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SKILLED IMMIGRATION AND INNOVATION: EVIDENCEFROM ENROLMENT FLUCTUATIONS IN US DOCTORAL

PROGRAMMES*

Eric T. Stuen, Ahmed Mushfiq Mobarak and Keith E. Maskus

We study the contribution of doctoral students to innovation at 2,300 American science and engin-eering departments from 1973 to 1998. Macroeconomic and policy shocks in source countries thatdifferentially affect enrolments across fields and universities isolate exogenous variation in the supplyof students. Both US and international students contribute significantly to the production ofknowledge at scientific laboratories, and their contributions are statistically comparable, consistentwith an optimising department. A theoretical model of scholarships helps us to infer the productivityeffects of student quality. Visa restrictions limiting entry of high-quality students are found to beparticularly costly for academic innovation.

This article explores whether and how domestic and foreign graduate studentscontribute to the development of knowledge in science and engineering (S&E) at USuniversities. We exploit fluctuations in the supply of foreign students stemming frommacroeconomic and policy shocks in source countries to examine the effects ofdoctoral students in specific disciplines and universities on scientific publications andcitations produced in those laboratories. We have three basic motivations for under-taking this analysis. The first is to shed light on the impact of US policy regardinginternational graduate students. Since the advent of tighter restrictions on US educa-tion visa issuance after 11 September 2001, it has been argued in the media1 and inprominent science journals2 that the ability of American universities to undertakescientific research is dependent on technically trained international graduate students.In turn, restrictive visa policies could cause �. . .a crisis in research and scholarship� andharm the nation�s innovative capacity.3 The mainstream media remains filled with

* Corresponding author: Ahmed Mushfiq Mobarak, Yale School of Management, 135 Prospect Street, NewHaven, CT 06520, USA. Email: [email protected].

We thank the National Bureau of Economic Research (NBER) Innovation Policy and the Economy programmeand the National Science Foundation SciSIP programme for financial support, the National Science Foun-dation Division of Science Resources and Statistics for providing data on Ph.D. recipients under a licensingagreement and Rich Beaudoin, James Choy and Christine Rohde for excellent research assistance. We aregrateful to Martin Boileau, Lee Branstetter, Benjamin Jones, Fiona Scott-Morton, Stephen Redding, MarkRosenzweig, Chris Udry, the editor Rachel Griffith, anonymous referees and seminar attendees at the NBERInnovation Policy and the Economy meetings, the NBER International Trade and Investment meetings,NBER Economics of Education Meetings, NSF SciSIP Conference, American Economic Association 2011Annual Meetings, Duke University, Yale University and London School of Economics for helpful comments.

1 �Academics Warn of Crisis over Visa Curbs,� Financial Times 16 May 2004 and �Visas and Science: Short-Sighted�, The Economist, 8 May 2004.

2 �Security Restrictions Lead Foreign Students to Snub US Universities�, Nature, 15 September 2004. Seealso �The Knowledge Economy: Is the United States Losing Its Competitive Edge?� The Report of the TaskForce on the Future of American Innovation, 16 February 2005.

3 Partly because of tighter limits on student visas since 2001, the number of foreign graduate students inthe US fell by 8% in 2002 and by a further 10% in 2003, reversing a 15-year trend of rapid growth. Computerscience and other S&E disciplines experienced the largest relative declines, as the US Department ofHomeland Security instituted the lengthy Visa Mantis security clearance programme. A key concern iswhether these trends presage a diminution in US leadership in science and innovation.

TheEconomic Journal,122(December),1143–1176.Doi:10.1111/j.1468-0297.2012.02543.x. �2012TheAuthor(s).TheEconomicJournal�2012Royal

Economic Society. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

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quotes from universities and employers on the economic dangers of visa restrictions.4

American politicians are now advocating easing immigration restrictions on scienceand maths Ph.D. students (New York Times, 28 October 2011). This debate has spread toGreat Britain where scientists, business leaders and universities have expressed graveconcern over the effects of newly proposed immigration caps and increases in foreign-student fees on UK science and innovation.5 We conduct careful analysis with microdata to shed light on these claims.

A second objective is to contribute to the literature on the effects of skilled immig-ration. Economists have primarily focused on the effects of immigration on natives�wages (Card, 1990; Altonji and Card, 1991; Borjas, 1994, 2003; Borjas et al., 1997;Ottaviano and Peri, 2005). Wage effects estimated in this literature are mixed anddepend on whether immigrants and native workers are substitutes or complements.Cortes (2008) finds that low-skilled immigration into US cities reduces the real wages ofpoorly educated natives but raises the purchasing power of high-skilled workers bylowering the prices of non-tradables, such as housekeeping services. Hunt (2011) showsthat immigrants entering on student visas outperform natives in wages, patenting andpublishing. In the skilled-labour category, Borjas (2005) points out that doctoral stu-dent immigration has a significant adverse effect on wages of competing high-skilledUS workers.

We extend this literature by adding innovation to the list of outcomes. The USretains a global comparative advantage in science and innovation and in creatingtechnology-driven new products and markets (Freeman, 2005). The US has the smallesttrade deficit in high-technology products and exports in this sector remained mostresilient during the 2009 financial crisis (NSF, 2011). Large imports of foreign doctoralstudents in S&E may be an important reason the US has sustained its primary positionas developer of new knowledge, even with deficiencies in mathematics and sciencetraining among American secondary school students.6

Third, our study contributes to an understanding of university admissions and theproduction of knowledge at US universities ( Jaffe and Trajtenberg, 2002; Thursby andKemp, 2002; Thursby and Thursby, 2002; Mowery et al., 2004; Azoulay et al., 2005).Borjas (2002, 2007) notes that training foreign students involves significant costs,including tuition subsidies and enrolment congestion. One open question is whetherdomestic and international students are substitutes at the margin, as departmentsoptimise over multiple substitutable inputs. Our results are largely consistent withthis idea.

There are clear descriptive indications that foreign students contribute to knowledgecreation and innovation. Foreign enrolments have increased in absolute and relative(to American enrolments) terms since the 1970s, and publishing and patenting have

4 See New York Times 3 March 2009 on researchers and academic conferences moving abroad, Wall StreetJournal 11 March 2009 arguing that productive foreign-born workers create more jobs and New York Times 12April 2009 on immigration laws making it more difficult for Google to recruit workers.

5 The Times, �8 Nobel laureates, including immigrants Geim & Novoselov, write to Times to condemnimmigration cap�, accessed 12 November 2010. Prominent newspaper editorials have also warned of a braindrain to other countries: �Government Cuts Will Trigger Brain Drain�, The Telegraph, 1 October 2010.

6 OECD (2006) reports that students aged 15 in the US ranked 24th in mathematics and 19th in scienceamong 29 countries. Freeman (2009) notes that �the US has come to rely extensively on the immigration ofhighly educated persons to maintain a lead position in science and technology�.

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grown in lockstep. Foreign students are disproportionately more likely to earn graduatedegrees in S&E and now outnumber Americans in US engineering departments (Bell,2011). Immigrants constitute 15.6% of the American workforce but 47% of engineer-ing doctorate holders and 24.5% of patent-application authors (US Census Bureau,2009). Black and Stephan�s (2008) survey of articles published in Science finds that86.5% of papers have a student or post-doc author and 60% of those authors areforeign-born. The authors conclude that foreign graduate students and post-docs stafflaboratories and play lead roles in university research. Kerr and Lincoln (2008) tieincreases in employment visas to increased patenting by inventors with Indian andChinese last names. Other recent studies document that patent applications in the USare correlated with foreign-student enrolments at the aggregate national level (Chel-laraj et al., 2008) and with post-doctoral enrolments at the university level (Gurmuet al., 2010). Further, Hunt and Gauthier-Loiselle (2010) find that increases in theshare of college-educated immigrants significantly raise per capita patenting at the statelevel.

Although the links between immigrants and innovation outcomes established in thisliterature are important, they do not by themselves allow us to gauge definitively whetherrestrictions on foreign entry would be harmful to US productivity. To answer that policy-relevant question, we need to examine whether foreign students are substitutable at themargin. One contribution of this article is the joint estimation of the effects of bothdomestic and foreign Ph.D. students at specific academic departments. We not onlyestimate the marginal contribution of foreign students to academic publishing but alsotheir contribution relative to their American counterparts. We do so by analysing de-tailed information on individual doctoral students by nationality and devising a novelinstrumental variables (IV) strategy using macroeconomic and policy shocks in sourcecountries to isolate plausibly exogenous fluctuations in the supply of students.

Our IV strategy is based on the idea that macroeconomic crises in East Asia ordecisions by Chinese authorities to permit their students to enter graduateprogrammes abroad (or to reinstitute restrictions) tended to alter student supplies inthe US exogenously. Moreover, these shocks would have differentially larger impacts onresearch output in fields of study that are traditionally more popular among Asians andon universities that have traditionally recruited more students from that region. Oneadvantage of this last insight is that even if some relevant events in the US happen tocoincide with those shocks, the former are unlikely to affect publishing along the samepatterns of universities and disciplines as the foreign shocks.7

We assemble a database of student enrolment counts by nationality for 2300 US S&Edepartments for 1973–2004 by aggregating individual records on each doctoral studentmaintained by the National Science Foundation. We combine these records with publica-tions in scientific journals from each of those departments over the same period.These figures are compiled from publication and citation searches on the Institute for

7 Consider, for example, the implementation of the Bayh-Dole Act in 1980 in the US. This law encourageduniversities to patent and license their discoveries and simplified the procedures under which they could ownthe intellectual property arising from publicly funded research (Mowery et al., 2004), around the same timethat China lifted its restrictions on graduate study abroad. Publishing, patenting and Chinese enrolments allrose after these events but our estimates will only rely on the differential publication response at certainuniversities and fields more or less popular with the Chinese.

