VoxEU Column Education

International graduate students are critical to scientific discovery

The UK is under fire for pulling up the drawbridge for bright foreign students by limiting visas and complicating the application process. This column argues that welcoming large numbers of foreign PhD students bodes well for countries and universities interested in scientific and engineering innovation. Science and engineering are, after all, critical for the growth and competitiveness of industrial economies. Policies that serve to limit or discourage the enrolment of international graduate students lead to reductions in the rate of scientific discovery.

With their commitment to academic freedom and the maintenance of liberal, open economies, the US and UK have historically been leading countries in welcoming and educating foreign students. Among the benefits of hosting international students appears to be increased scientific discovery and innovation. The US experienced a boom in the enrolment of foreign PhD students starting in the early 1980s that continued into the early 1990s, with US universities granting close to three times as many doctorates to international students in 1993 as in 1980.1

Visa restrictions

Yet, at times, concern about security and immigration has led both countries to restrict their foreign study programs. As noted by Keith Maskus in a related 2007 Vox article (Maskus 2007), after the attacks of 11 September 2001 the US sharply increased the documentation requirements of foreign doctoral students under the Visa Mantis security program. Recently, officials in the UK have responded to calls to limit immigration by targeting students: adding requirements to the application process and making it more difficult to stay and work after graduation (The Economist 2012). These reforms intend to discourage foreign students from applying. An unintended consequence, however, is to diminish the quality of the pool of applicants of PhD students in science and engineering, who are particularly valuable in terms of their contribution to knowledge and innovation.

While the heightened restrictions in the US were later relaxed and the number of doctorates awarded to foreign students continued to grow after 2003, competition for talented doctoral students has been on the rise internationally. China awarded 26,200 science and engineering doctorates in 2008, up from only 7,300 in 2000 (National Science Foundation 2012) while doctorates earned in Canada and Australia in 2010 were up 83% and 50%, respectively, over their 1998 levels (OECD). In the face of this competition and the growing recognition that success in natural sciences and engineering is essential to maintain internationally competitive industries, policymakers in the US have very recently proposed increasing both the number of temporary (that is, ‘H1B’) visas for skilled workers and the availability of green cards for foreigners earning masters and doctorate degrees, which would make US study more attractive (The New York Times 2013).

Measuring the scientific benefits of enrolling international graduate students

Yet there have been few empirical studies done on the actual scientific benefits of enrolling international graduate students. The fact that rising enrolment of foreign students coincided with significant increases in numbers of scientific publications proves nothing about whether the students themselves were instrumental in scientific discovery. Students are attracted to academic laboratories because of the talent of faculty mentors and the access to state-of-the-art equipment; perhaps those were the factors primarily behind the scientific upsurge. And even if international students were instrumental, would it have been possible for domestic students to take their places and have the same impact?

Clearly it is difficult to sort out the actual causal impacts of foreign doctoral enrolments in the growth of publications. However, our recently published paper attempts to do so (see Stuen, Mobarak and Maskus 2012). Using data from the National Science Foundation, we tabulated US and foreign enrolments in 100 research-intensive US universities, broken down into 23 science and engineering fields, over the period 1973 to 1998. We also broke down the foreign students into region of origin, permitting calculation, for example, of the number of eastern European enrolments in chemical engineering at Stanford in 1995. Because such enrolment decisions may depend on other factors related to the progress of science, such as department quality, we estimated first-stage instrumental variables equations to isolate exogenous variation in student supply. The instruments we used for the enrolment of international students were based on shocks in home countries, aggregated to five regions, to real per-capita income (GDP), policies restricting emigration to the US for study, and the number of tertiary (higher education) students studying in non-US destinations. For enrolment of domestic students, we used the US national unemployment rate, as well the regional unemployment rate for areas within the US. These shocks to source-region conditions were interacted with the enrolment histories of each region for each field-university ‘department’, creating instrumental variables at the department level. The following chart demonstrates the potential power of instruments based on emigration restrictions and per-capita income. The vertical bars in the figure mark the years in which China-US relations were normalised (1979), all restrictions on US study by Chinese Students were lifted (1984) and when study restrictions were partially re-implemented (1989).

