t t rt - - PowerPoint PPT Presentation

❘❡❧♦❝❛t✐♦♥ ♦❢ t❤❡ ❘✐❝❤✿ ▼✐❣r❛t✐♦♥ ✐♥ ❘❡s♣♦♥s❡ t♦ ❚♦♣ ❚❛① ❘❛t❡ ❈❤❛♥❣❡s ❢r♦♠ ❙♣❛♥✐s❤ ❘❡❢♦r♠s

❉❛✈✐❞ ❘✳ ❆❣r❛✇❛❧✱ ❯♥✐✈❡rs✐t② ♦❢ ❑❡♥t✉❝❦② ❛♥❞ ❈❊❙✐❢♦ ❉✐r❦ ❋♦r❡♠♥②✱ ❯♥✐✈❡rs✐t❛t ❞❡ ❇❛r❝❡❧♦♥❛ ❛♥❞ ■❊❇ ❙❦✐❧❧❡❞ ✇♦r❦❡rs ♣❧❛② ❛ ✈✐t❛❧ r♦❧❡ ✐♥ t❤❡ ✜s❝❛❧ s②st❡♠s ♦❢ ❛❞✈❛♥❝❡❞ ❡❝♦♥♦♠✐❡s✱ ❛♥❞ ♠❛② ❡❛s✐❧② ❜❡ ✏✇♦rt❤ t❤❡✐r ✇❡✐❣❤t ✐♥ ❣♦❧❞✑✱ ❜r✐♥❣✐♥❣ ✜s❝❛❧ ❞✐✈✐❞❡♥❞s ♦❢ s✉❜st❛♥t✐❛❧ s✐③❡ t♦ t❤❡ s♦❝✐❡t✐❡s ✐♥ ✇❤✐❝❤ t❤❡② r❡s✐❞❡✳ ✕ ❉❛✈✐❞ ❲✐❧❞❛s✐♥ ✭✷✵✵✾✮

❘❡s❡❛r❝❤ ❆❣❡♥❞❛

❍♦✇ s❡♥s✐t✐✈❡ ❛r❡ t❤❡ ✏r✐❝❤✑ t♦ ✐♥t❡rst❛t❡ t❛① ❞✐✛❡r❡♥t✐❛❧s❄ ❆r❡ ✐♥❞✐✈✐❞✉❛❧s ✐♥ ❝❡rt❛✐♥ ✐♥❞✉str✐❡s ❛♥❞ ♦❝❝✉♣❛t✐♦♥s ♠♦r❡ s❡♥s✐t✐✈❡❄ ❍♦✇ ❧❛r❣❡ ❛r❡ t❤❡ r❡✈❡♥✉❡ ✐♠♣❧✐❝❛t✐♦♥s ♦❢ t❛①✲✐♥❞✉❝❡❞ ♠✐❣r❛t✐♦♥❄ ■❞❡❛❧ ❝♦♥t❡①t t♦ st✉❞② ♠✐❣r❛t✐♦♥✿

◮ ❆ r❡❢♦r♠ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ✷✵✶✶ ❣r❛♥t❡❞ ❙♣❛♥✐s❤ r❡❣✐♦♥s t❤❡ ❛❜✐❧✐t② t♦

s❡t t❤❡✐r ♦✇♥ ✐♥❝♦♠❡ t❛① r❛t❡s ❛♥❞ ❜r❛❝❦❡ts✳

◮ ❚❛① r❛t❡s ❞✐✈❡r❣❡❞ s✉❜st❛♥t✐❛❧❧② ❛❝r♦ss r❡❣✐♦♥s✳

▼♦t✐✈❛t✐♦♥ t♦ ❙t✉❞② ▼✐❣r❛t✐♦♥

❍✐❣❤✲✐♥❝♦♠❡ ✐♥❞✐✈✐❞✉❛❧s ❛r❡ ♣♦t❡♥t✐❛❧❧② ✈❡r② r❡s♣♦♥s✐✈❡ t♦ t❛① ❞✐✛❡r❡♥t✐❛❧s✱ ❡s♣❡❝✐❛❧❧② ✇✐t❤✐♥ ❛ ❝♦✉♥tr② ✇❤❡♥ ♠♦❜✐❧✐t② ❜❛rr✐❡rs ❛r❡ ❧♦✇✳ ▼♦❜✐❧✐t② ✐s ❛ ❢♦r♠ ♦❢ ❜❡❤❛✈✐♦r❛❧ r❡s♣♦♥s❡✳

◮ ▼♦✈✐♥❣ ✐♥❝r❡❛s❡s t❤❡ ❡✣❝✐❡♥❝② ❝♦st ♦❢ t❛①❛t✐♦♥ ❛♥❞ ❧✐♠✐ts

r❡❞✐str✐❜✉t✐♦♥ ♣♦❧✐❝② ✭▼✐rr❧❡❡s ✶✾✽✷✿ ♦♣t✐♠❛❧ ❞❡❣r❡❡ ♦❢ r❡❞✐str✐❜✉t✐♦♥ ✇✐❧❧ ❞❡❝❧✐♥❡ ❛s t❤❡ ♠♦❜✐❧✐t② ❡❧❛st✐❝✐t② ✐♥❝r❡❛s❡s✮✳

◮ ▼♦❜✐❧❡ ❧❛❜♦r ♠❛② ✐♥❞✉❝❡ ✐♥❡✣❝✐❡♥t t❛① ❝♦♠♣❡t✐t✐♦♥ ✭❲✐❧❞❛s✐♥ ✷✵✵✻❀

❲✐❧s♦♥ ✷✵✵✾✮✳

❙✉❜st❛♥t✐❛❧❧② ❞✐s❝✉ss❡❞ ✐♥ t❤❡ ♠❡❞✐❛ ❛♥❞ ♣♦❧✐❝② ✇♦r❧❞✿ ❡✳❣✳✱ ✏❆❝t♦r ❉❡♣❛r❞✐❡✉ ❜✐❞s ✬❛❞✐❡✉✬ t♦ ❋r❛♥❝❡ t♦ ❛✈♦✐❞ t❛①❡s✳✑

❚❛①✲■♥❞✉❝❡❞ ▼✐❣r❛t✐♦♥✿ ❆♥ ❊①❛♠♣❧❡

❆❝❛❞❡♠✐❝ ❊✈✐❞❡♥❝❡

▲✐♠✐t❡❞ ✐♥ s❝♦♣❡ ❛♥❞ ✐♥ ❝♦♥✢✐❝t✿

◮ ▲❛r❣❡ ❡✛❡❝ts ❢♦✉♥❞ ✐♥ s❡❧❡❝t ❣r♦✉♣s ♦❢ t❤❡ s✉❜✲♣♦♣✉❧❛t✐♦♥✿ st❛r

s❝✐❡♥t✐sts ✭▼♦r❡tt✐ ❛♥❞ ❲✐❧s♦♥ ✷✵✶✼ ❆❊❘❀ ❆❝❦✐❣✐t✱ ❇❛s❧❛♥❞③❡✱ ❛♥❞ ❙t❛♥t❝❤❡✈❛ ✷✵✶✻ ❆❊❘✮✱ ❛t❤❧❡t❡s ✭❑❧❡✈❡♥✱ ▲❛♥❞❛✐s ❛♥❞ ❙❛❡③ ✷✵✶✸ ❆❊❘✮✱ ♦r ❢♦r❡✐❣♥❡rs s✉❜❥❡❝t t♦ ♣r❡❢❡r❡♥t✐❛❧ t❛①❛t✐♦♥ ✭❑❧❡✈❡♥✱ ▲❛♥❞❛✐s✱ ❙❛❡③✱ ❛♥❞ ❙❝❤✉❧t③ ✷✵✶✹ ◗❏❊✮

◮ ❙♠❛❧❧❡r ❡✛❡❝ts ❛❝r♦ss ❧♦❝❛❧✐t✐❡s ✐♥ ❙✇✐t③❡r❧❛♥❞ ✭❇rü❧❤❛rt ❛♥❞ P❛r❝❤❡t

✷✵✶✹ ❏P✉❜❊❝✮ ❛♥❞ st❛t❡s ✐♥ t❤❡ ❯❙❆ ✭❈♦♦♠❡s ❛♥❞ ❍♦②t ✷✵✵✽ ❏❯❊❀ ❨♦✉♥❣ ❛♥❞ ❱❛r♥❡r ✷✵✶✶ ◆❚❏❀ ❨♦✉♥❣✱ ❱❛r♥❡r✱ ▲✉r✐❡ ❛♥❞ Pr✐s✐♥③❛♥♦ ✷✵✶✻ ❆❙❘✮