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Scientific Information�s Web of Science. Our empirical specifications add fixed effects forall 2,300 departments and university-specific and field-specific trends, so that empiricalinference is based only on changes in publishing in an academic department followingfluctuations in student enrolments in that department.

We find that both foreign and domestic doctoral students contribute significantlyand positively to the production of publications and citations at US academic depart-ments. Each additional student leads to 0.9 extra S&E journal articles per year.8 Ouranalysis thus documents a key benefit of high-skilled immigration in the US, whichrelies on innovation for growth and helps to explain the vociferous complaints by USacademic departments about visa restrictions on foreign graduate students. However,our estimates also indicate that the marginal effects of foreign and American studentsare statistically comparable, which is consistent with optimising departments equatingproductivity at the margin. Universities would have equally strong reasons to complainabout any policy distortion that might keep Americans away from graduate study inS&E fields.

We further show that the quality of entering foreign doctoral students matters greatlyfor research productivity. To overcome a lack of direct measures of student quality, wedevelop a theoretical model of admissions decisions in which universities trade-offstudent quality and tuition income. This model shows that by comparing acrossdifferent sets of source-country shocks that differentially affect application propensitiesof students who are able to pay versus students who rely on scholarships, we maydistinguish empirically the productivity effects of higher quality and lower qualitystudents. Shocks that differentially increase enrolment decisions of foreign studentsreliant on scholarships are much more productive for US academic departments thanshocks that send students who pay for their own graduate education. These resultssuggest that from the perspective of US science education and innovation policy, visarestrictions for foreign students should not be applied uniformly or on the basis offinancial means; they ought to account for student-quality differences.

While an increase in foreign-student share changes the mix of nationalities, it alsoincreases geographical diversity in the average US S&E department (where 69% ofdoctoral students are American during the sample period). We find limited evidencethat diversity matters, controlling for nationality effects. Only in an ordinary leastsquares (OLS) model do we find that departments that enrol students from a widervariety of global regions experience larger gains in research output, and the effect isnot robust. Diversity increases coordination costs, which may mitigate any productivitybenefits it carries.

To summarise, our estimates suggest that having access to high-quality, well-trainedstudents is beneficial for US academic departments and likely crucial for continuedAmerican leadership in innovation sectors. Restrictions on student entry into S&Efields would be harmful, regardless of student nationalities.

The article proceeds as follows. We outline modelling frameworks in Section 1,including a tuition income model to motivate our empirical analysis of hetero-

8 Accounting for publication-inflation in our data due to multiple-authored articles sometimes beingdouble-counted, this implies a contribution of about 5 extra articles in the department over the course of adoctoral student�s 6-year graduate career. The estimate size is quite reasonable given publication rates inscience and engineering.



geneous student quality. We present the IV-based empirical approach in Section 2,data sources in Section 3 and discuss results in Section 4. We make concludingremarks in Section 5.

1. Modelling Framework

1.1. Insights from Neoclassical Production Function Analysis

The simplest theory by which to interpret our statistical results is a neoclassicalproduction function for an academic laboratory with domestic and foreign graduatestudents as inputs.9 A rational resource allocator wishing to maximise a single outputwith a budget constraint would choose inputs such that the marginal product per dollarspent on each were the same (Pritchett and Filmer, 1999). In our setting, researchdepartments would admit domestic and international graduate students to equate thecontribution of each type, scaled by some measure of department-level cost of edu-cating them. Such costs could include stipends and the opportunity costs of facultytime. For example, domestic graduate students may be cheaper if language difficultiesimpose greater training costs for foreign students. Similarly, scholarship students aremore costly to educate and must provide greater marginal value in equilibrium.

University departments generate multiple outputs (research and undergraduateteaching), so they would admit graduate students until the difference in per-dollarmarginal products in producing publications equals the difference in per-dollarmarginal products in teaching. If, for example, domestic students offer greater pro-ductivity as teaching assistants than foreign students, we would observe a greatermarginal contribution to producing publications from international doctoral studentsin equilibrium. In this model, all marginal products should be positive. And enrolmentshocks should not have a substantial impact on the production of publications becausedepartments would be able to substitute across inputs.

1.2. Outline of a Model of Knowledge Creation with Heterogeneous Inputs

This approach misses some important details of the reality of what happens inacademic research, as it is inaccurate to think of universities as operating with a fixedbudget constraint and highly divisible homogeneous inputs. In this subsection, weoutline a more suitable modelling framework to motivate our identification strategybased on student-supply shocks in the basic publication and citation regressions. Wethen solve a simpler version of the model to motivate how different types of macro-economic shocks can help us to separately identify the effects of scholarship (i.e. higherquality) students versus paying students, even when we do not have direct measures ofstudent quality.

Suppose that a department d produces knowledge, using as inputs �professors� P (i.e.an index of faculty, grant funding and the like) and quality-weighted students from theUS and two foreign regions. International students are indexed by g and h, g = 1,. . .,G

9 Hanushek (1979) is the seminal reference. See also Johnson (1978) and De Groot et al. (1991) forexamples. These models assume either one output (e.g. test scores) or multiple outputs (e.g. graduatediplomas and research) produced using a variety of inputs, such as faculty size and research funding.



and h = 1,. . .,H, whereas US students are indexed by i, i = 1,. . ., I. The correspondingknowledge production function is:

Kdt ¼ Kd Pdt ;XG

g¼1

qgdt þ

XHh¼1

qhdt þ

XI

i¼1

qidt

!: ð1Þ

The creation of knowledge rises in both faculty quality and the quality-weightednumber of graduate students. Departments limit enrolments due to resource con-straints and for quality control. For simplicity, assume that a department�s capacity toenrol graduate students at any time is strictly constrained:

Idt þ Gdt þHdt ¼ Sdt : ð2Þ

Foreign students are costly to admit but this cost declines as departments gainexperience with students from different regions:

Cdt ¼ cgdtðGd;t�1ÞGt þ ch

dtðHd;t�1ÞHt ; where cg ; ch � 0 and cg ; ch0 � 0: ð3Þ

This diminishing cost generates an implicit network effect leading to positive immig-rant selection (like that studied by McKenzie and Rapoport, 2010), where networksmitigate information deficiencies for both universities and applicants. With betterinformation, the quality of admitted students can improve even when the quality of theapplicant pool suffers. We normalise the cost of training an American to zero.

Economic conditions can affect both the supply and quality of students available,because their incentives and ability to apply depend on labour market conditions (e.g.wage available in alternative employment), macroeconomic and political factors (e.g.income growth that affects the ability to incur cost of travel and emigration limits orvisa restrictions). Thus, a student from region G applies to department d at time t ifPdt þ eg

dt � wGt ; or if the benefits he or she gets from studying at department d

(determined by department quality P plus his or her idiosyncratic preference to studythere) exceed the �outside option� w (e.g. the wage a college graduate would get in hisor her region).

Departments admit students with the highest value added (K � C), taking intoaccount student quality and region-specific costs. Experience with regions will matter inthese admissions decisions over time, as the cost of admitting students from a regiondecreases as universities invest in learning about students from that region (or con-versely, the region�s students learn about the university). As students prefer to attendhigher quality universities and universities prefer better students, the matching processassigning applicants to departments will be assortative.10

This framework highlights the endogeneity problem in estimating the effects ofstudents: a positive shock to department quality P would increase knowledge produc-tion independently of any changes to student enrolment but it would also attract bothmore Americans and more foreigners to apply. Thus, for example, in a regression ofpublications on the foreign-student share, the direction of the resulting bias would

10 A matching literature on college admissions starting with Roth (1985) suggests that under more com-plicated sets of preferences (e.g. if colleges have preferences over groups of students), there may not be astraightforward, efficient matching mechanism.



depend on which type of students ultimately enrols more as a result of this shock. Ifdepartments show a preference for Americans over foreigners in the admissionsdecision (e.g. because cg, ch � 0), enrolments will shift in favour of the former and thecoefficient on foreign-student enrolment in the publications regression would bebiased in the negative direction. More generally, if enrolments surge during recessionyears (when other departmental resources are low), the OLS coefficients on studentcounts would be biased downward.

Shocks to the outside option (i.e. wG, wH) may be used as instruments to identifyexogenous fluctuations in the numbers of foreigners enrolling in graduateprogrammes in the US. Moreover, shocks in particular regions may have differentialeffects on enrolments across different departments by virtue of the fact that adepartment�s history with students from a region can matter in the admissions decision½cg 0 ðGd;t�1Þ � 0�. Interaction terms between region-specific shocks and department-region enrolment histories yield instruments that identify shock-induced, department-specific fluctuations. We will take advantage of these insights in developing anestimation strategy in Section 2.2.

