Caribbean Small Island Developing States (SIDS) face specific social, economic and environmental vulnerabilities. This paper provides a simple overlapping generations model with migration and intergenerational transfers in an economy where production generates pollution. This pollution hampers the cognitive skills of the children and thus the efficiency of human capital accumulation in the economy. Therefore, kea features of Caribbean SIDS are introduced in the model in order to exacerbate the potential link between the demographic dynamics -- migration and human capital accumulation -- and pollution. Results reveal that the usual gain from migration in terms of human capital was no longer possible because of the environmental externality. Indeed, in most of the cases, in presence of the environmental externality, per capita variables (utility, production and capital) are decreased by migration, while the aggregated production can be enhanced thanks to the demographic growth that occurs with migration. Moreover, it has been shown that the conditions to have a profitable environmental tax depend on the environmental features of the economy. Finally, the interactions between the emigration rate and the form of intergenerational transfers -- solidarity from the domestic area and/or from the diaspora -- have an impact on the scale of the reduction of human capital due to migration. Thus, in this model a gain from an increase in the rate of emigration is still possible but only if migration is already very high.