We show empirically that aid given to poor developing countries enhances growth and reduces emigration once several dynamically interacting effects of aid are taken into account in a system of equations. We estimate equations for net immigration flows as a share of the labour force and GDP per capita growth and also for all their regressors including remittances and official development aid. We use dynamic panel data methods for a sample of poor countries with GDP per capita below $1200 (2000) for which aid is about 9.5% of GDP. The partial effects in these regressions are as follows. Remittances enhance net immigration, savings, public expenditure on education and growth, but reduce tax revenues, all as a share of GDP. Net immigration enhances labour force growth and the savings ratio. Official development aid decreases the savings ratio and the per capita GDP growth rate, but it increases investment, public expenditure on education and literacy and also labour force growth. Then we integrate all equations to a dynamic system and run a simulation. The result is an endogenous migration hump with several peaks. In a counterfactual simulation we double aid with the result that for more than a hundred years migration is reduced and the GDP per capita is enhanced, because the positive effects of aid on investment and education dominate the negative direct effects of aid on growth and the unfavourable effects on savings, tax revenues, and labour force growth.