1.3. A Simple Model with Student Quality, Tuition and Scholarships

A key visa policy question of interest is whether immigration restrictions should ac-count for the quality of incoming students. Given the costs associated with admittingforeign students (Borjas, 2002, 2005, 2007), the optimal policy may be to allow onlystudents who are likely to contribute more to innovation and US competitiveness. USvisa policy for foreign students has traditionally paid more attention to financialresources and assets held abroad to infer students� incentives to remain in the US pastgraduation, which is curiously viewed as a negative outcome.11

We would like to estimate the differential contributions to innovation from high-quality and low-quality foreign students to inform this debate. Unfortunately, there areno good direct empirical measures of a student�s �quality�. Further, even if suchmeasures existed, we would have to account for the endogenous placement of higherquality students. Given these constraints, we now solve a simplified version of aPh.D.-admissions model to highlight how student-quality effects can still be estimatedunder the reasonable premise that higher quality students are more likely to receivescholarships and certain source-country macroeconomic conditions cause differentiallylarger fluctuations in non-scholarship students.

Suppose universities care about student quality q and tuition income m (per-student).The population of potential students is divided into NR rich applicants who can affordto pay tuition and NP poor applicants who are credit-constrained and can only attendwith a scholarship. The university cannot observe whether students are rich or poor, soit gives scholarships to all students with quality exceeding qs, although some of thosestudents are rich. The distribution of student quality in both groups is f(q). With aconvex cost function cð�Þ that reflects the congestion costs of admitting more students

11 Applicants for F-1 student visas must demonstrate that they have enough readily available funds to meetall expenses during a course of study and agree to leave the US after completing their education (http://www.usastudyguide.com/American-immigration.htm).



and marginal benefits of quality and tuition to the university denoted as A and B,respectively, the university�s objective function becomes:

U ¼ N P A

Z 1qs

qf ðqÞdq þ N R A

Z 1qn

qf ðqÞdq þ Bm

Z qs

qn

f ðqÞdq

" #

� c N P

Z 1qs

f ðqÞdq þ N R

Z 1qn

f ðqÞdq

" #: ð4Þ

The university maximises the lower quality bounds for admitted scholarship and non-scholarship students over qs and qn, respectively. For algebraic tractability, we willassume that c(x) = (C ⁄ 2)x2 (with a constant C) and that f ðqÞ � U½0; q�12 The first-orderconditions simplify to the following:

�AN P qs þ BN R m þ N P C N P �q � qs

�qþ N R �q � qn

�q

� �¼ 0; ð5aÞ

�Aqn � Bm þ C N P �q � qs

�qþ N R �q � qn

�q

� �¼ 0: ð5bÞ

We can obtain closed-form solutions to qs and qn by solving (5a) and (5b). This showsthat qs > qn, as expected. Taking derivatives with respect to the numbers of rich andpoor students:

@qs

@N P¼ A2 �q2½CðN P Þ2 � BmN R � � 2ABCmN R �qðN P þ N RÞ � BC2mN RðN P þ N RÞ2

AðN P Þ2½A�q þ CðN P þ N RÞ�2

@qs

@N R¼ A2CN P �q2 þ Bm½A�q þ CðN P þ N RÞ�2

AN P ½A�q þ CðN P þ N RÞ�2

@qn

@N P¼ @qn

@N R¼ AC �q2

½A�q þ CðN P þ N R Þ�2: ð6Þ

Total graduate student quality is:

Q ¼ N P

Z 1qs

qf ðqÞdq þ N R

Z 1qn

qf ðqÞdq ¼ 1

2N P �q � q2

s

�q

� �þ 1

2N R �q � q2

n

�q

� �: ð7Þ

Therefore, the effects of a change in NR or NP on Q are:

@Q

@N P¼ 1

2�q � q2

s

2�q� N P

�qqs@qs

@N P� N R

�qqn

@qn

@N P

@Q

@N R¼ 1

2�q � q2

n

2�q� N P

�qqs@qs

@N R� N R

�qqn

@qn

@N R:

ð8Þ

12 A normal distribution for ability may be more realistic but the uniform distribution with a large upper-bound �q is a reasonable approximation to the far right tail of the normal distribution, where applicants toPh.D. programmes are likely to reside.



Substituting the expressions from (6) into (8), we get:

@Q

@N P� @Q

@N R¼ B2m2ðN P þ N RÞ2

2A2ðN P Þ2 �q: ð9Þ

This expression is always positive, so a positive shock to the number of poor applic-ants increases graduate student quality by more than a positive shock to the number ofrich applicants. This is the main insight we will take advantage of in our empiricalanalysis of the effects of student quality. Specifically, even in the absence of directmeasures of quality, we can infer quality effects through this scholarship mechanism ifwe can identify separate sets of foreign-country shocks that differentially affect theapplication propensities of rich versus poor students.

2. Empirical Methodology

2.1. Basic Specifications

We derive basic and straightforward implications from the two models outlined inSections 1.2 and 1.3 to conduct two related pieces of empirical analysis. First, the modelof a knowledge production function with heterogeneous inputs suggests that anacademic department�s output is a function of a number of different student andresource inputs. In the absence of accurate measures of other relevant inputs (such asfaculty resources and funding), the estimates of the contributions of students toknowledge creation can be biased. The model also suggests an IV strategy based onconditions students face in source countries. Our main empirical exercise estimatessuch a knowledge production function and adopts the strategy implied by the model.Second, the extended theoretical model included students of varying quality anddepartments that care about both tuition revenue and student quality. This approachoffers an indirect way to gauge the effects of student quality on knowledge productioneven when direct measures of quality are not available. We apply this insight to ouranalysis of student quality in Section 4.4.

We run the following basic specification to examine the effects of foreign anddomestic Ph.D. student enrolments on knowledge produced in specific fields of inquirywithin US universities over the period 1973–98:

Kf ;u;t ¼ af ;u þ dt þ cuðDuTrendÞ þ qf ðDf TrendÞ þ b1American Studentsf ;u;t�1

þ b2Foreign Studentsf ;u;t�1 þ ef ;u;t : ð10Þ

The variable K refers to either counts of publications or citations (by other, futurearticles) to those publications. The data set has four identifiers – the students� region oforigin (e.g. South Asia), the university u at which students are enrolled, the field ofinquiry f (e.g. industrial engineering) and year t. We will refer to the university-fieldpair as an academic �department�. Equation (10) explains variation in scientificpublications or citations in a given department and year as a function of American andforeign enrolments in the previous year, while controlling for fixed effects forevery department, linear trends specific to each university and each field, and yeardummies. The fixed-effects control for time-invariant differences in characteristics



across departments. The field-specific and university-specific trends capture any linearchanges in the norms regarding publishing at a particular university or within a field ofinquiry.13 We cannot construct a direct measure of faculty size for each department andeach year going back to 1973, but we control for departmental resources (equipment,physical plant and other research and development (R&D) expenditures, includingfaculty salary support) as an indirect measure of department size.

Our empirical specification is closely tied to the theory of a knowledge productionfunction with heterogeneous inputs that we outline in Section 1.2. That model suggeststhat the coefficients on American and foreign students will be biased if we do not havea good time-variant measure of P (departmental quality) and also informs our choiceof instruments for student counts. The empirical specification departs from the theoryin one place: if we take a literal interpretation of (2) (a fixed constraint on the totalnumber of graduate students), then the department fixed effects would not beseparately identified from the effects of foreign and domestic enrolment counts. Inreality, departments face �soft� enrolment constraints and total enrolments vary by year.We therefore include department fixed effects in our regressions to control fortime-invariant department characteristics.

After controlling for department and year fixed effects and field and university trends,the remaining objects of concern are unobservable characteristics of academic depart-ments that vary non-linearly over time and affect both the publications produced bythose departments and student enrolments. For example, if the quality of a departmentimproves, say through better faculty or funding in a way not fully captured by the R&Dexpenditure controls, it may attract greater numbers of foreign students and also havean independent effect on the department�s output. Conversely, if an improvement inthe quality of a department (and therefore a rise in students� earning potential) attractshigh-quality American students away from business, law and other professional degreesand into S&E fields, we may observe drops in foreign-student enrolments when adepartment�s quality improves.14 This is likely to bias the b2 coefficient downward.

2.2. Instrumental Variables Approach

Our solution to this problem is to use an IV estimator that takes advantage of plausiblyexogenous fluctuations in the supply of foreign students. We instrument for US andforeign enrolments using economic and policy shocks in the students� countries (orregions) of origin. We choose shocks that influence students� decisions about whether

13 The average number of publications per department rose from 25 in the 1970s to 54 in the 1980s, whilecitations rose from 832 to 1,654. Thus, it seems reasonable to think of the dependent variables as continuous,and we run linear regressions. We have also run negative binomial fixed-effects count-data models of thefollowing form Kf ;u;t ¼ eXf ;u;t �g � afu þ ef ;u;t (where Xf,u,t encompasses all variables in (10)), and verified that theresults are qualitatively similar. We show these results in Table A1 (in online Technical Appendix A). BothAmerican and foreign students display positive and statistically comparable effects on publications andcitations in these models.

14 Under a preference for Americans in admission due to language skills, wider ranges of financial-aidoptions available for natives, or greater productivity in teaching, foreign students may get crowded out in adepartment of limited size once more high-quality American students start applying. If the marketability orpopularity of a particular field of study among students at a given point in time varies non-linearly, that wouldbe another omitted variable that may bias the impact of foreign students in either direction, depending onhow Americans students respond to such changes.



to enter (or travel to the US for) graduate studies but that are plausibly uncorrelatedwith the publications produced at specific US academic departments. For example,eliminating or reinstituting study-abroad restrictions altered Chinese students� ability toenter graduate programmes in the US. These policy changes can cause fluctuations inChinese enrolment at US universities but may not affect publishing in specificacademic departments through other channels.

