•Citation patterns are examined empirically in a reduced-form gravity-style framework.•Administrative barriers to mobility reduce opportunities for knowledge diffusion.•Immigration policy and travel visa requirements reduce the bilateral knowledge flows.•Knowledge-exporter's policy has a larger short-term effect (relative to importer).•The results pass a placebo test using leading values of the policy. Face-to-face contact, even temporary one, helps researchers form personal ties and transfer tacit knowledge. The ability of researchers to colocate, including attendance at international conferences, workshops and seminars, is affected by the administrative barriers to international mobility. This paper uses a gravity-style empirical framework to examine the link between international knowledge flows and immigration policies. The results suggest that the paper walls erected by such policies reduce not just the mobility of individuals, but also the diffusion of knowledge. A moderately restrictive mobility barrier reduces incoming and outgoing knowledge flows by about 0.8–1.3% per year. The effect of knowledge-exporting country's policy persists for nearly 10 years. There is also a short-term asymmetry: diffusion of recent knowledge is affected more by the immigration policy of a knowledge-exporter rather than a knowledge-importer.