This paper constructs a multi-sector dynamic general equilibrium model for a trading economy. We incorporate three major factors of production: capital, skilled labor & unskilled labor. We solve and calibrate the model using data from Japan. We then consider changes to immigration policy. We are able to examine the effects on output, consumption, wages, and utility. We do this for both the new steady state and for the time-path leading to that steady state. In addition, we are able, if we so wish, to impose a series of unrelated macroeconomic shock to the model. This has the advantage of allowing us to calculate confidence bands around our policy impulse response functions. We find that allowing skilled labor to immigrate leads to greater welfare gains in the steady state. However, even with exclusively unskilled immigration, existing workers are made slightly better off on average when immigration restrictions are relaxed. We also show that there is a great deal of uncertainty surrounding the exact time path to a new steady state in the presence of the typical fluctuations associated with business cycles. We find a great deal of inertia in the transition to a new steady state.