We use fluctuations in source-country policies (e.g. lifting of restrictions on Russianand Chinese students regarding study abroad) and in economic conditions (e.g. incomegrowth) to instrument foreign-student enrolments. These instruments vary by countryand year, while our endogenous variables of interest (student counts) have richerdimensions of variation, at the level of university, field of study, years of study and origin.To exploit variation across all four dimensions in the data, we use the idea that thevulnerability to a student-supply shock from a particular country will differ by field anduniversity. For example, if Purdue University has traditionally recruited a larger share ofIndian students into its graduate programmes (and therefore has invested in developingan ability to identify good Indian students), a shock to supply from India is expected tohave a differentially larger impact on research at that institution. Similarly, if Indians aremore likely to study chemical engineering, then this shock would affect chemicalengineering departments more (and perhaps that field at Purdue the most).

Our university and field-specific approach to answering these research questions hasthe advantage that, in this example, the Indian student shock would manifest itself indisproportionately larger impacts on publishing at Purdue (an institution-specific ef-fect) and at relatively strong chemical engineering departments (a discipline-specificeffect). This allows us to distinguish better the effects of student enrolments fromcoincident changes in economic or policy conditions in the US that may alter publishingbehaviour. For example, the general decline in US high-technology industries in the late1990s may have affected university research output and it also happened to coincideroughly with the East Asian financial crisis. However, given our IV strategy�s reliance onthe disproportionate effects of the Asian shock to particular fields and universities, thiscoincidence would only be a concern if the decline in the high-technology industriesjust happened to have a greater effect on publishing in the departments that havetraditionally relied on East Asian students more. Observing events in the US that hadsuch specific patterns of influence on academic departments is considerably moreunlikely than just finding events that happened to coincide with a foreign-country policychange or economic shock, which increases our confidence in this estimation strategy.In the same vein, the fact that the foreign shocks might affect US undergraduate foreignenrolments that year (altering departmental revenues) is less of a concern, as our esti-mation approach relies on S&E-Ph.D. department-specific migrant networks.

Figures 1–4 demonstrate the empirical relevance of these ideas. Figure 1 shows theco-movement of Indian doctoral students enrolled at US universities and Indian GDPgrowth. Figure 2 shows that China�s partial (1979) and total (1984) lifting of restrictionson study abroad and subsequently re-instituting restrictions in 1989 acted like structuralbreaks in Chinese enrolment at American universities. Figures 3 and 4 further indicatethat the University of Texas benefited differentially more from this surge in Chineseenrolments than did the University of California at San Diego and that electricalengineering departments benefited more than biochemistry departments.



2000

3000

4000

5000

6000

S&E

PhD

Enr

olm

ent

100

200

300

400

500

Rea

l Per

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ita G

DP

1960 1970 1980 1990 2000Year

Real Per Capita GDP S&E PhD Enrolment

Enrolment from India and Income

Fig. 1. GDP Per Capita and Indian Doctoral Student EnrolmentNote. Some of the decline in enrolment at the end of the sample may be due to truncation, asstudents who graduated after 2004 were not included.

050

0010

000

1500

0S&

E P

hD E

nrol

men

t

020

040

060

080

0

Rea

l Per

Cap

ita G

DP

1960 1970 1980 1990 2000Year

Enrolment from China and Income

Real Per Capita GDP S&E PhD Enrolment

Fig. 2. Policy Changes, GDP Per Capita and Chinese Doctoral Student EnrolmentNotes. A policy shock in 1976 (Mao�s Death) and normalisation of relations in 1979 paved theway for the partial (1981) and total (1984) lifting of restrictions on Chinese study abroad(Orleans, 1988). GDP growth in the 1980s may explain some of the magnitude in this spikeof students. Partial restrictions on study abroad were re-imposed following the 1989Tiananmen Square Protests. Note that the decline 1996–8 reflects some truncation.



We implement these ideas in the statistical analysis using triple interaction terms asour instruments:

Instrumentf ;u;t ¼ ðShock in region r in year tÞ� ð fraction of university u foreign students who are from region r

at some initial date t0Þ� ð fraction of students in field f from region r at t0Þ: ð11Þ

010

020

030

040

0

S&E

PhD

Enr

ollm

ent

1980 1985 1990 1995 2000Year

Texas – Austin UC – San Diego

Chinese Enrolment at Texas, Austin and UCSD

Fig. 3. Differential Response of Chinese Enrolment Across Universities

010

0020

0030

0040

00

S&E

PhD

Enr

olm

ent

1980 1985 1990 1995 2000Year

Chinese Enrolment, Biochemistry and Electrical Engineering

Biochemistry Electrical Engineering

Fig. 4. Differential Response of Chinese Enrolment Across Disciplines



The second term in (11) measures the university�s historical dependence on studentsfrom that region, whereas the third term measures the regional dependence of thatfield of study. These interaction terms are motivated by papers on internationalmigration that show that historical migrant stocks are strongly predictive of futuremigration (Altonji and Card, 1991; Card, 2001; Munshi, 2003; Beine et al., 2011), andconsistent with the importance of ethnic networks in trade and innovation docu-mented in other work (Rauch and Trindade, 2002; Kerr, 2008; Javorcik et al., 2011). Weemploy aggregated regions rather than specific countries because to instrument at thecountry level would incorporate so many variables that the problem of having manyweak instruments in an over-identified system would be severe. Table A2 (in the onlineTechnical Appendix A) shows that historical (1970) student supply from a region to aspecific university (or to a specific field of study) is very strongly predictive of studentsupply from that region to that university (or field) in 1997.

The initial date t0 is defined to be the start of each decade (1970, 1980 and 1990).The use of start-of-decade dependence on foreign students may lead to a concern thatthose interaction terms subsequently affect departmental faculty quality (since Ph.D.students in 1980 become faculty in the late 1980s). Section 4.3 below will examine thispotential endogeneity concern by reporting results from alternative specificationswhere t 0 has a rolling definition (on the basis of a 5, 6 or 7-year lag rather than thefixed start-of-decade) and where we control for the historical dependence interactionterms directly in the second stage (so that we do not rely on those variables for iden-tification). Furthermore, in some of our regressions we will directly control for meas-ures of faculty resources.

We conduct a number of robustness checks by including or excluding US unem-ployment rates in the instrument set. A specification re-defines the endogenous vari-ables of interest as �total students� and �foreign share of students� and uses only foreignshocks as instruments, others instrument American and foreign enrolments with onlyforeign shocks (relying on displacement effects) and yet others add either the aggre-gate US unemployment or regional unemployment rates to the set of instruments. Ourmain results are qualitatively and quantitatively robust to all these variations.

3. Data

3.1. Publications and Citations

We create counts of all S&E publications associated with the 100 US universities thatgranted the largest number of foreign doctorates for the period 1973–2001, with datafrom the Thomson ⁄ ISI Web of Science database of publications and citations. Using aprocedure described more fully in the online Technical Appendix B, we sort eachuniversity�s publication records into 23 S&E fields. Although laboratories and depart-ments are the actual S&E administrative units at US universities, we define �depart-ments� as fields of S&E within a university. We extracted 3.2 million individualpublication records by writing Perl script on the internet-based Web of Science database.Using information on the authors� department affiliation(s), the publications� subjectcategories and the year of publication, each of these records was assigned to one ormore of 66,700 (100 � 23 � 29) university-field-year cells. Our final database is a count



of publications and total future citations to those publications in each university-field-year cell. Table 1 contains summary statistics on research outputs. This procedureraises a publication-inflation problem due to double-counting of co-authored publica-tions,15 but assigning outputs on a pro-rata basis or accounting for the order-of-authorship proved infeasible with the search programme. We estimate that thenominal publications numbers we report are inflated by about 20% and take this intoaccount in interpreting the coefficients.16

3.2. Enrolment Counts

We create Ph.D. enrolment counts for each data cell (incorporating a university, field,year and country of origin) by aggregating the National Science Foundation Survey ofEarned Doctorates (SED) micro-database, which contains a record for each individual

Table 1

Summary Statistics

Panel (a): Main variables

Variable Mean Std. Dev. Min. Max.

Publication Counts 44.06 62.81 0 1,159Publication Counts: 1970s 27.56 39.09 0 526Publication Counts: 1980s 42.22 58.03 0 807Publication Counts: 1990s 58.17 77.41 0 1,159

Citation Counts 1400.16 2925.61 0 71,051Citation Counts: 1970s 929.61 1868.14 0 30,056Citation Counts: 1980s 1365.91 2636.96 0 53,257Citation Counts: 1990s 1780.14 3723.19 0 71,051

Ph.D. Enrolment – Total 46.79 55.32 0 498Ph.D. Enrolment: Foreign 16.87 23.33 0 317Ph.D. Enrolment: US 29.92 38.41 0 380

International diversity index 0.64 0.27 0 1Equipment and physical plant expenditures 0.75 1.29 0 18.23Other R&D expenditures 3.68 6.01 0 103.53

Panel (b): Distribution of Ph.D. enrolments per university-field pair, by decade and region

1972–9 1980–9 1990–7

Region Mean Share Mean Share Mean Share

East Asia and China 2.874 0.084 8.075 0.175 13.769 0.243South Asia 1.487 0.043 2.149 0.047 3.173 0.056Mid-East and Africa 1.486 0.043 2.439 0.053 2.179 0.038Europe and Russia 0.998 0.029 1.700 0.037 2.920 0.052Western Hemisphere 1.162 0.034 1.719 0.037 2.156 0.038US 26.355 0.767 29.987 0.651 32.409 0.573

Notes. Number of university-field �department� observations: 47,959, number of university-field groups: 2,214.Expenditures measured in $ millions, 5 year moving average.

