In an attempt to control the flow of undocumented immigrants, successive US governments have considered everything from large scale deportation, amnesties, expanding visa programs, to fining firms who hire illegal workers. Using a comparative static model, Aguiar and Walmsley (2013), find that amnesties have a positive impact on the US economy. However such policies are one-time changes in the labor force, whose benefits diminish over time, and which are unlikely to stem the flow of undocumented workers or fulfill the demands of U.S. firms for cheap foreign labor. In this paper we use a global dynamic model to investigate the long run implications of three alternative policy scenarios: 1) a one-time amnesty for undocumented workers living in the US; 2) a permanent increase in the number of foreign worker visas; and 3) enhanced border security. We find that an amnesty is much less effective than a permanent increase in visas at promoting growth in the U.S., while enhanced border control by the U.S. is beneficial for Mexico in terms real GDP.