❋❯◆❉❆➬➹❖ ●❊❚❯▲■❖ ❱❆❘●❆❙ ❊❙❈❖▲❆ ❉❊ ❊❈❖◆❖▼■❆ ❉❊ ❙➹❖ P❆❯▲❖
❉✐♦❣♦ ❞❡ Pr✐♥❝❡ ▼❡♥❞♦♥ç❛
❊♥s❛✐♦s s♦❜r❡ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛
❉✐♦❣♦ ❞❡ Pr✐♥❝❡ ▼❡♥❞♦♥ç❛
❊♥s❛✐♦s s♦❜r❡ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛
❚❡s❡ ❛♣r❡s❡♥t❛❞❛ à ❊s❝♦❧❛ ❞❡ ❊❝♦♥♦♠✐❛ ❞❡ ❙ã♦ P❛✉❧♦ ❞❛ ❋✉♥❞❛çã♦ ●❡tú❧✐♦ ❱❛r❣❛s ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❞♦✉t♦r ❡♠ ❡❝♦♥♦♠✐❛✳
❖r✐❡♥t❛❞♦r✿ ❱❧❛❞✐♠✐r ❚❡❧❡s ❈♦♦r✐❡♥t❛❞♦r✿ ❇❡r♥❛r❞♦ ●✉✐♠❛rã❡s
Mendonça, Diogo de Prince.
Ensaios sobre Política Monetária / Diogo de Prince Mendonça. - 2015. 89 f.
Orientador: Vladimir Teles
Co-orientador: Bernardo Guimarães
Tese (doutorado) - Escola de Economia de São Paulo. 1. Política monetária - Brasil. 2. Crise financeira. 3. Áreas
subdesenvolvidas. I. Teles, Vladimir. II. Guimarães, Bernardo. III. Tese (doutorado) - Escola de Economia de São Paulo. IV. Título.
❉✐♦❣♦ ❞❡ Pr✐♥❝❡ ▼❡♥❞♦♥ç❛
❊♥s❛✐♦s s♦❜r❡ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛
❚❡s❡ ❛♣r❡s❡♥t❛❞❛ à ❊s❝♦❧❛ ❞❡ ❊❝♦♥♦♠✐❛ ❞❡ ❙ã♦ P❛✉❧♦ ❞❛ ❋✉♥❞❛çã♦ ●❡t✉❧✐♦ ❱❛r❣❛s ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❞♦✉t♦r ❡♠ ❡❝♦♥♦♠✐❛✳ ➪r❡❛ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✿ ▼❛❝r♦❡❝♦♥♦♠✐❛ ❉❛t❛ ❞❛ ❜❛♥❝❛✿ ✵✺✴✵✺✴✷✵✶✺ ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❱❧❛❞✐♠✐r ❑ü❤❧ ❚❡❧❡s ✭❊s❝♦❧❛ ❞❡ ❊❝♦♥♦♠✐❛ ❞❡ ❙ã♦ P❛✉❧♦✮
Pr♦❢✳ ❉r✳ ❇❡r♥❛r❞♦ ❱❛s❝♦♥❝❡❧❧♦s ●✉✐♠❛rã❡s ✭❊s❝♦❧❛ ❞❡ ❊❝♦♥♦♠✐❛ ❞❡ ❙ã♦ P❛✉❧♦✮
Pr♦❢✳ ❉r✳ ▲✉✐s ❋❡r♥❛♥❞♦ ❆r❛✉❥♦ ✭❊s❝♦❧❛ ❞❡ ❊❝♦♥♦♠✐❛ ❞❡ ❙ã♦ P❛✉❧♦✮
Pr♦❢✳ ❉r✳ ▼❛✉r♦ ❘♦❞r✐❣✉❡s ❏r✳ ✭❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✮
❆●❘❆❉❊❈■▼❊◆❚❖❙
Pr✐♠❡✐r❛♠❡♥t❡✱ ❡✉ s♦✉ ❣r❛t♦ ❛♦s ♠❡✉s ♣❛✐s ♣❡❧❛ ❛❥✉❞❛ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✱ ❡st❛♥❞♦ ❡✉ ❡♠ ❙ã♦ P❛✉❧♦✱ ❘✐❜❡✐rã♦ Pr❡t♦✱ ❆r❛r❛q✉❛r❛ ♦✉ ❡♠ tr❛♥s✐çã♦ ❡♥tr❡ ❡ss❛s ❝✐❞❛❞❡s✳ ❊✉ ♥ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r ❛ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❆r✐❡♥❡ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❛t❡♥çã♦✳ ❯♠❛ ♦✉tr❛ ♣❡ss♦❛ q✉❡ s♦♠❡♥t❡ ❝r❡s❝❡✉ ❞❡ ✐♠♣♦rtâ♥❝✐❛ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ❢♦✐ ♠❡✉ ♦r✐❡♥t❛❞♦r ❞❡ ♠❡str❛❞♦✱ ❙ér❣✐♦ ❑❛♥♥❡❜❧❡② ❏ú♥✐♦r✱ q✉❡ s❡ tr❛♥s❢♦r♠♦✉ ❡♠ ✉♠ ❣r❛♥❞❡ ❛♠✐❣♦✳ ❆❣r❛❞❡ç♦ ❛ ❡❧❡ ♣❡❧♦s ❝♦♥s❡❧❤♦s✱ ♣❡❧❛s ❝♦♥✈❡rs❛s✱ ❞✐❝❛s✱ ♣✉①õ❡s ❞❡ ♦r❡❧❤❛✱ ❡t❝✳ ❚❛♠❜é♠ ✜❝♦ ❢❡❧✐③ ♣❡❧♦ ❛✉①í❧✐♦ ❞♦ ❊♠❡rs♦♥ ▼❛rç❛❧ ✭❛ss✐♠ ❝♦♠♦ ❞❛ ♣r♦❢❡ss♦r❛ ❱❡r❛ ❚❤♦rst❡♥s❡♥✮ ♣r❛t✐❝❛♠❡♥t❡ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ ❞♦✉t♦r❛❞♦✱ ❛ss✐♠ ❝♦♠♦ ❞♦ ♣r♦❢❡ss♦r P❡❞r♦ ❱❛❧❧s ♣♦r ❧❡♠❜r❛r ❞❡ ♠✐♠ ❡ ♠❡ ❞❡s❝✉❧♣♦ ♣♦r ✐♥❝♦♠♦❞á✲❧♦ às ✈❡③❡s ✭às ✈❡③❡s ❛té ♥ã♦ ❞❡✈❡r✐❛ tê✲❧♦ ✐♥❝♦♠♦❞❛❞♦✮✳
❘❊❙❯▼❖
❊st❛ t❡s❡ é ❝♦♠♣♦st❛ ❞❡ três ❡♥s❛✐♦s ❛ r❡s♣❡✐t♦ ❞❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛✳ ❖ ♣r✐♠❡✐r♦ ❡♥s❛✐♦ ❛❜♦r❞❛ ♦ ❝❛♥❛❧ ❡♠ q✉❡ ❛s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s ❛✉♠❡♥t❛♠ ❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ♥♦s ♣❛ís❡s ❡♠❡r❣❡♥t❡s✳ ❖ s❡❣✉♥❞♦ ❡♥s❛✐♦ tr❛t❛ ❞♦ ❣r❛✉ ❞❡ ♥ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❞❛ ♠♦❡❞❛ ♥♦ ❇r❛s✐❧ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ ●♦❧♦s♦✈ ❡ ▲✉❝❛s ✭✷✵✵✼✮✳ ❖ t❡r❝❡✐r♦ ❡♥s❛✐♦ ❡st✐♠❛ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❤❛③❛r❞ ❢✉♥❝t✐♦♥ ❞❛ ♣r❡❝✐✜❝❛çã♦ ♣❛r❛ ♦ ❇r❛s✐❧ ♣❡❧❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧✳
❆❇❙❚❘❆❈❚
❚❤✐s t❤❡s✐s ✐♥❝❧✉❞❡s t❤r❡❡ ❡ss❛②s ❛❜♦✉t ♠♦♥❡t❛r② ♣♦❧✐❝②✳ ❚❤❡ ✜rst ❡ss❛② ❝♦✈❡rs t❤❡ ❝❤❛♥♥❡❧ t❤❛t ✜♥❛♥❝✐❛❧ ❝r✐s❡s ✐♥❝r❡❛s❡ t❤❡ ❛❧❧♦❝❛t✐✈❡ ✐♥❡✣❝✐❡♥❝② ✐♥ ❡♠❡r❣✐♥❣ ❝♦✉♥tr✐❡s✳ ❚❤❡ s❡❝♦♥❞ ❡ss❛② ❛❞❞r❡ss❡s t❤❡ ❞❡❣r❡❡ ♦❢ ♥♦♥✲♥❡✉tr❛❧✐t② ♦❢ ♠♦♥❡② ✐♥ ❇r❛③✐❧ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ●♦❧♦s♦✈ ❛♥❞ ▲✉❝❛s ✭✷✵✵✼✮ ♠♦❞❡❧✳ ❚❤❡ t❤✐r❞ ❡ss❛② ❝♦✈❡rs t❤❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ❤❛③❛r❞ ❢✉♥❝t✐♦♥ s❧♦♣❡ ✐♥ ♣r✐❝✐♥❣ t♦ ❇r❛③✐❧ ❜② t❤❡ ♠❡t❤♦❞♦❧♦❣② ♦❢ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧✳
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✷
✷ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛ ❡♠ ❚❡♠♣♦s ❞❡ ❈r✐s❡ ✶✺
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷ ❋❛t♦s ❡st✐❧✐③❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ❘❡❧❛çã♦ ❡♥tr❡ ❝❤♦q✉❡ ❡①t❡r♥♦ ❡ ♣r♦❞✉t♦ ❛tr❛✈és ❞❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ✳ ✳ ✶✾ ✷✳✸✳✶ ❈❛s♦ s❡♠ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✸✳✷ ❈❛s♦ ❝♦♠ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✹ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✹✳✶ ❋❛♠í❧✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✹✳✷ ❋✐r♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✹✳✸ ■♥t❡r♠❡❞✐ár✐♦ ❋✐♥❛♥❝❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✹✳✹ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✹✳✺ ❊q✉✐❧í❜r✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✺ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✺✳✶ P❛râ♠❡tr♦s ❈❛❧✐❜r❛❞♦s ❡ ❉✐str✐❜✉✐çã♦ ❞♦s Pr✐♦rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✺✳✶✳✶ P❛râ♠❡tr♦s ❈❛❧✐❜r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✺✳✶✳✷ Pr✐♦rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✺✳✷ P♦st❡r✐♦rs ❊st✐♠❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✻ Pr♦♣r✐❡❞❛❞❡s ❞♦ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✼ ❆♣❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✽ ■♠♣❧✐❝❛çõ❡s ♣❛r❛ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✾ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛ s❡❣✉♥❞♦ ♠♦❞❡❧♦ ❡st❛❞♦✲❞❡♣❡♥❞❡♥t❡ ✹✷ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✸ ▼♦❞❡❧♦ ❡st❛❞♦✲❞❡♣❡♥❞❡♥t❡ ❞❡ ●♦❧♦s♦✈ ❡ ▲✉❝❛s ✭✷✵✵✼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✹ ❈❛❧✐❜r❛çã♦ ❞♦ ♠♦❞❡❧♦ ♣❛r❛ ♦s ❊❯❆ ❡ ♣❛r❛ ♦ ❇r❛s✐❧ ❡ ♦ ❡❢❡✐t♦ ❞❛ ♣♦❧ít✐❝❛
♠♦♥❡tár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✺ P❛♣❡❧ ❞❛ ❈♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❊str❛té❣✐❝❛ ♥♦ ●r❛✉ ❞❡ ◆ã♦✲◆❡✉tr❛❧✐❞❛❞❡ ❞❛
▼♦❡❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✻ ❆♥á❧✐s❡ ❞❡ ❘♦❜✉st❡③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹ ❖ ♣✉③③❧❡ ❞❛s ❤❛③❛r❞ ❢✉♥❝t✐♦♥s ❞❡❝r❡s❝❡♥t❡s ✻✸
✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✸ ▼❡t♦❞♦❧♦❣✐❛ ❞♦s ▼♦❞❡❧♦s ❞❡ ❉✉r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✹ ❉❛❞♦s ❡ ❊str❛té❣✐❛ ❊♠♣ír✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✺ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❚r❛❥❡tór✐❛ ❞♦ P■❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❚r❛❥❡tór✐❛ ❞❛ P❚❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ❚r❛❥❡tór✐❛ ❞♦s ❚❡r♠♦s ❞❡ ❚r♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✹ ❋❧✉①♦ ❞❡ ❡♥tr❛❞❛ ❞❡ r❡❝✉rs♦s ❡str❛♥❣❡✐r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✺ ❘❡s♣♦st❛s ❛ ■♠♣✉❧s♦ ♥♦ ❋❧✉①♦ ❞❡ ❈❛♣✐t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✻ ❘❡s♣♦st❛s ❛ ✉♠ ■♠♣✉❧s♦ ♥♦ ■♥✈❡rs♦ ❞♦s ❚❡r♠♦s ❞❡ ❚r♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✼ ❘❡s♣♦st❛s ❛ ✉♠ ■♠♣✉❧s♦ ▼♦♥❡tár✐♦ ❈♦♥tr❛❝✐♦♥✐st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✽ ❉❡❝♦♠♣♦s✐çã♦ ❞♦s ❈❤♦q✉❡s ❞♦ Pr♦❞✉t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✾ ❍✐❛t♦ ❞❛ P❚❋ Pr❡✈✐st♦ ✈s ❖❜s❡r✈❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✶✵ Pr✐♦rs ❡ P♦st❡r✐♦s ❊st✐♠❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✶✶ Pr✐♦rs ❡ P♦st❡r✐♦s ❊st✐♠❛❞♦s ✭❝♦♥t✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶ ❍❛③❛r❞ ❋✉♥❝t✐♦♥s ❞♦ ▼♦❞❡❧♦ ❝❛❧✐❜r❛❞♦ ♣❛r❛ ❇r❛s✐❧ ❡ ❊❯❆ ❛♣❡♥❛s ❝♦♠ ❝❤♦✲
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ P❛râ♠❡tr♦s ❈❛❧✐❜r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✷ ❉✐str✐❜✉✐çã♦ ❡ ♣❛râ♠❡tr♦s✿ ❛ ♣r✐♦r✐ ❡ ❛ ♣♦st❡r✐♦r✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✸ ❆✈❛❧✐❛çã♦ ❞❡ ❞✐❢❡r❡♥t❡s r❡❣r❛s ❞❡ ❚❛②❧♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✶ ❈♦♠♣❛r❛çã♦ ❞❛ ❝❛❧✐❜r❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦s ❊❯❆ ❡ ♣❛r❛ ♦ ❇r❛s✐❧ ✳ ✳ ✺✸ ✸✳✷ ❈♦♠♣❛r❛çã♦ ❞❛s ❡st❛tíst✐❝❛s ❝❛❧✐❜r❛❞❛s ♣❛r❛ ♦s ❊❯❆ ❡ ♣❛r❛ ♦ ❇r❛s✐❧ ✳ ✳ ✳ ✳ ✺✸ ✸✳✸ ◆ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❞❛ ♠♦❡❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✹ ◆ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❈♦♥tr❛❢❛❝t✉❛❧ ❡ ♦ ❊❢❡✐t♦ ❞♦ ❝✉st♦ ❞❡ ♠❡♥✉ ❡ ❞♦ ❊❢❡✐t♦
❙❡❧❡çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✺ P❛râ♠❡tr♦s ♥❛ ❈❛❧✐❜r❛çã♦ ♣❛r❛ ❘❡❧❛çã♦ ♥❛ ♣r❡❝✐✜❝❛çã♦ ❞❛s ✜r♠❛s ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✻ P❛♣❡❧ ❞❛ ❈♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❊str❛té❣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✼ ◆ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❞❛ ♠♦❡❞❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡θ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✸✳✽ ❈❛❧✐❜r❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ❇r❛s✐❧ s❡ t✐✈❡ss❡ ❛ r✐❣✐❞❡③ ❞❡ ♣r❡ç♦ ❞♦s ❊❯❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✶ ❘❡s✉❧t❛❞♦s ❞♦ ▼♦❞❡❧♦ ❞❡ ❉✉r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✷ ❊s❝♦❧❤❛ ❞♦ ♥ú♠❡r♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ♥♦ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✸ ❘❡s✉❧t❛❞♦s ❞♦ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✹ ❊st❛tíst✐❝❛ ❉❡s❝r✐t✐✈❛ ❞♦s ❈♦♠♣♦♥❡♥t❡s ❞♦ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✺ ❘❡s✉❧t❛❞♦s ❞♦ ▼♦❞❡❧♦ ❞❡ ❉✉r❛çã♦ ❝♦♠ ❛ ■♥❝❧✉sã♦ ❞❛s ❈❛t❡❣♦r✐❛s ✳ ✳ ✳ ✳ ✳ ✽✶
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
■♥tr♦❞✉çã♦