15 The computerised Web of Science search procedure assigns publications with multiple authors once toeach cell with which an author was affiliated. For example, an article with six authors from two departmentswould be counted twice in the data.

16 We arrive at this inflation estimate by comparing our publications data with an overlapping datasetcompiled by the NBER, the Adams and Clemmons (2008) database of scientific papers.



who received a Ph.D. in the US between 1959 and the present. Doctoral recipients fillout this survey when they receive the Ph.D. degree, so the yearly enrolment counts wecreate are based on the graduation date and the date of entry into the doctoral pro-gramme reported by the students, and reflect only those students who have finished thedegree. We infer enrolment counts for the period 1960–97 only, since there are likelyto be many students who entered doctoral programmes in 1998 or thereafter whowould not have appeared in the SED database we had access to.

We assign each student to one of 23 fields of study based on the reported three-digitdissertation specialty. The student�s assignment by country of origin is based on thereported country of citizenship. Other definitions (such as country of high-schoolgraduation) would be more complicated but feasible, and analysis of a sub-sampleindicates that in practice the counts of foreign and US students under such alternativedefinitions would be very highly correlated with each other. We create university-field-year-country enrolment counts for foreign students from the 50 largest countries (thosethat have supplied at least 930 doctoral students to the US since 1960) studying in the100 largest universities (those with at least 2,100 doctoral students since 1960), in 23S&E fields (as defined by Goldberger et al. (1995), also used by Lach and Schankerman(2008)) during the period 1960–97. There are approximately 700,000 doctoral studentsin the sample we analyse. Our IV are defined by aggregated regions of origin. We definesix regions on the basis of economic, geographical and cultural similarities betweencountries.

Total doctoral enrolment in the average university-field-year was 47 students, 30 ofwhom were American. The East Asia ⁄ Pacific region, including China, was the nextlargest supplier of students at 8.4, followed by South Asia with 2.2. Due to truncation ofcitation and enrolment counts in the final years of the sample, we limit the sample to1973–98, with enrolments lagged one year in order to reflect the lag from research topublication. The evolution of student shares from various regions over the threedecades is summarised in Table 1. Chinese and other East Asian students experiencedthe largest growth in both absolute and relative terms over this period. The share ofAmericans in S&E departments declined from 76.7% in the 1970s to 57.3% in the 1990s.

3.3. Data on Instrumental Variables

We describe next the instruments we use for the first-stage prediction of enrolmentsand the share of foreign students.

3.3.1. GDP per capita in source countriesIn relatively poor countries, this variable captures long-term changes in foreigners�ability to pay for a US education (Figure 1). GDP growth can have the opposite effect inrich countries as it increases employment opportunities in local markets (Sakellaris andSpilimbergo, 2000).

3.3.2. Policy changes enabling study abroadChina lifted a ban on study abroad by Chinese S&E students between 1978 and 1984following the death of Mao Zedong (Orleans, 1988). Russia, Romania, Cuba, Poland,Hungary, Bulgaria, Czechoslovakia and (East) Germany also went through similar



policy changes during our sample period. Our instrument is a population-weightedaverage of these country-year specific indicators of �no restrictions on study abroad�:

Xn

i¼1

XT

t¼1

DitPopit=Xn

i¼1

XT

t¼1

Popit ;

where Dit ¼ 1 if country i permitted study in the US in year t, and 0 otherwise.Appendix B in the online Technical Appendix provides further details.

3.3.3. International students at non-US hostsWe create counts of the number of tertiary (university plus post-graduate) foreign stu-dents from each source-country studying abroad at other (non-US) host countries, suchas the UK, Australia, Singapore and Canada using the UNESCO Statistical Yearbooks (1963–2004). The idea is that fluctuations in the number of South Asian students in the UK ispartly related to changes in financial conditions and policy changes in South Asia, andpartly related to changes in conditions at different potential destinations. InstrumentingSouth Asian students in the US with this variable helps us to extract the portion of thevariation in the endogenous variable that is related to changes in economic and policyconditions in South Asia, rather than in the US. An analogous IV strategy has been usedby Bartik (1991), Blanchard and Katz (1992) and others to predict employment growth.

Our main empirical specifications aggregate across regions to create single IV ratherthan sets of region-level variables, to minimise problems associated with weak instru-ments in over-identified systems (Imbens and Wooldridge, 2007). In those cases, thetriple interaction terms are defined as the university or the field�s historical depen-dence on foreign students in aggregate. However, in Table A3, shown in onlineTechnical Appendix A, we run the disaggregated region-specific analogues to our first-stage regression to document that the instruments indeed work in the way that weclaim: that the lifting of study-abroad restrictions in China has the strongest supplyeffect on Chinese students, that the supply of students from a region to non-US hosts ispositively correlated with that region�s supply to the US and that GDP movements in aregion has the strongest effect on students from that region.17

4. Results

4.1. First-Stage Results

Table 2 shows the first stage of the two-stage limited-information maximum likelihood(LIML) regressions. All regressions control for a comprehensive set of fixed effects fordepartments (university-field pairs) and years, along with university-specific and field-specific time trends but these coefficients are not shown in the Tables.

The first stage includes one equation to predict foreign enrolments and another topredict American enrolments. Almost all instruments are the triple interactions offoreign macro and policy shocks with the university�s and field�s historical dependenceon students from that region. To check for robustness, Table 2 displays two sets of first-

17 There are a few unexpected signs in the large Table of numbers but in almost all such cases, thecoefficient on the lagged value of the instrument is of the expected sign.



Table 2

First Stage: Ph.D. Enrolments on Instrumental Variables

Dependent variables: 1-year lags of US and foreign enrolment

Source-country shocks plus USunemployment

Source country shocks plus US regionalunemployment

US students Foreign students US students Foreign students(1) (2) (3) (4)

Lifting of Policy Restriction Preventing Study Abroad to US (China, East Europe – population-weightedaverage)1-year lag 2.482 59.543*** �63.739*** 37.939***

(13.397) (11.284) (11.438) (8.854)2-year lag 64.679*** 4.472 80.617*** 8.419

(16.535) (16.097) (16.906) (15.655)

Tertiary students abroad, non-US hosts1-year lag 0.002 0.047*** 0.002 0.046***

(0.008) (0.008) (0.008) (0.008)2-year lag �0.029** �0.013 �0.022** �0.013

(0.012) (0.009) (0.010) (0.008)

Real average GDP per capita, East Asia1-year lag 0.003 �0.003 0.019*** 0.002

(0.004) (0.003) (0.004) (0.003)2-year lag �0.002 �0.016*** �0.010** �0.019***

(0.004) (0.004) (0.004) (0.004)

Real average GDP per capita, South Asia1-year lag �1.906*** 1.160*** �1.769*** 1.249***

(0.451) (0.442) (0.453) (0.445)2-year lag 0.307 0.215 0.356 0.257

(0.281) (0.296) (0.279) (0.295)

Real average GDP per capita, Mid-East and Africa1-year lag �0.098** 0.089** �0.100** 0.085*

(0.046) (0.044) (0.046) (0.044)2-year lag �0.034 0.072* �0.029 0.079**

(0.032) (0.039) (0.032) (0.039)

Real average GDP per capita, Europe and Russia1-year lag �0.011*** �0.011*** �0.005 �0.010***

(0.003) (0.003) (0.004) (0.003)2-year lag �0.011*** �0.004 �0.013*** �0.004

(0.003) (0.003) (0.003) (0.003)

Real average GDP per capita, Western Hemisphere1-year lag �0.225** �0.027 �0.253** �0.037

(0.109) (0.083) (0.108) (0.083)2-year lag 0.547*** 0.114* 0.545*** 0.111

(0.085) (0.069) (0.086) (0.069)

US national unemployment rate1-year lag 2.702*** 0.940***

(0.314) (0.298)2-year lag �0.801** �0.237

(0.320) (0.265)

US regional unemployment rate (Northeast)1-year lag 42.961*** 3.470

(7.889) (5.465)2-year lag 19.493* �6.102

(10.396) (6.982)



stage estimates that use either the aggregate US unemployment rate coupled with theforeign-country shocks, or US regional unemployment rates coupled with foreign-country shocks. As US aggregate unemployment may be subject to some endogeneityconcerns, we use a minimal set of US regions (Northeast and South) in the second setof specifications. The main regression tables also show some results with US instru-ments excluded altogether.

The first-stage estimates in Table 2 show that, as expected, the �foreign� instrumentshave stronger positive effects on foreign enrolments, whereas the US instruments havea positive effect on American enrolments. Source-country instruments generally havethe opposite effect on foreign enrolments and US enrolments, which suggests thatthere are some displacement effects. Increases in student supplies from the rest of theworld (the UNESCO instrument), or positive GDP shocks in any region, decreaseAmerican enrolments at US universities. The negative effect of European GDP growthon US enrolments is suggestive of a reverse attraction of American students to Euro-pean labour markets or European universities.

Removal of study-abroad restrictions in source countries is responsible for over oneextra foreign student per department-year over the course of the sample period.Foreigners studying abroad at non-US destinations are strongly positively correlatedwith foreign enrolments in the US, which suggests that the instrument picks up vari-ation in source-country conditions. In poorer regions, positive GDP movements areassociated with more students in the US as �ability to pay� is the relevant margin for thestudy-abroad decision. In more developed regions (East Asia and Europe), the effect isnegative, supporting the theory that the opportunity costs of home-country employ-ment is a more important determinant of study abroad from those countries.