◮ ❆❣r❛✇❛❧ ❛♥❞ ❍♦②t ✭✷✵✶✽✱ ❊❏✮ s❤♦✇ ❯✳❙✳ t❛① r✉❧❡s ❛r❡ ♦❢t❡♥ ♥♦t ♣✉r❡❧②

r❡s✐❞❡♥❝❡ ❜❛s❡❞ ⇒♠♦❜✐❧✐t② ♠❛② ❜❡ ✐♥ ❥♦❜s✱ ♥♦t ♣❡♦♣❧❡✳

❲❡ st✉❞② ❛♥ ❛❧t❡r♥❛t✐✈❡ s❝❡♥❛r✐♦✿ ♣♦♣✉❧❛t✐♦♥ r❡♣r❡s❡♥t❛t✐✈❡ ❛❞♠✐♥✐str❛t✐✈❡ ❞❛t❛ ✕ ❝♦♥t❛✐♥✐♥❣ ♦❝❝✉♣❛t✐♦♥ ❛♥❞ ✐♥❞✉str② ✐♥❢♦r♠❛t✐♦♥ ✕ ❜✉t ✐♥ ❛ ❝♦✉♥tr② ✇✐t❤ r❡❧❛t✐✈❡❧② ❧♦✇ ♠♦❜✐❧✐t② ✭❧❡ss t❤❛♥ ✶✪ ❢♦r t❤❡ r✐❝❤✮✳ ❚❤❡♥ ✇❡ ✉s❡ ♦❝❝✉♣❛t✐♦♥ ❛♥❞ ✐♥❞✉str② ❞❛t❛ t♦ ❛ss❡ss t❤❡ ❡①t❡r♥❛❧ ✈❛❧✐❞✐t② ♦❢ t❤❡ ♣r✐♦r ❧✐t❡r❛t✉r❡✳

▼❛✐♥ ❈♦♥tr✐❜✉t✐♦♥s ❛♥❞ ❋✐♥❞✐♥❣s

• r❛♣❤✐❝❛❧ ❡✈✐❞❡♥❝❡ ♦♥ ❛❣❣r❡❣❛t❡ ❡✛❡❝ts ✉s✐♥❣ st♦❝❦s✳

◮ ❈❧❡❛r ❡✛❡❝t ❛❢t❡r ❛❝❝♦✉♥t✐♥❣ ❢♦r ♦r✐❣✐♥ ❛♥❞ ❞❡st✐♥❛t✐♦♥ ✜①❡❞ ❡✛❡❝ts✳ ◮ ❇✉t✱ t❤❡ ❡❧❛st✐❝✐t② ♦❢ t❤❡ st♦❝❦ ❤❛s r❡❧❛t✐✈❡❧② s♠❛❧❧ r❡✈❡♥✉❡ ✐♠♣❧✐❝❛t✐♦♥s✳

❈❤♦✐❝❡ ♠♦❞❡❧✿ ♠♦✈❡rs ❛r❡ ♠♦r❡ ❧✐❦❡❧② t♦ s❡❧❡❝t ❧♦✇✲t❛① st❛t❡s✳

◮ ❚❤❡ ▼❛❞r✐❞ ✲ ❈❛t❛❧✉♥②❛ t❛① ❞✐✛❡r❡♥t✐❛❧ ✐♥❝r❡❛s❡s ♣r♦❜❛❜✐❧✐t② ♦❢ ♠♦✈✐♥❣

t♦ ▼❛❞r✐❞ ❜② ✷✳✷✺ ♣♦✐♥ts✳

◮ ❍❡t❡r♦❣❡♥❡✐t② ❜② ✈❛r✐♦✉s ♦❝❝✉♣❛t✐♦♥s✴✐♥❞✉str✐❡s✳

■♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ ❡❧❛st✐❝✐t✐❡s ✉s✐♥❣ ❛ s✐♠♣❧❡ t❤❡♦r❡t✐❝❛❧ ♠♦❞❡❧✳

◮ ❚❛① ❞❡❝r❡❛s❡s r❡s✉❧t ✐♥ r❡✈❡♥✉❡ ❧♦ss❡s s✉❣❣❡st✐♥❣ t❤❡ ♠❡❝❤❛♥✐❝❛❧ ❡✛❡❝t

♦❢ t❤❡ t❛① ❝❤❛♥❣❡ ♦✉t✇❡✐❣❤s t❤❡ ❜❡❤❛✈✐♦r❛❧ r❡s♣♦♥s❡✳

Pr❡✈✐❡✇ ♦❢ ❘❡s✉❧ts

−.06 −.04 −.02 .02 .04 .06 Probability of Moving to Region −.03 −.02 −.01 .01 .02 .03 log net−of−mtr

Pre−Reform

−.06 −.04 −.02 .02 .04 .06 Probability of Moving to Region −.03 −.02 −.01 .01 .02 .03 log net−of−mtr

Post−Reform

♣r❡✲r❡❢♦r♠✿ ♥♦ ❡✛❡❝t ♣♦st✲r❡❢♦r♠✿ ✏❧❛r❣❡✑ ❡✛❡❝t

■♥st✐t✉t✐♦♥❛❧ ❉❡t❛✐❧s

■♥st✐t✉t✐♦♥❛❧ ❉❡t❛✐❧s✿ ❘❡❢♦r♠

❙♣❛✐♥ ❝♦♥s✐sts ♦❢ ✶✼ ❛✉t♦♥♦♠♦✉s ❝♦♠♠✉♥✐t✐❡s ✭✐♥ ❙♣❛♥✐s❤✿ ❝♦♠✉♥✐❞❛❞❡s ❛✉tó♥♦♠❛s✮✳ ❙✐♥❝❡ t❤❡ ✾✵s r❡❣✐♦♥s ❛r❡ ❡♥t✐t❧❡❞ t♦ r❡❝❡✐✈❡ ❛ s❤❛r❡ ♦❢ t❤❡ P❡rs♦♥❛❧ ■♥❝♦♠❡ ❚❛① ✭■♠♣✉❡st♦ s♦❜r❡ ❧❛ ❘❡♥t❛ ❞❡ ❧❛s P❡rs♦♥❛s ❋ís✐❝❛s✮✱ ✇❤❡r❡ ✇❡ st✉❞② t❤❡ ❧❛❜♦r ✐♥❝♦♠❡ t❛① ❜❛s❡s✳

◮ ❈❛♣✐t❛❧ ✐♥❝♦♠❡ ✐s t❛①❡❞ ✉♥❞❡r ❛ s✐♥❣❧❡ ❢❡❞❡r❛❧ t❛① s②st❡♠✳

❆ ♠❛❥♦r ✇❛✈❡ ♦❢ ❞❡❝❡♥tr❛❧✐③❛t✐♦♥ ✐♥ ✷✵✶✶ ❤❛❞ s✉❜st❛♥t✐❛❧ ❝❤❛♥❣❡s✿

◮ ❚❤❡ s❤❛r❡ ♦❢ r❡✈❡♥✉❡ t❤❛t r❡❣✐♦♥s ❝♦✉❧❞ ❦❡❡♣✳ ◮ ❚❤❡ ❛✉t❤♦r✐t② t♦ ❝❤❛♥❣❡ t❤❡ t❛① r❛t❡s ✴ t❛① ❜r❛❝❦❡ts ✇❡r❡ ❣✐✈❡♥ t♦ t❤❡

r❡❣✐♦♥s✳

■♠♠❡❞✐❛t❡❧② ❢♦❧❧♦✇✐♥❣ t❤❡ ♥❡✇ ❧❛✇✱ t❤❡ r❡❣✐♦♥s ❜❡❣❛♥ ❝❤❛♥❣✐♥❣ t❛① r❛t❡s s✉❜st❛♥t✐❛❧❧②✱ ❜✉t ♠❛✐♥❧② ❛t t❤❡ t♦♣ ♣♦rt✐♦♥ ♦❢ t❤❡ ✐♥❝♦♠❡ ❞✐str✐❜✉t✐♦♥✳

❙♣❛♥✐s❤ P♦♣✉❧❛r Pr❡ss✿ ✏❋✐s❝❛❧ P❛r❛❞✐s❡✑

❚❛① ❈❤❛♥❣❡s ✭✷✵✶✶✮

• 2

2 4 mtr relative to central mtr in percentage points 100 200 300 income in thousands of Euros

AND ARA AST BAL CAN CAN CAL CAM CAT VAL EXD GAL MAD MUR RIO

2011

❚❛① ❈❤❛♥❣❡s ✭✷✵✶✷✮

• 2

2 4 mtr relative to central mtr in percentage points 100 200 300 income in thousands of Euros

AND ARA AST BAL CAN CAN CAL CAM CAT VAL EXD GAL MAD MUR RIO

2012

❚❛① ❈❤❛♥❣❡s ✭✷✵✶✸✮

• 2

2 4 mtr relative to central mtr in percentage points 100 200 300 income in thousands of Euros

AND ARA AST BAL CAN CAN CAL CAM CAT VAL EXD GAL MAD MUR RIO

2013

❚❛① ❈❤❛♥❣❡s ✭✷✵✶✹✮

• 2

2 4 mtr relative to central mtr in percentage points 100 200 300 income in thousands of Euros

AND ARA AST BAL CAN CAN CAL CAM CAT VAL EXD GAL MAD MUR RIO

2014

❚❛① ❉❡❝❧❛r❛t✐♦♥

❚❛① ❘❛t❡s ❛♥❞ ■♥❝♦♠❡ ❉✐str✐❜✉t✐♦♥✿ ✷✵✶✹

❬❈❛❧❝✉❧❛t♦r❪

❉❛t❛

❙♣❛✐♥✬s ❈♦♥t✐♥✉♦✉s ❙❛♠♣❧❡ ♦❢ ❊♠♣❧♦②♠❡♥t ❍✐st♦r✐❡s ✭▼✉❡str❛ ❈♦♥t✐♥✉❛ ❞❡ ❱✐❞❛s ▲❛❜♦r❛❧❡s✱ ▼❈❱▲✮

