜ͱΛͨΊΒ͍ͬͯΔͱߟ͑

ΒΕΔɻ

࣍ʹɺୈ̎ͷ݁Ռʹ͍ͭͯ͸ɺ্ड़ͷΑ͏ͳબ޷Λݸਓ͸༗͍ͯ͠Δͱߟ͑ΒΕΔͷ Ͱɺద੾ͳΠϯηϯςΟϒΛ༩͑Δ͜ͱͰ౒ྗਫ४͸ଟগ্ঢ͢Δ͕ɺ౷ܭతʹ༗ҙͳࠩ

͕ग़Δఔʹ͸վળ͠ͳ͍͜ͱΛ͍ࣔͯ͠Δɻݴ͍׵͑Δͱɺݸਓ͕ݱࡏόΠΞεΛ༗͠

͍ͯΔͨΊɺཧ࿦Ͱ૝ఆ͞Ε͍ͯΔఔͷޮՌ͸ಘΒΕͳ͍͜ͱ͕֬ೝ͞Εͨͱ͍͑Α͏ɻ

͜͏ͨ͠৬୳͠Λߦ͏ݸਓͷ౒ྗΠϯηϯςΟϒ໰୊Λݕূ͢Δຊݚڀʹ࠷΋ؔ࿈͢

Δݚڀͱͯ͠ɺ DellaVigna et al. (2017) ͕͋Δ ² ɻ DellaVigna et al. (2017) ͸ɺϋϯ ΨϦʔͰͷࣦۀอݥ੍౓͕ɺࣦۀظؒʹԠͯ̎͡ஈ֊ʹҾ͖Լ͛ΒΕΔ੍౓΁ͱมߋ͞

Εͨࣄ࣮ʹண໨ͯ͠ɺͦͷલޙͰݸਓͷ৬୳͠ΠϯηϯςΟϒ͕ͲͷΑ͏ʹมԽ͔ͨ͠

Λαʔνཧ࿦ʹجͮ͘ߏ଄ਪఆΛར༻ͯ͠ߟ࡯͍ͯ͠Δɻ൴ΒͷݚڀʹΑΕ͹ɺݸਓ͸

ඪ४తͳબ޷Ͱ͸ͳ͘ɺࢀর఺ґଘܕͷબ޷Λ࣋ͭͱਪఆ͞Εɺຊݚڀͱಉ͡Α͏ʹɺ

ࣦۀظؒʹԠͯ͡৬୳͠ͷ౒ྗਫ४͕௿Լ͢Δ͜ͱΛ؍࡯ͨ͠ɻ͞ΒʹɺϋϯΨϦʔͷ

ࣦۀอݥ੍౓͸ɺຊݚڀͱ͸ҟͳΓɺஈ֊తʹڅ෇ֹ͕Ҿ͖Լ͛ΒΕΔͨΊɺڅ෇ֹ͕

௿Լ͢ΔؒࡍʹͳΔͱɺٸʹ৬୳͠ͷ౒ྗΛ૿Ճ͞ΕΔͱ͍͏εύΠΫݱ৅Λใࠂͯ͠

͍Δɻ͔͠͠ͳ͕ΒɺຊݚڀͰ૝ఆ͢Δɺ Hopenhayn and Nicolini (1997) ܕͷ࠷దࣦ

ۀอݥ͸ɺࣦۀظؒʹԠͯ͡ଟஈճͰࡉ͔͘څ෇ֹ͕௿Լ͍ͯ͘͠ͷͰɺ DellaVigna et

al. (2017) Ͱൃݟ͞ΕͨΑ͏ͳεύΠΫݱ৅͸؍࡯͞Εͳ͔ͬͨɻ

͞Βʹɺຊݚڀ͸ɺϚΠΫϩλεΫܕΫϥ΢υιʔγϯάαʔϏεΛར༻ͯ͠Φϯϥ ΠϯͰͷ࣮ݧΛ࣮ࢪ͍ͯ͠ΔͨΊɺΦϯϥΠϯ࣮ݧΛ׆༻࣮ͨ͠ݧݚڀͱ΋ؔ࿈ͯ͠

͍Δɻۙ೥ɺ࣮ݧݚڀͷྖҬͰ͸ɺ Amazon ͷ Mechanical Turk ͱ͍͏Ϋϥ΢υιʔ γϯάαʔϏεʹΑΔ࣮ݧ͕গͣͭ͠Ͱ͸͋Δ͕ߦΘΕ͖͍ͯͯΔ (Mason and Suri (2012) ɺ Arechar et al. (2017a) ɺ Arechar et al. (2017b)) ɻ͜ΕΒҰ࿈ͷݚڀʹΑͬͯɺ

Mecanical Turk ͰͷඃݧऀͷࢀՃ࣌ؒଳผͷଐੑͳͲ্͕ड़ͷݚڀͰ໌Β͔ʹ͞Ε͖ͯ

͍ͯΔɻຊདྷͰ͋Ε͹ɺ͜ͷҰ࿈ͷݚڀ݁Ռʹج͍ͮͯ Mechanical Turk Ͱ࣮ݧΛߦ͏

ͷ͕๬·͍͕͠ɺ Mechanical Turk ্Ͱ࣮ݧΛߦ͏ʹ͸ɺถࠃͷॅॴʹඥ෇͚͞ΕͨΞ Χ΢ϯτ͕ඞཁͳΔɻͦ͜ͰɺถࠃͷॅॴΛ༗͍ͯ͠ͳ͍զʑ͸୅ସతͳํ๏ͱͯ͠ɺ

CrowdFlower ͱ͍͏גࣜձࣾΫϥ΢υϫʔΫε͕ӡӦ͢ΔɺϚΠΫϩλεΫܕΫϥ΢υ

ιʔγϯάαʔϏεΛར༻ͯ͠ΦϯϥΠϯͰͷ࣮ݧΛ࣮ࢪ͍ͯ͠Δɻຊݚڀ͸ɺΦϯϥ Πϯ࣮ݧͷख๏ʹ͍ͭͯͷ࿦จͰ͸ͳ͍ͷͰɺ CrowdFlower ͷࢀՃ࣌ؒଳผͷඃݧऀଐ

ੑΛௐࠪͨ͠Γɺ࣮ݧ࣮ࣨݧͱͷ੔߹ੑΛ֬ೝ͢Δ͜ͱ͕໨తͰ͸ͳ͍͕ɺ Mechanical Turk ͷ୅ସతͳखஈΛར༻ͯ͠ߦΘΕͨ਺গͳ͍ݚڀͱͳΔɻͦΕʹΑͬͯɺΦϯϥΠ ϯ࣮ݧͷख๏తಛੑΛ໌Β͔ʹ͢Δ୺ॹͱͳΔͰ͋Ζ͏ɻ

Ҏ߱ͷຊ࿦จͷߏ੒͸ҎԼͷ௨ΓͰ͋Δɻୈ 2 અͰཧ࿦Ϟσϧͷ঺հͱཧ࿦తͳ݁Ռ Λ঺հ͢Δɻୈ 3 અʹͯΦϯϥΠϯ࣮ݧͷ֓ཁΛઆ໌্ͨ͠Ͱɺୈ 4 અͰجૅύϥϝʔ λͷ࣮ݧͷઃܭͱ݁ՌΛड़΂ΔɻͦΕΒͷ݁Ռʹج͍ͮͯɺୈ 5 અʹ͓͍ͯຊݚڀͷओ ཁ෦෼Λߏ੒͢Δ࠷దࣦۀอݥʹ͍ͭͯͷ࣮ݧઃܭʹ͍ͭͯड़΂ɺଓ͍ͯୈ 6 અͰ࣮ݧ

2

ҟͳΔબ޷ʢ૒ۂׂҾʣΛԾఆͯ͠ߏ଄ਪఆΛߦͬͨ΋ͷͱͯ͠ɺDellaVigna and Paserman (2005) ͱ Paserman (2008) ͕͋Δɻ

3

1 ং࿦

೔ຊΛؚΉઌਐࠃͷଟ͘ʹ͓͚Δࣦۀอݥ੍౓͸ɺࣦۀޙͷ༗ݶͷҰఆظؒʹҰఆۚ

ֹͷڅ෇Λड͚Δͱ͍͏΋ͷͰ͋Δɻ͜ͷ࢓૊Έͷ໰୊఺ͷҰͭ͸ɺ৬୳͠ͷ౒ྗͷఔ

౓ʹ͔͔ΘΒͣɺܾΊΒΕͨڅ෇ֹ͕ड͚औΕΔͱ͜Ζʹ͋Δɻ΋ͪΖΜɺͨͱ͑͹೔

ຊͰ͸ɺϋϩʔϫʔΫ΁ͷ௨ॴͷٛ຿͕՝͞Ε͍ͯΔ͕ɺͦΕ͕౰֘ݸਓ͕අ΍͢ʹ;

͞Θ͍͠౒ྗਫ४͔͸ٙΘ͍͠ɻͭ·Γɺ৬୳͠ʹ͍ͭͯͷϞϥϧϋβʔυ͕ൃੜ͢Δ

͓ͦΕ͕͋Δɻ

͜ͷΑ͏ͳ؍఺͔Βɺ Hopenhayn and Nicolini (1997) ͸ɺࣦۀऀͷࣦۀظؒͷ௕͞

ʹԠͯ͡ɺద੾ͳਫ४ͷ౒ྗΛඅ΍͢ΠϯηϯςΟϒΛݸਓʹ༩͑ΔΑ͏ͳࣦۀอݥ੍

౓ͷ͋ΓํΛߟ࡯ͨ͠ ¹ ɻ൴Β͸ɺ࠷దͳࣦۀอݥͷಛ௃ͱͯ͠ɺࣦۀͯ͠΋ࣦۀظؒʹ Ԡࣦͯ͡ۀอݥͷڅ෇ֹ͕ঃʑʹݮֹ͞Ε͍ͯ͘ܗͷࣦۀอݥ͕࠷దʹͳΔ͜ͱΛࣔ͠

ͨɻ·ͨɺ͜ͷΑ͏ͳࣦۀอݥΛ࠾༻͢Δ͜ͱͰɺ੓෎ʹͱͬͯݱߦ੍౓ͷΑ͏ͳࣦۀ อݥʹൺ΂ͯɺ࣮ࢪඅ༻͕཈͑ΒΕΔ͜ͱΛ਺஋ܭࢉʹΑ͍ͬͯࣔͯ͠Δɻ

͜ͷ Hopenhayn and Nicolini (1997) ʹΑΔݚڀ͸ɺ੓෎ͷࡒ੓ͷޮ཰తͳӡӦͱٻ ৬ऀͷ৬୳͠ΠϯηϯςΟϒΛಉ࣌ʹ΋ͨΒ͢޼ົͳ࢓૊ΈͷΑ͏ʹΈ͑Δ͕ɺͦΕ͕

ຊ౰ʹཧ࿦͕૝ఆ͢ΔΑ͏ʹػೳ͢Δ͔ʹ͍࣮ͭͯࡍʹσʔλΛ༻͍ͯݕূ͢Δඞཁ͕

͋Δɻ͔͠͠ͳ͕Βɺ࣮ࡍʹ͜ͷ࠷దࣦۀอݥΛಋೖ͢Δࣄྫ͸ͳ͘ɺ࣮ࡍͷܦࡁσʔ λΛ༻͍ͨݕূ͸೉͍͠ɻͦ͜Ͱɺຊݚڀ͸ɺۙ೥੝Μʹݚڀ͕͓͜ͳΘΕ͍ͯΔܦࡁ

࣮ݧΛ༻͍ͯɺ্ड़ͷ࠷దࣦۀอݥ͕ཧ࿦͕૝ఆͨ͠Α͏ʹػೳ͢Δ͔Λݕূ͢Δ͜ͱ Λ໨తͱ͢Δɻ

۩ମతʹ͸ҎԼͷखॱʹΑ࣮ͬͯݧΛ࣮ࢪͨ͠ɻ·ͣɺඃݧऀΛΦϯϥΠϯͰืू͠ɺ

࠷దࣦۀอݥΛઃܭ͢Δ্ͰඞཁͱͳΔجૅతͳύϥϝʔλͱͯ͠ɺϦεΫճආ౓ͱ৬

୳͠ͷ౒ྗඅ༻ؔ਺ͷύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࣍ʹɺͦ͜ͰಘΒΕͨ

ύϥϝʔλΛ Hopenhayn and Nicolini (1997) ͷϞσϧʹ౰ͯ͸Ίͯɺ࠷దࣦۀอݥΛ ܭࢉͨ͠ɻͦͯ͠ɺ͜ͷ࠷దࣦۀอݥͷ΋ͱͰɺͲͷΑ͏ͳਫ४ͷ৬୳͠Λඃݧऀ͕࣮

ࢪ͢Δ͔ΛݟΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࠷ޙʹɺ౷੍܈ͱͯ͠ɺࣦۀอݥ͕ଘࡏ͠ͳ͍

Auturky ʹ͓͚Δඃݧऀͷ৬୳͠ߦಈΛௐ΂ͨɻ͜ͷ 2 ͭͷτϦʔτϝϯτΛൺֱ͢Δ

͜ͱͰɺ࠷దࣦۀอݥಋೖͷޮՌΛݕূ͢Δɻ

͜ͷΑ͏ʹઃܭ͞ΕͨΦϯϥΠϯ࣮ݧͰಘΒΕͨ݁Ռ͸࣍ͷ௨ΓͰ͋Δɻୈ̍ʹɺ࠷

దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ͸ҟͳΓɺඃݧ

ऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳɺ௿Լ͍ͯ͘͜͠ͱ͕෼͔ͬͨɻ

ୈ̎ʹɺ೚ҙͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗਫ४ͱ Auturky Ͱͷ౒ྗਫ ४Λൺֱ͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨ౷ܭతʹ༗ҙͳࠩͰ͸ͳ͔ͬͨɻ

·ͣɺୈ̍ͷ݁Ռʹ͍ͭͯ͸ɺ Hopenhayn and Nicolini (1997) Ͱ͸ى͜Γ͑ͳ͍ύ λʔϯΛ༗͍ͯ͠Δɻཧ࿦తʹ͸ɺࣦۀظ͕ؒ௕͘ͳΔͱͦͷঢ়ଶͰͷظ଴૯རಘ͕௿

