Stock Price Related Financial Fragility and Growth Patterns

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Faculty of Business Administration and Economics

33501 Bielefeld − Germany P.O. Box 10 01 31

Bielefeld University

Working Papers in Economics and Management No. 04-2015

April 2015

Stock Price Related Financial Fragility and Growth Patterns

Pascal Aßmuth

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Stock Price Related Financial Fragility and Growth Patterns

❛"❝❛❧ ❆&♠✉)❤

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❆♣,✐❧ ✷✵✶✺

❚❤❡ #♦#❛❧ ♦✉#♣✉# ♦❢ ❛♥ ❡❝♦♥♦♠② ✉.✉❛❧❧② ❢♦❧❧♦✇. ❝②❝❧✐❝❛❧ ♠♦✈❡♠❡♥#. ✇❤✐❝❤ ❛2❡ ❛❝❝♦♠♣❛♥✐❡❞

❜② .✐♠✐❧❛2 ♠♦✈❡♠❡♥#. ✐♥ .#♦❝❦ ♣2✐❝❡.✳ ❚❤❡ ❝♦♠♠♦♥ ❡①♣❧❛♥❛#✐♦♥ 2❡❧✐❡. ♦♥ #❤❡ ❞❡♠❛♥❞ .✐❞❡✳ ■#

♣♦✐♥#. ♦✉# #❤❛# .#♦❝❦ ♠❛2❦❡# ✇❡❛❧#❤ ❞2✐✈❡. ❝♦♥.✉♠♣#✐♦♥ ✇❤✐❝❤ #2✐❣❣❡2. ♣2♦❞✉❝#✐♦♥ ❛❢#❡2✇❛2❞✳

❚❤✐. ♣❛♣❡2 ❢♦❝✉.❡. ♦♥ ✐♥✢✉❡♥❝❡. ✈✐❛ #❤❡ .✉♣♣❧② .✐❞❡ ♦❢ #❤❡ ❡❝♦♥♦♠②✳ ❚❤❡ ❛✐♠ ♦❢ #❤❡ ♣❛♣❡2 ✐. #♦

❡①♣❧♦2❡ ❝❤❛♥♥❡❧. ✇❤❡2❡ .#♦❝❦ ♣2✐❝❡ ♣❛##❡2♥. ✐♥✢✉❡♥❝❡ #❤❡ ❛♠♦✉♥# ♦❢ ❝2❡❞✐# #❛❦❡♥ ❜② ✜2♠.✳ ❲❡

❡①❛♠✐♥❡ #2❡♥❞ ❛♥❞ ✈♦❧❛#✐❧✐#② ❝②❝❧❡. ❛# #❤❡ .#♦❝❦ ♠❛2❦❡# ❢♦2 #❤❡✐2 ✐♠♣❛❝# ♦♥ #❤❡ 2❡❛❧ ❡❝♦♥♦♠②✳ ❋♦2

❡❛❝❤ ♦♥❡ ✇❡ ✜♥❞ ❛♥ ❛♣♣❧✐❝❛#✐♦♥ #♦ #❤❡ ✐♥✈❡.#♠❡♥# ❜❡❤❛✈✐♦✉2 ♦❢ ✜2♠.✳ ❚❤❡2❡ ❛2❡ #❤2❡❡ ❝❤❛♥♥❡❧.

❛❞❞2❡..❡❞✿ #❤❡ .#♦❝❦ ♠❛2❦❡# ✈❛❧✉❛#✐♦♥ ❛. ♣✐❡❝❡ ♦❢ ✐♥❢♦2♠❛#✐♦♥ ❢♦2 #❤❡ ❛..❡..♠❡♥# ♦❢ ❛ ✜2♠✬.

❝2❡❞✐#✇♦2#❤✐♥❡..✱ #❤❡ ✐♥✢✉❡♥❝❡ ♦♥ 2❡.#2✉❝#✉2✐♥❣ ♣2♦.♣❡❝#. ✐♥ #✐♠❡. ♦❢ ✜♥❛♥❝✐❛❧ ❞✐.#2❡.. ❛♥❞ #❤❡

.#♦❝❦ ♠❛2❦❡# 2❡❧❛#❡❞ 2❡♠✉♥❡2❛#✐♦♥ ♦❢ #❤❡ #♦♣ ♠❛♥❛❣❡♠❡♥# ❛✛❡❝#✐♥❣ ❝❛♣✐#❛❧ ❞❡♠❛♥❞✳ ❲❡ ❛.❦ #♦

✇❤✐❝❤ ❡①#❡♥# ❛ ❝❤❛♥♥❡❧ ♠❛② ❝♦♥#2✐❜✉#❡ #♦ #❤❡ .#♦❝❦ ♣2✐❝❡ ✲ ♦✉#♣✉# 2❡❧❛#✐♦♥ ✇❤❡♥ #❤❡2❡ ✐. ♠✉#✉❛❧

❢❡❡❞❜❛❝❦✳ ❆ ♠♦❞❡❧ ❛ ❧❛ ❉❡❧❧✐ ●❛##✐ ❡# ❛❧✳ ✭✷✵✵✺✮ ❞2✐✈❡. #❤❡ 2❡.✉❧#.✳ ❋✐2♠. #❛❦❡ ❝2❡❞✐# #♦ ✜♥❛♥❝❡`

#❤❡✐2 ♣2♦❞✉❝#✐♦♥ ✇❤✐❝❤ ❞❡#❡2♠✐♥❡. #❤❡✐2 ✜♥❛♥❝✐❛❧ ❢2❛❣✐❧✐#②✳ ■❢ #❤❡✐2 .#♦❝❤❛.#✐❝ 2❡✈❡♥✉❡ ✐. #♦♦ ❧♦✇✱

#❤❡② ❛2❡ ❜❛♥❦2✉♣# ❛♥❞ ❧❡❛✈❡ #❤❡ ❡❝♦♥♦♠②✳ ❚❤❡ ❝❛♣✐#❛❧ ❧♦.. ❤✉2#. #❤❡ ❜❛♥❦✬. ❡K✉✐#② ❜❛.❡ ❛♥❞ ❢✉#✉2❡

❝2❡❞✐# .✉♣♣❧② ✐. ❞✐♠✐♥✐.❤❡❞✳ ❚❤✐. ❝❛✉.❡. ❜✉.✐♥❡.. ❝②❝❧❡.✳ ❘❡.✉❧#. .❤♦✇ #❤❛# ✐❢ #❤❡ ❜❛♥❦ ❛..❡..❡.

❝2❡❞✐#✇♦2#❤✐♥❡.. ❛❝❝♦2❞✐♥❣ #♦ #❤❡ .#♦❝❦ ♣2✐❝❡ #❤❡♥ ✐❞✐♦.②♥❝2❛#✐❝ .#♦❝❦ ♣2✐❝❡ ✢✉❝#✉❛#✐♦♥. ❤❛✈❡ ♦♥❧②

❛ .❧✐❣❤# ❡✛❡❝# ❛. #❤❡② ❞✐.#✉2❜ .❡❧❡❝#✐♦♥ ❛♥❞ ❤✐♥❞❡2 ❣2♦✇#❤✳ ■❢ .#♦❝❦ ♠❛2❦❡# ♦♣#✐♠✐.♠ ♠❛##❡2.

❢♦2 ❜❛♥❦2✉♣#❝② 2✉❧✐♥❣ #❤❡ ❧❡✈❡❧ ♦❢ .#♦❝❦ ♦✇♥❡2.✬ ✐♥✢✉❡♥❝❡ ❞♦❡. ♥♦# ♠❛##❡2✳ ■❢ ♦♣#✐♠✐.♠ ✐. ✇✐❞❡

.♣2❡❛❞ ❛♠♦♥❣ .#♦❝❦ ✐♥✈❡.#♦2. ❤♦✇❡✈❡2✱ ✐♥✈❡.#♠❡♥# ❜❡❤❛✈✐♦✉2 ✐. ❛❧.♦ ❝♦22❡❧❛#❡❞ #❤2♦✉❣❤ #❤❡ .#♦❝❦

♣2✐❝❡. ❛♥❞ #❤✐. 2❡.✉❧#. ✐♥ ❤✉❣❡ 2❡❛❧ ❡❝♦♥♦♠② ❝②❝❧❡. ✇✐#❤♦✉# ❛♥② ❧♦♥❣✲#❡2♠ ❣2♦✇#❤✳ ■❢ ✈♦❧❛#✐❧✐#② ✐.

❝♦♥.✐❞❡2❡❞ ✐♥ #❤❡ ❞❡❝✐.✐♦♥ ♦❢ ♠❛♥❛❣❡2. #❤❡② ❛❝# ♠♦2❡ ♣2✉❞❡♥#❧② ❛♥❞ #❤✐. ❢♦.#❡2. ❣2♦✇#❤✳

❑❡②✇♦%❞'✿ ❍❡#❡$♦❣❡♥❡♦✉) ❆❣❡♥#) ▼♦❞❡❧)✱ ❋✐♥❛♥❝✐❛❧ ❋$❛❣✐❧✐#②✱ ❙#♦❝❦ 6$✐❝❡)✱ ❇✉)✐♥❡)) ❈②❝❧❡)

❏❊▲ ❈❧❛))✐✜❝❛#✐♦♥✿ ❊✸✷✱ ●✸✵ ✱❈✻✸✳

∗ ❇✐❡❧❡❢❡❧❞ ●'❛❞✉❛*❡ ❙❝❤♦♦❧ ♦❢ ❊❝♦♥♦♠✐❝2 ❛♥❞ ▼❛♥❛❣❡♠❡♥* ✭❇✐●❙❊▼✮✱ ❈❡♥*❡' ❢♦' ▼❛*❤❡♠❛*✐❝❛❧ ❊❝♦♥♦♠✐❝2✱ ❇✐❡❧❡❢❡❧❞

❯♥✐✈❡'2✐*②✱ ❛♥❞ ❯♥✐✈❡'2✐*< =❛'✐2 ■ =❛♥*❤<♦♥✲❙♦'❜♦♥♥❡✱ ❈✳❊✳❙✳pascal.assmuth@uni-bielefeld.de

❚❤✐2 ✇♦'❦ ✇❛2 ❝❛''✐❡❞ ♦✉* ✇✐*❤✐♥ ■♥*❡'♥❛*✐♦♥❛❧ ❘❡2❡❛'❝❤ ❚'❛✐♥✐♥❣ ●'♦✉♣ ❊❇■▼ ✭❊❝♦♥♦♠✐❝ ❇❡❤❛✈✐♦' ❛♥❞ ■♥*❡'❛❝*✐♦♥

▼♦❞❡❧2✮ ✜♥❛♥❝❡❞ ❜② *❤❡ ❉❋● ✉♥❞❡' ❝♦♥*'❛❝* ●❘❑ ✶✶✸✹✴✷✳ ❋✉'*❤❡' ✜♥❛♥❝✐❛❧ 2✉♣♣♦'* ❜② *❤❡ ❋'❛♥❝♦✲●❡'♠❛♥ ❯♥✐✈❡'2✐*②

✭❉❋❍✴❯❋❆✮ ✐2 ❣'❛*❡❢✉❧❧② ❛❦♥♦✇❧❡❞❣❡❞✳

■ ✇♦✉❧❞ ❧✐❦❡ *♦ *❤❛♥❦ ❆♥*♦✐♥❡ ▼❛♥❞❡❧✱ ❍❡'❜❡'* ❉❛✇✐❞ ❛♥❞ *❤❡ ♣❛'*✐❝✐♣❛♥*2 ♦❢ *❤❡ ✽^❤ ❊❇■▼ ❉♦❝*♦'❛❧ ❲♦'❦2❤♦♣ ✷✵✶✸

✐♥ ❇✐❡❧❡❢❡❧❞ ❢♦' ✈❡'② ✉2❡❢✉❧ ❝♦♠♠❡♥*2 ❛♥❞ '❡♠❛'❦2✳

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1. Introduction

❊❝♦♥♦♠✐❝ ✢✉❝(✉❛(✐♦♥* ❛♥❞ ❜♦♦♠✲❜✉*( ♣❛((❡0♥* ✐♥ ❛**❡( ♣0✐❝❡* ♦❝❝✉0 *♦♠❡(✐♠❡* ✐♥ ❝♦♥❥✉♥❝(✐♦♥

✇❤✐❧❡ ❝0✐*❡* ✐♥ ✜♥❛♥❝✐❛❧ ♠❛0❦❡(* ❝❛♥ (✉0♥ ❡❝♦♥♦♠✐❝ ❝♦♥(0❛❝(✐♦♥* ✐♥(♦ 0❡❝❡**✐♦♥* ✭▼✐♥*❦②✱ ✶✾✼✵❀

❑✐♥❞❧❡❜❡0❣❡0 ❛♥❞ ❆❧✐❜❡0✱ ✷✵✵✺❀ ❇♦0❞♦ ❛♥❞ ▲❛♥❡✱ ✷✵✶✸✮✳ ❚❤✐* ♣❛♣❡0 ❛✐♠* (♦ ❡①♣❧♦0❡ (❤❡ ♣♦**✐❜❧❡

❝❛✉*❛❧ ❝♦♥(0✐❜✉(✐♦♥* ♦❢ ❛**❡(* (♦ ❡❝♦♥♦♠✐❝ ♣❡0❢♦0♠❛♥❝❡ ❜② ❛*❦✐♥❣ ✇❤✐❝❤ ❡✛❡❝( ❞♦ *(♦❝❦ ♣0✐❝❡*

❛♥❞ (❤❡✐0 ♣❛((❡0♥* ❤❛✈❡ ♦♥ ♦✉(♣✉( ✈✐❛ (❤❡ *✉♣♣❧② *✐❞❡❄ ❚❤❡ ♠♦❞❡❧ ❢♦❝✉*❡* ♦♥ ❜❛♥❦ ❝0❡❞✐( ❛*

(❤❡ ❝❤❛♥♥❡❧ (❤❛( (0❛♥*♠✐(* *❤♦❝❦* ♦♥ *(♦❝❦ ♣0✐❝❡* (♦ (❤❡ 0❡❛❧ ❡❝♦♥♦♠②✳ ❚❤✐* ❢♦❝✉* ♦♥ ❜❛♥❦

