migration effect of education

Electronic copy available at: http://ssrn.com/abstract=2832996

The Impact of International Students on US Graduate Education∗

Kevin Shih Rensselaer Polytechnic Institute

July 11, 2016

Abstract

This paper examines whether international students affect domestic enrollment in graduate education, focusing on a unique boom and bust in international enrollment at US universities from 1995-2005. Increases in international students expand domes- tic enrollment. These expansions arise from cross-subsidization–foreign tuition creates Research and Teaching positions (RA/TA) for domestic students. Decreases in in- ternational students during the bust have no effect, as universities decrease RA/TA positions held by international students to equalize the loss in tuition revenue. Effects are identified using instruments that interact universities’ historical foreign presence with supply shocks–population growth in sending countries for the boom, and post- 9/11 declines in visa issuance during the bust.

JEL Codes: F22, I21, I23, J11

∗ Assistant Professor, Department of Economics. 110 8th Street, Troy, NY 12210. E-mail: [email protected]. I am

thankful for helpful discussions with Giovanni Peri, Hilary Hoynes, Chad Sparber, Brian Cadena, David Sjoquist, Ariel Weinberger, Yury Yatsynovich, Norman Matloff and seminar participants at UC Davis, the Western Economic International Association dissertation workshop, and the Southern Economics Annual Conference. This research was supported by the National Bureau of Economic Research Predoctoral Fellowship. This research was conducted using confidential data from the Institute of International Education (IIE). Special thanks to Christine Farrugia and Dr. Rajika Bandhari of IIE for providing access to data. This research does not reflect the views of IIE and all errors are the authors own.

Electronic copy available at: http://ssrn.com/abstract=2832996

1 Introduction

US graduate education has sustained a remarkable internationalization. Non-

citizens on temporary student visas, commonly referred to as international or foreign

students, grew from 130,000 in 1970 to 720,000 in 2010, even outpacing immigration

which grew four-fold over this period.1 Currently, 15% of all graduate students and 1-

in-3 degree recipients in STEM (Science, Technology, Engineering, and Mathematics)

fields hail from overseas (NSF [2013]). While many factors have been linked to this

rise, such as global acclaim for US universities and less restrictive student visa policies,

much less is understood about how it has affected domestic students.

This paper examines whether international students impact the enrollment of

domestic (native-born and permanent resident) students in graduate programs. While

internationalization has occured at other academic levels (e.g. Hoxby [1998], Betts

[1998], Hunt [2012]), graduate education has continually received disproportionate

numbers of foreign students. In many graduate STEM fields, and even some non-

STEM fields like economics, they comprise over 50% of all enrollment (Bound, Turner,

& Walsh [2009], Freeman [2010]).

High attrition rates have also drawn attention toward graduate education. Recent

statistics revealed that only 50-60% of Ph.D. students graduate (Sowell [2008]). Wan-

ing interest in STEM fields has also magnified concerns over the size of the innovative

workforce, a statistic frequently linked to economic growth (e.g. Romer [1990], Jones

[2002]). Changes to domestic enrollment due to international student entry is espe-

cially relevant as immigration policy tightly restricts the number of individuals who

1International student figures come from http://www.iie.org/en/Research-and-Publications/ Open-Doors/Data/International-Students/Enrollment-Trends/1948-2015. Immigration figures come from http://www.census.gov/library/infographics/foreign born.html.

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can remain in the US after graduating.2 Distortions may therefore be particularly

pronounced if foreign students do not remain in the US to fill the gap.

Finally, debates over international migration in the US remain heavily focused on

labor market consequences. In rare instances when the education sector is consid-

ered, rhetoric often steers towards the impacts of foreign students on native workers.

Industry leaders argue that less restrictive employment pathways for foreign students

will solve skill shortages, while others counter that native workers would suffer. Curi-

ously, however, few ask how higher education and the outcomes of domestic students

fare, even though foreign students interact primarily within the confines of higher

education, and US policy places no caps on the number of student visas.

Equally compelling is that education has long been identified as an important

determinant of labor market success. Shocks to the composition or quantity of peers

have profound effects on individual achievement (e.g. Bound & Turner [2007], Carrell

et al. [2009]). Thus, understanding labor market impacts is not possible without

also elucidating effects on higher education. This paper complements the vast and

growing literature on the labor market effects of immigration by studying the impacts

on domestic students.

The few existing studies on graduate education report conflicting results. Panel

regressions from Borjas (2007) find foreign graduate students are not significantly cor-

related with overall domestic enrollment, though they appear to negatively correlate

with White male enrollment and positively correlate with enrollment of Blacks and

Asians. Regets (2007) uses a similar panel design and instead finds that foreign grad-

uate students positively correlate with domestic White enrollment, and negatively

2While there are no caps on the number of foreign students, there are strictly regulated caps on the entry of nearly all other types of foreign workers, making it very difficult for international students to secure employment in the US. Finn (2003) estimates that roughly 1/3rd of foreign doctoral recipients leave the US within 2 years from receiving their degree.

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correlate with domestic Asian enrollment. In doctoral programs, Zhang (2009) shows

that foreign students appear to raise native enrollment in STEM, and lower native

enrollment in non-STEM. Bound, Turner, & Walsh (2009) illustrate that the number

of native-born doctoral physics students actually grew following the large-scale ma-

triculation of Chinese students after the renormalization of relations with China in

1979.

Several studies have analyzed foreign presence at other academic levels, also with

equally conflicting findings. At the high school level, Betts (1998) finds that immi-

gration is associated with lower high school completion for American-born Blacks

and Hispanics. In contrast, Hunt (2012) finds net positive effects on high school

completion, which comprise of negative impacts from immigrant children and posi-

tive impacts from less-skilled immigrant workers. At the undergraduate level, Hoxby

(1998) finds foreign students displace minorities from undergraduate education. Dif-

ferently, Jackson (2015) finds immigrant college students do not displace natives from

undergraduate education, while immigrant workers appear to increase native college

attainment.

This study contributes to existing literature both theoretically and empirically.

With regards to theory, little intuition has been provided. Negative correlations

between foreign and domestic enrollment are often interpreted as crowding-out due

to competition over a fixed number of seats. Studies that report positive effects

usually fail to offer intuition for why foreign students may actually expand domestic

enrollment. Importantly, I develop a simple model in which negative (crowd-out) and

positive (expansionary/crowd-in) effects are both possible outcomes. In the model,

expansionary effects occur if foreign students pay sufficiently high tuition that cross-

subsidizes additional seats for domestic students. If foreign students do not sufficiently

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contribute to university resources, the number of seats remains fixed and domestic

students are crowded-out.

After clarifying the theory, this paper enhances empirical identification on the

impacts of international students. While conflicting results from existing studies may

reflect differences in data, time periods of analysis, or specification, more worrisome

is if such differences arise from endogeneity bias. Prior graduate-level studies have

adopted panel fixed-effects specifications (e.g. Borjas 2007, Regets 2007, Zhang 2009)

to account for unobserved time-invariant factors, such as university quality or shocks

to state funding for higher education, which may impact domestic and foreign students

alike. However, panel specifications fail to account for confounding factors that vary

within universities over time.

This paper improves empirical identification by focusing on a unique quasi-experiment–

an unprecedented boom and bust cycle in foreign graduate enrollment at Research

universities. From 1995-2001 foreign graduate enrollment grew by 50%–a tremendous

figure considering the mild 8% growth from 1990-1995. Suddenly, foreign enrollment

fell by roughly 2.5% between 2002 and 2005. While the decline was much smaller in

comparison to the late-90s boom, it marked the first time in three decades and only

the second occurrence since the 1950s that the US saw decreases in the number of

foreign students (Chin [2005]).

Crucially, this episode was fueled by supply shocks unrelated to other factors

affecting US graduate education. Specifically, rising populations of college-age (18-

30) individuals in foreign nations helped sustain the boom, as the growing supply

of students spilled overseas. The terrorist attacks of 9/11, and subsequent discovery

that several hijackers exploited student visas, led to more restrictive student visa

processing, thereby reducing access to US universities (GAO 2005; Freeman 2010).

4

My empirical strategy leverages these supply shocks as quasi-experiments to de-

velop instruments for actual changes in foreign enrollment within universities. The

instruments are formed by interacting these supply shocks with each university’s his-

torical presence of foreign graduate students. Instrumental variable regressions on

university panel data, help address any lingering endogeneity bias not contained by

fixed-effects.

In addition, I utilize a demanding panel specification that accounts not only for

time-invariant university factors, but also for university-specific factors that grow

linearly over time. Further, this paper is the first to explore two different sources

of variation–increases in foreign enrollment over the boom, and decreases during the

bust.

I find that increases in foreign graduate students expand domestic enrollment.

Point estimates are statistically significant for the boom and suggest each additional

international student leads to an additional domestic student. Domestic enrollment

on average is much larger and more variable, and thus standardized coefficients in-

dicate a 1 standard deviation increase in foreign enrollment raises native enrollment

by 0.17 standard deviations. For the bust, point estimates are also positive, but

rarely statistically different from 0. These results indicate non-symmetric responses

to increases and decreases in international students.

The findings are supported by the insights of the simple model, which reveals that

crowd-in can occur if international student net tuition payments subsidize the cost of

enrolling more domestic students. Stratified analysis supports the model’s predictions,

showing crowd-in to be present in public universities where foreign tuition rates are

2-3 times higher than domestic residents. Private universities, which do not advertise

separate tuition rates for foreign and domestic students, show little impact–foreign

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students do not appear to either crowd-out or expand domestic enrollment.