More Americans enrol in S&E doctoral programmes during periods of high unem-ployment in the US. The aggregate US unemployment rate may be subject to anendogeneity concern in that revenues of many academic departments suffer during

Table 2

(Continued)

Dependent variables: 1-year lags of US and foreign enrolment

Source-country shocks plus USunemployment

Source country shocks plus USregional unemployment

US students Foreign students US students Foreign students(1) (2) (3) (4)

US regional unemployment rate (South)1-year lag 7.821 31.766***

(8.810) (8.362)2-year lag �38.735*** 1.310

(9.099) (9.505)Observations 47,954 47,954 47,954 47,954No. of Field-University Pair FE 2,209 2,209 2,209 2,209R2 0.24 0.57 0.25 0.57F-stat of excluded IV 11.98 12.07 10.94 11.52

Notes. *Significant at 10%. **Significant at 5%. ***Significant at 1%. Robust standard errors in parentheses,errors clustered by field-university pairs. All regressions include field-university pair and year fixed effects,university- and field-specific trends and R&D measures. All instruments include interactions with region�sstart-of-decade university and field fractions of enrolment.



recessions. We therefore run alternative specifications where the unemployment ratesin two specific census regions (states MS, AL, TN, KY and New England) rather thanthe aggregate unemployment rate are used as instruments. The first-stage effects andstructural estimates (shown in the next Table) are qualitatively similar.

The F-statistics for joint significance of all instruments in explaining US and foreignenrolments are 11.98 and 12.07, respectively, showing that their power, while low, isadequate to produce IV estimates with little bias. We use a two-stage LIML estimator to beconservative against a weak instrument problem (Imbens and Wooldridge, 2007). Al-though our two-stage system is over-identified, we do not report over-identification testsbecause the theoretical model in Section 1.3 implies that the different source-countrymacro ⁄ policy shocks should have different effects on the productivity of foreign studentsas the different shocks alter the quality distribution of students in different ways. Asnoted by Angrist and Pischke (2009, p. 166), standard over-identification tests such as theSargan test are invalid for instruments with heterogeneous treatment effects.

4.2. Summary of Effects of Foreign and Domestic Doctoral Students

Table 3 reports the OLS and the two-stage IV estimates of the knowledge productionfunction (10). The dependent variables are the number of scientific publicationsassociated with each S&E department (university-field pair) in each year, and thenumber of future citations to those publications (which quality-weights the publicationcounts).18 The endogenous variables of interest are counts of the numbers of domesticand foreign students in the department. All regressions control for university-field fixedeffects, year effects and linear trends for each university and field. Some modelsadditionally control for measures of department size (R&D resources, including sup-port for faculty) computed from the National Science Foundation�s Survey of R&DExpenditures at Universities and Colleges.

In OLS regressions with the fixed effects and trends (columns 1 and 2), increases to adepartment�s student enrolment are associated with a larger number of publicationsthe following year. Each additional student leads to about 0.13–0.16 publications peryear and the productivities are not significantly different across Americans andforeigners. These estimates suggest that over the course of an average-length 6-yearPh.D. programme, the expected contribution of any Ph.D. student is 0.81–0.92publications. This number reflects both authorship by the students themselves andtheir indirect contribution to the productivity of the laboratory. It would be interestingto separate out these two effects in future research, but our Web of Science searchprocedure could not distinguish between student and faculty authors.

Columns 3 and 4 report the two-stage LIML estimates of the knowledge productionfunction using the full set of instruments that include US regional unemploymentrates. The marginal effects are much larger under IV than the OLS estimates. Here, thepoint estimate of the effect of foreign students is greater than that of domestic studentsbut again the difference is not statistically significant. Accounting for a co-authorship

18 Consistent with the approach in Jaffe and Trajtenberg (2002) we actually use (1 plus counts) as thevariable in order to distinguish between observations with no publications (a value of zero) and those withone or more publications that are not cited (a value of one).



Tab

le3

OL

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vari

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Year

(1)

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(5)

(6)

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d:

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LL

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san

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ent

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cou

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san

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SA

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gate

Un

emp

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US

stu

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ts0.

164*

**0.

154*

**0.

837*

0.74

51.

052*

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652*

**45

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.032

)(0

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8.31

4)In

tern

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stu

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152*

**0.

135*

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967*

**0.

924*

**0.

963*

**0.

351

33.3

66**

*(0

.033

)(0

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)(0

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)(0

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)(1

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2.12

6)T

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ents

0.89

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(0.3

59)

Inte

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23.5

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5.35

8)C

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�0.

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�0.

417

�16

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�27

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(0.3

03)

(0.3

92)

(0.4

3)(0

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4)C

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Ob

serv

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47,9

5947

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47,9

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47,9

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47,9

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214

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209

2,20

92,

214

2,20

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0.51

0.52

0.34

0.17

F-s

tat

of

excl

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edIV

on

US

stu

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10.7

210

.94

11.9

89.

6211

.98

F-s

tat

of

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on

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for

par

ity:

0.09

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740.

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wrt

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ts:

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104

0.51

30.

457

0.71

40.

728

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20.

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inflation factor of 20%, the estimates suggest that the marginal US student adds 0.67publications per year, whereas the marginal international student adds 0.77. By theseestimates, the contribution of each student to his or her department�s productivity overthe average 6-year Ph.D. tenure is 4–4.6 publications. Doctoral students in S&E labo-ratories often graduate with 4 or more publications themselves,19 and these estimatestherefore appear to be of reasonable magnitude. Our estimates are very similar whenwe replace regional unemployment rates with the US national unemployment rate incolumn 5.

Comparing across OLS and IV specifications, OLS appears to underestimate theeffects of both domestic and foreign students. This suggests that departments receivedmore (and higher quality) student applications in years when the other inputs todepartment quality (faculty, research funding, financial resources) were low. Thiswould be consistent with surges in student applications in recession years, whendepartmental budgets are tight.,20,21 Indeed, our first-stage regressions indicate exactlythis direction of correlation between unemployment rates and student enrolment.

This interpretation also suggests that the instrument for US students (regionalunemployment rates) may be correlated with departmental productivity through anotherchannel (funding at state universities may suffer during recessions). Column 6 thereforereports a specification where total enrolments and the foreign share of enrolments areinstrumented with only foreign source-country conditions, omitting US instrumentsaltogether. The two regressors are simple non-linear transformations of American andforeign enrolments that we use for our main specifications.22 The rows at the bottom ofthe Table compute elasticities of publications with respect to US and foreign enrolments,and they indicate that the implied elasticities at the means remain qualitatively verysimilar when US instruments are omitted (0.73 and 0.22, compared with 0.71 and 0.37).We do, however, lose first-stage power in explaining US enrolments.

Columns 7 and 8 of Table 3 present equations explaining citations. In OLS regres-sions, we find almost no effect of foreign students on citation production. As withpublications, the IV regressions show much higher productivities, with a marginalcontribution from Americans of 36 citations per year and 27 citations from inter-

19 Publication rates among graduate students in S&E are much higher than in economics and other socialscience disciplines partly due differences in co-authorship norms. We informally surveyed the Dean of theEngineering school and department chairs in Biology, Physics, Chemistry, Physiology and Mathematics at theUniversity of Colorado at Boulder – a representative university in our sample – and learned that in Engi-neering, doctoral students typically graduate with 4–5 publications, in natural sciences 3–4 and in mathe-matics, less than 3. These numbers were likely smaller in earlier decades.

20 There is substantial evidence that both applications to universities and enrolments increase whenunemployment rates are high (Card and Lemieux, 2001). Kahn (2010) shows that people graduating fromcollege during recessions are significantly more likely to enrol in graduate school. The Council of GraduateSchools notes that historically, graduate school applications have increased during recessions (Heiser, 2009;Bell, 2011).

21 In the online Technical Appendix Table A4, we show using our measure of university R&D spendingthat university resources experience a �5.8–6.5% decline during recession years. The time series plot in panel(b) clearly shows those periods of negative growth. The National Association of State Budget Officers (2011)notes that during economic downturns states frequently cut funding to state universities, allowing tuitiondollars to take up the slack. There are also indirect costs of recessions on university quality: the University ofCalifornia system and Princeton University instituted faculty and administrator salary freezes during the mostrecent recession (Montell, 2009a, b), which affected the university�s ability to recruit and retain high-qualityfaculty.

22 Total = American + Foreign, and Share = (Foreign ⁄ Total).



national students (again accounting for the 20% inflation from co-authored double-counting). Here too we cannot reject the hypothesis of parity between the US andforeign-student coefficients.23

4.3. Robustness of Main Results to Alternative Identification Strategies

An important threat to the exogeneity of the instruments arises from the fact thatfluctuations in policies and macroeconomic conditions in source countries (which areplausibly exogenous) are interacted with the historical student supplies in specificfields and departments. If the past composition of graduate students affects otherinputs in a department�s production function today (e.g. because past graduatestudents become post-docs and faculty today), then the interaction term in theinstrument may be correlated with the error term in the second stage.24

To evaluate and address these concerns, we report results from several alternativespecifications in Table 4. First, we redefine the lagged dependence of universities andfields on students from each region (the interaction terms in the instruments) on thebasis of a fixed 5, 6 or 7-year lag, rather than enrolments at the start of each decade, inorder to eliminate the very short lags in parts of the panel. Card (2001) also uses a fixedlag in his related IV strategy. The first three columns of Table 4 show that the resultsare qualitatively very similar under this alteration but the magnitudes are smaller.Accounting for the co-authorship inflation, the marginal American student contributes0.35–0.56 publications per year, whereas the marginal foreign student contributes0.25–0.32 publications. Importantly, the contribution of Americans relative to foreignersremains similar as in the original specification, and the two are not statistically differentfrom each other.