❆ ♣r❡s❡♥t❡ t❡s❡ é ❞✐✈✐❞✐❞❛ ❡♠ três ❡♥s❛✐♦s s♦❜r❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛✳ ❖ ♣r✐♠❡✐r♦ ❡♥s❛✐♦ ❛❜♦r❞❛ ♦ ❡❢❡✐t♦ ❞❡ ✉♠❛ ❝r✐s❡ ❡①t❡r♥❛ ♥♦ ❛✉♠❡♥t♦ ❞❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ❡♠ ✉♠ ♠♦❞❡❧♦ ❉✐♥â♠✐❝♦ ❊st♦❝ást✐❝♦ ❞❡ ❊q✉✐❧í❜r✐♦ ●❡r❛❧ ✭❉❙●❊✮✱ ❡♥q✉❛♥t♦ ♦ s❡❣✉♥❞♦ ❡ ♦ t❡r❝❡✐r♦ ❡♥s❛✐♦s ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s à ❧✐t❡r❛t✉r❛ ❞❡ ♣r❡ç♦s rí❣✐❞♦s✳ ❖ ♣r✐♠❡✐r♦ ❡♥s❛✐♦ ❜❛s❡✐❛✲s❡ ♥❛ t❡s❡ ❞❡ q✉❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s sã♦ ❛❝♦♠♣❛♥❤❛❞❛s ♣♦r q✉❡❞❛s ❞❛ Pr♦❞✉t✐✈✐❞❛❞❡ ❚♦t❛❧ ❞♦s ❋❛t♦r❡s ✭P❚❋✮✱ ❝♦♠♦ ❈❛❧✈♦ ❡t ❛❧ ✭✷✵✵✻✮✱ ❈❡rr♦ ❡ ❙❛①❡♥❛ ✭✷✵✵✽✮ ❡ ◗✉❡r❛❧t♦ ✭✷✵✶✷✮ ✐♥❞✐❝❛♠✳ ❖ ♠♦❞❡❧♦ ❝♦rr♦❜♦r❛ q✉❡ ❛ ❝r✐s❡ t❡♠ ❡❢❡✐t♦s r❡❛✐s ❛♦ ❝♦♥t❡♠♣❧❛r ❞♦✐s ❝❤♦q✉❡s ❡①t❡r♥♦s✿ t❡r♠♦s ❞❡ tr♦❝❛ ❡ ❧✐q✉✐❞❡③ ❡①t❡r♥❛✳ ❖ ❢♦❝♦ é ❛✈❛❧✐❛r ❛ ♣♦❧➫✙t✐❝❛ ♠♦♥❡t➫❛r✐❛ ❡♠ ❝r✐s❡s ♣r♦✈♦❝❛❞❛s ♣♦r s✉❞❞❡♥t✲st♦♣s ❡ ❝❤♦q✉❡s ♥♦s t❡r♠♦s ❞❡ tr♦❝❛✳ ◆♦ ❝❛s♦✱ ♦ s✉❞❞❡♥✲st♦♣ ❛✉♠❡♥t❛r✐❛ ❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ♣❡❧❛ ♣r❡s❡♥ç❛ ❞❡ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛✳ ❏á ✉♠ ❝❤♦q✉❡ ♥♦s t❡r♠♦s ❞❡ tr♦❝❛ ♠✉❞❛r✐❛ ♦ ♣r❡ç♦ r❡❧❛t✐✈♦ ❞♦s ❢❛t♦r❡s ♥♦ ♣❛ís ♣♦rq✉❡ ❛s ✜r♠❛s ✐♠♣♦rt❛♠ ✐♥s✉♠♦s✱ ♦ q✉❡ s❡r✐❛ ✉♠❛ ♦✉tr❛ ❢♦♥t❡ ❞❡ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛✳ ❖ ♠♦❞❡❧♦ ❉❙●❊ ❝♦♥str✉í❞♦ é ❡st✐♠❛❞♦ ♣❛r❛ ♦ ❇r❛s✐❧ ❝♦♠ ❡❝♦♥♦♠❡tr✐❛ ❜❛②❡s✐❛♥❛ ♣❛r❛ ♦ ♣❡rí♦❞♦ tr✐♠❡str❛❧ ❡♥tr❡ ✷✵✵✵ ❡ ✷✵✶✷✳ ❆ ❝❛♣❛❝✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ❣❡r❛r ✉♠❛ sér✐❡ ❞❡ P❚❋ ♣r❡✈✐st❛ ♣❛r❡❝❡ s❡r ❜❡♠ s✉❝❡❞✐❞❛ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ à P❚❋ ♦❜s❡r✈❛❞❛✳ P♦r ✜♠✱ ❛ r❡❣r❛ ❞❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛ q✉❡ ♠❛①✐♠✐③❛ ❜❡♠✲ ❡st❛r ❞❡♣❡♥❞❡ ❞❛ ❢♦♥t❡ ❞♦s ❝❤♦q✉❡s ♣♦rq✉❡ ❝❛❞❛ ✉♠ ❞❡❧❡s ❧❡✈❛ ❛ ❞✐❢❡r❡♥t❡s ❞✐st♦rçõ❡s✳
❖ s❡❣✉♥❞♦ ❡♥s❛✐♦ tr❛t❛ ❞♦ ❡❢❡✐t♦ r❡❛❧ ❞❛ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛ ♥♦ ♠♦❞❡❧♦ ❞❡ ●♦❧♦s♦✈ ❡ ▲✉❝❛s ✭✷✵✵✼✮✳ ❆ ♣r♦♣♦st❛ é ❝❛❧✐❜r❛r ♦ ♠♦❞❡❧♦ ❞❡ ●♦❧♦s♦✈ ❡ ▲✉❝❛s ✭✷✵✵✼✮ ♣❛r❛ ♦ ❇r❛s✐❧ ❡ ♦s ❊❯❆ ❡ ❝♦♠♣❛r❛r ♦ ❡❢❡✐t♦ ❞❛ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛✳ ❈♦♠♦ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ♠✉❞❛♥ç❛ ❞❡ ♣r❡ç♦s é ♠❛✐♦r ♥♦ ❇r❛s✐❧✱ ♦ ♠♦❞❡❧♦ ✐♥❞✐❝❛ q✉❡ ♦ ❣r❛✉ ❞❡ ♥ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❞❛ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛ é ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♠❡♥♦r ♣❛r❛ ♦ ❇r❛s✐❧ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦s ❊❯❆✳ ❖ ❝✉st♦ ❞❡ ♠❡♥✉ é ♦ ❣r❛♥❞❡ r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ❣r❛✉ ❞❡ ♥ã♦✲♥❡✉tr❛❧✐❞❛❞❡ s❡r ♠❡♥♦r ♥♦ ❇r❛s✐❧✱ ♠❛s t❛♠❜é♠ ❤á ✉♠ ❡❢❡✐t♦ s❡❧❡çã♦ q✉❡ ♥ã♦ é ❞❡s♣r❡③é✈❡❧✳ ❖ ❡❢❡✐t♦ s❡❧❡çã♦ s❡r✐❛ ♠❛✐♦r q✉❛♥t♦ ♠❛✐♦r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❝❤♦q✉❡ ❛❣r❡❣❛❞♦ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦ ❝❤♦q✉❡ ✐❞✐♦ss✐♥❝rát✐❝♦ ♥♦ ♣r♦❝❡ss♦ ❞❡ ♠✉❞❛♥ç❛ ❞❡ ♣r❡ç♦ ❞❛s ✜r♠❛s✳ ❊♥tr❡t❛♥t♦✱ ♦s r❡s✉❧t❛❞♦s sã♦ ❛❧t❡r❛❞♦s s❡♥s✐✈❡❧♠❡♥t❡ ❡ ❞❡ ❢♦r♠❛ ✐♥❡s♣❡r❛❞❛ s❡ ❝♦♥s✐❞❡r❛r q✉❡ ❛s ✜r♠❛s ✐♥t❡r❛❣❡♠ ❡str❛t❡❣✐❝❛♠❡♥t❡ ❡♥tr❡ s✐✳ ◆♦ ❝❛s♦ ❞❡ ❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❡str❛té❣✐❝❛✱ ♦ ❇r❛s✐❧ ❛♣r❡s❡♥t❛ ♠❛✐♦r ❣r❛✉ ❞❡ ♥ã♦✲♥❡✉tr❛❧✐❞❛❞❡ ❞❛ ♠♦❡❞❛ ❞♦ q✉❡ ♦s ❊❯❆✳ ❆✐♥❞❛ ❝♦♠♦ ✉♠ s✉❜♣r♦❞✉t♦✱ ❛❜♦r❞❛♠♦s ❛ ❤❛③❛r❞ ❢✉♥❝t✐♦♥ ✭♣r♦❜❛❜✐❧✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡ ♠✉❞❛r ♦ ♣r❡ç♦ ❡♠ t❡r♠♦s ❞♦ t❡♠♣♦✮ s✐♠✉❧❛❞❛ ♣❡❧♦ ♠♦❞❡❧♦✳ ❖ ♣♦♥t♦ é q✉❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❤❛③❛r❞ ❢✉♥❝t✐♦♥ ❛♣❡♥❛s ♣❛r❛ ♦s s♣❡❧❧s ✭♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❡♠ q✉❡ ❛ ✜r♠❛ ♠❛♥té♠ ♦ s❡✉ ♣r❡ç♦✮ ❝♦♠ ❛✉♠❡♥t♦ ❞❡ ♣r❡ç♦ ❞❡✈❡ s❡r ♠❛✐s ❢á❝✐❧ ❞❡ ❞❡t❡❝t❛r ♦ ❡❢❡✐t♦ ❞♦s ❝❤♦q✉❡s ❛❣r❡❣❛❞♦s ✭♣♦r ❡st❛r❡♠ ♠❛✐s s✉s❝❡tí✈❡✐s ❛♦s ♠❡s♠♦s✮ ❞♦ q✉❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❤❛③❛r❞ ❢✉♥❝t✐♦♥ ♣❛r❛ t♦❞♦s ♦s s♣❡❧❧s✳
❈❛♣ít✉❧♦ ✷
P♦❧ít✐❝❛ ▼♦♥❡tár✐❛ ❡♠ ❚❡♠♣♦s ❞❡ ❈r✐s❡
✷✳✶ ■♥tr♦❞✉çã♦
❈r✐s❡s ✜♥❛♥❝❡✐r❛s✱ ❝♦♠♦ ❛ ♦❝♦rr✐❞❛ ❡♠ ✷✵✵✽✱ sã♦ ❛❝♦♠♣❛♥❤❛❞❛s ♣♦r ❢♦rt❡s q✉❡❞❛s ❞❛ ♣r♦❞✉t✐✈✐❞❛❞❡ t♦t❛❧ ❞♦s ❢❛t♦r❡s ✭P❚❋✮ ♥♦s ♣❛ís❡s ❡♠❡r❣❡♥t❡s✳ ❚❛❧ ❡❢❡✐t♦ é ❛♠♣❧❛♠❡♥t❡ ❞♦❝✉♠❡♥t❛❞♦ ♣❛r❛ t♦❞❛s ❛s ❡❝♦♥♦♠✐❛s ❡♠❡r❣❡♥t❡s ♣♦r ❈❛❧✈♦ ❡t ❛❧ ✭✷✵✵✻✮ ❡ ❈❡rr♦ ❡ ❙❛①❡♥❛ ✭✷✵✵✽✮✱ ♣❛r❛ ❛s ❝r✐s❡s ♥❛s ❞é❝❛❞❛s ❞❡ ✽✵ ❡ ✾✵✱ ❡ ♣♦r ◗✉❡r❛❧t♦ ✭✷✵✶✷✮ ♣❛r❛ ❛ ❝r✐s❡ ❞❡ ✷✵✵✽✳ ◆❡st❡ ❛rt✐❣♦ ❛♣r❡s❡♥t❛♠♦s ❡✈✐❞ê♥❝✐❛s ❞❡ q✉❡ ❛ ❝r✐s❡ ❞❡ ✷✵✵✽ ❧❡✈♦✉ ❛ ✉♠❛ q✉❡❞❛ ❞❛ P❚❋ ♥♦ ❇r❛s✐❧ ❡ ❛♣r❡s❡♥t❛♠♦s ✉♠ ♠♦❞❡❧♦ ♦♥❞❡ ♦s ❡❢❡✐t♦s r❡❛✐s ❞❛ ❝r✐s❡ r❡s✉❧t❛♠ ❞❡ ❝❤♦q✉❡s ❡①t❡r♥♦s q✉❡ ✐♠♣❧✐❝❛♠ ❡♠ ♠✉❞❛♥ç❛s ♥♦s ♣r❡ç♦s r❡❧❛t✐✈♦s ❞♦s ❢❛t♦r❡s ❞❡ ♣r♦❞✉çã♦✱ ❡ ❛ss✐♠ ♥❛ P❚❋✳ ❚❛❧ ♠♦❞❡❧♦ é ❡st✐♠❛❞♦ ♣❛r❛ ❛ ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛✱ ❡ ❛s ✐♠♣❧✐❝❛çõ❡s ♣❛r❛ ❛ ❝♦♥❞✉çã♦ ❞❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛ sã♦ ❞✐s❝✉t✐❞❛s✳
◆ós ❛♥❛❧✐s❛♠♦s ❞♦✐s t✐♣♦s ❞❡ ❝❤♦q✉❡s ❡①t❡r♥♦s s♦❜ ♦s q✉❛✐s ❛ ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛ s❡ ❞❡♣❛r♦✉ r❡❝❡♥t❡♠❡♥t❡✱ ❡ s✉❛s ❝♦♥s❡q✉❡♥❝✐❛s s♦❜r❡ ❛ ❡❝♦♥♦♠✐❛✿ ❝❤♦q✉❡s ❞❡ s✉❞❞❡♥✲st♦♣s ❡ ❝❤♦q✉❡s ♥♦s t❡r♠♦s ❞❡ tr♦❝❛✳ ❉❡ss❛ ❢♦r♠❛✱ ♦ ❢♦❝♦ ❞♦ ❛rt✐❣♦ s❡rá ❛✈❛❧✐❛r ❛ ❝♦♥❞✉çã♦ ❞❡ ♣♦❧ít✐❝❛s ♠♦♥❡tár✐❛s ❡♠ ♣❡rí♦❞♦s ❞❡ ❝r✐s❡s ♣r♦✈♦❝❛❞❛s ♣♦r ❡st❡s ❞♦✐s t✐♣♦s ❞❡ ❝❤♦q✉❡s✳
