Migrants are typically self-selected from the population of their home country. While a large literature has identified the causes of self-selection, we turn in this paper to the consequences. Using a combination of non-parametric econometrics and calibrated simulation, we quantify the impact of migrant self-selection on per-capita GDP in both sending and receiving countries. Two episodes of mass migration serve as examples: the migration from Norway to the US in the 1880s and the migration from Mexico to the US in the 2000s. We first estimate the degree of selection, and show that Norwegians were positively and Mexicans negatively selected. In a simulation exercise, we compare the economy under selective migration with a counterfactual in which the same number of migrants are neutrally selected. In both periods, we find virtually no aggregate effect in the US. Findings are different for the sending countries; migrant selection decreases Norwegian GDP by 0.3%, and increases Mexican GDP by almost 1%. While these effects may appear small, we demonstrate that the effect in Mexico is as large as the difference between no migration and the current level of migration.