Լ͍ͯ͘͠ͷͰɺফඅͷฏ४ԽʹΑͬͯࣗΒͷޮ༻্͕ঢ͢Δ͜ͱΛߟ͑Δͱɺ৬Λͳ Δ΂͘ಘΒΕΔΑ͏ʹ౒ྗਫ४Λ্ঢͤ͞Δ͔ͩΒͰ͋Δɻͭ·Γɺ͜ͷ݁Ռ͕ҙຯ͢

1

Pavoni (2007) ͸ɺ௨ৗݸਓ͸࠷௿ݶͷޮ༻ਫ४Λอো͢Δٛ຿͕੓෎ʹ͋Δ͜ͱΛߟྀ͠ɺ Hopenhayn and Nicolini (1997) ʹ௥Ճతͳ੍໿Λ՝ͨ͠ϞσϧΛߟ࡯͍ͯ͠Δɻ͞ΒʹɺHopenhayn and Nicolini

(2009) ͸ɺब৬ޙʹ࠶౓ࣦۀ͢ΔՄೳੑ͕͋Δ৔߹ͷ࠷దࣦۀอݥʹ͍ͭͯ࿦͍ͯ͡Δɻ

2 345

1 ং࿦

೔ຊΛؚΉઌਐࠃͷଟ͘ʹ͓͚Δࣦۀอݥ੍౓͸ɺࣦۀޙͷ༗ݶͷҰఆظؒʹҰఆۚ

ֹͷڅ෇Λड͚Δͱ͍͏΋ͷͰ͋Δɻ͜ͷ࢓૊Έͷ໰୊఺ͷҰͭ͸ɺ৬୳͠ͷ౒ྗͷఔ

౓ʹ͔͔ΘΒͣɺܾΊΒΕͨڅ෇ֹ͕ड͚औΕΔͱ͜Ζʹ͋Δɻ΋ͪΖΜɺͨͱ͑͹೔

ຊͰ͸ɺϋϩʔϫʔΫ΁ͷ௨ॴͷٛ຿͕՝͞Ε͍ͯΔ͕ɺͦΕ͕౰֘ݸਓ͕අ΍͢ʹ;

͞Θ͍͠౒ྗਫ४͔͸ٙΘ͍͠ɻͭ·Γɺ৬୳͠ʹ͍ͭͯͷϞϥϧϋβʔυ͕ൃੜ͢Δ

͓ͦΕ͕͋Δɻ

͜ͷΑ͏ͳ؍఺͔Βɺ Hopenhayn and Nicolini (1997) ͸ɺࣦۀऀͷࣦۀظؒͷ௕͞

ʹԠͯ͡ɺద੾ͳਫ४ͷ౒ྗΛඅ΍͢ΠϯηϯςΟϒΛݸਓʹ༩͑ΔΑ͏ͳࣦۀอݥ੍

౓ͷ͋ΓํΛߟ࡯ͨ͠ ¹ ɻ൴Β͸ɺ࠷దͳࣦۀอݥͷಛ௃ͱͯ͠ɺࣦۀͯ͠΋ࣦۀظؒʹ Ԡࣦͯ͡ۀอݥͷڅ෇ֹ͕ঃʑʹݮֹ͞Ε͍ͯ͘ܗͷࣦۀอݥ͕࠷దʹͳΔ͜ͱΛࣔ͠

ͨɻ·ͨɺ͜ͷΑ͏ͳࣦۀอݥΛ࠾༻͢Δ͜ͱͰɺ੓෎ʹͱͬͯݱߦ੍౓ͷΑ͏ͳࣦۀ อݥʹൺ΂ͯɺ࣮ࢪඅ༻͕཈͑ΒΕΔ͜ͱΛ਺஋ܭࢉʹΑ͍ͬͯࣔͯ͠Δɻ

͜ͷ Hopenhayn and Nicolini (1997) ʹΑΔݚڀ͸ɺ੓෎ͷࡒ੓ͷޮ཰తͳӡӦͱٻ ৬ऀͷ৬୳͠ΠϯηϯςΟϒΛಉ࣌ʹ΋ͨΒ͢޼ົͳ࢓૊ΈͷΑ͏ʹΈ͑Δ͕ɺͦΕ͕

ຊ౰ʹཧ࿦͕૝ఆ͢ΔΑ͏ʹػೳ͢Δ͔ʹ͍࣮ͭͯࡍʹσʔλΛ༻͍ͯݕূ͢Δඞཁ͕

͋Δɻ͔͠͠ͳ͕Βɺ࣮ࡍʹ͜ͷ࠷దࣦۀอݥΛಋೖ͢Δࣄྫ͸ͳ͘ɺ࣮ࡍͷܦࡁσʔ λΛ༻͍ͨݕূ͸೉͍͠ɻͦ͜Ͱɺຊݚڀ͸ɺۙ೥੝Μʹݚڀ͕͓͜ͳΘΕ͍ͯΔܦࡁ

࣮ݧΛ༻͍ͯɺ্ड़ͷ࠷దࣦۀอݥ͕ཧ࿦͕૝ఆͨ͠Α͏ʹػೳ͢Δ͔Λݕূ͢Δ͜ͱ Λ໨తͱ͢Δɻ

۩ମతʹ͸ҎԼͷखॱʹΑ࣮ͬͯݧΛ࣮ࢪͨ͠ɻ·ͣɺඃݧऀΛΦϯϥΠϯͰืू͠ɺ

࠷దࣦۀอݥΛઃܭ͢Δ্ͰඞཁͱͳΔجૅతͳύϥϝʔλͱͯ͠ɺϦεΫճආ౓ͱ৬

୳͠ͷ౒ྗඅ༻ؔ਺ͷύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࣍ʹɺͦ͜ͰಘΒΕͨ

ύϥϝʔλΛ Hopenhayn and Nicolini (1997) ͷϞσϧʹ౰ͯ͸Ίͯɺ࠷దࣦۀอݥΛ ܭࢉͨ͠ɻͦͯ͠ɺ͜ͷ࠷దࣦۀอݥͷ΋ͱͰɺͲͷΑ͏ͳਫ४ͷ৬୳͠Λඃݧऀ͕࣮

ࢪ͢Δ͔ΛݟΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ࠷ޙʹɺ౷੍܈ͱͯ͠ɺࣦۀอݥ͕ଘࡏ͠ͳ͍

Auturky ʹ͓͚Δඃݧऀͷ৬୳͠ߦಈΛௐ΂ͨɻ͜ͷ 2 ͭͷτϦʔτϝϯτΛൺֱ͢Δ

͜ͱͰɺ࠷దࣦۀอݥಋೖͷޮՌΛݕূ͢Δɻ

͜ͷΑ͏ʹઃܭ͞ΕͨΦϯϥΠϯ࣮ݧͰಘΒΕͨ݁Ռ͸࣍ͷ௨ΓͰ͋Δɻୈ̍ʹɺ࠷

దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ͸ҟͳΓɺඃݧ

ऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳɺ௿Լ͍ͯ͘͜͠ͱ͕෼͔ͬͨɻ

ୈ̎ʹɺ೚ҙͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗਫ४ͱ Auturky Ͱͷ౒ྗਫ ४Λൺֱ͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨ౷ܭతʹ༗ҙͳࠩͰ͸ͳ͔ͬͨɻ

·ͣɺୈ̍ͷ݁Ռʹ͍ͭͯ͸ɺ Hopenhayn and Nicolini (1997) Ͱ͸ى͜Γ͑ͳ͍ύ λʔϯΛ༗͍ͯ͠Δɻཧ࿦తʹ͸ɺࣦۀظ͕ؒ௕͘ͳΔͱͦͷঢ়ଶͰͷظ଴૯རಘ͕௿

Լ͍ͯ͘͠ͷͰɺফඅͷฏ४ԽʹΑͬͯࣗΒͷޮ༻্͕ঢ͢Δ͜ͱΛߟ͑Δͱɺ৬Λͳ Δ΂͘ಘΒΕΔΑ͏ʹ౒ྗਫ४Λ্ঢͤ͞Δ͔ͩΒͰ͋Δɻͭ·Γɺ͜ͷ݁Ռ͕ҙຯ͢

1

Pavoni (2007) ͸ɺ௨ৗݸਓ͸࠷௿ݶͷޮ༻ਫ४Λอো͢Δٛ຿͕੓෎ʹ͋Δ͜ͱΛߟྀ͠ɺ Hopenhayn and Nicolini (1997) ʹ௥Ճతͳ੍໿Λ՝ͨ͠ϞσϧΛߟ࡯͍ͯ͠Δɻ͞ΒʹɺHopenhayn and Nicolini

(2009) ͸ɺब৬ޙʹ࠶౓ࣦۀ͢ΔՄೳੑ͕͋Δ৔߹ͷ࠷దࣦۀอݥʹ͍ͭͯ࿦͍ͯ͡Δɻ

344 2

ͱ݁ՌΛड़΂Δɻ࠷ޙʹɺୈ 7 અͰ݁࿦ͱࠓޙͷ՝୊Λड़΂Δɻ

2 ཧ࿦Ϟσϧͱཧ࿦త݁Ռ

͍·ɺࣦۀऀ͕

E

∑ ∞ t=0

β ^t [u(c _t ) − a _t ] (1)

ʹ΋ͱ͖ͮɺফඅͱ৬୳͠ͷ౒ྗਫ४ͷྻ { c _t , a _t } ^∞ t=0 Λબ୒͢Δঢ়گΛߟ͑Δɻ͜͜Ͱɺ c _t ɺ a _t ͸ඇෛͱ͢Δɻ·ͨɺ β ∈ (0, 1) ͸ׂҾҼࢠΛද͠ɺ u(c) ͸ݫີʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺ͱ͢Δɻ͢΂ͯͷ৬͸ಉ࣭తͰɺҰ୴৬ʹͭ͘ͱຖظ w ≥ 0 ΛӬԕʹ΋ͨΒ͢΋ͷͱ͢Δɻࣦۀऀ͸ຖظ౒ྗਫ४ a Ͱ৬୳͠Λߦ͍ɺ֬཰ p(a) Ͱ࣍

ظҎ߱ͷ৬ΛಘΔ͜ͱʹͳΔɻ৬Λಘͨޙ͸ a = 0 ͱͳΔ΋ͷͱ͢Δɻؔ਺ p(a) ͸ݫີ

ʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺Ͱɺ͢΂ͯͷ a ≥ 0 ʹ͍ͭͯ p(a) ∈ [0, 1] Λ

ຬͨ͠ɺ͔ͭɺ p(0) = 0 ͱ͢Δɻফඅऀ͸ফඅࡒΛஷଂ͢Δ͜ͱ͕ग़དྷͣɺ·ͨɺஷ஝

΍आΓೖΕΛ͢Δ͜ͱ͕ग़དྷͳ͍΋ͷͱ͢Δɻ

Ҏ্ͷઃఆͷ΋ͱͰɺ·ͣϕϯνϚʔΫͱࣦͯ͠ۀอݥΛར༻͢Δ͜ͱ͕ग़དྷͳ͍

Autarky ʹ͓͚Δ౰֘ݸਓͷՁ஋Λܭࢉ͢Δɻ·ͣɺࣦۀঢ়ଶʹ͋Δݸਓ͸Ұ୴ޏ༻͞

ΕΕ͹ɺϞσϧͷԾఆ্Ӭԕʹޏ༻͞Εଓ͚Δ͜ͱʹͳΓɺٵऩঢ়ଶͱͳΔ͜ͱʹ஫ҙ

͢Δɻͦͷͱ͖ɺ͔ͦ͜ΒޙΖ޲͖ʹղ͘͜ͱͰɺ࠷దͳՁ஋Λܭࢉ͢Δ͜ͱ͕Ͱ͖ɺ

ͦͷޏ༻ঢ়ଶʹ͓͚ΔׂҾ૯རಘΛ V ^e ͱ͢Δɻ·ͨɺ্ͰԾఆͨ͠௨ΓɺҰ୴ޏ༻͞

Εͯ͠·͑͹ɺ౰֘ݸਓ͸৬୳͠ͷͨΊͷ౒ྗඅ༻Λ෷ΘͣʹࡁΉͷͰɺ V ^e ͸ V ^e = u(w)

1 − β (2)

ͱͯ͠ܭࢉ͞ΕΔɻଞํɺ V ^u Λࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘΛද͢΋ͷͱ͢Δͱɺ

ͦͷϕϧϚϯํఔࣜ͸ɺ V ^u = max

a≥0

{

u(0) − β[p(a)V ^e + (1 − p(a)V ^u )] }

(3)

ͱͳΔɻ͞Βʹɺਖ਼ͷ౒ྗਫ४ΛҾ͖ग़ͨ͢Ίʹ͸ V ^e − V ^u > 0 Ͱͳ͚Ε͹ͳΒͳ͍ͱ

͍͏͜ͱͱɺ p ͕Ԝؔ਺ͳͷͰɺͦͷ 1 ֊ͷ৚݅͸

βp ^′ (a)(V ^e − V ^u ) = 1 (4)

ͱͳΔɻ͜ͷ໰୊Λղ͍ͨ݁ՌಘΒΕΔ࠷దՁ஋Λ V _aut ͱ͠ɺͦΕΛ༩͑Δ౒ྗਫ४Λ a _aut ͱ͓͘ɻ

࣍ʹɺ੓෎͕ଘࡏ͠ɺࣦۀอݥ੍౓͕͋Δঢ়گΛ Hopenhayn and Nicolini (1997) Λ

؆ૉԽͨ͠ Ljungqvist and Sargent (2012) ʹैͬͯߟ࡯͢Δɻ͜͜Ͱɺ੓෎͸ݸਓͷ

৬୳͠ͷ౒ྗਫ४ a Λ؍࡯Ͱ͖ͳ͍ͱ͢Δɻ͕ͨͬͯ͠ɺ੓෎͕௚໘͢Δ໰୊͸ɺࣦۀ

ঢ়ଶʹ͓͚Δফඅਫ४ c ɺ৬୳͠ͷ౒ྗਫ४ a ɺ͓Αͼɺෆ޾ʹ΋དྷظ΋ࣦۀঢ়ଶʹؕͬ

ͯ͠·ͬͨ࣌ͷՁ஋ͷਫ४ V ^u Λॴ༩ͱͯ͠ɺࣦۀอݥ࣮ࢪͷظ଴ׂҾ૯අ༻Λ࠷খԽ

͢Δ໰୊ͱͯ͠ఆࣜԽ͢Δ͜ͱ͕Ͱ͖Δɻͭ·Γɺ੓෎ͷ࠷దࣦۀอݥઃܭ໰୊͸

C(V ) = min

c,a,V

^u

{ c + β(1 − p(a))C(V ^u ) }

s.t.