In the next four specifications, we control for the lagged dependence of universitiesand fields of foreign students from each region (i.e. the potentially endogenouscomponent of the instrument) directly in the second stage. The idea is that if thecorrelation between the instrument and the error term is caused by the term involvingthe lagged share of foreign students, then the correlation should be absent once wecondition on the lagged share. The main results continue to be very robust in thesespecifications, and even the magnitude is now comparable with the main results fromTable 3 (1–1.2 publications per American, and 0.5–1 publications per foreigner; thetwo are not significantly different from each other).

Finally, we note that many of our specifications include a control for departmentalR&D resources (including salaries of faculty and other personnel), which alleviates the

23 Since the citations variable is measured as all future citations to each publication, values for later yearsare censored above, since recent publications have less time to accumulate citations. This is unlikely tointroduce bias in our coefficients, since our specifications control for year fixed effects and trends specific toeach field and each university. Furthermore, we include citations made until 2004, 6 years after the end of ourpanel.

24 As we analyse a department-level panel data set, this concern is most relevant when graduate students ina department are subsequently hired into other roles (post-docs and faculty) in the same department.Although this practice is not very common at US universities, Ph.D. graduates are sometimes offered post-doctoral positions in the same university immediately after graduation, and so the issue is most pronouncedwhen the lag in the interaction term is very short (e.g. in 1971, 72, 81, 82, 91, 92, immediately after the �start ofdecade�). Similarly, if fluctuations in student supplies are persistent, then the interaction term may becorrelated with the error term for those same observations where the lag is very short.



Tab

le4

Sen

siti

vity

Tes

tsu

sin

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nat

ive

Iden

tifi

cati

onSt

rate

giesy

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end

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vari

able

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lica

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ns

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(5,

6,7-

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lag)

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s

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tera

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ns

(1)

(2)

(3)

(4)

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(6)

(7)

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win

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cted

enro

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year

lag

6-ye

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year

lag

NA

US

stu

den

ts0.

440*

0.58

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0.69

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1.50

0***

1.28

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1.29

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1.65

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(0.2

43)

(0.2

33)

(0.2

01)

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82)

(0.4

46)

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76)

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59)

Inte

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669*

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41)

(0.2

67)

(0.2

76)

(0.1

88)

(0.2

14)

(0.3

50)

(0.4

52)

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Tab

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(Con

tin

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Dep

end

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vari

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serv

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92,

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92,

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41.

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and

un

iver

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and

fiel

d-s

pec

ific

tren

ds.

Inst

rum

ent

set

incl

ud

esfi

rst

and

seco

nd

lags

of

sou

rce

cou

ntr

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ock

san

dag

greg

ate

US

un

emp

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ent.y A

lter

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toT

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on

5.‡E

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(5ye

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.



concern that the historical composition of graduate students is correlated with theerror term because those graduate students subsequently take faculty positions.

4.4. Inferring Student-Quality Effects

We would like to examine heterogeneous productivity effects by the quality ofincoming foreign doctoral students, because the optimal visa policy may be conditionalon the quality of skilled immigrants. In the absence of a direct measure of studentquality, we use the insight developed in the model in Section 1.3. Specifically, if uni-versities trade-off tuition income against research productivity, shocks to the supply ofpoorer students (who are differentially more reliant on scholarships) will have largereffects on output as those shocks will pick up higher quality students on the margin.

We implement this idea in Table 5 by defining two sets of instruments. The firstincludes those IV that should have neutral effects across students of varying incomelevels, because they should uniformly affect the ability of all students to go abroad.These are source-country policy restrictions and changes in the number of tertiarystudents studying outside the US. The second set includes those IV that affect students�ability to bear the monetary cost of studying in the US. GDP per capita movements in thesource countries are more likely to affect study-abroad decisions for the set of studentspaying for a US education (Sakellaris and Spilimbergo, 2000).

The idea from the theory that we are trying to capture is that �pay-neutral� shocksshould have little effect on the quality distribution of students, while positive �ability topay� shocks could lower the average quality of students. The set of compliers in the IVregressions with instruments that affect �ability to pay� are more likely to be non-scholarship students. The latter set of shocks thus disproportionately shift enrolmentstowards lower quality applicants, and comparing across the two types of IV regressionsallows us to infer indirectly the effects of student quality on knowledge production.

Table 6 shows the results with these subsets of instruments. As our set of USinstruments is not amenable to such division, we include all US instruments in both setsand focus on the estimates of the coefficient on foreign enrolment. To deal with a weakinstrument problem that arises once the source-country instruments are split, we addtwo additional US instruments to regional unemployment rates: mean gross stateproduct for the E. S. Central and Mountain census regions. The coefficient on foreignstudents identified by the pay-affecting shocks is half as large as that identified by thepay-neutral shocks: 0.8 publications per year versus 1.6. This suggests that a positiveshock to the ability to pay reduces the measured contribution of students to publishingby reducing student quality, at the margin. In the model, this comes about because thepay-affecting shocks lead to greater enrolment of paying non-scholarship students onwhom departments set a lower admissions standard. With regard to their effects oncitations, we find that the effect of the marginal foreign student identified with �pay-neutral� shocks is much greater, 49.5 citations versus 31.5. A test based on Hausman(1978) reveals that these two coefficients are significantly different from each other (t-statistic of 5.62). This suggests the research impact of visa restrictions on foreigners willdepend on how the restriction affects the quality margin, which in turn depends onhow the immigration policy is implemented, that is, whether the agency issuing visasscreens for research ability or for �ability to pay�.



Table 5

First Stage for the Different Supply Shocks: Ph.D. Enrolments on Subsets of InstrumentalVariables

Dependent variables: 1-year lags of US and Foreign enrolment

Pay-neutral set Pay-affecting set

US students Foreign Students US students Foreign Students(1) (2) (3) (4)

Lifting of Policy Restriction Preventing Study Abroad to US (China, East Europe – population-weightedaverage)1-year lag �39.598*** 45.544***

(7.955) (5.834)2-year lag 30.943*** 6.612

(6.804) (6.146)

Tertiary students abroad, non-US hosts1-year lag 0.015* 0.016**

(0.009) (0.008)2-year lag 0.003 �0.086***

(0.016) (0.014)

Real average GDP per capita, East Asia1-year lag 0.002 0.013***

(0.003) (0.002)2-year lag 0.011*** �0.021***

(0.002) (0.002)

Real average GDP per capita, South Asia1-year lag �1.408*** 2.062***

(0.378) (0.368)2-year lag 0.277 �0.089

(0.277) (0.291)

Real average GDP per capita, Mid-East and Africa1-year lag �0.068* 0.173***

(0.038) (0.032)2-year lag �0.012 0.078*

(0.033) (0.040)

Real average GDP per capita, Europe and Russia1-year lag �0.015*** �0.002

(0.004) (0.003)2-year lag �0.002 �0.004

(0.003) (0.003)

Real average GDP per capita, Western Hemisphere1-year lag �0.195** 0.048

(0.095) (0.069)2-year lag 0.562*** 0.156**

(0.086) (0.070)

US regional unemployment rate (Northeast)1-year lag 41.285*** 6.065 48.879*** �8.458

(7.818) (5.485) (7.967) (5.369)2-year lag 27.948*** �13.386* 12.932 �4.131

(10.754) (7.241) (10.204) (6.902)

US regional unemployment rate (South)1-year lag 12.405 31.768*** 13.260 22.582***

(8.816) (8.494) (8.951) (8.198)2-year lag �40.351*** �13.913 �44.097*** 1.228

(8.808) (9.464) (9.071) (9.489)



Table 6

Inferring Student-Quality Effects from Different Subsets of Supply Shocks

Dependent variable:

(1) (2) (3) (4)

Publications Citations

IV set type: Pay-neutral Pay-affecting Pay-neutral Pay-affecting

US students 1.409 0.625** 36.904 54.299**(1.044) (0.307) (22.538) (24.259)

International students 1.621* 0.815*** 49.498*** 31.514*(0.848) (0.252) (17.500) (17.204)

Control for department size:Equipment R&Dy

�0.600 �0.351 �28.147 �28.838(0.592) (0.362) (21.432) (23.014)

Control for department size:R&D incl. salary support‡

�1.031 �0.157 �39.360 �38.632(1.111) (0.338) (24.334) (24.765)

Observations 47,954 47,954 47,954 47,954No. of Field-University Pair FE 2,209 2,209 2,209 2,209First-Stage StatisticsF-stat of excl. IV on US students 15.96 10.47 15.96 10.47F-stat of excl. IV on International 17.93 12.19 17.93 12.19Chi-squared stat. for parity of US andInternational Coefficients:

0.40 1.60 0.87 5.97

p-value of test: 0.525 0.206 0.351 0.015

Notes. *Significant at 10%. **Significant at 5%. ***Significant at 1%. Robust standard errors in parentheses,errors clustered by field-university pairs. All regressions include field-university pair and year fixed effects,university- and field-specific trends and R&D measures. All instruments interacted with region�s start-of-decade university and field fractions of enrolment yEquipment and physical plant expenditure (5 year MA,$millions). ‡R&D expenditure incl. faculty salary support, stipends (5 year MA, $millions).