◮ ❉❛t❛ ♠❛t❝❤❡s ✐♥❞✐✈✐❞✉❛❧ ♠✐❝r♦❞❛t❛ ❢r♦♠ ❢r♦♠ s♦❝✐❛❧ s❡❝✉r✐t② r❡❝♦r❞s

✇✐t❤ ❞❛t❛ ❢r♦♠ t❤❡ t❛① ❛❞♠✐♥✐str❛t✐♦♥ ✭❆❣❡♥❝✐❛ ❚r✐❜✉t❛r✐❛✱ ❆❊❆❚✮✱ ❛♥❞ ♦✣❝✐❛❧ ♣♦♣✉❧❛t✐♦♥ r❡❣✐st❡r ❞❛t❛ ✭P❛❞ró♥ ❈♦♥t✐♥✉♦✮ ❢r♦♠ t❤❡ ❙♣❛♥✐s❤ ◆❛t✐♦♥❛❧ ❙t❛t✐st✐❝❛❧ ❖✣❝❡ ✭■◆❊✮✳

◮ ❆ ✹✪ ♥♦♥✲str❛t✐✜❡❞ r❛♥❞♦♠ s❛♠♣❧❡ ✭♦✈❡r ✶ ♠✐❧❧✐♦♥ ♦❜s❡r✈❛t✐♦♥s ❡❛❝❤

②❡❛r✮ ♦❢ t❤❡ ♣♦♣✉❧❛t✐♦♥ ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✇❤✐❝❤ ❤❛❞ ❛♥② r❡❧❛t✐♦♥s❤✐♣ ✇✐t❤ ❙♣❛✐♥✬s ❙♦❝✐❛❧ ❙❡❝✉r✐t② s②st❡♠ ✐♥ ❛ ❣✐✈❡♥ ②❡❛r✳

■♥❝♦♠❡ t❛① ❞❛t❛ ♥♦t t♦♣ ❝♦❞❡❞✿ ✐❞❡❛❧ ❢♦r ❤✐❣❤✲✐♥❝♦♠❡✳

◮ ❲❡ ❝r❡❛t❡ ❛♥ ✐♥❝♦♠❡ ✈❛r✐❛❜❧❡ ✇❤✐❝❤ ✐s t❤❡ s✉♠ ♦❢ ❛❧❧ r❡♣♦rt❡❞ ✐♥❝♦♠❡

❜② ❞✐✛❡r❡♥t ❡♠♣❧♦②❡rs ✇✐t❤✐♥ ❡❛❝❤ ②❡❛r ✇❤✐❝❤ ✐s s✉❜❥❡❝t t♦ t❤❡ ♣❡rs♦♥❛❧ ✐♥❝♦♠❡ t❛① ✭❧❛❜♦r ✐♥❝♦♠❡✱ s❡❧❢ ❡♠♣❧♦②❡❞ ✐♥❝♦♠❡✱ ❡t❝✳✮✳

❲❡ ❞❡✜♥❡ ❛ ❝❤❛♥❣❡ ♦❢ ❧♦❝❛t✐♦♥ ✐❢ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ❝❤❛♥❣❡❞ ❤✐s ♦r ❤❡r r❡s✐❞❡♥❝❡ ✉s✐♥❣ ♦✣❝✐❛❧ ♣♦♣✉❧❛t✐♦♥ r❡❣✐st❡rs✳

◮ ■♥❢♦r♠❛t✐♦♥ ✐s t❛❦❡♥ ❢r♦♠ t❤❡ ♦✣❝✐❛❧ r❡❣✐st❡r ♦❢ t❤❡ ♠✉♥✐❝✐♣❛❧✐t② ✇❤❡r❡

♣❡♦♣❧❡ r❡❣✐st❡r❡❞ ✭❢♦r ❧♦❝❛❧ s❡r✈✐❝❡s✮✳

❚❛① ❘❛t❡s

❚❤❡ ❞❛t❛ ♦♥❧② ✐♥❝❧✉❞❡s ✐♥❝♦♠❡ r❡♣♦rt❡❞ ❜② ❡♠♣❧♦②❡rs ♦r s❡❧❢✲❡♠♣❧♦②❡❞✱ ♥♦t ❢✉❧❧ t❛① ❞❡❝❧❛r❛t✐♦♥s✳ ◆❇❊❘✬s ❚❆❳❙■▼ ❞♦❡s ♥♦t ❡①✐st ❢♦r ❙♣❛✐♥ ✕ ✇❡ ❞✐❣✐t✐③❡ ❙♣❛✐♥✬s t❛① ❝♦❞❡✳ ❲❡ ✇r✐t❡ ❛ t❛① ❝❛❧❝✉❧❛t♦r ✇❤❡r❡ ✇❡ s✐♠✉❧❛t❡ ❛✈❡r❛❣❡ ❛♥❞ ♠❛r❣✐♥❛❧ t❛① r❛t❡s ❢♦r ❡❛❝❤ ✐♥❞✐✈✐❞✉❛❧ ✐♥ ❡❛❝❤ ②❡❛r ❢♦r ❡❛❝❤ r❡❣✐♦♥ ❛♥❞ r❡❝♦♥str✉❝t t❤❡ t❛①❡s ♦❢ ❛❧❧ ✐♥❞✐✈✐❞✉❛❧s ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ❞❛t❛✳

◮ ❚❤✐s s✐♠✉❧❛t✐♦♥ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ✈❛r✐❛t✐♦♥ ♦❢ ♠❛r❣✐♥❛❧ t❛① r❛t❡s✱

t❤❡✐r ❜r❛❝❦❡ts✱ ❛♥❞ ❜❛s✐❝ ❞❡❞✉❝t✐♦♥s ❛♥❞ t❛① ❝r❡❞✐ts ❢♦r ❝❤✐❧❞r❡♥✱ ❡❧❞❡r❧②✱ ❛♥❞ ❞✐s❛❜✐❧✐t✐❡s✳

▼❡t❤♦❞ ■✿ ❆❣❣r❡❣❛t❡ ❆♥❛❧②s✐s ❊st✐♠❛t✐♦♥ ♦❢ ▲♦❝❛t✐♦♥ ❊q✉✐❧✐❜r✐✉♠ ❈♦♥❞✐t✐♦♥

❚❤❡♦r❡t✐❝❛❧ ▼♦t✐✈❛t✐♦♥

▲❡t t❤❡ ✉t✐❧✐t② ♦❢ ❛ t♦♣ ✐♥❝♦♠❡ ✐♥❞✐✈✐❞✉❛❧ ❧✐✈✐♥❣ ✐♥ r❡❣✐♦♥ r ✐♥ ♣❡r✐♦❞ t ❜❡ ❣✐✈❡♥ ❜②✿ Vr,t = αln(cr,t)+πln(gr,t)+ µr −γln(Nr,t) ✭✶✮

◮ ✇❤❡r❡ cr,t = (✶−τr,t)wr,t ❛♥❞ ln(Nr,t) ✐s ❛ ❞✐s✉t✐❧✐t② ✭❝♦♥❣❡st✐♦♥✮

❢✉♥❝t✐♦♥✳

■❢ ♣r♦❞✉❝t✐♦♥ ✐s ❣✐✈❡♥ ❜② ArNθ

r,t ¯

K ϑ

r ✇❡ ♠✉st ❤❛✈❡ wr,t = Ar ¯ K ϑ

r

Nθ

r,t ✳

❚❤❡♥✱ t❤❡ ❡q✉✐❧✐❜r✐✉♠ ❜❡t✇❡❡♥ r❡❣✐♦♥s r = {d, o} ✐s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ln(Nd,t No,t ) = ✶ θ + γ

α

ln ✶−τd,t ✶−τo,t

• +

π α(θ + γ

α )ln

gd,t go,t

• +ζd −ζo

✭✷✮

◮ ✇❤❡r❡ ζr ❞❡♣❡♥❞s ♦♥ t✐♠❡✲✐♥✈❛r✐❛♥t ♣❛r❛♠❡t❡rs µr✱ Ar ❛♥❞ ¯

Kr✳

◮ ❆❞❥✉st♠❡♥t ♦❢ ✇❛❣❡s✿

dln(wr,t) dln(✶−τr,t) = dln(Nr,t) dln(✶−τr,t) × dln(wr,t) dln(Nr,t) = −θ ✶ θ+ γ

α

❆❣❣r❡❣❛t❡ ❆♥❛❧②s✐s✿ ❙t♦❝❦s

ln(Ndt/Not)

• stock ratio

= β[ln(✶−atrdt)−ln(✶−atrot)]

• tax differentials

+ ζd

• ’d’ amenities

+ ζo

• ’o’ amenitiess

+ζt +δln gd,t go,t

• +Xodtφ +νodt

✭✸✮

❚❤❡ ❧❡❢t ❤❛♥❞ s✐❞❡ ✈❛r✐❛❜❧❡ ln(Ndt/Not) ✐s t❤❡ ❧♦❣ ♦❢ t❤❡ st♦❝❦ ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✐♥ t❤❡ t♦♣ ✶✪ ♦❢ t❤❡ ✐♥❝♦♠❡ ❞✐str✐❜✉t✐♦♥ ✐♥ r❡❣✐♦♥ d r❡❧❛t✐✈❡ t♦ r❡❣✐♦♥ o✳ ◆❡❡❞ t♦ ❛❞❞r❡ss ♣♦t❡♥t✐❛❧ t❛①❛❜❧❡ ✐♥❝♦♠❡ r❡s♣♦♥s❡s✳ ❉♦ s♦ ❜② ❢♦❝✉s✐♥❣ ♦♥ ✐♥❞✐✈✐❞✉❛❧s t❤❛t r❡♣❡❛t ❜❡✐♥❣ ✐♥ t❤❡ t♦♣ ✶✪✳ ❚❤❡ st♦❝❦ ❡❧❛st✐❝✐t② ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ♥❡t ♦❢ t❛① t♦♣ r❛t❡ ✐s ❛♣♣r♦①✐♠❛t❡❧② ❡q✉❛❧ t♦ β =

dln(Nd,t) dln(✶−atrd,t) − dln(No,t) dln(✶−atrd,t)✳

▼♦❞❡❧ ▼♦t✐✈❛t✐♦♥

▼♦❞❡❧ ❧❡❛❞s t♦ ❛ str✉❝t✉r❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ❡st✐♠❛t❡❞ ❝♦❡✣❝✐❡♥t✿