u(c) − a + β { p(a)V ^e + (1 − p(a))V ^u } = V, (5)

βp ^′ (a)(V ^e − V ^u ) = 1 (6)

ͱॻ͚Δɻ্ه੍໿৚݅ͷ͏ͪɺ (5) ͸ݸਓʹՁ஋ V Λ༩͑Δ౰֘ݸਓͷՁ஋࠶ؼࣜ

(promise-keeping constraint) Ͱ͋Γɺ (6) ͸౰֘ݸਓ͕੓෎͕ࢦఆͨ͠௨Γͷ౒ྗਫ४ a ΛͱΔͨΊͷ༠Ҽཱ྆ੑ৚݅ (incentive compatibility condition) _Ͱ͋Δɻ

͜ͷ࠷దࣦۀอݥઃܭ໰୊ʹ͓͚Δબ୒ม਺ c, a, V ^u ʹؔ͢Δ 1 ֊ͷ৚݅͸

λu ^′ (c) = 1 (7)

βp ^′ (a) {− C (V ^u ) } (8)

= λ [

− 1 + βp ^′ (a) { V ^e − V ^u } ]

+ ηβp ^′′ (a)(V ^e − V ^u ) C ^′ (V ^u ) = λ − η p ^′ (a)

1 − p(a) (9)

ͱͳΔɻ͜͜Ͱɺ λ ͸ (5) ʹ͍ͭͯͷɺ·ͨ η ͸ (6) ʹ͍ͭͯͷ৐਺Ͱ͋Δɻ্ه 1 ֊ͷ

৚݅ͷ͏ͪɺ (8) ͷӈลͷୈ 1 ߲͸ (6) ΑΓθϩͱͳΔͷͰɺ (8) ͸ C(V ^u ) = − η p ^′′ (a)

p ^′ (a) (V ^e − V ^u ) (10)

ͱͳΔɻ·ͨɺ (7) ΑΓ λ = 1/u ^′ (c) ͳͷͰɺ͜ΕΛ (9) ʹ୅ೖ͢Δͱɺ

C ^′ (V ^u ) = 1/u ^′ (c) − η p ^′ (a)

1 − p(a) (11)

ͱͳΔɻ࠷ޙʹɺแབྷઢ৚݅ΑΓ C ^′ (V ) = λ ͓Αͼ (7) ΑΓɺ

C ^′ (V ) = 1/u ^′ (c) (12)

ͱͳΔɻ

·ͣɺ (9) ͱ (12) ΑΓɺ C ^′ (V ^u ) < C ^′ (V ) ͱͳΔ͜ͱ͕෼͔Δɻ͜͜ͰɺΑΓߴ͍ਫ ४ͷ V ͷ΋ͱͰ͸ɺ౰֘ݸਓͷݶքޮ༻͸௿͘ͳΔͨΊɺͦͷ V Λ΋ͨΒͨ͢Ίͷඅ

༻͸ΑΓߴ͘ͳΔͷͰɺ C (V ) ͸ V ʹ͍ͭͯತؔ਺ͱͳΔ͜ͱʹ஫ҙ͢ΔɻͦΕΏ͑ɺ C ^′ (V ^u ) < C ^′ (V ) ͸ V ^u < V Λҙຯ͢Δɻ͞Βʹɺ͜ͷࣄ࣮ͱ (12) ɺ͓Αͼɺޮ༻ؔ਺

u ͕Ԝؔ਺Ͱ͋Δ͜ͱ͔ΒɺࣦۀதͷΤʔδΣϯτͷফඅਫ४͸ࣦۀظؒͷܦաͱڞʹ

5 ͱ݁ՌΛड़΂Δɻ࠷ޙʹɺୈ 7 અͰ݁࿦ͱࠓޙͷ՝୊Λड़΂Δɻ

2 ཧ࿦Ϟσϧͱཧ࿦త݁Ռ

͍·ɺࣦۀऀ͕

E

∑ ∞ t=0

β ^t [u(c _t ) − a _t ] (1)

ʹ΋ͱ͖ͮɺফඅͱ৬୳͠ͷ౒ྗਫ४ͷྻ { c _t , a _t } ^∞ t=0 Λબ୒͢Δঢ়گΛߟ͑Δɻ͜͜Ͱɺ c _t ɺ a _t ͸ඇෛͱ͢Δɻ·ͨɺ β ∈ (0, 1) ͸ׂҾҼࢠΛද͠ɺ u(c) ͸ݫີʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺ͱ͢Δɻ͢΂ͯͷ৬͸ಉ࣭తͰɺҰ୴৬ʹͭ͘ͱຖظ w ≥ 0 ΛӬԕʹ΋ͨΒ͢΋ͷͱ͢Δɻࣦۀऀ͸ຖظ౒ྗਫ४ a Ͱ৬୳͠Λߦ͍ɺ֬཰ p(a) Ͱ࣍

ظҎ߱ͷ৬ΛಘΔ͜ͱʹͳΔɻ৬Λಘͨޙ͸ a = 0 ͱͳΔ΋ͷͱ͢Δɻؔ਺ p(a) ͸ݫີ

ʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺Ͱɺ͢΂ͯͷ a ≥ 0 ʹ͍ͭͯ p(a) ∈ [0, 1] Λ

ຬͨ͠ɺ͔ͭɺ p(0) = 0 ͱ͢Δɻফඅऀ͸ফඅࡒΛஷଂ͢Δ͜ͱ͕ग़དྷͣɺ·ͨɺஷ஝

΍आΓೖΕΛ͢Δ͜ͱ͕ग़དྷͳ͍΋ͷͱ͢Δɻ

Ҏ্ͷઃఆͷ΋ͱͰɺ·ͣϕϯνϚʔΫͱࣦͯ͠ۀอݥΛར༻͢Δ͜ͱ͕ग़དྷͳ͍

Autarky ʹ͓͚Δ౰֘ݸਓͷՁ஋Λܭࢉ͢Δɻ·ͣɺࣦۀঢ়ଶʹ͋Δݸਓ͸Ұ୴ޏ༻͞

ΕΕ͹ɺϞσϧͷԾఆ্Ӭԕʹޏ༻͞Εଓ͚Δ͜ͱʹͳΓɺٵऩঢ়ଶͱͳΔ͜ͱʹ஫ҙ

͢Δɻͦͷͱ͖ɺ͔ͦ͜ΒޙΖ޲͖ʹղ͘͜ͱͰɺ࠷దͳՁ஋Λܭࢉ͢Δ͜ͱ͕Ͱ͖ɺ

ͦͷޏ༻ঢ়ଶʹ͓͚ΔׂҾ૯རಘΛ V ^e ͱ͢Δɻ·ͨɺ্ͰԾఆͨ͠௨ΓɺҰ୴ޏ༻͞

Εͯ͠·͑͹ɺ౰֘ݸਓ͸৬୳͠ͷͨΊͷ౒ྗඅ༻Λ෷ΘͣʹࡁΉͷͰɺ V ^e ͸ V ^e = u(w)

1 − β (2)

ͱͯ͠ܭࢉ͞ΕΔɻଞํɺ V ^u Λࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘΛද͢΋ͷͱ͢Δͱɺ

ͦͷϕϧϚϯํఔࣜ͸ɺ V ^u = max

a≥0

{

u(0) − β[p(a)V ^e + (1 − p(a)V ^u )] }

(3)

ͱͳΔɻ͞Βʹɺਖ਼ͷ౒ྗਫ४ΛҾ͖ग़ͨ͢Ίʹ͸ V ^e − V ^u > 0 Ͱͳ͚Ε͹ͳΒͳ͍ͱ

͍͏͜ͱͱɺ p ͕Ԝؔ਺ͳͷͰɺͦͷ 1 ֊ͷ৚݅͸

βp ^′ (a)(V ^e − V ^u ) = 1 (4)

ͱͳΔɻ͜ͷ໰୊Λղ͍ͨ݁ՌಘΒΕΔ࠷దՁ஋Λ V _aut ͱ͠ɺͦΕΛ༩͑Δ౒ྗਫ४Λ a _aut ͱ͓͘ɻ

࣍ʹɺ੓෎͕ଘࡏ͠ɺࣦۀอݥ੍౓͕͋Δঢ়گΛ Hopenhayn and Nicolini (1997) Λ

؆ૉԽͨ͠ Ljungqvist and Sargent (2012) ʹैͬͯߟ࡯͢Δɻ͜͜Ͱɺ੓෎͸ݸਓͷ ৬୳͠ͷ౒ྗਫ४ a Λ؍࡯Ͱ͖ͳ͍ͱ͢Δɻ͕ͨͬͯ͠ɺ੓෎͕௚໘͢Δ໰୊͸ɺࣦۀ ঢ়ଶʹ͓͚Δফඅਫ४ c ɺ৬୳͠ͷ౒ྗਫ४ a ɺ͓Αͼɺෆ޾ʹ΋དྷظ΋ࣦۀঢ়ଶʹؕͬ

4 347

ͱ݁ՌΛड़΂Δɻ࠷ޙʹɺୈ 7 અͰ݁࿦ͱࠓޙͷ՝୊Λड़΂Δɻ

2 ཧ࿦Ϟσϧͱཧ࿦త݁Ռ

͍·ɺࣦۀऀ͕

E

∑ ∞ t=0

β ^t [u(c _t ) − a _t ] (1)

ʹ΋ͱ͖ͮɺফඅͱ৬୳͠ͷ౒ྗਫ४ͷྻ { c _t , a _t } ^∞ t=0 Λબ୒͢Δঢ়گΛߟ͑Δɻ͜͜Ͱɺ c _t ɺ a _t ͸ඇෛͱ͢Δɻ·ͨɺ β ∈ (0, 1) ͸ׂҾҼࢠΛද͠ɺ u(c) ͸ݫີʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺ͱ͢Δɻ͢΂ͯͷ৬͸ಉ࣭తͰɺҰ୴৬ʹͭ͘ͱຖظ w ≥ 0 ΛӬԕʹ΋ͨΒ͢΋ͷͱ͢Δɻࣦۀऀ͸ຖظ౒ྗਫ४ a Ͱ৬୳͠Λߦ͍ɺ֬཰ p(a) Ͱ࣍

ظҎ߱ͷ৬ΛಘΔ͜ͱʹͳΔɻ৬Λಘͨޙ͸ a = 0 ͱͳΔ΋ͷͱ͢Δɻؔ਺ p(a) ͸ݫີ

ʹ૿Ճɺ͔ͭɺ 2 ճඍ෼ՄೳͳݫີͳԜؔ਺Ͱɺ͢΂ͯͷ a ≥ 0 ʹ͍ͭͯ p(a) ∈ [0, 1] Λ

ຬͨ͠ɺ͔ͭɺ p(0) = 0 ͱ͢Δɻফඅऀ͸ফඅࡒΛஷଂ͢Δ͜ͱ͕ग़དྷͣɺ·ͨɺஷ஝

΍आΓೖΕΛ͢Δ͜ͱ͕ग़དྷͳ͍΋ͷͱ͢Δɻ

Ҏ্ͷઃఆͷ΋ͱͰɺ·ͣϕϯνϚʔΫͱࣦͯ͠ۀอݥΛར༻͢Δ͜ͱ͕ग़དྷͳ͍

Autarky ʹ͓͚Δ౰֘ݸਓͷՁ஋Λܭࢉ͢Δɻ·ͣɺࣦۀঢ়ଶʹ͋Δݸਓ͸Ұ୴ޏ༻͞

ΕΕ͹ɺϞσϧͷԾఆ্Ӭԕʹޏ༻͞Εଓ͚Δ͜ͱʹͳΓɺٵऩঢ়ଶͱͳΔ͜ͱʹ஫ҙ

͢Δɻͦͷͱ͖ɺ͔ͦ͜ΒޙΖ޲͖ʹղ͘͜ͱͰɺ࠷దͳՁ஋Λܭࢉ͢Δ͜ͱ͕Ͱ͖ɺ

ͦͷޏ༻ঢ়ଶʹ͓͚ΔׂҾ૯རಘΛ V ^e ͱ͢Δɻ·ͨɺ্ͰԾఆͨ͠௨ΓɺҰ୴ޏ༻͞

Εͯ͠·͑͹ɺ౰֘ݸਓ͸৬୳͠ͷͨΊͷ౒ྗඅ༻Λ෷ΘͣʹࡁΉͷͰɺ V ^e ͸ V ^e = u(w)

1 − β (2)

ͱͯ͠ܭࢉ͞ΕΔɻଞํɺ V ^u Λࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘΛද͢΋ͷͱ͢Δͱɺ

ͦͷϕϧϚϯํఔࣜ͸ɺ V ^u = max

a≥0

{

u(0) − β[p(a)V ^e + (1 − p(a)V ^u )] }

(3)

ͱͳΔɻ͞Βʹɺਖ਼ͷ౒ྗਫ४ΛҾ͖ग़ͨ͢Ίʹ͸ V ^e − V ^u > 0 Ͱͳ͚Ε͹ͳΒͳ͍ͱ

͍͏͜ͱͱɺ p ͕Ԝؔ਺ͳͷͰɺͦͷ 1 ֊ͷ৚݅͸

βp ^′ (a)(V ^e − V ^u ) = 1 (4)

ͱͳΔɻ͜ͷ໰୊Λղ͍ͨ݁ՌಘΒΕΔ࠷దՁ஋Λ V _aut ͱ͠ɺͦΕΛ༩͑Δ౒ྗਫ४Λ a _aut ͱ͓͘ɻ

࣍ʹɺ੓෎͕ଘࡏ͠ɺࣦۀอݥ੍౓͕͋Δঢ়گΛ Hopenhayn and Nicolini (1997) Λ

؆ૉԽͨ͠ Ljungqvist and Sargent (2012) ʹैͬͯߟ࡯͢Δɻ͜͜Ͱɺ੓෎͸ݸਓͷ ৬୳͠ͷ౒ྗਫ४ a Λ؍࡯Ͱ͖ͳ͍ͱ͢Δɻ͕ͨͬͯ͠ɺ੓෎͕௚໘͢Δ໰୊͸ɺࣦۀ ঢ়ଶʹ͓͚Δফඅਫ४ c ɺ৬୳͠ͷ౒ྗਫ४ a ɺ͓Αͼɺෆ޾ʹ΋དྷظ΋ࣦۀঢ়ଶʹؕͬ

