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For context on the size of the potential benefit, an additional 1% migration rate would increase world GDP by about 1% (i.e. about one trillion dollars). The main question is the rate of migration if barriers are partially lowered, with estimates varying between 1% and 30%. Completely open migration could double world output. Based on Table 2 of Clemens (2011)
Do you happen to know of a scatter graph for immigration rate vs GDP? It might shed a little light on the matter, though fertility would be a cofounder.