Table 5

(Continued)

Dependent variables: 1-year lags of US and Foreign enrolment

Pay-neutral set Pay-affecting set

US students Foreign Students US students Foreign Students(1) (2) (3) (4)

US regional GDP (South)1-year lag 0.011*** 0.012*** 0.011*** 0.012***

(0.004) (0.003) (0.004) (0.003)

US regional GDP (Mountain)1-year lag 0.028*** 0.003 0.029*** 0.005

(0.009) (0.008) (0.009) (0.008)Observations 47,954 47,954 47,954 47,954No. of Field-University Pair FE 2,209 2,209 2,209 2,209R2 0.24 0.57 0.25 0.57F-stat of excluded IV: 15.96 17.93 10.47 12.19

Notes. *Significant at 10%. **Significant at 5%. ***Significant at 1%. Robust standard errors in parentheses,errors clustered by field-university pairs. All regressions include field-university pair and year fixed effects,university- and field-specific trends and R&D measures. All instruments interacted with region�s start-of-decade university and field fractions of enrolment.



4.5. Diversity Effects

Increasing the enrolment of foreign students also has the effect of diversifyingproduction teams within the laboratory, as foreigners have been the minority in USdoctoral programmes. Team members bringing complementary skills and training mayhave multiplicative effects on innovation. The increasing dominance of laboratoryteams and co-authoring in the production of scientific knowledge is well documented(Wuchty et al., 2007) and diversity may result in positive spillovers from the exchangeand mixing of ideas and methods if students from different regions bring comple-mentary and heterogeneous skills (Berliant and Fujita, 2004; Fujita and Weber,2004; Alesina and La Ferrara, 2005; Ottaviano and Peri, 2006; Sparber, 2009; Niebuhr,2010).

Table 7 incorporates a variable capturing diversity of international doctoral stu-dent enrolments, a Herfindahl index of regional shares. After controlling for USand foreign enrolments, the OLS regressions show that diversity has a positive andsignificant effect on both publications and citations. The elasticity of publicationsand citations with respect to diversity is about 0.04. This effect is small but quan-titatively significant. For example, a department with ten foreign students from five

Table 7

Effects of Diversity in the Student Population

Dependent variable:

(1) (2) (3) (4)

OLS LIML OLS LIML

Publications Citations

US students 0.151*** 0.720** 6.555*** 51.363**(0.032) (0.325) (1.566) (20.278)

International students 0.135*** 0.912*** 0.351 33.586**(0.033) (0.258) (1.444) (13.466)

Index of international diversity 2.543*** 1.191 95.538** �1.714(0.754) (1.097) (45.533) (64.936)

Control for department size:Equipment R&Dy

�0.163 �0.376 �15.639 �28.598(0.302) (0.381) (17.253) (22.613)

Control for department size:R&D incl. salary support‡

0.478*** �0.263 4.495 �38.214*(0.155) (0.350) (6.051) (20.903)

Observations 47,959 47,954 47,959 47,954Number of group(univ field) 2,214 2,209 2,214 2,209R2 0.52 0.34Elasticity of publications with respect toInternational Diversity, at mean

0.04 0.04

F-stat of excluded IV on US students 10.52 10.52F-stat of excluded IV on International 11.13 11.13

Notes. *Significant at 10%. **Significant at 5%. ***Significant at 1%. Robust standard errors in parentheses,errors clustered by field-university pairs. All regressions include field-university pair and year fixed effects,university and field-specific trends and R&D measures. All instruments interacted with region�s start-of-decade university and field fractions of enrolment. International Diversity Index is Herfindahl index of sharesof international enrolment for seven foreign regions. Instrument set in LIML regressions includes main setplus GSP instruments for E. S. Central and Mountain census regions. yEquipment and physical plantexpenditure (5 year MA, $millions). ‡R&D expenditure incl. faculty salary support, stipends (5 year MA,$millions).



regions is expected to generate 0.76 more publications and 28.65 more citations peryear than a department with 10 foreign students from two regions. The effect be-comes smaller and statistically insignificant once US and foreign enrolments areinstrumented, as we do not have strong instruments to separately identify bothvariation in the number of international students and the regional composition ofthose students. This mixed evidence on the link between diversity to productivitysuggests that any productivity benefits from the mixing of complementary ideasfrom different regions may be mitigated by increased communication and coordina-tion costs.

4.6. More Robustness Checks

The last 4 columns of Table A1 (in the online Technical Appendix A) shows theresults of additional robustness checks that have not yet been discussed: a double-log specification (columns 4 and 5), and re-defining our instruments along thelines of an approach used in Card (2001). The double-log specifications displayelasticities of publications and citations with respect to students, and the results arequantitatively and qualitatively very similar to our main specifications. That is, theelasticities with respect to both foreign and domestic students are positive, andAmericans have a higher elasticity because each additional American is a smallerpercentage increase than each additional foreigner at their respective samplemeans.

Motivated by Card (2001), we construct fourteen instruments (for the five foreignregions and nine US census regions) in which a region�s Ph.D. enrolment is interactedwith that region�s share of total enrolment per university and field, lagged 7 years. Ourpreferred IV approach is an extension of this, in that it uses foreign macro and policyshocks, thereby totally avoiding the use of potentially endogenous enrolment counts.The Card (2001) IV approach produces estimates that are closer to the OLS resultscompared with our preferred approach.

Finally, in Table A5 (online Technical Appendix A), we show estimates of the effectsof domestic and foreign-student enrolments on patent applications associated withthose academic departments. This is a smaller sample since patenting as a regularacademic activity has taken place at a smaller set of universities and for fewer years.25

Unfortunately, our instruments are quite weak in this smaller sample (with first-stageF-statistics on excluded instruments in the range of 6–8). In an OLS regression, we find asmall positive effect of Ph.D. student enrolment on a department�s patent count, witheach US student contributing an extra 0.012 patents per year, while an extra interna-tional student contributes 0.006 patents. These variables become statistically insignifi-cant in the IV regression. We can thus provide only suggestive evidence that Ph.D.students contribute also to commercially valuable innovation, when measured at thedepartment level.

25 Hence, the sample is limited to 1980–98 and for 80 universities to limit the degree of observations withzero patents. Here, patents are assigned to one of twenty technical fields, instead of the 23 fields of scienceused for publications.



5. Concluding Remarks

Research scientists in American universities continue to argue strongly that their abilityto develop knowledge, raise grants and ultimately expand technology-based innovationdepends on unimpeded access to the highest calibre graduate students they can attractfrom anywhere in the world. Politicians� and policy makers� views are also starting toshift in this direction. While this claim is intuitively plausible, it is important to gofurther and carefully test with micro data whether skilled foreign students are substi-tutable by their domestic counterparts. It is also important to avoid mixing cause andeffect. The novel IV based estimation strategy with detailed micro data helps this articledevelop evidence relevant to these issues.

American and European policy makers concerned with the relative decline of theireconomies in the face of China�s and India�s ascent may worry less about sunset sectorsin which they no longer hold a comparative advantage and more about their con-tinued ability to innovate and generate new products and new markets at the fron-tier.26 If foreign-born skilled labour is an important input for the production for newideas and products, then immigration policy may be intricately tied to innovationpolicy.

Our analysis demonstrates that both domestic and foreign students significantlyincrease the scientific productivity of US S&E departments, and their marginal effectsare statistically comparable, which is consistent with the behaviour of an optimisingdepartment. Further, the positive contribution of foreign students is muted when thestudents arrive as a result of macroeconomic shocks that differentially increase theproportion of paying (non-scholarship) students. High-quality scholarship students areparticularly valuable from the perspective of US innovation policy.

That the quality of international students has a significant impact at the marginimplies that US student-visa policy may be misguided if an important objective is toexpand the research capacity of American universities. Rather than relying largely on ademonstration of financial wealth sufficient to support graduate study and returnhome, a key criterion for issuing a visa could be indicators of student quality (easilymeasured by admission with scholarship to top-ranked programmes) independent ofassets or incomes.

To summarise, proponents of increasing the numbers of foreign graduate studentsseem to be correct, in that they clearly have had a positive effect on the conduct ofscience. However, we also find that the US supplies an equally high-quality contingentof skilled labour at S&E departments and the issue is therefore not specific to visapolicy: it is a more general issue about any policy or economic factor that keeps stu-dents of any nationality away from S&E fields. Although it is difficult to place a dollarfigure on the costs of skilled-student visa restrictions in terms of reduced innovation,the fact that the American economy is dependent on new products, new markets andinnovation for growth is strong indication that the consequences of limiting foreignenrolments are potentially large.

26 There is evidence that innovation and patenting shifted to China during the recent (2009–10) globalrecession. See �Innovation Shifted to China During the Downturn: U.N. Report�, The Huffington Post, 16September 2010 and �China Shifts away from Low-cost Factories�, New York Times, 15 September 2010.



University of IdahoYale UniversityUniversity of Colorado at Boulder

Submitted: 14 November 2011Accepted: 15 March 2012

Additional supporting information may be found in the online version of this article:

Appendix A. Additional Tables.Appendix B. Data Compilation Details.

Please note: The RES and Wiley-Blackwell are not responsible for the content orfunctionality of any supporting information supplied by the authors. Any queries(other than missing material) should be directed to the author of the article.

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