❝0❡❞✐( ✐* ❜❛*❡❞ ♦♥ (✇♦ ♦❜*❡0✈❛(✐♦♥*✿ ✜0♠* ✜♥❛♥❝❡ ❛ *✐❣♥✐✜❝❛♥( ♣❛0( ♦❢ (❤❡✐0 ❜✉*✐♥❡** ❜② 0❡❧②✐♥❣

♦♥ ❡①(❡0♥❛❧ *♦✉0❝❡* ♦❢ ❢✉♥❞* ❛♥❞✱ ❛❧(❤♦✉❣❤ ✜♥❛♥❝✐❛❧ *②*(❡♠* ❞✐✛❡0 ❛0♦✉♥❞ (❤❡ ✇♦0❧❞✱ ❝0❡❞✐( ✐*

❛♥ ✐♠♣♦0(❛♥( ❡①(❡0♥❛❧ *♦✉0❝❡ ♦❢ ❢✉♥❞*✳

❙(♦❝❦ ♣0✐❝❡* ❛0❡ ♣❛0( ♦❢ (❤❡ ✜♥❛♥❝✐❛❧ ♠❛0❦❡(✳ ◆❡✈❡0(❤❡❧❡**✱ (❤❡② ❛0❡ ❧✐❦❡❧② (♦ ❛✛❡❝( 0❡❛❧ ♠❛0❦❡(

❛❝(✐✈✐(②✳ ❚❤❡✐0 ✐♠♣❛❝( ♠✐❣❤( ❜❡ *♦ *❡✈❡0❡ (❤❛( (❤❡② ❝❛✉*❡ ✜♥❛♥❝✐❛❧ ♠❛0❦❡( ❜0❡❛❦❞♦✇♥* ❛♥❞

0❡❝❡**✐♦♥* ✭▼✐♥*❦②✱ ✶✾✼✵✮✳ ✏❚❤❡0❡ ❛0❡ ❢♦✉0 ❝❤❛♥♥❡❧* (❤0♦✉❣❤ ✇❤✐❝❤ *(♦❝❦ ♣0✐❝❡* ❝❛♥ ❜❡ ❝♦♥✲

*✐❞❡0❡❞ (♦ ❛✛❡❝( ❬0❡❛❧❪ ❛❝(✐✈✐(②✿ ✭✶✮ (❤❡ ✇❡❛❧(❤ ❡✛❡❝( ♦♥ ❝♦♥*✉♠♣(✐♦♥✱ ✭✷✮ (❤❡ ❚♦❜✐♥✬* ◗ ❡✛❡❝(

♦♥ ✐♥✈❡*(♠❡♥(✱ ✭✸✮ (❤❡ ❜❛❧❛♥❝❡ *❤❡❡( ❡✛❡❝( ♦♥ ♣0✐✈❛(❡ *♣❡♥❞✐♥❣ ✭✈✐❛ (❤❡ ❝0❡❞✐( ❝❤❛♥♥❡❧✮ ❛♥❞

✭✹✮ (❤❡ ❝♦♥✜❞❡♥❝❡ ❡✛❡❝( ♦♥ ♣0✐✈❛(❡ *♣❡♥❞✐♥❣✳✑ ✭❆❧(✐**✐♠♦ ❡( ❛❧✳✱ ✷✵✵✺✱ ♣✳ ✹✳✮ ■♥ ❛❝❛❞❡♠✐❝ 0❡✲

*❡❛0❝❤✱ ❡✛❡❝( ✭✶✮ ❤❛* ❜❡❡♥ *(✉❞✐❡❞ (❤❡ ♠♦*( ✇❤✐❧❡ ❛❧*♦ ❝❤❛♥♥❡❧ ✭✷✮ ❣♦( *♦♠❡ ❞✐*(✐♥❝( ❛((❡♥(✐♦♥✳

❚❤❡ ♦(❤❡0 ❝❤❛♥♥❡❧* ❛0❡ ✉*✉❛❧❧② ♥♦( ♣♦✐♥(❡❞ ♦✉( *❡♣❛0❛(❡❧② ✭❙❡♠♠❧❡0✱ ✷✵✶✶✱ ♣✳ ✼✾✮✳ ▼❛♥② ❡❛0❧②

♣❛♣❡0* ❢♦❝✉* ♦♥ (❤❡ 0♦❧❡ ♦❢ ✐♥❝0❡❛*❡❞ ✭♣❡0❝❡✐✈❡❞✮ ✇❡❛❧(❤ ✐♥ (✐♠❡* ♦❢ *(♦❝❦ ♠❛0❦❡( ❜♦♦♠* ❛*

*♦✉0❝❡ ♦❢ ✐♥❝0❡❛*❡❞ ❝♦♥*✉♠♣(✐♦♥ ✇❤✐❝❤ ❡*(❛❜❧✐*❤❡* (❤❡ ❧✐♥❦ ❜❡(✇❡❡♥ *(♦❝❦ ♠❛0❦❡(* ❛♥❞ (❤❡ 0❡❛❧

❡❝♦♥♦♠②✳ ❇② (❤✐* ❝♦♥❝❡♣(✱ (❤❡ *(♦❝❦ ♠❛0❦❡( ❧❡❛❞* (❤❡ ❡❝♦♥♦♠②✬* ❞②♥❛♠✐❝ ✭❙❡♠♠❧❡0✱ ✷✵✶✶✱

♣✳ ✼✾✮✳ ▼♦0❡ ❣❡♥❡0❛❧❧②✱ (❤❡ ❞✐*(✐♥❝(✐♦♥ ❜❡(✇❡❡♥ ❛**❡( ♣0✐❝❡* ❛♥❞ (❤❡ ✜♥❛♥❝✐❛❧ ♠❛0❦❡( ✐* ✐♥

♦0❞❡0✳ ❲❤✐❧❡ ✐( ✐* *❤♦✇♥ (❤❛( ❛**❡( ♣0✐❝❡* ✐♥❞❡❡❞ ❝♦♥(0✐❜✉(❡ (♦ (❤❡ 0❡❛❧ ❡❝♦♥♦♠②✱ ❢♦0 ✐♥*(❛♥❝❡

✈✐❛ ✐♥✈❡*(♠❡♥( ✐♥ ♦✇♥❡❞ ❤♦✉*❡* ✭❍✐❣❣✐♥* ❛♥❞ ❖*❧❡0✱ ✶✾✾✽❀ ❙❡♠♠❧❡0✱ ✷✵✶✶✮✱ (❤❡ ❧✐♥❦ ❜❡(✇❡❡♥

♦(❤❡0 ❛**❡(*✱ (0❛❞❡❞ ❛( (❤❡ ✜♥❛♥❝✐❛❧ ♠❛0❦❡( ❧✐❦❡ ❜♦♥❞* ♦0 *(♦❝❦* ✐* ❧❡** ♣0♦✈❡♥✳ ◆❡✈❡0(❤❡❧❡**✱

*(♦❝❦ ♣0✐❝❡* ❛0❡ ❛ ❣♦♦❞ ✐♥❞✐❝❛(♦0 ❢♦0 ❢♦❧❧♦✇✐♥❣ ✐♥✈❡*(♠❡♥( ❛♥❞ ❡❝♦♥♦♠✐❝ ❣0♦✇(❤ ✭❇❛00♦✱ ✶✾✾✵✮✳

■♥ (❤✐* ♣❛♣❡0 *(♦❝❦ ♣0✐❝❡* ✢✉❝(✉❛(❡ ❞✉❡ (♦ 0❡❛❧ ❛❝(✐✈✐(② ❜✉( ❛❧*♦ ❞✉❡ (♦ ❡①♦❣❡♥♦✉* 0❛♥❞♦♠

❞❡✈✐❛(✐♦♥* ♦♥ (♦♣ ♦❢ (❤❛(✳ ❚❤❡ ♣❛♣❡0 ❜✉✐❧❞* ✉♣♦♥ ❛ ♠♦❞❡❧ ❜② ❉❡❧❧✐ ●❛((✐ ❡( ❛❧✳ ✭✷✵✵✺✮

✇❤❡0❡ ❡①❝❡**✐✈❡ ❧❡✈❡0❛❣❡ ✐♥ ❝0❡❞✐( ✜♥❛♥❝❡❞ ♣0♦❞✉❝(✐♦♥ ♠❛② ❝❛✉*❡ ❜❛♥❦0✉♣(❝✐❡*✳ ❚❤❡② *❤♦✇

(❤❛( ❝♦❧❧❛(❡0❛❧ ❜❛*❡❞ ❝0❡❞✐( ❣0❛♥(✐♥❣ ♠❛② ❝♦♥(0✐❜✉(❡ (♦ ♠♦❞❡❧ ♦✉(♣✉( ❞②♥❛♠✐❝* (❤❛( ❡①❤✐❜✐(

❢❡❛(✉0❡* ♦❢ 0❡❛❧ ✇♦0❧❞ ♦✉(♣✉( ❞②♥❛♠✐❝*✳ ❆❧*♦✱ ✜0♠ *✐③❡* ❛♥❞ (❤❡✐0 ❣0♦✇(❤ ❡①❤✐❜✐( ♣❛((❡0♥* ✇❤✐❝❤

♠❛(❝❤ ✇✐(❤ ❡♠♣✐0✐❝❛❧ 0❡❣✉❧❛0✐(✐❡*✳ ❚❤❡ ♠♦❞❡❧ ✐* ❛♥ ❛❣❡♥(✲❜❛*❡❞ ♠♦❞❡❧ ❛❧❧♦✇✐♥❣ ❢♦0 ❡♥♦✉❣❤

✢❡①✐❜✐❧✐(② (♦ ✐♥❝♦0♣♦0❛(❡ ♠✉❧(✐♣❧❡ *❝❡♥❛0✐♦* ❛❜♦✉( *(♦❝❦ ♠❛0❦❡( ❝❤❛♥❣❡*✳ ■♥ (❤✐* ♣❛♣❡0 (❤❡0❡

✇✐❧❧ ❜❡ (❤0❡❡ ✈❛0✐❛(✐♦♥* ♦❢ (❤❡ ♠♦❞❡❧ ❝❛00✐❡❞ ♦✉( ❜② ❝♦♠♣✉(❡0 *✐♠✉❧❛(✐♦♥ ✉*✐♥❣ (❤❡ *♦❢(✇❛0❡

Wolfram Mathematica✳ ❚✇♦ ♦❢ (❤❡ (❤0❡❡ ♠♦❞❡❧ ❡①(❡♥*✐♦♥* ❝♦♠♣❧② ✇✐(❤ (❤❡ ♦0✐❣✐♥❛❧

♣❛♣❡0 ❛* ✐( ✐* ❛ *♣❡❝✐❛❧ ❝❛*❡ ♦❢ (❤❡ ❡①(❡♥❞❡❞ ♠♦❞❡❧✳ ❚❤❡0❡❢♦0❡✱ (❤❡ ♦0✐❣✐♥❛❧ ♠♦❞❡❧ ✇✐❧❧ *❡0✈❡ ❛*

❛ ❜❡♥❝❤♠❛0❦ ❝❛*❡✳ ❚❤❡ (❤✐0❞ ✈❛0✐❛(✐♦♥ ✐* ♦♥❧② *❧✐❣❤(❧② ❞✐✛❡0❡♥( ❛♥❞ ❡①❤✐❜✐(* *✐♠✐❧❛0 ❞②♥❛♠✐❝*✳

❚❤❡ (❤0❡❡ ♣♦**✐❜❧❡ ✐♥✢✉❡♥❝❡* (0❡❛(❡❞ ❛0❡ ✜0*( (❤❡ ✇❛② ❝0❡❞✐( ✐* ❣0❛♥(❡❞ ❞❡♣❡♥❞* ♦♥ (❤❡ *(♦❝❦

(4)

♣!✐❝❡%✳ ❲❤❡♥ ❜❛♥❦% ❡%-✐♠❛-❡ -❤❡ ❝!❡❞✐-✇♦!-❤✐♥❡%% ♦❢ ❜♦!!♦✇❡!% -❤❡② ❛❧%♦ !❡❢❡! -♦ -❤❡ %-♦❝❦ ♣!✐❝❡

❛% ♣✐❡❝❡ ♦❢ ✐♥❢♦!♠❛-✐♦♥✳ ❙❡❝♦♥❞❧②✱ ✜!♠% ✐♥ ✜♥❛♥❝✐❛❧ ❞✐%-!❡%% ♠✐❣❤- ❜❡ %✉❜❥❡❝- -♦ !❡%-!✉❝-✉!✐♥❣

❛♥❞ -❤✉% %✉!✈✐✈❡ ✐♥ ❝❛%❡% ✇❤❡!❡ -❤❡ %-♦❝❦ ♠❛!❦❡- ❞♦❡% ❡✈❛❧✉❛-❡ ✐-% ❢✉-✉!❡ ♣!♦%♣❡❝-% !❛-❤❡!

