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Mass migrations can impact the amount of labor misallocation in the host country if immigrants, relative to natives, face more frictions that prevent them from working in their preferred occupations. The resulting misallocation would imply an aggregate productivity loss in the short run while migration occurs, but an subsequent lapse of productivity growth when the immigrants start to be assimilated by the labor market. We study the case of Colombia during 2015-2019, a period when the country received a massive inflow of migrants from Venezuela. Through the lens of a Roy model of occupational choice with two types of frictions - discrimination and barriers preventing workers from choosing their preferred occupations - we quantify the extent of occupational misallocation for immigrants, and its implications for Colombian aggregate labor productivity. Our estimates indicate that both type of frictions significatively misallocate Venezuelan immigrants. Removing those frictions would lead at least one third of immigrants to reallocate, permanently increasing Colombian aggregate productivity by 0.9%.