Immigrants in Rome or Paris are more visible to the public eye than the Italian or French engineers in Silicon Valley, especially when it comes to the debate on the effects of immigration on the employment and wages of natives in high-income countries. This paper argues that such public fears, especially in European countries are misplaced; instead, more concern should be directed towards emigration. Using a new dataset on migration flows by education levels for the period 1990-2000, the results show the following: First, immigration had zero to small positive long-run effect on the average wages of natives, ranging from zero in Italy to +1.7 percent in Australia. Second, emigration had a mild to significant negative long-run effect ranging from zero for the US to -0.8 percent in the UK. Third, over the period 1990-2000, immigration generally improved the income distribution of European countries while emigration worsened it by increasing the wage gap between the high and low skilled natives. These patterns hold true using a range of parameters for the simulations, accounting for the estimates of undocumented immigrants, and correcting for the quality of schooling and/or labor-market downgrading of skills. All results go counter to the popular beliefs about migration, but they are due to the higher skill intensity of both emigration and immigration relative to non-migrants.