The impact of international students in the United States on innovative activity is estimated using a model of idea generation. Results indicate that the presence of foreign graduate students has a significant and positive impact on both future patent applications and future patents awarded to university and non-university institutions. Our central estimates suggest that a 10% increase in the number of foreign graduate students would raise patent applications by 4.5%, university patent grants by 6.8% and non-university patent grants by 5.0%. Thus, reductions in foreign graduate students from visa restrictions could significantly reduce US innovative activity. Increases in skilled immigration also have a positive, but smaller, impact on patenting.