The impact of international students and skilled immigration in the United States on innovative activity is estimated using a model of idea generation. In the main specification a system of three equations is estimated, where dependent variables are total patent applications, patents awarded to U.S. universities, and patents awarded to other U.S. entities, each scaled by the domestic labor force. Results indicate that both international graduate students and skilled immigrants have a significant and positive impact on future patent applications, as well as on future patents awarded to university and nonuniversity institutions. The central estimates suggest that a 10 percent increase in the number of foreign graduate students would raise patent applications by 4.7 percent, university patent grants by 5.3 percent, and nonuniversity patent grants by 6.7 percent. Thus, reductions in foreign graduate students from visa restrictions could significantly reduce U.S. innovative activity. Increases in skilled immigration also have a positive, but smaller, impact on patenting.