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The Roy Model Notes

This document explores the A.D. Roy model of self-selection within two occupational sectors: fishing and hunting. It examines how individuals with different skill endowments choose between these occupations and the resulting implications for earnings distribution. Key concepts include the impact of skill variance, price changes on occupational choices, and the Production Possibility Frontier representing aggregate supply. The analysis reveals the effects of absolute and comparative advantages on skill levels in both occupations and how self-selection influences market dynamics.

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The Roy Model Notes

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  1. The Roy Model Notes Petra Todd

  2. 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

  3. Distribution of skills • Talent matters more in occupation with higher variance in skills lnF lnH

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

  5. 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

  6. Think of a Production Possibility Frontier that Determines the Aggregate Supply of fish and hunting output Σ F PPF Σ H

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

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

  9. How does change in price affect average ability levels?

  10. 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.

  11. 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.

  12. 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.

  13. 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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