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"In this review, we examine theories, data, and research on the macroeconomic relationship between international migration and national development in all world regions. Earlier reviews have generally been pessimistic about the prospects for economic development as a result of international migration. Until recently, however, theories and data have not recognized the complex, multifaceted, and often indirect ways that international migration can influence the economic status of households, communities, and nations, and they have generally failed to appreciate how these relationships can change over time. When these complexities are incorporated into theoretical models, research designs, and data collection, a more nuanced and far more positive picture emerges. Given a supportive mix of macroeconomic policies and infrastructure, international migration may function as a dynamic force promoting economic growth and national development, so long as it does not bring about the selective emigration of scarce human capital needed for development at home."
Taylor et al. (Mon,) studied this question.