♦♣-✐♠✐%-✐❝❛❧❧②✳ ❚❤❡ -❤✐!❞ ✐♥✢✉❡♥❝❡ ✐% -❤❛- ♠❛♥❛❣❡!% ♠❛② ❛❝- ✐♥ !❡%♣♦♥%❡ -♦ -❤❡ %-♦❝❦ ♣!✐❝❡ ✐❢

-❤❡✐! ♣❛②♠❡♥- ✐% ❛❧%♦ ❞❡♣❡♥❞❡♥- ♦♥ -❤❡ %-♦❝❦ ♣!✐❝❡✳ ❚❤✐% ✐♥✢✉❡♥❝❡% !✐%❦ -❛❦✐♥❣✳ ❚❤❡ >✉❡%-✐♦♥

❛❞❞!❡%%❡❞ ✐% -♦ ✇❤❛- ❡①-❡♥- %-♦❝❦ ♣!✐❝❡% ❤❛✈❡ ❛♥ ✐♠♣❛❝- ♦♥ ✜!♠%✬ ❞②♥❛♠✐❝ ❛♥❞ ♦✉-♣✉- ✈✐❛

-❤♦%❡ ✈❛!✐♦✉% ❝❤❛♥♥❡❧%✳ ❚❤❡ ❛♥❛❧②%✐% ✇✐❧❧ ❜❡ ❜❛%❡❞ ♦♥ ❝♦♠♣❛!✐♥❣ %❝❡♥❛!✐♦% ✇✐-❤ ✈❛!②✐♥❣ ❧❡✈❡❧%

♦❢ ❝!✉❝✐❛❧ ♣❛!❛♠❡-❡! ✈❛❧✉❡% -♦ -❤❡ ❜❛%❡❧✐♥❡ ❝❛%❡ ✇❤❡!❡ %-♦❝❦ ♣!✐❝❡% ❞♦ ♥♦- ♣❧❛② ❛ !♦❧❡✳

❚❤✐% ♣❛♣❡! ❝♦♥-!✐❜✉-❡% -♦ -❤❡ ✐♥✈❡%-♠❡♥- ❧✐-❡!❛-✉!❡ ❜② ❞❡❛❧✐♥❣ ✇✐-❤ -❤❡ ✐♥✢✉❡♥❝❡ ♦❢ %-♦❝❦ ♣!✐❝❡%

♦♥ -❤❡ ✐♥✈❡%-♠❡♥- ❜❡❤❛✈✐♦! ♦❢ ✜!♠% ✭%❡❡ ❊❈❇✱ ✷✵✶✸❀ ❖!♠❡!♦❞✱ ✷✵✵✾✮✳ ❉✉❡ -♦ -❤❡ ❛❣❡♥- ❜❛%❡❞

%-!✉❝-✉!❡ ✐- ❝❛♥ ❛❞❞ ❢✉!-❤❡! ✐♥%✐❣❤- -♦ -❤❡ ✐♠♣❛❝- ♦❢ ✜!♠ ❧❡✈❡❧ ✜♥❛♥❝✐♥❣ -♦ ❛❣❣!❡❣❛-❡ ❣!♦✇-❤✳

■- !❡❧❛-❡% -♦ ▼✐♥%❦②✬% ❛♣♣!♦❛❝❤ ♦❢ ❧❡✈❡!❛❣❡ ❛♥❞ ✜♥❛♥❝✐❛❧ ❢!❛❣✐❧✐-② ❞✉❡ -♦ ❝!❡❞✐- ❛♥❞ ✐♥✈❡%-♠❡♥- -❤❛- ❝❛✉%❡% %✐♥❣❧❡ ❢❛✐❧✉!❡% ❢❡❡❞✐♥❣ ❜❛❝❦ -♦ -❤❡ !❡%- ♦❢ -❤❡ ❡❝♦♥♦♠②✳ ❚❤✐% -✇♦✲%✐❞❡❞ !❡❧❛-✐♦♥%❤✐♣

✐% ♥♦- ❣!❡❛-❧② ❝♦✈❡!❡❞ ✐♥ ❝❧❛%%✐❝❛❧ ♠❛❝!♦❡❝♦♥♦♠✐❝%✿ ✏❬♠❪♦!❡♦✈❡!✱ ✐- ✐% ✇♦!-❤ ♥♦-✐♥❣ -❤❛- ✐♥ -❤❡

%-♦❝❤❛%-✐❝ ❣!♦✇-❤ ♠♦❞❡❧ -❤❡!❡ ✐% ♦♥❧② ❛ ♦♥❡ ✲%✐❞❡❞ !❡❧❛-✐♦♥%❤✐♣✳ ❘❡❛❧ %❤♦❝❦% ❛✛❡❝- %-♦❝❦ ♣!✐❝❡%

❛♥❞ !❡-✉!♥% ❜✉- %❤♦❝❦% -♦ ❛%%❡- ♣!✐❝❡% ✲ ♦! ♦✈❡!!❡❛❝-✐♦♥ ♦❢ ❛%%❡- ♣!✐❝❡% !❡❧❛-✐✈❡ -♦ ❝❤❛♥❣❡% ✐♥

❢✉♥❞❛♠❡♥-❛❧% ✲ ❤❛✈❡ ♥♦ ❡✛❡❝-% ♦♥ !❡❛❧ ❛❝-✐✈✐-②✳✑ ✭❙❡♠♠❧❡!✱ ✷✵✶✶✱ ♣✳ ✽✷✳✮

❚❤❡ !❡%✉❧-% %❤♦✇ -❤❛- ❛❧❧ ❝❤❛♥♥❡❧% ❞♦ ❤❛✈❡ ❛ %✐❣♥✐✜❝❛♥- ✐♠♣❛❝- ♦♥ -❤❡ ❞②♥❛♠✐❝% ♦❢ -❤❡

✜!♠% ❛♥❞ -♦-❛❧ ♦✉-♣✉-✳ ■❢ ❜❛♥❦% -❛❦❡ -❤❡ %-♦❝❦ ♣!✐❝❡ ✐♥-♦ ❛❝❝♦✉♥- ❢♦! -❤❡✐! ❝!❡❞✐- ♦✛❡!✱ -❤✐%

❧❡❛❞% -♦ ❛ ♠♦!❡ %✐♠✐❧❛! ❡✈♦❧✉-✐♦♥ ❛❝!♦%% ✜!♠% ❜❡❝❛✉%❡ ❧❡✈❡!❛❣❡ ❞♦❡% ♣❛② ♦✛ ❧❡%% ❢♦! -❤❡♠✳

❚❤❡!❡❢♦!❡✱ ✜♥❛♥❝✐❛❧ ❤❡❛❧-❤ ❣❛✐♥% ❛ ❤✐❣❤❡! ✐♠♣♦!-❛♥❝❡ ❛♥❞ -❤✐% ✐♥❞✉❝❡% ♠♦!❡ ♣❡!%✐%-❡♥❝❡ ✐♥

✜!♠%✬ ❞✐✛❡!❡♥❝❡% ✇❤❡!❡ -❤❡ ♣❛❝❡ ♦❢ ❣!♦✇-❤ ✐% ❝♦♠♣❛!❛-✐✈❡❧② ❧♦✇❡!✳ ■❢ %-♦❝❦ ♣!✐❝❡% ♠❛--❡! ❢♦!

❧❡❣❛❧❧② ❞❡❝❧❛!❡❞ ❜❛♥❦!✉♣-❝② ❛ ❤✐❣❤ ❜❛!❣❛✐♥✐♥❣ ♣♦✇❡! ♦❢ %❤❛!❡❤♦❧❞❡!% ✐% ♦❢ ❛❧♠♦%- ♥♦ ❡✛❡❝- ✐❢

%-♦❝❦ ♣!✐❝❡% ❛!❡ ✉♥❝♦!!❡❧❛-❡❞✳ ■❢ %-♦❝❦ ♣!✐❝❡% ❤❛✈❡ ❛ ❜♦♦♠✲❜✉%- ♣❛--❡!♥ -❤❡ !❡❛❧ ❡❝♦♥♦♠②

%❤♦✇% ❝♦!!❡❧❛-✐♥❣ ♣❛--❡!♥% ♦✈❡! -✐♠❡ ❜❡❝❛✉%❡ ❛❧❧ ✜!♠% ❛❝- ♦♥ -❤♦%❡ ♣!✐❝❡% %✐♠✉❧-❛♥❡♦✉%❧②✳ ■♥

-❤❡ ❧❛%- %❝❡♥❛!✐♦✱ ✇❤❡!❡ ♠❛♥❛❣❡!% !❡❛❝- ♦♥ -❤❡ %-♦❝❦ ♣!✐❝❡✱ -❤❡② ❜❡❤❛✈❡ ❛♠❜✐✈❛❧❡♥-✿ ✐♥ ❤✐❣❤❧②

❧❡✈❡!❛❣❡❞ ❝♦♠♣❛♥✐❡% -❤❡② ✐♥❝!❡❛%❡ ❝❛♣✐-❛❧ ❞❡♠❛♥❞ ❞✉❡ -♦ ❛ ❧♦✇❡! ❡①♣❡❝-❡❞ !❡♠✉♥❡!❛-✐♦♥

❜❛%❡❞ ♦♥ ❜❛♥❦!✉♣-❝② !✐%❦ ✇❤✐❧❡ ✐♥ ❤❡❛❧-❤② ✜!♠% -❤❡② !❡❞✉❝❡ !✐%❦ ❜② ❞❡♠❛♥❞✐♥❣ ❧❡%% ❝❛♣✐-❛❧

❛♥❞ ❛❝-✐♥❣ ♠♦!❡ ♣!✉❞❡♥-✳ ▼❛♥❛❣❡!% ♦❢ ❤✐❣❤❧② ❧❡✈❡!❛❣❡❞ ✜!♠% ❤❛✈❡ ❛ %♠❛❧❧ ❞♦✇♥%✐❞❡ !✐%❦ ❛%

-❤❡✐! ♣❛②♦✛ ✐% ❡①♣❡❝-❡❞ -♦ ❜❡ ❧❡%% ❝❡!-❛✐♥ ✐♥ -❤❡ ✜!%- ♣❧❛❝❡✳

■♥ -❤❡ ❡❝♦♥♦♠✐❝ ❧✐-❡!❛-✉!❡ ❢♦!♠❛❧ ❛♣♣!♦❛❝❤❡% -♦ -❤❡ ❝❛✉%❡% ♦❢ ❝!✐%❡% ✐♥ ❡❝♦♥♦♠✐❝ ❛❝-✐✈✐-②

❧✐♥❦❡❞ -♦ ✜♥❛♥❝✐❛❧ ♠❛!❦❡- !❛♥❣❡ ❢!♦♠ ❢❛✐❧✉!❡ ♣!♦♣❛❣❛-✐♦♥ ❛♣♣!♦❛❝❤❡% ✐♥ ♥❡-✇♦!❦% ✭❇❛--✐%-♦♥

❡- ❛❧✳✱ ✷✵✵✼✮ -♦ ❛%②♠♠❡-!✐❝ ✐♥❢♦!♠❛-✐♦♥ ❝♦♥❝❡♣-% ✭❙-✐❣❧✐-③ ❛♥❞ ❲❡✐%%✱ ✶✾✽✶✮✳ ❚❤❡ ♣❛!-✐❝✉❧❛!

♠✉-✉❛❧ ❞❡♣❡♥❞❡♥❝② ♦❢ ❝!❡❞✐- ♦❜❧✐❣❛-✐♦♥% ❜❡-✇❡❡♥ ✲✐♥ ❣❡♥❡!❛❧ ❜❛♥❦% ❛♥❞ ✜!♠%✱ ❜✉- ❛❧%♦ ❛♠♦♥❣

✜!♠% ❛♥❞ ❜❛♥❦% -❤❡♠%❡❧✈❡% ✲ ♠✐❣❤- ❝♦♥-!✐❜✉-❡ -♦ ❛♥ ❛♠♣❧✐✜❝❛-✐♦♥ ♦❢ ❢❛✐❧✉!❡%✳ ◆♦- ♦♥❧② ✐% -❤❡

❡✛❡❝- ♦❢ ✐❞✐♦%②♥❝!❛-✐❝ ❢❛✐❧✉!❡ ♦❢ ❞✐✛❡!❡♥- ❡✛❡❝- ♦♥ ❛♥ ❡❝♦♥♦♠② ❛% ●❛❜❛✐① ✭✷✵✶✶✮ ♣♦✐♥-% ♦✉-

✐♥ ❤✐% ❣!❛♥✉❧❛! ♠♦❞❡❧✱ ❜✉- -❤❡ ❝♦♥♥❡❝-❡❞♥❡%% ♦❢ ❡❝♦♥♦♠✐❝ ❛❣❡♥-% ♠✐❣❤- ❧❡❛❞ -♦ ❝♦♥-❛❣✐♦♥✳

(5)

●❛❜❛✐① ✭✷✵✶✶✮ *❤♦✇* .❤❛. ✐. ♠❛..❡1* ✇❤✐❝❤ ✜1♠ ✐* ❤✐. ❜② ❛ *❤♦❝❦ ♦1 ❛ ❝1✐*❡* ❢♦1 .❤❡ ❡❝♦♥♦♠②✱

❢♦1 ✐♥*.❛♥❝❡ ❞✉❡ .♦ .❤❡ ✜1♠ *✐③❡ ❛ *❤♦❝❦ .♦ ♠❛❥♦1 ♣❧❛②❡1* ❧✐❦❡ ●❡♥❡1❛❧ ❊❧❡❝.1✐❝ ♠✐❣❤. ✐♥✢✉❡♥❝❡

.❤❡ ❡❝♦♥♦♠② ♠♦1❡ .❤❛♥ ❢♦1❡❝❧♦*✉1❡ ♦❢ .❤❡ ♥❡✐❣❤❜♦1❤♦♦❞ ❣1♦❝❡1② *.♦1❡✳ ❍❡ *❤♦✇* .❤❛. .❤❡

❡♠♣✐1✐❝❛❧❧② ♣1♦✈❡♥ ♣♦✇❡1 ❧❛✇ ❞✐*.1✐❜✉.✐♦♥ ♦❢ ✜1♠ *✐③❡* ❝❛♥ ♣1♦♣❛❣❛.❡ ✐❞✐♦*②♥❝1❛.✐❝ *❤♦❝❦* ✐♥ ❛

✇❛② *✉❝❤ .❤❛. ❜✉*✐♥❡** ❝②❝❧❡* ❡♠❡1❣❡ ✭●❛❜❛✐①✱ ✷✵✶✶✮✳

❆❝❝♦1❞✐♥❣ .♦ .❤❡ ❇❛*❡❧ ■■ 1❡❣✉❧❛.✐♦♥* ❜❛♥❦* ♥❡❡❞ .♦ ❤❛✈❡ .❤❡✐1 ❝1❡❞✐. ❡♥❣❛❣❡♠❡♥.* 1❛.❡❞✳ ❚❤❡②

❝❛♥ ❞♦ .❤✐* .❤❡♠*❡❧✈❡* ✭✐♥.❡1♥❛❧ 1❛.✐♥❣✮ ♦1 ❤✐1❡ *♦♠❡ 1❛.✐♥❣ ❛❣❡♥❝② .♦ ❞♦ ✐. ✭❡①.❡1♥❛❧ 1❛.✐♥❣✮✳

❘❛.✐♥❣* ✇✐❧❧ ❜❡ ❞♦♥❡ ✉*✐♥❣ ❛ ♠✐① ♦❢ ✐♥❢♦1♠❛.✐♦♥ ❝♦♥*✐*.✐♥❣ ♦❢ J✉❛♥.✐.❛.✐✈❡ ❛♥❞ J✉❛❧✐.❛.✐✈❡

✐♥❢♦1♠❛.✐♦♥ ✭❘❡✐❝❤❧✐♥❣ ❡. ❛❧✳✱ ✷✵✵✸✮✳ ❚♦ .❤❡ ❜❡*. ♦❢ ♦✉1 ❦♥♦✇❧❡❞❣❡✱ .❤❡1❡ ✐* ♥♦ ❧✐.❡1❛.✉1❡ .❤❛.

