The purpose of this paper is to introduce a dynamic version of the global trade and migration model (GMig2), which has been modified to include undocumented, unskilled workers in the United States. The development of a dynamic model is important because migration policy interacts with changes in population (e.g., the decline in population caused by declining birth rates in many developed countries) and human capital affecting the supply of skilled and unskilled workers, which, when combined with capital accumulation, are essential for ensuring continued high economic growth. We chose to examine US immigration policy because the US is a significant importer of migrant labor and in particular of undocumented workers. We show how this model can be used to examine the following policy scenarios: increased border control, one-time legalization (amnesty), and increased quota of foreign unskilled workers.