providing that the derivative of Pp with respect to p is positive at p = 0. We obtain: Note that this derivative corresponds to the numerator in @P° h @° i°h(!¡1)=k!<sup>.</sup> As in previous cases, liquidity constraints are likely to lower the size of the incentive e¤ect. If cp > cL, the incentive e¤ect will be limited to agents with education costs comprised between cn and cL. A similar constraint applies if cp > cM .

What is the empirical evidence on this ”prospect” channel? To the best of our knowledge, the ...rst study to attempt at estimating the growth e¤ects of the brain drain using cross-country comparisons is that of Beine, Docquier and Rapoport (2001); in a cross-section of 37 developing countries, and after controlling for remittances, they found that migration prospects have a positive and signi...cant impact on human capital formation at origin, especially for countries with low initial GDP per capita levels. This was a ...rst but imperfect try since they used gross migration rates as a proxy measure for the brain drain due to the lack of comparative data on international migration by education levels.

In a subsequent study, Beine et al. (2003) then used the Carrington-Detragiache estimates of emigration rates for the highest (tertiary) education as their measure of brain drain; again, they found a positive and highly signi...cant e¤ect of migration prospects on human capital formation, this time in a cross-section of 50 developing countries. They also computed country speci...c e¤ects, with the following results. First, countries that experienced a positive growth e¤ect (the ’winners’) generally combined low levels of human capital and low migration rates, whereas the ’losers’ were typically characterized by high migration rates and/or high enrollment rates in higher education (this is quite intuitive, since in this case most migrants are picked up from a stock of people that would have engaged in education even without contemplating emigration). Second, they showed that except for extreme cases such as Guyana and Jamaica, the growth e¤ects of the brain drain were relatively limited: around plus or minus a maximum of 0.2% in terms of annual GDP per capita growth; this is not negligible, however, in a dynamic perspective. Finally, it was also striking that while there were more losers than winners, the latter included the largest countries in terms of demographic size (China, India, Indonesia, Brazil) and represented more than 80% of the total population of the sample. For the most part, these results are apparent on Figure 6; incidentaly, it may be seen from the ...gure that the within-country result predicted by the theory outlined above (i.e., that some migration should be good as long as it is not excessive) is what comes out at the cross-country level apparent on Figure 6. The X-axis gives the Carrington-Detragiache migration rates for the highly educated and the Y-axis gives the net growth e¤ect of the brain drain as computed by Beine et al. (2003). The variability across countries at given migration rates is due to the impact of other right hand side variables, and the curve itself is adjusted using a second-order polynomial.

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