❛**❡**❡* .❤❡ ✐♠♣❛❝. ♦❢ 1❛.✐♥❣ *.1❛.❡❣✐❡* ❛. ❛♥ ❡❝♦♥♦♠②✲✇✐❞❡ *❝❛❧❡✳ ▲✐.❡1❛.✉1❡ ❞❡❛❧✐♥❣ ✇✐.❤

1❛.✐♥❣ ♠❡.❤♦❞* ✐* ❝♦♥❝❡1♥❡❞ ❛❜♦✉. .❤❡ ♣1❡❞✐❝.✐✈❡ ❛❝❝✉1❛❝② ♦❢ .❤❡ ♠❡.❤♦❞ ❛* .❤✐* ✐* ❝1✉❝✐❛❧

❢♦1 ♣1❛❝.✐.✐♦♥❡1* *✉❝❤ ❛* ❜❛♥❦* ♦1 1❛.✐♥❣ ❛❣❡♥❝✐❡*✳ ❋♦1 ✐♥*.❛♥❝❡✱ ❆❧.♠❛♥ ❝♦✐♥❡❞ .❤❡ ✧❩✲❙❝♦1❡✧

❛* ❛ ❜❛♥❦1✉♣.❝② ♣1❡❞✐❝.♦1 ✭❆❧.♠❛♥✱ ✶✾✻✽✮✳ ❚❤✐* ❛♣♣1♦❛❝❤ ✐* ✉*❡❞ ✐♥ ♠❛♥② 1❡✜♥❡❞ ✇❛②* *♦

.❤❛. 1❛.✐♥❣ ❛❣❡♥❝✐❡* ❛♥❞ ❜❛♥❦* ❤❛✈❡ .❤❡✐1 ♦✇♥ *❧✐❣❤.❧② ❞✐✛❡1❡♥. ♠❡.❤♦❞* ♦❢ 1❛.✐♥❣ ✭❆❧.♠❛♥

❛♥❞ ❙❛✉♥❞❡1*✱ ✶✾✾✽❀ ❈1♦✉❤② ❡. ❛❧✳✱ ✷✵✵✵❀ ❘❡✐❝❤❧✐♥❣ ❡. ❛❧✳✱ ✷✵✵✸✮✳ ❖✉1 ❛♣♣1♦❛❝❤ ❞❡❛❧* ✇✐.❤

.❤❡ ✐♠♣❛❝. ♦❢ ❛❝.✉❛❧ ❝✉*.♦♠* ❛. ✜♥❛♥❝✐❛❧ ♠❛1❦❡.* ✐♥ ❛♥ ❡❝♦♥♦♠②✲✇✐❞❡ ❝♦♥.❡①.✳ ❲❡ ♠♦.✐✈❛.❡

♦✉1 ❛♥❛❧②*✐* ✇✐.❤ 1❛.✐♥❣ ♠❡.❤♦❞* .❤❛. ❝♦♠♣1✐*❡ *.♦❝❦ ♠❛1❦❡. ✈❛❧✉❛.✐♦♥* ❛* ♣✐❡❝❡ ♦❢ J✉❛❧✐.❛.✐✈❡

✐♥❢♦1♠❛.✐♦♥ ✭❈1♦✉❤② ❡. ❛❧✳✱ ✷✵✵✵❀ ❘❡✐❝❤❧✐♥❣ ❡. ❛❧✳✱ ✷✵✵✸❀ ❙.❛♥❞❛1❞ ❛♥❞ Z♦♦1✬*✱ ✷✵✶✶✮✳ ❖✉1 1❡*✉❧.* ❝♦♥.1✐❜✉.❡ .♦ .❤❡ ❜✉*✐♥❡** ❝②❝❧❡ ❧✐.❡1❛.✉1❡ ✇✐.❤ ✜♥❛♥❝✐❛❧ ❝♦♥*.1❛✐♥.* ❛* .❤❡② ❛**❡** .❤❡

♦✈❡1❛❧❧ ✐♠♣❛❝. ♦❢ .❤❡ ✐♥❢♦1♠❛.✐♦♥ ✉*❛❣❡ ♦♥ ❡❝♦♥♦♠✐❝ ♦✉.❝♦♠❡*✳

❆* .❤❡ ❧❡❣❛❧ ♣1♦❝❡**❡* ❛1❡ ❛ ♠❛❥♦1 *♦✉1❝❡ ♦❢ ♣♦❧✐.✐❝❛❧ 1✐*❦ ✐♥ ❛♥② ❝♦✉♥.1② .❤♦*❡ ❜❛♥❦1✉♣.❝② ❧❛✇*

❛1❡ ✐♠♣♦1.❛♥. ❢♦1 ✐♥✈❡*.♠❡♥. ❞❡❝✐*✐♦♥*✳ ❲❡ ❝♦♥.1✐❜✉.❡ .♦ .❤❡ ❧✐.❡1❛.✉1❡ ♦❢ ❡❝♦♥♦♠✐❝ ✐♠♣❛❝.*

♦❢ ❜❛♥❦1✉♣.❝② ❧❛✇* ❜② ❛**❡**✐♥❣ .❤❡ ✐♠♣❛❝. ♦❢ *.❛❦❡❤♦❧❞❡1*✬ ✐♥✢✉❡♥❝❡ ♦♥ .❤❡ ❜✉*✐♥❡** ❝②❝❧❡✳

■♥ ♦✉1 ♠♦❞❡❧ .❤❡ ❞❡❣1❡❡ ♦❢ .❤❡ .1❛♥*♠✐**✐♦♥ ♦❢ *.♦❝❦ ♣1✐❝❡ ✈❛1✐❛.✐♦♥ ✐* .❤❡ ♠❛✐♥ ♠❡❝❤❛♥✐*♠✳

❚❤❡ ✐♠♣❛❝. ♦❢ ❜❛♥❦1✉♣.❝② ❧❛✇ ♦♥ ❜✉*✐♥❡** ❝②❝❧❡* ✐* ❛❞❞1❡**❡❞ ❜② ❙✉❛1❡③ ❛♥❞ ❙✉**♠❛♥ ✭✷✵✵✼✮✳

❚❤❡② ✜♥❞ .❤❛. ♠♦1❡ ✜1♠ ❢1✐❡♥❞❧② ❧❛✇*✱ .❤❛. ✐* ❛ ❤✐❣❤❡1 ❝❤❛♥❝❡ ♦❢ ♥♦. ❜❡✐♥❣ ❞❡❝❧❛1❡❞ ❜❛♥❦1✉♣.✱

❤❛* ❛ ♣♦**✐❜❧❡ ❛❞✈❡1*❡ ❧♦♥❣✲.❡1♠ ❡✛❡❝.✳ ❲❤✐❧❡ ♠♦1❡ ✜1♠* ❝♦♥.✐♥✉❡ .♦ ❡①✐*. ✐♥ .❤❡ *❤♦1. 1✉♥✱

❧❡♥❞❡1* ♠❛② 1❡J✉✐1❡ ❤✐❣❤❡1 ❧❡✈❡❧* ♦❢ ❝♦❧❧❛.❡1❛❧ ✐♥ .❤❡ ❧♦♥❣✲1✉♥ ✇❤✐❝❤ ❞✐♠✐♥✐*❤❡* ❣1♦✇.❤✳ ❚❤❡✐1

✐❞❡❛ ♦❢ *♦❢. ❧❛✇* ✐* ❜❛*❡❞ ❛❧*♦ ♦♥ *❤❛1❡❤♦❧❞❡1*✬ ❜❛1❣❛✐♥✐♥❣ ♣♦✇❡1 ✇❤✐❝❤ ✐* .❤❡ .1❛♥*♠✐**✐♦♥

❝❤❛♥♥❡❧ ♦❢ *.♦❝❦ ♣1✐❝❡* ✐♥ ♦✉1 ♠♦❞❡❧✳ ■♥ ❛ *✐♠♣❧❡1 ❛1❣✉♠❡♥. ▲❡❡ ❡. ❛❧✳ ✭✷✵✵✼✮ ♣♦✐♥. ♦✉. .❤❛.

*♦❢. ❧❛✇* ♠❛② ❜❡ ❜❡♥❡✜❝✐❛❧ ❛* .❤❡② ♣1♦♠♦.❡ ❛ ❧❛1❣❡1 ✈❛1✐❡.② ♦❢ ✜1♠*✳ ❚❤❡② ❞❡❡♠ .❤✐* ❞❡*✐1❛❜❧❡

❢♦1 .❤❡ *♦❝✐❡.②✳ ■♥ ❛ ❣❡♥❡1❛❧ ❡J✉✐❧✐❜1✐✉♠ ❝♦♥.❡①.✱ ♠♦❞❡*. ❧❡✈❡❧* ♦❢ ❜❛♥❦1✉♣.❝② ♣✉♥✐*❤♠❡♥. ❝❛♥

❜❡ ❜❡♥❡✜❝✐❛❧ ❜❡❝❛✉*❡ .❤❡② ♠❛❦❡ ❝1❡❞✐.♦1* ❛♥❞ ❧❡♥❞❡1* ❜❡..❡1 ♦✛ ✭❉✉❜❡② ❡. ❛❧✳✱ ✶✾✾✺✮✳

❖✉1 1❡*✉❧.* ✐♥❞✐❝❛.❡ .❤❛. .❤❡ ❧❛✇ ✐* ♦❢ ♠✐♥♦1 ❡✛❡❝. ✐❢ .❤❡ ✜1♠* ❛1❡ ❛✛❡❝.❡❞ ✐❞✐♦*②♥❝1❛.✐❝❛❧❧② ❜②

*.♦❝❦ ♣1✐❝❡*✳ ■❢ .❤❡1❡ ✐* ❝♦11❡❧❛.✐♦♥ ❛♠♦♥❣ *.♦❝❦ ♣1✐❝❡*✱ ❢♦1 ✐♥*.❛♥❝❡ .❤1♦✉❣❤ ❜♦♦♠✲❜✉*. ❝②❝❧❡*✱

❛ ✜1♠ ❢1✐❡♥❞❧② 1✉❧✐♥❣ ✇♦✉❧❞ ❛❧*♦ 1❡*✉❧. ✐♥ ❡①.1❡♠❡ ✈❛1✐❛.✐♦♥* ❛♥❞ ❜✉*✐♥❡** ❝②❝❧❡*✳ ❚❤♦*❡ ❝♦♠❡

❤♦✇❡✈❡1✱ ✇✐.❤ ♥♦ ❧♦♥❣ .❡1♠ ❣1♦✇.❤ ✐♥ .❤❡ ♠♦❞❡❧ ❜❡❝❛✉*❡ .❤❡1❡ ✐* ♥♦ ❢✉1.❤❡1 ❡J✉✐.② ✐♥❥❡❝.❡❞✳

❚❤❡1❡❢♦1❡✱ ✐♥ .❤❡ ♣1❡*❡♥❝❡ ♦❢ ❜♦♦♠✲❜✉*. ❝②❝❧❡* ❛. .❤❡ *.♦❝❦ ♠❛1❦❡. ✇❡ ✇♦✉❧❞ 1❡❝♦♠♠❡♥❞ ❛

❜❛♥❦1✉♣.❝② ❧❛✇ .❤❛. ✐* ♥♦. .♦♦ ✜1♠ ❢1✐❡♥❞❧②✳

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❚❤❡ ❝♦♠♣❡♥(❛*✐♦♥ ♦❢ ♠❛♥❛❣❡.( ❝❛♥ ❛❝*✉❛❧❧② ❝♦♥(✐(* ♦❢ (❡✈❡.❛❧ ❝♦♠♣♦♥❡♥*(✳ ❇❡(✐❞❡( ❢.♦♠ *❤❡

(❛❧❛.② *❤❡.❡ ❛.❡ ♣❡.❢♦.♠❛♥❝❡ ❜❛(❡❞ ♣❛②♦✛( *❤❛* (❡.✈❡ ❛( ✐♥❝❡♥*✐✈❡ ❢♦. *❤❡ ♠❛♥❛❣❡.(✳ ❚❤✐(

✐♥❝❡♥*✐✈❡ ❝❛♥ ❞✐✛❡.✳ ❇.②❛♥ ❡* ❛❧✳ ✭✷✵✵✵✮ ♣♦✐♥* ♦✉* *❤❛* ❢♦. ✐♥(*❛♥❝❡✱ ❣.❛♥*❡❞ (*♦❝❦( ♠❛② ❧❡❛❞

*♦ ♠♦.❡ ♣.✉❞❡♥* ❜❡❤❛✈✐♦✉. ✇❤✐❧❡ (*♦❝❦ ♦♣*✐♦♥( ♠✐❣❤* ✐♥❝.❡❛(❡ *❤❡ .✐(❦ *❛❦✐♥❣✳ ❚❤✐( ✐( ❞✉❡ *♦

*❤❡ ❞✐✛❡.❡♥* ♣❛②♦✛ (*.✉❝*✉.❡ ✇❤✐❝❤ ✐( ❧✐♥❡❛. ✐♥ ❣.❛♥*❡❞ (*♦❝❦( ❜✉* ♥♦* ✐♥ (*♦❝❦ ♦♣*✐♦♥( ✇❤❡.❡

♠❛♥❛❣❡.( ❞♦ ♥♦* ❜❡❛. *❤❡ ❞♦✇♥(✐❞❡ .✐(❦✳

❚❤❡.❡ ✐( ❛ .❡❝❡♥* ❞❡❜❛*❡ ❛( *♦ ❝❛♣ *❤❡ ❜♦♥✉(❡( ♦❢ ❜❛♥❦ ♠❛♥❛❣❡.( (✐♥❝❡ ✇.♦♥❣ ✐♥❝❡♥*✐✈❡( ❤❛✈❡

❜❡❡♥ ❞❡❡♠❡❞ *♦ ❝♦♥*.✐❜✉*❡ ✐♥ *❤❡ ✜♥❛♥❝✐❛❧ ❝.✐(✐( ♦❢ ✷✵✵✼✳ ❆( ❛ .❡(✉❧*✱ *❤❡ ❊✉.♦♣❡❛♥ ❯♥✐♦♥ ❬❊❯❪

♣❛((❡❞ ❛ ❧❛✇ ✇✐*❤ ❡✛❡❝* ♦❢ ❏❛♥✉❛.② ✶✱ ✷✵✶✹ *❤❛* ❡✛❡❝*✐✈❡❧② ❧✐♠✐*( *❤❡ ❜♦♥✉( ♣❛②♠❡♥*( ♦❢ ❜❛♥❦

♠❛♥❛❣❡.( *♦ ✶✵✵✪ ♦❢ *❤❡✐. ✜①❡❞ (❛❧❛.②✳ ✭❊❯✱ ✷✵✶✸✿ ❆.*✐❝❧❡ ✾✹✱✶✱❣✱✭✐✮ ❛♥❞ ✭✐✐✮✮✳ ▼❛♥❛❣❡.(

✐♥ *❤❡ ❯♥✐*❡❞ ❑✐♥❣❞♦♠ ❡✈❡♥ ❢❛❝❡ ❛ ❝❧❛✇✲❜❛❝❦ .✉❧❡ ♣✉* ✐♥*♦ ❡✛❡❝* ❢.♦♠ ❏❛♥✉❛.② ✷✵✶✺ ♦♥✳

❆❝❝♦.❞✐♥❣ *♦ *❤❛*✱ *❤❡② ❝❛♥ ❜❡ ❢♦.❝❡❞ *♦ ♣❛② ❜❛❝❦ ❜♦♥✉(❡( ♦✈❡. ❛ ♣❡.✐♦❞ ♦❢ (❡✈❡♥ ②❡❛.( ❛❢*❡.