Finally, I find evidence of cross-subsidization behavior that both reveals a key

mechanism behind the crowd-in effects during the boom, and reconciles the lack of

effects for the bust. Increases in foreign students do not raise the number of foreign

Teaching or Research Assistants (TAs/RAs), but do raise the number of domestic TAs

and RAs. Hence, foreign student tuition payments help create TA and RA positions

for domestic students. In contrast, decreases in international students do not affect the

number of domestic TAs and RAs, but do lead to fewer international TAs and RAs.

When foreign enrollment declines universities countervail losses in tuition revenue

by reducing funding opportunities for existing foreign TAs and RAs. This prevents

reductions in domestic student subsidies, and preserves domestic enrollment.

The next section introduces the simple theoretical model. Section 3 discusses

the boom and bust in further detail, describes the data, and details the instrumental

variable strategy. Section 4 presents the main results. Section 5 examines the validity

of the instruments, and performs various robustness checks. Section 6 confirms the

model’s insights and reconciles the findings. Section 7 concludes.

2 Theory on Crowding-out and Expansionary Ef-

fects in Universities

Prior work has provided little theoretical intuition on the impacts of international

graduate students on domestic enrollment. Negative correlations between domestic

and foreign enrollment are often justified by assuming an inelastic number of seats.

Hence, greater competition from abroad necessarily crowds-out domestic students.

Positive correlations are usually interpreted as evidence against crowd-out, and little

is discussed about how foreign students may actually increase domestic enrollment.

6

In practice, however, three stylized facts motivate closer scrutiny at theory. First,

many universities in the US charge different tuition to foreign and domestic students.

Public universities advertise out-of-state (sticker price) tuition rates that are 2-3 times

higher than what domestic in-state residents pay (figure 1). While private universities

do not advertise different tuition rates, foreign and domestic students may still end

up paying different net tuition rates.

Second, while graduate students do compete for seats as consumers, they are also

inputs to higher education (Rothschild & White [1995]). Universities may provide

substantial subsidies to graduate students, often in the form of fellowships or paid

positions as Teaching or Research Assistants. Sometimes, these subsidies are accom-

panied by tuition remission, leading to actual net tuition payments that can be 0 or

even negative. Failing to consider graduate students as both consumers and inputs

can lead to misleading conclusions.

Third, US universities are complex non-profit organizations. Research on non-

profit behavior characterizes such institutions as optimizing the preferences (or ob-

jectives) of their board of trustees, president, administrators, or some amalgamation

of these interest groups (James [1978], Winston [1999]). Unlike profit maximizing

firms, they face a non-distribution constraint (Hansmann [1980])–any excess of rev-

enue above costs cannot be distributed as profit. While in aggregate, total revenues

must equate total costs, universities are multi-product organizations and may take

on profit-generating activities to cover more important loss-generating activities.

With these facts in mind I build from basic theory of the non-profit organization

and adapt a model of university production from James (1978) to understand the

impact of international students. I examine the behavior of a non-profit university

assuming two general objectives–to educate students and to provide high quality

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education.

2.1 Model

Consider a non-profit university that aims to maximize the utility function of its

board of trustees, given as,

U(D,F,q)

D denote domestic graduate enrollment and F denotes foreign enrollment. Assume

US universities have preferences for educating domestic students ( ∂U ∂D

> 0), and for

offering higher quality education (∂U ∂q > 0), where quality is measured in expenditures

per student, q = C D+F

. US universities may have preferences for educating foreign

students, although they may not be as strong as those for educating domestic stu-

dents. Alternatively, universities may have no preference or even receive disutility

from educating foreign students. Therefore, I allow ∂U ∂F

R 0.

Universities generate revenue by charging domestic and international students

tuition prices, tD and tF , respectively, and receive fixed revenue from government

funds and/or endowment payouts (FR). Tuition rates and fixed revenue are taken

as constant and exogenously given.3 At the same time, because graduate students

can and are often used as productive inputs, universities may offer funding in the

form of fellowhips, or RA/TA positions, which increase their total expenditures C.

Universities choose D, F , and total expenditures C to maximize U(D,F,q) subject

3While tuition rates evolve over the long run, they are generally sticky in the short run. Univer- sities do not lower tuition prices within an academic year upon realizing that extra seats remain.

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to the non-profit constraint,

C − tDD − tFF − FR = 0

With E = D + F , the first-order conditions are:

UD − Uq ( C

E2

) + λtD = 0 (1)

UF − Uq ( C

E2

) + λtF = 0 (2)

Uq

( 1

E

) − λ = 0 (3)

The first-order conditions reveal intuitively how universities trade-off admitting more

students against quality. For example, equation 1 shows that at the optimum, the

marginal utility from increasing domestic enrollment plus marginal tuition revenue

must equate marginal disutility from lower quality.

How would domestic enrollment change after an exogenous shock to foreign stu-

dent supply, holding all else constant? This can be understood by substituting equa-

tion 3 in 1 and 2, and using the implicit function theorem, which yields:

∂D

∂F = −

UF UD

= − tF − CE tD − CE

(4)

Equation 4 is particularly enlightening. Relative differences in tuition payments

and average costs (i.e. relative net tuition) determine the direction of the impact.

Assuming domestic students on average receive a positive net subsidy (tD − CE < 0),

crowd-out will occur if foreign net tuition is negative (tF − CE < 0). If foreign student

tuition exactly covers their cost, domestic enrollment will not change. If marginal

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revenue from foreign students exceeds the average per student cost, then the extra

revenue can be used provide subsidies to more domestic students, hence leading to

crowd-in. Note that if per student costs exactly equal the average of foreign and

domestic tuition (C E

= tF +tD 2

), the model predicts a 1-for-1 crowd-in effect–the revenue

from an international student provides a subsidy for an additional domestic student.4

2.2 Model Predictions

Before turning to the empirical analysis, some summary statistics on graduate

tuition rates help inform the model. Figure 1 shows in-state and out-of-state tuition

rates at public universities, and tuition at private universities. Public universities

charge foreign students an amount that is on average 2-3 times what domestic res-

idents pay.5 Private universities have much higher sticker price tuition than pub-

lic universities, but do not have separate rates for domestic and foreign students.

Nonetheless, crowd-in can still occur if domestic students receive net subsidies in

the form of fellowships, or RA/TA positions, while foreign students pay tuition that

exceeds their average costs.

Figure 2 shows that in 1995 only 34% of foreign graduate students reported their

primary source of funds as coming from university support (which includes TA and RA

positions), while 66% report outside sources–most of which come from personal/family

funds. Thus, while data on average graduate student costs are not available, the

evidence on tuition rates and primary source of funds suggest that foreign student

net tuition is plausibly positive–the average foreign student pays a high amount and

is not primarily supported by university funding.

4This simple partial equilibrium model ignores the domestic student supply side. In particular social interactions may occur between foreign and domestic students that may affect domestic supply. For example, domestic students may gain from or value diversity brought by foreign peers.

5Because many states allow domestic out-of-state students to claim in-state residency, in-state tuition is the more relevant price for domestic students.

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Finally, if cross-subsidization, and hence crowd-in, were to occur, 4 implies that

foreign students provide negative marginal utility while domestic students provide

positive marginal utility. These preferences are reasonable for public universities,

who are accountable to constituents of their state. It is less clear whether private

universities exhibit such preferences.

This simple model has some interesting implications. First, exogenous increases

in international enrollment can in fact expand domestic enrollment. Second, such

crowd-in arises when foreign students pay positive net tuition, which then provides

more net subsidies to domestic students. Lastly, data on tuition rates and the nature

of the university objectives suggest crowd-in is likely to occur at public universities,

while the direction of impact is less clear for private universities. The remainder of

the paper evaluates these insights empirically.

3 Methodology & Data

In the absence of random assignment, estimating the impact of international stu-

dents on domestic enrollment is challenging. To overcome endogeneity concerns, I

exploit a particularly volatile decade between 1995 and 2005 (figure 3A). During this

decade the percentage of foreign graduate students climbed nearly 3 percentage points

before falling by more than 1 percentage point after 2002 (figure 3B).

3.1 The Boom and Bust of 1995-2005

Stagnant foreign enrollment in the early-1990s generated uncertainty over whether

US universities would remain leaders in attracting students from around the world.6

6For example, the 11/23/1995 NY Times article, “Fewer Foreigners Choosing US Colleges” ex- pressed concern that increased competition from other nations would lower foreign enrollments in the US. See http://www.nytimes.com/1995/11/24/us/fewer-foreigners-are-choosing-us-colleges.html.

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Few signs hinted at the surge in international students that was to come. Unex-

pectedly, foreign enrollment began growing rapidly from 1995 through the turn of

the millennium. In 2002 this surge abruptly came to a halt, and foreign enrollment

declined in the following years.

Interestingly, graduate programs at Research universities sustained most of the

boom and bust. Figure 4 plots foreign enrollment from 1995-2005 by academic level

and by institution type according to the 2000 Carnegie Classification.7 Graduate en-

rollment at Masters institutions, and undergraduate enrollment at all institutions also

saw similar fluctuations, but on a far smaller scale. Importantly, this episode provides

unprecedented and dramatic variation most suited to identify the effects of foreign

students on domestic enrollment in graduate programs at Research universities.

