Following Grossman and Rossi-Hansberg (2008) we present a model in which tasks of varying complexity are matched to workers of varying skill in order to develop and test predictions regarding the effects of immigration and offshoring on US native-born workers. We find that immigrant and native-born workers do not compete much due to the fact that they tend to perform tasks at opposite ends of the task complexity spectrum, with offshore workers performing the tasks in the middle. An effect of offshoring and a positive effect of immigration on native-born employment suggest that immigration and offshoring improve industry efficiency. (JEL J24, J41, J61, L24)

We study a reform that granted European cross-border workers free access to the Swiss labor market and had a stronger effect on regions close to the border. The greater availability of cross-border workers increased foreign employment substantially. Although many cross-border workers were highly educated, wages of highly educated natives increased. The reason is a simultaneous increase in labor demand: the reform increased the size, productivity, and innovation performance of skill-intensive incumbent firms and attracted new firms, creating opportunities for natives to pursue managerial jobs. These effects are mainly driven by firms that reported skill shortages before the reform. (JEL J15, J23, J24, J31, J61, K37)

We evaluate a Danish reform focused on improving language training for those granted refugee status on or after January 1, 1999. Using a Regression Discontinuity Design, we find a significant, permanent, positive effect on earnings. This effect emerged after completion of language classes and was accompanied by additional schooling and a higher probability of working in complex jobs, consistent with language training, rather than other minor aspects of the reform, producing the results.