The Determinants of International Enrollment in U.S.Higher Education: Labor market openness, and the

unintended consequences of H-1B policy.

Kevin Shih∗

University of California at Davis

August 16, 2014

Abstract

International students have long comprised an important part of U.S. higher ed-ucation. While much speculation exists, there is little empirical work that identifiesthe important economic factors that encourage thousands of students across the worldto seek U.S. post-secondary education each year. This paper explores the relationshipbetween foreign post-secondary enrollment and various home country and U.S.-specificfactors that affect the demand and supply of higher education. Results reveal a posi-tive and robust relationship between the college age population in a country and thenumber of students it sends to U.S. universities. In addition, the openness of the U.S.labor markets to college-educated foreigners, as proxied by H-1B visa policy, is alsopositively related to international enrollment. I explore the causal effect of labor mar-ket openness by exploiting a dramatic fall in the H-1B visa cap, from 195,000 to 65,000per year, that occurred in 2004. Triple difference estimates suggest that the fall in thecap lowered foreign enrollment by 9%.

JEL Codes: F22, I21, J11Keywords: International enrollment, Foreign students, Determinants, Globalization,Higher Education.

∗This research was conducted while the author was a Research Associate of the Institute of InternationalEducation and a Doctoral candidate at the UC Davis Economics Department. The author thanks ChristineFarrugia, Rajika Bhandari, Giovanni Peri, and Chad Sparber for insightful discussions and suggestions. Thisresearch does not reflect the views of the IIE. The author is accountable for all errors contained herein.

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1 Introduction

International students have long comprised a large portion of higher education enrollment

in the U.S. Today over 800,000 individuals from across the world study at U.S. colleges and

universities on temporary student visas.1 However, remarkably little is known about the

factors that encourage thousands of students to apply and enroll at U.S. post-secondary

institutions each year. Strong growth in foreign enrollment over the last half century (see

figure 1), combined with unprecedented recent surges in undergraduates from abroad beckons

the need to identify the determinants of international student flows.

Additionally, the presence of foreign students carries strong implications for U.S. higher

education. Prior research suggests that foreign students may impact the educational attain-

ment of natives. Foreign students might crowd natives out of higher education (Borjas 2004;

Hoxby 1998) by increasing competition for seats. Alternatively, international students may

bring positive externalities which could offset the increased competition (Hunt 2012; Jack-

son 2012). Furthermore, because foreign students often pay full sticker price tuition they

contribute to expanding university resources.2 Understanding the forces that affect foreign

enrollment in the U.S. has important implications for both the education of U.S. natives and

the U.S. higher education sector.

Fluctuations in foreign enrollment may also have implications for the U.S. labor market.

Although student visas do not allow international students to remain in the U.S. following

completion of their studies, a large number of international students do remain by transfer-

ring to a work visa.3 Thus, inflows of highly educated foreigners into the U.S. labor market

1Open Doors (2013) puts the actual number at 819,644.2A recent study (NAFSA 2013) estimated that over the 2012-2013 academic year international students

contributed over $17 billion to U.S. higher education through tuition and fees.3Ruiz (2013) reports that 35% of all H-1B visas awarded in 2010 were to individuals transferring from an

F-1 student visa. Furthermore, among those F-1 visa holders transferring to an H-1B visa, nearly 75% were

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may have strong impacts on the wages and productivity of U.S. natives (e.g. Borjas 2009;

Peri et al. 2013).

Finally, very recent research has identified foreign students and high skill workers as key

contributors to advances in science, engineering, and technological innovation in the U.S.

(Kerr & Lincoln 2010; Chellaraj et al. 2008; Stuen et al. 2012). Innovation and technological

advances, in turn, are the main drivers of economic growth. Therefore, identifying the forces

that govern foreign student mobility may be an important policy tool for the U.S. to remain

at the technological frontier.