Importantly, two key factors during this period helped fuel the boom and bust

cycle, while remaining exogenous to US graduate education. Through the 1990s,

many sending nations saw expansions in the number of college-age individuals and

improvements in their post-secondary education systems (Bound, turner & Walsh

[2009]). Prior studies have shown such expansions strongly predicted the volume of

foreign students coming to the US, as the extra supply spilled overseas (e.g. Bird &

Turner [2014], Shih [2016]). Importantly, changes to the college age (18-30 year old)

population in foreign nations was plausibly unrelated to other factors affecting US

graduate programs.

The 9/11 attacks and later discovery that terrorists exploited student visas cre-

ated a sudden shock that limited foreign student entry. The enactment of policies

in late 2001 and early 2002 increased the intensity of screening student visa appli-

7Baccalaureate institutions have award least 10% of all degrees as Bachelor’s degrees. Masters institutions award at least 50 masters degrees, but less than 20 doctorates. Research institutions award at least 20 doctorates each year. See http://carnegieclassifications.iu.edu.

12

cants, generating lengthy wait-times (Wasem [2003]; GAO [2005]). Additionally, the

mandatory implementation of the Student Exchange and Visitors Information Ser-

vice (SEVIS)–a new digitized system to monitor foreign students–across colleges and

universities in 2003 was rife with glitches that led to further delays. These issues were

short-lived–SEVIS errors and visa processing delays were cleared up by 2005, after

which graduate enrollment from abroad continued its upward climb (Alberts [2007],

Freeman [2010]).

A final observation about this episode is that while their numbers changed dra-

matically, the composition of foreign students remained stable. Figure 5 examines

the share of international students across five fields of study (panel A), and across

origin countries (panel B). Importantly, the composition across fields of study was rel-

atively unchanged, with 40-50% of all foreign graduate students in STEM disciplines

throughout the boom and bust. Additionally, the boom and bust did not appear to

be driven by any single foreign country. The composition across countries remained

stable, with 40-50% hailing from Asia, and much smaller shares held by Europe, the

Americas, the Middle East and Africa.

Foreign college-age population growth and 9/11 security policies contributed to

the boom and bust cycle, while remaining unrelated to other factors affecting domes-

tic students. These supply shocks propagated across Research universities, providing

a quasi-experiment to analyze whether foreign graduate students affect domestic en-

rollment. The next section describes the main empirical design to provide context for

how these supply shocks are leveraged for identification.

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3.2 Empirical Design

I estimate the impact of international students on domestic graduate enrollment

with the following specification:

∆Dut Eut−1

= α + β ∆Fut Eut−1

+ γu + γt + εut (5)

The dependent variable in 5 captures variation in domestic graduate enrollment,

taking first-differences (∆Dut = Dut − Dut−1) and dividing by total graduate enroll-

ment in the initial year (Eut−1). Foreign enrollment (Fut) is transformed in the same

manner. First-differencing effectively removes the influence of fixed university char-

acteristics. Standardizing by total graduate enrollment in the initial year prevents

inherent specification bias from scale effects (Peri & Sparber [2011]). If β > 0, each

international student increases domestic enrollment (crowd-in). If β < 0, then foreign

students crowd-out domestic students. β = 0 corresponds to no effect. Finally, since

the outcome and key explanatory variable are simple transformations of enrollment

levels, the key coefficient β can also be interpreted in numbers of students.

Including additional university fixed effects (γu) controls for unobserved charac-

teristics that grow linearly within universities. Time-period dummies (γt) account

for changes in aggregate conditions that affect all universities equally. Hence, identi-

fication in 5 relies changes in changes of foreign graduate enrollment within univer-

sities. Lastly, εut is a zero-mean error term. The analysis estimates 5 for the boom

(t = 1995-2001) and bust (t = 2002-2005), separately, to distinguish increases and

decreases in foreign students.

While 5 controls for a wider array of potential factors, unobserved university-

specific factors that evolve non-linearly remain a concern. To correct these remaining

14

issues I develop novel instruments from supply shocks that exogenously altered inter-

national graduate enrollment in the US.

3.3 IV Strategy

College-age population growth in countries around the world generated supply

spillovers of international students to US universities. Security measures after 9/11

restricted student visa issuance, which lowered international graduate enrollment.

Importantly, expansions in college age populations of foreign nations and the security

policies that restricted visa issuance were likely unrelated to other factors affecting

US graduate education.

These supply shocks are transformed into instruments by interacting them with

the historical presence of foreign graduate students at universities, similar to the clas-

sic “shift share” approach used to estimate the labor market impacts of immigration

(e.g. Altonji & Card [1991]; Card [2001]). Predictive power derives from the no-

tion that a university’s historical familiarity with foreign students generates strong

networks (Bound, Turner, & Walsh [2009]; Beine, Noël & Ragot [2014]). Within

such networks, previous foreign students return home and inform younger cohorts of

their graduate school experience, building brand recognition. Future supply shocks

disproportionately affect those institutions that have strong networks.

Prior graduate enrollment proxies for network strength. Since networks operate

more strongly among students from the same country, I use historical graduate en-

rollment by country of origin at each university to enhance power. The instruments

are constructed by propagating these supply-shocks across universities with varying

intensity, based on each university’s historical stock of foreign graduate students.

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Specifically,

F̂ut =

 

∑ c F̂

pop cut =

∑ c Fcul ∗ g

pop ct =

∑ c Fcul ∗

( popct popcl

) if t ≤ 2001

∑ c F̂

9/11 cut =

∑ c Fcul ∗ g

pop c2001 ∗ g

9/11 ct =

∑ c F̂

pop cu2001 ∗

( visact

visac2001

) if t ≥ 2002

(6)

For each country, lagged foreign graduate enrollment at a university (Fcul) is multi-

plied by the college-age population growth factor (g pop ct =

popct popcl

). For the years during

the bust period, aggregate reductions in student visa issuance by country since 2001

(g 9/11 ct =

visact visac2001

) are used instead. Summing across countries yields a prediction of

total international enrollment in a given year, F̂ut.

Recall the key explanatory variable in 5 specifies foreign graduate enrollment in

first-differences standardized by total graduate enrollment. Thus, the instruments are

formed similarly by taking first-differences in predicted foreign graduate enrollment

and standardizing by total graduate enrollment in the initial period8:

∆F̂ut

Êut−1 = F̂ut − F̂ut−1 Êut−1

(7)

3.4 Data for Instruments

Data on historical foreign enrollment by country for each university comes from

restricted-use surveys from the Institute of International Education (IIE). Specifi-

cally, I utilize the International Student Census surveys which IIE conducts each year

8To avoid introducing endogeneity in the instruments when standardizing, I predict domestic enrollment in a similar manner (D̂ut = Dul ∗ g

pop usa,t), interacting historical domestic graduate enroll-

ment with college-age population growth in the US. The denominator is the sum of the foreign and domestic predictions (Êut−1 = F̂ut−1 + D̂ut−1).

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and uses to publish its annual “Open Doors” reports. The earliest available foreign

enrollment counts come from Fall 1993.

To reduce dimensionality countries are collapsed into 17 nationality groups based

on ethnic/regional similarity. The top 10 countries that send international students to

the US (China, India, South Korea, Japan, Thailand, Indonesia, Germany, Canada,

Mexico, and Turkey) are each their own nationality group. The remaining countries

are aggregated into 7 nationality groups: Rest of Asia, Rest of Americas, Middle

East/North Africa, Eastern Europe, Western Europe, Africa, and Oceania.

College-age population counts by country come from the UNESCO Institute of

Statistics. Data on student visa issuance by country comes from the Department

of State Non-immigrant Visa Statistics.9 Because visas are issued while students

are abroad and before they arrive on campus, issuances are a more exogenous and

cleaner measure of policy impacts than actual enrollment.10 I utilize the primary

class of students visas, the F-1 visa, though other classes exist, such as the J-visa for

cultural exchange and M-visa for border commuters. Visa issuances represent flows

rather than stocks, but the instrument relies on shocks to total foreign enrollment.

Therefore, I develop a stock measure of the total number of F-1 visas in each year

by first aggregating visa issuances to the 17 nationality groups, and then cumulating

F-1 visas issued to each nationality over the prior 3 years.11

9Data from UNESCO were retrived from http://data.uis.unesco.org/. Non-immigrant visa statis- tics from the State Department were retrieved from https://travel.state.gov/content/visas/en/law- and-policy/statistics/non-immigrant-visas.html.

10For example, though the policy restricted entry, actual enrollment would also reflect students who were issued visas but decided not to enroll and students who weren’t issued visas but found ways to enroll anyways. Fluctuations in these two groups of foreign students may be endogenously related to other factors changing in US graduate education.

11Thus, visact in 6 is computed as visact = visa i ct + visa

i ct−1 + visa

i ct−2 + visa

i ct−3. The idea in

this exercise is that visact approximates the total stock of student visa holders in year t, as students issued new student visas in years t − 1, t − 2, and t − 3 are likely still continuing their education in year t.

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3.5 Data for Analysis

Data on domestic and foreign enrollment by university during the boom and bust

period (1995-2005) come from the Integrated Postsecondary Education Data System

(IPEDS). Enrollment counts report the number of degree-seeking students by aca-

demic level during the fall of each academic year. IPEDS identifies international

students via separate enrollment counts for “non-residents”, defined as persons who

are not a citizen or national of the United States and who are in the country on a

temporary visa and do not have the right to remain indefinitely. IPEDS’ “resident”

counts measure domestic enrollment, which include natives and permanent residents.

