The Roy Model Notes

Petra Todd

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

Distribution of skills

• Talent matters more in occupation with higher variance in skills

lnH

lnF

What is the average amount of fish for those who chose the fishing occupation?

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

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

Σ H

Σ F

PPF

What are the implications of self-selection for the distribution of earnings?

Are earnings for hunters or fisherman higher or lower than they would be if assignment to occupations were random?

How does change in price affect average ability levels?

Absolute Advantage Case (best hunters are best fisherman)

H

F

F=(PH/PF)H

Skills (F,H) on this line

Here, decrease in PF or increase in PH induces higher ability fisherman to enter thehunting occupation, which raises skill level in both occupations.

Absolute Advantage Case (best hunters are best fisherman)

H

F

F=(PH/PF)H

Skills (F,H) on this line

Here, decrease in PF or increase in PH induces higher ability fisherman to enter thehunting occupation, which raises skill level in both occupations.

Become hunters

Comparative Advantage Case (best hunters are worst fisherman)

H

F

F=(PH/PF)H

Skills (F,H) on this line

Here, decrease in PF or increase in PH induces lower ability fisherman to enter thehunting occupation, which raises avg skill level fishing, but lowers it in hunting.

Comparative Advantage Case (best hunters are worst fisherman)

H

F

F=(PH/PF)H

Skills (F,H) on this line

Here, decrease in PF or increase in PH induces lower ability fisherman to enter thehunting occupation, which raises avg skill level fishing, but lowers it in hunting.