126:. Borjas then uses the implications of the Roy model to infer something about what wages for immigrants in country 1 would have been had they stayed in country 0 and what wages for non-immigrants in country 0 would have been had they migrated. The third, and final, element needed for this is the correlation between the wages in the two countries,
40:
in the original paper is whether the best hunters will hunt, and the best fishermen will fish. While the discussion is non-mathematical, it is observed that choices will depend on the distribution of skills, the correlation between these skills in the population, and the technology available to use these skills.
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Roy's original paper deals with workers selecting into fishing and hunting professions, where there is no uncertainty about the amount of goods (fish or rabbits) that will be caught in a given period, but fishing is more costly as it requires more skill. The central question that Roy tries to answer
467:
613:
Heckman, J. J.; Vytlacil, E. (2007). "Econometric evaluation of social programs, part I: Causal models, structural models and econometric policy evaluation". In
Heckman, J. J.; Leamer, E. E. (eds.).
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is the standard normal cdf. This leads to the famous central result that the expected wage for immigrants depends on the selection mechanism, as shown in equation (1), where
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While Borjas was the first to mathematically formalize the Roy model, it has guided thinking in other fields of research as well. A famous example by
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procedure. More generally, Heckman and
Vytlacil propose the Roy model as an alternative to the LATE framework proposed by
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associated with migrating from country 0 to country 1 and workers know all parameters and their own realization of e
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was the first to formalize the model of Roy in a mathematical sense and apply it to self-selection in
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55:. Specifically, assume source country 0 and destination country 1, with log earnings in a country
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31:. The basic model considers two types of workers that choose occupation in one of two sectors.
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462:{\displaystyle E=a_{0}+\rho s_{0}\left({\frac {\phi ({v})}{1-\phi ({v})}}\right)}
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Heckman, J. J.; Honoré, B. E. (1990). "The
Empirical Content of the Roy Model".
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28:
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Borjas, G. J. (1987). "Self-Selection and the
Earnings of Immigrants".
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630:"Identification and Estimation of Local Average Treatment Effects"
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Roy, A. (1951). "Some
Thoughts on the Distribution of Earnings".
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using the Roy model, where the choice equation leads to the
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282:{\displaystyle {\frac {-(a_{1}-a_{0}-{C})}{s_{v}}}}
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201:{\displaystyle a_{1}-a_{0}-C+e_{1}-e_{0}>0}
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130:. A worker will choose to immigrate if
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628:Imbens, G. W.; Angrist, J. D. (1994).
16:Model for self-selection in economics
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208:which will happen with probability
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617:. Vol. 6. North Holland.
296:is the standard deviation of
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483:labor market participation
105:{\displaystyle s_{i}^{2}}
615:Handbook of Econometrics
553:American Economic Review
517:Oxford Economic Papers
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53:immigration
501:References
481:who study
665:153123153
479:Bo Honoré
439:ϕ
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417:ϕ
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346:∣
256:−
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59:given by
29:A. D. Roy
21:Roy model
679:Category
74:, where
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600:2938303
565:1814529
538:2662082
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27:due to
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212:where
210:1-Φ(v)
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