There have been many descriptive studies regarding trends in international student mo-

bility (e.g. Bound, Turner, & Walsh 2009; Bound & Turner 2010; Verbik & Lasanowski

2007; Guruz 2011; Findlay 2011). These works have importantly recognized the rising global

movement of students across borders for higher education, and particularly into U.S. uni-

versities. Additionally, there has been a great amount of effort in identifying the economic

factors that influence international migration (e.g. Hanson & McIntosh 2010; Hatton 2005;

Hatton & Williamson 2005; Mayda 2010; Ortega & Peri 2013, 2014). In contrast, however,

there is much less research on the determinants of international student flows.

In theory the number of students coming from abroad each year is the equilibrium result

of competition between supply and demand in the market for U.S. higher education. Factors,

such as changes to the relative benefits of a U.S. degree, the relative costs of receiving a U.S.

education, or preferences for study abroad in the U.S., may affect foreign demand for U.S.

higher education. Alternatively, factors such as changes to student visa policy or fluctuations

in federal higher education funding may alter the supply of higher education (the number of

seats) available for foreign students.

individuals with graduate degrees.

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This paper provides an empirical analysis of the determinants of foreign enrollment at

U.S. colleges and universities in two parts. The first part uses a panel data on 137 sending

countries and examines a wide range of demand and supply factors. Using a panel fixed-

effects regression model, I assess the importance of various factors including tertiary age

population and real GDP per capita in sending countries, bilateral USD exchange rates,

imports from and exports to the U.S. Additionally, I evaluate the importance of U.S. labor

market opportunities by using measures of expected wages (average wages of immigrants

from sending countries) and labor market openness (H-1B visas issued to sending countries).4

The results show that tertiary age population in sending countries is a strong and robust

determinant of international enrollment. Further, labor market openness/access, as proxied

by H-1B visa issuances, is also positively related to international enrollment.

The second part explores the role of U.S. labor market openness in greater detail by

exploiting a policy shift that greatly decreased access to the U.S. labor market for highly

educated foreigners. Specifically, in 2004 the cap on H-1B visas was reduced from 195,000 per

year to 65,000 per year. Interestingly, however, this reform did not represent a great reduction

in labor market access for all sending countries. By 2004, a group of countries (Australia,

Canada, Mexico, Chile, Singapore) had established preferential trade agreements with the

U.S., which created alternative visas for their highly educated nationals. Furthermore, not

all foreign students saw decreased access. Foreign graduate students were less affected than

undergraduates because Congress had set aside an extra 20,000 H-1B visas for holders of

graduate degrees, and exempted applicants seeking employment in Universities from the

cap.5 I assess this natural experiment using a triple difference framework, and find that the

4The H-1B visa is the main visa for highly educated foreign-born individuals to work in the U.S. TheH-1B visa is described in more detail in sections 5 and 7.

5Since many foreign graduate students go on to become Professors or researchers within Universities, theexemption meant that the fall in the cap represented a much smaller decrease in U.S. labor market opennessthan for undergraduates.

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2004 drop in the size of the H-1B program reduced international enrollment by 9%.

Section 2 briefly reviews the existing literature on the determinants of international higher

education enrollment in the U.S. Section 3 provides some descriptive statistics on interna-

tional students in the U.S. to help provide context to the analyses. Section 4 provides a

theoretical context to how various economic factors affect foreign enrollment in the U.S.

Section 5 outlines the empirical model and data used to assess the importance of various

determinants of international enrollment at the graduate and undergraduate levels. Section

6 presents the main results, and provides some extensions and robustness checks. Section 7

describes the H-1B policy experiment and discusses the results. Section 8 concludes.

2 Literature Review

A large and active body of research has attempted to identify the determinants of interna-

tional migration. These papers generally use cross-sectional or panel data on several countries

to relate immigrant stocks or flows to a range of economic variables, such as GDP, exchange

rates, distance, language, trade, and income. For example, Mayda (2010) and Ortega & Peri

(2013) examine determinants of bilateral migration flows between OECD countries and find

that increases in income per capita in destination countries tend to attract more immigrants.

Clark et al. (2007) focus specifically on the U.S. and find that policy plays an important

role in regulating the flow of immigrants.6

In contrast, there is much less empirical work exploring the forces that cause millions to

seek higher education abroad each year.7 This research question bears special importance

6Other examples include Hanson & McIntosh (2010), Hatton (2005), