❈♦r♦♥❛✈✐r✉s✿ ■♠♣❛❝t ♦♥ ❙t♦❝❦ Pr✐❝❡s ❛♥❞ ●r♦✇t❤ ❊①♣❡❝t❛t✐♦♥s ◆✐❡❧s ❏✳ ●♦r♠s❡♥ ❛♥❞ ❘❛❧♣❤ ❙✳❏✳ ❑♦✐❥❡♥ ∗ ❆✉❣✉st ✸✱ ✷✵✷✵ ❆❜str❛❝t ❲❡ ✉s❡ ❞❛t❛ ❢r♦♠ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ❛♥❞ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ♠❛r❦❡ts t♦ q✉❛♥t✐❢② ❤♦✇ ✐♥✲ ✈❡st♦rs✬ ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ❡✈♦❧✈❡ ❛❝r♦ss ❤♦r✐③♦♥s ✐♥ r❡s♣♦♥s❡ t♦ t❤❡ ♥❡✇ ❝♦r♦♥❛✈✐r✉s ✭❈❖❱■❉✲✶✾✮ ♦✉t❜r❡❛❦ ❛♥❞ s✉❜s❡q✉❡♥t ♣♦❧✐❝② r❡s♣♦♥s❡s ✉♥t✐❧ ❏✉❧② ✷✵✷✵✳ ❉✐✈✐❞❡♥❞ ❢✉t✉r❡s✱ ✇❤✐❝❤ ❛r❡ ❝❧❛✐♠s t♦ ❞✐✈✐❞❡♥❞s ♦♥ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ✐♥ ❛ ♣❛rt✐❝✉❧❛r ②❡❛r✱ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❞✐r❡❝t❧② ❝♦♠♣✉t❡ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❛❝r♦ss ♠❛t✉r✐t✐❡s ♦r t♦ ❡st✐♠❛t❡ ❡①♣❡❝t❡❞ ❣r♦✇t❤ ✉s✐♥❣ ❛ ❢♦r❡❝❛st✐♥❣ ♠♦❞❡❧✳ ❲❡ s❤♦✇ ❤♦✇ t❤❡ ❛❝t✉❛❧ ❢♦r❡❝❛st ❛♥❞ t❤❡ ❜♦✉♥❞ ❡✈♦❧✈❡ ♦✈❡r t✐♠❡✳ ❆s ♦❢ ❏✉❧② ✷✵✱ ♦✉r ❢♦r❡❝❛st ♦❢ ❛♥♥✉❛❧ ❣r♦✇t❤ ✐♥ ❞✐✈✐❞❡♥❞s ♣♦✐♥ts t♦ ❛ ❞❡❝❧✐♥❡ ♦❢ ✽✪ ✐♥ ❜♦t❤ t❤❡ ❯❙ ❛♥❞ ❏❛♣❛♥ ❛♥❞ ❛ ✶✹✪ ❞❡❝❧✐♥❡ ✐♥ t❤❡ ❊❯ ❝♦♠♣❛r❡❞ t♦ ❏❛♥✉❛r② ✶✳ ❖✉r ❢♦r❡❝❛st ♦❢ ●❉P ❣r♦✇t❤ ♣♦✐♥ts t♦ ❛ ❞❡❝❧✐♥❡ ♦❢ ✷✪ ✐♥ t❤❡ ❯❙ ❛♥❞ ❏❛♣❛♥ ❛♥❞ ✸✪ ✐♥ t❤❡ ❊❯✳ ❚❤❡ ❧♦✇❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝❤❛♥❣❡ ✐♥ ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞s ✐s ✲✶✼✪ ✐♥ t❤❡ ❯❙ ❛♥❞ ❏❛♣❛♥ ❛♥❞ ✲✷✽✪ ✐♥ t❤❡ ❊❯ ❛t t❤❡ ✷✲②❡❛r ❤♦r✐③♦♥✳ ◆❡✇s ❛❜♦✉t ✜s❝❛❧ st✐♠✉❧✉s ❛r♦✉♥❞ ▼❛r❝❤ ✷✹ ❜♦♦sts t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ❧♦♥❣✲t❡r♠ ❣r♦✇t❤ ❜✉t ❞✐❞ ❧✐tt❧❡ t♦ ✐♥❝r❡❛s❡ s❤♦rt✲t❡r♠ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s✳ ❊①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❤❛s ✐♠♣r♦✈❡❞ s✐♥❝❡ ❆♣r✐❧ ✶ ✐♥ ❛❧❧ ❣❡♦❣r❛♣❤✐❡s✳ ♥✐❡❧s✳❣♦r♠s❡♥❅❝❤✐❝❛❣♦❜♦♦t❤✳❡❞✉✱ r❛❧♣❤✳❦♦✐❥❡♥❅❝❤✐❝❛❣♦❜♦♦t❤✳❡❞✉✳ ❯♥✐✈❡rs✐t② ♦❢ ❈❤✐❝❛❣♦✱ ❇♦♦t❤ ❙❝❤♦♦❧ ♦❢ ❇✉s✐♥❡ss✳ ❲❡ ❛r❡ ❣r❛t❡❢✉❧ t♦ ◆✐❝♦❧❛ ❇❡♥✐❣♥✐✱ ❳❛✈✐❡r ●❛❜❛✐①✱ ❊❧✐s❛ ▼❛✣♦❧✐✱ ❚②❧❡r ▼✉✐r✱ ▲❛ss❡ P❡❞❡rs❡♥✱ ◆✐❦♦❧❛✐ ❘♦✉ss❛♥♦✈✱ ❆♠✐r ❙✉✜✱ ❙t✐❥♥ ❱❛♥ ◆✐❡✉✇❡r❜✉r❣❤✱ ❛♥❞ ▼♦t♦❤✐r♦ ❨♦❣♦ ❛s ✇❡❧❧ ❛s s❡♠✐♥❛r ♣❛rt✐❝✐♣❛♥ts ❛t ❍❊❈ P❛r✐s✱ ◆❇■▼✱ ❯◆❙❲ ❙②❞♥❡②✱ ❛♥❞ t❤❡ ❱✐rt✉❛❧ ❋✐♥❛♥❝❡ ❲♦r❦s❤♦♣ ✭❱✐rt✉❛❧❋✐♥❛♥❝❡✳♦r❣✮ ❢♦r ❞✐s❝✉ss✐♦♥s ❛♥❞ s✉❣❣❡st✐♦♥s✳ ❲❡ t❤❛♥❦ ❉♦♥❣ ❘②❡♦❧ ▲❡❡ ❢♦r ❡①❝❡❧❧❡♥t r❡s❡❛r❝❤ ❛ss✐st❛♥❝❡✳ ●♦r♠s❡♥ ❛♥❞ ❑♦✐❥❡♥ ❛❝❦♥♦✇❧❡❞❣❡s ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ❢r♦♠ t❤❡ ❈❡♥t❡r ❢♦r ❘❡s❡❛r❝❤ ✐♥ ❙❡❝✉r✐t② Pr✐❝❡s ❛t t❤❡ ❯♥✐✈❡rs✐t② ♦❢ ❈❤✐❝❛❣♦ ❇♦♦t❤ ❙❝❤♦♦❧ ♦❢ ❇✉s✐♥❡ss✳ ∗ ✶ Electronic copy available at: https://ssrn.com/abstract=3555917 ✶ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ ♦✉t❜r❡❛❦ ♦❢ t❤❡ ♥❡✇ ❝♦r♦♥❛✈✐r✉s ❤❛s ❝❛✉s❡❞ ❛ ♣❛♥❞❡♠✐❝ ♦❢ r❡s♣✐r❛t♦r② ❞✐s❡❛s❡ ✭❈❖❱■❉✲ ✶✾✮ ❢♦r ✇❤✐❝❤ ✈❛❝❝✐♥❡s ❛r❡ ✉♥❛✈❛✐❧❛❜❧❡ ❛s ♦❢ ❏✉❧② ✷✵✷✵✳ ❚❤❡ ♦✉t❜r❡❛❦ ❤❛s ❝❛✉s❡❞ ♠❛❥♦r ❝♦♥❝❡r♥s ❛❜♦✉t ♣✉❜❧✐❝ ❤❡❛❧t❤ ❛r♦✉♥❞ t❤❡ ✇♦r❧❞✳ ❆t t❤❡ s❛♠❡ t✐♠❡✱ t❤❡r❡ ❛r❡ ❣r♦✇✐♥❣ ❝♦♥❝❡r♥s ❛❜♦✉t t❤❡ ❡❝♦♥♦♠✐❝ ❝♦♥s❡q✉❡♥❝❡s ❛s ♠❛♥② ❤♦✉s❡❤♦❧❞s ❛r❡ r❡q✉✐r❡❞ t♦ st❛② ❤♦♠❡✱ ♦r ❧✐♠✐t s♦❝✐❛❧ ✐♥t❡r❛❝t✐♦♥s✱ t♦ s❧♦✇ t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ✈✐r✉s✳ ❚❤❡ ✐♠♣❛❝t t❤❛t ✏♣❛✉s✐♥❣✑ t❤❡ ❡❝♦♥♦♠② ♠❛② ❤❛✈❡ ♦♥ t❤❡ ❣❧♦❜❛❧ ❡❝♦♥♦♠② ❛♥❞ t❤❡ ✜♥❛♥❝✐❛❧ st❛❜✐❧✐t② ♦❢ ✜r♠s✱ t❤❡ ✜♥❛♥❝✐❛❧ s❡❝t♦r✱ ❛♥❞ ❤♦✉s❡❤♦❧❞s ✐s ❧❛r❣❡❧② ✉♥❦♥♦✇♥✳ ❆s ❛ r❡s✉❧t✱ ♣♦❧✐❝②♠❛❦❡rs✱ ❜✉s✐♥❡ss❡s✱ ❛♥❞ ❤♦✉s❡❤♦❧❞s str✉❣❣❧❡ t♦ ❡st✐♠❛t❡ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❢♦r t❤❡ ②❡❛rs t♦ ❝♦♠❡ ❛♥❞ ❛ss❡ss t❤❡ s❤❛♣❡ ♦❢ t❤❡ r❡❝♦✈❡r②✳ ❆s t❤❡ ❝✉rr❡♥t s✐t✉❛t✐♦♥ ✐s ✉♥♣r❡❝❡❞❡♥t❡❞✱ ❛♥❞ ❡✈♦❧✈✐♥❣ r❛♣✐❞❧②✱ ♠♦❞❡❧s t❤❛t ✉s❡ ♠❛❝r♦✲ ❡❝♦♥♦♠✐❝ ❢✉♥❞❛♠❡♥t❛❧s ♠❛② ❜❡ s❧♦✇ t♦ ✉♣❞❛t❡ ❣✐✈❡♥ t❤❡ ❢r❡q✉❡♥❝② ✇✐t❤ ✇❤✐❝❤ ♠❛❝r♦✲ ❡❝♦♥♦♠✐❝ ❞❛t❛ ❜❡❝♦♠❡ ❛✈❛✐❧❛❜❧❡✳ ❆❧t❡r♥❛t✐✈❡❧②✱ ✇❡ ❝❛♥ tr② t♦ ❡①tr❛❝t ✐♥❢♦r♠❛t✐♦♥ ❢r♦♠ ❛ss❡t ♣r✐❝❡s s✉❝❤ ❛s st♦❝❦s✱ ❜♦♥❞s ✭❍❛r✈❡② ✭✶✾✽✾✮✮✱ ❛♥❞ ❝r❡❞✐ts ✭●✐❧❝❤r✐st ❛♥❞ ❩❛❦r❛❥s❡❦ ✭✷✵✶✷✮✮✱ ❛s t❤❡② ❛r❡ ❢♦r✇❛r❞ ❧♦♦❦✐♥❣✳ ■t ✐s t❤❡r❡❢♦r❡ ✉♥s✉r♣r✐s✐♥❣ t❤❛t✱ ✐♥ ♣❛rt✐❝✉❧❛r✱ ♠♦✈❡♠❡♥ts ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t ❤❛✈❡ r❡❝❡✐✈❡❞ ❛ ❧♦t ♦❢ ❛tt❡♥t✐♦♥✳ ■♥ t❤✐s ♣❛♣❡r✱ ✇❡ ♣r♦✈✐❞❡ ❛ ♣❡rs♣❡❝t✐✈❡ ♦♥ ❤♦✇ t♦ ✐♥t❡r♣r❡t ♠♦✈❡♠❡♥ts ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ✇❤❛t t❤❡② t❡❧❧s ✉s ❛❜♦✉t ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② ❝♦♠❜✐♥✐♥❣ ✐t ✇✐t❤ ❛ss❡t ♣r✐❝✐♥❣ ❞❛t❛ ❢r♦♠ ♦t❤❡r ♠❛r❦❡ts✳ ✶ ❊q✉✐t② ♠❛r❦❡ts ✐♥ t❤❡ ❊❯✱ ❏❛♣❛♥✱ ❛♥❞ t❤❡ ❯❙ ❞r♦♣♣❡❞ ❜② ❛s ♠✉❝❤ ❛s ✸✵✪✳ ❚❤✐s ✐s ❛♥ ❡①tr❛♦r❞✐♥❛r② ❛♠♦✉♥t✳ ❚♦ ✐♥t❡r♣r❡t t❤✐s ❞❡❝❧✐♥❡✱ ✐t ✐s ✉s❡❢✉❧ t♦ r❡❝❛❧❧ t❤❛t t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t✱ St ✱ ✐s ❡q✉❛❧ t♦ t❤❡ ❞✐s❝♦✉♥t❡❞ ✈❛❧✉❡ ♦❢ ❛❧❧ ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ∞ St = Et [Dt+n ] (n) n=1 , + µt Et Dt+n ✐s t❤❡ ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞ ✐♥ n ②❡❛rs (n) ♠❛t✐♦♥✱ ❛♥❞ µt t❤❡ ❝✉♠✉❧❛t✐✈❡ ❞✐s❝♦✉♥t r❛t❡ ❢♦r ✇❤❡r❡ ✭✶✮ ❢r♦♠ t♦❞❛②✱ ❝♦♥❞✐t✐♦♥❛❧ ♦♥ t♦❞❛②✬s ✐♥❢♦r✲ t❤❛t ❝❛s❤ ✢♦✇✳ ■❢ t❤❡ st♦❝❦ ♠❛r❦❡t ❢❛❧❧s✱ t❤❡♥ ❡✐t❤❡r ❡①♣❡❝t❡❞ ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❢❛❧❧ ♦r ✐♥✈❡st♦rs ❞✐s❝♦✉♥t ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❛t ❛ ❤✐❣❤❡r r❛t❡✱ t❤❛t ✐s✱ (n) µt r✐s❡s✳ ✶ ❘❛♠❡❧❧✐ ❛♥❞ ❲❛❣♥❡r ✭✷✵✷✵✮ ❧♦♦❦ ❛t t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ♦❢ st♦❝❦ ♣r✐❝❡ r❡❛❝t✐♦♥s t♦ ❈❖❱■❉✲✶✾ ❡✈❡♥ts t♦ ✉♥❞❡rst❛♥❞ t❤❡ ❢❛❝t♦rs t❤❛t ✐♠♣❛❝t❡❞ ✐♥✈❡st♦rs✬ ❞❡♠❛♥❞ ❞✉r✐♥❣ t❤❡ ♦♥s❡t ♦❢ t❤❡ ❝r✐s✐s✳ ✷ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋♦r t❤❡ st♦❝❦ ♠❛r❦❡t t♦ ❞❡❝❧✐♥❡ ❜② ✸✵✪ ♦♥❧② ❞✉❡ t♦ r❡✈✐s❡❞ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s✱ t❤❡ s❤♦❝❦ t♦ ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ♥❡❡❞s t♦ ❜❡ ❧❛r❣❡ ❛♥❞ ❤✐❣❤❧② ♣❡rs✐st❡♥t✳ ■t ✇♦✉❧❞ ❢♦r ✐♥st❛♥❝❡ ❜❡ ✐♥❝♦♥s✐st❡♥t ✇✐t❤ ❛ ❱✲s❤❛♣❡❞ r❡❝♦✈❡r②✳ ❚♦ s❡❡ t❤✐s✱ ✇❡ ❝❛♥ s✉♠ t❤❡ ✈❛❧✉❡ ♦❢ ❞✐✈✐❞❡♥❞s ❞✉r✐♥❣ t❤❡ ✜rst ✶✵ ②❡❛rs ❛♥❞ ✜♥❞ t❤❛t t❤✐s ❛❝❝♦✉♥ts ❢♦r ❛❜♦✉t ✷✵✪ ♦❢ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t✳ ❚❤✐s ✐♠♣❧✐❡s t❤❛t ✐❢ ❞✐s❝♦✉♥t r❛t❡s ❞♦ ♥♦t ♠♦✈❡ ❛♥❞ ✐❢ t❤❡ ❡❝♦♥♦♠✐❝ ✐♠♣❛❝t ♦♥ ❞✐✈✐❞❡♥❞s ❧❛sts ♥♦ ♠♦r❡ t❤❛♥ ✶✵ ②❡❛rs✱ ❛ ✸✵✪ ❞❡❝❧✐♥❡ ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t ✇♦✉❧❞ ♠❡❛♥ t❤❛t ✜r♠s ♣❛② ♥♦ ❞✐✈✐❞❡♥❞s ✐♥ t❤❡ ♥❡①t ✶✵ ②❡❛rs ✲ s❡❡♠✐♥❣❧② ❛ r❛t❤❡r ❡①tr❡♠❡ s❝❡♥❛r✐♦✳ ■t ✇♦✉❧❞ ❜❡ ♠♦r❡ ❝♦♥s✐st❡♥t ✇✐t❤ ❛♥ ▲✲s❤❛♣❡❞ r❡❝♦✈❡r② ✐♥ ✇❤✐❝❤ ❞✐✈✐❞❡♥❞s ♣❡r♠❛♥❡♥t❧② ❞r♦♣ ❜② ✸✵✪✱ ✇✐t❤ ♥♦ ❝❛t❝❤✲✉♣ ❣r♦✇t❤✳ ❍♦✇❡✈❡r✱ ❢♦❝✉s✐♥❣ ♦♥ ❢✉♥❞❛♠❡♥t❛❧s ♦♥❧② ✐s t②♣✐❝❛❧❧② ♥♦t t❤❡ r✐❣❤t ✇❛② t♦ ✐♥t❡r♣r❡t ♠♦✈❡✲ ♠❡♥ts ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t✳ ❚❤❡ s❡♠✐♥❛❧ ✇♦r❦ ❜② ❙❤✐❧❧❡r ✭✶✾✽✶✮ ❛♥❞ ❈❛♠♣❜❡❧❧ ❛♥❞ ❙❤✐❧❧❡r ✭✶✾✽✽✮ s❤♦✇s t❤❛t ♠♦st ♦❢ t❤❡ ✈❛r✐❛t✐♦♥ ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t ✐s ❞✉❡ t♦ ❝❤❛♥❣❡s ✐♥ ❡①♣❡❝t❡❞ r❡t✉r♥s✱ (n) µt ✱ ♥♦t r❡✈✐s✐♦♥s ✐♥ ❡①♣❡❝t❡❞ ❢✉t✉r❡ ❣r♦✇t❤ r❛t❡s✳ ❙❡❡ ❈♦❝❤r❛♥❡ ✭✷✵✶✶✮ ❢♦r ❛♥ ❡①❝❡❧❧❡♥t r❡✈✐❡✇✳ ❚❤✐s ✐♥s✐❣❤t ❜r✐♥❣s ❣♦♦❞ ❛♥❞ ❜❛❞ ♥❡✇s✳ ❚❤❡ ❣♦♦❞ ♥❡✇s ✐s t❤❛t ✐♥✈❡st♦rs✬ ❡①♣❡❝t❛t✐♦♥s ❞✐❞ ♥♦t ❞❡❝❧✐♥❡ ❛s ❞r❛♠❛t✐❝❛❧❧② ❛s ✐♥ t❤❡ ❡❛r❧✐❡r ❝❛❧❝✉❧❛t✐♦♥✳ ❚❤❡ ❜❛❞ ♥❡✇s✱ ❤♦✇❡✈❡r✱ ✐s t❤❛t ✇❡ ❧❡❛r♥ ❧✐tt❧❡ ❛❜♦✉t ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② t❛❦✐♥❣ ❝✉❡s ❢r♦♠ t❤❡ st♦❝❦ ♠❛r❦❡t✳ ■♥st❡❛❞✱ ✇❡ ❧❡❛r♥ ❛❜♦✉t ✐♥✈❡st♦rs✬ ❝❤❛♥❣❡s ✐♥ ❞✐s❝♦✉♥t r❛t❡s t❤❛t ♠❛② ❜❡ ❞r✐✈❡♥ ❜② s❤✐❢ts ✐♥ r✐s❦ ❛✈❡rs✐♦♥✱ s❡♥t✐♠❡♥t✱ ♦r ✉♥❝❡rt❛✐♥t② ❛❜♦✉t ❧♦♥❣✲r✉♥ ❣r♦✇t❤✳ ❖✉r ♠❛✐♥ ♣♦✐♥t ✐s t❤❛t ❞❛t❛ ❢r♦♠ ❛ r❡❧❛t❡❞ ♠❛r❦❡t✱ t❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ♠❛r❦❡t✱ ❛r❡ ✉s❡❢✉❧ t♦ ♦❜t❛✐♥ ❡st✐♠❛t❡s ♦❢ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② ♠❛t✉r✐t②✳ ❉✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛r❡ ❝♦♥tr❛❝ts t❤❛t ✷ ♦♥❧② ♣❛② t❤❡ ❞✐✈✐❞❡♥❞s ♦❢ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ✐♥ ❛ ❣✐✈❡♥ ②❡❛r✳ ❲❡ ❝❛♥ ❝♦♥✈❡rt t❤❡s❡ ♣r✐❝❡s t♦ ♠❛❦❡ ❡❛❝❤ ♦❢ t❤❡ ❝♦♠♣♦♥❡♥ts ♦❢ ✭✶✮✱ (n) Pt ❞✐r❡❝t❧② ♦❜s❡r✈❛❜❧❡✳ ❲❡ r❡❢❡r t♦ (n) Pt = Et [Dt+n ] (n) , + µt ✭✷✮ n−②❡❛r ❞✐✈✐❞❡♥❞ str✐♣ ❛t t✐♠❡ t✳ ■❢ (n) ∞ ♠❛r❦❡t✱ St = n=1 Pt ❚❤❡r❡ ❛r❡ t✇♦ ❛s t❤❡ ♣r✐❝❡ ♦❢ t❤❡ ✇❡ s✉♠ ❛❧❧ ❞✐✈✐❞❡♥❞ str✐♣ ♣r✐❝❡s✱ t❤❡② ❛❞❞ t♦ t❤❡ ✐♠♣♦rt❛♥t r❡❛s♦♥s t❤❛t ❞❛t❛ ♦♥ ❞✐✈✐❞❡♥❞ str✐♣ ♣r✐❝❡s ❛r❡ ✐♥❢♦r♠❛t✐✈❡✳ ❋✐rst✱ ✈❛♥ ❇✐♥s❜❡r❣❡♥ ❡t ❛❧✳ ✭✷✵✶✸✮ s❤♦✇ t❤❛t ♣r✐❝❡s ♦❢ ❞✐✈✐❞❡♥❞ str✐♣s ♣r♦✈✐❞❡ ❣♦♦❞ ❢♦r❡❝❛sts ♦❢ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ✷ ❙❡❡ ✈❛♥ ❇✐♥s❜❡r❣❡♥ ❡t ❛❧✳ ✭✷✵✶✷✮✱ ✈❛♥ ❇✐♥s❜❡r❣❡♥ ❡t ❛❧✳ ✭✷✵✶✸✮✱ ✈❛♥ ❇✐♥s❜❡r❣❡♥ ❛♥❞ ❑♦✐❥❡♥ ✭✷✵✶✼✮✱ ❛♥❞ ●♦r♠s❡♥ ✭✷✵✷✵✮ ❢♦r ❡❛r❧✐❡r ✇♦r❦ ♦♥ ❞✐✈✐❞❡♥❞ str✐♣s ❛♥❞ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s✳ ✸ Electronic copy available at: https://ssrn.com/abstract=3555917 ❛♥❞ ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ♠♦r❡ ❜r♦❛❞❧②✳ ❙❡❝♦♥❞✱ ❛♥❞ ♣❛rt✐❝✉❧❛r❧② r❡❧❡✈❛♥t ❞✉r✐♥❣ t❤✐s ♣❡r✐♦❞✱ ❞✐✈✐❞❡♥❞ str✐♣s ❛r❡ ❞✐✛❡r❡♥t✐❛t❡❞ ❜② ♠❛t✉r✐t②✱ ❥✉st ❧✐❦❡ ♥♦♠✐♥❛❧✱ r❡❛❧✱ ❛♥❞ ❝♦r♣♦r❛t❡ ❜♦♥❞s✳ ❲❡ ✉s❡ t❤✐s ❢❡❛t✉r❡ ♦❢ t❤❡ ❞❛t❛ t♦ ♣r♦✈✐❞❡ ❛♥ ❡st✐♠❛t❡ ♦❢ ❡①♣❡❝t❡❞ ❣r♦✇t❤ ♦✈❡r t❤❡ ♥❡①t ②❡❛r ❛♥❞ t♦ ♦❜t❛✐♥ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② ♠❛t✉r✐t②✳ ❲❡ ❡①♣❧♦r❡ t❤❡ ❡✈♦❧✉t✐♦♥ ♦❢ ❡①♣❡❝t❡❞ ❣r♦✇t❤ r❛t❡s ❞✉r✐♥❣ t❤❡ ❈❖❱■❉✲✶✾ ❝r✐s✐s ✉♥t✐❧ ❏✉❧② ✷✵✱ ✷✵✷✵✳ ❲❡ ❛❧s♦ ❞❡r✐✈❡ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❜② ❤♦r✐③♦♥✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ❞✐r❡❝t❧② ✉s✐♥❣ ♦❜s❡r✈❡❞ ♣r✐❝❡s✳ ❚❤❡ ❧♦✇❡r ❜♦✉♥❞ ✐s ❢♦r✇❛r❞ ❧♦♦❦✐♥❣ ❛♥❞ r❡q✉✐r❡s ♥❡✐t❤❡r ❛ ❢♦r❡❝❛st✐♥❣ ♠♦❞❡❧ ♥♦r ❤✐st♦r✐❝❛❧ ❞❛t❛✱ ✇❤✐❝❤ ♠❛❦❡s ✐t ✉s❡❢✉❧ ✐♥ ♦✉r s❡tt✐♥❣✱ ❛♥❞ ♦♥❧② r❡❧✐❡s ♦♥ t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t ❡①♣❡❝t❡❞ ❡①❝❡ss r❡t✉r♥s ❤❛✈❡ ♥♦t ❞❡❝r❡❛s❡❞✳ ❲❡ ❝♦♠♣❛r❡ t❤❡ ❧♦✇❡r ❜♦✉♥❞ ♦❜s❡r✈❡❞ ❞✉r✐♥❣ t❤❡ ❈❖❱■❉✲✶✾ ❝r✐s✐s t♦ t❤❡ ❧♦✇❡r ❜♦✉♥❞ ♦❜s❡r✈❡❞ ❞✉r✐♥❣ t❤❡ ◆♦✈❡♠❜❡r ✷✵✵✽ ♦❢ t❤❡ ❣❧♦❜❛❧ ✜♥❛♥❝✐❛❧ ❝r✐s✐s ✭●❋❈✮✳ ❚❤✐s ✐s ✉s❡❢✉❧ ❛s t❤❡ ❧♦✇❡r❜♦✉♥❞ ❞✉r✐♥❣ t❤❡ ●❋❙ t✉r♥❡❞ ♦✉t t♦ ❜❡ q✉✐t❡ t✐❣❤t ♦♥❝❡ ❝♦♠♣❛r❡❞ t♦ t❤❡ s✉❜s❡q✉❡♥t ❞✐✈✐❞❡♥❞s t❤❛t r❡❛❧✐③❡❞✳ ❲❡ ❛❧s♦ ✉s❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s t♦ ❜❡tt❡r ✉♥❞❡rst❛♥❞ t❤❡ ♦✈❡r❛❧❧ ♠♦✈❡♠❡♥t ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t✳ ❉✉r✐♥❣ t❤❡ ♦♥s❡t ♦❢ t❤❡ ❝r✐s✐s✱ t❤❡ st♦❝❦ ♠❛r❦❡t ❞r♦♣s s✉❜st❛♥t✐❛❧❧② ♠♦r❡ t❤❛♥ t❤❡ ✶✲ t♦ ✼✲②❡❛r ❞✐✈✐❞❡♥❞ str✐♣s✳ ❚❤✐s ✜♥❞✐♥❣ ✐♠♣❧✐❡s t❤❛t t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ✕ ❞✐✈✐❞❡♥❞s ♣❛✐❞ ♦✉t ♠♦r❡ t❤❛♥ ✼ ②❡❛rs ❢r♦♠ t♦❞❛② ✕ ♠✉st ❤❛✈❡ ❞r♦♣♣❡❞ ❜② ♠♦r❡ t❤❛♥ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ♥❡❛r✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✳ ❆s ✇❡ ✜♥❞ ✐t ✉♥❧✐❦❡❧② t❤❛t ❧♦♥❣✲r✉♥ ❞✐✈✐❞❡♥❞s✱ ✐♥ ❧❡✈❡❧s✱ ❛r❡ ❤✐t ❤❛r❞❡r t❤❛♥ ♥❡❛r✲t❡r♠ ❞✐✈✐❞❡♥❞s✱ t❤❡ ❞r♦♣ ♠✉st ❝♦♠❡ ❢r♦♠ ❞✐s❝♦✉♥t r❛t❡s✳ ✸ ❍❡♥❝❡✱ ♣r✐❝❡s ♦♥ t❤❡ ♠❛r❦❡t ❛♥❞ t❤❡ ❢✉t✉r❡s ❥♦✐♥t❧② s✉❣❣❡st t❤❛t ❞✐s❝♦✉♥t r❛t❡s ✐♥✐t✐❛❧❧② ✐♥❝r❡❛s❡❞ s✉❜st❛♥t✐❛❧❧② ♦♥ ❧♦♥❣✲♠❛t✉r✐t② ❝❧❛✐♠s s✉❝❤ ❛s t❤❡ ♠❛r❦❡t ♣♦rt❢♦❧✐♦✳ ✹ ❲❡ ❢♦r♠❛❧✐③❡ t❤✐s ❛♥❛❧②s✐s ❛t t❤❡ ❡♥❞ ♦❢ t❤❡ ♣❛♣❡r✳ ❆s ♦❢ ❏✉❧② ✷✵✱ t❤❡ ❡①♣❡❝t❡❞ r❡t✉r♥ ♦♥ t❤❡ ♠❛r❦❡t ❤❛s r❡t✉r♥❡❞ t♦ t❤❡ ♣r❡✲❝r✐s✐s ❧❡✈❡❧✳ ❖♥ ❏✉❧② ✷✵✱ t❤❡ ❙✫P ✺✵✵ tr❛❞❡s ❛t ✩✸✷✺✶✱ ✇❤✐❝❤ ✐s ✩✶✸✺ ❧♦✇❡r t❤❛♥ t❤❡ ♣❡❛❦ ♦❢ ✩✸✸✽✻ ♦♥ ❋❡❜r✉❛r② ✶✾✳ ❚❤✐s ❞r♦♣ ❝❛♥ ❧❛r❣❡❧② ❜❡ ❡①♣❧❛✐♥❡❞ ❜② t❤❡ ✜rst ✶✵ ②❡❛rs ♦❢ ❞✐✈✐❞❡♥❞s✱ ❛s t❤❡② ❛r❡ ❞♦✇♥ ❜② ❛ t♦t❛❧ ♦❢ ✩✶✶✷✳ ❆s s✉❝❤✱ t❤❡ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✱ t❤❡ ❞✐✈✐❞❡♥❞s ❜❡②♦♥❞ ②❡❛r ✶✵✱ ♠✉st ❤❛✈❡ ❛♣♣r♦①✐♠❛t❡❧② t❤❡ s❛♠❡ ✈❛❧✉❡ ❛s ❜❡❢♦r❡ t❤❡ ❝r✐s✐s✳ ■❢ ❡①♣❡❝t❡❞ ❧♦♥❣✲ r✉♥ ❞✐✈✐❞❡♥❞s ❛r❡ t❤❡ s❛♠❡ ❛s ❜❡❢♦r❡ t❤❡ ❝r✐s✐s✱ ❡①♣❡❝t❡❞ r❡t✉r♥s ♦♥ t❤❡ ❧♦♥❣✲r✉♥ ❞✐✈✐❞❡♥❞s ✸ ❲❡ r❡❢❡r t♦ ❊✐❝❤❡♥❜❛✉♠ ❡t ❛❧✳ ✭✷✵✷✵✮ ❢♦r ❛ ♠❛❝r♦❡❝♦♥♦♠✐❝ ♠♦❞❡❧ ♦❢ ❡♣✐❞❡♠✐❝s t❤❛t ✐s ❝♦♥s✐st❡♥t ✇✐t❤ t❤✐s ❛ss✉♠♣t✐♦♥✳ ✹ ❚❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❧♦♥❣✲❤♦r✐③♦♥ ❞✐s❝♦✉♥t r❛t❡ ✈❛r✐❛t✐♦♥ t♦ ✉♥❞❡rst❛♥❞ ♠♦✈❡♠❡♥ts ✐♥ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ✐s ❝♦♥s✐st❡♥t ✇✐t❤ ✭●♦r♠s❡♥✱ ✷✵✷✵✮✳ ✹ Electronic copy available at: https://ssrn.com/abstract=3555917 ♠✉st t❤❡r❡❢♦r❡ ❛❧s♦ ❜❡ t❤❡ s❛♠❡ ❛s ❜❡❢♦r❡ t❤❡ ❝r✐s✐s✳ ❍♦✇❡✈❡r✱ ✐♥t❡r❡st r❛t❡s ❤❛✈❡ ❞r♦♣♣❡❞ s✉❜st❛♥t✐❛❧❧②✱ ✇❤✐❝❤ ♠❡❛♥s t❤❡ ❡①♣❡❝t❡❞ r❡t✉r♥ ✐♥ ❡①❝❡ss ♦❢ t❤❡ ✐♥t❡r❡st r❛t❡s ✐s ❤✐❣❤❡r t❤❛♥ ❜❡❢♦r❡ t❤❡ ❝r✐s✐s✳ ❖✉r r❡s✉❧ts ❤❛✈❡ ✐♠♣❧✐❝❛t✐♦♥s ❢♦r ❛ss❡t ♣r✐❝✐♥❣ t❤❡♦r✐❡s✳ ■t ✐s ✇❡❧❧ ❦♥♦✇♥ t❤❛t ✐t ✐s ♦❢t❡♥✲ t✐♠❡s ❞✐✣❝✉❧t t♦ ✐❞❡♥t✐❢② t❤❡ ❡❝♦♥♦♠✐❝ s❤♦❝❦s t❤❛t ❝❛✉s❡❞ ❛ss❡t ♣r✐❝❡s t♦ ♠♦✈❡ ✭❈✉t❧❡r ❡t ❛❧✳ ✭✶✾✽✾✮✮✳ ❚❤❡ ✉♥✐q✉❡ ❢❡❛t✉r❡ ♦❢ t❤❡ ♦♥❣♦✐♥❣ ❡✈❡♥ts ✐s t❤❛t t❤❡ ♥❛t✉r❡ ♦❢ t❤❡ s❤♦❝❦ ✐s ❝❧❡❛r✱ ❛♥❞ ✇❡ ❤❛✈❡ ❛ ♣r✐♦r r❡❣❛r❞✐♥❣ t❤❡ t❡♠♣♦r❛❧ str✉❝t✉r❡✳ ■♥❞❡❡❞✱ ❧♦♦❦✐♥❣ ❛t t❤❡ ❈❡♥t❡rs ❢♦r ❉✐s❡❛s❡ ✺ ❛♥❞ ❈♦♥tr♦❧ ❛♥❞ Pr❡✈❡♥t✐♦♥✬s ♦✈❡r✈✐❡✇ ♦❢ ♣❛st ♣❛♥❞❡♠✐❝s✱ ✻ ❜❡ r❡❧❛t✐✈❡❧② s❤♦rt✲❧✐✈❡❞✳ ✇❡ ❧❡❛r♥ t❤❛t ♣❛♥❞❡♠✐❝s t❡♥❞ t♦ ❲❤✐❧❡ t❤❡ ♣❛♥❞❡♠✐❝ ♠❛② s♣r❡❛❞ ♠♦r❡ ❡❛s✐❧② ✐♥ t♦❞❛②✬s ✐♥t❡r❝♦♥✲ ♥❡❝t❡❞ ✇♦r❧❞✱ t❤❡ ❡①♣❡❝t❛t✐♦♥ ✐s t❤❛t ❛ ✈❛❝❝✐♥❡ ❝❛♥ ❜❡ ❛✈❛✐❧❛❜❧❡ ✇✐t❤✐♥ ♦♥❡ t♦ t✇♦ ②❡❛rs✳ ❙♦ ✇❤✐❧❡ t❤❡ ❡❝♦♥♦♠✐❝ ❝♦♥tr❛❝t✐♦♥ ♠❛② ❜❡ ✈❡r② s❤❛r♣✱ ❛♥❞ ♣♦t❡♥t✐❛❧❧② ❤❛✈❡ ❧♦♥❣✲❧❛st✐♥❣ ❡✛❡❝ts ❞✉❡ t♦ ❞❡❢❛✉❧ts ♦❢ ❤♦✉s❡❤♦❧❞s✱ ✜r♠s✱ ♣❛rts ♦❢ t❤❡ ✜♥❛♥❝✐❛❧ s❡❝t♦r✱ ❛♥❞ ❡✈❡♥ ❣♦✈❡r♥♠❡♥ts✱ ✇❡ ❜❡❧✐❡✈❡ ❛t t❤❡ t✐♠❡ ♦❢ ✇r✐t✐♥❣ t❤❛t ✐t ✐s r❡❛s♦♥❛❜❧❡ t♦ ❛ss✉♠❡ t❤❛t t❤❡ ❡❝♦♥♦♠✐❝ ❝♦♥s❡q✉❡♥❝❡s ❛r❡ ♠♦st s❡✈❡r❡ ✐♥ t❤❡ ♥❡①t ♦♥❡ ♦r t✇♦ ②❡❛rs✳ ■♥❞❡❡❞✱ t❤✐s r❡❛s♦♥✐♥❣ ❤❛s ♣r♦♠♣t❡❞ ♣♦❧✐❝② ♣r♦♣♦s❛❧s t♦ ✢❛tt❡♥ ♥♦t ♦♥❧② t❤❡ ♣❛♥❞❡♠✐❝ ❝✉r✈❡✱ ❜✉t ❛❧s♦ t❤❡ r❡❝❡ss✐♦♥ ❝✉r✈❡ ✭●♦✉r✐♥❝❤❛s ✭✷✵✷✵✮✮✳ ❲❡ ✇✐❧❧ ✐♥t❡r♣r❡t t❤❡ ❞②♥❛♠✐❝s ♦❢ ❡q✉✐t② ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts t❤r♦✉❣❤ t❤✐s ❧❡♥s ❛♥❞ ❞✐s❝✉ss t❤✐s ✐♥ ♠♦r❡ ❞❡t❛✐❧ ✐♥ ❙❡❝t✐♦♥ ✺✳ ✷ ❚❤❡ ❘❡s♣♦♥s❡ ♦❢ ❙t♦❝❦✱ ❇♦♥❞✱ ❛♥❞ ❉✐✈✐❞❡♥❞ ❋✉t✉r❡s ▼❛r❦❡ts t♦ ❈❖❱■❉✲✶✾ ✷✳✶ ❚❤❡ ❘❡s♣♦♥s❡ ♦❢ ❙t♦❝❦ ❛♥❞ ❇♦♥❞ ▼❛r❦❡ts ❋✐❣✉r❡ ✶ s❤♦✇s t❤❡ ❝✉♠✉❧❛t✐✈❡ r❡t✉r♥ ♦♥ t❤❡ st♦❝❦ ♠❛r❦❡ts ✐♥ t❤❡ ❯❙✱ t❤❡ ❊❯✱ ❛♥❞ ❏❛♣❛♥ ✐♥ t❤❡ t♦♣ ♣❛♥❡❧s✳ ❲❡ ✉s❡ t❤❡ ❙✫P✺✵✵ ✐♥❞❡① ❛s t❤❡ r❡♣r❡s❡♥t❛t✐✈❡ st♦❝❦ ✐♥❞❡① ✐♥ t❤❡ ❯❙✱ t❤❡ ❊✉r♦ ❙t♦①① ✺✵ ✐♥❞❡① ✐♥ t❤❡ ❊❯✱ ❛♥❞ t❤❡ ◆✐❦❦❡✐ ✷✷✺ ✐♥❞❡① ✐♥ ❏❛♣❛♥✳ ❚❤❡ ❜♦tt♦♠ ♣❛♥❡❧s s❤♦✇ t❤❡ ❝✉♠✉❧❛t✐✈❡ r❡t✉r♥ ♦♥ ✸✵✲②❡❛r ♥♦♠✐♥❛❧ ❜♦♥❞s ✐♥ t❤❡ ❯❙✱ ●❡r♠❛♥②✱ ❛♥❞ ❏❛♣❛♥✳ ◆♦♥❡ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡ts r❡s♣♦♥❞❡❞ str♦♥❣❧② t♦ t❤❡ ♦✉t❜r❡❛❦ ✐♥ ❈❤✐♥❛ ♦r t❤❡ ❧♦❝❦❞♦✇♥ ♦❢ ❲✉❤❛♥✱ ✺ ❤tt♣s✿✴✴✇✇✇✳❝❞❝✳❣♦✈✴✢✉✴♣❛♥❞❡♠✐❝✲r❡s♦✉r❝❡s✴❜❛s✐❝s✴♣❛st✲♣❛♥❞❡♠✐❝s✳❤t♠❧✳ ✻ ❋♦r ✐♥st❛♥❝❡✱ t❤❡ ❍✶◆✶ ✈✐r✉s s♣r❡❛❞ ✐♥ ✶✾✶✽ ❛♥❞ ✶✾✶✾✱ t❤❡ ❍✷◆✷ ✈✐r✉s ✐♥ ✶✾✺✼ ❛♥❞ ✶✾✺✽✱ t❤❡ ❍✸◆✷ ✈✐r✉s ✐♥ ✶✾✻✽✱ ❛♥❞ t❤❡ ❍✶◆✶♣❞♠✵✾ ✈✐r✉s ✐♥ ✷✵✵✾✳ ✺ Electronic copy available at: https://ssrn.com/abstract=3555917 ❈❤✐♥❛✱ ♦♥ ❏❛♥✉❛r② ✷✸✳ ❍♦✇❡✈❡r✱ ♦♥❝❡ ✐t ✐s ❛♣♣❛r❡♥t t❤❛t t❤❡ ♦✉t❜r❡❛❦ s♣r❡❛❞ t♦ ■t❛❧②✱ ❙♦✉t❤ ❑♦r❡❛✱ ❛♥❞ ■r❛♥✱ ❛r♦✉♥❞ ❋❡❜r✉❛r② ✷✵✱ st♦❝❦ ♠❛r❦❡ts ❞❡❝❧✐♥❡❞ s❤❛r♣❧②✳ ■♥ r❡s♣♦♥s❡ t♦ t❤❡ ❯❙✬ ❞❡❝✐s✐♦♥ ♦♥ ▼❛r❝❤ ✶✷ t♦ s❡✈❡r❡❧② r❡str✐❝t tr❛✈❡❧ ❢r♦♠ t❤❡ ❊❯ ❛♥❞ ❞❡❝✐s✐♦♥s ❜② ❣♦✈❡r♥♠❡♥ts ✐♥ t❤❡ ❊❯ t♦ ✐♠♣♦s❡ ❧♦❝❦❞♦✇♥s t♦ ✈❛r✐♦✉s ❞❡❣r❡❡s✱ st♦❝❦ ♠❛r❦❡ts ❛r♦✉♥❞ t❤❡ ✇♦r❧❞ ❞❡❝❧✐♥❡❞ ❜② ✶✵✪ ♦r ♠♦r❡✳ ❇② ▼❛r❝❤ ✶✽✱ st♦❝❦ ♠❛r❦❡ts ❤❛✈❡ ❞r♦♣♣❡❞ ♠♦r❡ t❤❛♥ ✸✵✪ ❢r♦♠ t❤❡✐r ♣❡❛❦✳ ❖♥ ▼❛r❝❤ ✷✹✱ ❙✫P ✺✵✵ r❛❧❧✐❡s ❛❧♠♦st ✶✵✪ ❢♦❧❧♦✇✐♥❣ ♥❡✇s ♦❢ ✜s❝❛❧ st✐♠✉❧✐ ❛♥❞ ❢✉rt❤❡r ♠♦♥❡t❛r② ♣♦❧✐❝② ❛❝t✐♦♥s✳ ■♥ s❡❛r❝❤ ♦❢ s❛❢❡t②✱ ✐♥✈❡st♦rs✬ ❞❡♠❛♥❞ ❢♦r ❧♦♥❣✲t❡r♠ ❣♦✈❡r♥♠❡♥t ❜♦♥❞s ✐ss✉❡❞ ❜② t❤❡ ❯❙✱ ●❡r♠❛♥②✱ ❛♥❞ t♦ s♦♠❡ ❡①t❡♥❞ ❏❛♣❛♥✱ ✐♥❝r❡❛s❡❞✳ ❖✈❡r t❤❡ s❛♠❡ ♣❡r✐♦❞✱ t❤❡ ②✐❡❧❞ ♦♥ ✸✵✲②❡❛r ❯❙ ❚r❡❛s✉r✐❡s ❞❡❝r❡❛s❡s ❜② ❛❧♠♦st ❛ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥t✱ ❞r✐✈✐♥❣ ♣r✐❝❡s ♦❢ ✸✵✲②❡❛r ❜♦♥❞s ✉♣ ❜② ❛♣♣r♦①✐♠❛t❡❧② ✸✵✪✳ ❲❡ s❡❡ ❛ s✐♠✐❧❛r r❛❧❧② ✐♥ ●❡r♠❛♥ ❜✉♥❞s✱ ✇❤✐❝❤ ❛r❡ t❤❡ s❛❢❡ ❛ss❡ts ✐♥ t❤❡ ❊✉r♦ ❛r❡❛✳ ❙t♦❝❦ r❡t✉r♥s ❛r❡ ♦❢t❡♥ ♠❡❛s✉r❡❞ ✐♥ ❡①❝❡ss ♦❢ t❤❡ r❡t✉r♥ ♦♥ ❜♦♥❞s✳ ❲❤❡♥ ♠❡❛s✉r❡❞ ✐♥ ❡①❝❡ss ♦❢ ✸✵✲②❡❛r ❜♦♥❞s✱ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ❢❛❧❧s ❜② ❛❧♠♦st ✻✵✪ ❛t t❤❡ ❜♦tt♦♠✳ ❚❤✐s ✐s ❛ ❧♦✇❡r ❡①❝❡ss r❡t✉r♥ t❤❛♥ ♦❜s❡r✈❡❞ ✐♥ ❛♥② ❝❛❧❡♥❞❛r ♠♦♥t❤ ✐♥ ♠♦❞❡r♥ ❯❙ ❤✐st♦r②✳ ❆ ❝❡♥tr❛❧ q✉❡st✐♦♥ ❢♦r ♣♦❧✐❝②♠❛❦❡rs ❛♥❞ ♠❛r❦❡t ♣❛rt✐❝✐♣❛♥ts ✐s ❤♦✇ t♦ r❡❛❞ t❤✐s ❞❡❝❧✐♥❡ ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t✳ ❚❤❛t ✐s✱ ✇❤❛t ❞♦❡s t❤❡ ❞❡❝❧✐♥❡ t❡❧❧ ✉s ❛❜♦✉t t❤❡ ❡①♣❡❝t❡❞ tr❛❥❡❝t♦r② ♦❢ ❢✉t✉r❡ ❣r♦✇t❤ ♦r ❝❤❛♥❣❡s ✐♥ ❡①♣❡❝t❡❞ ❡①❝❡ss r❡t✉r♥s✳ ■♥ t❤❡ r❡♠❛✐♥❞❡r ♦❢ t❤✐s ♣❛♣❡r✱ ✇❡ s❤♦✇ t❤❛t ✇❡ ❝❛♥ ♠❛❦❡ ♣r♦❣r❡ss ♦♥ t❤✐s q✉❡st✐♦♥ ❜② ✉s✐♥❣ ❞❛t❛ ♦♥ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛♥❞ t❤❡ st♦❝❦ ♠❛r❦❡t ❥♦✐♥t❧②✳ ✷✳✷ ❚❤❡ ❘❡s♣♦♥s❡ ♦❢ ❉✐✈✐❞❡♥❞ ❋✉t✉r❡s ▼❛r❦❡ts ❚♦ ❜❡tt❡r ✉♥❞❡rst❛♥❞ t❤❡ ❡①♣❡❝t❡❞ ✐♠♣❛❝t ♦❢ ❈❖❱■❉✲✶✾ ♦♥ t❤❡ ❡❝♦♥♦♠② ♦✈❡r t❤❡ ♥❡①t ❢❡✇ ②❡❛rs✱ ✇❡ t✉r♥ t♦ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❞✐✈✐❞❡♥❞ ♣r✐❝❡s✳ ❚❤❡ ❡q✉✐t② t❡r♠ str✉❝t✉r❡ ❛r❡ ♣r✐❝❡s ♦❢ ❝❧❛✐♠s t♦ t❤❡ ❞✐✈✐❞❡♥❞s ♦❢ ❛❧❧ ✜r♠s ✐♥ ❛♥ ✐♥❞❡① ✐♥ ❛ ❣✐✈❡♥ ②❡❛r✳ ❚♦ ✐♥t❡r♣r❡t t❤❡ ❞✐✈✐❞❡♥❞ str✐♣ ♣r✐❝❡✱ ✇❡ ❝❛♥ ✇r✐t❡ ✭✷✮ ❛s (n) (n) Pt = Dt Gt (n) , + µt ✻ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✶✿ ❚❤❡ r❡s♣♦♥s❡ ♦❢ t❤❡ st♦❝❦ ❛♥❞ ♥♦♠✐♥❛❧ ❜♦♥❞ ♠❛r❦❡ts ✐♥ t❤❡ ❯❙ ❛♥❞ ❊❯ ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ ❝✉♠✉❧❛t✐✈❡ r❡t✉r♥ ♦♥ t❤❡ ❙✫P ✺✵✵✱ t❤❡ ❊✉r♦ ❙t♦①① ✺✵ ✐♥❞❡①✱ ✸✵✲②❡❛r ❯❙ ❚r❡❛s✉r✐❡s✱ ❛♥❞ ✸✵✲②❡❛r ●❡r♠❛♥ ❜✉♥❞s✳ ❲❡ ❞❡♣✐❝t ✉s✐♥❣ ❞❛s❤❡❞ ✈❡rt✐❝❛❧ ❧✐♥❡s t❤❡ ❢♦❧❧♦✇✐♥❣ ✜✈❡ ❡✈❡♥ts✿ ❚❤❡ ❧♦❝❦❞♦✇♥ ♦❢ ❲✉❤❛♥✱ ❈❤✐♥❛ ♦♥ ❏❛♥✉❛r② ✷✸✱ t❤❡ ❛♥♥♦✉♥❝❡♠❡♥t ♦❢ t❤❡ q✉❛r❛♥t✐♥❡ ✐♥ ■t❛❧② ♦♥ ❋❡❜r✉❛r② ✷✷✱ t❤❡ ❛♥♥♦✉♥❝❡♠❡♥t ❜② t❤❡ ❯❙ ❣♦✈❡r♥♠❡♥t t❤❛t ✐t ✇♦✉❧❞ ❜❛♥ tr❛✈❡❧ ❢r♦♠ t❤❡ ❊❯ ♦♥ ▼❛r❝❤ ✶✶✱ t❤❡ ❞❡❝❧❛r❛t✐♦♥ ♦❢ ♥❛t✐♦♥❛❧ ❡♠❡r❣❡♥❝② ✐♥ t❤❡ ❯❙ ♦♥ ▼❛r❝❤ ✶✸✱ ❛♥❞ t❤❡ ♥❡✇s t❤❛t ❝♦♥❣r❡ss ✐s ❝❧♦s❡ t♦ ♣❛ss✐♥❣ ❛ st✐♠✉❧✉s ❜✐❧❧ ♦♥ ▼❛r❝❤ ✷✹✳ ✼ Electronic copy available at: https://ssrn.com/abstract=3555917 (n) Gt ✇❤❡r❡ = Et Dt+n Dt ✐s t❤❡ ❡①♣❡❝t❡❞ ❣r♦✇t❤ r❛t❡ ❜❡t✇❡❡♥ ②❡❛rs t ❛♥❞ t✰♥✳ ■♥ ♣r❛❝t✐❝❡✱ ✇❡ ❞♦ ♥♦t ❞✐r❡❝t❧② ♦❜s❡r✈❡ t❤❡ ❞✐✈✐❞❡♥❞ str✐♣ ♣r✐❝❡✱ ❜✉t ✐♥st❡❛❞ ♦❜s❡r✈❡ t❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ♣r✐❝❡✱ ✇❤✐❝❤ ✇❡ ❞❡♥♦t❡ ❜② (n) Ft = (n) Pt (1 + (n) Ft ❚❤❡ t✇♦ ♣r✐❝❡s ❛r❡ ❧✐♥❦❡❞ ❜② t❤❡ ♥♦✲❛r❜✐tr❛❣❡ r❡❧❛t✐♦♥s❤✐♣ (n) yt )✱ ✇❤✐❝❤ ✐♠♣❧✐❡s (n) (n) Ft (n) = Dt Gt (n) , + θt (n) (n) 1+µ t n−②❡❛r r✐s❦✲❢r❡❡ ✐♥t❡r❡st r❛t❡ ❛♥❞ θt = (n) −1 ✐s t❤❡ ❡①♣❡❝t❡❞ 1+yt ❡①❝❡ss ♥✲♣❡r✐♦❞ r❡t✉r♥ ♦♥ n−♣❡r✐♦❞ ❞✐✈✐❞❡♥❞ r✐s❦✳ (n) ❲❡ ❞✐r❡❝t❧② ♦❜s❡r✈❡ t❤❡ ❢✉t✉r❡s ♣r✐❝❡✱ Ft ✱ ✇❤✐❝❤ ✐♥❢♦r♠s ✉s ❛❜♦✉t t❤❡ ♠❛r❦❡t✬s ❡①♣❡❝t❛✲ (n) t✐♦♥ ♦❢ t❤❡ ❣r♦✇t❤ r❛t❡ ❜② ♠❛t✉r✐t② ❛♥❞ t❤❡ ❡①♣❡❝t❡❞ ❡①❝❡ss r❡t✉r♥✱ θt ✱ ❛❣❛✐♥✱ ❜② ♠❛t✉r✐t②✳ ✇❤❡r❡ yt ✐s t❤❡ ❝✉♠✉❧❛t✐✈❡ ❚❤❡ ✉♥✐q✉❡ ❢❡❛t✉r❡ ✐s t❤❛t ✇❡ ❝❛♥ ❣❡t ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② ♠❛t✉r✐t②✱ ✇❤✐❧❡ t❤❡ st♦❝❦ ♠❛r❦❡t ✐s ✐♥❢♦r♠❛t✐✈❡ ❛❜♦✉t ❣r♦✇t❤ r❛t❡s ❛♥❞ ❡①♣❡❝t❡❞ r❡t✉r♥s ❛❝r♦ss ❛❧❧ ♠❛t✉r✐t✐❡s ❝♦♠❜✐♥❡❞✳ ❉✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛r❡ ❡①❝❤❛♥❣❡✲tr❛❞❡❞ ♣r♦❞✉❝ts✳ ❉✐✈✐❞❡♥❞ ❢✉t✉r❡s ❢♦r t❤❡ ❙✫P✺✵✵✱ ❊✉r♦ ❙t♦①① ✺✵✱ ❛♥❞ ◆✐❦❦❡✐ ✷✷✺ tr❛❞❡ ♦♥ t❤❡ ❈❤✐❝❛❣♦ ▼❡r❝❛♥t✐❧❡ ❊①❝❤❛♥❣❡✱ t❤❡ ❊✉r❡① ❊①❝❤❛♥❣❡✱ ✼ ❛♥❞ t❤❡ ❙✐♥❣❛♣♦r❡ ❡①❝❤❛♥❣❡✱ r❡s♣❡❝t✐✈❡❧②✳ ❇❡❝❛✉s❡ t❤❡ ❝♦♥tr❛❝ts ❡①♣✐r❡ ✐♥ ❉❡❝❡♠❜❡r✱ t❤❡ ♠❛t✉r✐t② ♦❢ t❤❡ ❛✈❛✐❧❛❜❧❡ ❝♦♥tr❛❝ts ✈❛r✐❡s ♦✈❡r t❤❡ ❝❛❧❡♥❞❛r ②❡❛r✳ ✽ ❲❡ t❤❡r❡❢♦r❡ ✐♥t❡r♣♦❧❛t❡ ♣r✐❝❡s ❛❝r♦ss t❤❡ ❞✐✛❡r❡♥t ❝♦♥tr❛❝ts t♦ ♦❜t❛✐♥ ❝♦♥st❛♥t ♠❛t✉r✐t② ♣r✐❝❡s✳ ❲❡ ✉s❡ t❤❡ ♠✐❞✲ q✉♦t❡s ❛t ❝❧♦s❡ ❛s ♣r✐❝✐♥❣ ❞❛t❛ ✐♥ t❤❡ ❯❙✱ s❡tt❧❡♠❡♥t ♣r✐❝❡s✱ ✇❤✐❝❤ ✐s t❤❡ ✈♦❧✉♠❡✲✇❡✐❣❤t❡❞ ❛✈❡r❛❣❡ ♣r✐❝❡ ❞✉r✐♥❣ t❤❡ ❞❛②✱ ✐♥ t❤❡ ❊❯✱ ❛♥❞ t❤❡ ❧❛st tr❛❞✐♥❣ ♣r✐❝❡ ❢♦r ❛ ❣✐✈❡♥ ❞❛② ❢♦r ◆✐❦❦❡✐ ✷✷✺✳ ❋✐❣✉r❡ ✷ s❤♦✇s ❤♦✇ t❤❡ ♣r✐❝❡s ♦♥ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❡✈♦❧✈❡ ❜❡t✇❡❡♥ ❏❛♥✉❛r② ✶ ❛♥❞ ❏✉❧② ✷✵✳ ❚❤❡ ✜❣✉r❡ s❤♦✇s t❤❡ ❝❤❛♥❣❡ ✐♥ ♣r✐❝❡s ♦❢ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s r❡❧❛t✐✈❡ t♦ t❤❡ ♣r✐❝❡ ♦❢ t❤❡ s❛♠❡✲♠❛t✉r✐t② ❝❧❛✐♠ ♦♥ ❏❛♥✉❛r② ✶✳ ♣r✐❝❡s ♦♥ ▼❛r❝❤ ✺✳ ❚❤❡ t♦♣ ❧❡❢t ❝♦r♥❡r s❤♦✇s t❤❡ ❝✉♠✉❧❛t✐✈❡ ❝❤❛♥❣❡ ✐♥ Pr✐❝❡s ❞r♦♣ ♦♥❧② ♠♦❞❡st❧② ❞✉r✐♥❣ t❤❡ ✐♥✐t✐❛❧ s♣r❡❛❞ ♦❢ t❤❡ ✈✐r✉s ❢r♦♠ ❏❛♥✉❛r② ✶ t♦ ▼❛r❝❤ ✺✳ ■♥ ❝♦♥tr❛st✱ ❡q✉✐t② ♠❛r❦❡ts ❞r♦♣ ❜② ♠♦r❡ t❤❛♥ ✶✵✪ ❜❡t✇❡❡♥ ❏❛♥✉❛r② ✼ ❉✐✈✐❞❡♥❞ ❢✉t✉r❡s ❢♦r ◆✐❦❦❡✐ ✷✷✺ ❛❧s♦ tr❛❞❡ ♦♥ t❤❡ ❖s❛❦❛ ❡①❝❤❛♥❣❡✱ ❛❧t❤♦✉❣❤ ✐♥ ❧♦✇❡r ✈♦❧✉♠❡ t❤❛♥ ♦♥ t❤❡ ❙✐♥❣❛♣♦r❡ ❡①❝❤❛♥❣❡✳ ✽ ❚❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s t❡❝❤♥✐❝❛❧❧② ❡①♣✐r❡ ✐♥ ▼❛r❝❤ ✇❤❡♥ t❤❡ ✜♥❛❧ ❞✐✈✐❞❡♥❞s ❢♦r t❤❡ ◆✐❦❦❡✐ ✐♥❞❡① ❢♦r ❛ ❣✐✈❡♥ ❝❛❧❡♥❞❛r ②❡❛r ✐s ❛♥♥♦✉♥❝❡❞✳ ✽ Electronic copy available at: https://ssrn.com/abstract=3555917 ❛♥❞ ❡❛r❧② ▼❛r❝❤✳ ❙✐♥❝❡ ♥❡❛r✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❞♦ ♥♦t ❞r♦♣ ✐♥ ✈❛❧✉❡✱ t❤❡ ✐♥✐t✐❛❧ ❞r♦♣ ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t ♠✉st ❝♦♠❡ ❢r♦♠ ❛ ❞r♦♣ ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✳ ❉✐✈✐❞❡♥❞ ♣r✐❝❡s ❞r♦♣ s✉❜st❛♥t✐❛❧❧② ❜❡t✇❡❡♥ ▼❛r❝❤ ✺ ❛♥❞ ▼❛r❝❤ ✷✵✳ ❚❤❡ t♦♣ r✐❣❤t ❝♦r♥❡r s❤♦✇s t❤❡ ❝❤❛♥❣❡ ✐♥ ♣r✐❝❡❞ ❢r♦♠ ❏❛♥✉❛r② ✶ t♦ ▼❛r❝❤ ✷✵✳ Pr✐❝❡s ❛r❡ ❞♦✇♥ ❜② ♠♦r❡ t❤❛♥ ✸✵✪ ❢♦r t❤❡ ❙✫P ✺✵✵ ❛♥❞ ♠♦r❡ t❤❛♥ ✹✵✪ ❢♦r t❤❡ ❊✉r♦ ❙t♦①① ✺✵✳ ❚❤❡ ❞r♦♣ ✐s ❜✐❣❣❡st ♦♥ t❤❡ ✷✲②❡❛r ❤♦r✐③♦♥ ❢♦r t❤❡s❡ ✐♥❞❡①❡s✳ ❇❡t✇❡❡♥ ▼❛r❝❤ ✺ ❛♥❞ ▼❛r❝❤ ✷✵✱ st♦❝❦ ♠❛r❦❡ts ❞r♦♣ s✉❜st❛♥t✐❛❧❧② ✐♥ ❜♦t❤ t❤❡ ❯❙ ❛♥❞ t❤❡ ❊❯✱ ✇✐t❤ t❤❡ ❙✫P ✺✵✵ ❡①♣❡r✐❡♥❝✐♥❣ ✐ts ❜✐❣❣❡st ❞❛✐❧② ❧♦ss s✐♥❝❡ ✶✾✽✼✳ ■♠♣♦rt❛♥t ❞❛t❡s ❛r❡ ▼❛r❝❤ ✶✶✱ ✇❤❡♥ t❤❡ ❯❙ ❧✐♠✐ts tr❛✈❡❧ ❢r♦♠ t❤❡ ❊❯✱ ❛♥❞ ▼❛r❝❤ ✶✸✱ ✇❤❡♥ t❤❡ ❯❙ ❞❡❝❧❛r❡s ❛ st❛t❡ ♦❢ ❡♠❡r❣❡♥❝②✳ ❖♥ ▼❛r❝❤ ✶✸✱ st♦❝❦ ♠❛r❦❡ts s♦❛r ❛❢t❡r t❤❡ ❞❡❝❧❛r❛t✐♦♥ ♦❢ t❤❡ ♥❛t✐♦♥❛❧ ❡♠❡r❣❡♥❝②✳ ❉✐✈✐❞❡♥❞ ♣r✐❝❡s ❛❧s♦ ✐♥❝r❡❛s❡ ♦♥ t❤✐s ❞❛②✱ ❜✉t ♦♥❧② ❛t t❤❡ ❧♦♥❣ ❡♥❞✳ ❚❤❡ ❜♦tt♦♠ ❧❡❢t ❝♦r♥❡r s❤♦✇s t❤❡ ❝❤❛♥❣❡ ✐♥ ♣r✐❝❡s ❢r♦♠ ❏❛♥✉❛r② ✶ t♦ ▼❛r❝❤ ✷✻✳ ▼❛r❝❤ ✷✺✱ ❈♦♥❣r❡ss ❝♦♠❡s ❝❧♦s❡ t♦ ♣❛ss✐♥❣ ❛ ✶✳✽ tr✐❧❧✐♦♥ ❞♦❧❧❛r ✜s❝❛❧ st✐♠✉❧✉s ❜✐❧❧✳ ❖♥ ❙t♦❝❦ ♠❛r❦❡ts s♦❛r ❛❧r❡❛❞② ♦♥ t❤❡ ▼❛r❝❤ ✷✹ ❢♦❧❧♦✇✐♥❣ ♥❡✇s ♦❢ t❤❡ ❜✐❧❧ ❛♥❞ ❢✉rt❤❡r ♠♦♥❡t❛r② ♣♦❧✐❝② ❛❝t✐♦♥s✳ ✾ ❖✈❡r❛❧❧✱ st♦❝❦ ♠❛r❦❡ts ✐♥❝r❡❛s❡ ❜② ❛r♦✉♥❞ ✶✵✪ ❢r♦♠ ▼❛r❝❤ ✷✵ t♦ ▼❛r❝❤ ✷✻✱ ♣r❡s✉♠❛❜❧② ❞r✐✈❡♥ ❜② t❤❡s❡ ❣♦✈❡r♥♠❡♥t ✐♥t❡r✈❡♥t✐♦♥s✳ ✶✵ ❍♦✇❡✈❡r✱ t❤❡ s❤♦rt✲t❡r♠ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛❝t✉❛❧❧② ❞❡❝r❡❛s❡ s❧✐❣❤t❧② ♦✈❡r t❤✐s ♣❡r✐♦❞✳ ❚❤✐s ✜♥❞✐♥❣ ✐♠♣❧✐❡s t❤❛t ✜s❝❛❧ st✐♠✉❧✉s ❧✐❢t❡❞ t❤❡ st♦❝❦ ♠❛r❦❡t ❜② ❧✐❢t✐♥❣ t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✱ ♥♦t ❜② ✐♠♣r♦✈✐♥❣ ♣r✐❝❡s ♦❢ ♥❡❛r✲t❡r♠ ❝❛s❤ ✢♦✇s✳ ❋✐♥❛❧❧②✱ t❤❡ ❜♦tt♦♠ r✐❣❤t ❝♦r♥❡r s❤♦✇s t❤❡ ❝❤❛♥❣❡ ✐♥ ♣r✐❝❡ ❢r♦♠ ❏❛♥✉❛r② ✶ t♦ ❏✉❧② ✷✵✳ ❉✐✈✐❞❡♥❞ ♣r✐❝❡s ✐♥❝r❡❛s❡s ♦✈❡r❛❧❧ ❜❡t✇❡❡♥ ▼❛r❝❤ ✷✻ ❛♥❞ ❏✉❧② ✷✵✳ ❙t♦❝❦ ♣r✐❝❡s ❛❧s♦ ✐♥❝r❡❛s❡ s✉❜st❛♥t✐❛❧❧② ♦✈❡r t❤✐s ♣❡r✐♦❞✱ ✇✐t❤ t❤❡ ❙✫P ✺✵✵ ❛❧♠♦st r❡t✉r♥✐♥❣ t♦ t❤❡ ❧❡✈❡❧ ♦❢ ❏❛♥✉❛r② ✶ ✷✵✷✵✳ ✾ ❤tt♣s✿✴✴✇✇✇✳❢❡❞❡r❛❧r❡s❡r✈❡✳❣♦✈✴♥❡✇s❡✈❡♥ts✴♣r❡ssr❡❧❡❛s❡s✴♠♦♥❡t❛r②✷✵✷✵✵✸✷✸❜✳❤t♠✳ ✶✵ ❈♦♥❣r❡ss ✐s ❛❧s♦ r✉♠♦r❡❞ t♦ ✐♥❝❧✉❞❡ ❛ ❜❛♥ ♦♥ ♣❛②✐♥❣ ❞✐✈✐❞❡♥❞s ✉♥t✐❧ ❙❡♣t❡♠❜❡r ✷✵✷✵ ❢♦r ✜r♠s r❡❝❡✐✈✐♥❣ ✜♥❛♥❝✐❛❧ s✉♣♣♦rt✱ s♦♠❡t❤✐♥❣ t❤❛t ✐s ❧✐❦❡❧② t♦ ❞❡❝r❡❛s❡ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ✷✵✷✵ ❞✐✈✐❞❡♥❞ ❝❧❛✐♠ ❜✉t ❤❛s ❧❡ss ♦❢ ❛♥ ✐♠♣❛❝t ♦♥ t❤❡ ✷✲②❡❛r ❝❧❛✐♠✳ ✾ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✷✿ ❚❤❡ ❉❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❉✐✈✐❞❡♥❞ ❚❡r♠ ❙tr✉❝t✉r❡ ♦✈❡r t❤❡ ❈❖❱■❉✲✶✾ ❖✉t❜r❡❛❦ ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ r❡❧❛t✐✈❡ ♣r✐❝❡ ♦❢ ❞✐✈✐❞❡♥❞ ♦❢ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ✇✐t❤ ❞✐✛❡r❡♥t ♠❛t✉r✐t②✳ ❲❡ ❝♦♥s✐❞❡r t❤❡ ♣❡r❝❡♥t❛❣❡ ❝❤❛♥❣❡ ✐♥ ♣r✐❝❡s s✐♥❝❡ ❏❛♥✉❛r② ✶✳ ❚❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛r❡ ❝❧❛✐♠s ♦♥ t❤❡ ❞✐✈✐❞❡♥❞ ♣❛✐❞ ♦✉t ♦♥ t❤❡ ✐♥❞❡① ✐♥ ❛ ❣✐✈❡♥ ②❡❛r✳ ❲❡ ❝♦♥s✐❞❡r t❤❡ ❙✫P ✺✵✵ ✐♥❞❡①✱ t❤❡ ❊✉r♦ ❙t♦①① ✺✵ ✐♥❞❡①✱ ❛♥❞ t❤❡ ◆✐❦❦❡✐ ✷✷✺ ✐♥❞❡①✳ ▼❛t✉r✐t② ♠❡❛s✉r❡❞ ♦♥ t❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s ❡①♣r❡ss❡❞ ✐♥ ②❡❛rs✳ ❋♦r ✐♥st❛♥❝❡✱ t❤❡ t♦♣ ❧❡❢t ✜❣✉r❡ s❤♦✇s t❤❛t✱ ❜❡t✇❡❡♥ ❏❛♥✉❛r② ✶ ❛♥❞ ▼❛r❝❤ ✺✱ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ♣r✐❝❡s ❢❛❧❧ ❜② ♦♥❧② ❛ ❢❡✇ ♣❡r❝❡♥t ❢♦r t❤❡ ✶✲②❡❛r ❝❧❛✐♠ ❜✉t ❜② ❛s ♠✉❝❤ ❛s ✶✵✪ ❢♦r t❤❡ ✼✲②❡❛r ❝❧❛✐♠✳ ✶✵ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✼✿ ❈②❝❧✐❝❛❧ ❝♦♠♣♦♥❡♥ts ♦❢ ❧♦❣ r❡❛❧ ❞✐✈✐❞❡♥❞s ❛♥❞ ❧♦❣ r❡❛❧ ●❉P✳ Dividends GDP -1 -2 -3 -4 1985 1990 1995 2000 2005 2010 2015 2020 (n) Et [∆n Yit ] − ≥ ∆Fi,t − × bi , ✭✹✮ Et [∆n Yit ] ✐s t❤❡ ❝❤❛♥❣❡ ✐♥ ❡①♣❡❝t❡❞ ●❉P ❣r♦✇t❤ ❛t ❤♦r✐③♦♥ ♥ ❢♦r ❝♦✉♥tr② ✐✳ ❚❤❡ ❝♦♥st❛♥t bi ♠❡❛s✉r❡s ❤♦✇ ♠✉❝❤ ●❉P ❝❤❛♥❣❡s ✇❤❡♥ ❞✐✈✐❞❡♥❞s ❝❤❛♥❣❡✳ ❖♥❡ ✇❛② t♦ ❡st✐♠❛t❡ bi ✐s t♦ r❡❣r❡ss ●❉P ❣r♦✇t❤ ♦♥ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✳ ❍♦✇❡✈❡r✱ t❤✐s ❡st✐♠❛t❡ ✐s ❧✐❦❡❧② t♦ ❜❡ ✇❤❡r❡ ❜✐❛s❡❞ ❞♦✇♥✇❛r❞s ❞✉❡ t♦ ❛s②♥❝❤r♦♥✐❝✐t✐❡s ❜❡t✇❡❡♥ t❤❡ s❡r✐❡s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✼ ❛♥❞ ♦t❤❡r ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛t✐♦♥ ✐♥ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✳ ❆ ❞♦✇♥✇❛r❞ ❜✐❛s ✐♥ bi ✇♦✉❧❞ ❜❡ ♣r♦❜❧❡♠❛t✐❝ ❛s ✐t ❧❡❛❞s t♦ ❛♥ ✉♣✇❛r❞ ❜✐❛s ✐♥ ♦✉r ❧♦✇❡r ❜♦✉♥❞ ❞✉r✐♥❣ ❡❝♦♥♦♠✐❝ ❞♦✇♥t✉r♥s✳ ❚♦ ❡♥s✉r❡ t❤❛t ♦✉r ❧♦✇❡r ❜♦✉♥❞ ✐s ❝♦♥s❡r✈❛t✐✈❡✱ ✇❡ ✐♥st❡❛❞ r✉♥ t❤❡ r❡❣r❡ss✐♦♥ ∆1 Dit = a0i + a1i ∆1 Yit + εt+4 , ❛♥❞ ✉s❡ bi = ✳ a1i ✭✺✮ ■♥ t❤✐s ✇❛②✱ ❛s②♥❝❤r♦♥✐❝✐t✐❡s ❜❡t✇❡❡♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞s✱ ❛♥❞ ♦t❤❡r ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛t✐♦♥ ✐♥ ●❉P✱ ❧❡❛❞s t♦ ❛ ❧♦✇❡r ❡st✐♠❛t❡ ♦❢ ❛♥❞ ❛ ❤✐❣❤❡r ❡st✐♠❛t❡ ♦❢ ❚❤✐s r❡s✉❧ts ✐♥ ❛ ♠♦r❡ ❝♦♥s❡r✈❛t✐✈❡ ❧♦✇❡r ❜♦✉♥❞✳ ✷✵ Electronic copy available at: https://ssrn.com/abstract=3555917 bi ✳ ❲❡ r✉♥ s❡♣❛r❛t❡ r❡❣r❡ss✐♦♥s ✐♥ t❤❡ ❯❙✱ t❤❡ ❊❯✱ ❛♥❞ ❏❛♣❛♥✳ ■♥ t❤❡ ❯❙✱ ✇❡ ✉s❡ t❤❡ ✶✾✽✺ t♦ ✷✵✶✾ s❛♠♣❧❡ ♦❢ r❡❛❧ ❣r♦✇t❤ ✐♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞s✳ ■♥ t❤❡ ❊❯✱ ✇❡ ✉s❡ ❛ s❤♦rt❡r ✷✵✵✸ t♦ ✷✵✶✾ s❛♠♣❧❡ ♦❢ r❡❛❧ ❣r♦✇t❤ ✐♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞s ♦♥ t❤❡ ❊✉r♦ ❙t♦①① ✺✵✳ ■♥ ❏❛♣❛♥✱ ✇❡ ✉s❡ t❤❡ ✶✾✾✺✲✷✵✶✾ s❛♠♣❧❡✳ ❲❡ ✉s❡ r❡❛❧ s❡r✐❡s t♦ ❛✈♦✐❞ ♣✉tt✐♥❣ t♦♦ ♠✉❝❤ ✇❡✐❣❤t ♦♥ t❤❡ ❡❛r❧② ❯❙ s❛♠♣❧❡ ✇✐t❤ ❤✐❣❤ ✐♥✢❛t✐♦♥✳ ✱ ❊❯ ❛♥❞ ✵✳✹✻ ✐♥ ❏❛♣❛♥ ✶✺ ❚❤❡ r❡s✉❧t✐♥❣ ❡st✐♠❛t❡s ♦❢ bi ❛r❡ ✵✳✻✼ ✐♥ t❤❡ ❯❙✱ ✵✳✸✸ ✐♥ t❤❡ ✳ ❚❤❡ ❧♦✇❡r ❜♦✉♥❞ ✐s ♣❧♦tt❡❞ ✐♥ ❋✐❣✉r❡ ✽✳ ❚❤❡ ❧♦✇❡r ❜♦✉♥❞ s✉❣❣❡st ❛ ❞❡❝❧✐♥❡ ✐♥ ●❉P ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ♦❢ ✼✪ ✐♥ ❏❛♣❛♥✱ ✽✪ ✐♥ t❤❡ ❯❙ ❛♥❞ s❧✐❣❤t❧② ♠♦r❡ t❤❛♥ ✶✵✪ ✐♥ t❤❡ ❊❯✳ ❆s ❛ ♣♦✐♥t ♦❢ r❡❢❡r❡♥❝❡✱ ✇❡ ❝♦♠♣❛r❡ t❤❡s❡ ❡st✐♠❛t❡s t♦ ❇❛❦❡r ❡t ❛❧✳ ✭✷✵✷✵❜✮✳ ❚❤❡② ✉s❡ ❡st✐♠❛t❡s ❢r♦♠ ❇❛❦❡r ❡t ❛❧✳ ✭✷✵✷✵❛✮ ❛♥❞ ❝❛❧✐❜r❛t❡ ✐t t♦ t❤❡ ❈❖❱■❉✲✶✾ s❤♦❝❦ ✐♥ t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ✐ts ✈♦❧❛t✐❧✐t②✱ ❛♥❞ ♣r❡❞✐❝t ❛ ②❡❛r✲♦♥✲②❡❛r ❝♦♥tr❛❝t✐♦♥ ✐♥ ♦✉t♣✉t ♦❢ ✶✶✪ ✐♥ ✷✵✷✵◗✹✱ ✇❤✐❝❤ ✐s s❧✐❣❤t❧② ♠♦r❡ ♥❡❣❛t✐✈❡ t❤❛♥ ♦✉r ❧♦✇❡r ❜♦✉♥❞ ✐♠♣❧✐❡❞ ❜② ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s✳ ✹✳✸ ●❉P ●r♦✇t❤ ❊①♣❡❝t❛t✐♦♥s ❚♦ ❡st✐♠❛t❡ ●❉P ❡①♣❡❝t❛t✐♦♥s✱ ✇❡ ❝♦✉❧❞ ❢♦❧❧♦✇ t❤❡ ♣r♦❝❡❞✉r❡ ♦❢ s❡❝t✐♦♥ ✸✳✸ ❛♥❞ ✉s❡ t❤❡ ❡q✉✐t② ②✐❡❧❞s t♦ ❢♦r❡❝❛st ●❉P ❣r♦✇t❤✳ ❍♦✇❡✈❡r✱ t♦ ♦❜t❛✐♥ t❤❡ ♠♦st ❛❝❝✉r❛t❡ ❡st✐♠❛t❡✱ ✇❡ ✇❛♥t t♦ ❛❝❝♦✉♥t ❢♦r ✭✐✮ t❤❡ s♠❛❧❧ ❛s②♥❝❤r♦♥✐❝✐t✐❡s ❜❡t✇❡❡♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞s ❞♦❝✉♠❡♥t❡❞ ✐♥ ❋✐❣✉r❡ ✼ ❛♥❞ ✭✐✐✮ t❤❡ ♣♦t❡♥t✐❛❧❧② str♦♥❣❡r r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ t✇♦ s❡r✐❡s ✇❤❡♥ ❣r♦✇t❤ ✐s ❜❡❧♦✇ ❛✈❡r❛❣❡✱ ✇❤✐❝❤ ♠♦st ❝❧♦s❡❧② ♠✐♠✐❝s t❤❡ ❝✉rr❡♥t s✐t✉❛t✐♦♥✳ ❚❤❡ s❛♠♣❧❡ ✇✐t❤ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ✐s t♦♦ s❤♦rt t♦ ❡✛❡❝t✐✈❡❧② ❞❡❛❧ ✇✐t❤ t❤❡s❡ ✐ss✉❡s ❛♥❞ ✇❡ t❤❡r❡❢♦r❡ ♣r❡❢❡r ❛ s❧✐❣❤t❧② ❞✐✛❡r❡♥t ❛♣♣r♦❛❝❤✳ ❲❡ ✜rst ✉s❡ t❤❡ ❧♦♥❣ ❯❙ s❛♠♣❧❡ t♦ ♠❛♣ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ✐♥t♦ ●❉P ❣r♦✇t❤✱ ❛♥❞ ✇❡ t❤❡♥ ✉s❡ t❤✐s ♠❛♣♣✐♥❣ t♦ tr❛♥s❢♦r♠ ♦✉r ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❢r♦♠ s❡❝t✐♦♥ ✸✳✸ ✐♥t♦ ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t ●❉P ❣r♦✇t❤✳ ❲❡ ♥♦t❡ t❤❛t ♦♥❡ ❝♦✉❧❞ ♠❛❦❡ ♦t❤❡r r❡❛s♦♥❛❜❧❡ ♠♦❞❡❧✐♥❣ ❛ss✉♠♣t✐♦♥s t❤❛t ♠❛② ❧❡❛❞ t♦ ❞✐✛❡r❡♥t ❡st✐♠❛t❡s✳ ❲❡ ✜rst ♠❛♣ r❡❛❧ ●❉P ❣r♦✇t❤ t♦ r❡❛❧ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ✉s✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ r❡❣r❡ss✐♦♥ ✐♥ t❤❡ ✶✾✽✺✲✷✵✶✾ ❯❙ s❛♠♣❧❡✿ ∆n Yt = An + Bn ∆n Dt + et+4n , ♦♥❧② ✉s✐♥❣ ❞❛t❛ ✇❤❡♥ ∆n Dt < ∆n Dt ✱ ✇✐t❤ x¯ ≡ T t xt , ❛♥❞ Yt ❞❡♥♦t✐♥❣ r❡❛❧ ●❉P✳ ❚❤❡r❡ ❛r❡ t✇♦ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡s ♦❢ t❤✐s r❡❣r❡ss✐♦♥✳ ❋✐rst✱ ❜② ♦♥❧② ❝♦♥s✐❞❡r✐♥❣ ♦❜s❡r✈❛t✐♦♥s ✇❤❡r❡ r❡❛❧✐③❡❞ ❣r♦✇t❤ ✐s ❜❡❧♦✇ ❛✈❡r❛❣❡✱ ✇❡ ❡st✐♠❛t❡ t❤❡ ❞♦✇♥s✐❞❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ t✇♦ s❡r✐❡s✱ ✶✺ ❚❤❡ ❧♦✇❡r ❜♦✉♥❞ ✐s ♥♦♥❡t❤❡❧❡ss st✐❧❧ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ♥♦♠✐♥❛❧ ❣r♦✇t❤✳ ✷✶ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✽✿ ❆ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ●❉P ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❜② ♠❛t✉r✐t② ❛s ✐♠♣❧✐❡❞ ❜② ❞✐✈✐❞❡♥❞ ♠❛r❦❡ts ❚❤❡ ✜❣✉r❡ s❤♦✇s ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ❝❤❛♥❣❡s ✐♥ ❡①♣❡❝t❡❞ ●❉P ❛t t❤❡ ✶ t♦ ✼✲②❡❛r ❤♦r✐③♦♥✳ ❚❤❡ ❝❤❛♥❣❡s ❛r❡ ♠❡❛s✉r❡❞ r❡❧❛t✐✈❡ t♦ ❡①♣❡❝t❛t✐♦♥s ♦♥ ❏❛♥✉❛r② ✶✳ ❚❤❡ ✜❣✉r❡ s❤♦✇s t❤❛t ❡①♣❡❝t❡❞ ●❉P ♠❛② ❤❛✈❡ ❜❡❡♥ r❡✈✐s❡❞ ❞♦✇♥ ❜② ❛s ♠✉❝❤ ❛s ✶✷✪ ✐♥ t❤❡ ❯❙✱ ✶✶✪ ✐♥ t❤❡ ❊❯✱ ❛♥❞ ✽✪ ✐♥ ❏❛♣❛♥✳ ■t ✐s r❡✈✐s❡❞ ❞♦✇♥ t❤❡ ♠♦st ♦♥ t❤❡ ✶✲ t♦ ✷✲②❡❛r ❤♦r✐③♦♥✳ ❚❤✐s ❡st✐♠❛t❡ ✐s ❛ ❧♦✇❡r ❜♦✉♥❞ ♠❡❛♥✐♥❣ ❛❝t✉❛❧ ❡①♣❡❝t❛t✐♦♥s ❛r❡ ❧✐❦❡❧② ❜❡ ❤✐❣❤❡r ✭s❡❡ t❡①t ❢♦r ❞❡s❝r✐♣t✐♦♥✮✳ ✷✷ Electronic copy available at: https://ssrn.com/abstract=3555917 ✇❤✐❝❤ ✐s ✇❤❛t ✐s r❡❧❡✈❛♥t ✐♥ ♦✉r ❝♦♥t❡①t✳ ❙❡❝♦♥❞✱ ❜② ✉s✐♥❣ ❧♦♥❣❡r ❤♦r✐③♦♥s✱ ♥✱ ✇❡ ❝❛♥ ♠✐t✐❣❛t❡ t❤❡ ❡✛❡❝t ♦❢ s♠❛❧❧ ❛s②♥❝❤r♦♥✐❝✐t✐❡s✳ ❆s ♦✉r ❜❡♥❝❤♠❛r❦ ❝❛s❡✱ ✇❡ ❡st✐♠❛t❡ Bn ✉s✐♥❣ ✷✲②❡❛r ❣r♦✇t❤ ✭n = 2✮ ✐♥ t❤❡ ✶✾✽✺ t♦ ✷✵✶✾ ❯❙ s❛♠♣❧❡✳ ❚❤❡ ❜❛s❡❧✐♥❡ ❡st✐♠❛t❡ ✐s ✵✳✷✷✱ ♠❡❛♥✐♥❣ t❤❛t ❞✐✈✐❞❡♥❞s ♠♦✈❡ ❛♣♣r♦①✐♠❛t❡❧② ❢♦✉r t✐♠❡s ❛s ♠✉❝❤ ❛s ●❉P ✐♥ ❞♦✇♥t✉r♥s ✭s❡❡ ❚❛❜❧❡ ✷ ✐♥ t❤❡ ❆♣♣❡♥❞✐① ❢♦r ❞❡t❛✐❧s✮✳ ❚❤❡ ❜❛s❡❧✐♥❡ ❡st✐♠❛t❡ ✐s r♦❜✉st t♦ ✉s✐♥❣ ❛ ❧♦♥❣❡r s❛♠♣❧❡ ♣❡r✐♦❞ ❛♥❞ t♦ ✉s✐♥❣ ✸✲ ✐♥st❡❛❞ ♦❢ ✷✲②❡❛r ❣r♦✇t❤✱ ❛s r❡♣♦rt❡❞ ✐♥ t❤❡ ❆♣♣❡♥❞✐① ❇✳ ❚❤❡ ❡st✐♠❛t❡ ✐s ❧♦✇❡r ✐❢ ✇❡ ❝♦♥s✐❞❡r ✶✲②❡❛r ❣r♦✇t❤✱ ✇❤✐❝❤ ✐❧❧✉str❛t❡s ♦♥❝❡ ♠♦r❡ t❤❛t ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❛r❡ ♥♦t ♣❡r❢❡❝t❧② s②♥❝❤r♦♥✐③❡❞✳ ■❢ ✇❡ ❝♦♥s✐❞❡r t❤❡ ✉♥❝♦♥❞✐t✐♦♥❛❧ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✱ t❤❡ s❧♦♣❡ ❝♦❡✣❝✐❡♥t ✐s ♦♥❧② ❤❛❧❢ ❛s ❧❛r❣❡✱ s✉❣❣❡st✐♥❣ ❛ ✇❡❛❦❡r ✉♣s✐❞❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✳ ❍❛✈✐♥❣ ❡st✐♠❛t❡❞ t❤❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ●❉P ❛♥❞ ❞✐✈✐❞❡♥❞s✱ ✇❡ ❢♦r❡❝❛st ●❉P ❣r♦✇t❤ ❛s✿ (2) Et [∆1 Yit ] = Ai + B2 β1D ei,t , ✇❤❡r❡ t❤❡ Ai ✐s ✐rr❡❧❡✈❛♥t ❛s ✇❡ ❢♦r❡❝❛st t❤❡ ❝❤❛♥❣❡ ✐♥ ❡①♣❡❝t❛t✐♦♥s s✐♥❝❡ ❏❛♥✉❛r② ✷✵✷✵✱ ✇❤✐❝❤ ♦♥❧② ❞❡♣❡♥❞s ♦♥ t❤❡ s❧♦♣❡ ❝♦❡✣❝✐❡♥ts ❛♥❞ t❤❡ ❡q✉✐t② ②✐❡❧❞✳ ❲❡ ✉s❡ t❤❡ s❛♠❡ ❡st✐♠❛t❡ ♦❢ Bn ✱ ✇❤✐❝❤ ✐s ❜❛s❡❞ ♦♥ ❯❙ ❞❛t❛✱ ❢♦r t❤❡ ❯❙✱ t❤❡ ❊❯✱ ❛♥❞ ❏❛♣❛♥✱ ❛s ✇❡ ❤❛✈❡ ❛ ❧♦♥❣❡r s❛♠♣❧❡ ❛✈❛✐❧❛❜❧❡ ❢♦r t❤❡ ❯❙✳ ❲❡ ❡♠♣❤❛s✐③❡ ♦♥❝❡ ♠♦r❡ t❤❛t t❤❡s❡ ❡st✐♠❛t❡s ❛r❡ ❜❛s❡❞ ♦♥ ❛ ❢♦r❡❝❛st✐♥❣ ♠♦❞❡❧ ❡st✐♠❛t❡❞ ✉s✐♥❣ ❤✐st♦r✐❝❛❧ ❞❛t❛✳ ■♥ ✉♥♣r❡❝❡❞❡♥t❡❞ t✐♠❡s✱ t❤❡r❡ ✐s ❛ r✐s❦ t❤❛t ❤✐st♦r✐❝❛❧ r❡❧❛t✐♦♥s ❝❤❛♥❣❡✱ ✐♠♣❧②✐♥❣ t❤❛t t❤❡s❡ ❡st✐♠❛t❡s ❝♦♠❡ ✇✐t❤ ✉♥❝❡rt❛✐♥t②✳ ❚❤❡ r✐❣❤t ♣❛♥❡❧ ♦❢ ❋✐❣✉r❡ ✺ s❤♦✇s t❤❡ ❞②♥❛♠✐❝s ♦❢ ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ✐♥ t❤❡ ❯❙✱ t❤❡ ❊❯✱ ❛♥❞ ❏❛♣❛♥ ✉♥t✐❧ ❏✉❧② ✷✵✳ ❚❤❡ t✉r♥✐♥❣ ♣♦✐♥ts ❛r❡✱ ❜② ❞❡s✐❣♥✱ t❤❡ s❛♠❡ ❛s ❢♦r ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✳ ❲❤❡♥ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛r❡ ❛t t❤❡✐r ❧♦✇❡st ♣♦✐♥t ❛t t❤❡ ❡♥❞ ♦❢ ▼❛r❝❤✱ ●❉P ❣r♦✇t❤ ✐s ❡①♣❡❝t❡❞ t♦ ❞❡❝❧✐♥❡ ❜② ❛❧♠♦st ✽✪ ✐♥ t❤❡ ❊❯✱ ❝❧♦s❡ t♦ ✻✪ ✐♥ t❤❡ ❯❙✱ ❛♥❞ ❛❧♠♦st ✺✪ ✐♥ ❏❛♣❛♥✳ ❆s t❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s r❡❝♦✈❡r❡❞ s✐♥❝❡ t❤❡♥✱ t❤❡ ❡st✐♠❛t❡ ♦❢ ●❉P ❣r♦✇t❤ ♦✈❡r t❤❡ ♥❡①t ②❡❛r ✐s ❞♦✇♥ ❜② ✷✪ ✐♥ t❤❡ ❯❙ ❛♥❞ ❏❛♣❛♥ ❛♥❞ ✸✪ ✐♥ t❤❡ ❊❯ ❜② ❏✉❧② ✷✵✳ ✶✻ ❆♥ ✶✻ ❛❞❞✐t✐♦♥❛❧ r❡❛s♦♥ ❢♦r t❤❡ ❝❤❛♥❣✐♥❣ ❧✐♥❦ ❜❡t✇❡❡♥ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛♥❞ ❢✉t✉r❡ ●❉P ❣r♦✇t❤ ✐s t❤❛t ❣♦✈❡r♥♠❡♥ts ❛♥❞ r❡❣✉❧❛t♦rs ♠❛② ✐♠♣♦s❡ r❡str✐❝t✐♦♥s ♦♥ ✜r♠s✬ ♣❛②♦✉t ♣♦❧✐❝✐❡s ✐♥ r❡t✉r♥ ❢♦r ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ♦r t♦ s❛❢❡❣✉❛r❞ t❤❡ ✜♥❛♥❝✐❛❧ s②st❡♠ ✐♥ ❝❛s❡ ♦❢ ❜❛♥❦s ❛♥❞ ✐♥s✉r❛♥❝❡ ❝♦♠♣❛♥✐❡s✳ ✷✸ Electronic copy available at: https://ssrn.com/abstract=3555917 ✺ ❘❡❝♦♥❝✐❧✐♥❣ t❤❡ Pr✐❝❡ ♦❢ t❤❡ ❙t♦❝❦ ▼❛r❦❡t ✇✐t❤ ❉✐✈✐✲ ❞❡♥❞ ❙tr✐♣ Pr✐❝❡s ❲❡ ✉s❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s t♦ ❧❡❛r♥ ❛❜♦✉t t❤❡ ♣r✐❝✐♥❣ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ✐♥ ♣❛rt✐❝✉❧❛r ❤♦✇ ✐t ❞❡✈❡❧♦♣❡❞ ❞✉r✐♥❣ t❤❡ ❈❖❱■❉✲✶✾ ❝r✐s✐s✳ ❚♦ t❤✐s ❡♥❞✱ ✇❡ ✜t ❛ s✐♠♣❧❡ ♠♦❞❡❧ ❢♦r ❞✐✈✐❞❡♥❞ ♣r✐❝❡s t❤❛t ✇❡ r❡q✉✐r❡ t♦ s✐♠✉❧t❛♥❡♦✉s❧② ♣r✐❝❡ t❤❡ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❛s ✇❡❧❧ ❛s t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t✳ ❙t❛rt✐♥❣ ❢r♦♠ ✭✶✮✱ ✇❡ ♦❜s❡r✈❡ t❤❡ ❞✐✈✐❞❡♥❞ ♣r✐❝❡s ❢♦r t❤❡ ✜rst ✶✵ ②❡❛rs ❛♥❞ ✇❡ ♦❜s❡r✈❡ St ❲❡ ♠♦❞❡❧ ❡①♣❡❝t❡❞ ❣r♦✇t❤ ♠✐♥✉s t❤❡ ❡①♣❡❝t❡❞ ❡①❝❡ss r❡t✉r♥✱ gtn − θtn ✱ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ♠❛t✉r✐t②✳ ❚❤❡ ❢✉♥❝t✐♦♥❛❧ ❢♦r♠ t❤❛t ✇❡ ✜t ✐♥ ❡❛❝❤ ♣❡r✐♦❞ ❢♦❧❧♦✇s ◆❡❧s♦♥ ❛♥❞ ❙✐❡❣❡❧ ✭✶✾✽✼✮✳ ❚❤❡ r❡s✉❧ts ❢♦r t❤❡ ❙✫P ✺✵✵ ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❋✐❣✉r❡ ✾✳ ■♥ t❤❡ ✐♥✐t✐❛❧ ♣❤❛s❡ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t ❞r♦♣✱ ❢r♦♠ t❤❡ ♣❡❛❦ ♦♥ ❋❡❜r✉❛r② ✶✾ t♦ ▼❛r❝❤ ✺✱ t❤❡ ♠❛r❦❡t ❞❡❝❧✐♥❡s ❞✉❡ t♦ ❛ ❞r♦♣ ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✳ ❆s ✇❡ ♠❛✐♥t❛✐♥ t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t ❞✐st❛♥t✲ ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❛r❡ ❡①♣❡❝t❡❞ t♦ ❢❛❧❧ ❧❡ss t❤❛♥ ♥❡❛r✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❜❡❝❛✉s❡ ♦❢ t❤❡ ♥❛t✉r❡ ♦❢ ♣❛♥❞❡♠✐❝s✱ t❤❡ ❧❛r❣❡ ❞r♦♣ ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❝❛♥♥♦t ❝♦♠❡ ❢r♦♠ ❞❡❝r❡❛s❡s ✐♥ ❡①♣❡❝t❡❞ ❞✐✈✐❞❡♥❞s ❜✉t ♠✉st ✐♥st❡❛❞ ❜❡ ❞✉❡ t♦ ❛♥ ✐♥❝r❡❛s❡ ✐♥ ❞✐s❝♦✉♥t r❛t❡s✳ ❙✉❝❤ ✐♥❝r❡❛s❡s ✐♥ ❞✐s❝♦✉♥t r❛t❡s ♦♥ ❞✐st❛♥t✲❢✉t✉r❡ ❝❧❛✐♠s ✐s ❝♦♠♠♦♥❧② ♦❜s❡r✈❡❞ ❞✉r✐♥❣ t✐♠❡s ♦❢ str❡ss ✭●♦r♠s❡♥ ✭✷✵✷✵✮✮✳ ❋r♦♠ ▼❛r❝❤ ✺ t♦ ✶✷✱ ❛ ♣❡r✐♦❞ ✐♥ ✇❤✐❝❤ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❝❤❛♥❣❡❞ s❤❛r♣❧②✱ ✇❡ s❡❡ t❤❛t ♣r✐❝❡s ♦♥ ❜♦t❤ ♥❡❛r✲ ❛♥❞ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❢❛❧❧ s❤❛r♣❧②✳ ❋✐♥❛❧❧②✱ ❢r♦♠ ▼❛r❝❤ ✶✷ t♦ ❏✉❧② ✷✵✱ ❛ ♣❡r✐♦❞ ❞✉r✐♥❣ ✇❤✐❝❤ t❤❡ st♦❝❦ ♠❛r❦❡t r❡❝♦✈❡rs✱ ✇❡ s❡❡ t❤❛t t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ✐♥❝r❡❛s❡s✱ ✇❤❡r❡❛s t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ✈❡r② ♥❡❛r✲ ❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❝♦♥t✐♥✉❡s t♦ ❞❡❝r❡❛s❡✳ ❙✐♥❝❡ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❧❛r❣❡❧② r❡t✉r♥s t♦ ♣r❡✲❝r✐s✐s ❧❡✈❡❧s✱ ✐t s❡❡♠s r❡❛s♦♥❛❜❧❡ t♦ ❝♦♥❥❡❝t✉r❡ t❤❛t t❤❡ ❞✐s❝♦✉♥t r❛t❡s ♦♥ t❤❡s❡ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❛❧s♦ ❤❛✈❡ r❡t✉r♥❡❞ t♦ ♣r❡✲❝r✐s✐s ❧❡✈❡❧s✳ ❚❛❦❡♥ t♦❣❡t❤❡r✱ ❋✐❣✉r❡ ✾ ✐❧❧✉str❛t❡s ❤♦✇ t❤❡ ❝r❛s❤ ♦❢ t❤❡ st♦❝❦ ♠❛r❦❡t ✇❛s ❞r✐✈❡♥ ❜② ❛ ❞r♦♣ ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ ❜♦t❤ t❤❡ ♥❡❛r✲ ❛♥❞ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✱ ✇❤❡r❡❛s t❤❡ r❡❜♦✉♥❞ ✇❛s ❞r✐✈❡♥ ❧❛r❣❡❧② ❜② ❛ r❡❝♦✈❡r② ✐♥ t❤❡ ✈❛❧✉❡ ♦❢ ❞✐st❛♥t✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s✳ ❲❡ ♣r♦✈✐❞❡ s✐♠✐❧❛r ❛♥❛❧②s✐s ❢♦r ❊✉r♦ ❙t♦①① ✺✵ ❛♥❞ ◆✐❦❦❡✐ ✷✷✺ ✐♥ ❋✐❣✉r❡ ✶✷ ✐♥ t❤❡ ❆♣♣❡♥❞✐①✳ ❚❤❡s❡ r❡s✉❧ts ❤❛✈❡ ✐♠♣❧✐❝❛t✐♦♥s ❢♦r ❛ss❡t ♣r✐❝✐♥❣ t❤❡♦r✐❡s✳ ■t ✐s ✇❡❧❧ ❦♥♦✇♥ t❤❛t ✐t ✐s ♦❢t❡♥t✐♠❡s ❞✐✣❝✉❧t t♦ ✐❞❡♥t✐❢② t❤❡ ❡❝♦♥♦♠✐❝ s❤♦❝❦s t❤❛t ❝❛✉s❡❞ ❛ss❡t ♣r✐❝❡s t♦ ♠♦✈❡ ✭❈✉t❧❡r ❡t ❛❧✳ ✭✶✾✽✾✮✮✳ ❚❤❡ ✉♥✐q✉❡ ❢❡❛t✉r❡ ♦❢ t❤❡ ♦♥❣♦✐♥❣ ❡✈❡♥ts ✐s t❤❛t t❤❡ ♥❛t✉r❡ ♦❢ t❤❡ s❤♦❝❦ ✷✹ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✾✿ ❘❡❝♦♥❝✐❧✐♥❣ t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ❞✐✈✐❞❡♥❞ ♣r✐❝❡ r❡s♣♦♥s❡s ❚❤✐s ✜❣✉r❡ s❤♦✇s ❡st✐♠❛t❡❞ ♣r✐❝❡s ♦❢ ❞✐✈✐❞❡♥❞s ❢♦r ❞✐✛❡r❡♥t ♠❛t✉r✐t②✳ ❲❡ ✜t t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❞✐✈✐❞❡♥❞ ♣r✐❝❡s t♦ t❤❡ ❢✉♥❝t✐♦♥❛❧ ❢♦r♠ ♦♥ ◆❡❧s♦♥ ❛♥❞ ❙✐❡❣❡❧ ✭✶✾✽✼✮ ✉♥❞❡r t❤❡ r❡str✐❝t✐♦♥ t❤❛t t❤❡ ♣r✐❝❡ ♦❢ ❛❧❧ t❤❡ ❞✐✈✐❞❡♥❞s s✉♠ t♦ t❤❡ ♠❛r❦❡t✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ♣r✐❝❡s s❡♣❛r❛t❡❧② ♦♥ ❋❡❜r✉❛r② ✶✾✱ ▼❛r❝❤ ✺✱ ▼❛r❝❤ ✶✷✱ ❛♥❞ ❏✉❧② ✷✵✳ ▼❛t✉r✐t② ♠❡❛s✉r❡❞ ♦♥ t❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s ✐♥ ②❡❛rs✳ ✷✺ Electronic copy available at: https://ssrn.com/abstract=3555917 ✐s ❝❧❡❛r✱ ❛s ✇❡❧❧ ❛s t❤❡ t❡♠♣♦r❛❧ str✉❝t✉r❡✳ ❆❧t❤♦✉❣❤ t❤❡r❡ ✐s ✉♥❝❡rt❛✐♥t② ❛❜♦✉t t❤❡ ❧♦♥❣✲ t❡r♠ ❝♦♥s❡q✉❡♥❝❡s✱ ✐t s❡❡♠s r❡❛s♦♥❛❜❧❡ t♦ ❛ss✉♠❡ t❤❛t t❤❡ s❤♦rt✲t❡r♠ ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ❝♦♥s❡q✉❡♥❝❡s ❛r❡ ♠♦r❡ s❡✈❡r❡ t❤❛♥ t❤❡ ❝♦♥s❡q✉❡♥❝❡s ❛❢t❡r✱ s❛②✱ ✜✈❡ ②❡❛rs✳ ▼♦r❡♦✈❡r✱ t❤❡ ✐♥✐t✐❛❧ ❞❡❝❧✐♥❡ ✐♥ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ✐♥ t❤❡ ❯❙✱ ✇✐t❤ ❛ s♠❛❧❧ r❡s♣♦♥s❡ t♦ s❤♦rt✲t❡r♠ ❞✐✈✐❞❡♥❞ ♣r✐❝❡s✱ s✉❣❣❡sts t❤❛t ♠♦❞❡st s❤♦❝❦s t♦ s❤♦rt✲t❡r♠ ❡①♣❡❝t❛t✐♦♥s ❝❛♥ tr✐❣❣❡r ❧❛r❣❡ ❛♥❞ ♣❡rs✐st❡♥t ❝❤❛♥❣❡s ✐♥ ❡①♣❡❝t❡❞ ❡①❝❡ss r❡t✉r♥s✳ ❆s s✉❝❤✱ s❤♦❝❦s t♦ ♥❡❛r✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ❛♣♣❡❛r r✐s❦② ✐♥ t❤❡ ❡②❡s ♦❢ ✐♥✈❡st♦rs✱ ❛ ❢❛❝t t❤❛t ♠❛② ❤❡❧♣ ❡①♣❧❛✐♥ t❤❡ ❞♦✇♥✇❛r❞ s❧♦♣✐♥❣ ❡q✉✐t② t❡r♠ str✉❝t✉r❡ ❛♥❞ t❤❡ ❤✐❣❤ r❡t✉r♥s t♦ ✜r♠s t❤❛t ♣r♦❞✉❝❡ ♥❡❛r✲❢✉t✉r❡ ❞✐✈✐❞❡♥❞s ✭❉❡❝❤♦✇ ❡t ❛❧✳✱ ✷✵✵✹❀ ●♦r♠s❡♥ ❛♥❞ ▲❛③❛r✉s✱ ✷✵✶✾✮✳ ✻ ❈♦♥❝❧✉s✐♦♥ ■♥ ♣❡r✐♦❞s ♦❢ ❡❝♦♥♦♠✐❝ ❛♥❞ ✜♥❛♥❝✐❛❧ ❞✐str❡ss✱ ❣❡tt✐♥❣ ❢r❡q✉❡♥t❧②✲✉♣❞❛t❡❞ ❛♥❞ ❢♦r✇❛r❞✲❧♦♦❦✐♥❣ ♠❡❛s✉r❡s ♦❢ t❤❡ ❡①♣❡❝t❡❞ ♣❛t❤ ♦❢ t❤❡ ❡❝♦♥♦♠② ✐s ❦❡② ❢♦r ♣♦❧✐❝② ♠❛❦❡rs ❛♥❞ ♠❛r❦❡t ♣❛rt✐❝✐✲ ♣❛♥ts✳ ❲❡ s❤♦✇ t❤❛t ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ❝❛♥ ❝♦♥st✐t✉t❡ ❛ ✉s❡❢✉❧ t♦♦❧ ✐♥ t❤✐s r❡❣❛r❞✳ ❲❡ s❤♦✇ ❤♦✇ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ✐♥ t❤❡ ❯❙✱ ❊❯✱ ❛♥❞ ❏❛♣❛♥ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❞❡r✐✈❡ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ❡①♣❡❝t❡❞ ❣r♦✇t❤ ✐♥ ❞✐✈✐❞❡♥❞s ❛♥❞ ●❉P✱ ❛s ✇❡❧❧ ❛s ❛♥ ❡st✐♠❛t❡ ♦❢ ❡①♣❡❝t❡❞ ❣r♦✇t❤ ❞✉r✐♥❣ t❤❡ ❡✈♦❧✈✐♥❣ ❈❖❱■❉✲✶✾ ❝r✐s✐s✳ ✷✻ Electronic copy available at: https://ssrn.com/abstract=3555917 ❘❡❢❡r❡♥❝❡s ❇❛❦❡r✱ ❙❝♦tt ❘✳✱ ◆✐❝❤♦❧❛s ❇❧♦♦♠✱ ❛♥❞ ❙t❡♣❤❡♥ ❚❡rr②✱ ✏❯s✐♥❣ ❉✐s❛st❡rs t♦ ❊st✐♠❛t❡ t❤❡ ■♠♣❛❝t ♦❢ ❯♥❝❡rt❛✐♥t②✱✑ ✱ ✇♦r❦✐♥❣ ♣❛♣❡r✱ ✷✵✷✵✳ ✱ ❙t❡✈❡♥ ❏✳ ❉❛✈✐s✱ ❛♥❞ ❙t❡♣❤❡♥ ❏✳ ❚❡rr②✱ ✏❈❖❱■❉✲✐♥❞✉❝❡❞ ❊❝♦♥♦♠✐❝ ❯♥❝❡r✲ t❛✐♥t②✱✑ ✇♦r❦✐♥❣ ♣❛♣❡r✱ ✷✵✷✵✳ ❈❛♠♣❜❡❧❧✱ ❏♦❤♥ ❨✳ ❛♥❞ ❘♦❜❡rt ❏✳ ❙❤✐❧❧❡r✱ ✏❚❤❡ ❉✐✈✐❞❡♥❞✲Pr✐❝❡ ❘❛t✐♦ ❛♥❞ ❊①♣❡❝t❛t✐♦♥s ♦❢ ❋✉t✉r❡ ❉✐✈✐❞❡♥❞s ❛♥❞ ❉✐s❝♦✉♥t ❋❛❝t♦rs✱✑ ❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s✱ ✶✾✽✽✱ ✶ ✭✸✮✱ ✶✾✺✕ ✷✷✽✳ ❈♦❝❤r❛♥❡✱ ❏♦❤♥ ❍✳✱ ✏Pr❡s✐❞❡♥t✐❛❧ ❆❞❞r❡ss✿ ✷✵✶✶✱ ✻✻ ✭✹✮✱ ✶✵✹✼✕✶✶✵✽✳ ❉✐s❝♦✉♥t ❘❛t❡s✱✑ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝❡✱ ❈✉t❧❡r✱ ❉❛✈✐❞ ▼✳✱ ❏❛♠❡s ▼✳ P♦t❡r❜❛✱ ❛♥❞ ▲❛✇r❡♥❝❡ ❍✳ ❙✉♠♠❡rs✱ ✏❲❤❛t ♠♦✈❡s st♦❝❦ ♣r✐❝❡s❄✱✑ ❏♦✉r♥❛❧ ♦❢ P♦rt❢♦❧✐♦ ▼❛♥❛❣❡♠❡♥t✱ ✶✾✽✾✱ ✶✺ ✭✸✮✱ ✹✕✶✷✳ ❉❡❝❤♦✇✱ P❛tr✐❝✐❛ ▼✱ ❘✐❝❤❛r❞ ● ❙❧♦❛♥✱ ❛♥❞ ▼❛r❦ ❚ ❙♦❧✐♠❛♥✱ ✏■♠♣❧✐❡❞ ❡q✉✐t② ❞✉r❛✲ t✐♦♥✿ ❆ ♥❡✇ ♠❡❛s✉r❡ ♦❢ ❡q✉✐t② r✐s❦✱✑ ❘❡✈✐❡✇ ♦❢ ❆❝❝♦✉♥t✐♥❣ ❙t✉❞✐❡s✱ ✷✵✵✹✱ ✾ ✭✷✲✸✮✱ ✶✾✼✕✷✷✽✳ ❊✐❝❤❡♥❜❛✉♠✱ ▼❛rt✐♥ ❙✳✱ ❙❡r❣✐♦ ❘❡❜❡❧♦✱ ❛♥❞ ▼❛t❤✐❛s ❚r❛❜❛♥❞t✱ ✏❚❤❡ ▼❛❝r♦❡❝♦✲ ♥♦♠✐❝s ♦❢ ❊♣✐❞❡♠✐❝s✱✑ ✷✵✷✵✳ ❲♦r❦✐♥❣ P❛♣❡r ◆♦rt❤✇❡st❡r♥ ❯♥✐✈❡rs✐t②✳ ●✐❧❝❤r✐st✱ ❙✐♠♦♥ ❛♥❞ ❊❣♦♥ ❩❛❦r❛❥s❡❦✱ ✏❈r❡❞✐t ❙♣r❡❛❞s ❛♥❞ ❇✉s✐♥❡ss ❈②❝❧❡ ❋❧✉❝t✉❛✲ t✐♦♥s✱✑ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇✱ ✷✵✶✷✱ ✶✵✷ ✭✹✮✱ ✶✻✾✷✕✶✼✷✵✳ ●♦r♠s❡♥✱ ◆✐❡❧s ❏✳ ❛♥❞ ❊❜❡♥ ▲❛③❛r✉s✱ ✏❉✉r❛t✐♦♥✲❉r✐✈❡♥ ❘❡t✉r♥s✱✑ ✸✸✺✾✵✷✼✱ ✷✵✶✾✳ ❆✈❛✐❧❛❜❧❡ ❛t ❙❙❘◆ ●♦r♠s❡♥✱ ◆✐❡❧s ❏♦❛❝❤✐♠✱ ✏❚✐♠❡ ❱❛r✐❛t✐♦♥ ♦❢ t❤❡ ❊q✉✐t② ❚❡r♠ ❙tr✉❝t✉r❡✱✑ ❋✐♥❛♥❝❡✱ ❢♦rt❤❝♦♠✐♥❣✱ ✷✵✷✵✳ ●♦✉r✐♥❝❤❛s✱ ❏♦✉r♥❛❧ ♦❢ P✐❡rr❡✲❖❧✐✈✐❡r✱ ✏❋❧❛tt❡♥✐♥❣ t❤❡ P❛♥❞❡♠✐❝ ❛♥❞ ❘❡❝❡ss✐♦♥ ❈✉r✈❡s✱✑ ❲♦r❦✐♥❣ P❛♣❡r ❍❛❛s ❇❡r❦❡❧❡②✳ ✷✼ Electronic copy available at: https://ssrn.com/abstract=3555917 ✷✵✷✵✳ ❍❛♠✐❧t♦♥✱ ❏❛♠❡s ❉✳✱ ✏❲❤② ❨♦✉ ❙❤♦✉❧❞ ◆❡✈❡r ❯s❡ t❤❡ ❍♦❞r✐❝❦✲Pr❡s❝♦tt ❋✐❧t❡r✱✑ ❘❡✈✐❡✇ ♦❢ ❊❝♦♥♦♠✐❝s ❛♥❞ ❙t❛t✐st✐❝s✱ ✷✵✶✽✱ ✶✵✵ ✭✺✮✱ ✽✸✶✕✽✹✸✳ ❚❤❡ ❍❛r✈❡②✱ ❈❛♠♣❜❡❧❧ ❘✳✱ ✏❋♦r❡❝❛sts ♦❢ ❊❝♦♥♦♠✐❝ ●r♦✇t❤ ❢r♦♠ t❤❡ ❇♦♥❞ ❛♥❞ ❙t♦❝❦ ▼❛r❦❡ts✱✑ ❋✐♥❛♥❝✐❛❧ ❆♥❛❧②sts ❏♦✉r♥❛❧✱ ✶✾✽✾✱ ✹✺ ✭✺✮✱ ✸✽✕✹✺✳ ❍❡✱ ❩❤✐❣✉♦✱ ❙t❡❢❛♥ ◆❛❣❡❧✱ ❛♥❞ ❩❤❛♦❣❛♥❣ ❙♦♥❣✱ ✏❚r❡❛s✉r② ■♥❝♦♥✈❡♥✐❡♥❝❡ ❨✐❡❧❞s ❞✉r✐♥❣ ✇♦r❦✐♥❣ ♣❛♣❡r✱ ✷✵✷✵✳ t❤❡ ❈❖❱■❉✲✶✾ ❈r✐s✐s✱✑ ▲❛③❛r✉s✱ ❊❜❡♥✱ ❉❛♥✐❡❧ ❏ ▲❡✇✐s✱ ❛♥❞ ❏❛♠❡s ❍ ❙t♦❝❦✱ ✏❚❤❡ s✐③❡✲♣♦✇❡r tr❛❞❡♦✛ ✐♥ ❍❆❘ ✐♥❢❡r❡♥❝❡✱✑ ❆✈❛✐❧❛❜❧❡ ❛t ❙❙❘◆ ✸✹✸✻✸✼✷✱ ✷✵✶✾✳ ◆❡❧s♦♥✱ ❈❤❛r❧❡s ❘ ❛♥❞ ❆♥❞r❡✇ ❋ ❙✐❡❣❡❧✱ ✏ P❛rs✐♠♦♥✐♦✉s ▼♦❞❡❧✐♥❣ ♦❢ ❨✐❡❧❞ ❈✉r✈❡s✱✑ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❇✉s✐♥❡ss✱ ❖❝t♦❜❡r ✶✾✽✼✱ ✻✵ ✭✹✮✱ ✹✼✸✕✹✽✾✳ ❘❛♠❡❧❧✐✱ ❙t❡❢❛♥♦ ❛♥❞ ❆❧❡①❛♥❞❡r ❋✳ ❲❛❣♥❡r✱ ✏❋❡✈❡r✐s❤ ❙t♦❝❦ Pr✐❝❡ ❘❡❛❝t✐♦♥s t♦ ❈❖❱■❉✲✶✾✱✑ ✷✵✷✵✳ ❲♦r❦✐♥❣ P❛♣❡r ❯♥✐✈❡rs✐t② ♦❢ ❩✉r✐❝❤✳ ❙❤✐❧❧❡r✱ ❘♦❜❡rt ❏✳✱ ✏❉♦ ❙t♦❝❦ Pr✐❝❡s ▼♦✈❡ ❚♦♦ ▼✉❝❤ t♦ ❜❡ ❏✉st✐✜❡❞ ❜② ❙✉❜s❡q✉❡♥t ❈❤❛♥❣❡s ✐♥ ❉✐✈✐❞❡♥❞s❄✱✑ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇✱ ✶✾✽✶✱ ✼✶ ✭✸✮✱ ✹✷✶✕✹✸✻✳ ✈❛♥ ❇✐♥s❜❡r❣❡♥✱ ❏✉❧❡s ❍✳ ❛♥❞ ❘❛❧♣❤ ❙✳❏✳ ❑♦✐❥❡♥✱ ✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ r❡t✉r♥s✿ ❋❛❝ts ❛♥❞ t❤❡♦r②✱✑ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝✐❛❧ ❊❝♦♥♦♠✐❝s✱ ✷✵✶✼✱ ✶✷✹ ✭✶✮✱ ✶ ✕ ✷✶✳ ✈❛♥ ❇✐♥s❜❡r❣❡♥✱ ❏✉❧❡s✱ ▼✐❝❤❛❡❧ ❇r❛♥❞t✱ ❛♥❞ ❘❛❧♣❤ ❑♦✐❥❡♥✱ ✏❖♥ t❤❡ ❚✐♠✐♥❣ ❛♥❞ Pr✐❝✐♥❣ ♦❢ ❉✐✈✐❞❡♥❞s✱✑ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❘❡✈✐❡✇✱ ✷✵✶✷✱ ✶✵✷ ✭✹✮✱ ✶✺✾✻✕✶✻✶✽✳ ✱ ❲♦✉t❡r ❍✉❡s❦❡s✱ ❘❛❧♣❤ ❑♦✐❥❡♥✱ ❛♥❞ ❊✈❡rt ❱r✉❣t✱ ✏❊q✉✐t② ②✐❡❧❞s✱✑ ❋✐♥❛♥❝✐❛❧ ❊❝♦♥♦♠✐❝s✱ ✷✵✶✸✱ ✶✶✵ ✭✸✮✱ ✺✵✸ ✕ ✺✶✾✳ ✷✽ Electronic copy available at: https://ssrn.com/abstract=3555917 ❏♦✉r♥❛❧ ♦❢ ❆ ❚❡❝❤♥✐❝❛❧ ❉❡t❛✐❧s ♦❢ t❤❡ ▲♦✇❡r ❇♦✉♥❞s ■♥ t❤✐s ❛♣♣❡♥❞✐①✱ ✇❡ ❞❡t❛✐❧ t❤❡ ❛ss✉♠♣t✐♦♥s ✇❡ ✉s❡ t♦ ❞❡r✐✈❡ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ❞✐✈✐❞❡♥❞ ✭✐♥ ❙❡❝t✐♦♥ ❆✳✶✮ ❛♥❞ ●❉P ❣r♦✇t❤ r❛t❡s ✭✐♥ ❙❡❝t✐♦♥ ❆✳✷✮✳ ❆✳✶ ❉✐✈✐❞❡♥❞ ●r♦✇t❤ ❲❡ ❞❡r✐✈❡ t❤❡ ❧♦✇❡r ❜♦✉♥❞ ❢♦r t❤❡ ♦♥❡✲♣❡r✐♦❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ t❤❡ ❛r❣✉✲ ♠❡♥ts ❞✐r❡❝t❧② ❡①t❡♥❞ t♦ ❧♦♥❣❡r✲t❡r♠ ❣r♦✇t❤ ❡①♣❡❝t❛t✐♦♥s✳ ❇② ♥♦ ❛r❜✐tr❛❣❡✱ t❤❡ ♣r✐❝❡ ♦❢ ❛ ♦♥❡✲♣❡r✐♦❞ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s✱ (1) Ft ✱ ✐s ❣✐✈❡♥ ❜② (1) Ft ✇❤❡r❡ Mt+1 = Et [Mt+1 Dt+1 ] , Et [Mt+1 ] ❞❡♥♦t❡s t❤❡ st♦❝❤❛st✐❝ ❞✐s❝♦✉♥t ❢❛❝t♦r✳ ❲❡ r❡✇r✐t❡ t❤❡ ❡q✉❛t✐♦♥ ❛s (1) Et Mt+1 DDt+1 Ft t = , Dt Et [Mt+1 ] ❛♥❞ ✉s✐♥❣ E [XY ] = E [X] E [Y ] + Cov (X, Y )✱ ✇❡ ❤❛✈❡ (1) Cov Mt+1 , DDt+1 Ft t (1) = Gt + , Dt Et [Mt+1 ] (1) = Gt (1) , Θt ✇❤❡r❡ (1) Θt = 1 + Cov Mt+1 , DDt+1 t (1) Et [Mt+1 ]Gt −1 , ✐s t❤❡ ✭❣r♦ss✮ r✐s❦ ♣r❡♠✐✉♠ ♦♥ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤✳ ❖✉r ❝❡♥tr❛❧ ❛ss✉♠♣t✐♦♥ ✐s t❤❛t ❢♦❧❧♦✇✐♥❣ t❤❡ ❝r✐s✐s ❛t t > t✱ ✐♥✈❡st♦rs✬s r✐s❦ ❛✈❡rs✐♦♥ ✐♥❝r❡❛s❡s✱ ✐♠♣❧②✐♥❣ (1) (1) Θt ≥ Θt ✷✾ Electronic copy available at: https://ssrn.com/abstract=3555917 ✳ ❆s ❛ r❡s✉❧t✱ ✇❡ ❤❛✈❡ (1) Ft = (1) Ft (1) (1) (1) (1) Gt Θt Gt Θt (1) ≤ Gt , (1) Gt ✇❤✐❝❤ ②✐❡❧❞s t❤❡ ❧♦✇❡r ❜♦✉♥❞ (1) Gt (1) (1) ≥ Gt ❆✳✷ Ft (1) ✭✻✮ Ft ●❉P ●r♦✇t❤ ❚♦ ❞❡r✐✈❡ ❛ ❧♦✇❡r ❜♦✉♥❞ ♦♥ ●❉P ❣r♦✇t❤✱ ✇❡ st❛rt ❢r♦♠ ❛ r❡❣r❡ss✐♦♥ ❛s ✐♥ ✭✺✮✱ ✇❤❡r❡ ✇❡ r❡❣r❡ss ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ♦♥ ●❉P ❣r♦✇t❤ Dt+1 Yt+1 − = α0 + α1 −1 + Dt Yt t+1 ❚❛❦✐♥❣ ❝♦♥❞✐t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ r❡✇r✐t✐♥❣ ❣✐✈❡s (1) Gt (1) + α0 + α1 Et Yt+1 Yt −1 + α0 + α1 E t Yt+1 Yt −1 = Gt + α1 Et ✉s✐♥❣ t❤❛t α0 ❛♥❞ t❤❛t t❤❛t ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t 1+x 1+y −1 x−y 1+x 1+y −1 Yt+1 Yt+1 − Et Yt Yt x−y ❛r❡ ♥♦t ✉♣❞❛t❡❞ , (x, y) s♠❛❧❧✳ ❚❤❡ ❛❜♦✈❡ st❡♣ ❛ss✉♠❡s ❜❡t✇❡❡♥ t❛♥❞ t ✳ ■♥s❡rt✐♥❣ ✐♥t♦ ✻ ❛♥❞ ✉s✐♥❣ ❢♦r ❛❣❛✐♥ ❣✐✈❡s Et Yt+1 Yt Et Yt+1 Yt (1) Ft −1≥ −1 α1 Ft(1) ✸✵ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✶✵✿ ◆♦t✐♦♥❛❧ ❖✉tst❛♥❞✐♥❣ ❢♦r ❊✉r♦ ❙t♦①① ✺✵ ❉✐✈✐❞❡♥❞ ❋✉t✉r❡s ❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ t♦t❛❧ ♥♦t✐♦♥❛❧ ♦✉tst❛♥❞✐♥❣ ♦♥ ❊✉r♦ ❙t♦①① ✺✵ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s ♦♥ t❤❡ ❊✉r❡① ❡①❝❤❛♥❣❡✳ ❇ ❆❞❞✐t✐♦♥❛❧ ❋✐❣✉r❡s ❛♥❞ ❚❛❜❧❡s ✸✶ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✶✶✿ ❉❛✐❧② ❱♦❧✉♠❡ ✐♥ t❤❡ ▼❛r❦❡t ❢♦r ❊✉r♦ ❙t♦①① ✺✵ ❉✐✈✐❞❡♥❞ ❋✉t✉r❡s ❚❤❡ ❧❡❢t s✐❞❡ ♦❢ t❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ ❞❛✐❧② ✈♦❧✉♠❡ tr❛❞❡❞ ✐♥ t❤❡ ♠❛r❦❡t ❢♦r ❊✉r♦ ❙t♦①① ✺✵ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s✳ ❊❛❝❤ ❝♦♥tr❛❝t ✐s ❢♦r ✶✵✵ ❞✐✈✐❞❡♥❞ ♣♦✐♥ts✳ ❚❤❡ r✐❣❤t s✐❞❡ ♦❢ t❤❡ ✜❣✉r❡ s❤♦✇s t❤❡ t♦t❛❧ ✈❛❧✉❡ ♦❢ t❤❡ ❝♦♥tr❛❝ts tr❛❞❡❞ ♦♥ ❛ ❣✐✈❡♥ ❞❛②✳ ❙❛♠♣❧❡ ✐s ❏❛♥ ✶ t♦ ▼❛② ✶✾ ✷✵✷✵✳ ❚❛❜❧❡ ✶✿ Pr❡❞✐❝t✐✈❡ ❘❡❣r❡ss✐♦♥s ♦❢ ❉✐✈✐❞❡♥❞ ●r♦✇t❤ ♦♥ ❉✐✈✐❞❡♥❞ ❨✐❡❧❞s ❚❤✐s t❛❜❧❡ s❤♦✇s r❡s✉❧ts ❢r♦♠ r❡❣r❡ss✐♦♥s s✐♠✐❧❛r t♦ ✭✸✮✳ ■♥ ❛ ♣♦♦❧❡❞ s❛♠♣❧❡ ❛❝r♦ss ❙✫P ✺✵✵✱ ❊✉r♦ ❙t♦①① ✺✵✱ ❛♥❞ ◆✐❦❦❡✐ ✷✷✺✱ ✇❡ r❡❣r❡ss r❡❛❧✐③❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ♦♥t♦ t❤❡ ❡①✲❛♥t❡ t✇♦✲②❡❛r ②✐❡❧❞ ❛♥❞ ❛ ❞✉♠♠② ❡q✉❛❧ t♦ ✶ ❢♦r ❊✉r♦ ❙t♦①① ✺✵ ♦❜s❡r✈❛t✐♦♥s ❛♥❞ ❛ ❞✉♠♠② ❡q✉❛❧ t♦ ✶ ❢♦r ◆✐❦❦❡✐ ✷✷✺ ♦❜s❡r✈❛t✐♦♥s✳ ❍❆❈ st❛♥❞❛r❞ ❡rr♦rs ❜❛s❡❞ ♦♥ ✭▲❛③❛r✉s ❡t ❛❧✳✱ ✷✵✶✾✮ ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ♣❛r❡♥t❤❡s✐s✳ ❖❜s❡r✈❛t✐♦♥s ❛r❡ q✉❛rt❡r❧②✳ ∆1 Di,t (2) eit ■♥t❡r❝❡♣t ❊❯ ❞✉♠♠② ◆✐❦❦❡✐ ✷✷✺ ❞✉♠♠② ✵✳✵✸✺ ✵✳✵✵✼ ✵✳✵✹✸ ✲✵✳✽✷ ✭✵✳✵✷✮ ✭✵✳✵✸✮ ✭✵✳✵✸✮ ✭✵✳✶✶✮ ✸✷ Electronic copy available at: https://ssrn.com/abstract=3555917 R2 ★ ❖❜s ✵✳✺✽ ✶✹✸ ❋✐❣✉r❡ ✶✷✿ ❘❡❝♦♥❝✐❧✐♥❣ t❤❡ st♦❝❦ ♠❛r❦❡t ❛♥❞ ❞✐✈✐❞❡♥❞ ♣r✐❝❡ r❡s♣♦♥s❡s ✐♥ ❊✉r♦♣❡ ❛♥❞ ❏❛♣❛♥ ❚❤✐s ✜❣✉r❡ s❤♦✇s ❡st✐♠❛t❡❞ ♣r✐❝❡s ♦❢ ❞✐✈✐❞❡♥❞s ❢♦r ❞✐✛❡r❡♥t ♠❛t✉r✐t②✳ ❲❡ ✜t t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❞✐✈✐❞❡♥❞ ♣r✐❝❡s t♦ t❤❡ ❢✉♥❝t✐♦♥❛❧ ❢♦r♠ ♦♥ ◆❡❧s♦♥ ❛♥❞ ❙✐❡❣❡❧ ✭✶✾✽✼✮ ✉♥❞❡r t❤❡ r❡str✐❝t✐♦♥ t❤❛t t❤❡ ♣r✐❝❡ ♦❢ ❛❧❧ t❤❡ ❞✐✈✐❞❡♥❞s s✉♠ t♦ t❤❡ ♠❛r❦❡t✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ♣r✐❝❡s s❡♣❛r❛t❡❧② ♦♥ ❋❡❜r✉❛r② ✶✾✱ ▼❛r❝❤ ✺✱ ▼❛r❝❤ ✶✷✱ ❛♥❞ ❏✉❧② ✷✵✳ ▼❛t✉r✐t② ♠❡❛s✉r❡❞ ♦♥ t❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s ✐♥ ②❡❛rs✳ ✸✸ Electronic copy available at: https://ssrn.com/abstract=3555917 ❚❛❜❧❡ ✷✿ ▼❛♣♣✐♥❣ ❉✐✈✐❞❡♥❞s t♦ ●❉P ❚❤✐s t❛❜❧❡ s❤♦✇s t❤❡ s❧♦♣❡ ❝♦❡✣❝✐❡♥t Bn ❢♦r ❛ r❡❣r❡ss✐♦♥ ♦❢ ●❉P ❣r♦✇t❤ ♦♥t♦ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❛t ❞✐✛❡r❡♥t ❤♦r✐③♦♥s ✭♥ ✮✱ ❝♦♥❞✐t✐♦♥s ❛♥❞ s❛♠♣❧❡ ♣❡r✐♦❞s✳ ❚❤❡ ❜❛s❡❧✐♥❡ ❝♦❡✣❝✐❡♥t ✐s ❡st✐♠❛t❡❞ ✐♥ t❤❡ ✶✾✽✺✲✷✵✶✾ s❛♠♣❧❡ ✉s✐♥❣ ✉s✐♥❣ r♦❧❧✐♥❣ ✷✲②❡❛r ❣r♦✇t❤ ❛♥❞ ♦♥❧② ❝♦♥s✐❞❡rs ♦❜s❡r✈❛t✐♦♥s ✇❤❡r❡ r❡❛❧✐③❡❞ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ✐s ❜❡❧♦✇ t❤❡ t✐♠❡✲s❡r✐❡s ❛✈❡r❛❣❡✳ ❉✐✈✐❞❡♥❞ ❣r♦✇t❤ ✐s r❡❛❧ ❞✐✈✐❞❡♥❞ ❣r♦✇t❤ ❢♦r ❙✫P ✺✵✵ ❛♥❞ ●❉P ❣r♦✇t❤ ✐s r❡❛❧ ●❉P ❣r♦✇t❤ ✐♥ ❯❙✳ ❍❆❈ st❛♥❞❛r❞ ❡rr♦rs ❜❛s❡❞ ♦♥ ✭▲❛③❛r✉s ❡t ❛❧✳✱ ✷✵✶✾✮ ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ♣❛r❡♥t❤❡s✐s✳ ❖❜s❡r✈❛t✐♦♥s ❛r❡ q✉❛rt❡r❧②✳ ❇❛s❡❧✐♥❡✿ ❍♦r✐③♦♥ ✭②❡❛rs✮ ✷ ❈♦♥❞✐t✐♦♥✿ ❉♦✇♥s✐❞❡ ❙❛♠♣❧❡✿ ✶✾✽✺✲✷✵✶✾ ❘♦❜✉st♥❡ss ✸ ✷ ✷ ❉♦✇♥s✐❞❡ ✶✾✽✺✲✷✵✶✾ ✸ ❯♥❝♦♥❞✐t✐♦♥❛❧ ✶✾✺✽✲✷✵✶✾ ✶✾✽✺✲✷✵✶✾ Bn ✵✳✷✷ ✵✳✶✹ ✵✳✸✶ ✵✳✷✸ ✵✳✷✼ ✵✳✶✸ ✵✳✶✷ s✳❡✳ ✭✵✳✵✸✮ ✭✵✳✵✺✮ ✭✵✳✵✹✮ ✭✵✳✵✼✮ ✭✵✳✶✶✮ ✭✵✳✵✻✮ ✭✵✳✵✼✮ R2 ✵✳✺✵ ✵✳✶✽ ✵✳✻✼ ✵✳✶✾ ✵✳✷✸ ✵✳✶✹ ✵✳✶✷ ✻✷ ✻✻ ✻✷ ✶✷✺ ✶✸✶ ✷✹✵ ✷✸✻ ❖❜s❡r✈❛t✐♦♥s ✸✹ Electronic copy available at: https://ssrn.com/abstract=3555917 ... ♦✉t❧✐❡r✳ ✶✾ Electronic copy available at: https://ssrn.com/abstract=3555917 ❋✐❣✉r❡ ✼✿ ❈②❝❧✐❝❛❧ ❝♦♠♣♦♥❡♥ts ♦❢ ❧♦❣ r❡❛❧ ❞✐✈✐❞❡♥❞s ❛♥❞ ❧♦❣ r❡❛❧ ●❉P✳ Dividends GDP -1 -2 -3 -4 198 5 199 0 199 5 2000 2005... ❑♦✐❥❡♥ ✭✷✵✶✼✮✱ ❛♥❞ ●♦r♠s❡♥ ✭✷✵✷✵✮ ❢♦r ❡❛r❧✐❡r ✇♦r❦ ♦♥ ❞✐✈✐❞❡♥❞ str✐♣s ❛♥❞ ❞✐✈✐❞❡♥❞ ❢✉t✉r❡s✳ ✸ Electronic copy available at: https://ssrn.com/abstract=3555917 ❛♥❞ ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ♠♦r❡ ❜r♦❛❞❧②✳ ❙❡❝♦♥❞✱... ✉♥❞❡rst❛♥❞ ♠♦✈❡♠❡♥ts ✐♥ t❤❡ ❛❣❣r❡❣❛t❡ st♦❝❦ ♠❛r❦❡t ✐s ❝♦♥s✐st❡♥t ✇✐t❤ ✭●♦r♠s❡♥✱ ✷✵✷✵✮✳ ✹ Electronic copy available at: https://ssrn.com/abstract=3555917 ♠✉st t❤❡r❡❢♦r❡ ❛❧s♦ ❜❡ t❤❡ s❛♠❡ ❛s ❜❡❢♦r❡