◮ β ✐s t❤❡ ❡✛❡❝t ♦❢ t❛① ❝❤❛♥❣❡s ✐♥❝❧✉❞✐♥❣ t❤r♦✉❣❤ t❤❡✐r ✐♥❞✐r❡❝t ❡✛❡❝t ♦♥

r❡❣✐♦♥❛❧ ✇❛❣❡s✱ ✐✳❡✳ t❤❡ ❡✛❡❝t t❛❦✐♥❣ ❛❧❧ ✜①❡❞ r❡❣✐♦♥❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ✭❛♠❡♥✐t✐❡s✮ ❛♥❞ ♣✉❜❧✐❝ s❡r✈✐❝❡s ❛s ❣✐✈❡♥ ❡①❝❡♣t ❢♦r t❛①❡s ❛♥❞ ✇❛❣❡s✳

❱✐s✉❛❧ ❘❡s✉❧ts✿ ❙t♦❝❦ ❊❧❛st✐❝✐t②

t❤❡♦r②✿ ↓t❛① ❞✐✛❡r❡♥t✐❛❧ = ⇒ ↑ ♥❡t ♦❢ t❛① ❞✐✛❡r❡♥t✐❛❧ = ⇒ ↑ st♦❝❦ ♦❢ r✐❝❤

❘❡s✉❧ts ✿ ❙t♦❝❦ ❊❧❛st✐❝✐t②

❇❛s❡❧✐♥❡ ❙♣❡❝✐✜❝❛t✐♦♥s ❆❞❞r❡ss✐♥❣ ❚❛①❛❜❧❡ ■♥❝♦♠❡ ❆❚❘ ✭✶✮ ❆❚❘ ✭✷✮ ▼❚❘ ✭✸✮ ❆❚❘ ✭✹✮ ▼❚❘ ✭✺✮ ln[(✶−atrd)/(✶−atro)] ✵✳✾✶✼✯ ✶✳✶✶✻✯✯ ✵✳✻✺✻✯✯ ✵✳✽✼✽✯ ✵✳✺✺✻✯✯ ✭✵✳✺✸✼✮ ✭✵✳✺✹✺✮ ✭✵✳✸✵✵✮ ✭✵✳✺✵✵✮ ✭✵✳✷✻✼✮

• ♦✈❡r♥♠❡♥t ❙♣❡♥❞✐♥❣❄

❨ ❨ ❨ ❨ ❨ ❋❊❄ ❨ ❨ ❨ ❨ ❨ ❈♦♥tr♦❧s❄ ◆ ❨ ❨ ❨ ❨ ◆✉♠❜❡r ♦❢ ❖❜s❡r✈❛t✐♦♥s ✶✵✺✵ ✶✵✺✵ ✶✵✺✵ ✶✵✺✵ ✶✵✺✵

❱✐s✉❛❧ ❘❡s✉❧ts ✿ ▲♦✇❡r P❛rts ♦❢ ❉✐str✐❜✉t✐♦♥

❱✐s✉❛❧ ❘❡s✉❧ts ✿ Pr❡✲r❡❢♦r♠ ❙t♦❝❦ ✫ P♦st✲r❡❢♦r♠ ❚❛①❡s

❊✈❡♥t ❙t✉❞②

▼❡t❤♦❞ ■■✿ ■♥❞✐✈✐❞✉❛❧ ❆♥❛❧②s✐s ❲❤❡r❡ t♦ ▼♦✈❡❄

■♥❞✐✈✐❞✉❛❧ ❈❤♦✐❝❡ ▼♦❞❡❧

❬❊st✐♠❛t✐♦♥❪

▲❡tt✐♥❣ j ✐♥❞❡① ❧♦❝❛t✐♦♥ ❛♥❞ (i,t) ✐♥❞❡① ❛ ♣❛rt✐❝✉❧❛r ♠♦✈❡✱ ✇❡ ❡st✐♠❛t❡ ✉s✐♥❣ ♠♦✈❡rs ♣r❡✲r❡❢♦r♠ ✭✷✵✵✺✲✷✵✶✵✮ ❛♥❞ ♣♦st✲r❡❢♦r♠ ✭✷✵✶✶✲✷✵✶✹✮✿

di,t,j = βln(✶−τi,t,j)

• tax differentials

+ ζj①i,t

wage differentials

+ γ③i,t,j

moving costs

+

region-year effects

• ιt,j

+ αi,t

• case FE

+εi,t,j ✭✹✮

✇✐t❤ di,t,j = ✶ ✐❢ s❡❧❡❝t❡❞ r❡❣✐♦♥ ❛♥❞ ✵ ♦t❤❡r✇✐s❡✳

■❞❡♥t✐✜❝❛t✐♦♥✿ ❚❛①❡s

❆♣♣r♦❛❝❤ ❆✿

◮ ❇❡❝❛✉s❡ ❝♦✉♥t❡r❢❛❝t✉❛❧ ✇❛❣❡s ❛r❡ ♥♦t ♦❜s❡r✈❡❞✱ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡

❝♦✉♥t❡r❢❛❝t✉❛❧ ❛✈❡r❛❣❡ t❛① r❛t❡ ♣r❡s❡♥ts ❝❤❛❧❧❡♥❣❡s ✐❢ ✇❛❣❡s ❛r❡ ♥♦t s✐♠✐❧❛r ❛❝r♦ss r❡❣✐♦♥s✳

◮ ■♥✐t✐❛❧❧② ✉s❡ t❤❡ ♠❛r❣✐♥❛❧ t❛① r❛t❡ ♦❢ ✐♥❞✐✈✐❞✉❛❧ i✳ ■♥❞❡♣❡♥❞❡♥t ♦❢

❡❛r♥✐♥❣s ✐❢ ✐♥❝♦♠❡ ❝❤❛♥❣❡s ❛❝r♦ss r❡❣✐♦♥s ❞♦ ♥♦t ✐♥❞✉❝❡ t❛① ❜r❛❝❦❡t ❝❤❛♥❣❡s ❛❝r♦ss r❡❣✐♦♥s✳

❆♣♣r♦❛❝❤ ❇✿

◮ ❆❧s♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❛✈❡r❛❣❡ t❛① r❛t❡ ❛ss✉♠✐♥❣ t❤❛t ✇❛❣❡s ❛r❡ ❝♦♥st❛♥t

❛❝r♦ss r❡❣✐♦♥s✳

◮ ■♥❞✐✈✐❞✉❛❧s ❛r❡ ♠♦r❡ ❧✐❦❡❧② t♦ s❡❧❡❝t st❛t❡s ✇✐t❤ ❤✐❣❤ ✇❛❣❡s =

⇒ ♦✈❡r❡st✐♠❛t❡ ❝♦✉♥t❡r❢❛❝t✉❛❧ ✇❛❣❡s = ⇒ ♦✈❡r❡st✐♠❛t❡ ❝♦✉♥t❡r❢❛❝t✉❛❧ ❛✈❡r❛❣❡ t❛① r❛t❡s ✭♣r♦❣r❡ss✐✈❡✮✳

◮ ❘❡s♦❧✈❡❞ ✉s✐♥❣ ❛♥ ■❱ ❛♣♣r♦❛❝❤✳

■❞❡♥t✐✜❝❛t✐♦♥✿ ❲❛❣❡ ❉✐✛❡r❡♥t✐❛❧s

❇✉t✱ ✇❡ ❛❧s♦ ♥❡❡❞ t♦ ❝♦♥tr♦❧ ❢♦r ✇❛❣❡s ❛❝r♦ss ♦t❤❡r r❡❣✐♦♥s✳ ❚♦ ❞♦ t❤✐s✱ ✇❡ ❝♦♥str✉❝t ♠❡❛s✉r❡s ♦❢ ✏❛❜✐❧✐t②✑ ✉s✐♥❣ ❡❞✉❝❛t✐♦♥✱ ♠❛❧❡✱ ❛❣❡✱ ❛♥❞ ❛❣❡ sq✉❛r❡❞✳

◮ ❲❡ t❤❡♥ ✐♥t❡r❛❝t t❤❡s❡ ✈❛r✐❛❜❧❡s ✇✐t❤ st❛t❡ ❞✉♠♠② ✈❛r✐❛❜❧❡s t♦ ❛❧❧♦✇

❢♦r ❞✐✛❡r❡♥t ❡✛❡❝ts ❛❝r♦ss st❛t❡s✳

◮ ❚❤✐s ❛❧❧♦✇s t❤❡ r❡t✉r♥s t♦ ❡❞✉❝❛t✐♦♥ ❛♥❞ t❤❡ s❦✐❧❧ ♣r❡♠✐✉♠ ♦❢ ❛❣❡ t♦

✈❛r② ❜② r❡❣✐♦♥✳

■❞❡♥t✐✜❝❛t✐♦♥✿ ❖t❤❡r P♦❧✐❝✐❡s ✴ ❆♠❡♥✐t✐❡s

❲❡ ❝♦♥tr♦❧ ❢♦r ♦t❤❡r ♣♦❧✐❝② ❝❤❛♥❣❡s ❛♥❞ ❛♠❡♥✐t✐❡s ❛❝r♦ss r❡❣✐♦♥s✳

◮ ❲❡ ❞♦ t❤✐s ❜② ✐♥❝❧✉❞✐♥❣ r❡❣✐♦♥ ❜② ②❡❛r ✜①❡❞ ❡✛❡❝ts t♦ ❝❛♣t✉r❡ ❛♥②

❛❧t❡r♥❛t✐✈❡ s♣❡❝✐✜❝ ♣♦❧✐❝✐❡s t❤❛t ♠❛② ✈❛r② ♦✈❡r t✐♠❡✳

◮ ■♠♣❧✐❝✐t❧② ❛ss✉♠❡s ❛❧❧ ♣♦❧✐❝✐❡s ❛r❡ ❝♦♥st❛♥t ❛❝r♦ss ✐♥❞✐✈✐❞✉❛❧s ✇✐t❤✐♥ ❛

r❡❣✐♦♥✳

◮ P✉❜❧✐❝ s❡r✈✐❝❡s ❝♦♥s✉♠♣t✐♦♥ ❧✐❦❡❧② s✐♠✐❧❛r ✐♥ t❤❡ t♦♣ ✶✪✳

■❞❡♥t✐✜❝❛t✐♦♥✿ ▼♦✈✐♥❣ ❈♦sts

❲❡ ❝♦♥tr♦❧ ❢♦r ♠♦✈✐♥❣ ❝♦sts✳

◮ ❈❛❧❝✉❧❛t❡ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛❧❧ ❛❧t❡r♥❛t✐✈❡s ❛♥❞ t❤❡ r❡❣✐♦♥ ♦❢ ♦r✐❣✐♥

✭❣r❛✈✐t② ♠♦❞❡❧ ♦❢ ♠✐❣r❛t✐♦♥✮✳

◮ ❉✉♠♠② ✈❛r✐❛❜❧❡ ❢♦r r❡❣✐♦♥ ♦❢ ❜✐rt❤✳ ◮ ❉✉♠♠② ✈❛r✐❛❜❧❡ ❢♦r r❡❣✐♦♥ ♦❢ ✜rst ❥♦❜✳ ◮ ❉✉♠♠② ✈❛r✐❛❜❧❡ ❢♦r r❡❣✐♦♥ ♠♦✈✐♥❣ ❢r♦♠✳ ◮ ❉✉♠♠② ✈❛r✐❛❜❧❡ ❢♦r r❡❣✐♦♥ ♦❢ ✜r♠ ❤❡❛❞q✉❛rt❡rs✳

❙❛♠♣❧❡ ❙❡❧❡❝t✐♦♥

❲❡ ❢♦❝✉s ♦♥ ♠♦✈❡rs✳ ❇❡❝❛✉s❡ ♠♦✈❡rs ❛r❡ ❛ ✈❡r② s♠❛❧❧ s❤❛r❡ ♦❢ t❤❡ ♣♦♣✉❧❛t✐♦♥✱ ✐t ✐s ❧✐❦❡❧② t❤❛t t❤❡ ❡q✉✐❧✐❜r✐✉♠ t❛① r❛t❡s s❡❧❡❝t❡❞ ❢♦❧❧♦✇✐♥❣ t❤❡ ✜s❝❛❧ ❞❡❝❡♥tr❛❧✐③❛t✐♦♥ ❛r❡ ❞r✐✈❡♥ ❜② t❤❡ ❧❛r❣❡ s❤❛r❡ ♦❢ t❤❡ st❛②❡rs ✕ r❡❞✉❝✐♥❣ ❡♥❞♦❣❡♥❡✐t② ❝♦♥❝❡r♥s ✭❇r✉❧❤❛rt✱ ❇✉❝♦✈❡ts❦② ❛♥❞ ❙❝❤♠✐❞❤❡✐♥② ✷✵✶✺✮✳ ❙❝❤♠✐❞❤❡✐♥② ✭✷✵✵✻✮✿ ✏❍♦✉s❡❤♦❧❞s ❞♦ ♥♦t ❞❛✐❧② ❞❡❝✐❞❡ ✉♣♦♥ t❤❡✐r ♣❧❛❝❡ ♦❢ r❡s✐❞❡♥❝❡✳ ❚❤❡r❡ ❛r❡ s♣❡❝✐✜❝ ♠♦♠❡♥ts ✐♥ ❛♥② ✐♥❞✐✈✐❞✉❛❧✬s ❧✐❢❡ ❬✜rst ❥♦❜✱ ❢❛♠✐❧② ❝❤❛♥❣❡s✱ ❝❛r❡❡r ♦♣♣♦rt✉♥✐t✐❡s❪ ✇❤❡♥ t❤❡ ❞❡❝✐s✐♦♥ ❛❜♦✉t ✇❤❡r❡ t♦ ❧✐✈❡ ❜❡❝♦♠❡s ✉r❣❡♥t✳✳✳✳ ▲✐♠✐t✐♥❣ t❤❡ ❛♥❛❧②s✐s t♦ ♠♦✈✐♥❣ ❤♦✉s❡❤♦❧❞s t❤❡r❡❢♦r❡ ❡❧✐♠✐♥❛t❡s t❤❡ ❜✐❛s ✇❤❡♥ ✐♥❝❧✉❞✐♥❣ ❤♦✉s❡❤♦❧❞s t❤❛t st❛② ✐♥ ❛ ♣❡r s❡ s✉❜✲♦♣t✐♠❛❧ ❧♦❝❛t✐♦♥ ❜❡❝❛✉s❡ ♦❢ ❤✐❣❤ ♠♦♥❡t❛r② ❛♥❞ ♣s②❝❤♦❧♦❣✐❝❛❧ ❝♦sts ♦❢ ♠♦✈✐♥❣✳ ❍♦✇❡✈❡r✱ t❤❡ ❧✐♠✐t❛t✐♦♥ t♦ ♠♦✈✐♥❣ ❤♦✉s❡❤♦❧❞s ✐♥tr♦❞✉❝❡s ❛ ♣♦t❡♥t✐❛❧ s❡❧❡❝t✐♦♥ ❜✐❛s ✇❤❡♥ t❤❡ ✉♥♦❜s❡r✈❡❞ ✐♥❞✐✈✐❞✉❛❧ ❢❛❝t♦rs t❤❛t tr✐❣❣❡r t❤❡ ❞❡❝✐s✐♦♥ t♦ ♠♦✈❡ ❛r❡ ❝♦rr❡❧❛t❡❞ ✇✐t❤ t❤❡ ✉♥♦❜s❡r✈❡❞ ✐♥❞✐✈✐❞✉❛❧ t❛st❡ ❢♦r ❝❡rt❛✐♥ ❧♦❝❛t✐♦♥s✳✑

❙❛♠♣❧❡ ❙❡❧❡❝t✐♦♥

❆❞❞r❡ss t❤❡s❡ ❝♦♥❝❡r♥s ❜②✿

◮ ❚❡st✐♥❣ ❢♦r ❞✐✛❡r❡♥❝❡s ✐♥ ❝♦✈❛r✐❛t❡s ❜❡t✇❡❡♥ ♠♦✈❡rs ❛♥❞ st❛②❡rs✳ ◮ ❊st✐♠❛t❡ t❤❡ ♠♦❞❡❧ ❢♦r t❤❡ ❢✉❧❧ s❛♠♣❧❡ ♦❢ st❛②❡rs ❛♥❞ ♠♦✈❡rs ✭s♠❛❧❧❡r✱

❜✉t s❛♠❡ s✐❣♥✮✳

❘❡s✉❧ts✿ ▼❚❘

✭✶✮ ✭✷✮ ✭✸✮ ln(✶−mtri,j,t) ✵✳✺✻✾ ✵✳✻✵✹✯✯ ✵✳✻✼✼✯✯ ✭✵✳✸✻✼✮ ✭✵✳✸✵✺✮ ✭✵✳✸✵✽✮ ♣❧❛❝❡ ♦❢ ♦r✐❣✐♥ ✲✵✳✼✾✼✯✯✯ ✲✵✳✼✻✻✯✯✯ ✭✵✳✵✻✶✮ ✭✵✳✵✻✵✮ ♣❧❛❝❡ ♦❢ ❜✐rt❤ ✵✳✷✵✼✯✯✯ ✵✳✷✵✻✯✯✯ ✭✵✳✵✷✷✮ ✭✵✳✵✷✶✮ ♣❧❛❝❡ ♦❢ ✜rst ✇♦r❦ ✵✳✶✽✻✯✯✯ ✵✳✶✼✼✯✯✯ ✭✵✳✵✷✵✮ ✭✵✳✵✷✵✮ ✇♦r❦ ♣❧❛❝❡ ✵✳✷✽✽✯✯✯ ✵✳✷✻✶✯✯✯ ✭✵✳✵✶✽✮ ✭✵✳✵✷✶✮ ln(distance) ✲✵✳✵✼✺✯✯✯ ✲✵✳✵✼✷✯✯✯ ✭✵✳✵✵✾✮ ✭✵✳✵✵✾✮ ✐♥❞✐✈✐❞✉❛❧ ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ②❡❛r ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ❡❞✉❝❛t✐♦♥ ◆ ◆ ❨ j ❜② ❛❣❡ ◆ ◆ ❨ j ❜② ❛❣❡ sq✉❛r❡❞ ◆ ◆ ❨ j ❜② ♠❛❧❡ ◆ ◆ ❨ ♦❜s❡r✈❛t✐♦♥s ✶✸✱✸✾✺ ✶✸✱✸✾✺ ✶✸✱✸✾✺