346 4

ݮগ͍ͯ͘͜͠ͱ͕Θ͔Δɻ

͜ΕΒͷࣄ࣮Λ·ͱΊΔͱ࣍ͷ໋୊ΛಘΔɻ

Proposition 1 (Hopenhayn and Nicolini (1997)) V ^u < V ͕੒ཱ͢Δɻ·ͨɺ

ࣦۀอݥʹΑΔڅ෇͸ࣦۀظ͕ؒ௕͘ͳΔఔݮগ͍ͯ͘͠ɻ

3 CrowdFlower ʹΑΔΦϯϥΠϯ࣮ݧ

ຊݚڀʹ͓͚Δɺ࠷దࣦۀอݥͷ࣮ݧ͸ɺ࣮ݧ࣮ࢪऀଆͰ࠷దࣦۀอݥΛఆΊͯ͠·

͑͹ɺ࢒Δҙࢥܾఆ໰୊͸ɺ֤ݸਓͷಈֶతܾఆ໰୊ͱͳΔɻͦΕΛ࣮ݧ࣮ࣨݧʹ࣮ͯ

ࢪ͢Δ৔߹͸ɺେྔͷඃݧऀϓʔϧ͕ඞཁͱͳΓɺ౷ܭ෼ੳΛ࣮ࢪ͢Δҙຯͷ͋Δਓ਺

ͷඃݧऀΛूΊΔ͜ͱ͸େม೉͍͠ɻͦ͜Ͱɺզʑ͸େྔͷඃݧऀΛ୹ظؒͰूΊΔ͜

ͱ͕Ͱ͖ΔɺΦϯϥΠϯʹ͓͚Δ࣮ݧʹண໨͠ɺࠓճ͸ͦͷதͰ΋ถࠃॅॴͷऔಘ౳ͷ

࣮ݧ࣮ࢪ্ͷ੍໿͕؇͍ɺ CrowdFlower ʹ࣮ͯݧΛ࣮ࢪͨ͠ɻ

ຊݚڀʹ͓͚Δ࣮ݧͱͯ͠͸ɺඃݧऀͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧͱɺϝΠϯ ͷ࣮ݧͰ͋Δ࠷దࣦۀอݥͷ࣮ݧ͔Βߏ੒͞Ε͍ͯΔɻجૅύϥϝʔλͷ࣮ݧ͸ถࠃࡏ

ॅͷඃݧऀΛ 167 ਓूΊɺ࠷దࣦۀอݥͷ࣮ݧʹ͍ͭͯ͸ถࠃࡏॅͷඃݧऀΛ 43 ਓू

Ίͨɻ࣍અҎ߱Ͱɺ֤࣮ݧͷৄࡉΛड़΂͍ͯ͘ɻ

4 جૅύϥϝʔλͷ࣮ݧ

·ͣɺຊݚڀʹ͓͚Δ࠷దࣦۀอݥΛܭࢉ͢Δʹ͋ͨͬͯ͸ɺ࣮ࡍͷඃݧऀͷޮ༻͓

Αͼ౒ྗඅ༻Λਪఆ͢Δඞཁ͕͋Δɻ࠷దࣦۀอݥͷ࣮ݧʹઌཱͪɺԼهʹड़΂Δ௨Γɺ

͜ΕΒͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ

4.1 ϦεΫܭଌ࣮ݧ

ඃݧऀͷϦεΫΛଌఆ͢Δʹ͋ͨͬͯɺຊݚڀͰ͸ Holt and Laury (2002) ʹΑͬͯ

ఏࣔ͞Εͨํ๏ʹΑͬͯɺඃݧऀͷ૬ରతϦεΫճආ౓ r Λਪఆ͢Δɻޮ༻ؔ਺ͱͯ͠ɺ ૬ରతϦεΫճආ౓Ұఆʢ CRRA _{ʣͷޮ༻ؔ਺} u(c) = _1−r ¹ c ^1−r _{ΛԾఆ͢Δɻ۩ମతʹ}

͸ɺද 1 ʹ͋ΔΑ͏ͳબ୒ࢶ A ͱબ୒ࢶ B ͔ΒͳΔ͘͡ (Lottery) Λඃݧऀʹબ୒ͤ͞ɺ

ͦͷબ୒σʔλ͔Βඃݧऀ͸ɺ

P (Choose Option A) = U _A ^1/µ

U _A ^1/µ + U _B ^1/µ (13) ͱ͍͏֬཰ʹैͬͯબ୒ࢶ A Λબ୒͢ΔͱԾఆͯ͠ɺ࠷໬๏ʹΑͬͯύϥϝʔλ (r, µ) Λਪఆ͢Δɻ͜͜Ͱɺ U _A ɺ U _B ͸ͦΕͧΕબ୒ࢶ A ɺબ୒ࢶ B ͔Βͷظ଴ޮ༻Λදͯ͠

͍Δɻ

·ͨɺ૬ରతϦεΫճආ౓Λਪఆ͢Δผͷํ๏ͱͯ͠ɺ Goeree, Holt and Palfrey (2003)

ʹΑͬͯఏҊ͞Εͨɺ࣭తԠ౴Ϟσϧ (Quantal Response Model) ʹΑΔਪఆ͕͋Δɻͦ

Option A Option B

Decision 1 ⃝ A ⃝ B 1/10 of $2.00, 9/10 of $1.60 1/10 of $3.85, 9/10 of $0.10 Decision 2 ⃝ A ⃝ B 2/10 of $2.00, 8/10 of $1.60 1/10 of $3.85, 9/10 of $0.10

· · · · · · · · · · · ·

Decision 10 ⃝ A ⃝ B 10/10 of $2.00, 0/10 of $1.60 10/10 of $3.85, 0/10 of $0.10

ද 1: Holt and Laury Test

Ε͸ɺબ୒ࢶ A ͷબ୒֬཰ʹ͍ͭͯϩδοτϞσϧΛԾఆ͢Δɻ͢ͳΘͪɺબ୒ࢶ A ͷ બ୒֬཰ʹ͍ͭͯ

P (Choose Option A) = exp( ¹ _λ U _A )

exp( ¹ _λ U _A ) + exp( _λ ¹ U _B ) (14) ͱ͍͏֬཰ΛԾఆ͠ɺ࠷໬๏ʹΑͬͯύϥϝʔλ (r, λ) Λਪఆ͢Δ΋ͷͰ͋Δɻ͜ΕΒ ͷํ๏ͰಘΒΕͨਪఆ݁Ռ͕ද 2 ͷ࠷ॳͷ 2 ྻͰ͋ΔɻͲͪΒͷํ๏ͰݟͯΈͯ΋ɺਪ ఆ͞Εͨ૬ରతϦεΫճආ౓ͷେ͖͞͸ͦΕ΄Ͳ૬ҧ͸ͳ͍ɻ

Holt and Laury (1) QR (1) Holt and Laury (2) QR(2)

Relative Risk Aversion (r) 0.886 0.858 0.559 0.554

Noise Parameter (µ) 0.222 - 0.209 -

Precision Parameter (λ) - 1.839 - 0.496

Log Likelihood -954.393 -954.1786 -252.107 -242.151

Observations 103 53

ද 2: ૬ରతϦεΫճආ౓ͷਪఆ݁Ռ

͔͠͠ͳ͕Βɺ͜ͷਪఆʹ͸ҎԼʹड़΂ΔΑ͏ͳ໰୊఺Λ͍࣋ͬͯΔɻ͜͜Ͱද 1 Λ

ΈΔͱɺ Decision10 ͸໌Β͔ʹબ୒ࢶ B ͷํ͕ྑ͍બ୒ࢶͰ͋Δ͕ɺ͔ͦ͜Β൪߸͕খ

͘͞ͳΔʹैͬͯɺ୯ௐʹબ୒ࢶ A ͷັྗ͕૿ͯ͘͠Δߏ଄Λ͍ͯ͠Δɻ͜Ε͸ɺඃݧ

ऀ͕टඌҰ؏ͨ͠બ޷Λ͍࣋ͬͯΔͱԾఆ͢ΔͳΒ͹ɺ Decision 1 ͔Β࢝Ίͯ͋Δ໰୊

Ҏ߱͸ɺબ୒ࢶ A _{͔Βબ୒ࢶ} B Λબ୒͢ΔΑ͏ʹͳΔڥքઢ͕Ұ౓͚ͩଘࡏ͢Δʢ͋Δ

͍͸ɺҰ౓΋ͦͷΑ͏ͳ੾Γସ͕͑ى͜Βͳ͍ʣ͸ͣͰ͋Δ͜ͱΛҙຯ͍ͯ͠Δɻͭ·

Γɺબ୒ࢶ A ͱબ୒ࢶ B ΁ͷ੾Γସ͕͑ෳ਺ى͜Δͱ͍͏͜ͱ͸ɺͦ͏ͨ͠ඃݧऀ͸

टඌҰ؏ͨ͠બ޷Λ͍࣋ͬͯͳ͍ͱ͍͏͜ͱΛ͍ࣔͯ͠Δɻ͜͏ͨ͠टඌҰ؏ͨ͠બ޷

Λ࣋ͨͳ͍ඃݧऀ͸ɺཧ࿦ͷ૝ఆΛӽ͑ΔඃݧऀͰ͋ΔͷͰɺ͜͏ͨ͠ඃݧऀΛαϯϓ ϧ͔Βআ֎ͯ͠ɺಉ༷ͷਪఆΛߦͬͨ΋ͷ͕ද 2 ͷӈ 2 ྻͰ͋Δɻ

4.2 අ༻ܭଌ࣮ݧ

զʑ͸ɺඃݧऀͷ౒ྗඅ༻Λܭଌ͢ΔͨΊʹɺ Gill and Prowse (2011) _ɺ Gill and

Prowse (2012) ΛԠ༻ͨ͠ҎԼͷΑ͏ͳεϥΠυόʔΛҠಈͤ͞Δ࣮࡞ۀ࣮ݧΛߦͬͨɻ

͜ͷ࣮ݧͰ͸ɺඃݧऀ͸ਤ 1 ʹ͋ΔΑ͏ͳεϥΠυɾόʔΛࢦఆ͞ΕͨҐஔʹҠಈͤ͞

7

Option A Option B

Decision 1 ⃝A ⃝B 1/10 of $2.00, 9/10 of $1.60 1/10 of $3.85, 9/10 of $0.10 Decision 2 ⃝A ⃝B 2/10 of $2.00, 8/10 of $1.60 1/10 of $3.85, 9/10 of $0.10

· · · · · · · · · · · ·

Decision 10 ⃝ A ⃝ B 10/10 of $2.00, 0/10 of $1.60 10/10 of $3.85, 0/10 of $0.10

ද 1: Holt and Laury Test

Ε͸ɺબ୒ࢶ A ͷબ୒֬཰ʹ͍ͭͯϩδοτϞσϧΛԾఆ͢Δɻ͢ͳΘͪɺબ୒ࢶ A ͷ બ୒֬཰ʹ͍ͭͯ

P (Choose Option A) = exp(

¹_λ

U

A

)

exp(

_λ¹

U

A

) + exp(

_λ¹

U

B

) (14) ͱ͍͏֬཰ΛԾఆ͠ɺ࠷໬๏ʹΑͬͯύϥϝʔλ (r, λ) Λਪఆ͢Δ΋ͷͰ͋Δɻ͜ΕΒ ͷํ๏ͰಘΒΕͨਪఆ݁Ռ͕ද 2 ͷ࠷ॳͷ 2 ྻͰ͋ΔɻͲͪΒͷํ๏ͰݟͯΈͯ΋ɺਪ ఆ͞Εͨ૬ରతϦεΫճආ౓ͷେ͖͞͸ͦΕ΄Ͳ૬ҧ͸ͳ͍ɻ

Holt and Laury (1) QR (1) Holt and Laury (2) QR(2)

Relative Risk Aversion (r) 0.886 0.858 0.559 0.554

Noise Parameter (µ) 0.222 - 0.209 -

Precision Parameter (λ) - 1.839 - 0.496

Log Likelihood -954.393 -954.1786 -252.107 -242.151

Observations 103 53

ද 2: ૬ରతϦεΫճආ౓ͷਪఆ݁Ռ

͔͠͠ͳ͕Βɺ͜ͷਪఆʹ͸ҎԼʹड़΂ΔΑ͏ͳ໰୊఺Λ͍࣋ͬͯΔɻ͜͜Ͱද 1 Λ ΈΔͱɺDecision10 ͸໌Β͔ʹબ୒ࢶ B ͷํ͕ྑ͍બ୒ࢶͰ͋Δ͕ɺ͔ͦ͜Β൪߸͕খ