The analysis centers on US Research universities, identified by the Carnegie Clas-

sification. Revisions of this classification, which categorizes institutions based on the

number of degrees awarded in a reference year, occur routinely. Thus, the analysis

focuses on a time-consistent group of Research universities defined as all institutions

that are ever classified as a Research institution in the 1994, 2000, 2005, or 2010

Carnegie classifications.

Constructing the main sample for analysis requires identifying Research universi-

ties consistently available in the IPEDS 1995-2005 surveys, and in the IIE 1993 survey.

To mitigate measurement error, I remove universities that ever had data imputed by

survey administrators, and records that appear to be extreme outliers/errors.12 The

resulting sample consists of a panel of 193 research universities.

Excluding imputed records in IPEDS removes a large number from the panel (65).

Thus, results are also presented from a larger sample of 258 institutions that includes

imputations. Conducting analysis on the larger sample also requires imputation of

12Outliers are institutions reporting changes in foreign enrollment outside the 1st-99th percentile in the sample. For example, a prominent public university in Colorado reported roughly 500 foreign students in 1998, 0 in 1999, and 600 in 2000.

18

graduate enrollment by country of origin in 1993, as some of these additional univer-

sities are also missing in the IIE data.13

Table I displays summary statistics, measured in 1995, for non-Research universi-

ties (left panel), and the main sample of Research universities (right panel). Compar-

ing the two panels reveals Research institutions were much larger than non-Research

schools on average, both in terms of undergraduate and graduate enrollment. While

nearly identical in the percentage of foreign undergraduates, the average percentage

of foreign graduate students at Research universities (12%) was double that of non-

Research institutions (6%). Additionally, Research universities had a much larger

focus on graduate education, awarding over 10 times the average number graduate

degrees conferred at non-Research institutions.

The main sample of Research universities comprised a large bulk of US graduate

education, awarding 42% of all professional degrees, 47% of masters degrees, and 70%

of Ph.D. degrees. They educated 61% of all foreign graduate students, and nearly half

of all graduate students. The majority of the sample universities are public (63%),

span the 50 states, and include a wide diversity of schools, from elite ivy-league

institutions to prestigious public flagship schools to smaller private universities.

3.6 First Stage Power

For valid inference the instruments must strongly predict actual changes in foreign

enrollment. I examine first stage power, separately for the boom (1995-2001) and bust

13The basic imputation procedure interacts the share of all international students from that coun- try (measured for the state in which the university is located) with each university’s total foreign graduate enrollment in 1993. Further details are available in section A.1 of the appendix.

19

(2002-2005), using the following specification14:

∆Fut Eut−1

= α + βfs ∆F̂ut

Êut−1 + γu + γt + �ut (8)

Specification 8 regresses actual foreign graduate enrollment flows on the instrument,

and controls for university fixed effects and year effects. The instrument is based on

college-age population growth for the boom, and on 9/11 policy-induced declines in

student visa issuance for the bust.

Table II presents first stage results. Regressions are weighted, unless otherwise

specified, by total graduate enrollment in the initial year to correct for heteroskedas-

ticity induced by the standardization of first-differences (Solon, Haider, & Wooldridge

[2015]). Standard errors are clustered at the university level to account for within-

university correlation in residuals. The top panel shows results for the boom, while

the bottom panel displays results for the bust.

Column 1 uses the main sample to estimate 8. Results show that the college-age

population- and 9/11-based instruments are good predictors of actual foreign student

growth over the boom and declines over the bust, respectively. F-statistics of 38.42

for the boom and 16.47 for the bust exceed the recommended level of 10 to avoid

weak instrument bias (Staiger & Stock [1997]).

Column 2 displays unweighted results from the main sample. Comparing columns

1 and 2, weighting improves precision substantially for the bust while results are vir-

tually unaffected for the boom. Without weights the 9/11-based IV loses substantial

power (F-statistics fall by more than half) and is at-risk for weak instrument bias.

Subsequent analyses prefer weighting, as it yields strong first stage power without

14I drop the 2001-2002 period from the analysis because the enactment of policies in late 2001 and 2002 (Wasem [2003]) make it unclear whether this period should be assigned to the boom or bust.

20

substantially altering point estimates.

Columns 3 and 4 perform weighted and unweighted regressions, respectively, on

the larger sample that includes imputed data. While the increase in sample size

may actually raise precision, adding imputed data may generate attenuation bias

from measurement error. The results show that including imputed data results in

slightly more precise estimates. While, point estimates appear slightly smaller than

those without imputed data, the extent of attenuation bias is small. Nonetheless, to

remain conservative specifications without imputed data will be preferred.

The coefficient estimates of βfs range between 3.75-3.85 for the boom and 1.23-

2.08 for the bust. The magnitudes can be understood by considering the regression

line fit between the dependent variable (actual changes in foreign enrollment) and the

instrument (predicted changes). If the regression line coincided with the 45 degree

line, point estimates would equal 1, indicating actual foreign enrollment grew at

exactly rate the rate of college-age population in sending countries over the boom,

and fell at the rate of declines in student visa issuance during the bust. First stage

estimates show the regression line is steeper than the 45 degree line. Thus, actual

international enrollment, on average, grew faster within universities than they would

have if college-age population in sending countries and declines in aggregate student

visa issuance were the only contributing factors.

Overall, the instruments are strong predictors of actual international graduate

enrollment. Weighting is important to achieve sufficient power, particularly for the

bust period. First-stage analysis also demonstrated that removing imputed data to

guard against measurement error does not generate sample selection bias–results are

similar to specifications that include imputations. The next section presents the main

results on whether foreign students affect domestic enrollment in graduate programs.

21

4 The Impact of International Students on Domes-

tic Enrollment

To assess whether international students affect domestic enrollment, I estimate

two-stage least squares (2SLS) regressions of 5, separately for the boom and bust.

The instrument for the boom period is based on college-age population growth, and

on post- 9/11 declines in student visa issuance for the bust. All specifications include

university fixed effects and time-period dummies. Standard errors are clustered at

the university level.

Table III presents results from 2SLS regressions of 5. The top and bottom pan-

els report coefficients and standard errors, for the boom and bust, respectively. F-

statistics from the first stage are reprinted for reference. Columns 1 and 2 present

weighted and unweighted results, respectively, using the main sample, and columns 3

and 4 do the same for the larger sample that includes imputations. Column 5 presents

OLS results.

2SLS point estimates for the boom are all positive and statistically significant at

the 5% level, indicating that foreign students do not crowd-out, but rather expand

domestic enrollment. These empirical results are supported by the simple model pre-

diction that demonstrated that crowd-in is possible, and occurs when foreign students

effectively cross-subsidize domestic students.

The magnitude of the point estimates fall between 1.30-2.14. None are statistically

different from 1, and hence they can be interpreted as revealing a 1 percentage-point

increase in foreign enrollment as a share of total enrollment leads to a 1-percentage-

point increase in domestic enrollment as a share of total enrollment. Because the

outcome and key explanatory variable are simple transformations of enrollment lev-

22

els, point estimates also reveal that within universities each additional foreign student

raises domestic enrollment by 1. Succinctly, foreign students expand domestic enroll-

ment 1-for-1.

There are three important factors to consider when assessing these magnitudes.

First, 1-for-1 crowd-in is entirely within the realm of feasible predictions from the

model. Specifically, the model predicts 1-for-1 crowd-in if the costs per student are

exactly equal to the midpoint between domestic and foreign tuition rates. Second,

domestic enrollment flows within universities are larger and more variable than for-

eign enrollment flows. Standardizing the coefficients indicate a 1 standard deviation

increase in foreign enrollment increases domestic enrollment by roughly 0.17 stan-

dard deviations. Finally, standard confidence intervals do not rule out much smaller

effects.

The bottom panel of table III shows results for the bust period. Interestingly,

while coefficients for the bust are also positive, they are seldom distinguishable from

0. These results indicate very little or no response to decreasing international enroll-

ment. Thus, while increases in international students generate expansions in domestic

enrollment, decreases appear to have little impact. Quite interestingly, there appears

to be an asymmetric response to changes in international enrollment.

Finally, column 5 presents OLS estimates corresponding to the main specification

in column 1. Notice OLS estimates–0.42 for the boom and 0.58 for the bust–are

also positive, but smaller in magnitude than their 2SLS counterparts. The increase

in point estimates when instrumenting is inconsistent with the notion of endogeneity

bias due to factors that attract domestic and foreign students alike, such as university

quality. Instead, the IVs appear to account for endogenous factors that have opposing

23

effects on foreign and domestic enrollment.15

Overall the analysis revealed three interesting findings. First, increases in inter-

national students do not crowd-out domestic students, but rather expand domestic

enrollment. Second, the magnitudes suggest a 1-for-1 crowd-in effect, which is a fea-

sible prediction of the model. Third, the impacts of international students are not

symmetric–decreases in international enrollment have no significant effect.

While clarifying and reconciling these results is important, bolstering the validity

of the IV strategy is crucial. The next section closely examines the IV strategy and

demonstrates the robustness of the main findings to various checks.

5 Instrument Validity & Robustness

Section 3.6 demonstrated the instruments have strong first stage power. Addi-

tionally, the instruments must not violate the exclusion restriction–they must em-

body supply shocks that only affect actual international enrollment, while remaining

unrelated to any other determinants of domestic enrollment. Because 2SLS regres-

sions are just-identified, it is not possible to directly test the exclusion restriction.

Nevertheless several checks rule out issues of first order concern.