Figure 1. Emigration restrictions in China and doctoral student enrolment

We then used these student-supply shocks to estimate the independent contribution of domestic and international students to science and engineering journal publications. For this purpose, we developed a database from the ‘ISI Web of Science’ that counts every publication in indexed science and engineering journals associated with at least one author at each department, amounting to over three million articles. These were aggregated to the university-department-year level, generating over 57,000 observations. The empirical method involved estimation of a ‘knowledge production function’, with the counts of publications (and alternatively the number of citations to those publications) as dependent variables, and instrumented international and domestic students, department-level research expenditures, and an extensive set of fixed effects for field-university pairs, field trends and university trends as independent variables.


The results made clear that international and American graduate students were essential to scientific discovery, and, barring any major changes in the conduct of research, will probably continue to be. Both types of student contributed strongly to scientific discovery. Each additional international PhD student was estimated to contribute 0.97 publications per year while a student, with these publications leading to 33.4 citations per year. Given sample averages of 46.8 students, 44.1 publications and 1400.2 citations per field-university-year observation, these marginal effects account for 2.2-2.4% of the research output of the average university-field pair (department), coming from a single enrolled student. Each additional domestic PhD student contributed 0.84 publications and 45.3 citations, or 1.9 and 3.2% of their department’s research output, respectively. The contributions of international and domestic PhD students were indistinguishable from each other statistically, suggesting that on the margin, departments’ enrolment decisions are optimal.

A second line of analysis we pursued was a comparison of the productivities of two types of international students. Here we separated the set of instrumental variables into those correlated with students’ ability to pay for foreign study and other variables that were ‘pay-neutral’. The idea was that two types of shocks should have different effects on the quality distribution of foreign applicants. We develop a model of PhD enrolments with high- and low-income classes of students, which predicts that ‘ability to pay’ shocks should lower the average quality of enrolled students by expanding enrollments to include less qualified students. We find that the publication productivity of international students estimated in regressions using the pay-neutral instruments was about twice as high as when estimated with pay-affecting instruments, a statistically significant difference. Similarly, the marginal effect in terms of citations was 57% higher with the pay-neutral shocks.

A final hypothesis was whether diversity in students’ regions of origins has a beneficial effect on research outcomes. Other studies have shown that team research is becoming more important, and that team members bringing complementary skills and training may have multiplicative effects on research. However, diversity also brings with it coordination difficulties due to communication problems. Adding an index of international diversity to our models, we find positive effects of diversity in ordinary least squares regressions. Our instruments from the main analysis were insufficient to identify variation in diversity among international regions separately from the overall number of international students, so we cannot claim that diversity has a causal effect on scientific discovery.


Discoveries of scientific and engineering principles, which may later lead to an array of innovations, are critical for the growth and competitiveness of industrial economies. While we find international and domestic PhD students to be substitutable at the margin, large reductions in enrolments of either group would likely lead to substantial drops in productivity in academic research, if the more talented members of one group were to be replaced by the less talented members of the other. Policies that serve to limit or discourage the enrolment of international graduate students, such as complicating the application process, limiting the eligibility to work after graduation or the denial of student visas to applicants with insufficient financial means, lead to reductions in the rate of scientific discovery. On the other hand, maintaining and growing scholarship support for all graduate students, international and domestic, will encourage and enable talented individuals to pursue careers in science and engineering, while contributing to the strength of university research.


National Science Foundation (2012), Science and Engineering Indicators.

New York Times (2013), “Skilled Science Workers at Focus of Second Senate Proposal on Immigration”, 28 January.

Maskus, Keith E (2007), “International graduate students: are they critical for scientific discovery?”, VoxEU.org, 15 August.

Organization for Economic Cooperation and Development (OECD), Online Education Database.

Stuen, Eric T, Ahmed Mushfiq Mobarak and Keith E Maskus (2012), “Skilled Immigration and Innovation: Evidence from Enrolment Fluctuations in US Doctoral Programmes”, The Economic Journal 122, 1143–1176.

The Economist (2012), “Foreign Students Not Welcome Here”, 9 October.

1 Authors' own calculation from data from the National Science Foundation’s Survey of Earned Doctorates.

1,680 Reads