͘͞ͳΔʹैͬͯɺ୯ௐʹબ୒ࢶ A ͷັྗ͕૿ͯ͘͠Δߏ଄Λ͍ͯ͠Δɻ͜Ε͸ɺඃݧ

ऀ͕टඌҰ؏ͨ͠બ޷Λ͍࣋ͬͯΔͱԾఆ͢ΔͳΒ͹ɺDecision 1 ͔Β࢝Ίͯ͋Δ໰୊

Ҏ߱͸ɺબ୒ࢶ A ͔Βબ୒ࢶ B Λબ୒͢ΔΑ͏ʹͳΔڥքઢ͕Ұ౓͚ͩଘࡏ͢Δʢ͋Δ

͍͸ɺҰ౓΋ͦͷΑ͏ͳ੾Γସ͕͑ى͜Βͳ͍ʣ͸ͣͰ͋Δ͜ͱΛҙຯ͍ͯ͠Δɻͭ·

Γɺબ୒ࢶ A ͱબ୒ࢶ B ΁ͷ੾Γସ͕͑ෳ਺ى͜Δͱ͍͏͜ͱ͸ɺͦ͏ͨ͠ඃݧऀ͸

टඌҰ؏ͨ͠બ޷Λ͍࣋ͬͯͳ͍ͱ͍͏͜ͱΛ͍ࣔͯ͠Δɻ͜͏ͨ͠टඌҰ؏ͨ͠બ޷

Λ࣋ͨͳ͍ඃݧऀ͸ɺཧ࿦ͷ૝ఆΛӽ͑ΔඃݧऀͰ͋ΔͷͰɺ͜͏ͨ͠ඃݧऀΛαϯϓ ϧ͔Βআ֎ͯ͠ɺಉ༷ͷਪఆΛߦͬͨ΋ͷ͕ද 2 ͷӈ 2 ྻͰ͋Δɻ

4.2 අ༻ܭଌ࣮ݧ

զʑ͸ɺඃݧऀͷ౒ྗඅ༻Λܭଌ͢ΔͨΊʹɺGill and Prowse (2011)ɺGill and

Prowse (2012) ΛԠ༻ͨ͠ҎԼͷΑ͏ͳεϥΠυόʔΛҠಈͤ͞Δ࣮࡞ۀ࣮ݧΛߦͬͨɻ

͜ͷ࣮ݧͰ͸ɺඃݧऀ͸ਤ 1 ʹ͋ΔΑ͏ͳεϥΠυɾόʔΛࢦఆ͞ΕͨҐஔʹҠಈͤ͞

7 ݮগ͍ͯ͘͜͠ͱ͕Θ͔Δɻ

͜ΕΒͷࣄ࣮Λ·ͱΊΔͱ࣍ͷ໋୊ΛಘΔɻ

Proposition 1 (Hopenhayn and Nicolini (1997)) V ^u < V ͕੒ཱ͢Δɻ·ͨɺ

ࣦۀอݥʹΑΔڅ෇͸ࣦۀظ͕ؒ௕͘ͳΔఔݮগ͍ͯ͘͠ɻ

3 CrowdFlower ʹΑΔΦϯϥΠϯ࣮ݧ

ຊݚڀʹ͓͚Δɺ࠷దࣦۀอݥͷ࣮ݧ͸ɺ࣮ݧ࣮ࢪऀଆͰ࠷దࣦۀอݥΛఆΊͯ͠·

͑͹ɺ࢒Δҙࢥܾఆ໰୊͸ɺ֤ݸਓͷಈֶతܾఆ໰୊ͱͳΔɻͦΕΛ࣮ݧ࣮ࣨݧʹ࣮ͯ

ࢪ͢Δ৔߹͸ɺେྔͷඃݧऀϓʔϧ͕ඞཁͱͳΓɺ౷ܭ෼ੳΛ࣮ࢪ͢Δҙຯͷ͋Δਓ਺

ͷඃݧऀΛूΊΔ͜ͱ͸େม೉͍͠ɻͦ͜Ͱɺզʑ͸େྔͷඃݧऀΛ୹ظؒͰूΊΔ͜

ͱ͕Ͱ͖ΔɺΦϯϥΠϯʹ͓͚Δ࣮ݧʹண໨͠ɺࠓճ͸ͦͷதͰ΋ถࠃॅॴͷऔಘ౳ͷ

࣮ݧ࣮ࢪ্ͷ੍໿͕؇͍ɺ CrowdFlower ʹ࣮ͯݧΛ࣮ࢪͨ͠ɻ

ຊݚڀʹ͓͚Δ࣮ݧͱͯ͠͸ɺඃݧऀͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧͱɺϝΠϯ ͷ࣮ݧͰ͋Δ࠷దࣦۀอݥͷ࣮ݧ͔Βߏ੒͞Ε͍ͯΔɻجૅύϥϝʔλͷ࣮ݧ͸ถࠃࡏ

ॅͷඃݧऀΛ 167 ਓूΊɺ࠷దࣦۀอݥͷ࣮ݧʹ͍ͭͯ͸ถࠃࡏॅͷඃݧऀΛ 43 ਓू

Ίͨɻ࣍અҎ߱Ͱɺ֤࣮ݧͷৄࡉΛड़΂͍ͯ͘ɻ

4 جૅύϥϝʔλͷ࣮ݧ

·ͣɺຊݚڀʹ͓͚Δ࠷దࣦۀอݥΛܭࢉ͢Δʹ͋ͨͬͯ͸ɺ࣮ࡍͷඃݧऀͷޮ༻͓

Αͼ౒ྗඅ༻Λਪఆ͢Δඞཁ͕͋Δɻ࠷దࣦۀอݥͷ࣮ݧʹઌཱͪɺԼهʹड़΂Δ௨Γɺ

͜ΕΒͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ

4.1 ϦεΫܭଌ࣮ݧ

ඃݧऀͷϦεΫΛଌఆ͢Δʹ͋ͨͬͯɺຊݚڀͰ͸ Holt and Laury (2002) ʹΑͬͯ

ఏࣔ͞Εͨํ๏ʹΑͬͯɺඃݧऀͷ૬ରతϦεΫճආ౓ r Λਪఆ͢Δɻޮ༻ؔ਺ͱͯ͠ɺ ૬ରతϦεΫճආ౓Ұఆʢ CRRA _{ʣͷޮ༻ؔ਺} u(c) = _1−r ¹ c ^1−r _{ΛԾఆ͢Δɻ۩ମతʹ}

͸ɺද 1 ʹ͋ΔΑ͏ͳબ୒ࢶ A ͱબ୒ࢶ B ͔ΒͳΔ͘͡ (Lottery) Λඃݧऀʹબ୒ͤ͞ɺ

ͦͷબ୒σʔλ͔Βඃݧऀ͸ɺ

P (Choose Option A) = U _A ^1/µ

U _A ^1/µ + U _B ^1/µ (13) ͱ͍͏֬཰ʹैͬͯબ୒ࢶ A Λબ୒͢ΔͱԾఆͯ͠ɺ࠷໬๏ʹΑͬͯύϥϝʔλ (r, µ) Λਪఆ͢Δɻ͜͜Ͱɺ U _A ɺ U _B ͸ͦΕͧΕબ୒ࢶ A ɺબ୒ࢶ B ͔Βͷظ଴ޮ༻Λදͯ͠

͍Δɻ

·ͨɺ૬ରతϦεΫճආ౓Λਪఆ͢Δผͷํ๏ͱͯ͠ɺ Goeree, Holt and Palfrey (2003) ʹΑͬͯఏҊ͞Εͨɺ࣭తԠ౴Ϟσϧ (Quantal Response Model) ʹΑΔਪఆ͕͋Δɻͦ

6 ₃₄₉

ݮগ͍ͯ͘͜͠ͱ͕Θ͔Δɻ

͜ΕΒͷࣄ࣮Λ·ͱΊΔͱ࣍ͷ໋୊ΛಘΔɻ

Proposition 1 (Hopenhayn and Nicolini (1997)) V ^u < V ͕੒ཱ͢Δɻ·ͨɺ

ࣦۀอݥʹΑΔڅ෇͸ࣦۀظ͕ؒ௕͘ͳΔఔݮগ͍ͯ͘͠ɻ

3 CrowdFlower ʹΑΔΦϯϥΠϯ࣮ݧ

ຊݚڀʹ͓͚Δɺ࠷దࣦۀอݥͷ࣮ݧ͸ɺ࣮ݧ࣮ࢪऀଆͰ࠷దࣦۀอݥΛఆΊͯ͠·

͑͹ɺ࢒Δҙࢥܾఆ໰୊͸ɺ֤ݸਓͷಈֶతܾఆ໰୊ͱͳΔɻͦΕΛ࣮ݧ࣮ࣨݧʹ࣮ͯ

ࢪ͢Δ৔߹͸ɺେྔͷඃݧऀϓʔϧ͕ඞཁͱͳΓɺ౷ܭ෼ੳΛ࣮ࢪ͢Δҙຯͷ͋Δਓ਺

ͷඃݧऀΛूΊΔ͜ͱ͸େม೉͍͠ɻͦ͜Ͱɺզʑ͸େྔͷඃݧऀΛ୹ظؒͰूΊΔ͜

ͱ͕Ͱ͖ΔɺΦϯϥΠϯʹ͓͚Δ࣮ݧʹண໨͠ɺࠓճ͸ͦͷதͰ΋ถࠃॅॴͷऔಘ౳ͷ

࣮ݧ࣮ࢪ্ͷ੍໿͕؇͍ɺ CrowdFlower ʹ࣮ͯݧΛ࣮ࢪͨ͠ɻ

ຊݚڀʹ͓͚Δ࣮ݧͱͯ͠͸ɺඃݧऀͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧͱɺϝΠϯ ͷ࣮ݧͰ͋Δ࠷దࣦۀอݥͷ࣮ݧ͔Βߏ੒͞Ε͍ͯΔɻجૅύϥϝʔλͷ࣮ݧ͸ถࠃࡏ

ॅͷඃݧऀΛ 167 ਓूΊɺ࠷దࣦۀอݥͷ࣮ݧʹ͍ͭͯ͸ถࠃࡏॅͷඃݧऀΛ 43 ਓू

Ίͨɻ࣍અҎ߱Ͱɺ֤࣮ݧͷৄࡉΛड़΂͍ͯ͘ɻ

4 جૅύϥϝʔλͷ࣮ݧ

·ͣɺຊݚڀʹ͓͚Δ࠷దࣦۀอݥΛܭࢉ͢Δʹ͋ͨͬͯ͸ɺ࣮ࡍͷඃݧऀͷޮ༻͓

Αͼ౒ྗඅ༻Λਪఆ͢Δඞཁ͕͋Δɻ࠷దࣦۀอݥͷ࣮ݧʹઌཱͪɺԼهʹड़΂Δ௨Γɺ

͜ΕΒͷجૅύϥϝʔλΛಘΔͨΊͷ࣮ݧΛ࣮ࢪͨ͠ɻ

4.1 ϦεΫܭଌ࣮ݧ

ඃݧऀͷϦεΫΛଌఆ͢Δʹ͋ͨͬͯɺຊݚڀͰ͸ Holt and Laury (2002) ʹΑͬͯ

ఏࣔ͞Εͨํ๏ʹΑͬͯɺඃݧऀͷ૬ରతϦεΫճආ౓ r Λਪఆ͢Δɻޮ༻ؔ਺ͱͯ͠ɺ ૬ରతϦεΫճආ౓Ұఆʢ CRRA _{ʣͷޮ༻ؔ਺} u(c) = _1−r ¹ c ^1−r _{ΛԾఆ͢Δɻ۩ମతʹ}

͸ɺද 1 ʹ͋ΔΑ͏ͳબ୒ࢶ A ͱબ୒ࢶ B ͔ΒͳΔ͘͡ (Lottery) Λඃݧऀʹબ୒ͤ͞ɺ

ͦͷબ୒σʔλ͔Βඃݧऀ͸ɺ

P (Choose Option A) = U _A ^1/µ

U _A ^1/µ + U _B ^1/µ (13) ͱ͍͏֬཰ʹैͬͯબ୒ࢶ A Λબ୒͢ΔͱԾఆͯ͠ɺ࠷໬๏ʹΑͬͯύϥϝʔλ (r, µ) Λਪఆ͢Δɻ͜͜Ͱɺ U _A ɺ U _B ͸ͦΕͧΕબ୒ࢶ A ɺબ୒ࢶ B ͔Βͷظ଴ޮ༻Λදͯ͠

͍Δɻ

·ͨɺ૬ରతϦεΫճආ౓Λਪఆ͢Δผͷํ๏ͱͯ͠ɺ Goeree, Holt and Palfrey (2003) ʹΑͬͯఏҊ͞Εͨɺ࣭తԠ౴Ϟσϧ (Quantal Response Model) ʹΑΔਪఆ͕͋Δɻͦ

348 6

Δ࣮࡞ۀΛߦ͏ɻ·ͣɺҠಈͤ͞ΔεϥΠυɾόʔͷ୯ҐຖʹɺݻఆใुֹΛఆΊ͓ͯ

͘ɻ࣍ʹɺ͜ͷݻఆใुֹ͸ඃݧऀʹ͸஌Βͤͣɺඃݧऀʹ 5 ୯Ґຖͷ࠷௿อূֹΛه

ೖͤ͞Δɻ࠷ޙʹɺϥϯμϜʹεϥΠυόʔΛҠಈͤ͞Δݸ਺Λܾఆ͠ɺͦ͜ʹ͓͚Δ

ඃݧऀͷ࠷௿อূֹ͕ͪ͜ΒͷఆΊͨݻఆใुֹΑΓ௿͍৔߹ʹ͸࣮ࡍʹҠಈ࡞ۀΛ͠

ͯ΋Β͍ɺݻఆใुΛ༩͑Δɻ࠷௿อূֹ͕ݻఆใुΑΓ΋ߴ͍৔߹ʹ͸ɺԿΒใु͸

༩͑ͣɺ࣮ݧ͸ऴྃͱ͢Δɻ͜͏ͨ͠ํ๏͸ɺ Becker-DeGroot-Marschak ϝΧχζϜͱ Α͹ΕΔɺඃݧऀͷཹอޮ༻ΛҾ͖ग़ͨ͢Ίͷ࣮ݧखଓ͖ͱͯ͠஌ΒΕ͍ͯΔ΋ͷͰ͋

Δ (Becker et al. (1964)) ɻ͜ͷ࣮ݧͰ͸ɺඃݧऀ͸ਅ࣮ͷ࠷௿อূֹΛਃࠂ͢Δ͜ͱ͕

ਤ 1: ඃݧऀ͕ૢ࡞͢ΔεϥΠυόʔ

࠷దͱͳ͍ͬͯΔ͜ͱʹ஫ҙ͠Α͏ɻͭ·Γɺਅ࣮ΑΓ΋ߴֹ͍ۚΛਃࠂ͢Δͱɺਅ࣮

ͷֹۚΛਃࠂ͓͚ͯ͠͹࣮ࢪͰ͖ͨͰ͋Ζ͏࡞ۀΛࣦ͏Մೳੑ͕ߴ·Γɺଞํɺਅ࣮Α Γ΋௿ֹ͍ۚΛਃࠂ͢ΔͱຊདྷͰ͋Ε͹Ҿ͖ड͚ͳͯ͘΋ྑ͍࡞ۀΛҾ͖ड͚ͯͳͯ͘

͸͍͚ͳ͍Մೳੑ͕ߴ·ͬͯ͠·͏͔ΒͰ͋Δɻ

͜͏ͯ͠ಘΒΕͨɺεϥΠυɾόʔͷݸ਺ͱ࠷௿อূֹͷσʔλΛ༻͍ͯɺඃݧऀͷ

౰࣮֘࡞ۀʹ͍ͭͯͷඅ༻ؔ਺Λਪఆͨ͠ɻࠓճ͸αϯϓϧɾαΠζ͕খ͍͜͞ͱͱɺ

͍͔ͭ͘ͷ֎Ε஋͕ݟΒΕͨͨΊʹɺϩόετਪఆΛ࣮ࢪͨ͠ɻͦͷਪఆ݁Ռ͕ද 3 ͷ ௨ΓͰ͋Δɻ

Estimate Standard Error p-value Intercept 11.9595 3.0705 0.000123 SliderNum 0.3944 0.1599 0.014216