To clarify how the exclusion restriction applies in this setting, recall that the in-

struments are derived from interacting two separate pieces–a university’s historical

foreign graduate enrollment by nationality, and the supply shocks to each national-

ity group. Each piece must be unrelated to other factors that also affect domestic

enrollment.

Using historical foreign enrollment in 1993 raises concerns due to its proximity

15An example would be if foreign enrollment is correlated with the hiring of foreign faculty, which may repel domestic students that have preferences for native faculty.

24

to the period under study. Recall specification 5 accounts for early factors that are

time-invariant or that persist at linear rates. However, initial factors whose impact on

future domestic enrollment evolves non-linearly may confound the IV strategy. For

example, the exclusion restriction would be violated if university prestige in 1993 had

effects on future enrollment decisions that evolved non-linearly.

A classic solution is to use longer lags. Lacking earlier data, however I provide

an alternative check to assuage these concerns. Specifically, I construct a falsified

instrument, that instead interacts foreign undergraduate enrollment in 1993 with the

supply shocks. Then first stage analysis is repeated with this falsified instrument to

check whether it can predict actual foreign graduate enrollment.

The intuition of this check stems from the notion that the predictive power of the

instrument may actually come from two sources. First, historical graduate enrollment

measures network strength–a good indicator of whether a university can attract future

foreign graduate students. Second, historical enrollment also reflects initial university-

specific features. If such features, such as quality or prestige, endogenously influence

future foreign enrollment, they too will contribute to the instrument’s predictive

power.

The aforementioned check attempts to disentangle these two sources of predictive

power. Constructing a falsified instrument using historical undergraduate, rather

than graduate, enrollment reduces predictive power coming from graduate student

networks, while preserving initial university features that generate endogenous pre-

dictive power. Intuitively, networks carrying information about undergraduate educa-

tion are less useful for future graduate students. Empirically, strong foreign graduate

presence in 1993 did not necessarily imply large foreign undergraduate presence–the

correlation between foreign undergraduate and graduate enrollment in 1993 was only

25

0.23. If the falsified instrument still had power in predicting actual graduate enroll-

ment, there would be strong concern over whether endogenous initial factors confound

the IV strategy.

Row 1 of table IV performs this check using the main sample in columns 1 and 3,

and the sample with imputations in columns 2 and 4. All specifications are weighted

and first stage F-statistics appear in the adjoining column. Results reveal that the

falsified instruments have no power over the boom or bust. Thus, any endogenous

initial factors appear to be well captured by the first-differencing and university fixed-

effects.

The second piece of the instrument–the aggregate supply shocks–also raises con-

cerns. College-age population growth and 9/11-induced declines in student visa is-

suance may have simultaneously altered foreign undergraduate enrollment. Changes

to the undergraduate population, in turn, may alter the number of graduate students,

as universities often may require more graduate instructors or TAs.

Rows 2 and 3 of table IV assess this concern by replacing the dependent variable in

8 with the change in foreign or domestic undergraduate enrollment, respectively, stan-

dardized by total undergraduate enrollment in the initial year ( ∆X

ug ut

EUGut−1 =

XUGut −X UG ut−1

EUGut−1 ,

where X = D,F). Generally, the results show no significant correlation between the

instruments and undergraduate enrollment. The one exception is the small positive

correlation with foreign undergraduate enrollment during the boom, when using the

larger sample containing imputations (row 2, column 2).

To ensure the main findings are not contaminated by this slight positive corre-

lation, I perform a robustness check that controls for changes in foreign undergrad-

uate enrollment directly in 2SLS regressions. Including actual changes in foreign

undergraduate enrollment would risk introducing further endogeneity. Instead, row 4

26

includes the falsified instrument from row 1, constructed using historical foreign un-

dergraduate enrollments, as a control. Reassuringly, the results are nearly identical

to the main findings, reprinted for reference in the last row.

Another concern pertains to coincident shocks during the boom and bust. Most

notably the US sustained an expansion and subsequent contraction in the H-1B visa

cap on foreign skilled workers (figure 6A), a dramatic spike and fall in the stock prices

of internet-based firm known as the “Dot-Com” boom and bust (figure 6B), and

rapid increases in federal funding to higher education (figure 6C). These factors are

especially worrisome if they contributed to the boom and bust, and the instruments

fail to abstract from their influence.

To examine the sensitivity of the results, I develop control variables for these phe-

nomena.16 Prior work by Kato & Sparber (2013) and Shih (2016) has shown foreign

students are indeed quite sensitive to changes in H-1B visa policy. Thus, to control

for the influence of H-1B policy, I construct a control variable from interactions of

historical foreign graduate enrollment by nationality with nationality-specific growth

in H-1B visa issuances. Summing across nationalities, taking first-differences, and fi-

nally standardizing by total graduate enrollment yields a variable that helps accounts

for the influence of H-1B policy.

The Dot-Com boom and bust dramatically altered the equity prices of many

internet firms. Prior literature has shown stock market fluctuations can impact higher

education through altering university endowments (Kantor & Whalley [2014], Brown

et al. [2014]). Therefore, to control for the influence of the Dot-Com boom and bust,

I interact historical university endowment per student values, measured in 1993, with

growth in the Nasdaq Composite Index. The yearly percentage change in predicted

16Detailed descriptions of these control variables and their data sources are provided in section A.2 of the appendix.

27

endowment per student is used as a control in 2SLS regressions.

Finally, a dramatic increase in federal research funding through the turn of the

millennium likely increased both foreign and domestic enrollment. I interact historical

levels of university research funding per student, measured in 1993, with aggregate

growth in federal R&D outlays to universities. Percentage changes in predicted re-

search funds per student are incorporated as controls in 2SLS.

Row 5 of table IV adds the control for H-1B policy, row 6 adds the control for the

Dot-Com boom and bust, and row 7 controls for federal R&D funding. Importantly,

the central findings remain robust. Point estimates remain positive and always sta-

tistically significant for the boom, while failing to be significant for the bust. Also

worth noting is that the first stage power remains strong when incorporating these

controls.

Table V provides some final robustness checks of the instruments and main results.

Row 1 ensures that the results are not driven by endogenous changes within a few large

universities. Specifically, I remove the 8 universities that are consistently ranked in

the top 10 in terms of international graduate enrollment in each year from 1995-2005.

Rows 2-5 check if the results simply reflect the performance of universities that

host large numbers of students from particular nations. For example, aggregate de-

clines in student visas issued to Indians could simply reflect declining quality among

universities that host large numbers of Indian students. Row 2 utilizes a similar in-

strument that eliminates the nationality dimension, simply interacting total foreign

graduate enrollment in 1993 with growth in the world’s college-age population and to-

tal 9/11-induced declines in student visas. Rows 3 and 4 reconstruct the instruments,

excluding the two largest foreign student groups–India and China, respectively. Fi-

nally, row 5 reconstructs the instruments, removing predominantly Muslim nations

28

to examine whether the post-9/11 declines were driven by the heightened attention

toward this group.

The results from table V provide a consistent message. During the boom, inter-

national students expand domestic enrollment. During the bust, the point-estimates

remain positive but are usually statistically insignificant.

Having established the robustness of the IV strategy, the next section explores

whether the crowd-in effects observed from the boom can be explained by cross-

subsidization, as predicted by the model from section 2. Additionally, I examine why

declines in international students appear to have little impact.

6 Cross-subsidization

The model from section 2 showed foreign students can expand (crowd-in) domestic

enrollment if they pay positive net tuition (foreign tuition payment > average cost

per student), thereby providing subsidies for additional domestic students (domestic

tuition payment < average cost per student). While data on graduate student costs

are not available, sticker price tuition rates suggest that crowd-in is likely at public

universities, where foreign students pay 2-3 times more than domestic residents. The

direction of the impact for private universities is less clear–they charge only one

sticker price rate, but may still receive different net tuition from domestic and foreign

students.

Table VI examines whether differences in the impact of international students

exist between public and private universities. The first two columns of each panel

regresses foreign inflows on domestic student enrollment, separately for public and

private universities. The left panel displays results for the boom, while the right panel

shows results for the bust. Each row corresponds to a slightly different specification:

29

row 1 displays 2SLS results for the main sample, while rows 2-5 add in the controls

for foreign undergraduate enrollment, H-1B policy, the Dot Com boom and bust,

and Federal R&D funding. Row 6 presents OLS results. The findings support the

model’s prediction–crowd-in appear active at public universities during the boom.

Point estimates during the bust, and for private universities in either period are

positive, but statistically insignificant.

The model’s predictions could be directly tested if data on cost per graduate

student were available from each university, to allow calculation of relative net tuition

(−tF −q tD−q

) from equation 4. Unfortunately, universities do not publicly release such costs

separately by academic level or by student nativity. A partial test can be performed,

however, by approximating relative net tuition using sticker price tuition rates and

per student costs calculated over the entire university. These proxies for relative net

tuition are constructed using data from the Delta Cost Project (Lenihan [2012]) on

average per-student costs and average sticker price tuition rates from 1990-1995. The

sample is then divided into those universities with high relative net tuition (above

the median), which are likely to experience crowd-in, and those with low relative net

tuition (below the median). 2SLS regressions of 5 are performed separately for high

and low relative net tuition universities in columns 3 and 4 of each panel in table VI.

The results support the notion of crowd-in due to cross subsidization. Nearly

all specifications on universities with high relative net tuition appear to have crowd-

in effects that are statistically different from zero at the 10% level. While point

estimates are positive, none of the specifications for low relative net tuition universities

are statistically different from zero. Additionally, coefficients remain statistically

indistinguishable from zero for the bust period.