❘❡s✉❧ts✿ ❆❚❘

✭✶✮ ✭✷✮ ✭✸✮ ln(✶−atri,j,t) ✵✳✺✽✽ ✵✳✼✶✹✯✯ ✵✳✾✵✹✯✯✯ ✭✵✳✹✷✵✮ ✭✵✳✸✹✸✮ ✭✵✳✸✸✷✮ ♣❧❛❝❡ ♦❢ ♦r✐❣✐♥ ✲✵✳✼✾✼✯✯✯ ✲✵✳✼✻✻✯✯✯ ✭✵✳✵✻✶✮ ✭✵✳✵✻✵✮ ♣❧❛❝❡ ♦❢ ❜✐rt❤ ✵✳✷✵✼✯✯✯ ✵✳✷✵✻✯✯✯ ✭✵✳✵✷✷✮ ✭✵✳✵✷✶✮ ♣❧❛❝❡ ♦❢ ✜rst ✇♦r❦ ✵✳✶✽✺✯✯✯ ✵✳✶✼✼✯✯✯ ✭✵✳✵✷✵✮ ✭✵✳✵✷✵✮ ✇♦r❦ ♣❧❛❝❡ ✵✳✷✽✽✯✯✯ ✵✳✷✻✶✯✯✯ ✭✵✳✵✶✽✮ ✭✵✳✵✷✶✮ ln(distance) ✲✵✳✵✼✺✯✯✯ ✲✵✳✵✼✷✯✯✯ ✭✵✳✵✵✾✮ ✭✵✳✵✵✾✮ ✐♥❞✐✈✐❞✉❛❧ ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ②❡❛r ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ❡❞✉❝❛t✐♦♥ ◆ ◆ ❨ j ❜② ❛❣❡ ◆ ◆ ❨ j ❜② ❛❣❡ sq✉❛r❡❞ ◆ ◆ ❨ j ❜② ♠❛❧❡ ◆ ◆ ❨ ♦❜s❡r✈❛t✐♦♥s ✶✸✱✸✾✺ ✶✸✱✸✾✺ ✶✸✱✸✾✺

❘❡s✉❧ts✿ ❆❚❘ ✇✐t❤ ■❱

✭✶✮ ✭✷✮ ✭✸✮ ln(✶−atri,j,t) ✶✳✹✺✷ ✶✳✺✹✷✯ ✶✳✼✸✶✯✯ ✭✵✳✾✹✽✮ ✭✵✳✼✽✽✮ ✭✵✳✼✾✼✮ ♣❧❛❝❡ ♦❢ ♦r✐❣✐♥ ✲✵✳✼✾✼✯✯✯ ✲✵✳✼✻✻✯✯✯ ✭✵✳✵✻✶✮ ✭✵✳✵✻✵✮ ♣❧❛❝❡ ♦❢ ❜✐rt❤ ✵✳✷✵✼✯✯✯ ✵✳✷✵✻✯✯✯ ✭✵✳✵✷✷✮ ✭✵✳✵✷✶✮ ♣❧❛❝❡ ♦❢ ✜rst ✇♦r❦ ✵✳✶✽✺✯✯✯ ✵✳✶✼✼✯✯✯ ✭✵✳✵✷✵✮ ✭✵✳✵✷✵✮ ✇♦r❦ ♣❧❛❝❡ ✵✳✷✽✽✯✯✯ ✵✳✷✻✶✯✯✯ ✭✵✳✵✶✽✮ ✭✵✳✵✷✶✮ ln(distance) ✲✵✳✵✼✺✯✯✯ ✲✵✳✵✼✷✯✯✯ ✭✵✳✵✵✾✮ ✭✵✳✵✵✾✮ ✐♥❞✐✈✐❞✉❛❧ ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ②❡❛r ✜①❡❞ ❡✛❡❝ts ❨ ❨ ❨ j ❜② ❡❞✉❝❛t✐♦♥ ◆ ◆ ❨ j ❜② ❛❣❡ ◆ ◆ ❨ j ❜② ❛❣❡ sq✉❛r❡❞ ◆ ◆ ❨ j ❜② ♠❛❧❡ ◆ ◆ ❨ ♦❜s❡r✈❛t✐♦♥s ✶✸✱✸✾✺ ✶✸✱✸✾✺ ✶✸✱✸✾✺ ❋✐rst ❙t❛❣❡ ❈♦❡✣❝✐❡♥t ✵✳✸✾✷✯✯✯ ✵✳✸✾✷✯✯✯ ✵✳✸✾✶✯✯✯ ✭✵✳✵✶✺✮ ✭✵✳✵✶✹✮ ✭✵✳✵✶✹✮ ❋✲st❛t✐st✐❝ ✼✸✺✳✶ ✼✹✵✳✷ ✼✾✷✳✾

▼❛❣♥✐t✉❞❡s

❊✛❡❝t ♦❢ ▼❛❞r✐❞✲❈❛t❛❧✉♥②❛ ❛✈❡r❛❣❡ t❛① ❞✐✛❡r❡♥t✐❛❧ ✭✵✳✼✺ ♣♦✐♥ts ✐♥ ✷✵✶✸✮

◮ ✐♥❝r❡❛s❡s ♣r♦❜❛❜✐❧✐t② ♦❢ ♠♦✈✐♥❣ t♦ ▼❛❞r✐❞ ❜② ✷✳✷✺ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts✳

❊✛❡❝t ♦❢ ▼❛❞r✐❞✬s t❛① ❝✉t ✐♥ ✷✵✶✹ ✭✵✳✹ ♣♦✐♥ts✮

◮ ❋✉rt❤❡r ✐♥❝r❡❛s❡s ♣r♦❜❛❜✐❧✐t② ♦❢ ♠♦✈✐♥❣ t♦ ▼❛❞r✐❞ ❜② ❛♥♦t❤❡r ✶✳✶✺

♣♦✐♥ts✳

❘❡s✉❧ts✿ ■❱ ❋✐①❡❞ ❇r❛❝❦❡t

❊①❝❧✉❞❡ ♦❜s❡r✈❛t✐♦♥s ✶✱ ✷✳✺ ❛♥❞ ✺✪ ❛❜♦✈❡✴❜❡❧♦✇ ❝✉t✲♦✛s✳ ■❞❡❛✿ r❡❞✉❝❡s t❤❡ ♣♦ss✐❜✐❧✐t② t❤❛t t❤❡ ✐♥str✉♠❡♥t ✐s ✐♥✢✉❡♥❝❡❞ ❜② ❝♦✉♥t❡r❢❛❝t✉❛❧ ✐♥❝♦♠❡✳

✭✶✮ ✭✷✮ ✭✸✮ ✶✪ ❛❜♦✈❡✴❜❡❧♦✇ ✷✳✺✪ ❛❜♦✈❡✴ ❜❡❧♦✇ ✺✪ ❛❜♦✈❡✴❜❡❧♦✇ ln(✶−atri,j,t) ✶✳✼✽✷✯✯ ✶✳✽✻✹✯✯ ✸✳✼✸✹✯✯✯ ✭✵✳✽✾✻✮ ✭✵✳✽✼✶✮ ✭✶✳✷✼✼✮ ♦❜s❡r✈❛t✐♦♥s ✶✷✱✷✺✺ ✶✵✱✻✷✵ ✽✱✵✹✵

P❧❛❝❡❜♦ ❚❡st✿ ❉♦ P♦st✲r❡❢♦r♠ ❘❛t❡s Pr❡❞✐❝t Pr❡✲r❡❢♦r♠ ▼✐❣r❛t✐♦♥❄

✭✶✮ ✭✷✮ ✭✸✮ ✭✹✮ ▼❚❘ ❆❚❘ ▼❚❘ ❆❚❘ Pr❡✲❘❡❢♦r♠ P♦st✲❘❡❢♦r♠ ln(✶−τ) ✵✳✵✸✽ ✵✳✵✾✸ ✵✳✽✻✻✯✯✯ ✷✳✵✺✶✯✯✯ ✭✵✳✶✾✹✮ ✭✵✳✹✻✾✮ ✭✵✳✷✽✶✮ ✭✵✳✻✽✼✮ ♦❜s❡r✈❛t✐♦♥s ✻✱✶✽✵ ✻✱✶✽✵ ✹✱✾✻✺ ✹✱✾✻✺