Observations 167

ද 3: ౒ྗඅ༻ؔ਺ͷਪఆ݁Ռ

5 ࠷దࣦۀอݥ࣮ݧͷઃܭ

લઅͰಘΒΕͨجૅύϥϝʔλΛ΋ͱʹͯ͠ɺຊݚڀͷϝΠϯͷ࣮ݧͱͳΔ࠷దࣦۀ อݥͷ࣮ݧʹ͍ͭͯड़΂Δɻ৬୳͠ͷ౒ྗਫ४Λ a ͱ͢Δͱ͖ʹ࣮ࡍʹ৬͕ݟ͔ͭΔ֬

཰ p(a) Λ Hopenhayn and Nicolini (1997) ʹैͬͯɺp(a) = 1 − exp( − γ · a) ͱ͓͘ɻ

͜͜Ͱɺγ ͸ਖ਼ͷύϥϝʔλͰɺp(a aut ) = 0.1 ͱͳΔΑ͏ʹఆΊΒΕ͍ͯΔɻ·ͨɺ૬ ରతϦεΫճආ౓ʹ͍ͭͯ͸ɺϩόετਪఆޙͷਪఆ஋Λখ਺఺ୈ 3 ҐΛ੾Γ্͛Δͱɺ Holt and Laury ๏ɺ QRE ๏ڞʹ 0.56 ͱͳΔͷͰɺr = 0.56 ͱͨ͠ɻ͞Βʹɺݸਓͷ౒ྗ

අ༻ʹ͍ͭͯ͸ɺલઅͰਪఆͨ͠ઢܗͷඅ༻ؔ਺Λར༻͢Δɻ࠷ޙʹɺׂҾҼࢠ β ͸ 0.9 ͱ͠ɺब৬ޙͷ௞ۚ w Λ 1.5ʢυϧʣͱͨ͠ɻͦͯ͠ɺ͜ΕΒͷύϥϝʔλͷ΋ͱͰ࠷

దͳࣦۀอݥΛ਺஋ܭࢉʹΑͬͯٻΊΔͱਤ 2 ͷΑ͏ʹͳͬͨʢ਺஋ͷৄࡉ͸ Appendix ͷද 5 Λࢀরͷ͜ͱʣɻ

ਤ 2: ࠷దࣦۀอݥ਺஋ܭࢉ

͜ͷ਺஋ܭࢉʹΑͬͯٻΊΒΕࣦͨۀอݥΛ༻͍࣮ͨݧΛ Optimal Insurance τϦʔ τϝϯτͱΑͼɺࣦۀอݥΛ༻͍ͣʹ৬୳͠Λߦ͏τϦʔτϝϯτΛ Auturky τϦʔτ ϝϯτͱΑͿɻࠓճͷ༧උ࣮ݧͰ͸ɺͦΕͧΕ̍ηογϣϯ࣮ͣͭࢪͨ͠ɻ·ͨɺ֤ηο γϣϯʹ͓͚Δݸਓͷ৬୳͠ʹ͍ͭͯͷ౒ྗਫ४ͷબ୒ʹ͋ͨͬͯ͸ɺ·ͣૢ࡞͢Δε ϥΠυόʔͷݸ਺Λબ୒͠ɺͦͷޙ࣮ࡍʹεϥΠυόʔΛૢ࡞͢Δͱ͍͏ܗͰߦͬͨɻ

9 Δ࣮࡞ۀΛߦ͏ɻ·ͣɺҠಈͤ͞ΔεϥΠυɾόʔͷ୯ҐຖʹɺݻఆใुֹΛఆΊ͓ͯ

͘ɻ࣍ʹɺ͜ͷݻఆใुֹ͸ඃݧऀʹ͸஌Βͤͣɺඃݧऀʹ 5 ୯Ґຖͷ࠷௿อূֹΛه

ೖͤ͞Δɻ࠷ޙʹɺϥϯμϜʹεϥΠυόʔΛҠಈͤ͞Δݸ਺Λܾఆ͠ɺͦ͜ʹ͓͚Δ

ඃݧऀͷ࠷௿อূֹ͕ͪ͜ΒͷఆΊͨݻఆใुֹΑΓ௿͍৔߹ʹ͸࣮ࡍʹҠಈ࡞ۀΛ͠

ͯ΋Β͍ɺݻఆใुΛ༩͑Δɻ࠷௿อূֹ͕ݻఆใुΑΓ΋ߴ͍৔߹ʹ͸ɺԿΒใु͸

༩͑ͣɺ࣮ݧ͸ऴྃͱ͢Δɻ͜͏ͨ͠ํ๏͸ɺ Becker-DeGroot-Marschak ϝΧχζϜͱ Α͹ΕΔɺඃݧऀͷཹอޮ༻ΛҾ͖ग़ͨ͢Ίͷ࣮ݧखଓ͖ͱͯ͠஌ΒΕ͍ͯΔ΋ͷͰ͋

Δ (Becker et al. (1964)) ɻ͜ͷ࣮ݧͰ͸ɺඃݧऀ͸ਅ࣮ͷ࠷௿อূֹΛਃࠂ͢Δ͜ͱ͕

ਤ 1: ඃݧऀ͕ૢ࡞͢ΔεϥΠυόʔ

࠷దͱͳ͍ͬͯΔ͜ͱʹ஫ҙ͠Α͏ɻͭ·Γɺਅ࣮ΑΓ΋ߴֹ͍ۚΛਃࠂ͢Δͱɺਅ࣮

ͷֹۚΛਃࠂ͓͚ͯ͠͹࣮ࢪͰ͖ͨͰ͋Ζ͏࡞ۀΛࣦ͏Մೳੑ͕ߴ·Γɺଞํɺਅ࣮Α Γ΋௿ֹ͍ۚΛਃࠂ͢ΔͱຊདྷͰ͋Ε͹Ҿ͖ड͚ͳͯ͘΋ྑ͍࡞ۀΛҾ͖ड͚ͯͳͯ͘

͸͍͚ͳ͍Մೳੑ͕ߴ·ͬͯ͠·͏͔ΒͰ͋Δɻ

͜͏ͯ͠ಘΒΕͨɺεϥΠυɾόʔͷݸ਺ͱ࠷௿อূֹͷσʔλΛ༻͍ͯɺඃݧऀͷ

౰࣮֘࡞ۀʹ͍ͭͯͷඅ༻ؔ਺Λਪఆͨ͠ɻࠓճ͸αϯϓϧɾαΠζ͕খ͍͜͞ͱͱɺ

͍͔ͭ͘ͷ֎Ε஋͕ݟΒΕͨͨΊʹɺϩόετਪఆΛ࣮ࢪͨ͠ɻͦͷਪఆ݁Ռ͕ද 3 ͷ ௨ΓͰ͋Δɻ

Estimate Standard Error p-value Intercept 11.9595 3.0705 0.000123 SliderNum 0.3944 0.1599 0.014216

Observations 167

ද 3: ౒ྗඅ༻ؔ਺ͷਪఆ݁Ռ

8 ₃₅₁

Δ࣮࡞ۀΛߦ͏ɻ·ͣɺҠಈͤ͞ΔεϥΠυɾόʔͷ୯ҐຖʹɺݻఆใुֹΛఆΊ͓ͯ

͘ɻ࣍ʹɺ͜ͷݻఆใुֹ͸ඃݧऀʹ͸஌Βͤͣɺඃݧऀʹ 5 ୯Ґຖͷ࠷௿อূֹΛه

ೖͤ͞Δɻ࠷ޙʹɺϥϯμϜʹεϥΠυόʔΛҠಈͤ͞Δݸ਺Λܾఆ͠ɺͦ͜ʹ͓͚Δ

ඃݧऀͷ࠷௿อূֹ͕ͪ͜ΒͷఆΊͨݻఆใुֹΑΓ௿͍৔߹ʹ͸࣮ࡍʹҠಈ࡞ۀΛ͠

ͯ΋Β͍ɺݻఆใुΛ༩͑Δɻ࠷௿อূֹ͕ݻఆใुΑΓ΋ߴ͍৔߹ʹ͸ɺԿΒใु͸

༩͑ͣɺ࣮ݧ͸ऴྃͱ͢Δɻ͜͏ͨ͠ํ๏͸ɺ Becker-DeGroot-Marschak ϝΧχζϜͱ Α͹ΕΔɺඃݧऀͷཹอޮ༻ΛҾ͖ग़ͨ͢Ίͷ࣮ݧखଓ͖ͱͯ͠஌ΒΕ͍ͯΔ΋ͷͰ͋

Δ (Becker et al. (1964)) ɻ͜ͷ࣮ݧͰ͸ɺඃݧऀ͸ਅ࣮ͷ࠷௿อূֹΛਃࠂ͢Δ͜ͱ͕

ਤ 1: ඃݧऀ͕ૢ࡞͢ΔεϥΠυόʔ

࠷దͱͳ͍ͬͯΔ͜ͱʹ஫ҙ͠Α͏ɻͭ·Γɺਅ࣮ΑΓ΋ߴֹ͍ۚΛਃࠂ͢Δͱɺਅ࣮

ͷֹۚΛਃࠂ͓͚ͯ͠͹࣮ࢪͰ͖ͨͰ͋Ζ͏࡞ۀΛࣦ͏Մೳੑ͕ߴ·Γɺଞํɺਅ࣮Α Γ΋௿ֹ͍ۚΛਃࠂ͢ΔͱຊདྷͰ͋Ε͹Ҿ͖ड͚ͳͯ͘΋ྑ͍࡞ۀΛҾ͖ड͚ͯͳͯ͘

͸͍͚ͳ͍Մೳੑ͕ߴ·ͬͯ͠·͏͔ΒͰ͋Δɻ

͜͏ͯ͠ಘΒΕͨɺεϥΠυɾόʔͷݸ਺ͱ࠷௿อূֹͷσʔλΛ༻͍ͯɺඃݧऀͷ

౰࣮֘࡞ۀʹ͍ͭͯͷඅ༻ؔ਺Λਪఆͨ͠ɻࠓճ͸αϯϓϧɾαΠζ͕খ͍͜͞ͱͱɺ

͍͔ͭ͘ͷ֎Ε஋͕ݟΒΕͨͨΊʹɺϩόετਪఆΛ࣮ࢪͨ͠ɻͦͷਪఆ݁Ռ͕ද 3 ͷ ௨ΓͰ͋Δɻ

Estimate Standard Error p-value Intercept 11.9595 3.0705 0.000123 SliderNum 0.3944 0.1599 0.014216

Observations 167

ද 3: ౒ྗඅ༻ؔ਺ͷਪఆ݁Ռ

350 8

6 ࣮ݧͷ݁Ռͱߟ࡯

զʑ͕࣮ࢪͨ͠ೋͭͷτϦʔτϝϯτʹ͓͚Δ৬୳͠ߦಈͷ౒ྗਫ४͸ද 4 _ͷ௨ΓͰɺ

ͦΕΛਤࣔͨ͠΋ͷ͕ਤ 3 Ͱ͋Δɻ͜ͷද͔ΒΘ͔Δ͜ͱ͸ɺ·ͣɺͲͪΒͷτϦʔτ ϝϯτʹ͓͍ͯ΋ࣦۀظ͕ؒਐΉʹͭΕͯɺ౒ྗਫ४͕௿Լ͍ͯ͠Δ͜ͱͰ͋Δɻ͜Ε

͸ɺࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४্͕ঢ͢Δͱ͍͏ཧ࿦݁Ռͱ͸େ͖͘ҟͳΔ΋ͷ Ͱ͋Δɻ

Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7

ɹ Optimal Insurance 63.45 38.66 16.33 11 7 7 7

Auturky 56.46 30.6 11.33 - - - -

ද 4: ฏۉతͳ౒ྗਫ४ͷબ୒

102030405060Averaged Level of Effort

1 2 3 4 5 6 7

Period

Optimal Insurance Auturky

ਤ 3: ౒ྗਫ४ͷൺֱ

͜͏ͨ݁͠Ռ͸ɺ௨ৗͷ࣌ؒબ޷Ͱ͸ى͜Γ͑ͳ͍ɻͳͥͳΒɺ࠷దࣦۀอݥͷ΋ͱ

Ͱ΋ɺ Auturky ͷ΋ͱͰ΋ࣦۀظ͕ؒ௕͘ͳΔͱࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘ͸௿

Լ͢ΔͷͰɺফඅͷฏ४ԽΛߟ͑ΔͱɺͳΔ΂͘৬ΛಘΔՄೳੑ͕ߴ·ΔΑ͏ʹɺ౒ྗ

ਫ४Λ্͛Δ͔ΒͰ͋Δɻ

ͦ͜Ͱɺඪ४తͰ͸ͳ͍࣌ؒબ޷ͷதͰ΋ɺࢀর఺ґଘܕબ޷Λ࣋ͭݸਓͰ͋Ε͹࣍

ͷΑ͏ͳ௚؍తઆ໌ʹΑͬͯɺ͜ͷࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४͕௿Լ͢Δͱ͍͏

ݱ৅Λઆ໌͢Δ͜ͱ͕Ͱ͖Δɻͦͷ௚؍తͳઆ໌Λߦ͏ʹ͋ͨΓɺ౰֘ݸਓ͸Ұظલͷ

ޮ༻ਫ४Λࢀর఺ͱͯ࣋ͭ͠ͱԾఆ͢Δɻ͢Δͱɺࣦۀظؒத͸ॴಘਫ४͕௿Լ͢Δͷ Ͱɺඞવతʹࢀর఺͕Լ͕ΔͷͰɺ৬୳͠ͷ౒ྗΛ͢Δ͜ͱΛ΍Ίͯɺ௿͍ਫ४ͷޮ༻

Ͱ΋ຬ଍ͯ͠͠·͏ɻͦΕΏ͑ɺ౒ྗਫ४͕௿Լͯ͠͠·͏ͱ͍͏͜ͱ͕ߟ͑ΒΕΔ ³ ɻ

3

ઌߦݚڀͷҰͭͰ͋Δ DellaVigna et al. (2017) ͸͜ͷछͷબ޷ΛԾఆͯ͠৬୳͠ߦಈΛݚڀ͍ͯ͠

Δɻ

6 ࣮ݧͷ݁Ռͱߟ࡯

զʑ͕࣮ࢪͨ͠ೋͭͷτϦʔτϝϯτʹ͓͚Δ৬୳͠ߦಈͷ౒ྗਫ४͸ද 4 ͷ௨ΓͰɺ

ͦΕΛਤࣔͨ͠΋ͷ͕ਤ 3 Ͱ͋Δɻ͜ͷද͔ΒΘ͔Δ͜ͱ͸ɺ·ͣɺͲͪΒͷτϦʔτ ϝϯτʹ͓͍ͯ΋ࣦۀظ͕ؒਐΉʹͭΕͯɺ౒ྗਫ४͕௿Լ͍ͯ͠Δ͜ͱͰ͋Δɻ͜Ε

͸ɺࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४্͕ঢ͢Δͱ͍͏ཧ࿦݁Ռͱ͸େ͖͘ҟͳΔ΋ͷ Ͱ͋Δɻ

Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7

ɹ Optimal Insurance 63.45 38.66 16.33 11 7 7 7

Auturky 56.46 30.6 11.33 - - - -

ද 4: ฏۉతͳ౒ྗਫ४ͷબ୒

102030405060Averaged Level of Effort

1 2 3 4 5 6 7

Period

Optimal Insurance Auturky

ਤ 3: ౒ྗਫ४ͷൺֱ

͜͏ͨ݁͠Ռ͸ɺ௨ৗͷ࣌ؒબ޷Ͱ͸ى͜Γ͑ͳ͍ɻͳͥͳΒɺ࠷దࣦۀอݥͷ΋ͱ

Ͱ΋ɺ Auturky ͷ΋ͱͰ΋ࣦۀظ͕ؒ௕͘ͳΔͱࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘ͸௿

Լ͢ΔͷͰɺফඅͷฏ४ԽΛߟ͑ΔͱɺͳΔ΂͘৬ΛಘΔՄೳੑ͕ߴ·ΔΑ͏ʹɺ౒ྗ

ਫ४Λ্͛Δ͔ΒͰ͋Δɻ

ͦ͜Ͱɺඪ४తͰ͸ͳ͍࣌ؒબ޷ͷதͰ΋ɺࢀর఺ґଘܕબ޷Λ࣋ͭݸਓͰ͋Ε͹࣍

ͷΑ͏ͳ௚؍తઆ໌ʹΑͬͯɺ͜ͷࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४͕௿Լ͢Δͱ͍͏

ݱ৅Λઆ໌͢Δ͜ͱ͕Ͱ͖Δɻͦͷ௚؍తͳઆ໌Λߦ͏ʹ͋ͨΓɺ౰֘ݸਓ͸Ұظલͷ

ޮ༻ਫ४Λࢀর఺ͱͯ࣋ͭ͠ͱԾఆ͢Δɻ͢Δͱɺࣦۀظؒத͸ॴಘਫ४͕௿Լ͢Δͷ Ͱɺඞવతʹࢀর఺͕Լ͕ΔͷͰɺ৬୳͠ͷ౒ྗΛ͢Δ͜ͱΛ΍Ίͯɺ௿͍ਫ४ͷޮ༻

Ͱ΋ຬ଍ͯ͠͠·͏ɻͦΕΏ͑ɺ౒ྗਫ४͕௿Լͯ͠͠·͏ͱ͍͏͜ͱ͕ߟ͑ΒΕΔ

³

ɻ

3ઌߦݚڀͷҰͭͰ͋ΔDellaVigna et al. (2017)͸͜ͷछͷબ޷ΛԾఆͯ͠৬୳͠ߦಈΛݚڀ͍ͯ͠

Δɻ

10

·ͨɺผͷઆ໌ͱͯ͠͸ɺ૒ۂׂҾͷΑ͏ʹۃ୺ͳݱࡏόΠΞεΛݸਓ͕͍࣋ͬͯΔ ͱߟ͑Δ͜ͱͰ͋Δɻͭ·ΓɺຊདྷͰ͋Ε͹ɺ্ड़ͷΑ͏ʹɺ࣍ୈʹ௿͘ͳΔظ଴ׂҾ ૯རಘʹඋ͑ͯɺফඅͷฏ४Խ͔ΒɺͳΔ΂͘৬ΛಘΔՄೳੑ͕ߴ·ΔΑ͏ʹ౒ྗਫ४ Λ্͛Δ͜ͱͰࣗΒͷརಘ͕վળ͢ΔͷͰ͋Δ͕ɺݱࡏόΠΞεΛ͍࣋ͬͯΔ͜ͱͰɺ কདྷརಘͷධՁΛۃ୺ʹׂΓҾ͍ͯ͠·͏ɻͦΕΏ͑ɺݱࡏࢧ෷Θͳͯ͘͸͍͚ͳ͍ɺ

౒ྗඅ༻Λݏ͕Δ܏޲Λ࣋ͭͨΊɺ౒ྗਫ४͕௿Լ͢Δͱ͍͏આ໌Ͱ͋Δ ⁴ ɻ

͜ͷͲͪΒ͕ݪҼͰ͜ͷΑ͏ͳݱ৅͕ੜ͍ͯ͡Δ͔ʹ͍ͭͯ͸ɺࠓճͷ࣮ݧ͔Β͸ࣝ

ผͰ͖ͣɺকདྷతͳ͞ΒͳΔ࣮ݧ͕ඞཁͱͳΔɻ

࣍ʹɺτϦʔτϝϯؒΛൺֱ͢Δͱɺ࠷దࣦۀอݥͷํ͕ɺ Auturky ΑΓ΋౒ྗਫ४

͕ߴ͘ͳ͍ͬͯΔ͜ͱ͕Θ͔Δɻಛʹɺࣦۀظؒͷॳظஈ֊ఔɺͦͷ͕ࠩେ͖͘ͳ͍ͬͯ

Δɻ͔͠͠ͳ͕Βɺ͜ͷࠩ͸౷ܭతʹ΋༗ҙͳࠩͰ͸ͳ͔ͬͨ ( ୈ 1 ظʹ͓͚Δ Auturky ͱ࠷దࣦۀอݥͷࠩɿ Mann-Whitney test, U = − 0.497, p-value=0.6193) ɻ͜Ε͸ɺࣦ

ۀอݥʹΑΔΠϯηϯςΟϒ෇͚͕ݱࡏόΠΞεͷӨڹͰۃ୺ʹऑΊΒΕ͍ͯΔͨΊͰ

͸ͳ͍͔ͱਪଌͰ͖Δɻ

͜ͷΑ͏ʹɺ্ड़ͷΑ͏ͳԿΒ͔ͷݱࡏόΠΞε͕ಇ͘ͱਪଌ͞ΕΔ؀ڥͰ͸ɺࠓճ ͷࣦۀอݥͷਫ४Ͱ͸౒ྗਫ४͕ࣦۀظ͕ؒ௕͘ͳΔʹͭΕͯɺ্ঢ͢Δ΄Ͳʹ͸Πϯ ηϯςΟϒΛݸਓʹ༩͑Δ͜ͱ͸೉͍͠ͱݴΘ͟ΔΛ͑ͳ͍ɻݱࡏόΠΞεΛ࣋ͭݸਓ Λ૝ఆͨ͠Ϟσϧʹ͓͍ͯɺ࠷దͳࣦۀอݥ੍౓ΛվΊͯߟҊ͠௚͢ඞཁ͕͋Δɻ͞Β ʹɺͦΕʹج͍ͮͯ·ͣ͸ݸਓͷݱঢ়ҡ࣋όΠΞεͷఔ౓Λ࣮ݧͰଌఆ্ͨ͠Ͱɺ࠷ద ͳࣦۀอݥΛ਺஋తʹٻΊͯɺݸਓͷ৬୳͠ͷ౒ྗਫ४ͷมԽΛߟ࡯͢Δ͜ͱ͕ඞཁͱ ͳΔɻ

7 ݁࿦ͱࠓޙͷ՝୊

ຊݚڀ͸ΦϯϥΠϯ࣮ݧΛ௨ͯ͡ Hopenhayn and Nicolini (1997) _{ʹΑΔ࠷దࣦۀอ} ݥͷԼͰͷݸਓͷ৬୳͠ߦಈ͕ࣦۀظؒʹԠͯ͡ͲͷΑ͏ʹมԽ͠ɺ Auturky ͱൺֱ͠

ͯͲͷఔ౓ͦͷڧ౓͕มԽ͢Δ͔ʹ͍ͭͯߟ࡯ͨ͠ɻಘΒΕͨ݁Ռͱͯ͠ɺୈ̍ʹɺ࠷

దࣦۀอݥɺ Auturky ͷͲͪΒͷτϦʔτϝϯτͰ΋ɺཧ࿦Ͱͷ૝ఆͱ͸ҟͳΓɺඃݧ

ऀͷ৬୳͠ͷ౒ྗਫ४͸ࣦۀظ͕ؒ௕͘ͳΕ͹ͳΔ΄Ͳɺ௿Լ͍ͯ͘͜͠ͱ͕෼͔ͬͨɻ

͜ͷ݁Ռ͕ҙຯ͢Δ͜ͱ͸ɺඃݧऀ͸ඪ४తͳબ޷Λ༗͓ͯ͠ΒͣɺԿΒ͔ͷܗͰݱࡏ ʹ͓͚Δޮ༻Λۃ୺ʹॏࢹ͓ͯ͠Γɺͦͷ݁Ռͱͯ͠৬୳͠ͷ౒ྗΛඅ΍͢͜ͱΛͨΊ Β͍ͬͯΔͱߟ͑ΒΕΔɻୈ̎ʹɺ೚ҙͷࣦۀظؒΛݻఆͯ͠ɺ࠷దࣦۀอݥͰͷ౒ྗ

ਫ४ͱ Auturky Ͱͷ౒ྗਫ४Λൺֱ͢Δͱલऀ͕ৗʹ্ճ͍͕ͬͯͨɺ͜Ε͸౷ܭతʹ

͸༗ҙͳࠩͰ͸ͳ͔ͬͨɻ͜ͷ݁Ռʹ͍ͭͯ͸ɺ্ड़ͷΑ͏ͳબ޷Λݸਓ͸༗͍ͯ͠Δ ͱߟ͑ΒΕΔͷͰɺ౒ྗਫ४͸ཧ࿦͕૝ఆ͢ΔΑ͏ʹ্ঢ͢Δ͜ͱ͸ͳ͍͜ͱΛࣔͯ͠

͍ΔɻҎ্ͷ 2 ͭͷ݁ՌΛ૯߹తʹଊ͑Δͱɺݸਓ͕ݱࡏόΠΞεΛ༗͍ͯ͠ΔͨΊɺ ཧ࿦Ͱ૝ఆ͞Ε͍ͯΔఔͷޮՌ͸ಘΒΕ͓ͯΒͣɺগͳ͘ͱ΋౒ྗਫ४Λ্ঢͤ͞Δ࢓

ֻ͚ͱͯ͠͸ػೳ͠ͳ͍͜ͱ͕֬ೝ͞Εͨͱ͍͑Α͏ɻ

4

ຊݚڀͷؔ࿈ݚڀͰ͋Δ DellaVigna and Paserman (2005) ͱ Paserman (2008) ͸͜ͷछͷબ޷Λ Ծఆͯ͠৬୳͠ߦಈΛݚڀ͍ͯ͠Δɻ

11

₃₅₃

6 ࣮ݧͷ݁Ռͱߟ࡯

զʑ͕࣮ࢪͨ͠ೋͭͷτϦʔτϝϯτʹ͓͚Δ৬୳͠ߦಈͷ౒ྗਫ४͸ද 4 _ͷ௨ΓͰɺ

ͦΕΛਤࣔͨ͠΋ͷ͕ਤ 3 Ͱ͋Δɻ͜ͷද͔ΒΘ͔Δ͜ͱ͸ɺ·ͣɺͲͪΒͷτϦʔτ ϝϯτʹ͓͍ͯ΋ࣦۀظ͕ؒਐΉʹͭΕͯɺ౒ྗਫ४͕௿Լ͍ͯ͠Δ͜ͱͰ͋Δɻ͜Ε

͸ɺࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४্͕ঢ͢Δͱ͍͏ཧ࿦݁Ռͱ͸େ͖͘ҟͳΔ΋ͷ Ͱ͋Δɻ

Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7

ɹ Optimal Insurance 63.45 38.66 16.33 11 7 7 7

Auturky 56.46 30.6 11.33 - - - -

ද 4: ฏۉతͳ౒ྗਫ४ͷબ୒

102030405060Averaged Level of Effort

1 2 3 4 5 6 7

Period

Optimal Insurance Auturky

ਤ 3: ౒ྗਫ४ͷൺֱ

͜͏ͨ݁͠Ռ͸ɺ௨ৗͷ࣌ؒબ޷Ͱ͸ى͜Γ͑ͳ͍ɻͳͥͳΒɺ࠷దࣦۀอݥͷ΋ͱ

Ͱ΋ɺ Auturky ͷ΋ͱͰ΋ࣦۀظ͕ؒ௕͘ͳΔͱࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘ͸௿

Լ͢ΔͷͰɺফඅͷฏ४ԽΛߟ͑ΔͱɺͳΔ΂͘৬ΛಘΔՄೳੑ͕ߴ·ΔΑ͏ʹɺ౒ྗ

ਫ४Λ্͛Δ͔ΒͰ͋Δɻ

ͦ͜Ͱɺඪ४తͰ͸ͳ͍࣌ؒબ޷ͷதͰ΋ɺࢀর఺ґଘܕબ޷Λ࣋ͭݸਓͰ͋Ε͹࣍

ͷΑ͏ͳ௚؍తઆ໌ʹΑͬͯɺ͜ͷࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४͕௿Լ͢Δͱ͍͏

ݱ৅Λઆ໌͢Δ͜ͱ͕Ͱ͖Δɻͦͷ௚؍తͳઆ໌Λߦ͏ʹ͋ͨΓɺ౰֘ݸਓ͸Ұظલͷ

ޮ༻ਫ४Λࢀর఺ͱͯ࣋ͭ͠ͱԾఆ͢Δɻ͢Δͱɺࣦۀظؒத͸ॴಘਫ४͕௿Լ͢Δͷ Ͱɺඞવతʹࢀর఺͕Լ͕ΔͷͰɺ৬୳͠ͷ౒ྗΛ͢Δ͜ͱΛ΍Ίͯɺ௿͍ਫ४ͷޮ༻

Ͱ΋ຬ଍ͯ͠͠·͏ɻͦΕΏ͑ɺ౒ྗਫ४͕௿Լͯ͠͠·͏ͱ͍͏͜ͱ͕ߟ͑ΒΕΔ ³ ɻ

3

ઌߦݚڀͷҰͭͰ͋Δ DellaVigna et al. (2017) ͸͜ͷछͷબ޷ΛԾఆͯ͠৬୳͠ߦಈΛݚڀ͍ͯ͠

Δɻ

10 6 ࣮ݧͷ݁Ռͱߟ࡯

զʑ͕࣮ࢪͨ͠ೋͭͷτϦʔτϝϯτʹ͓͚Δ৬୳͠ߦಈͷ౒ྗਫ४͸ද 4 ͷ௨ΓͰɺ

ͦΕΛਤࣔͨ͠΋ͷ͕ਤ 3 Ͱ͋Δɻ͜ͷද͔ΒΘ͔Δ͜ͱ͸ɺ·ͣɺͲͪΒͷτϦʔτ ϝϯτʹ͓͍ͯ΋ࣦۀظ͕ؒਐΉʹͭΕͯɺ౒ྗਫ४͕௿Լ͍ͯ͠Δ͜ͱͰ͋Δɻ͜Ε

