The Roy Model Notes

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The Roy Model Notes

• Petra Todd

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Two-sector model of self-selection

• References
• A.D. Roy (1951), Heckman and Honore (1990, EMA)
• Relevant for
• theory of occupational choice (blue collar, white
  collar),
• union choice
• educational self-selection (high school, college)
• Two occupational choices
• fisherman
• Hunter
• Skill endowments (F, H) known to individuals

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Distribution of skills

• Talent matters more in occupation with higher
  variance in skills

lnF
lnH
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What is the average amount of fish for those who
chose the fishing occupation?
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What is the total supply of fish in the
population?

• As the price of fish increases, more people
  become fisherman and the supply of fish increases

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Think of a Production Possibility Frontier that
Determines the Aggregate Supply of fish and
hunting output

S F
PPF
S H
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What are the implications of self-selection for
the distribution of earnings?
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Are earnings for hunters or fisherman higher or
lower than they would be if assignment to
occupations were random?
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How does change in price affect average ability
levels?
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Absolute Advantage Case (best hunters are best
fisherman)
F(PH/PF)H
F
Skills (F,H) on this line
H
Here, decrease in PF or increase in PH induces
higher ability fisherman to enter the hunting
occupation, which raises skill level in both
occupations.
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Absolute Advantage Case (best hunters are best
fisherman)
F(PH/PF)H
F
Become hunters
Skills (F,H) on this line
H
Here, decrease in PF or increase in PH induces
higher ability fisherman to enter the hunting
occupation, which raises skill level in both
occupations.
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Comparative Advantage Case (best hunters are
worst fisherman)
F(PH/PF)H
F
Skills (F,H) on this line
H
Here, decrease in PF or increase in PH induces
lower ability fisherman to enter the hunting
occupation, which raises avg skill level fishing,
but lowers it in hunting.
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Comparative Advantage Case (best hunters are
worst fisherman)
F(PH/PF)H
F
Skills (F,H) on this line
H
Here, decrease in PF or increase in PH induces
lower ability fisherman to enter the hunting
occupation, which raises avg skill level fishing,
but lowers it in hunting.