❉✐s❝✉ss✐♦♥

❘❡❛❧ r❡s♣♦♥s❡ ✈s✳ t❛① ❡✈❛s✐♦♥

◮ ❚❤❡ t♦♣ ✶✪ ♠❛② ❤❛✈❡ t❤❡ ❛❜✐❧✐t② t♦ ❝❤❛♥❣❡ r❡s✐❞❡♥❝❡ t♦ ❛ s❡❝♦♥❞ ❤♦♠❡

✇✐t❤♦✉t s♣❡♥❞✐♥❣ t❤❡ ♠❛❥♦r✐t② ♦❢ t❤❡ ②❡❛r t❤❡r❡✳

◮ ❋r♦♠ ❛ t❛① r❡✈❡♥✉❡ ♣❡rs♣❡❝t✐✈❡ r❡❛❧ r❡s♣♦♥s❡ ❛♥❞ t❛① ❡✈❛s✐♦♥ ❛r❡ ❜♦t❤

✐♠♣♦rt❛♥t✳

❆ t❛① ♣r♦❢❡ss✐♦♥❛❧ ✇❡ s♣♦❦❡ t♦✿ r❡❝♦♠♠❡♥❞s ❤✐s ❝❧✐❡♥ts t♦ ✬♠♦✈❡✬ ✇❤❡♥ ✐♥❝♦♠❡ ✐s ❛❜♦✈❡ ✽✵✱✵✵✵ ❡✉r♦s✳ ❲❡ ❝♦♥❞✉❝t ❤❡t❡r♦❣❡♥❡✐t② ❛♥❛❧②s✐s t♦ tr② t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♠❡❝❤❛♥✐s♠✳

❍❡t❡r♦❣❡♥❡✐t② ♦❢ ❊✛❡❝t

■♥❞✐✈✐❞✉❛❧ ❝❤❛r❛❝t❡r✐st✐❝s✿

◮ ❨♦✉♥❣❡r t❤❛♥ ✹✵ ✭ ✶✳✻✽✵✯✮ ✈s✳ ♦❧❞❡r t❤❛♥ ✹✵ ✭✶✳✼✺✾✯✯✮ ◮ ❑✐❞s ✭✶✳✼✻✼✯✮ ✈s✳ ♥♦ ❦✐❞s ✭✶✳✼✵✾✯✯✮✳ ◮ ❯♥✐✈❡rs✐t② ❞❡❣r❡❡ ✭✷✳✶✽✺✯✯✮ ✈s✳ ♥♦ ❞❡❣r❡❡ ✭✶✳✵✵✽✮✳ ◮ ▼❡♥ ✭✶✳✹✽✸✮ ✈s✳ ✇♦♠❡♥ ✭✸✳✵✶✷✯✯✯✮✳

❏♦❜ ❝❤❛r❛❝t❡r✐st✐❝s✿

◮ ◆♦t ✜r❡❞ ✭✷✳✵✶✺✯✯✮ ✈s✳ ✜r❡❞ ✭✵✳✽✹✼✮✳ ◮ ◆♦ ❝♦♥tr❛❝t ❝❤❛♥❣❡ ✭✶✳✻✻✵✯✯✮ ✈s✳ ❝♦♥tr❛❝t ❝❤❛♥❣❡ ✭✷✳✹✷✾✯✯✮✳

❖❝❝✉♣❛t✐♦♥✴■♥❞✉str②

❚❤❡ ♣r✐♦r ❧✐t❡r❛t✉r❡ ❤❛s ❜❡❡♥ ✉♥❛❜❧❡ t♦ ❛♥s✇❡r t❤❡ q✉❡st✐♦♥ ✇❤❡t❤❡r ♣♦❧✐❝②♠❛❦❡rs ❝❛♥ t❛❦❡ t❤❡ ❡st✐♠❛t❡s ❞❡r✐✈❡❞ ❢♦r st❛r s❝✐❡♥t✐sts ❛♥❞ ❛t❤❧❡t❡s ❛♥❞ ❛♣♣❧② t❤❡s❡ ❡❧❛st✐❝✐t✐❡s t♦ t❤❡ t♦♣ ♦❢ t❤❡ ✐♥❝♦♠❡ ❞✐str✐❜✉t✐♦♥ ♠♦r❡ ❣❡♥❡r❛❧❧②✳ ❚❤❡ ❙♣❛♥✐s❤ ❞❛t❛ ✇❡ ❤❛✈❡ ❛❝❝❡ss t♦ ❤❛s ♦❝❝✉♣❛t✐♦♥ ❛♥❞ ✐♥❞✉str② r❡♣♦rt❡❞ ✐♥ t❤❡ ❞❛t❛✳ ❚❤✐s s❡❝t✐♦♥ ❛❧s♦ ❤❡❧♣s t♦ ✐♥❢♦r♠ t❤❡ r❡❝❡♥t ♣♦❧✐❝② ❞❡❜❛t❡ ♦♥ t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❛① s❝❤❡♠❡s ❢♦r t♦♣ ❡❛r♥❡rs ✐♥ s♣❡❝✐✜❝ ♦❝❝✉♣❛t✐♦♥s✳ ❙❡✈❡r❛❧ ❖❊❈❉ ❝♦✉♥tr✐❡s ❤❛✈❡ ♣r❡❢❡r❡♥t✐❛❧ t❛① s❝❤❡♠❡s ❢♦r ❢♦r❡✐❣♥❡rs ✐♥ ❝❡rt❛✐♥ ❤✐❣❤✲✐♥❝♦♠❡ ♦❝❝✉♣❛t✐♦♥s✳ ▼❛❥♦r ❝♦♥tr✐❜✉t✐♦♥✿ ♣r✐♦r ❧✐t❡r❛t✉r❡ ❢♦❝✉s✐♥❣ ♦♥ st❛r s❝✐❡♥t✐sts ❛♥❞ ❛t❤❧❡t❡s ♠❛s❦s s✉❜st❛♥t✐❛❧ ❤❡t❡r♦❣❡♥❡✐t② ❜② ♦t❤❡r ♦❝❝✉♣❛t✐♦♥s✴✐♥❞✉str✐❡s✳

❖❝❝✉♣❛t✐♦♥

self-employed engineers, college graduates managers and graduate assistants

• thers
• 2

2 4 6

effects by occupation

■♥❞✉str②

Health Other Real Estate Information Financial Professional/Scientific Construction Education Wholesale/Retail Extraterritorial Activities Manufacturing Transportation Arts/Entertainment Administrative Agriculture Tourism Electricity

• 10
• 5

5 10

effects by industry

■♥t❡r♣r❡t❛t✐♦♥ ♦❢ ▼❛❣♥✐t✉❞❡s

▼❛❣♥✐t✉❞❡s

❚♦ ✐♥t❡r♣r❡t✱ ✇❡ ❝♦♥str✉❝t ❛ s✐♠♣❧❡ ♠♦❞❡❧ ♦❢ t❛① r❡✈❡♥✉❡ ♠❛①✐♠✐③❛t✐♦♥ ❢r♦♠ t❤❡ r✐❝❤✳ ❚❤❡♥ ❛ t♦♣ t❛① r❛t❡ ❝❤❛♥❣❡ ❛❜♦✈❡ ✐♥❝♦♠❡ y ✇✐❧❧ ❤❛✈❡ ♠❡❝❤❛♥✐❝❛❧ ❛♥❞ ❜❡❤❛✈✐♦r❛❧ ❡✛❡❝ts✿

dR = [N(y − ¯ y)]dτ

• ♠❡❝❤❛♥✐❝❛❧

−εa

• N(y − ¯

y) τ ✶−τ

• dτ
• t❛①❛❜❧❡ ✐♥❝♦♠❡

−ηN(y − ¯ y)

• T(y)

y −T(y)

• dτ
• ♠♦❜✐❧✐t②

❊❚■ ❢♦r ❣♦✈❡r♥♠❡♥ts t❤❛t ❤✐ts t❤❡ ▲❛✛❡r ❈✉r✈❡ P❡❛❦✿

• ε =

✶−η

• T(y)

y−T(y)

• a
• τ

✶−τ

• .

❘❡✈❡♥✉❡ ❈❤❛♥❣❡s ✴ ▲❛✛❡r ❚❛① ❘❛t❡s

❲❡ ❝❛❧❝✉❧❛t❡ t❤❡ ❝❤❛♥❣❡ ✐♥ r❡✈❡♥✉❡ r❡❧❛t✐✈❡ t♦ ✇❤❛t ✇♦✉❧❞ ❤❛✈❡ ❜❡❡♥ ♦❜t❛✐♥❡❞ ✐❢ t❤❡ r❡❣✐♦♥ ❤❛❞ s✐♠♣❧② ♠✐♠✐❝❦❡❞ t❤❡ ❢❡❞❡r❛❧ ❣♦✈❡r♥♠❡♥t t❛① r❛t❡✳

◮ ❋♦❝✉s ♦♥ ❛ τ ❛♣♣❧✐❡❞ t♦ ✐♥❝♦♠❡ ❛❜♦✈❡ ✾✹✱✵✵✵ ❡✉r♦s ✭t♦♣ ✶✪✮✳ ◮ ❲❡ ❡st✐♠❛t❡ t❤❡ P❛r❡t♦ ♣❛r❛♠❡t❡r ✭✇❡ ❡st✐♠❛t❡ t❤✐s ❢♦r ❡❛❝❤ r❡❣✐♦♥✮✳ ◮ ❊❧❛st✐❝✐t② ♦❢ t❛①❛❜❧❡ ✐♥❝♦♠❡ ✐s t❛❦❡♥ ❢r♦♠ ❙❛❡③✱ ❙❧❡♠r♦❞ ❛♥❞ ●✐❡rt③