*❤❡✐. ❛✇❛.❞✐♥❣✳ ❚❤✐( ✐( ❛ ❢♦.♠ ♦❢ ❡① ♣♦(* .✐(❦ ❛❞❥✉(*♠❡♥* ✐♥ ♦.❞❡. *♦ ✏❛❧✐❣♥ ❜❡**❡. *❤❡ ✐♥*❡.❡(*(

♦❢ (*❛✛ (✉❜❥❡❝* *♦ *❤❡ ❘❡♠✉♥❡.❛*✐♦♥ ❈♦❞❡ ✇✐*❤ *❤❡ ❧♦♥❣ ✲*❡.♠ ✐♥*❡.❡(*( ♦❢ *❤❡ ✜.♠✳✑ ✭❇❛♥❦

♦❢ ❊♥❣❧❛♥❞✱ ✷✵✶✹✳✮ ■♥ *❤❡ ♠♦❞❡❧ *❤❡ ❜❛♥❦.✉♣*❝② ❝♦(*( ❛.❡ *❛❦❡♥ ✐♥*♦ ❛❝❝♦✉♥* ❜② *❤❡ ♠❛♥❛❣❡.(

(✐♥❝❡ *❤❡② (✉✛❡. ❢.♦♠ *❤❡ *❡.♠✐♥❛*✐♦♥ ♦❢ *❤❡✐. ❝♦♥*.❛❝*(✳ ■❢ *❤❡.❡ ✐( ♦♥❧② ✜①❡❞ (❛❧❛.②✱ *❤❡②

❧♦♦(❡ ♦♥❧② *❤❡✐. (❛❧❛.② ✇❤✐❝❤ ♠❛*❝❤❡( ✇✐*❤ *❤❡ ❝♦(* ❝♦♥❝❡♣* ♦❢ ❉❡❧❧✐ ●❛**✐ ❡* ❛❧✳ ❍♦✇❡✈❡.✱ ✐❢

♣❛.* ♦❢ *❤❡✐. (❛❧❛.② ✐( ❛❧(♦ ❣.❛♥*❡❞ (*♦❝❦( ✐♥ ❛ ♣❡.❢♦.♠❛♥❝❡ ❜❛(❡❞ .❡♠✉♥❡.❛*✐♦♥ (❝❤❡♠❡✱ *❤❡.❡

♠✐❣❤* ❜❡ ❛❧(♦ ❛ ❧♦(( ♣♦(✐*✐✈❡❧② .❡❧❛*❡❞ *♦ *❤❡ ❝✉..❡♥* (*♦❝❦ ♣.✐❝❡✳

❖✉. ♠♦❞❡❧ .❡(✉❧*( ✐♥❞✐❝❛*❡ *❤❛* *❤❡.❡ ✐( ❛ ❝♦♠♣❧❡① ✐♠♣❛❝* ♦❢ ♣❡.❢♦.♠❛♥❝❡ ❜❛(❡❞ ❝♦♠♣❡♥(❛*✐♦♥✳

❋♦. ❧♦✇ ❧❡✈❡❧( ✭(❤❛.❡ ✐( ❜❡❧♦✇ ❛❜♦✉* ✶✴✷✮ ❛♥② ✐♥❝.❡❛(❡ ❞♦❡( ❤❛.❞❧② ✐♥❝.❡❛(❡ ♦✉*♣✉* ❜✉* ❝❛✉(❡(

❛ ❤✐❣❤❡. ✐♥*❡.❡(* .❛*❡✳ ❍♦✇❡✈❡.✱ ❢♦. ❛ (❤❛.❡ ❛❜♦✈❡ ✶✴✷ ❛ ❢✉.*❤❡. ✐♥❝.❡❛(❡ ❞♦❡( ✐♥❝.❡❛(❡ *❤❡

✐♥*❡.❡(* .❛*❡ ♦♥❧② ♠❛.❣✐♥❛❧❧② ❜✉* ❜♦♦(*( ♦✉*♣✉*✳ ^♦❧✐❝② ❛❞✈✐(❡ ✐( *❤❡.❡❢♦.❡ ❞❡♣❡♥❞✐♥❣ ♦♥ *❤❡

❝✉..❡♥* ❧❡✈❡❧ ♦❢ ♣❡.❢♦.♠❛♥❝❡ ❜❛(❡❞ ❝♦♠♣❡♥(❛*✐♦♥ ❛♥❞ ♦♥ *❤❡ ♣❛.*✐❝✉❧❛. ✐((✉❡ *❤❛* (❤♦✉❧❞ ❜❡

♣.♦♠♦*❡❞✳ ■♥ ❝♦♠♣❛.✐(♦♥ *♦ *❤❡ ❊❯ ❧❛✇ *❤✐( ♠❡❛♥( *❤❛* ✐* ♠❛❦❡( (❡♥(❡ *♦ ❤♦❧❞ *❤❡ ♠❛♥❛❣❡.(

❛❝❝♦✉♥*❛❜❧❡ (✐♥❝❡ *❤✐( ✐♥❞✉❝❡( (❡♥(✐*✐✈❡ ❜❡❤❛✈✐♦✉.✳ ■❢ ♠❛♥❛❣❡.( ❜❡❤❛✈❡ (❡♥(✐*✐✈❡✱ ✈♦❧❛*✐❧✐*②

❝②❝❧❡( ❛* *❤❡ (*♦❝❦ ♠❛.❦❡* ❞♦ ♥♦* ❤❛.♠ *❤❡ ❡❝♦♥♦♠② ✈❡.② ♠✉❝❤✳

❚❤❡ ♣❛♣❡. ✐( ♦.❣❛♥✐③❡❞ ❛( ❢♦❧❧♦✇(✿ (❡❝*✐♦♥ ✷ ❣✐✈❡( ❛♥ ♦✈❡.✈✐❡✇ ♦❢ *❤❡ ♠♦❞❡❧✳ ❚❤❡♥✱ *❤❡ ✐♠♣❛❝*

♦❢ ❜❛♥❦ ♣♦❧✐❝② ✐( ✐♥*.♦❞✉❝❡❞ ✐♥ (❡❝*✐♦♥ ✸✳ ❚❤❡ ✐♠♣❛❝* ♦❢ ❞✐✛❡.❡♥* ❜❛♥❦.✉♣*❝② ❝✐.❝✉♠(*❛♥❝❡(

✐( ❞✐(❝✉((❡❞ ✐♥ (❡❝*✐♦♥ ✹ ❛♥❞ ❧❛(* *❤❡ ✐♠♣❛❝* ♦❢ ♠❛♥❛❣❡.✐❛❧ ❜❡❤❛✈✐♦✉. ✇✐*❤ .❡(♣❡❝* *♦ (*♦❝❦

♣.✐❝❡( ✐( ❡①❛♠✐♥❡❞ ✐♥ (❡❝*✐♦♥ ✺✳ ❙❡❝*✐♦♥ ✻ ❞✐(❝✉((❡( *❤❡ .❡(✉❧*(✳

2. The Model

❚❤❡ ♠♦❞❡❧ ✐( ❜❛(❡❞ ♦♥ ✇♦.❦ ♦❢ ●.❡❡♥✇❛❧❞ ✫ ❙*✐❣❧✐*③ ❛♥❞ (✉❜(❡c✉❡♥* ✇♦.❦ ♦❢ ❉❡❧❧✐ ●❛**✐ ❡*

❛❧✳ ✭●.❡❡♥✇❛❧❞ ❛♥❞ ❙*✐❣❧✐*③✱ ✶✾✾✵✱✶✾✾✸❀ ❉❡❧❧✐ ●❛**✐ ❡* ❛❧✳✱ ✷✵✵✺✮✳ ❆ ❝♦.❡ ❢❡❛*✉.❡ ✐( *❤❛*

✜.♠(✬ ♠❛♥❛❣❡.( ❛❝* ✐♥ ❛ .✐(❦ ❛✈❡.(❡ ♠❛♥♥❡. ❜❡❝❛✉(❡ ❜❛♥❦.✉♣*❝② ♦❢ *❤❡ ✜.♠ ✐( ❝♦(*❧② ❢♦. *❤❡♠

♣❡.(♦♥❛❧❧②✳ ❈.❡❞✐* ✜♥❛♥❝✐♥❣ ❛♥❞ ❧❡✈❡.❛❣❡ ❡①♣♦(❡( *❤❡ ✜.♠ *♦ ✜♥❛♥❝✐❛❧ ❢.❛❣✐❧✐*②✳ ❚❤❡.❡❢♦.❡✱

*❤❡② *❛❦❡ ♣♦((✐❜❧❡ ❜❛♥❦.✉♣*❝② ❝♦(*( ✐♥*♦ ❝♦♥(✐❞❡.❛*✐♦♥ ✇❤❡♥ *❤❡② ✉(❡ ❜❛♥❦ ❧♦❛♥( ❢♦. ✜♥❛♥❝✐♥❣

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❞❡"✐$❡❞ ♣$♦❞✉❝)✐♦♥✳ ❚❤❡ ✉"❡ ♦❢ ❝$❡❞✐) ❞$✐✈❡" )❤❡ ❡❝♦♥♦♠② ❛♥❞ ❤❛" ❛♥ ❛♠❜✐✈❛❧❡♥) ✐♠♣❛❝) ✇❤✐❝❤

✐♥❞✉❝❡" ✢✉❝)✉❛)✐♦♥"✿ ❛ ❤✐❣❤❡$ ❛♠♦✉♥) ♦❢ ❝$❡❞✐) ✐♥❝$❡❛"❡" ❧❡✈❡$❛❣❡ ✇❤✐❝❤ ♣♦""✐❜❧② ✐♥❞✉❝❡" ❤✐❣❤❡$

♣$♦✜)" ❜✉) ❛) )❤❡ "❛♠❡ )✐♠❡ ❛❧"♦ ✐♥❝$❡❛"❡" ✜♥❛♥❝✐❛❧ ❢$❛❣✐❧✐)②✳

❇❛♥❦$✉♣)❝② ✐" ❝♦")❧② ❢♦$ )❤❡ ♠❛♥❛❣❡♠❡♥) ✜$") ♦❢ ❛❧❧ ❞✉❡ )♦ )❤❡ ❧♦"" ♦❢ "❛❧❛$② ❜✉) ❛❧"♦ )❤❡ ❧♦""

♦❢ $❡♣✉)❛)✐♦♥ ❛♥❞ ❢✉$)❤❡$ $❡❡♠♣❧♦②♠❡♥) ♠✐❣❤) ❜❡❝♦♠❡ ♠♦$❡ ❞✐✣❝✉❧)✳ ❆ ❢✉$)❤❡$ ❛""✉♠♣)✐♦♥

✐" )❤❛) )❤❡ ❝♦")" ♦❢ ❜❛♥❦$✉♣)❝② ✐♥❝$❡❛"❡ ✐♥ ✜$♠ "✐③❡ ❜❡❝❛✉"❡ ✉"✉❛❧❧② )❤❡$❡ ❛$❡ ♠♦$❡ ♠❛♥❛❣❡$"

✐♥✈♦❧✈❡❞ ✐♥ ❧❛$❣❡ ❝♦♠♣❛♥✐❡" ✭●$❡❡♥✇❛❧❞ ❛♥❞ ❙)✐❣❧✐)③✱ ✶✾✾✵✱ ♣✳ ✶✼✮✳ ●$❡❡♥✇❛❧❞ ❛♥❞ ❙)✐❣❧✐)③

❛❧"♦ ♣♦✐♥) ♦✉) )❤❛) ✜♥❛♥❝✐❛❧ ❞✐")$❡"" ❝❛♥ ♦❝❝✉$ ✐♥ ❞✐✛❡$❡♥) ✇❛②" ❛♥❞ ❞♦❡" ♥♦) ❛❧✇❛②" ❧❡❛❞

)♦ ❜❛♥❦$✉♣)❝② ✭●$❡❡♥✇❛❧❞ ❛♥❞ ❙)✐❣❧✐)③✱ ✶✾✾✵✱ ♣✳ ✶✼✱ ❢♦♦)♥♦)❡ ✺✮✳ ❲❤✐❧❡ ❢♦$ )❤❡ ❝♦♠♣❛♥②

