International students are a key component of highly skilled migration, with a direct impact on innovation in host countries and possibly some diffusion effect in the home countries. According to UNESCO (2015) data, the number of students enrolled in a foreign higher education institution in 2005 was less than 3 million; in 2017, it was over 5 million. Most foreign students take a science or technology degree (29% in 2012), especially when it comes to doctoral studies (63%). Previous research (Hunt, 2013; Hunt and Gauthier-Loiselle, 2010) shows that foreign graduates in the US are more likely than native ones to become scientists or inventors, and to appear in the right tail of the productivity distribution. Yet, policy-makers in host countries hold at best ambivalent attitudes towards granting long-term or permanent visas to foreign graduates: Crown et al.’s (2020) study on Australian skilled visas shows that retaining talented foreign-born graduates can stimulate technological invention at the regional level, and that immigration policies that facilitate the stay of migrants play an important role in this. Khan and MacGarvie (2020) show that delays in obtaining permanent residency status can affect severely the stay rates of Chinese and Indian PhD graduates in the United States, with negative consequences for innovation. Besides, among the largest employers of migrant graduates, MNEs play a special role, especially in the high-tech sector. First, they make the universities from which they recruit the most especially attractive for STEM foreign students. Second, they lobby heavily in order to ease these students’ stay after graduation, at least in the United States. Last, they also recruit abroad and often move new hires around the globe, thus further feeding the overall migration flows. Labour economists have mostly focussed on evaluating the effectiveness of various company-sponsored visa systems in selecting the “best and brightest” scientists and engineers, as opposed to exploiting cheap and young graduates (Doran et al., 2014; Kerr et al., 2015). 

Yet, numerous issues regarding students’ migration, particularly that of graduates, are still poorly understood. Much can be investigated on the real role of students in driving innovation and knowledge production in host and home countries. Moreover, it is not clear whether some regions and cities benefit more than others, even within the same national borders. Among other things, the lack of micro data linking students to their technological and scientific outcomes does not facilitate answering some of the questions mentioned above.