❊♠ ✉♠❛ ❡❝♦♥♦♠✐❛ ❝♦♠ ❢r✐❝çõ❡s ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ é ❞❡ s❡ ❡s♣❡r❛r ✉♠ ❝❡rt♦ ❣r❛✉ ❞❡ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛✳ ❯♠❛ q✉❡❞❛ ❞❡ ♣r♦❞✉t✐✈✐❞❛❞❡ ❛❝❡♥t✉❛❞❛ ❞✉r❛♥t❡ ✉♠❛ ❝r✐s❡ ✜✲ ♥❛♥❝❡✐r❛ r❡✈❡❧❛ q✉❡ ❛ ❝r✐s❡ ♣♦❞❡ ❝❛✉s❛r ✉♠ ❛✉♠❡♥t♦ ❞❡st❛ ✐♥❡✜❝✐ê♥❝✐❛✳ ❆ss✐♠ ❡①♣❧♦r❛♠♦s ❝♦♠♦ ✉♠ s✉❞❞❡♥✲st♦♣ ✐♠♣❧✐❝❛ ❡♠ ✉♠ ❛✉♠❡♥t♦ ❞❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ❝❛✉s❛❞❛ ♣♦r ❢r✐❝✲ çõ❡s ✜♥❛♥❝❡✐r❛s✳ ❆♦ ♠❡s♠♦ t❡♠♣♦✱ q✉❛♥❞♦ ✉♠❛ ❡❝♦♥♦♠✐❛ ♣r❡❝✐s❛ ✐♠♣♦rt❛r ✐♥s✉♠♦s✱ ✉♠ ❝❤♦q✉❡ ♥♦s t❡r♠♦s ❞❡ tr♦❝❛ r❡s✉❧t❛ ❡♠ ✉♠❛ ♠✉❞❛♥ç❛ ❞♦s ♣r❡ç♦s r❡❧❛t✐✈♦s ❞❛ ❡❝♦♥♦♠✐❛✱ ✐♠♣❧✐❝❛♥❞♦ ❡♠ ♦✉tr❛ ❢♦♥t❡ ❞❡ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛✳
❖ ♠♦❞❡❧♦ é ❞❡s❡♥✈♦❧✈✐❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ♠❡s❝❧❛ ❞❡ ✐♥s✐❣❤ts ❢♦r♥❡❝✐❞♦s ♣♦r ♠♦❞❡❧♦s ❞❡ ✇♦r❦✐♥❣ ❝❛♣✐t❛❧ ❝♦♠ ❝❛s❤ ✐♥ ❛❞✈❛♥❝❡ ✭❡✳❣✳ ❈❛r❧str♦♠ ❡ ❋✉❡rst✱ ✶✾✾✺✮✱ ❞❡ ❢r✐❝çõ❡s ✜♥❛♥❝❡✐r❛s ❡♠ ❡❝♦♥♦♠✐❛s ❛❜❡rt❛s ❡ ♣❡q✉❡♥❛s ✭❡✳❣✳ ◆❡✉♠❡②❡r ❡ P❡rr✐✱ ✷✵✵✺❀ ❡ Pr❛t❛♣ ❡ ❯rr✉t✐❛✱ ✷✵✶✷✮✱ ❡ ♠♦❞❡❧♦s ❝♦♠ ✐♠♣♦rt❛çã♦ ❞❡ ✐♥s✉♠♦s✱ ❞❡ ❢♦r♠❛ q✉❡ ♦s t❡r♠♦s ❞❡ tr♦❝❛ sã♦ r❡❧❡✈❛♥t❡s ♥❛ ❛❧♦❝❛çã♦ ❞❡ r❡❝✉rs♦s ♣r♦❞✉t✐✈♦s ✭❡✳❣✳ ▼❡♥❞♦③❛✱ ✶✾✾✺✱ ❡ ❆❝❡♠♦❣❧✉ ❡ ❱❡♥t✉r❛✱ ✷✵✵✷✮✳
❉❡ss❛ ❢♦r♠❛ ♦ ♠♦❞❡❧♦ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❡❝♦♥♦♠✐❛ ❡♠ q✉❡ ♦ ❧❛❞♦ r❡❛❧ s❡❣✉❡ ✉♠ ♠♦❞❡❧♦ ♣❛❞rã♦ ❞❡ ❘❡❛❧ ❇✉s✐♥❡ss ❈②❝❧❡s ✭❘❇❈✮✳ ❆ ♠♦❡❞❛ é ✐♥s❡r✐❞❛ ♥♦ ♠♦❞❡❧♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ r❡str✐çã♦ ❝❛s❤✲✐♥✲❛❞✈❛♥❝❡ ♥❛ ❞❡❝✐sã♦ ❞❡ ❝♦♥s✉♠♦ ❞❛s ❢❛♠í❧✐❛s✱ ❡ ❡♠ ✉♠❛ r❡str✐çã♦ ❞❡ ✇♦r❦✐♥❣ ❝❛♣✐t❛❧ ♥❛ ❞❡❝✐sã♦ ❞❡ ❝♦♥tr❛t❛çã♦ ❞❡ tr❛❜❛❧❤❛❞♦r❡s ♣❡❧❛s ✜r♠❛s✳ ❈♦♠♦ é ❜❡♠ s❛❜✐❞♦✱ t❛✐s r❡str✐çõ❡s ✐♠♣❧✐❝❛♠ ❡♠ ❞✉❛s ✐♥❡✜❝✐ê♥❝✐❛s s♦❜r❡ ❛ ❡❝♦♥♦♠✐❛✿ ✶✮ ❛ r❡str✐çã♦ ❞❡ ♠♦❡❞❛ ♣❡❧❛s ✜r♠❛s ❢❛③ ❝♦♠ q✉❡ ♦s ❥✉r♦s ❝♦❜r❛❞♦s ♣❡❧♦ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦ ❛❢❡t❡ ♦ ❝✉st♦ ❞♦ tr❛❜❛❧❤♦✱ ❡✱ ❛ss✐♠✱ ❛ s✉❛ ❞❡♠❛♥❞❛ ✭❋✉❡rst✱ ✶✾✾✹✮❀ ✷✮ ❛ r❡str✐çã♦ ❞❡ ♠♦❡❞❛ ❞❛s ❢❛♠í❧✐❛s ✐♠♣❧✐❝❛ ❡♠ ✉♠❛ ❞✐st♦rçã♦ ♥❛ ❞❡❝✐sã♦ ❞❡ ❝♦♥s✉♠♦ ✭❈♦♦❧❡② ❡ ❍❛♥s❡♥✱ ✶✾✽✾✮✳
2006 2007 2008 2009 2010 2011 2012 2013 170000
180000 190000 200000 210000 220000 230000
❋✐❣✉r❛ ✷✳✶✿ ❚r❛❥❡tór✐❛ ❞♦ P■❇
2004 2005 2006 2007 2008 2009 2010 2011 1.100
1.125 1.150 1.175 1.200 1.225 1.250 1.275
❋✐❣✉r❛ ✷✳✷✿ ❚r❛❥❡tór✐❛ ❞❛ P❚❋
✉♠ ❛❣❡♥t❡ q✉❡ ❡♠♣r❡st❛ r❡❝✉rs♦s ♣❛r❛ ♦ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦✱ s❡♥❞♦ ✉♠❛ ❢♦♥t❡ ❞❡ ❧✐q✉✐❞❡③✱ ♦ q✉❡ r❡❞✉③ ❛ ♣r✐♠❡✐r❛ ❢♦♥t❡ ❞❡ ❞✐st♦rçã♦ ❧✐st❛❞❛ ♥♦ ♣❛rá❣r❛❢♦ ❛♥t❡r✐♦r❀ ❡ ❡♠ s❡❣✉♥❞♦ ❧✉❣❛r✱ ❝♦♠♦ ♣r♦❞✉③✐♥❞♦ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s q✉❡ sã♦ ✐♠♣♦rt❛❞♦s ♣❡❧❛s ✜r♠❛s ♣❛r❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♥❛ ♣r♦❞✉çã♦✳ ❈♦♠♦ r❡s✉❧t❛❞♦✱ ♦s t❡r♠♦s ❞❡ tr♦❝❛ ❛❢❡t❛♠ ♦s ♣r❡ç♦s r❡❧❛t✐✈♦s ❞♦s ❢❛t♦r❡s✱ ❡ ❛ss✐♠✱ ❛ ❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ❞❛ ❡❝♦♥♦♠✐❛✱ ❞❡ ❢♦r♠❛ q✉❡ ❝❤♦q✉❡s ♥♦s t❡r♠♦s ❞❡ tr♦❝❛ t❡rã♦ ✉♠ ❡❢❡✐t♦ s✐♠✐❧❛r ❛ ✉♠ ❝❤♦q✉❡ ❞❡ ♣r♦❞✉t✐✈✐❞❛❞❡✳
❖ ♠♦❞❡❧♦ é ❧♦❣✲❧✐♥❡❛r✐③❛❞♦ ❡♠ t♦r♥♦ ❞♦ ❡q✉✐❧í❜r✐♦ ❡ ❡st✐♠❛❞♦ ♣❛r❛ ❛ ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛ ♣❛r❛ ♦ ♣❡rí♦❞♦ ✷✵✵✵✲✷✵✶✷✳ ❆ ♣❛rt✐r ❞♦s ♣❛râ♠❡tr♦s ❡st✐♠❛❞♦s ❡ ❝❛❧✐❜r❛❞♦s✱ ♦ ♠♦❞❡❧♦ ❢♦✐ ❝❛♣❛③ ❞❡ ❝♦♥str✉✐r ✉♠❛ sér✐❡ ❞❡ P❚❋ q✉❡ s❡❣✉❡ ❛s ♠❡s♠❛s ❞✐r❡çõ❡s ❞❛ sér✐❡ ♦❜s❡r✈❛❞❛ ♥♦s ❞❛❞♦s✱ ❡①♣❧✐❝❛♥❞♦ ❜♦❛ ♣❛rt❡ ❞♦ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦ ♥♦ ♣❡rí♦❞♦✳ ❆❧é♠ ❞✐ss♦✱ ♦s r❡s✉❧t❛❞♦s ✐♥❞✐❝❛♠ q✉❡ ❛ r❡❣r❛ ❞❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛ q✉❡ ♠❛①✐♠✐③❛ ♦ ❜❡♠ ❡st❛r ❞❡♣❡♥❞❡ ❞❛ ❢♦♥t❡ ❞♦s ❝❤♦q✉❡s✱ ✉♠❛ ✈❡③ q✉❡ ❝❛❞❛ ❝❤♦q✉❡ ✐♠♣❧✐❝❛ ❡♠ ❞✐st♦rçõ❡s ❞✐❢❡r❡♥t❡s s♦❜r❡ ♦ ♠♦❞❡❧♦✳
✷✳✷ ❋❛t♦s ❡st✐❧✐③❛❞♦s
❆ ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛ ❛♣r❡s❡♥t♦✉ ♠✉❞❛♥ç❛ ♥❛ s✉❛ tr❛❥❡tór✐❛ ❛♣ós ❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ❞❡ ✷✵✵✽✳ ◆❡st❛ s❡çã♦✱ ❛ ♠✉❞❛♥ç❛ ♥❛ tr❛❥❡tór✐❛ é ❛♣♦♥t❛❞❛ ❡ ❛❧❣✉♥s ❢❛t♦r❡s q✉❡ ♣♦❞❡♠ ❡①♣❧✐❝❛r ❡ss❛ ❛❧t❡r❛çã♦ ❞♦ ♣r♦❞✉t♦ ❜r❛s✐❧❡✐r♦ ❡ q✉❡ s❡rã♦ ❛❜♦r❞❛❞♦s ♥♦ ♠♦❞❡❧♦✳ ❆ ✜❣✉r❛ ✷✳✶ ❛♣r❡s❡♥t❛ ♦ P■❇ ✭Pr♦❞✉t♦ ■♥t❡r♥♦ ❇r✉t♦✮ ❞♦ ❇r❛s✐❧ ❞❡ss❛③♦♥❛❧✐③❛❞♦ ❡♠ t❡r♠♦s r❡❛✐s tr✐♠❡str❛❧ ❡♥tr❡ ✷✵✵✻ ❡ ✷✵✶✷✳ ❖ ♣r♦❞✉t♦ ❜r❛s✐❧❡✐r♦ ❛♣r❡s❡♥t❛✈❛ ✉♠❛ tr❛❥❡tór✐❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❛té ♦ ✜♥❛❧ ❞❡ ✷✵✵✽✱ q✉❛♥❞♦ ❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ❧❡✈♦✉ à ❞✐♠✐♥✉✐çã♦ ❞♦ P■❇✳ ❉❡♣♦✐s ♦ P■❇ r❡t♦♠❛ ❛ tr❛❥❡tór✐❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡ ❡st❛❣♥❛ ❛ ♣❛rt✐r ❞❡ ✷✵✶✶✳
2005 2006 2007 2008 2009 2010 2011 2012 2013 95
100 105 110 115 120 125 130
❋✐❣✉r❛ ✷✳✸✿ ❚r❛❥❡tór✐❛ ❞♦s ❚❡r♠♦s ❞❡ ❚r♦❝❛
2008 2009 2010 2011 2012 2013 −10000
−5000 0 5000 10000 15000
❋✐❣✉r❛ ✷✳✹✿ ❋❧✉①♦ ❞❡ ❡♥tr❛❞❛ ❞❡ r❡❝✉rs♦s ❡str❛♥❣❡✐r♦s