These exercises help bridge the model predictions with the empirical findings and

30

support cross-subsidization as a key mechanism by which crowd-in effects operate.

However, proving the existence of cross-subsidization requires concrete evidence that

universities use foreign tuition payments to provide subsidies to domestic students.

The next section provides evidence of such behavior in practice that also reconciles

asymmetric effects of international students.

6.1 Cross-subsidization in practice

Actually observing universities redistribute foreign tuition as subsidies to domestic

students would reassure the estimated crowd-in effects. While no existing surveys

directly ask about this behavior, changes in the number of foreign and domestic

Research Assistant (RA) and Teaching Assistant (TA) positions allow us to observe

cross-subsidization in practice.

University expenditures on graduate students often comprise of salaries paid to

RAs and TAs. These positions are sometimes linked with tuition remission, such

students who secure RA or TA positions may receive positive subsidies to attend

graduate school. Thus, one way cross-subsidization may manifest is if revenue from

international students are used to provide RA or TA positions for domestic students.

In this case, exogenous increases in international students should raise the number of

such positions held by domestic students.

To empirically evaluate this behavior, table VII runs 2SLS regressions, replacing

the dependent variable with the change in foreign or domestic RAs and TAs, stan-

dardized by total graduate enrollment ( ∆XRAT Aut Eut−1

= XRAT Aut −X

RAT A ut−1

Eut−1 , where X = D,F).17

17The number of domestic and foreign students with TA or RA positions by university come from IPEDS. These data are available biennially during the boom and annually during the bust. Because they are available only biennially during the boom, I calculate growth rates over two years and annualize them. Lack of consistent responses to this survey, requires some imputations of the number of RAs and TAs. More details on the construction of the imputation and annualization procedures are available in section A.3 of the appendix.

31

The key independent variable and instruments are the same as before. Columns

1-5 represent different specifications, as controls are progressively added. The final

column displays OLS results.

The results are quite revealing. For the boom, increases in international students

are not associated with more foreign RAs and TAs. Thus, on average, the large

numbers of international students matriculating during the boom period were not

offered RA or TA positions. However, increases in international students are positively

and significantly related to the number of domestic RAs and TAs. Point-estimates fall

between 1.36-1.78, revealing that on average, each additional international student

created one additional domestic RA and TA position. These findings reaffirm the

crowd-in effects and reveal a strategic manner in which cross-subsidization occurs in

practice.

An interesting pattern emerges during the bust period which explains the lack of

effects. Declines in international students do not appear related to domestic RAs and

TAs. Instead, they are positive and significantly correlated with the number of foreign

RAs and TAs. The point estimates lie between 2.80-3.05, and suggest that the loss

of one international student leads to 2-3 fewer RA and TA positions held by foreign

students. Thus, as foreign enrollment declines, universities lose tuition revenue and

act to prevent domestic enrollment from shrinking by reducing the number of RA and

TA positions held by foreign students.

7 Conclusion

For decades, international students have maintained a large and growing presence

in US higher education. However, the effects of this internationalization are poorly

understood, and in particular, little is known regarding the consequences for domestic

32

students. This paper provides insight into these issues by assessing the impact of

foreign students on domestic enrollment in graduate education.

I focus on an unusual boom and bust in foreign graduate enrollment that took

place at Research universities over the 1995-2005 decade. Contributing to this episode

were exogenous supply shocks, that provide a means to empirical identification. Inter-

acting historical foreign graduate enrollment in 1993 with these supply shocks–growth

in the college-age population in sending countries during the boom, and declines in

student visa issuance after 9/11 during the bust–forms instruments to bolster causal

identification.

The results show that increases in foreign students expand domestic students. In-

terestingly, however, decreases in foreign enrollment have little impact on domestic

enrollment. A simple model of university behavior reveals that foreign students can

expand domestic enrollment if they cross-subsidize domestic students. Analyses fur-

ther support the model by finding such expansionary effects appear concentrated at

public universities, where foreign students pay 2-3 times the tuition rates of domestic

students.

Finally, I find concrete evidence of cross-subsidization behavior that also recon-

ciles the asymmetric impacts of international students. Increases in foreign students

are associated with greater numbers of domestic TAs and RAs, revealing universi-

ties use foreign tuition revenue to provide funded positions for additional domestic

students. Decreases in international students, however, do not lower the number of

domestic RAs and TAs. Instead, they reduce RA and TA positions held by foreign

students. Thus, when universities sustain exogenous declines in foreign enrollment,

they counterbalance the lost tuition revenue via reductions in foreign student TA and

RA.

33

These results contribute to research showing positive contributions of foreign grad-

uate students to innovation (Chelleraj, Maskus, & Mattoo [2008], Black & Stephan

[2010], Stuen, Mobarak, & Maskus [2012]). Given that international students do not

appear to displace domestic students from graduate education, their benefit to inno-

vation may come at little cost. Additionally, in the face of shrinking revenue sources,

policymakers may turn to foreign students to bolster resources for additional domestic

enrollment.

Importantly, however, these results speak to average effects. The impacts may

differ substantially across types of institutions, disciplines, or academic levels.18 For

example, some elite doctoral programs guarantee full-funding for all students, ren-

dering cross-subsidization infeasible. Additionally, different responses might occur

between Masters and Ph.D. programs. Future work with more detailed data would

help elucidate the heterogeneity across institutions, departments, and disciplines.

Finally, this research has focused exclusively on quantities. Understanding for-

eign student quality and its consequences for domestic peers is equally crucial. The

selection and quality of foreign students (Gaule & Piacentini [2013]) has important

implications for how social interactions ultimately affect domestic peers. Continued

research on the role of international students will help inform policy and expand our

understanding of globalization in higher education.

18For example, a recent working paper by Borjas et al. (2015) Chinese doctoral students led to lower research productivity of native Professors in Math departments. They argue this effect arises because Chinese students crowd-out natives that would-be productive RAs for native professors. Such crowd-out may occur in disciplines that do not receive positive net tuition from foreign students.

34

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36

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37

Table I: Summary Statistics of Research Universities, 1995

Academic Level Mean Std. Dev. Mean Std. Dev.

Undergraduates Total 1,570 2,617 12,093 8,086 International 4% 9% 3% 3% Domestic 94% 13% 93% 8%

Graduates Total 340 688 4,815 3,312 International 6% 12% 12% 8% Domestic 90% 19% 83% 11%

White 73% 26% 69% 13% Asian 4% 10% 4% 5% Minority 12% 19% 10% 9%

1st Prof. Degrees Total 15 54 169 204 International 5% 13% 2% 4% Domestic 93% 16% 96% 6%

Masters Degrees Total 69 167 971 744 International 8% 16% 14% 8% Domestic 88% 20% 82% 12%

Ph.D. Degrees Total 2 12 165 185 International 12% 22% 23% 14% Domestic 83% 27% 74% 15%

# of Universities Type

Public Private For Profit

Share of Total: International Graduates

Graduate Enrollment

1st Prof. Degrees Masters Degrees Ph.D. Degrees

38% 47% 10% 70%

40% 45%

43% 42%

7% 0%

20% 61%

18% 66% 74% 34%

Non-Research Research

2,448 193

Note: Statistics calculated from IPEDS 1995 Fall Enrollment, Completions, and Institutional Characteristics surveys. Non-research institutions include those that provide baccalaureate level education or higher, and are not classified as Research universities.

38

Table II: First Stage Power of the Instruments

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

Main Unweighted w/ Imputed Unweighted

Boom (1995-2001)

3.85*** 3.83*** 3.75*** 3.82*** (0.62) (0.62) (0.55) (0.55)

F-Statistic 38.42 38.26 46.55 48.87

N 1,158 1,158 1,548 1,548

Bust (2002-2005)

2.08*** 1.43** 1.94*** 1.23*** (0.51) (0.55) (0.42) (0.46)

F-Statistic 16.47 6.63 20.79 7.10

N 579 579 774 774

# of Universities 193 193 258 258

College Age Population IV

9/11-Based IV

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time-period dummies. Standard errors are clustered at the university level. Columns 1 and 3 weight regressions by total graduate enrollment in the initial year.

39

Table III: 2SLS Results for Domestic Enrollment

(1) (2) (3) (4) (5) Main Unweighted w/ Imputed Unweighted OLS

Boom (1995-2001)

1.80*** 2.14** 1.30** 1.71** 0.42** (0.67) (0.99) (0.59) (0.85) (0.17)

N 1,158 1,158 1,548 1,548 1,158

F-Statistic 38.45 38.29 46.58 48.90

Bust (2002-2005)

1.38 0.50 1.59* 1.09 0.58* (0.91) (1.42) (0.85) (1.52) (0.33)

N 579 579 774 774 579

F-Statistic 16.50 6.64 20.82 7.11

# of Universities 193 193 258 258 193

Int'l Graduate Enrollment

Int'l Graduate Enrollment

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time-period dummies. Standard errors are clustered at the university level. Columns 1 and 3 weight regressions by total graduate enrollment in the initial year.