͸ɺࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४্͕ঢ͢Δͱ͍͏ཧ࿦݁Ռͱ͸େ͖͘ҟͳΔ΋ͷ Ͱ͋Δɻ

Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7

ɹ Optimal Insurance 63.45 38.66 16.33 11 7 7 7

Auturky 56.46 30.6 11.33 - - - -

ද 4: ฏۉతͳ౒ྗਫ४ͷબ୒

102030405060Averaged Level of Effort

1 2 3 4 5 6 7

Period

Optimal Insurance Auturky

ਤ 3: ౒ྗਫ४ͷൺֱ

͜͏ͨ݁͠Ռ͸ɺ௨ৗͷ࣌ؒબ޷Ͱ͸ى͜Γ͑ͳ͍ɻͳͥͳΒɺ࠷దࣦۀอݥͷ΋ͱ

Ͱ΋ɺ Auturky ͷ΋ͱͰ΋ࣦۀظ͕ؒ௕͘ͳΔͱࣦۀঢ়ଶʹ͓͚Δظ଴ׂҾ૯རಘ͸௿

Լ͢ΔͷͰɺফඅͷฏ४ԽΛߟ͑ΔͱɺͳΔ΂͘৬ΛಘΔՄೳੑ͕ߴ·ΔΑ͏ʹɺ౒ྗ

ਫ४Λ্͛Δ͔ΒͰ͋Δɻ

ͦ͜Ͱɺඪ४తͰ͸ͳ͍࣌ؒબ޷ͷதͰ΋ɺࢀর఺ґଘܕબ޷Λ࣋ͭݸਓͰ͋Ε͹࣍

ͷΑ͏ͳ௚؍తઆ໌ʹΑͬͯɺ͜ͷࣦۀظ͕ؒਐΉʹͭΕͯ౒ྗਫ४͕௿Լ͢Δͱ͍͏

ݱ৅Λઆ໌͢Δ͜ͱ͕Ͱ͖Δɻͦͷ௚؍తͳઆ໌Λߦ͏ʹ͋ͨΓɺ౰֘ݸਓ͸Ұظલͷ

ޮ༻ਫ४Λࢀর఺ͱͯ࣋ͭ͠ͱԾఆ͢Δɻ͢Δͱɺࣦۀظؒத͸ॴಘਫ४͕௿Լ͢Δͷ Ͱɺඞવతʹࢀর఺͕Լ͕ΔͷͰɺ৬୳͠ͷ౒ྗΛ͢Δ͜ͱΛ΍Ίͯɺ௿͍ਫ४ͷޮ༻

Ͱ΋ຬ଍ͯ͠͠·͏ɻͦΕΏ͑ɺ౒ྗਫ४͕௿Լͯ͠͠·͏ͱ͍͏͜ͱ͕ߟ͑ΒΕΔ

³

ɻ

3ઌߦݚڀͷҰͭͰ͋ΔDellaVigna et al. (2017)͸͜ͷछͷબ޷ΛԾఆͯ͠৬୳͠ߦಈΛݚڀ͍ͯ͠

Δɻ

10

352

ࠓճͷݚڀ͸ɺ͋͘·Ͱ΋༧උతͳ࣮ݧͰ͋ΓɺҎԼͷΑ͏ͳ఺Ͱࠓޙղܾ͠ͳ͚Ε

͹͍͚ͳ͍՝୊Λ༗͍ͯ͠Δɻ 1 ͭ͸ɺ࣮ݧͷηϯγϣϯ਺͕গͳ͍ͨΊʹɺࠓճಘΒ Εͨ݁Ռ͕Ͳͷఔ౓ҰൠੑΛ࣋ͭ݁Ռͳͷ͔ʹ͍ͭͯ͸ɺ৻ॏʹۛຯ͍ͯ͘͠ඞཁ͕͋

ΔɻಛʹɺجૅύϥϝʔλͷਪఆͰ͸ɺαϯϓϧαΠζ͕খ͍͞ঢ়گԼͰ࠷໬๏Λ༻͍

ͯਪఆ͍ͯ͠Δɻ͞ΒʹɺϦεΫճආ౓ͷଌఆͰ΋ɺҰ౓ͷ੾Γସ͑఺ͷΈΛ༗͍ͯ͠

Δඃݧऀʹߜͬͯਪఆ͍ͯ͠Δ͕ɺຊདྷ͸ϊΠζύϥϝʔλ͕͜ͷΑ͏ͳෆنଇੑΛଊ

͍͑ͯͳͯ͘͸͍͚ͳ͍͜ͱΛߟྀ͢Δඞཁ΋͋Δɻ

2 ͭ໨͸ɺ CrowdFlower ͷΦϯϥΠϯͷඃݧऀʹͲ͜·Ͱ͖ͪΜͱΠϯηϯςΟϒΛ

༩͑Δ͜ͱ͕Ͱ͖͍ͯΔ͔ʹ͍ͭͯɺ CrowdFlower ͷඃݧऀଐੑʹ͍ͭͯͷ௥࣮ݧ͕ඞ ཁͰ͋Δɻকདྷతʹ͸ɺ͜͏ͨ͠ଐੑΛ͖ͪΜͱίϯτϩʔϧ͢Δඞཁ͕͋Δͱߟ͑Δɻ

࠷ޙʹɺ DellaVigna et al. (2017) ͷΑ͏ʹࢀর఺ґଘܕޮ༻ΛԾఆͯ͠ɺ Hopenhayn

and Nicolini (1997) ܕͷ࠷దࣦۀอݥܖ໿Λ਺஋తʹܭࢉ͠ɺͦͷ͏͑Ͱ࣮ݧΛ࣮ࢪ͢

Δ͜ͱͰɺݸਓ͕͍͔ͳΔબ޷Λ࣋ͪɺͦͷ΋ͱͰͲͷΑ͏ͳ৬୳͠Λߦ͏ͷ͔Λ͖ͪ

Μͱௐ΂Δ͜ͱ͕ඞཁͱͳΔɻҎ্ͷ఺Λ౿·͑ͨ૯߹తͳ࣮ݧݚڀ͕଴ͨΕΑ͏ɻ

Appendix

Round Reward Round Reward

1 4 cents 27 1 cents

2 3 cents 28 1 cents

3 3 cents 29 1 cents

4 3 cents 30 1 cents

5 3 cents 31 1 cents

6 3 cents 32 1 cents

7 2 cents 33 1 cents

8 2 cents 34 1 cents

9 2 cents 35 1 cents

10 2 cents 36 1 cents

11 2 cents 37 1 cents

12 2 cents 38 1 cents

13 2 cents 39 1 cents

14 2 cents 40 1 cents

15 1 cents 41 1 cents

16 1 cents 42 0 cents

17 1 cents 43 0 cents

18 1 cents 44 0 cents

19 1 cents 45 0 cents

20 1 cents 46 0 cents

21 1 cents 47 0 cents

22 1 cents 48 0 cents

23 1 cents 49 0 cents

24 1 cents 50 0 cents

25 1 cents more than 50 0 cents 26 1 cents

ද 5: ࠷దࣦۀอݥڅ෇ֹ

13 ࠓճͷݚڀ͸ɺ͋͘·Ͱ΋༧උతͳ࣮ݧͰ͋ΓɺҎԼͷΑ͏ͳ఺Ͱࠓޙղܾ͠ͳ͚Ε

͹͍͚ͳ͍՝୊Λ༗͍ͯ͠Δɻ 1 ͭ͸ɺ࣮ݧͷηϯγϣϯ਺͕গͳ͍ͨΊʹɺࠓճಘΒ Εͨ݁Ռ͕Ͳͷఔ౓ҰൠੑΛ࣋ͭ݁Ռͳͷ͔ʹ͍ͭͯ͸ɺ৻ॏʹۛຯ͍ͯ͘͠ඞཁ͕͋

ΔɻಛʹɺجૅύϥϝʔλͷਪఆͰ͸ɺαϯϓϧαΠζ͕খ͍͞ঢ়گԼͰ࠷໬๏Λ༻͍

ͯਪఆ͍ͯ͠Δɻ͞ΒʹɺϦεΫճආ౓ͷଌఆͰ΋ɺҰ౓ͷ੾Γସ͑఺ͷΈΛ༗͍ͯ͠

Δඃݧऀʹߜͬͯਪఆ͍ͯ͠Δ͕ɺຊདྷ͸ϊΠζύϥϝʔλ͕͜ͷΑ͏ͳෆنଇੑΛଊ

͍͑ͯͳͯ͘͸͍͚ͳ͍͜ͱΛߟྀ͢Δඞཁ΋͋Δɻ

2 ͭ໨͸ɺ CrowdFlower ͷΦϯϥΠϯͷඃݧऀʹͲ͜·Ͱ͖ͪΜͱΠϯηϯςΟϒΛ

༩͑Δ͜ͱ͕Ͱ͖͍ͯΔ͔ʹ͍ͭͯɺ CrowdFlower ͷඃݧऀଐੑʹ͍ͭͯͷ௥࣮ݧ͕ඞ ཁͰ͋Δɻকདྷతʹ͸ɺ͜͏ͨ͠ଐੑΛ͖ͪΜͱίϯτϩʔϧ͢Δඞཁ͕͋Δͱߟ͑Δɻ

࠷ޙʹɺ DellaVigna et al. (2017) ͷΑ͏ʹࢀর఺ґଘܕޮ༻ΛԾఆͯ͠ɺ Hopenhayn

and Nicolini (1997) ܕͷ࠷దࣦۀอݥܖ໿Λ਺஋తʹܭࢉ͠ɺͦͷ͏͑Ͱ࣮ݧΛ࣮ࢪ͢

Δ͜ͱͰɺݸਓ͕͍͔ͳΔબ޷Λ࣋ͪɺͦͷ΋ͱͰͲͷΑ͏ͳ৬୳͠Λߦ͏ͷ͔Λ͖ͪ

Μͱௐ΂Δ͜ͱ͕ඞཁͱͳΔɻҎ্ͷ఺Λ౿·͑ͨ૯߹తͳ࣮ݧݚڀ͕଴ͨΕΑ͏ɻ

12

₃₅₅

ࠓճͷݚڀ͸ɺ͋͘·Ͱ΋༧උతͳ࣮ݧͰ͋ΓɺҎԼͷΑ͏ͳ఺Ͱࠓޙղܾ͠ͳ͚Ε

͹͍͚ͳ͍՝୊Λ༗͍ͯ͠Δɻ 1 ͭ͸ɺ࣮ݧͷηϯγϣϯ਺͕গͳ͍ͨΊʹɺࠓճಘΒ Εͨ݁Ռ͕Ͳͷఔ౓ҰൠੑΛ࣋ͭ݁Ռͳͷ͔ʹ͍ͭͯ͸ɺ৻ॏʹۛຯ͍ͯ͘͠ඞཁ͕͋

ΔɻಛʹɺجૅύϥϝʔλͷਪఆͰ͸ɺαϯϓϧαΠζ͕খ͍͞ঢ়گԼͰ࠷໬๏Λ༻͍

ͯਪఆ͍ͯ͠Δɻ͞ΒʹɺϦεΫճආ౓ͷଌఆͰ΋ɺҰ౓ͷ੾Γସ͑఺ͷΈΛ༗͍ͯ͠

Δඃݧऀʹߜͬͯਪఆ͍ͯ͠Δ͕ɺຊདྷ͸ϊΠζύϥϝʔλ͕͜ͷΑ͏ͳෆنଇੑΛଊ

͍͑ͯͳͯ͘͸͍͚ͳ͍͜ͱΛߟྀ͢Δඞཁ΋͋Δɻ

2 ͭ໨͸ɺ CrowdFlower ͷΦϯϥΠϯͷඃݧऀʹͲ͜·Ͱ͖ͪΜͱΠϯηϯςΟϒΛ

༩͑Δ͜ͱ͕Ͱ͖͍ͯΔ͔ʹ͍ͭͯɺ CrowdFlower ͷඃݧऀଐੑʹ͍ͭͯͷ௥࣮ݧ͕ඞ ཁͰ͋Δɻকདྷతʹ͸ɺ͜͏ͨ͠ଐੑΛ͖ͪΜͱίϯτϩʔϧ͢Δඞཁ͕͋Δͱߟ͑Δɻ

࠷ޙʹɺ DellaVigna et al. (2017) ͷΑ͏ʹࢀর఺ґଘܕޮ༻ΛԾఆͯ͠ɺ Hopenhayn

and Nicolini (1997) ܕͷ࠷దࣦۀอݥܖ໿Λ਺஋తʹܭࢉ͠ɺͦͷ͏͑Ͱ࣮ݧΛ࣮ࢪ͢

Δ͜ͱͰɺݸਓ͕͍͔ͳΔબ޷Λ࣋ͪɺͦͷ΋ͱͰͲͷΑ͏ͳ৬୳͠Λߦ͏ͷ͔Λ͖ͪ

Μͱௐ΂Δ͜ͱ͕ඞཁͱͳΔɻҎ্ͷ఺Λ౿·͑ͨ૯߹తͳ࣮ݧݚڀ͕଴ͨΕΑ͏ɻ

354

12

ࢀߟจݙ

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