❞♦ P■❇ ❡ ❞❛ ♣r♦❞✉çã♦ ✐♥❞✉str✐❛❧✳ ❆ ✜❣✉r❛ ✷✳✷ ❛♣r❡s❡♥t❛ ❛ tr❛❥❡tór✐❛ ❞❛ P❚❋ ♥♦ ❇r❛s✐❧ ❞❡ ✷✵✵✹ ❛ ✷✵✶✶✱ ♥♦ q✉❛❧ ♦ ❛♣ê♥❞✐❝❡ ✐♥❞✐❝❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥str✉çã♦ ❞❛ P❚❋✳ ❍á ✉♠❛ t❡♥❞ê♥❝✐❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❛ P❚❋✱ ✐♥t❡rr♦♠♣✐❞❛ ❝♦♠ ❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ❞❡ ✷✵✵✽ ❡ q✉❡ ♥ã♦ ❝❤❡❣❛ ❛ r❡t♦♠❛r ♦ ❝r❡s❝✐♠❡♥t♦ ♣ré✈✐♦✳ ❖ ♥♦ss♦ ❛r❣✉♠❡♥t♦ é q✉❡ ❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ✐♥❝♦rr❡✉ ♥❛ q✉❡❞❛ ❞❛ P❚❋ q✉❡✱ ♣♦r s✉❛ ✈❡③✱ r❡❞✉③✐✉ ♦ P■❇✳
❖ ♣ró①✐♠♦ ♣♦♥t♦ é ♦ q✉❡ ♣♦❞❡r✐❛ ✐♥t❡r❢❡r✐r ♥❛ P❚❋ ❝♦♠ ❛ ❝r✐s❡ ❞❡ ✷✵✵✽✳ ❖ ♠♦❞❡❧♦ ❞♦ tr❛❜❛❧❤♦ ❛r❣✉♠❡♥t❛ q✉❡ ❛ ✈❛r✐á✈❡❧ t❡r♠♦s ❞❡ tr♦❝❛ ✐♠♣❛❝t❛r✐❛ ❛ P❚❋✳ ❙❡❣✉♥❞♦ ❛ ✜❣✉r❛ ✷✳✸✱ ❤á ✉♠ ❝r❡s❝✐♠❡♥t♦ ❞♦s t❡r♠♦s ❞❡ tr♦❝❛✱ ✐♥t❡rr♦♠♣✐❞♦ ♣❡❧❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ❞❡ ✷✵✵✽✳ ◆♦ ✜♠ ❞❡ ✷✵✵✾✱ ♦ ❝r❡s❝✐♠❡♥t♦ ❞♦s t❡r♠♦s ❞❡ tr♦❝❛ é r❡t♦♠❛❞♦ ❡ ✈♦❧t❛ ❛ ❞✐♠✐♥✉✐r✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦✱ ❛ ❞❡t❡r✐♦r❛çã♦ ❞♦s t❡r♠♦s ❞❡ tr♦❝❛ r❡❞✉③ ❛ P❚❋✱ q✉❡ tr❛♥s❢❡r❡ ❡ss❛ q✉❡❞❛ ♣❛r❛ ♦ P■❇✳ ❍á ✉♠❛ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ❛s tr❛❥❡tór✐❛s ❞♦s t❡r♠♦s ❞❡ tr♦❝❛ ❡ ❞♦ P■❇✳ ❆ss✐♠✱ ❡ss❡ s❡r✐❛ ✉♠ ❝❛♥❛❧ ♣❡❧♦ q✉❛❧ ❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ❛❢❡t❛r✐❛ ♦ ♣r♦❞✉t♦✳
✷✳✸ ❘❡❧❛çã♦ ❡♥tr❡ ❝❤♦q✉❡ ❡①t❡r♥♦ ❡ ♣r♦❞✉t♦ ❛tr❛✈és ❞❛
✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛
◆❡st❛ s❡çã♦✱ ✐r❡♠♦s ❛♣r❡s❡♥t❛r ♦s ❛r❣✉♠❡♥t♦s ❜ás✐❝♦s ♣♦r trás ❞♦ ♠♦❞❡❧♦ q✉❡ s❡rá ❞❡s❡♥✲ ✈♦❧✈✐❞♦ ♥❛ ♣ró①✐♠❛ s❡çã♦✳ P❛r❛ ❡st❛ ✜♥❛❧✐❞❛❞❡ ✉♠ ♠♦❞❡❧♦ ❜❡♠ s✐♠♣❧❡s ❢♦✐ ❝♦♥str✉í❞♦ ♦♥❞❡ ✜❝❛ ❝❧❛r♦ ♦ ✐♥s✐❣❤t ❞❛ r❡❧❛çã♦ ❡♥tr❡ ❝❤♦q✉❡s ❞❡ ❧✐q✉✐❞❡③ ❡①t❡r♥❛ ❡ ❛ P❚❋✳
❖ ❡①❡r❝í❝✐♦ r❡❛❧✐③❛❞♦ ♥❡st❛ s❡çã♦ ✐♥❝❧✉✐ ❛ ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ❡♠ ✉♠❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❙♦❧♦✇✳ ❇❛s✐❝❛♠❡♥t❡✱ ❞✉❛s ❡①t❡♥sõ❡s sã♦ ❢❡✐t❛s ❛♦ ♠♦❞❡❧♦ ♣❛❞rã♦ ❞❡ ❙♦❧♦✇✳ ❆ ♣r✐♠❡✐r❛ é ❝♦♥s✐❞❡r❛r ♦ ♣❛♣❡❧ ❞❛ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛✳ ❖ ♠♦❞❡❧♦ t❡♠ ✉♠ s❡t♦r ✜♥❛♥❝❡✐r♦ q✉❡ ❡♠♣r❡st❛ r❡❝✉rs♦s às ✜r♠❛s ♣❛r❛ q✉❡ ♣♦ss❛♠ ❝♦♠♣r❛r ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✳ ❊ss❡ s❡t♦r ✜♥❛♥❝❡✐r♦ t♦♠❛ ❡♠♣r❡st❛❞♦ r❡❝✉rs♦s ❞❡ ❡①t❡r✐♦r ❡ r❡❡♠♣r❡st❛ às ✜r♠❛s✳ ❆ ❝r✐s❡ ❡①t❡r♥❛ ❧❡✈❛ à ❡s❝❛ss❡③ ❞❡ t❛✐s r❡❝✉rs♦s ♣♦r ❝♦♥t❛ ❞❛ ♣❡r❞❛ ❞❡ ❧✐q✉✐❞❡③✳ ❆ s❡❣✉♥❞❛ ❡①t❡♥sã♦ é ❛ ✐♥❝❧✉sã♦ ❞❡ ✉♠ s❡t♦r ❞❡ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✳ ❆ss✐♠✱ ❛ ♣r♦❞✉çã♦ ❞❡ ❜❡♠ ✜♥❛❧ ♥❡❝❡ss✐t❛ ❞❡ ❝❛♣✐t❛❧ ❡ ❞❡ ❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦✳ ❙❡ ❤♦✉✈❡r ✐♥❡✜❝✐ê♥❝✐❛ ❛❧♦❝❛t✐✈❛ ♥❛ ❝♦♥tr❛t❛çã♦ ❞❡ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✱ ❤❛✈❡rá ✉♠❛ q✉❡❞❛ ♥❛ P❚❋ ❡ ❛ ❡❝♦♥♦♠✐❛ t❡♥❞❡ ❛ ✉♠ st❡❛❞②✲st❛t❡ ♠❛✐s ♣♦❜r❡✳
❈♦♥s✐❞❡r❡ Qt ❛ ♣r♦❞✉çã♦ ❜r✉t❛✱ ❝♦♠ ❛ s❡❣✉✐♥t❡ ❢♦r♠❛ ❢✉♥❝✐♦♥❛❧
Qt= ¯AKtαX γ
t ✭✷✳✶✮
♥♦ q✉❛❧0 < α+γ < 1✱ K é ♦ ❝❛♣✐t❛❧ ❡ X ♦ ❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦✳ ❆ ♣r♦❞✉çã♦ ❜r✉t❛ ♣♦❞❡
s❡r ❝♦♥s✉♠✐❞❛ ♦✉ ✐♥✈❡st✐❞❛✱ ♦✉ ❝❛rr❡❣❛❞❛ ❛té ♦ ♣ró①✐♠♦ ♣❡rí♦❞♦ ❡ ✉t✐❧✐③❛❞❛ ❝♦♠♦ ❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦✳ ❯♠❛ ❢r❛çã♦ ❝♦♥st❛♥t❡ x ❞❛ ♣r♦❞✉çã♦ ❜r✉t❛ é ❛❧♦❝❛❞❛ ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡
❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s ❞❡ ♠♦❞♦ q✉❡
Xt+1 =xQt ✭✷✳✷✮
❖ P■❇ ✭Pr♦❞✉t♦ ■♥t❡r♥♦ ❇r✉t♦✮ ❞❡ss❛ ❡❝♦♥♦♠✐❛ é ♦❜t✐❞♦ ♣❡❧♦ ♣r♦❞✉t♦ ❧íq✉✐❞♦ ❞❡ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✱Yt ≡(1−x)Qt ✳
◆♦ st❡❛❞②✲st❛t❡✱ t❡♠♦s q✉❡
Q∗
= ¯Axγ1−1γ K1−αγ ✭✷✳✸✮
Y∗
=P T F.K1−αγ ✭✷✳✹✮
♥♦ q✉❛❧P T F = (1−x)1−γ
xγA¯
❆ ❡q✉❛çã♦ ❞❡ ♠♦✈✐♠❡♥t♦ ❞♦ ❝❛♣✐t❛❧ é ❞❛❞❛ ♣♦r✿
Kt+1 =sYt+ (1−δ)Kt ✭✷✳✺✮
♥♦ q✉❛❧sé ❛ ♣r♦♣❡♥sã♦ ♠❛r❣✐♥❛❧ ❛ ♣♦✉♣❛r ❡δ❛ t❛①❛ ❞❡ ❞❡♣r❡❝✐❛çã♦ ❞♦ ❝❛♣✐t❛❧✳ ❆ ❡q✉❛çã♦
✭✷✳✺✮ ❝♦♥❞✉③ às ❡q✉❛çõ❡s ❞❡ st❡❛❞②✲st❛t❡ ❞❛❞❛s ♣♦r✿
K∗
=
P T F.s δ
1−1−γ−γα
✭✷✳✻✮
Y∗
=
P T F. s δ
1α −γ
11−γ −γ−α
=
(1−x¯)1−γ
¯
xγA¯1−γ1−α s
δ
1 α −γ−α
✭✷✳✼✮ ❆ss✐♠✱ P T F ❡ Y∗ ❞❡♣❡♥❞❡♠ ❞❛ ❛❧♦❝❛çã♦
x✳ ▼✉❞❛♥ç❛s ♥❛ ❛❧♦❝❛çã♦ ❞✐♠✐♥✉❡♠ ♦ ✈❛❧♦r
❞♦ ♣r♦❞✉t♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❡ sã♦ ♣♦t❡♥❝✐❛❧✐③❛❞❛s ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ 1
1−γ−α > 1✳ ❖✉ s❡❥❛✱ ♣❡q✉❡♥♦s ❞❡s✈✐♦s ❞❛ ❛❧♦❝❛çã♦ ❝❛✉s❛♠ ✉♠❛ ❣r❛♥❞❡ ♣❡r❞❛ ❞❡ ♣r♦❞✉t♦✳
✷✳✸✳✶ ❈❛s♦ s❡♠ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛
❊♠ ✉♠ ♠♦❞❡❧♦ s❡♠ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛✱ ❛ ❡s❝♦❧❤❛ ❞♦ s❡t♦r ❞❡ ❜❡♠ ✜♥❛❧ é ❞❛❞❛ ♣❡❧❛ s✉❛ ♠❛①✐♠✐③❛çã♦ ❞❡ ❧✉❝r♦✱ πF✳ ❖ ♣r♦❞✉t♦r ❞❡ ❜❡♠ ✜♥❛❧ t❡♠ ❝✉st♦ ✉♥✐tár✐♦ ♣❛r❛ ❛❞q✉✐r✐r ♦
❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦ X✱ ❞❡ ♠♦❞♦ q✉❡ s❡✉ ❧✉❝r♦ é ❞❛❞♦ ♣♦r✿
πF,t=Qt−Xt = ¯AKtαX γ
t −Xt ✭✷✳✽✮
❆ ❝♦♥❞✐çã♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡st❛❜❡❧❡❝❡ q✉❡
Xt= (γAK¯ tα)
1
1−γ ✭✷✳✾✮
❆♦ ❝♦♠❜✐♥❛r ❡ss❛ ❡q✉❛çã♦ ❞❡ ❞❡♠❛♥❞❛ ♣♦r ❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ ♣r♦❞✉✲ çã♦ ✭✷✳✶✮✱ ❡ ❝♦♠ ❛ ❝♦♥❞✐çã♦ ❞❡ st❡❛❞②✲st❛t❡ ✭✷✳✸✮✱ t❡r❡♠♦s ♦ ✈❛❧♦r ❞❡ ❡q✉✐❧í❜r✐♦ ❞❡ ❛❧♦❝❛çã♦ ót✐♠❛✿
x=γ ✭✷✳✶✵✮
✷✳✸✳✷ ❈❛s♦ ❝♦♠ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛
❆❣♦r❛ ❝♦♥s✐❞❡r❡♠♦s ❛ ❡s❝♦❧❤❛ ❞♦ s❡t♦r ❞❡ ❜❡♠ ✜♥❛❧ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❢r✐❝çã♦ ✜♥❛♥❝❡✐r❛✳ ❆s ✜r♠❛s ♣r❡❝✐s❛♠ t♦♠❛r ❡♠♣rést✐♠♦s ♣❛r❛ ❝♦♠♣r❛r ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s ❡ ♣❛❣❛♠ ♦s ❡♠♣rést✐♠♦s ❛♣ós r❡❛❧✐③❛r ❛ ♣r♦❞✉çã♦✳ ◆❡st❡ ❝❛s♦✱ ♦ ❝✉st♦ ❞♦s ❜❡♥s ✐♥t❡♠❡❞✐ár✐♦s ♣❛ss❛ ❛ ❞❡♣❡♥❞❡r ❞♦ ❝✉st♦ ❞♦ ❡♠♣rést✐♠♦✿
πF,t =Qt−(1 +r
′
t)Xt = ¯AKtαX γ
t −(1 +r
′
t)Xt ✭✷✳✶✶✮
❞❡ ♠♦❞♦ q✉❡ r′ é ❛ t❛①❛ ❞❡ ❥✉r♦s q✉❡ ❛ ✜r♠❛ ♣❛❣❛ ❛♦ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦✳ ❆ ♣❛rt✐r ❞❛ ♠❛①✐♠✐③❛çã♦ ❞❡ ❧✉❝r♦✱ ❛ ❞❡♠❛♥❞❛ ♣♦r ❜❡♠ ✐♥t❡r♠❡❞✐ár✐♦ é ❞❛❞❛ ♣♦r✿
Xt=
γAK¯ α t
1 +r′
t
1−1γ
✭✷✳✶✷✮ ❆ss✐♠✱ ❛ ❞❡♠❛♥❞❛ ♣♦r ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s ♣❛ss❛ ❛ ❞❡♣❡♥❞❡r ❞♦ ❝✉st♦ ❞♦ ❡♠♣rést✐♠♦ ❡ t❡r❡♠♦s ♦ ✈❛❧♦r ❞❡ ❡q✉✐❧í❜r✐♦ ❞❡ ❛❧♦❝❛çã♦ ót✐♠❛✿
x= γ
1 +r′∗ ✭✷✳✶✸✮
♥♦ q✉❛❧r′∗ é ❛ t❛①❛ ❞❡ ❥✉r♦s ❞❡ st❡❛❞②✲st❛t❡✳
❖s ❡♠♣rést✐♠♦s sã♦ t♦♠❛❞♦s ❥✉♥t♦ ❛ ✐♥t❡r♠❡❞✐ár✐♦s ✜♥❛♥❝❡✐r♦s✱ q✉❡ ❛♦ ❡st❛r❡♠ ✐♥t❡✲ ❣r❛❞♦s ♥♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦s ❡①t❡r♥♦✱ ❝♦❜r❛♠ ❥✉r♦s q✉❡ ❞❡♣❡♥❞❡♠ ❞❛ ❧✐q✉✐❞❡③ ✐♥t❡r♥❛❝✐✲ ♦♥❛❧✳ ❆ss✐♠✱ ❛ r❡❞✉çã♦ ❞❡ ❧✐q✉✐❞❡③ ✐♥t❡r♥❛❝✐♦♥❛❧ ✐♠♣❧✐❝❛ ❡♠ ✉♠❛ ♠✉❞❛♥ç❛ ♥❛s ❝♦♥❞✐çõ❡s ❞❡ ❝ré❞✐t♦ ♣❛r❛ ❛ ❝♦♠♣r❛ ❞❡ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✱ r❡♣r❡s❡♥t❛♥❞♦ ✉♠ ❛✉♠❡♥t♦ ♥♦ ❝✉st♦ ❞❡ ❝♦♠♣r❛r ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s✳ ❚❛❧ ❛✉♠❡♥t♦ ♥♦ ❝✉st♦ ♠✉❞❛ ❛ ❛❧♦❝❛çã♦ ❞❡ r❡❝✉rs♦s ❞✐♠✐✲ ♥✉✐♥❞♦ ❛ P❚❋✱ ❡ ❛ss✐♠✱ ❞✐♠✐♥✉✐♥❞♦ ♦ ♣r♦❞✉t♦ ❞❡ st❡❛❞②✲st❛t❡✳
❉❡ss❛ ❢♦r♠❛✱ ✜❝❛ ❜❡♠ ❝❧❛r♦ ♥❡st❡ ♠♦❞❡❧♦ ❡st✐❧✐③❛❞♦ q✉❡ ✉♠ ❝❤♦q✉❡ ❞❡ ❞✐♠✐♥✉✐çã♦ ❞❡ r❡❝✉rs♦s ❡①t❡r♥♦s✱ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ❝♦♠ ❢r✐❝çõ❡s ✜♥❛♥❝❡✐r❛s✱ ❞✐♠✐♥✉✐ ♦ ♣r♦❞✉t♦ ♣♦r ♠❡✐♦ ❞❡ ❞♦✐s ❝❛♥❛✐s✿ ✶✮ ❞✐♠✐♥✉✐ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ r❡❝✉rs♦s ♣❛r❛ ❛ ❝♦♥tr❛t❛çã♦ ❞❡ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s à ♣r♦❞✉çã♦✱ ❛❢❡t❛♥❞♦ ❞❡ ❢♦r♠❛ ❞✐r❡t❛ ♦ ♣r♦❞✉t♦❀ ✷✮ ❝❛✉s❛ ✉♠❛ ✐♥❡✜❝✐❡♥❝✐❛ ❛❧♦❝❛t✐✈❛ ❛♦ ♠✉❞❛r ❛ ♣r♦♣♦rçã♦ ❝♦♥tr❛t❛❞❛ ❞♦s ❢❛t♦r❡s ❞❡ ♣r♦❞✉çã♦✱ ❡ ❛ss✐♠ r❡❞✉③ ❛ P❚❋✳
✷✳✹ ▼♦❞❡❧♦
♣❡q✉❡♥❛✱ q✉❡ ✐♠♣♦rt❛ ✐♥s✉♠♦s ♣❛r❛ ❛ ♣r♦❞✉çã♦✱ ❡ q✉❡ ❡♠♣r❡st❛ r❡❝✉rs♦s ❡①t❡r♥♦s✱ ✐✳❡✳ r❡❝❡❜❡ ✉♠ ✢✉①♦ ❞❡ ❝❛♣✐t❛❧✱ q✉❡ ❛✉♠❡♥t❛ ❛ ❧✐q✉✐❞❡③ ❞♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦✳ ❖s t❡r♠♦s ❞❡ tr♦❝❛ q✉❡ ❛s ✜r♠❛s s❡ ❞❡♣❛r❛♠ ♣❛r❛ ✐♠♣♦rt❛r ♦s ✐♥s✉♠♦s ❡ ♦ ♠♦♥t❛♥t❡ ❞❡ r❡❝✉rs♦s r❡✲ ❝❡❜✐❞♦s s❡❣✉❡♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❡st♦❝ást✐❝♦✳ ❆ss✐♠ ❝❤♦q✉❡s ♥❡st❛s ✈❛r✐á✈❡✐s s❡rã♦ ❛s ❢♦♥t❡s ❞❡ ❝r✐s❡s ❞❡ ♥♦ss❛ ❡❝♦♥♦♠✐❛✳
❖ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦ r❡❝❡❜❡ r❡❝✉rs♦s ❞♦ ❡①t❡r✐♦r ❡ ❞❡♣ós✐t♦s ❞❛s ❢❛♠í❧✐❛s✱ q✉❡ r❡♣❛ss❛ às ✜r♠❛s✳ ❆♦ ♠❡s♠♦ t❡♠♣♦ ❛ ❛✉t♦r✐❞❛❞❡ ♠♦♥❡tár✐❛ ♣♦❞❡ ❢❛③❡r ✉♠❛ ✐♥❥❡çã♦ ❞❡ ♠♦❡❞❛ ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ♣♦r ♠❡✐♦ ❞❡ ❝♦♠♣r❛s ♦✉ ✈❡♥❞❛s ❞❡ tít✉❧♦s ♣ú❜❧✐❝♦s ❡♠ ♦♣❡r❛çõ❡s ❞❡ ♠❡r❝❛❞♦ ❛❜❡rt♦✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ❛ t❛①❛ ❞❡ ❥✉r♦s ❝♦❜r❛❞❛ às ✜r♠❛s s❡rá ❞✐❢❡r❡♥t❡ ❞❛ t❛①❛ ♣❛❣❛ às ❢❛♠í❧✐❛s✱ ✉♠❛ ✈❡③ q✉❡ ❛s ❢❛♠í❧✐❛s ♥ã♦ ♣♦❞❡♠ r❡✈❡r s❡✉ ♣♦rt❢ó❧✐♦ ❛♣ós ❛ ✐♥t❡r✈❡♥çã♦ ❞♦ ❇❛♥❝♦ ❈❡♥tr❛❧✳ ❆ss✐♠✱ ♦ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦ t❡♠ ❞✉❛s ❢✉♥çõ❡s✿ ✶✮ s❡r ♦ ❝❛♥❛❧ ❞❡ r❡❝✉rs♦s ✜♥❛♥❝❡✐r♦s ❞♦ ❡①t❡r✐♦r ❡ ❞❛s ❢❛♠í❧✐❛s ♣❛r❛ ❛s ✜r♠❛s❀ ✷✮ s❡r ♦ ❝❛♥❛❧ ❞❡ tr❛♥s♠✐ssã♦ ❞❛ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛✳
❆ ❡❝♦♥♦♠✐❛ é ❢♦r♠❛❞❛ ♣♦r três t✐♣♦s ❞❡ ❛❣❡♥t❡s✿ ❢❛♠í❧✐❛s✱ ✜r♠❛s ❡ ✐♥t❡r♠❡❞✐ár✐♦s ✜♥❛♥❝❡✐r♦s✳ ❚♦❞♦s sã♦ ♥✉♠❡r♦s♦s ❞❡ ❢♦r♠❛ ❛ ❛❣✐r❡♠ ❡♠ ❝♦♠♣❡t✐çã♦ ♣❡r❢❡✐t❛✱ ❧♦❣♦ ✐r❡♠♦s ♥♦s r❡str✐♥❣✐r ❛♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❛❣❡♥t❡ r❡♣r❡s❡♥t❛t✐✈♦ ❞❡ ❝❛❞❛ ✉♠ ❞❡❧❡s✱ ❡ ❛♣ós ✐ss♦ ❝♦♥s✐❞❡r❛r ❛s ✐♠♣❧✐❝❛çõ❡s ♣❛r❛ ❡q✉✐❧í❜r✐♦ ❣❡r❛❧✳
✷✳✹✳✶ ❋❛♠í❧✐❛s
❆s ❢❛♠í❧✐❛s ♣♦ss✉❡♠ ♦ ❝❛♣✐t❛❧✱ ❡ r❡❝❡❜❡♠ r❡♥❞❛ ❞♦ ❝❛♣✐t❛❧ ❡ ❞♦ tr❛❜❛❧❤♦✱ ❡ ❞❡ ❥✉r♦s s♦❜r❡ ❞❡♣ós✐t♦s ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ❞♦ ♣❡rí♦❞♦ ❛♥t❡r✐♦r✳ ❆ss✐♠✱ ♥♦ ✐♥í❝✐♦ ❞♦ ♣❡rí♦❞♦ ❛s ❢❛♠í❧✐❛s ❞❡❝✐❞❡♠ s❡ ✉s❛rã♦ s❡✉s r❡❝✉rs♦s ❡♠ ❝♦♥s✉♠♦✱ ✐♥✈❡st✐♠❡♥t♦ ❡♠ ❝❛♣✐t❛❧✱ ♦✉ ❡♠ ❞❡♣ós✐t♦s ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ♣❛r❛ r❡❝❡❜❡r ❥✉r♦s ♥♦ ♣❡rí♦❞♦ s❡❣✉✐♥t❡✳
❆s ❢❛♠í❧✐❛s ✈✐✈❡♠ ✐♥✜♥✐t❛♠❡♥t❡✱ ❡ ❝❛❞❛ ❢❛♠í❧✐❛ i ❜✉s❝❛ ♠❛①✐♠✐③❛r ❛ ❢✉♥çã♦ ✉t✐❧✐❞❛❞❡
❡s♣❡r❛❞❛ ❞❛❞❛ ♣♦r
Et
∞ X
t=0
Dtu(cit,1−hit) ✭✷✳✶✹✮
♦♥❞❡ ct é ♦ ❝♦♥s✉♠♦ ❞❛ ❢❛♠í❧✐❛ ❡♠ t✱ h é ♦ tr❛❜❛❧❤♦ ♦❢❡rt❛❞♦✱ ❡ D ∈ (0,1) é ❛ t❛①❛ ❞❡
❞❡s❝♦♥t♦ t❡♠♣♦r❛❧✳
❆s ❢❛♠í❧✐❛s ❡stã♦ s✉❥❡✐t❛s ❛ ✉♠❛ r❡str✐çã♦ ❝❛s❤✲✐♥✲❛❞✈❛♥❝❡✿
Ptcit ≤mit−1−N
i
❡ ❛ r❡str✐çã♦ ♦rç❛♠❡♥tár✐❛✿
kti+1+m
i t
Pt
=wthit+rtkti+ (1−δ)kit+
rn tNti
Pt ✭✷✳✶✻✮
♦♥❞❡ Pt é ♦ í♥❞✐❝❡ ❞❡ ♣r❡ç♦s ❡♠ t✱ ❡ mt é ❛ ♠♦❡❞❛ q✉❡ ❛s ❢❛♠í❧✐❛s ♣♦❞❡♠ ✉t✐❧✐③❛r ♣❛r❛
❝♦♥s✉♠♦ ♦✉ ♣❛r❛ ❞❡♣ós✐t♦(Nt) ♥❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s✱ s♦❜ ♦ q✉❛❧ r❡❝❡❜❡rã♦ ♦ ❥✉r♦s
rn✳
❆ss✐♠✱ ❛s ❢❛♠í❧✐❛s ✐♥✐❝✐❛♠ ♦ ♣❡rí♦❞♦ ❝♦♠ ♦ s❛❧ár✐♦ r❡❝❡❜✐❞♦ ✭w✮✱ ♦ r❡t♦r♥♦ ❞♦ ❝❛♣✐t❛❧
