One idea I've read, although did not find corroborating evidence of, stated that the drive to emigrate drove up the capabilities of the people left behind. Yes, developed countries often take the best of the developing world, but the drive to emigrate focuses many on education, so the ones left behind, and the country they inhabit, are better off. As an example, if you have 100 people in a country, and you have a system that says 10 can leave that score highest on an exam. Sixty (60) try to raise themselves by studying. At the end, 10 leave, leaving 50 more educated than when they started. So yes, the 10 best were taken, but 50 raised themselves’ up, benefiting not only themselves but also their community.
A synopsis of a study by the Rand Corporation:
While the effects of immigration on the receiving country have received a great deal of attention, less has been paid to its effects on the sending country. The available data suggest that, on net, emigration has a positive effect on the sending country. For example, by decreasing the labor pool in the sending country, emigration helps to alleviate unemployment and increase the incomes of the remaining workers. Also, emigres often send money home, enhancing their families' standards of living and thereby contributing both to the home economy and the nation's trade balance. Most emigres are young, male, and married, however, so there can be a destabilizing effect on the family. Some countries have attempted to restrict immigration, in the belief that it does not enhance economic development. However, the evidence suggests that, because of the benefits noted above, this might result in an even greater economic decline than such countries fear.
Another positive study:
The two most salient ways migration influences development within Mexico is through remittances and labor markets, according to this report from MPI's Regional Migration Study Group.
When looking at Mexico, this analysis finds that when the labor market effects and household income benefits of remittances are compiled into a model of the Mexican economy, Mexico’s fiscal balance appears to benefit from emigration — its economic output rising by 8.8 percent and tax collection by 7.4 percent over the last decade.
And even more positive effects:
Research has shown that workers migrate, find employment, and then move on or return home which discredits the myth that immigrants are flooding into western nations to settle permanently. This temporary migration has a positive effect on the sending nations as the returning workers are more highly-skilled and experienced, able to boost their home economy due to the skills learned abroad.
Further evidence has proven that migrants rarely take native workers’ jobs, and they boost employment effects in the long term. In her paper on the impact of immigrant labor on native workers, Amelie F. Constant says that migrants often “accept jobs that natives don’t want or can’t do [and] they create new jobs by increasing production, engaging in self-employment, and easing upward job mobility for native workers.