40

Table IV: Instrument Validity

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

Model Specification Main F w/

Imputed F Main F

w/ Imputed

F

-2.07 -0.07 2.05 1.11 (2.42) (1.62) (1.88) (1.25)

0.40 0.44* 0.01 0.01 (0.30) (0.26) (0.16) (0.15)

3.17 1.25 0.79 0.10 1.53 0.81 1.49 1.20 (2.84) (2.44) (1.70) (1.36)

1.64*** 1.35** 1.17 1.27 (0.60) (0.55) (0.89) (0.80)

1.75** 1.15* 1.51* 1.75** (0.75) (0.67) (0.87) (0.89)

1.79** 1.55** 0.92 1.15 (0.73) (0.65) (0.80) (0.78)

1.73*** 1.26** 1.37 1.59* (0.65) (0.58) (0.90) (0.85)

1.80*** 1.30** 1.38 1.59* (0.67) (0.59) (0.91) (0.85)

20.8216.50

2S L S

Control for Int'l Undergrad.

Domestic Undergrad. (Dep. Var.)

15.82

38.10

31.94

45.75

43.05

Control for H-1B Policy

Control for Dot Com Boom/Bust

Control for Fed. Funding

Main (from Table 3)

48.3540.62

39.04

1s t

St ag

e

46.5838.45

Int'l Undergrad. (Dep. Var.)

Falsified IV (Int'l Undergrad.)

19.12

18.53

20.8516.67

14.77

17.08

0.00

2.91

49.06

Bust (2002-2005)Boom (1995-2001)

1.81

0.73 0.79

0.01

20.62

0.01

1.19

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time-period dummies, and are weighted by total graduate enrollment in the initial year. Those specifications with imputed data include an additional 65 universities. Standard errors are clustered at the university level.

4 1

Table V: Robustness Checks

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

Specification Main F W/

Imputed F Main F

W/ Imputed

F

1.78** 1.28** 1.35 1.60 (0.72) (0.62) (1.10) (0.99)

1.73** 1.28** 2.28** 3.17** (0.69) (0.61) (1.15) (1.54)

1.74*** 1.26** 1.34 1.28 (0.66) (0.59) (1.07) (1.05)

1.67* 0.98 1.58* 1.84** (0.93) (0.77) (0.95) (0.91)

1.80*** 1.28** 1.43 1.64* (0.67) (0.60) (0.91) (0.86)

Boom (1995-2001) Bust (2002-2005)

Remove Top 8 Universities

47.5639.44 17.0612.33

13.69

IV w/out India 47.5740.17 10.0110.08

IV w/out country dimension

47.9940.18 9.75

IV w/out Muslim nations

45.4137.52 20.5416.59

IV w/out China 23.6616.42 19.5116.50

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time-period dummies, and are weighted by total graduate enrollment in the initial year. Those specifications with imputed data include an additional 65 universities. Standard errors are clustered at the university level.

4 2

Table VI: Further evidence on Cross Subsidization

Boom (1995-2001) Bust (2002-2005)

Specification Public Private High Low Public Private High Low

2.36*** 0.7 2.49* 1.25 1.93 1.05 1.50 0.53 (0.78) (1.31) (1.32) (0.84) (1.31) (2.54) (1.66) (0.89)

2.11*** 0.55 2.60* 1.13 1.47 0.55 1.19 0.36 (0.72) (1.09) (1.33) (0.75) (1.18) (3.47) (1.60) (0.94)

2.81** 0.84 2.51* 1.29 2.44* 0.85 2.77 0.28 (1.14) (1.38) (1.30) (0.87) (1.45) (2.30) (2.01) (0.85)

2.31*** 0.58 2.49* 1.15 0.78 1.46 0.67 0.49 (0.86) (1.25) (1.32) (0.82) (1.00) (2.97) (1.34) (0.87)

2.36*** 0.58 2.49* 1.15 1.95 0.87 1.50 0.49 (0.77) (1.25) (1.32) (0.82) (1.32) (2.42) (1.66) (0.88)

0.20 0.76* 0.13 0.64** 0.69 0.41 0.61 0.55* (0.15) (0.40) (0.15) (0.31) (0.47) (0.34) (0.57) (0.30)

OLS

Main

Control for Int'l undergraduates

Control for H1B

Control for Dot Com Boom/Bust

Control for Fed. Funding

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time- period dummies. Standard errors are clustered at the university level. All specifications are weighted by total graduate enrollment in the initial year.

4 3

Table VII: Mechanism: Cross Subsidization - RAs and TAs

(1) (2) (3) (4) (5) (6) Main Main Main Main Main OLS

0.25 0.21 0.27 0.08 0.26 0.06* (0.32) (0.29) (0.38) (0.34) (0.32) (0.03)

F 31 36 25 31 31

1.59** 1.36** 1.78* 1.62* 1.57** 0.10 (0.80) (0.65) (0.95) (0.88) (0.80) (0.09)

F 31 36 25 31 31

2.83** 2.80** 3.05** 2.84** 2.83** 0.17 (1.18) (1.17) (1.43) (1.28) (1.19) (0.20)

F 10 10 10 8.4 10

-0.31 -0.24 -0.35 -0.89 -0.30 -0.12 (0.85) (0.82) (1.12) (0.93) (0.86) (0.19)

F 10 10 10 8.4 10

Controls: Foreign Undergrads x H-1B x Dot Com x Federal Funds x

Domestic RA & TAs

Bust (2002-2005)

Boom (1995- 2001) Int'l

RA & TAs

Domestic RA & TAs

Int'l RA & TAs

Note: ***, **, * denote significance at the 1%, 5%, and 10% levels, respectively. All specifications include university fixed effects and time-period dummies. Standard errors are clustered at the university level. All specifications are weighted by total graduate enrollment in the initial year.

44

Figure 1: Sticker Price Tuition Rates at Research Universities , 1990-2009

5,000

10,000

15,000

20,000

25,000

30,000

T u

iti o

n (

2 0

1 0

$ )

1990 1993 1996 1999 2002 2005 2008

In-state Public Out-state Public Private

Note: Above series show average in-state and out-of-state tuition at public universities, and average private university tuition. Dashed lines represent 95% confidence intervals. Sample consists of Research Universities. Data comes from the IPEDS Delta Cost Project (Lenihan [2012]). Dollar amounts have been converted to constant 2010 $.

45

Figure 2: Primary Source of Funding for Foreign Graduate Students, 1995

Personal & Family 50%

US College or University

34%

Home Govt/University 6%

US Gov't 1%

Private US Sponsor 2%

Foreign Private Sponsor

4%Current Employment 1%

International Organization

2%

Note: Above shows the primary source of funding for foreign graduate students. Figures reflect the fraction of students reporting each category as the main source of financial support to finance their education. Data from IIE Open Doors report for the 1995-1996 academic year (Davis [1996]).

46

Figure 3: Trends in International Graduate Enrollment in the US, 1990-2013

150

200

250

300

in 1

,0 0

0 s

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

A: International Enrollment

9

10

11

12

13

% o

f T

o ta

l E

n ro

ll m

e n

t

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

B: Percent International

Note: Series constructed from IPEDS Fall Enrollment Surveys, 1990-2013. Figures above include total international graduate enrollment (in Panel A) and international graduate enrollment as a percent of total graduate enrollment in Baccalaureate, Masters, and Research Universities as defined by the 2000 Carnegie Classification. Data reflect enrollment for the Fall of the corresponding year.

47

Figure 4: International Enrollment by Academic Level and University Type, 1995-2005

0

50,000

100,000

150,000

200,000

250,000

0

50,000

100,000

150,000

200,000

250,000

1995 2000 2005 1995 2000 2005 1995 2000 2005

Graduate, Baccalaureate Graduate, Masters Graduate, Research/Doctoral

Undergraduate, Baccalaureate Undergraduate, Masters Undergraduate, Research/Doctoral

Note: Series constructed from IPEDS Fall Enrollment Surveys, 1995-2006. Figures above include total un- dergraduate and graduate enrollment of non-resident aliens in Baccalaureate, Masters, and Research/Doctoral Universities as defined by the 2000 Carnegie Classification. Data reflect enrollment for Fall of the corresponding academic year.

4 8

Figure 5: Composition of International Students, 1995-2005

A: Country of Origin

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

1995 1997 1999 2001 2003 2005

Americas Europe China India

Asia (Total) Middle East/South Asia Africa

B: Field of Study

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

1997 1999 2001 2003 2005

STEM Agriculture, Environment & Health

Social Science Business

Arts & Humanities Other

Note: Series constructed from IIE International Student Census restricted-use data from 1995-2005. Graduate enrollment by field of study was available only from 1997 on.

49

Figure 6: Coincident Shocks During the Boom and Bust

50,000

100,000

150,000

200,000

1995 1997 1999 2001 2003 2005

H-1B Issued H-1B Annual Cap

A: H-1B Visas Issued & Cap

140,000

160,000

180,000

200,000

220,000

1995 1997 1999 2001 2003 2005

D: Foreign Graduate Enrollment

15,000,000

20,000,000

25,000,000

30,000,000

1995 1997 1999 2001 2003 2005

C: Federal Research Funding to Universities (in constant 2010$s)

1,000

2,000

3,000

4,000

5,000

1995 1997 1999 2001 2003 2005

B: Nasdaq Index (NDX) Closing Price, Q2 Avg. (in constant 2010$s)

Note: Panel A: H-1B visas issued are from the Department of States Non-immigrant Visa Statistics. Panel B: Nasdaq Composite Index stock prices are from Yahoo Finance Historical Prices and reflect the average daily closing price over the 2nd quarter, when students generally make enrollment decisions. Panel C: Series shows data from the NSF on total federal research and development obligations to universities and colleges excluding FFRDCs. All dollar values are converted into constant 2010 dollars using the Bureau of Labor Statistics’ inflation calculator.