✭✷✵✶✷✱ ❏❊▲✮✳ ❲❡ t❛❦❡ t❤❡ ♠✐❞♣♦✐♥t ♦❢ t❤❡ ❧✐t❡r❛t✉r❡ ✭✵✳✷✺✮ ❛♥❞ ❛❞❥✉st ✐t ❞♦✇♥✇❛r❞ s❧✐❣❤t❧② ❜❡❝❛✉s❡ ♦❢ t❤❡ s♠❛❧❧❡r ♥✉♠❜❡r ♦❢ ❞❡❞✉❝t✐♦♥s ✐♥ ❙♣❛✐♥ ✭❝♦♥s✐st❡♥t ✇✐t❤ ♦✉r ❡st✐♠❛t❡s✮✳

❯s❡ t❤❡ ♣❛r❛♠❡tr✐❝ ❜♦♦tstr❛♣ t♦ ❝♦♥str✉❝t ❝♦♥✜❞❡♥❝❡ ❜❛♥❞s✳

❘❡✈❡♥✉❡ ❊✛❡❝ts

• .5

.5 1 1.5 percent of revenue La Rioja Murcia Madrid Galicia Extremadura Valencia Catalunya Castilla la Mancha Castilla y Leon Cantabria Canarias Islas Balears Asturia Aragon Andalusia mechanical taxable income mobility

❲❤❛t ❉♦❡s t❤❡ ❊❚■ ◆❡❡❞ t♦ ❇❡ t♦ ❇r❡❛❦ ❊✈❡♥❄

.25 .5 .75 1 1.25 1.5 elasticity of taxable income A n d a l u s i a A r a g

• n

A s t u r i a I s l a s B a l e a r s C a n a r i a s C a n t a b r i a C a s t i l l a y L e

• n

C a s t i l l a l a M a n c h a C a t a l u n y a V a l e n c i a E x t r e m a d u r a G a l i c i a M a d r i d M u r c i a L a R i

• j

a

• .03
• .02
• .01

.01 .02 .03 log share of income to the top 1%

• .04
• .02

.02 .04 log net of tax rate

❈♦♥❝❧✉s✐♦♥

❙t❛t❡ t❛①❡s ❤❛✈❡ ❛ s✐❣♥✐✜❝❛♥t ❛♥❞ st❛❜❧❡ ❡✛❡❝t ♦♥ t❤❡ ❧♦❝❛t✐♦♥ ❞❡❝✐s✐♦♥s ♦❢ t❤❡ r✐❝❤✱ ❜✉t t❤❡ r❡✈❡♥✉❡ ✐♠♣❧✐❝❛t✐♦♥s ❛♣♣❡❛r t♦ ❜❡ s♠❛❧❧✳ ❚❤✉s✱ ✇❡ ✜♥❞ s❤♦rt✲r✉♥ ❡✈✐❞❡♥❝❡ ❝♦♥s✐st❡♥t ✇✐t❤ ❊♣♣❧❡ ❛♥❞ ❘♦♠❡r ✭✶✾✾✶✮ t❤❛t s❤♦✇s ❧♦❝❛❧ r❡❞✐str✐❜✉t✐♦♥ ✐s ❢❡❛s✐❜❧❡ ❡✈❡♥ ✇✐t❤ ♠✐❣r❛t✐♦♥✳ ■♥ t❤❡ ❧♦♥❣✲r✉♥✱ t❤✐s ♠❛② ❝r❡❛t❡ s✉❜st❛♥t✐❛❧ s♦rt✐♥❣ ❡✛❡❝ts ❛s ♠✐❣r❛t✐♦♥ ✢♦✇s ♣❡rs✐st✱ ✐♥ ♣❛rt✐❝✉❧❛r ✇❤❡♥ ❛✈♦✐❞❛♥❝❡ ✐s ❡❛s②✳

◮ ▼♦❜✐❧✐t② ✐s ❧✐❦❡❧② t♦ r✐s❡ ♦✈❡r t✐♠❡ ❣✐✈❡♥ ❞❡♠♦❣r❛♣❤✐❝ s❤✐❢ts ❛♥❞

t❡❝❤♥♦❧♦❣✐❝❛❧ ✐♥♥♦✈❛t✐♦♥s✱ ✇❤✐❝❤ ♠❛② ✐♥ t✉r♥ ✐♠♣♦s❡ ❛❞❞❡❞ ❝♦♥str❛✐♥ts ♦♥ t❤❡ ❛❜✐❧✐t② t♦ ❡♥❣❛❣❡ ✐♥ r❡❞✐str✐❜✉t✐✈❡ ✜s❝❛❧ ♣♦❧✐❝② ✭❲✐❧❞❛s✐♥ ✷✵✶✺✮✳

❲✐t❤✐♥ ❱❛r✐❛t✐♦♥

❬❇❛❝❦❪ .5 1 1.5 within standard deviation 2004 2006 2008 2010 2012 2014 year Top 1% Top 2% Top 3%

❆❣❣r❡❣❛t❡ ❆♥❛❧②s✐s✿ ❋❧♦✇s

❬❇❛❝❦❪

ln(Podt/Poot) = e[ln(✶−mtrdt)−ln(✶−mtrot)]+ζo +ζd +ζt +Xodtβ +νodt ✭✺✮ ❚❤❡ ❧❡❢t ❤❛♥❞ s✐❞❡ ✈❛r✐❛❜❧❡ ln(Podt/Poot) ✐s t❤❡ ❧♦❣ ♦❞❞s r❛t✐♦ ✇❤❡r❡ Podt ✐s t❤❡ t❤❡ s❤❛r❡ ♦❢ t❤❡ ♣♦♣✉❧❛t✐♦♥ t❤❛t ♠♦✈❡s ❢r♦♠ st❛t❡ o t♦ st❛t❡ d ✐♥ ②❡❛r t ❛♥❞ Poot ✐s t❤❡ ❢r❛❝t✐♦♥ ♦❢ t❤❡ ♣♦♣✉❧❛t✐♦♥ t❤❛t st❛②s ✐♥ st❛t❡ o ✐♥ t❤❡ s❛♠❡ ②❡❛r✳ ε ✐s t❤❡ ❛♣♣r♦①✐♠❛t❡ ✢♦✇ ❡❧❛st✐❝✐t② ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ♥❡t ♦❢ t❛① r❛t❡✳

❱✐s✉❛❧ ❘❡s✉❧ts✿ ❋❧♦✇ ▼♦❞❡❧

t❤❡♦r②✿ ↓t❛① ❞✐✛❡r❡♥t✐❛❧ = ⇒ ↑ ♥❡t ♦❢ t❛① ❞✐✛❡r❡♥t✐❛❧ = ⇒ ↑ ♦❞❞s ♦❢ ♠♦✈✐♥❣

❊st✐♠❛t✐♦♥

❬❇❛❝❦❪

❋♦r ❡❛s❡ ♦❢ ♥♦t❛t✐♦♥✱ ✇❡ ♣r♦✈❡ t❤✐s ❢♦r ❛♥ ❡q✉❛t✐♦♥ ✇✐t❤ ❛ s✐♥❣❧❡ ❝♦✈❛r✐❛t❡ ❞❡♥♦t❡❞ ❜② xi,t,j✱ t❤❡ s✉♠ ♦❢ t❤❡ ♣r❡❞✐❝t❡❞ ♣r♦❜❛❜✐❧✐t✐❡s ❢♦r ❛ ❣✐✈❡♥ ♠♦✈❡ ✭i,t✮ ❢r♦♠ ♦✉r r❡❣r❡ss✐♦♥ ✐s ❣✐✈❡♥ ❜②

∑j( βxi,t,j + αi,t) = ∑j βxi,t,j +∑j αi,t =

• β ·J ·xi,t +J ·

αi,t = J ·[ βxi,t + αi,t] ✭✻✮

✇❤❡r❡ t❤❡ ✉♣♣❡r✲❜❛r ❞❡♥♦t❡s ❛♥ ❛✈❡r❛❣❡ ♦✈❡r t❤❡ j✬s✳ ●✐✈❡♥ ✇❡ ❤❛✈❡ J ❛❧t❡r♥❛t✐✈❡ r❡❣✐♦♥s ❛♥❞✱ ❢♦r ❛ ❣✐✈❡♥ ♠♦✈❡✱ ♦♥❧② ♦♥❡ r❡❣✐♦♥ ❝❛♥ ❜❡ ❝❤♦s❡♥✿ di,t = ✶ J . ✭✼✮ ❆s s❤♦✇♥ ✐♥ ●r❡❡♥❡ ✭✷✵✵✸✮✱ t❤❡ ❧✐♥❡❛r ♠♦❞❡❧ ✐♠♣❧✐❡s t❤❛t t❤❡ ❡st✐♠❛t❡❞ ✜①❡❞ ❡✛❡❝ts✱ αi,t✱ ❛r❡ ❣✐✈❡♥ ❜②

• αi,t = di,t −

βxi,t ⇒ di,t = βxi,t + αi,t. ✭✽✮ ❆❧❣❡❜r❛ ♣r♦✈❡s t❤❛t ∑j( βxi,t,j + αi) = J ·di,t = J · ✶

J = ✶✳ ❚❤✐s✱ t❤❡♥✱

♥❡❝❡ss❛r✐❧② ✐♠♣❧✐❡s t❤❛t ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ s❡❧❡❝t✐♥❣ ♦♥❡ r❡❣✐♦♥ ♠✉st ❧♦✇❡r t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ t❤❡ ❛❧t❡r♥❛t✐✈❡ r❡❣✐♦♥s✳