✭r✮✱ ♦ ❡st♦q✉❡ ❞❡ ❝❛♣✐t❛❧ q✉❡ ♥ã♦ ❞❡♣r❡❝✐♦✉✱ ❡ ♦ s❛❧❞♦ r❡s✉❧t❛♥t❡ ❞♦s ❞❡♣ós✐t♦s ❜❛♥❝ár✐♦s✱
❡ ❞❡✈❡ ❞❡❝✐❞✐r ❡♥tr❡ ✐♥✈❡st✐r ❡ ♠❛♥t❡r ♠♦❡❞❛✱ q✉❡ s❡rá ✉t✐❧✐③❛❞❛ ♣❛r❛ ♥♦✈♦s ❞❡♣ós✐t♦s ♦✉ ♣❛r❛ ❝♦♥s✉♠✐r ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦✳
❯t✐❧✐③❛♥❞♦ ✉♠❛ ❢✉♥çã♦ ✉t✐❧✐❞❛❞❡ ❧♦❣❛rít♠✐❝❛ ❝♦♠ tr❛❜❛❧❤♦ ✐♥❞✐✈✐sí✈❡❧✱ ❛ s✉❜✲❢✉♥çã♦ ✉t✐❧✐❞❛❞❡ é ❞❛❞❛ ♣♦r✿ u(ci
t,1−hit) =lncit+
h
b0ln(1
−h0)
h0
i
hi
t✱ ❡ ♣♦r s✐♠♣❧✐✜❝❛çã♦ ✈❛♠♦s ❞❡✜♥✐r
q✉❡Z =hb0ln(1
−h0)
h0
i ✳
✷✳✹✳✷ ❋✐r♠❛s
❆ ✜r♠❛ r❡♣r❡s❡♥t❛t✐✈❛ ❝♦♥tr❛t❛ tr❛❜❛❧❤❛❞♦r❡s ✭H✮✱ ✐♠♣♦rt❛ ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s ✭Xf✮ ❡
❛❧✉❣❛ ❝❛♣✐t❛❧ ✭K✮ s♦❜ ❝♦♠♣❡t✐çã♦ ♣❡r❢❡✐t❛✱ ♠❛①✐♠✐③❛♥❞♦ ♦ ❧✉❝r♦✱ ❡ ❞❡♣❛r❛✲s❡ ❝♦♠ ✉♠❛
❢✉♥çã♦ ❞❡ ♣r♦❞✉çã♦ ❞❛❞❛ ♣♦r
Yt=λtKtθXf tαH1
−θ−α
t ✭✷✳✶✼✮
❊ ♠❛①✐♠✐③❛ ❧✉❝r♦s s✉❥❡✐t♦ à r❡str✐çã♦ ♦rç❛♠❡♥tár✐❛✿
Yt =rtfwtHt+rtKt+pf tXf t ✭✷✳✶✽✮
❆ss✐♠✱ ❛ ✜r♠❛ t❡♠ ❞❡ ♣❛❣❛r s❛❧ár✐♦s✱ ♠❛s t❛♠❜é♠ t❡♠ ❞❡ ♣❛❣❛r ♦s ❥✉r♦s rf ♣❡❧♦
❝❛♣✐t❛❧ ❞❡ ❣✐r♦ q✉❡ t✐✈❡r❛♠ ❞❡ t♦♠❛r ❡♠♣r❡st❛❞♦ ♣❛r❛ ♣❛❣❛r❡♠ ♦s s❛❧ár✐♦s✳ ❊st❛ ♠✉❞❛♥ç❛ s✐❣♥✐✜❝❛ q✉❡ ❝❤♦q✉❡s ♥❛ t❛①❛ ❞❡ ❥✉r♦s ❛❧t❡r❛♠ ❛s ❞❡❝✐sõ❡s ❞❡ ♣r♦❞✉çã♦ ❡ tê♠ ✉♠ ❡❢❡✐t♦ ❞✐r❡t♦ ♥♦ ♣r♦❞✉t♦✳ ❆❧é♠ ❞✐ss♦✱ ❛♦ ✐♠♣♦rt❛r❡♠ ❜❡♥s✱ ❛s ✜r♠❛s ♣❛❣❛♠ ✉♠ ♣r❡ç♦ pf q✉❡ é
♦ ✐♥✈❡rs♦ ❞♦s t❡r♠♦s ❞❡ tr♦❝❛✳
◆♦t❡ q✉❡ ❛ ❝♦♥❞✐çã♦ ❞❡ ♠❛①✐♠✐③❛çã♦ ❞♦ ❧✉❝r♦ ❢❛③ ❝♦♠ q✉❡ ❛s ✜r♠❛s t❡♥❤❛ ✉♠❛ ❞❡✲ ♠❛♥❞❛ ♣♦r ❜❡♥s ✐♥t❡r♠❡❞✐ár✐♦s ✐♠♣♦rt❛❞♦s ❞❛❞❛ ♣♦r
Xf =α
❙✉❜st✐t✉✐♥❞♦ ❡st❛ ❡q✉❛çã♦ ♥❛ ❢✉♥çã♦ ❞❡ ♣r♦❞✉çã♦✱ ♣❛ss❛♠♦s ❛ t❡r q✉❡ ♦s t❡r♠♦s ❞❡ tr♦❝❛ ❛❢❡t❛♠ ❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ❞❛ ❡❝♦♥♦♠✐❛✿
Yt=
α pf t
(1−αα)
λ(
1 1−α)
t K
( θ
1−α)
t H
(1−θ−α
1−α )
t
♥♦ q✉❛❧ β = 1−θ−α✳
❉❡ss❛ ❢♦r♠❛✱ ✉♠ ❛✉♠❡♥t♦ ♥♦s t❡r♠♦s ❞❡ tr♦❝❛ ✭q✉❡❞❛ ❡♠pf✮ ✐♠♣❧✐❝❛ ❡♠ ✉♠ ❛✉♠❡♥t♦
❞❛ ♣r♦❞✉t✐✈✐❞❛❞❡ t♦t❛❧ ❞♦s ❢❛t♦r❡s ❞❛ ❡❝♦♥♦♠✐❛✳
✷✳✹✳✸ ■♥t❡r♠❡❞✐ár✐♦ ❋✐♥❛♥❝❡✐r♦
❖ ✐♥t❡r♠❡❞✐ár✐♦ ✜♥❛♥❝❡✐r♦ ♦♣❡r❛ ❡♠ ✉♠ ♠❡r❝❛❞♦ ❝♦♠♣❡t✐t✐✈♦✱ ❝♦♠ ❝ré❞✐t♦ s❡♠ r✐s❝♦ t♦♠❛♥❞♦ ♦s ❡♠♣rést✐♠♦s ❞❛s ❢❛♠í❧✐❛s✱Nt✱ ❞♦ ❡①t❡r✐♦r✱Bt✱ ❡ ❛s ✐♥❥❡çõ❡s ❞❡ ♠♦❡❞❛ r❡❝❡❜✐❞❛s
♣❡❧❛ ❛✉t♦r✐❞❛❞❡ ♠♦♥❡tár✐❛✱ (gt−1)Mt−1✱ ❡ r❡✲❡♠♣r❡st❛♥❞♦ às ✜r♠❛s✳
◆❛ ❧✐t❡r❛t✉r❛✱ ❛ r❡str✐çã♦ ❞❡ t♦♠❛❞❛ ❞❡ ❝ré❞✐t♦ ❡①t❡r♥♦ ♣♦❞❡ ♦❝♦rr❡r ♣♦r ❝❛✉s❛ ❞❡ r❡str✐çõ❡s ❞❡ ❝♦❧❛t❡r❛❧✱ ♦ q✉❡ ✐♠♣❧✐❝❛r✐❛ q✉❡ ❛ r❡str✐çã♦ s❡r✐❛ ❡♥❞ó❣❡♥❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❝♦♥❞✐çõ❡s ♠❛❝r♦❡❝♦♥ô♠✐❝❛s ✐♥t❡r♥❛s✱ ❝♦♠♦ ❡♠ ❆r❡❧❧❛♥♦ ❡ ▼❡♥❞♦③❛ ✭✷✵✵✸✮✱ ♦✉ ♣♦r ❝❛✉s❛ ❞❡ ♣❛râ♠❡tr♦s ❡①t❡r♥♦s✱ ❝♦♠♦ ✈❛r✐❛çõ❡s ♥❛s ♣r❡❢❡rê♥❝✐❛s✱ t❡❝♥♦❧♦❣✐❛✱ ♣r♦❞✉t♦ ♦✉ ❢r✐❝çõ❡s ✜♥❛♥❝❡✐r❛s ❞♦s ♣❛ís❡s ❞❡s❡♥✈♦❧✈✐❞♦s✱ ❝♦♠♦ ♥♦ ♠♦❞❡❧♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❣❧♦❜❛❧ ❞❡ ❈❛❜❛❧❧❡r♦ ❡ P❛♥❛❣❡❛s ✭✷✵✵✼✮✱ s❡♥❞♦ ❞❡t❡r♠✐♥❛❞♦ ❡①♦❣❡♥❛♠❡♥t❡✳
◆ós ❛ss✉♠✐♠♦s q✉❡ ♦ ✢✉①♦ ❞❡ ❝❛♣✐t❛✐s é ❧✐♠✐t❛❞♦ ♣♦r ❝♦♥❞✐çõ❡s ❡①t❡r♥❛s ✉♠❛ ✈❡③ q✉❡ ❞❡s❡❥❛♠♦s ✐♥t❡r♣r❡t❛r ❛ ❝r✐s❡ ❞❡ ✷✵✵✽✱ ♣♦r ❡①❡♠♣❧♦✱ q✉❡ ❝❧❛r❛♠❡♥t❡ ❢♦✐ ❝❛✉s❛❞❛ ♣♦r ✉♠ ❝❤♦q✉❡ ❡①t❡r♥♦ ❞❡ ❧✐q✉✐❞❡③✳ ❈♦♠♦ ❝♦♥s❡qüê♥❝✐❛✱ ❤á ✉♠❛ ❢r✐❝çã♦ ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ q✉❡ ♣❡r♠✐t❡ q✉❡ ♦s ❜❛♥❝♦s t♦♠❡♠ ❡♠♣r❡st❛❞♦ ❞♦ s❡t♦r ❡①t❡r♥♦ ❡ ❞❛s ❢❛♠í❧✐❛s ♣❛❣❛♥❞♦ t❛①❛s ❞❡ ❥✉r♦s ❞✐❢❡r❡♥t❡s✱ ♣♦✐s ❛ r❡str✐çã♦ s♦❜r❡ ♦ ❝ré❞✐t♦ ❡①t❡r♥♦ ❧✐♠✐t❛ t❛❧ ❢♦♥t❡✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦s ❜❛♥❝♦s t❡♥❤❛♠ ❞❡ ❜✉s❝❛r ♦ ❝ré❞✐t♦ ❞❛s ❢❛♠í❧✐❛s ❛ ♣❛rt✐r ❞❡ ❝❡rt♦ ♣♦♥t♦ ❛♣❡s❛r ❞❡ t❡r❡♠ ❞❡ ♣❛❣❛r ✉♠ ❥✉r♦ ♠❛✐♦r✳
❆ss✐♠✱ ❛ss✉♠✐♥❞♦ q✉❡ ♦s ❜❛♥❝♦s ❛❣❡♠ s♦❜ ❝♦♠♣❡t✐çã♦ ♣❡r❢❡✐t❛✱ ❡❧❡s s❡ ❞❡♣❛r❛♠ ❝♦♠ ❛ s❡❣✉✐♥t❡ r❡str✐çã♦ ♦rç❛♠❡♥tár✐❛ ✭❝♦♥❞✐çã♦ ❞❡ ❧✉❝r♦ ③❡r♦✮✱
rtf(Nt+Bt+ (gt−1)Mt−1) =
ˆ 1
0
rtnNtidi+r∗
Bt=rntNt+r
∗
Bt ✭✷✳✶✾✮
♦✉ s❡❥❛✱ ✉♠ ❛✉♠❡♥t♦ ❞❛ ♦❢❡rt❛ ❞❡ ♠♦❡❞❛ ✐♠♣❧✐❝❛ ❡♠ ✉♠ ❡❢❡✐t♦ ❞❡ ❧✐q✉✐❞❡③✱ ❞✐♠✐♥✉✐♥❞♦ ♦s ❥✉r♦s ♣❛❣♦s ♣❡❧♦ ❝❛♣✐t❛❧ ❞❡ ❣✐r♦ ♣❛r❛ ❛s ✜r♠❛s✳
❡♠♣rést✐♠♦s ❞❛s ❢❛♠í❧✐❛s✱ ❞♦ s❡t♦r ❡①t❡r♥♦ ❡ ❞❛ ❛✉t♦r✐❞❛❞❡ ♠♦♥❡tár✐❛ s❡ tr❛❞✉③ ❡♠ ♣❛❣❛✲ ♠❡♥t♦ ❞❡ s❛❧ár✐♦s ♣❛r❛ ❛s ✜r♠❛s✱
(Nt+Bt+ (gt−1)Mt−1) =PtwtHt ✭✷✳✷✵✮ ♦✉ s❡❥❛✱ é ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ♣❛r❛ ♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦✳
❉❡ss❛ ❢♦r♠❛ ✉♠❛ q✉❡❞❛ ❡♠ Bt✱ ♦✉ s❡❥❛✱ ✉♠ s✉❞❞❡♥✲st♦♣✱ t❡r✐❛ ✉♠ ✐♠♣❛❝t♦ ♥♦ ❧❛❞♦
r❡❛❧ ❞❛ ❡❝♦♥♦♠✐❛ ♣♦r r❡❞✉③✐r ♦s r❡❝✉rs♦s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❛ ❝♦♥tr❛t❛çã♦ ❞❡ tr❛❜❛❧❤❛❞♦r❡s✳ ◆♦ ♠♦❞❡❧♦✱ ✐r❡♠♦s ❛ss✉♠✐r q✉❡ ❛ t❛①❛ ❞❡ ❥✉r♦s ♣❛❣❛ ♣❡❧♦s ❡♠♣rést✐♠♦s ❡①t❡r♥♦s é ✉♠❛ ❝♦♥st❛♥t❡r∗
✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ✢✉①♦ ❞❡ ❝❛♣✐t❛✐s é ✉♠❛ ✈❛r✐á✈❡❧ s✉❥❡✐t❛ ❛ ❝❤♦q✉❡s ❡st♦❝ást✐❝♦s✳
✷✳✹✳✹ P♦❧ít✐❝❛ ▼♦♥❡tár✐❛
❖ ❇❛♥❝♦ ❈❡♥tr❛❧ ✭❇❈✮ ❡s❝♦❧❤❡ ❛ t❛①❛ ❞❡ ❡①♣❛♥sã♦ ♠♦♥❡tár✐❛ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❛r ♦ ✈❛❧♦r ❞❛ t❛①❛ ❞❡ ❥✉r♦s ❞❡ ❡♠♣rést✐♠♦s às ✜r♠❛s✳ P❛r❛ t❛♥t♦✱ ❛♦ ✉t✐❧✐③❛r ❛s ❝♦♥❞✐çõ❡s ✭✷✳✶✾✮ ❡ ✭✷✳✷✵✮ ♦ ❇❈ ♦❜té♠ ❛ t❛①❛ ❞❡ ❥✉r♦s rtf ❛♦ ❞❡t❡r♠✐♥❛r ❛ t❛①❛ ❜r✉t❛ ❞❡ ❡①♣❛♥sã♦
♠♦♥❡tár✐❛ ✭gt✮ ❞♦ ♣❡rí♦❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❝♦♥❞✐çã♦ ❞❛❞❛ ♣♦r
gt=
rn t −r
f t
rft
!
Nt
Mt−1
+ r
∗
t −r f t
rtf
!
