In this paper we develop and estimate a model to explain variations in immigration to the United States by source country since the early 1970s. The explanatory variables include ratios to the United States of source country income and education as well as relative inequality. In addition, we incorporate the stock of previous immigrants and a variety of variables representing different dimensions of the immigration quotas set by policy. We use the results to shed light on the impact of policy by simulating the effects of the key changes in immigration policy since the late 1970s. We also examine the factors that influenced the composition of U.S. immigration by source region over the entire period.