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International graduate students: are they critical for scientific discovery?

New research shows that visa policies that restrict foreign grad students in general, and favour those with greater financial resources, harm the research output of US science and engineering departments. American policy currently makes both of these mistakes, and needs fundamental reform.

In the aftermath of the attacks of September 11, 2001, the US government significantly tightened the restrictions that foreign doctoral students needed to meet to qualify for student visas. Partly for this reason, the number of foreign graduate students in the United States fell by 18% from 2001-2003. In the face of strong opposition from universities and businesses needing technically skilled workers, procedures since then have been streamlined and enrolments are slowly rebuilding. However, in some scientific and engineering fields, especially computer science, the Visa Mantis security clearance continues to raise lengthy delays and increase costs for international students wishing to study in the United States.

In truth, this shock simply exacerbated what appears to be a sustained decline in US graduate enrolments of international students in science and engineering, relative to universities in other countries, which began in the late 1990s. There are several factors behind this change, including the high cost of American study, the increasing quality of technical training at universities in numerous countries, and more relaxed immigration policies in Europe, Canada and Australia that make it easier for international students to remain post-graduation on an accelerated track to citizenship. Further, the extraordinary investments currently being made to enhance university science in China, Singapore, the United Kingdom, and elsewhere are making their institutions attractive locations for graduate students and faculty.

In short, there is rapidly growing competition for an input that had been almost the exclusive province of American universities: highly proficient international doctoral students in science and engineering. Educational officials have widely decried the evident reduction in the “competitiveness” of American universities in this regard, claiming that this trend risks an eventual slowdown of US technological leadership. It has also attracted considerable attention from the National Academies (2005) and is a common subject for the public media. Indeed, in their intermittent battles over the future of immigration policy, one central question for the US Congress and the Bush Administration is how to treat foreign-born scientists and engineers.

All of this raises an obvious question: how true is it that foreign doctoral students actually are causal contributors to knowledge development in the United States? Casual inspection of the data would support this idea. For example, the first chart below demonstrates that the number of international students receiving science and engineering doctorates (given by the line labelled “temporary visa holders”) rose from around 3,000 in 1980 to 8,000 in 2001, while the share of foreigners in graduate enrolments increased markedly. Many of these students became faculty members at US universities and established research programs of their own. At the same time, the number of scientific publications mushroomed over this period. It is possible that this increase in international students actually contributed to the expansion of knowledge, which is the question at hand. But it is also possible that both trends were driven by other factors, such as improvements in research capacities at universities arising from the growth in grant funding. As always, correlation is not causation.

For this reason, it is difficult to sort out the actual causal impacts of foreign doctoral enrolments in the growth of publications. However, a current working paper, which I have co-authored, makes considerable progress (Stuen, Mobarak and Maskus 2007; hereafter SMM). Using data from the National Science Foundation, SMM calculate US and foreign enrolments in 100 research-intensive American universities, broken down into 23 science and engineering fields, over the period 1973 to 1998. SMM also break down the foreign students into country of origin, permitting calculation, for example, of the number of Russian enrolments in chemical engineering at Stanford in 1995. Because such enrolment decisions are endogenous to department quality, SMM estimate a first-stage instrumental variables (IV) equation to isolate the exogenous variations in student supply functions. The IV list they choose includes shocks in home countries, aggregated to eight regions, to GDP growth rates, real exchange rates, the oil share of GDP, policies restricting emigration to the US for study, and other variables. The potential power of these instruments may be seen in the second chart, which shows that Chinese enrolments in US programs expanded greatly after the restrictions on foreign study were relaxed in the early 1980s. It also demonstrates that Chinese doctoral students track increases in GDP per capita in that country.

Policy Changes on Foreign Study Abroad in China and Doctoral Student Enrolment

SMM use these student-supply shocks, which are specific to the 2300 individual department-university pairs, to estimate the independent contribution of domestic and international students to science and engineering journal publications. For this purpose, SMM 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 3 million articles. These were aggregated to the university-department-year level, generating over 57,000 observations. SMM then estimated a “knowledge production function”, with the counts of publications (and also the number of citations of department publications) as dependent variables, and instrumented total graduate students, the international student share, department-level research expenditures, and an extensive set of fixed effects for field-university pairs, field trends and university trends. Because the dependent variables are integer counts rather than continuous variables, SMM estimate negative binomial regressions in their second stage.

The results of the estimation are striking. To save space here, I summarise the results for the regressions explaining publication citations, which are probably the more relevant measure of scientific discovery. First, both US and international students are important contributors to publishing. Measured at the mean values of citation counts, an increase in enrolment of one American or one foreign student (holding total students constant) would raise the average number of department citations by 1.2% per year (about 15 citations).

However, these impacts varied in interesting ways as the samples were broken down. For example, while a domestic student would raise citations in “elite” universities (those with high undergraduate admission standards) by 20, another international student would do so by 32, suggesting the latter are more productive in high-quality institutions. However, American students were more productive at the margin in “non-elite” universities. Breaking down the students into whether their BA degree came from higher-quality or lower-quality undergraduate students, SMM find that both US and international students from higher-quality schools significantly raised citation counts at elite universities, while foreign candidates from lower-quality schools actually reduced publication productivities. Lower-ranked departments that admit more such students, which may be necessary simply to have enough graduate enrolments to meet needs for teaching assistants, may be diminishing their own research productivity.

Perhaps the most interesting result arises when SMM break down the instrumental variables into shocks that would be neutral across foreign students and those that would differentially affect students who could not afford to pay for schooling. The idea is that “neutral” shocks should not affect the quality distribution of foreign students, while negative “ability to pay” shocks should lower their average quality by cutting out productive students who cannot marshal the financial resources. Indeed, SMM find that neutral shocks generate a foreign-student productivity of about 19 publications, while non-neutral shocks generate a corresponding figure of 10 publications. The inference they draw is that shocks that restrict the supply of higher-quality students reduce the publishing productivity of American universities.

The SMM results are relevant for assessing the wisdom of restrictive visa policies imposed on international doctoral students. The fact that all graduate students, whether domestic or foreign, directly expand knowledge creation, implies that enrolment restrictions on the latter do, in fact, hamper the research efforts of US universities. At a deeper level, visa policies that favour foreign students with greater financial resources are likely to have a particularly pernicious impact on the ability of science and engineering departments to thrive. American policy currently makes both of these mistakes, and needs fundamental reform.


National Academies (2005). Policy Implications of International Graduate Students and Postdoctoral Scholars in the United States. Washington: The National Academies Press.
Stuen, Eric T., Ahmed Mushfiq Mobarak and Keith E. Maskus. 2007. Foreign PhD Students and Knowledge Creation at US Universities: Evidence from Enrollment Fluctuations. Working Paper, Department of Economics, University of Colorado at Boulder.


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