In this dissertation, I develop a novel two-country general equilibrium model of immigration with heterogeneous skilled and unskilled labor. I use the model to study the short-run and long-run impacts of permanently doubling the US H-1B visa quota on the skill distribution, wages, output, and welfare in the United States and the source countries. I find that once the policy change takes place, less talented skilled foreigners who would not have applied for the visa at the old steady state now apply en masse such that the probability of obtaining the H-1B visa increases by only 11 percentage points. In the long-run, the United States experiences a 0.79% gain in output per capita once the economy completes transitioning to its new steady state. However, this aggregate gain hides wide heterogeneity in the effects on wages and welfare both across and within skill groups and age cohorts. In addition, I show that models that ignore return migration underestimate the average skill of an immigrant skilled worker, but overestimate the long-run increase in immigrant stock in response to reducing barriers to labor mobility. Because the latter effect dominates the former, I find that models with no return migration overestimate the changes in welfare by more than sixfold for certain cohorts compared to the benchmark model.