✜♥❛♥❝✐❛❧ ❞✐")$❡"" ❞♦❡" ♥♦) ❛✉)♦♠❛)✐❝❛❧❧② ♠❡❛♥ )❤❡ ❡♥❞ ♦❢ )❤❡ ✜$♠✱ ✉"✉❛❧❧② ♦♥❡ ♦❢ )❤❡ ✜$")

♠❡❛"✉$❡" ✉♥❞❡$)❛❦❡♥ ✐♥ "✉❝❤ "✐)✉❛)✐♦♥" ✐" )♦ $❡♣❧❛❝❡ ♠❛♥❛❣❡♠❡♥)✳ ❚❤❡$❡❢♦$❡✱ ❛" "♦♦♥ ❛" )❤❡$❡

✐" ✜♥❛♥❝✐❛❧ ❞✐")$❡""✱ ♠❛♥❛❣❡$" ♠♦") ♣$♦❜❛❜❧② "✉✛❡$ ❢$♦♠ ❛ ♠♦♥❡)❛$② ❧♦"" ✇❤✐❝❤ ✐" ❛) ❧❡❛")

❢♦$❡❣♦♥❡ "❛❧❛$②✳ ❚❤❡ ✐""✉❡ ♦❢ ✜♥❛♥❝✐❛❧ ❞✐")$❡"" ❛♥❞ ❜❛♥❦$✉♣)❝② ✐" ✐♥❝♦$♣♦$❛)❡❞ ✐♥ )❤❡ ♠♦❞❡❧ ❜②

❉❡❧❧✐ ●❛))✐ ❡) ❛❧✳ ✭✷✵✵✺✮ ✐♥ )❤❡ "✐♠♣❧❡ ✇❛② )❤❛) ✜♥❛♥❝✐❛❧ ❞✐")$❡"" ❛✉)♦♠❛)✐❝❛❧❧② ❧❡❛❞" )♦ )❤❡

❧✐M✉✐❞❛)✐♦♥ ♦❢ )❤❡ ✜$♠✳

2.1. baseline setup

❲❡ ✜$") $❡❝❛❧❧ )❤❡ ♠♦❞❡❧ ✐♥)$♦❞✉❝❡❞ ❜② ❉❡❧❧✐ ●❛))✐ ❡) ❛❧✳ ✭✷✵✵✺✮✳ ❲❡ ❛❞❞ ❡M✉✐)② ❛♥❞ ")♦❝❦

♣$✐❝❡" ✐♥ "❡❝)✐♦♥ ✷✳✷✳ ❖)❤❡$ ❡①)❡♥"✐♦♥" ❛$❡ ♣$❡"❡♥)❡❞ ✐♥ )❤❡ ❢♦❧❧♦✇✐♥❣ "❡❝)✐♦♥"✳ ◆❡) ✇♦$)❤ ♦❢ ❛

✜$♠i❛) )✐♠❡t✱ )❤❛) ✐" ✐♥ ❣❡♥❡$❛❧ ❛""❡)" ♠✐♥✉" ❧✐❛❜✐❧✐)✐❡" ❞✉❡ ✐♥ t✱ ✐" ❞❡♥♦)❡❞A_it✳ ❚❤✐" ♥♦)❛)✐♦♥

$❡❢❡$" )♦ )❤❡ ♥❡) ✇♦$)❤ ❛! !❤❡ ❡♥❞ ♦❢ ♣❡$✐♦❞ t✳ ■) ❝♦♥"✐")" ♦❢ )❤❡ ♥❡) ✇♦$)❤ ❛) )❤❡ ❡♥❞ ♦❢ )❤❡

♣$✐♦$ ♣❡$✐♦❞ ♣❧✉" ♥❡! ♣$♦✜)" ❢$♦♠ )❤❡ ❝✉$$❡♥) ♣❡$✐♦❞✳ ❖❢)❡♥✱ )❤✐" ♥❡) ✇♦$)❤ ✐" ❛❧"♦ $❡❢❡$$❡❞ )♦

❛" ✧❡M✉✐)②✧✳ ■❢ )❤❡ ✜$♠ ❤❛" ♥♦) ✐""✉❡❞ ❛♥② "❤❛$❡"✱ ♥❡) ✇♦$)❤ ✐" )❤❡ "❛♠❡ ❛" )❤❡ "✉♠ ♦❢ ❛❧❧

$❡)❛✐♥❡❞ ♣$♦✜)" ✉♣ )♦ )❤❡ ❡♥❞ ♦❢ ♣❡)✐♦❞ t✳

A_it =A_it₋₁+π_it (1)

❆""✉♠❡ )❤❛) )❤❡ ✜$♠" )$❛♥"❢♦$♠ ✜♥❛♥❝✐❛❧ ♠❡❛♥" ✐♥)♦ ♣$♦❞✉❝)✐✈❡ ❝❛♣✐)❛❧ ✇✐)❤♦✉) ❛♥② ❝♦")"✳

S$♦❞✉❝)✐✈❡ ❝❛♣✐)❛❧ K_it ✐" )❤❡♥ )❤❡ "✉♠ ♦❢ ♥❡) ✇♦$)❤ )❛❦❡♥ ♦✈❡$ ❢$♦♠ )❤❡ ♣$✐♦$ ♣❡$✐♦❞ A_it₋₁ ❛♥❞

❝$❡❞✐) )❛❦❡♥ ✐♥ )❤❡ ❝✉$$❡♥) ♣❡$✐♦❞✱ L_it✿

K_it =^Ait−1+^Lit (2)

❖✉)♣✉) Y_it ✐" ♣$♦❞✉❝❡❞ ❜② ❛♣♣❧②✐♥❣ ❝♦♥")❛♥) $❡)✉$♥" )♦ "❝❛❧❡ φ )♦ ♣$♦❞✉❝)✐✈❡ ❝❛♣✐)❛❧✿

Y_it =φK_it (3)

S$♦✜) ❞❡♣❡♥❞" ♦♥ )❤❡ ♣$✐❝❡ u_it )❤❛) ❛♣♣❧✐❡" )♦ )❤❡ ♦✉)♣✉) ❛♥❞ )❤❡ ❝♦")" ❢♦$ "❡))✐♥❣ ✉♣ ❝❛♣✐)❛❧

✇❤✐❝❤ ❝♦♥"✐")" ♦❢ $❡)♦♦❧✐♥❣ ❝♦")" g>0 ❛♥❞ $❡♥)❛❧ ❝♦")" ❢♦$ ❝❛♣✐)❛❧ r_it✳ ❆""✉♠❡ )❤❛) )❤❡ ❝♦")"

❢♦$ ❝$❡❞✐) ❛♥❞ )❤❡ $❡❛❧ $❡)✉$♥ )♦ ❝❛♣✐)❛❧ ❛$❡ )❤❡ "❛♠❡ ❛♥❞ ❛♣♣❧② ❤❡♥❝❡ )♦ )❤❡ ❡♥)✐$❡ ")♦❝❦ ♦❢

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♣!♦❞✉❝&✐✈❡ ❝❛♣✐&❛❧✿

π_it =u_itφK_it−gr_itK_it (4)

✇✐&❤u_it ❜❡✐♥❣ !❛♥❞♦♠ ❛♥❞ ✉♥✐❢♦!♠❧② ❞✐5&!✐❜✉&❡❞ ✇✐&❤ 5✉♣♣♦!& ❜❡&✇❡❡♥ ③❡!♦ ❛♥❞ &✇♦✳ ❚❤❡!❡❢♦!❡✱

E[π_it] = (φ−gr_it)K_it✳ ❆ ✜!♠ ✐5 ❜❛♥❦!✉♣& ✇❤❡♥ ✐&5 ❛55❡&5 ❛!❡ ✐♥5✉✣❝✐❡♥& &♦ !❡♣❛② &❤❡ ❞❡❜& ❛&

&❤❡ ❡♥❞ ♦❢ ❛ ♣❡!✐♦❞✿

A_it <0 (5)

❚❤✐5 ❝♦♥❞✐&✐♦♥ 5&❛&❡5 &❤❛& ❛ ✜!♠ ✇❤♦5❡ ❡>✉✐&② ✭♥❡& ✇♦!&❤✮ ✐5 ❜❡❧♦✇ ③❡!♦ ✇✐❧❧ ❜❡ ❞✐55♦❧✈❡❞ ❛♥❞

❧❡❛✈❡5 &❤❡ ❡❝♦♥♦♠②✳ ■& ✐5 ❛55✉♠❡❞ &❤❛& ✜!♠5 ❝❛♥ 5❡❧❧ &❤❡✐! ♣!♦❞✉❝&5 ❛& ❛ ♠❛!❦❡& ✐5♦❧❛&❡❞ ❢!♦♠

❛❧❧ ♦&❤❡!5 ✭✧✐5❧❛♥❞5✧✮ ❛♥❞ &❤❛& &❤❡② ❝❛♥ 5❡❧❧ &❤❡✐! ❡♥&✐!❡ ♣!♦❞✉❝&✐♦♥✳ ◆❡✈❡!&❤❡❧❡55✱ &❤❡② ❢❛❝❡

✉♥❝❡!&❛✐♥&② ✐♥ &❤❡ ♣!✐❝❡ u_it ✇❤✐❝❤ ✐5 ✉♥✐>✉❡ ♦♥ ❡❛❝❤ ✐5❧❛♥❞ ❛♥❞ ♣❡!✐♦❞✳ ❚❤✐5 ❛♣♣!♦❛❝❤ ✐5 ✐♥

❧✐♥❡ ✇✐&❤ &❤❡ ❢❛❝& &❤❛& ❛ ❧♦& ♦❢ ✜♥❛♥❝✐❛❧ ❞✐5&!❡55 5&❡♠5 ❢!♦♠ ❞❡❢❛✉❧&✐♥❣ ❝✉5&♦♠❡!5 ✭❘❡✐❝❤❧✐♥❣ ❡&

❛❧✳ ✭✷✵✵✼✮✱ ♣✳✷✷✸✮✳ ❚❤❡!❡❢♦!❡✱ &❤❡ !❛♥❞♦♠ ♣!✐❝❡ ✇❤✐❝❤ ②✐❡❧❞5 ❛ !❛♥❞♦♠ !❡✈❡♥✉❡ ❝❛♥ ❛❧5♦ ❜❡

✐♥&❡!♣!❡&❡❞ ❛5 &❤❡ 5❤❛!❡ ♦❢ 5❛❧❡5 &❤❛& ✐5 ❛❝&✉❛❧❧② ♣❛✐❞ ❢♦!✳ ❚❛❦✐♥❣ ✐♥&♦ ❛❝❝♦✉♥& &❤❡ ❜❛♥❦!✉♣&❝②

❝♦♥❞✐&✐♦♥ ❛♥❞ ❡>✉❛&✐♦♥5 ✭✶✮ ❛♥❞ ✭✹✮✱ &❤❡ ♣!✐❝❡ &❤❛& ❥✉5& 5✉5&❛✐♥5 ❛ ✜!♠ ✐5 uit =^gr^it

φ −A_it₋₁

K_itφ (6)

❆55✉♠❡ &❤❛& &❤❡ ❝♦5&5 ♦❢ ❜❛♥❦!✉♣&❝② ❞❡♣❡♥❞ ♦♥ &❤❡ 5✐③❡ ♦❢ &❤❡ ❡♥&❡!♣!✐5❡ ✐♥ &❤❡ ❢♦!♠ c^f =cY²

✇✐&❤ c>0 ❜❡✐♥❣ ❛ ❝♦♥5&❛♥&✳ ❆55✉♠❡ ❢✉!&❤❡! &❤❛& ♠❛♥❛❣❡!5 &❛❦❡ ✐♥&♦ ❛❝❝♦✉♥& &❤❡5❡ ❝♦5&5

♦❢ ❜❛♥❦!✉♣&❝② ✇❤❡♥ ❞❡❝✐❞✐♥❣ ❛❜♦✉& &❤❡ ❞❡♠❛♥❞ ❢♦! ❝❛♣✐&❛❧ ✐♥ ❡❛❝❤ ♣❡!✐♦❞✳ ❚❤❡② ❜❛5❡ &❤❡✐!

❞❡❝✐5✐♦♥ ♦♥ &❤❡ ❡①♣❡❝&❡❞ ♣!♦✜&

Γ_it = (^φ₋grit)Kit−E(c^f) ⁽⁷⁾

✇❤✐❧❡ &❤❡ ❡①♣❡❝&❡❞ ❝♦5&5 ♦❢ ❜❛♥❦!✉♣&❝② E(^c^f) ❛!❡ ❞❡&❡!♠✐♥❡❞ ❜② &❤❡ ♣!♦❜❛❜✐❧✐&② ♦❢ ❜❛♥❦!✉♣&❝② M!♦❜(BR) =M!♦❜(u_it <u_it) =u_it/2 ❢♦! u∼❯♥✐❢♦!♠[0, 2]✳ ❉❡♠❛♥❞ ❢♦! ❝❛♣✐&❛❧ ✐5 &❤❡ !❡5✉❧&

♦❢ &❤❡ ♠❛①✐♠✐③❛&✐♦♥ ♦❢ ❡①♣❡❝&❡❞ ♣!♦✜&✳ ❯5✐♥❣ &❤❡ ✜!5& ♦!❞❡! ❝♦♥❞✐&✐♦♥ ❛♥❞ 5♦❧✈✐♥❣ ❢♦! ❝❛♣✐&❛❧

②✐❡❧❞5 K_it^d = ^φ_cφgr⁻^gr_itît +Â_2grît⁻_it¹✳ ❈!❡❞✐& ❞❡♠❛♥❞ ✐5 &❤❡ ❞✐✛❡!❡♥❝❡ ❜❡&✇❡❡♥ ❞❡♠❛♥❞ ❢♦! ❝❛♣✐&❛❧ ❛♥❞

!❡&❛✐♥❡❞ ♣!♦✜&5 L^d_it =K_it^d−A_it₋₁✱ ②✐❡❧❞✐♥❣

L^d_it = ¹ cφgrit

cφ

2 A_it₋₁(¹₋^2grit) +^φ₋^grit

(8)

❚❤❡ ❜❛♥❦5✬ ♣!♦✜& (^π_t^B) ❞❡♣❡♥❞5 ♦♥ &❤❡ !❡✈❡♥✉❡ ❢!♦♠ ❧♦❛♥5 ❣!❛♥&❡❞ ♠✐♥✉5 &❤❡ ❝♦5&5 ♦❢ !❛✐5✐♥❣

&❤♦5❡ ❢✉♥❞5 ❢!♦♠ ❡>✉✐&② E_t^B ❛♥❞ ❞❡♣♦5✐&5 D_t✿ π_t^B=

∑

i∈Nt

r_itL^s_it−r_t[(1−ω)D_t₋₁+E_t^B₋₁] (9)

❍❡!❡✱ ω ❞❡5❝!✐❜❡5 &❤❡ ❞❡❣!❡❡ ♦❢ ❝♦♠♣❡&✐&✐♦♥ ✇✐&❤✐♥ &❤❡ ❜❛♥❦✐♥❣ 5❡❝&♦! ❛♥❞ ✐5 ❛ ♠❡❛5✉!❡ ❢♦!