Bt
Mt−1
+ 1 ✭✷✳✷✶✮
P♦r s✉❛ ✈❡③✱ ♦ ❇❈ ❞❡t❡r♠✐♥❛ ❛ t❛①❛ ❞❡ ❥✉r♦s ❞❡ ❡♠♣rést✐♠♦s às ✜r♠❛s rft ❞❡s❡❥❛❞❛ ❛
♣❛rt✐r ❞❛ r❡❣r❛ ❞❡ ❚❛②❧♦r ❛ s❡❣✉✐r✱ q✉❡ r❡❛❣❡ ❛ ❞❡s✈✐♦s ❞❛ ❡❝♦♥♦♠✐❛ ❛♦ st❡❛❞②✲st❛t❡✳
rft =a Yt−Y¯
+b(πt−π¯) + ¯rf +tt ✭✷✳✷✷✮
♥♦ q✉❛❧ ❛s ✈❛r✐á✈❡✐s ❝♦♠ tr❛ç♦ sã♦ ♦s ✈❛❧♦r❡s ❞❡ st❡❛❞②✲st❛t❡✱a✱b ♦s ♣❛râ♠❡tr♦s ❞❡ r❡❛çã♦
❞❛ r❡❣r❛ ❞❡ ❚❛②❧♦r✱πt é ❛ ✐♥✢❛çã♦ ❞❛ ❡❝♦♥♦♠✐❛ ❡ tt é ♦ ❝❤♦q✉❡ ❞❡ ♣♦❧ít✐❝❛ ♠♦♥❡tár✐❛✳
❉✐❢❡r❡♥t❡♠❡♥t❡ ❞♦ ✉s✉❛❧✱ ❛ t❛①❛ ❞❡ ❥✉r♦s ❛ s❡r ❞❡t❡r♠✐♥❛❞❛ ♣❡❧❛ r❡❣r❛ ❞❡ ❚❛②❧♦r é ✉♠❛ t❛①❛ ❞❡ ❥✉r♦s r❡❛❧ ❡ ♥ã♦ ♥♦♠✐♥❛❧ ♣♦rq✉❡ ♦s ❡♠♣rést✐♠♦s sã♦ t♦♠❛❞♦s ♥♦ ✐♥í❝✐♦ ❞♦ ♣❡rí♦❞♦ ❡ ♣❛❣♦s ♥♦ ✜♠ ❞♦ ♣❡rí♦❞♦✳ ❊ss❛ ❞✐❢❡r❡♥ç❛ ❢❛③ ❝♦♠ q✉❡ ♦ ♣❛râ♠❡tr♦ b = ˆb−1✱ ♥♦ q✉❛❧ ˆb
✷✳✹✳✺ ❊q✉✐❧í❜r✐♦
❖ ♠♦❞❡❧♦ ❝♦♥s✐st❡ ♥❛ ❞✐♥â♠✐❝❛ ❞❛s ✈❛r✐á✈❡✐swt✱ rt✱Ct✱ Pt✱ Mt✱Nt✱Kt✱Yt✱Ht✱rtn✱ r f t ❡gt✱
❛❧é♠ ❞♦s ❝❤♦q✉❡s ♥♦ ✢✉①♦ ❞❡ ❝❛♣✐t❛✐s ❡ ♥♦s t❡r♠♦s ❞❡ tr♦❝❛✳
❆s ❝♦♥❞✐çõ❡s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❞❛s ❢❛♠í❧✐❛s✱ ❛♣ós ❝♦♥s✐❞❡r❛r ❛s ❝♦♥❞✐çõ❡s ❞❡ ❛❣r❡❣❛✲ çã♦✱ ❧❡✈❛♠ às ❡q✉❛çõ❡s✿
Z wt
=−DEt
Pt
Pt+1Ct+1 ✭✷✳✷✸✮
1
wt
=DEt
rt+1+ 1−δ
wt+1 ✭✷✳✷✹✮
rnt =− wt ZCt
= 1
EtPDPt+1tCCt+1t
✭✷✳✷✺✮ ❊ ❛s r❡str✐çõ❡s ❛❣r❡❣❛❞❛s ♣❛r❛ ❛s ❢❛♠í❧✐❛s✱ sã♦✱
PtCt=Mt−1−Nt ✭✷✳✷✻✮
Mt
Pt
+Kt+1 =wtHt+rtKt+ (1−δ)Kt+
rn tNt
Pt ✭✷✳✷✼✮
P❛r❛ ❛s ✜r♠❛s ♦ ♣r♦❞✉t♦ ♠❛r❣✐♥❛❧ ❞♦ tr❛❜❛❧❤♦ ❞❡✈❡ ✐❣✉❛❧❛r✲s❡ ❛♦ s❛❧ár✐♦ r❡❛❧ ❡ ❛♦s ❝✉st♦s ❞❡ ✜♥❛♥❝✐❛♠❡♥t♦
rtfwt = (1−θ)λtKtθH
−θ
t ✭✷✳✷✽✮
❡ ♦ ♣r♦❞✉t♦ ♠❛r❣✐♥❛❧ ❞♦ ❝❛♣✐t❛❧ ✐❣✉❛❧❛✲s❡ à t❛①❛ ❞❡ ❥✉r♦s
rt=θλtKθ
−1
t H1
−θ
t ✭✷✳✷✾✮
❆ ❢✉♥çã♦ ❞❡ ♣r♦❞✉çã♦ é ❞❛❞❛ ♣♦r ✭✷✳✶✼✮✱ ❡ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ♣❛r❛ ♦ ✐♥t❡r♠❡✲ ❞✐ár✐♦ ✜♥❛♥❝❡✐r♦ sã♦ ✭✷✳✶✾✮ ❡ ✭✷✳✷✵✮✳ P♦r ✜♠✱ ❛ss✉♠❡✲s❡ q✉❡ ♦ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❡st♦q✉❡ ❞❡ ♠♦❡❞❛ é ❞❛❞♦ ♣♦r✱
Mt =gtMt−1 ✭✷✳✸✵✮
♥♦s t❡r♠♦s ❞❡ tr♦❝❛✱ ❡ ♥♦ ✢✉①♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❝❛♣✐t❛✐s ✭▲✐q✉✐❞❡③ ❊①t❡r♥❛✮✳ ❆ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞♦ ♠♦❞❡❧♦ ❧♦❣✲❧✐♥❡❛r✐③❛❞♦ ❡♥❝♦♥tr❛✲s❡ ♥♦ ❛♣ê♥❞✐❝❡ ❇✳
✷✳✺ ❊st✐♠❛çã♦
❚♦❞❛s ❛s sér✐❡s ✉t✐❧✐③❛❞❛s ❢♦r❛♠ ❞❡ss❛③♦♥❛❧✐③❛❞❛s ❡ ✜❧tr❛❞❛s ♣❡❧❛ té❝♥✐❝❛ ❞❡ ❍♦❞r✐❝❦✲ Pr❡s❝♦tt ✭❝♦♠ ♦ ♣❛râ♠❡tr♦ ❞❡ s✉❛✈✐③❛çã♦ ♣❛r❛ ❞❛❞♦s tr✐♠❡str❛✐s ♥♦ ✈❛❧♦r ❞❡ ✶✻✵✵✮✳ ❖ ❣❛♣ ❞♦ ♣r♦❞✉t♦ ❢♦✐ ♦❜t✐❞♦ ❛ ♣❛rt✐r ❞❛ sér✐❡ ❞❡ P■❇ ✭Pr♦❞✉t♦ ■♥t❡r♥♦ ❇r✉t♦✮ ♦r✐✉♥❞❛ ❞♦ ❇❛♥❝♦ ❈❡♥tr❛❧ ❞♦ ❇r❛s✐❧ ✭❇❈❇✮✳ ❆ t❛①❛ ❞❡ ❥✉r♦s ❞❡ ❡♠♣rést✐♠♦ às ✜r♠❛s ❢♦✐ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ t❛①❛ ❞❡ ❥✉r♦s ❞❡ ❝❛♣✐t❛❧ ❞❡ ❣✐r♦✱ ❢♦r♥❡❝✐❞♦ ♣❡❧♦ ❇❈❇✳ ❖ ✐♥❞✐❝❛❞♦r ❞❡ ❧✐q✉✐❞❡③ ❡①t❡r♥❛ ❛❞✈é♠ ❞♦ ♠♦♥t❛♥t❡ ❧íq✉✐❞♦ ❞❛ ❝♦♥t❛ ✜♥❛♥❝❡✐r❛ ❛♦ s✉❜tr❛✐r ♦ ✐♥✈❡st✐♠❡♥t♦ ❞✐r❡t♦ ❡str❛♥❣❡✐r♦ ❧íq✉✐❞♦✱ ❢♦r♥❡❝✐❞♦ ♣❡❧♦ ❇❈❇✳ ❆ ♣❛rt✐r ❞❡ t❛❧ ♠♦♥t❛♥t❡✱ ✉♠ í♥❞✐❝❡ ❞❡ ❧✐q✉✐❞❡③ ❡①t❡r♥❛ ❢♦✐ ❝♦♥str✉í❞♦✳ ❆ sér✐❡ ❞❡ t❡r♠♦s ❞❡ tr♦❝❛ ❢♦✐ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ ❋✉♥❞❛çã♦ ❈❡♥tr♦ ❞❡ ❊st✉❞♦s ❞❡ ❈♦♠ér❝✐♦ ❊①t❡r✐♦r ✭❋❯◆❈❊❳✮✳
✷✳✺✳✶ P❛râ♠❡tr♦s ❈❛❧✐❜r❛❞♦s ❡ ❉✐str✐❜✉✐çã♦ ❞♦s Pr✐♦rs
✷✳✺✳✶✳✶ P❛râ♠❡tr♦s ❈❛❧✐❜r❛❞♦s
❆ ❝❛❧✐❜r❛çã♦ ❞♦ ♠♦❞❡❧♦ ❡st✐♣✉❧❛ q✉❡ ♦s ✈❛❧♦r❡s ❞❡δ✱Z ❡Ds❡❣✉❡♠ ♦s tr❛❜❛❧❤♦s ❛♣❧✐❝❛❞♦s ❛♦
❇r❛s✐❧ ❞❡ ❇♦♥❡❧❧✐ ❡ ❋♦♥s❡❝❛ ✭✶✾✾✽✮✱ ❆r❛ú❥♦ ❡ ❋❡rr❡✐r❛ ✭✶✾✾✾✮✱ ❑❛♥❝③✉❦ ✭✷✵✵✶✱ ✷✵✵✷✮✱ ❊❧❧❡r② ❡t ❛❧ ✭✷✵✵✷✮✱ ❆♥❞r❛❞❡ ❡ ❚❡❧❡s ✭✷✵✵✺✮ ❡ ❙♦❜r✐♥❤♦ ✭✷✵✶✶✮✳ ❖ ♣❛râ♠❡tr♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❜r✉t♦ ❞❛ ♠♦❡❞❛ tr❛♥s❢❡r✐❞❛ ♣❛r❛ ♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ♥♦ st❡❛❞②✲st❛t❡g¯❢♦✐ ❡st❛❜❡❧❡❝✐❞♦ ❝♦♠♦ ❛
t❛①❛ ❞❡ ✐♥✢❛çã♦ ❞❡ ✻✱✺✪ tr✐♠❡str❛❧✐③❛❞❛ ❡♥tr❡ ✷✵✵✵ ❡ ✷✵✶✷✳ ❆ t❛①❛ ❞❡ ❥✉r♦s ✐♥t❡r♥❛❝✐♦♥❛❧ r∗
❢♦✐ ❝❛❧✐❜r❛❞❛ ❝♦♠ ❜❛s❡ ♥❛ t❛①❛ ❞❡ ❥✉r♦s ♠é❞✐❛ ❞♦s ❊❯❆ ♥♦ ♣❡rí♦❞♦✳ ❖ ✢✉①♦ ❞❡ r❡❝✉rs♦s ❡①t❡r♥♦s B¯
P
❡♠ t❡r♠♦s r❡❛✐s ❢♦✐ ❡st❛❜❡❧❡❝✐❞♦ ❞❡ ♠♦❞♦ q✉❡ s❡ ❛♣r♦①✐♠❛ss❡ ❞❡ ✷✱✺✪ ❞♦ ♣r♦❞✉t♦ ❞❡ st❡❛❞②✲st❛t❡ ❞❛ ❡❝♦♥♦♠✐❛✱ ✉♠❛ ♠é❞✐❛ ♦❜s❡r✈❛❞❛ ♣❛r❛ ♦ ❇r❛s✐❧ ❞❡ ❛❝♦r❞♦ ❛s sér✐❡s ✉t✐❧✐③❛❞❛s✳ ❆ t❛❜❡❧❛ ✷✳✶ ❛♣r❡s❡♥t❛ ♦s ✈❛❧♦r❡s ❝❛❧✐❜r❛❞♦s ♣❛r❛ ♦s ♣❛râ♠❡tr♦s✳
✷✳✺✳✶✳✷ Pr✐♦rs