5 0

A Appendix - For Online Publication

A.1 Imputations to 1993 IIE Data

Including the 65 universities that have data imputed by IPEDS administrators results in a panel of 258 universities. To perform 2SLS analysis with these additional 65 universities requires that the instrument can be calculated for each of them. Only 201 of these 258 Research universities provided enrollment counts by country of origin and academic level to the 1993 IIE survey. Thus, I must impute the IIE graduate and undergraduate enrollments by country of origin for the 57 non-respondents.

I do this by taking advantage of a large amount of non-Research universities that did respond to the survey. These include Masters and Baccalaureate level institutions, and also community colleges and vocational colleges. In what follows, I describe the imputation procedure for graduate enrollments by country of origin. The procedure for undergraduate enrollments is identical, the only difference being that I use available data on undergraduate enrollments rather than graduate enrollments.

To impute graduate enrollment by country of origin, I obtain total graduate enrollment in 1993 from the IPEDS Fall Enrollment survey for each of the 57 universities missing in the IIE data. Using only non-Research universities in the 1993 IIE data, I calculate the share of graduate enrollment from each country of origin by state. This procedure involves first aggregating graduate enrollment by country of origin (c) for all non-Research universities (i) within the same state (s),

Fcs1993 = ∑ i

Fcis1993 (A.1)

Hence I obtain for each state total enrollment by country of origin in non-Research univer- sities. Next, enrollments by country of origin for each state are then aggregated across all countries of origin,

Fs1993 = ∑ s

Fcs1993 = ∑ s

∑ i

Fcis1993

Dividing the state level country of origin enrollment by total foreign enrollment in that state yields the share of students from country c in each state in 1993,

shcs1993 = Fcs1993 Fs1993

I then multiply total enrollment in 1993, measured from IPEDS, with the share of students by country of origin in the corresponding state.

F̂cu1993 = Fu1993 ∗ sh c s1993

To be precise, the state share assigned to the university is that of the state in which the uni- versity is located. Lastly, I aggregate the country of origin imputations to the 17 nationality

51

groups. These imputations of graduate enrollment by nationality in 1993 for each university are then interacted with the supply shocks to form the instruments, as detailed in 7.

A.2 Construction of control variables

This section describes, in further detail, the construction of the various different control variables used in the analysis, and the data sources. These include variables that control for contemporaneous phenomena that may have affected US graduate education during the 1995-2005 decade.

H-1B Control

The H-1B-driven control accounts for the possible influence that national changes to H-1B visa policy may have had on both international student entry and domestic enrollment. The control variable is essentially a prediction of how international enrollment would have evolved if all nationality groups had grown at the rate of H-1B visa issuance to that nationality from 1993 to each of the sample years (1995-2005).

The first step in forming this prediction requires calculating the number of H-1B visas issued to each nationality for 1993 and the sample years 1995-2005. Data on H-1B visa issued by country of origin is available from 1997-2005 from the Department of State.19 Lack of data prior to 1997 poses an issue for constructing this control for 1993, 1995, and 1996. However, yearly data on the total number of H-1B visas issued from 1990-2005 are available. This allows imputation of H-1B visas issued by country of origin in the missing years (i.e. 1993, 1995, 1996), as follows:

Sn97−05 =

∑2005 t=1997 H1Bnt∑2005 t=1997 H1Bt

H̃1Bnτ =S n 97−05 ∗ H1Bnτ for τ = 1993, 1995, 1996

I first calculate the share of all H-1B visas awarded to each nationality group n from 1997 to 2005 (Sn97−05). This is done by cumulating all visas issued to that nationality group (H1Bnt) and dividing by the total H-1B visas awarded over the 1997-2005 period. The second step imputes the number of H-1B visas issued to each nationality group in the years

prior to 1997 (H̃1Bnτ ) by interacting the share of all H-1B visas awarded to that nationality group over the 1997-2005 period with the total number of H-1B visas in missing years.

A second challenge is that data on visa issuances measure flows not stocks. To transform

19Data comes from the FY1997-2012 NIV Detail Table, available at https://travel.state.gov/content/visas/ en/law-and-policy/statistics/non-immigrant-visas.html.

52

flows into stocks I use the fact that H-1B visas are 3-year work permits. I first aggregate the country of origin data on H-1B visas issued to the 17 nationality groups, obtaining the number of visas issued by nationality group in each year (H1Bnt). For each year, I then cumulate the number of H-1B visas issued over the past three years to obtain predictions of

the stock of H-1B workers (Ĥ1Bnt) of each nationality in the US,

Ĥ1Bnt = 2∑ s=0

H1Bn,t−s = H1Bnt + H1Bn,t−1 + H1Bn,t−2 for t = 1993, 1995, . . . , 2005

After estimating the stock of H-1B workers of each nationality group in each year, I calculate the aggregate growth rates of H-1B workers by nationality from 1993 to each of the sample years.

gH1Bn,93−t = Ĥ1Bnt

Ĥ1Bn1993

This growth factor is then interacted with the historical foreign graduate enrollment across universities, and these predictions are then aggregated across all nationalities,

F̂H1But = ∑ n

F̂H1Bnut = ∑ n

Fnul · gH1Bn,93−t = ∑ n

Fnul · Ĥ1Bnt

Ĥ1Bn1993

Similar to 6 in the paper, this procedure yields a variable that captures the contribution of changes in H-1B policy on foreign graduate enrollment.

Formalizing this into a control for 2SLS regressions requires taking first differences and standardizing. Instead of standardizing by total foreign graduate enrollment, I use imputed foreign graduate enrollment that equals the sum of F̂H1But and imputed domestic enrollment

D̂H1But , in which the same procedure is performed by interacting total growth in H-1B visa issuances with domestic enrollment in 1993. Hence, the control variable is,

∆F̂H1But

ÊH1But−1 = F̂H1But − F̂H1But−1

ÊH1But−1

The Dot Com Boom and Bust

The Dot-Com boom and bust dramatically altered the stock prices of internet based firms. To capture these fluctuations I use the Nasdaq Composite Index (NCI), which is comprised of 3,000+ actively traded securities on the Nasdaq stock exchange, and is often used to track the performance of technology-based companies.

I compute a simple average of the NCI daily closing price over the 2nd quarter of each year,

53

around when universities offer admissions to students. I correct these values for inflation, and calculate growth in the average NCI values from 1993 to each of the years in the sample (1995-2005),

gNCI93−t = NCIt NCI1993

Since fluctuations in equity prices during the Dot-Com episode materialized as shocks to university endowments, I interact these growth rates with average per student endowment funds for each university in 1993,

êpsut = endowmentu93

Etotalu93 · gNCI93−t

Endowment per student values are constructed for each university by dividing ending mar- ket value of endowment assets (endowmentu93) by total enrollment (E

total u93 ), available from

IPEDS data.

The control used in 2SLS is the yearly percentage change in Dot-Com-predicted endow- ment per student,

∆êpsut êpsut−1

= êpsut − êpsut−1

êpsut−1

Federal R&D Funding to Universities

Data on Federal funding to universities comes from the National Science Foundation. To measure Federal funding to universities I use total Federal R&D outlays to Colleges and Universities, excluding Federally Funded Research and Development Centers from 1993- 2005.20 I adjust these values for inflation by transforming all data into constant 2010$.

To measure the impact of these aggregate changes in Federal funding on each university, I first define each university’s historical reliance on Federal funds. I capture historical reliance as Federal research funding per student measured in 1993, using IPEDS data, calculated by dividing the total value of Federal grants and contracts by total enrollment (FedFundsu93

Etotalu93 ),

I then interact historical Federal funds per student with growth in total Federal R&D outlays,

f̂psut = FedFundsu93

Etotalu93 · grFedR&D93−t =

FedFundsu93 Etotalu93

· FedR&Dt FedR&D1993

20Data retrieved from https://ncsesdata.nsf.gov/webcaspar/OlapBuilder on 11/3/2015 .

54

The control variable is the percentage change in predicted federal funds per student,

∆f̂psut

f̂psut−1 = f̂psut − f̂psut−1

f̂psut−1

A.3 Annualization and Imputation of RA/TA Data

Data on the number of domestic and foreign students employed by each university as either a TA or RA at is available from IPEDS. From 1995 to 2001, these counts are available only biennially. After 2001 they are available every year.

Since data is only available every two years during the boom period, I first calculate the growth in foreign or domestic RAs and TAs standardized by total graduate enrollment in the initial year as,

∆2X RATA ut

Eut−2 = XRATAut − XRATAut−2

Eut−2 , with X = F,D and t = 1997, 1999, 2001

I then approximate the yearly growth rate by annualizing the two year growth rates as follows:

XRATAut − XRATAut−1 Eut−1

≈ ̂XRATAut − XRATAut−1 Eut−1

=

√ 1 +

∆2X RATA ut

Eut−2

The annualized growth rates are then used in the analysis of the boom period in section 6.

Since yearly data is available after 2001, yearly growth rates ( XRAT Aut −X

RAT A ut−1

Eut−1 ) are used for

analysis of the bust period.

Because some universities did not respond to this survey in certain years, I impute data where possible. The imputation procedure used is often referred to mid-point imputation. Essentially, I calculate the number of domestic or foreign RAs and TAs in missing years by taking the average of those values from the preceding and subsequent years. For example, to impute the number of foreign RAs and TAs in 2003, I take the average of the values in 2002 and 2004. Note that RA and TA counts are used as the dependent variable in analysis. Thus, to the extent imputations introduce measurement error, this will only lower precision, without attenuating point estimates.

55