&❤❡ ♠❛!❦ ✉♣ &❤❡ ❜❛♥❦ ❝❛♥ ❝❤❛!❣❡ ♦♥ ✐♥&❡!❡5& ❛❜♦✈❡ ❞❡♣♦5✐&5✳ ❚❤❡ ✐♥&❡!❡5& ♣❛✐❞ ♦♥ ❞❡♣♦5✐& ✐5 r_t(1−ω) ✇❤❡!❡ r_t ✐5 ❛55✉♠❡❞ &♦ ❜❡ &❤❡ ✇❡✐❣❤&❡❞ ❛✈❡!❛❣❡ ❧❡♥❞✐♥❣ ✐♥&❡!❡5& !❛&❡✳ ❲❤❡♥ ❛ ✜!♠

❣♦❡5 ❜❛♥❦!✉♣& ❛! !❤❡ ❡♥❞ ♦❢ ❛ ♣❡)✐♦❞✱ &❤❡ ❜❛♥❦✐♥❣ 5❡❝&♦! ❛5 ❛ ✇❤♦❧❡ 5✉✛❡!5 ❛ ❧♦55 ❡>✉❛❧ &♦ &❤❡

(9)

❞✐✛❡$❡♥❝❡ ❜❡(✇❡❡♥ (❤❡ ❛♠♦✉♥( ♦❢ ❝$❡❞✐( 0✉♣♣❧✐❡❞ ✐♥ ♣❡$✐♦❞t ❛♥❞ (❤❡ $❡❧❛(✐✈❡ ♠♦$(❣❛❣❡ ✭✈❛❧✉❡ ♦❢

❛00❡(0✮✱ ✇❤✐❝❤ ✐0 (❤❡ 0❛♠❡ ❛0 (❤❡ ✭♥❡❣❛(✐✈❡✮ ❛♠♦✉♥( ♦❢ ♥❡( ✇♦$(❤✿ B_it=^Lit−(^Kit+^πit) =₋^Ait✳

❚❤❡ ❜❛♥❦✐♥❣ 0❡❝(♦$✬0 ❡=✉✐(② ❜❛0❡ ❡✈♦❧✈❡0 ❛❝❝♦$❞✐♥❣ (♦ (❤❡ ❧❛✇ ♦❢ ♠♦(✐♦♥✿

E_t^B=^π_t^B+E_t^B₋₁−

∑

i∈ Ω_t

Bit (10)

❍❡$❡✱ Ω_t ✐0 (❤❡ 0❡( ♦❢ ❛❧❧ ❜❛♥❦$✉♣( ✜$♠0 ✐♥ ♣❡$✐♦❞ t✳ ❚❤❡ ❜❛♥❦ ❧❡♥❞0 ❛ ♠✉❧(✐♣❧❡ ♦❢ ✐(0 ♣$✐♦$

❡=✉✐(② ❜❛0❡ ❛❝❝♦$❞✐♥❣ (♦ 0♦♠❡ ♠✉❧(✐♣❧✐❡$ L^s_t =_ν¹E_t^B₋₁ ✇❤✐❝❤ ✐0 ❜❛0❡❞ ♦♥ $❡❣✉❧❛(♦$② ❝♦♥0($❛✐♥(0✳

❈$❡❞✐( 0✉♣♣❧② ❡♠❡$❣❡0 ❢$♦♠ (❤❡ ❜❛♥❦0 ❡=✉✐(② ❜❛0❡E_t^B❛♥❞ ❞❡♣♦0✐(0Dt ✐♥ (❤❡ ❢♦$♠L^s_t =E_t^B+Dt

✇❤✐❧❡ ❞❡♣♦0✐(0 ❛$❡ ($❡❛(❡❞ ❛0 ❛ $❡0✐❞✉❛❧✳ ❲$✐(❡ α_it =A_it/∑_iA_it ❛♥❞ κ_it =K_it/∑_iK_it✳ ❈$❡❞✐(

0✉♣♣❧② ✐0 (❤❡♥

L^s_it =L^s_t[^{λ κ}it−1+ (1−λ)α_it₋₁] ⁽¹¹⁾

❚❤❡ ✐♥(❡$❡0( $❛(❡ r_it ❢♦$ ❡❛❝❤ ✜$♠ ✐0 ❞❡(❡$♠✐♥❡❞ ❜② (❤❡ ❡=✉✐❧✐❜$✐✉♠ 0✐(✉❛(✐♦♥ ✇❤❡$❡ ❝$❡❞✐(

❞❡♠❛♥❞ ♠❛(❝❤❡0 ❝$❡❞✐( 0✉♣♣❧②✳ ❋$♦♠ (❤❛( ❝♦♥❞✐(✐♦♥ (❤✐0 $❛(❡ ✐0

r_it = ¹

2cgL^s_it+2gc(_φ¹_c+A_it₋₁)(2+A_it₋₁) (12)

❊♥($② ❞❡♣❡♥❞0 ♦♥ (❤❡ ❛✈❡$❛❣❡ ✐♥(❡$❡0( $❛(❡ r_t ✇❤✐❝❤ ❞❡(❡$♠✐♥❡0 (❤❡ ♥✉♠❜❡$ ♦❢ ♣♦00✐❜❧❡ ❡♥($❛♥(0

❛♥❞ (❤❡ ❢❡❛(✉$❡0 ♦❢ (❤❡ ❡♥($❛♥( ✐0 ❞❡(❡$♠✐♥❡❞ ❜② ❛ $❛♥❞♦♠ ❞$❛✇✳ ❚❤❡ (❡$♠ ✐0✿

N_t^entry=NProb(entry) = ^N

1+e^d⁽^r^t⁻¹⁻^f) ⁽¹³⁾

✇❤❡$❡N>1✱d✱ ❛♥❞ f ❛$❡ ❝♦♥0(❛♥(0✳ ❚❤✐0 ❛00✉$❡0 (❤❛( (❤❡ ♣$♦❜❛❜✐❧✐(② ♦❢ ♥✉♠❜❡$ ♦❢ ❡♥($❛♥(0 ✐0

❧♦✇ ✐❢ (❤❡ ♦✈❡$❛❧❧ ✐♥(❡$❡0( $❛(❡ ✐0 ❤✐❣❤✳ ❚❤❡ (❡$♠ ✐0 (❤❡♥ $♦✉♥❞❡❞ (♦ ❛♥ ✐♥(❡❣❡$✳^✶ ◆❡✇ ✜$♠0 ❛$❡

❡♥❞♦✇❡❞ ✇✐(❤ ❝❛♣✐(❛❧ ❛♥❞ ♥❡( ✇♦$(❤ $❛♥❞♦♠❧②✳ ❚❤❡ ❞$❛✇ ❢♦$ ❛♥ ❡♥($❛♥(✬0 ❝❛♣✐(❛❧ ❡♥❞♦✇♠❡♥(

✐0 ❢$♦♠ ❛ ✉♥✐❢♦$♠ ❞✐0($✐❜✉(✐♦♥ ✇✐(❤ ❛ ❝❡♥(❡$ ❛( (❤❡ ♠♦❞❡ ♦❢ ✐♥❝✉♠❜❡♥(0✬ ❝❛♣✐(❛❧✳ ❚❤❡♥✱ (❤❡

❡=✉✐(② $❛(✐♦α_it=A_it/∑_iA_it ✐0 ❞❡(❡$♠✐♥❡❞ ❜② (❤❡ ♠♦❞❡ ♦❢ ❛❧❧ ✐♥❝✉♠❜❡♥(0✬ ❡=✉✐(② ❜❛0❡ A_it ❛♥❞

(❤❡ ❝❛♣✐(❛❧ $❛(✐♦ ✐0 κ_it=^Kit/∑_iK_it✳ ❚❤♦0❡ $❛(✐♦0 ❛$❡ ♥❡❡❞❡❞ ❜② (❤❡ ❜❛♥❦ ✐♥ ♦$❞❡$ (♦ ❞❡(❡$♠✐♥❡

(❤❡ ❝$❡❞✐( 0✉♣♣❧② ❢♦$ ❡❛❝❤ ♥❡✇ ✜$♠✳

2.2. stock price

❲❡ ♥♦✇ ✐♥❝❧✉❞❡ ❡=✉✐(② ❛♥❞ 0(♦❝❦ ♣$✐❝❡0 ✐♥ (❤❡ ♠♦❞❡❧✳ ■❢ ✜$♠0 ❤❛✈❡ ❛❧0♦ ❛❝❝❡00 (♦ ❡=✉✐(②

♠❛$❦❡(0✱ (❤❡② ❝❛♥ $❛✐0❡ ❝❛♣✐(❛❧ ❜② ✐00✉✐♥❣ 0❤❛$❡0✳ ■❢ (❤♦0❡ ❛$❡ ($❛❞❡❞ ❛( ❛ 0(♦❝❦ ❡①❝❤❛♥❣❡ (❤❡✐$

♣$✐❝❡ ❝❛♥ ❜❡ (❤♦✉❣❤( ♦❢ (♦ ❝♦♥0✐0( ♦❢ ❛ ✏❢❛✐$✑ ❝♦♠♣♦♥❡♥(✱ (❤❛( ✐0 (❤❡ ❢✉♥❞❛♠❡♥(❛❧ ✈❛❧✉❡ Fit✱

❛♥❞ ❛ ❞❡✈✐❛(✐♦♥ θ_it ❢$♦♠ (❤❛(✳

P_it =F_it+θ_it (14)

1In the original paper, the number of initial firms is 100,N=180,d=100 and f=0.1. with 1000 iterations.

(10)

❚❤❡ ❢❛✐& '(♦❝❦ ♠❛&❦❡( ✈❛❧✉❡ ❞❡♣❡♥❞' ♦♥ ♥❡( ✇♦&(❤ ❛♥❞ ♦♥ (❤❡ ♦✈❡&❛❧❧ ❡4✉✐(② (❤❛( ❛ ✜&♠ ❤❛' F_itE_it ≡E_it+^Πit =A_it (15)

❍❡&❡ Π_it &❡❢❡&' (♦ &❡(❛✐♥❡❞ ♣&♦✜(' ✉♣ (♦ ♣❡&✐♦❞ t✳ ◆♦(❡ (❤❛( (♦(❛❧ ❡4✉✐(② ♦❢ ❛ ✜&♠ ✇✐❧❧ ❝♦♥'✐'(

♦❢ (❤❡ ❡4✉✐(② &❛✐'❡❞ (❤&♦✉❣❤ ✐''✉❡❞ '❤❛&❡' E_it ❛♥❞ ♥❡( ✇♦&(❤ ✇❤✐❝❤ ✐' ❛❝❝✉♠✉❧❛(❡❞ ♣&♦✜(' Π_it✳

❚❤❡ ❛❜♦✈❡ '♣❡❝✐✜❝❛(✐♦♥ ✐' ❜❛'❡❞ ♦♥ (❤❡ ❛''✉♠♣(✐♦♥ (❤❛( ❡❛❝❤ '❤❛&❡ ❤❛' ❛ ♥♦♠✐♥❛❧ ✈❛❧✉❡ ♦❢

✶ ✉♥✐( ♦❢ ❝✉&&❡♥❝②✱ (❤❡&❡❢♦&❡ (❤❡ ♥✉♠❜❡& ♦❢ '❤❛&❡' ❡4✉❛❧' (❤❡ ♥♦♠✐♥❛❧ ✈❛❧✉❡ ♦❢ '❤❛&❡❤♦❧❞❡&'✬

❡4✉✐(②✱ ❜♦(❤ ❞❡♥♦(❡❞ ❜② E_it✳ ❍❡♥❝❡ (❤❡&❡ ✐' ❡①❛❝(❧② ♦♥❡ '❤❛&❡ ♦❢ ♥♦♠✐♥❛❧ ✈❛❧✉❡ ✶ ❢♦& ❡❛❝❤ ✜&♠✳

❋✉&(❤❡&♠♦&❡✱ (❤❡ ❢❛✐& '❤❛&❡ ♣&✐❝❡ ✐' ❥✉'( (❤❡ ♥❡( ✈❛❧✉❡ ♦✈❡& (❤❡ ♥✉♠❜❡& ♦❢ '❤❛&❡' ✐''✉❡❞✳ ■♥

(❤❡ &❡♠❛✐♥❞❡& ♦❢ (❤❡ ♣❛♣❡& ✇❡ ✇✐❧❧ ❛''✉♠❡ (❤❛( E_it =1 ❢♦& ❛❧❧ i,t✱ ✐♠♣❧②✐♥❣ (❤❛( A_it =F_it ❛♥❞

P_it =^Ait+^θit✳

❚❤❡ ❛❝(✉❛❧ '(♦❝❦ ♣&✐❝❡ P_it ❝♦✉❧❞ ❞❡✈✐❛(❡ ❢&♦♠ (❤❡ ✏❢❛✐&✑ ♣&✐❝❡ ❜❡❝❛✉'❡ ♦❢ (❤❡ ❡①♣❡❝(❛(✐♦♥' ♦❢

✐♥✈❡'(♦&'✿

✶✳ (❤❡ ❢✉(✉&❡ ✐♥✢♦✇ ♦❢ ❝❛'❤ ✐' '✉♣♣♦'❡❞ (♦ ❜❡ '✐❣♥✐✜❝❛♥(❧② ❧❛&❣❡ ♦& '♠❛❧❧❀

✷✳ '♣❡❝✉❧❛(♦&' ♣❛② ♣&❡♠✐✉♠' ✭'❡❧❧ ❛( ❞✐'❝♦✉♥('✮ ✐♥ ♦&❞❡& (♦ ❜❡♥❡✜( ❢&♦♠ ❡①♣❡❝(❡❞ ❡✈❡♥ ❧❛&❣❡&

✭❧♦✇❡&✮ ♣&✐❝❡' ✐♥ (❤❡ ❢✉(✉&❡✳^✷

❚❤✐' '♣❡❝✐✜❝❛(✐♦♥ ❢♦❧❧♦✇' (❤❡ ✐❞❡❛ (❤❛( ♠❛&❦❡( ✈❛❧✉❛(✐♦♥ ♦♥ ❛✈❡&❛❣❡ &❡♣&❡'❡♥(' (❤❡ ❞✐'❝♦✉♥(❡❞

'✉♠ ♦❢ ❛❧❧ ❡①♣❡❝(❡❞ ❝❛'❤ ✢♦✇✱ &❡♣&❡'❡♥(❡❞ ❜② ♣&♦✜(' ✐♥ (❤✐' '❡(✉♣✳ ■❢ (❤❡'❡ ❡①♣❡❝(❛(✐♦♥' ❛&❡ ✈❡&②

♦♣(✐♠✐'(✐❝✱ (❤❡&❡ ❝❛♥ ❜❡ ❛ ♠❛&❦ ✉♣ ✇❤✐❝❤ ✐' ♥♦( ❥✉'(✐✜❡❞ ❛❧♦♥❡ ❜② ❥✉'( (❤❡ ❛❝(✉❛❧❧② ♦❜'❡&✈❛❜❧❡

♣&♦✜(✳ ❚❤❡ &❡❧❛(✐♦♥ ❜❡(✇❡❡♥ (❤❡ ♠❛&❦ ✉♣ ♦♥ ✜&♠ ✈❛❧✉❡ ❛♥❞ (❤❡ ❡&&♦& ✐♥ ♣&♦✜( ❡'(✐♠❛(✐♦♥ ✐' θ_it =_|^πit|ε_it.

❚❤✐' ❡①♣&❡''❡' (❤❛( (❤❡ ♠❛&❦✉♣ ♦♥ ✜&♠ ✈❛❧✉❡ ✭▲❍❙✮ ✐' ❥✉'( (❤❡ ♠❛&❦✉♣ ♦♥ ❡①♣❡❝(❡❞ ❝❛'❤ ✢♦✇✱

❤❡&❡ (♦❞❛②✬' ♣&♦✜( ✭❘❍❙✮✳

❚❤✐' ♠❛&❦✉♣ ♦♥ ✭❢❛✐&✮ ♠❛&❦❡+ ✈❛❧✉❡ ✐' ❛''✉♠❡❞ (♦ ❜❡ ❛ ❢✉♥❝(✐♦♥ ♦❢ ♣&♦✜(' ❛♥❞ ❛ &❛♥❞♦♠

❝♦♠♣♦♥❡♥(✳ ❚❤❡ ♦✈❡&❛❧❧ ♠❛&❦❡( ✈❛❧✉❡ ♦❢ ❝❛0❤ ✢♦✇ ❜❛'❡❞ ♦♥ ♣&♦✜(' ❛♥❞ (❤❡ ❡&&♦& ✐' '✉♣♣♦'❡❞

(♦ ❜❡ ❣✐✈❡♥ ❜② π_it+_|π_it|ε_it =ρ(π_it,ε_it)✳ ❚❤✐' ♠❡❛♥' (❤❛( ❛ ♣♦'✐(✐✈❡ ❡&&♦& ❛❧✇❛②' ❧❡❛❞' (♦ ❛

♠♦&❡ ❢❛✈♦&❛❜❧❡ ♣&♦✜( ❡'(✐♠❛(✐♦♥✱ ❛❧'♦ ❢♦& ♥❡❣❛(✐✈❡ ♣&♦✜('✳ ❚❤❡ '✐❣♥ ♦❢ (❤❡ ❡&&♦& ✐' ♣&❡'❡&✈❡❞

✐♥ (❤✐' ✇❛②✳ ❚❤❡ ❡&&♦& ♠✐❣❤( ♦❝❝✉& ❢♦& '♦♠❡ (✐♠❡ '♣❛♥✳ ❚❤❡ ♣❡&'✐'(❡♥❝❡ ✐♥ (❤✐' ❡&&♦& ❝❛♥ ❜❡

✐♥❞✉❝❡❞ ✐❢ (❤❡ ❡&&♦& ✐' ♠♦❞❡❧❡❞ ❛' ❛ &❛♥❞♦♠ ✇❛❧❦✳^✸

ε_it =ε_it₋₁+η_itσ_η (16)

✇❤❡&❡ η ∼N (0, 1) ❛♥❞ 0<σ_η <1✳ ❍❡♥❝❡✱ E(ε_it) =ε_it₋₁✳

❚❤❡ ❝♦♠♣❧❡(❡ ❡①♣&❡''✐♦♥ ❢♦& (❤❡ '(♦❝❦ ♣&✐❝❡ ✐' ❤❡♥❝❡

P_it =A_it+_|π_it|(ε_it₋₁+η_itσ_η).

2Note that 1. affects the fair value of shares while 2. may occur due to speculation (exogenous to the firm) .

3If there is also a drift in the random walk, then this would represent general phases of optimism or pessimism.

(11)

3. The Role of the Stock Market Value in Credit Decisions

❚❤❡ #$♦❝❦ ♠❛*❦❡$ ✈❛❧✉❡ ♦❢ ❛ ✜*♠ ❝❛**✐❡# ✐♥❢♦*♠❛$✐♦♥ $❤❛$ ✐# ✈❛❧✉❛❜❧❡ ❢♦* ❛ ❜❛♥❦ ❢♦* $✇♦ *❡❛#♦♥#✳

❋✐*#$✱ $❤❡ ✈❛❧✉❛$✐♦♥ ♦♥ $❤❡ #$♦❝❦ ♠❛*❦❡$ ♠✐❣❤$ *❡✈❡❛❧ #♦♠❡ ✐♥❢♦*♠❛$✐♦♥ ❛❜♦✉$ ❛ ✜*♠✬# ❛❜✐❧✐$②

$♦ *❛✐#❡ ❢✉♥❞# ❢*♦♠ $❤❡ ❛##❡$ ♠❛*❦❡$✳ ❙❡❝♦♥❞✱ ✐$ *❡✈❡❛❧# ✐♥❢♦*♠❛$✐♦♥ ❛❜♦✉$ $❤❡ ♠❛*❦❡$✬#

❡#$✐♠❛$✐♦♥ ♦❢ $❤❡ *❡❧❛$✐✈❡ ♣*♦#♣❡❝$ ♦❢ $❤❡ ✜*♠✳ ❚❤❡ #$♦❝❦ ♠❛*❦❡$ ✉#✉❛❧❧② ✐♥❞✐❝❛$❡# ❝❤❛♥❣❡#

♦❢ ✜*♠✬# ♣*♦#♣❡❝$# ❡❛*❧✐❡* $❤❛♥ $❤❡ ✐♥❝♦♠❡ #$❛$❡♠❡♥$ ♦* $❤❡ ❜❛❧❛♥❝❡ #❤❡❡$✳^✹ ❚❤❡*❡❢♦*❡✱ $❤❡

#$♦❝❦ ♠❛*❦❡$ ✈❛❧✉❡ ✐# ❛ ♣✐❡❝❡ ♦❢ ❢♦*✇❛*❞ ❧♦♦❦✐♥❣ ✐♥❢♦*♠❛$✐♦♥ *❛$❤❡* $❤❛♥ $❤❡ ❜❛❝❦✇❛*❞ ❧♦♦❦✐♥❣

❜❛❧❛♥❝❡ #❤❡❡$ ❛♥❛❧②#✐#✳ ❋✉*$❤❡*♠♦*❡✱ ✏❬#❪$♦❝❦ ♠❛*❦❡$ ❜❛#❡❞ ✐♥❢♦*♠❛$✐♦♥ ✳✳✳ ❤❛# *❡#♣♦♥❞❡❞ ♠♦*❡

@✉✐❝❦❧② $♦ ❝❤❛♥❣✐♥❣ ✜♥❛♥❝✐❛❧ ❝♦♥❞✐$✐♦♥# $❤❛♥ *❛$✐♥❣# ♦❢ ❝*❡❞✐$ *✐#❦ ❛❣❡♥❝✐❡#✳✑ ✭❇♦♥❣✐♥✐ ❡$ ❛❧✳

✭✷✵✵✷✮✱ ♣✳ ✶✵✶✶✳✮ ❚❤✐# ✐# ❛♥ ✐♥❝❡♥$✐✈❡ $♦ ❢*❡❡✲*✐❞❡ ♦♥ ❡①$❡*♥❛❧ ✐♥❢♦*♠❛$✐♦♥ #✐♥❝❡ ❛##❡##✐♥❣

❝*❡❞✐$✇♦*$❤✐♥❡## ✐# ❝♦#$❧②✱ ❛# ✐# ♠♦♥✐$♦*✐♥❣✳

■♥ ♦*❞❡* $♦ *❡♣*❡#❡♥$ $❤❡ ✐♠♣❛❝$ ♦❢ $❤❡ #$♦❝❦ ♣*✐❝❡ ♦♥ ❝*❡❞✐$ #✉♣♣❧② ✇❡ #❤❛❧❧ ❛##✉♠❡ ✐♥ $❤✐#

#❡$$✐♥❣ $❤❛$ ❝*❡❞✐$ #✉♣♣❧② ✐# ❞❡$❡*♠✐♥❡❞ ❛❝❝♦*❞✐♥❣ $♦✿

L^s_it =L_t^s

(1−µ)λK_it₋₁

K_t₋₁ + (1−µ)(1−λ)^A^it⁻¹

A_t₋₁ +µ P_it^EE_it

∑_iP_it^EE_it

(11a)

✇❤❡*❡ 0<λ <1 *❡♣*❡#❡♥$# $❤❡ ✇❡✐❣❤$ ♣✉$ ♦♥ *❡❧❛$✐✈❡ ✜*♠ #✐③❡ ❛♥❞ 0<µ <1 #$❛♥❞# ❢♦* $❤❡

✇❡✐❣❤$ ♣✉$ ♦♥ $❤❡ *❡❧❛$✐✈❡ #$♦❝❦ ♠❛*❦❡$ ✈❛❧✉❡✳ ❚❤❡ $❤✐*❞ ♣✐❡❝❡ ♦❢ ✐♥❢♦*♠❛$✐♦♥ ✉#❡❞ ❢♦* $❤❡

❞❡❝✐#✐♦♥ ✐# $❤❡ *❡❧❛$✐✈❡ ♥❡$ ✈❛❧✉❡✳ ❲❡ *✉♥ #✐♠✉❧❛$✐♦♥# ❢♦* ✐♥❝*❡❛#✐♥❣ ✈❛❧✉❡# ♦❢ µ ✇❤✐❧❡ ❢♦* ❡❛❝❤

✈❛❧✉❡ $❤❡*❡ ❛*❡ ❛ ♥✉♠❜❡* ♦❢ *❡♣❡$✐$✐♦♥#✳ ❘❡#✉❧$# ❛*❡ $❛❦❡♥ ❢*♦♠ ❛♥ ✐♥$❡*✈❛❧ ♦✈❡* ✺✶ ♣❡*✐♦❞#✱

❜❡$✇❡❡♥ t =¹⁰⁰⁰ ❛♥❞ t =¹⁰⁵⁰✳ ❚❤❡ ❛✈❡*❛❣❡ ✐# ❝♦♠♣✉$❡❞✳ ❚❤✐# ✐# ❞♦♥❡ ❢♦* ❡❛❝❤ ♦❢ ✶✵✵

*❡♣❡$✐$✐♦♥# ❢♦* ❛♥② ♣❛*❛♠❡$❡* ✈❛❧✉❡ ❛♥❞ ❢♦* $❤♦#❡ ✶✵✵ *❡#✉❧$# ❢*♦♠ ❡❛❝❤ ♣❛*❛♠❡$❡* ✈❛❧✉❡ ❛❧#♦

$❤❡ ❛✈❡*❛❣❡ ✐# $❛❦❡♥✳ ◆♦$❡ $❤❛$ $❤❡ #✐♠✉❧❛$✐♦♥# ❢♦* µ =0 ❛❧#♦ *❡♣*❡#❡♥$ $❤❡ ❜❡♥❝❤♠❛*❦ ❝❛#❡

✇❤✐❝❤ ♠❛$❝❤❡# $❤❡ ❉❡❧❧✐ ●❛$$✐ ❡$ ❛❧✳ ✭✷✵✵✺✮ ♠♦❞❡❧✳ ❚❤❡ *❡#✉❧$# ✐♥ ♦✉* ❜❛#❡❧✐♥❡ ❝❛#❡ ❛*❡ ✐♥ ❧✐♥❡

✇✐$❤ $❤❡ ✜♥❞✐♥❣# ♦❢ ❉❡❧❧✐ ●❛$$✐ ❡$ ❛❧✳ ✭✷✵✵✺✮✳ ❲❤✐❧❡ $❤❡② ❢♦❝✉# ♦♥ $❤❡ ❞✐#$*✐❜✉$✐♦♥ ♦❢ ✜*♠

#✐③❡# ❛♥❞ $❤❡✐* ❣*♦✇$❤ *❛$❡# ✇❡ ✇✐❧❧ ♣✉$ ❡♠♣❤❛#✐③❡ ♦♥ $♦$❛❧ ♦✉$♣✉$ ❛♥❞ $❤❡ ❛✈❡*❛❣❡ ✐♥$❡*❡#$

*❛$❡ ✐♥ ♦✉* ❛♥❛❧②#✐#✳

(a) output over time baseline case

(b) output over timeµ=1

(c) output Figure 1:Impact ofµ on output

4For a more detailed discussion, see Atiya (2001), p. 930-932 or Altman (1968).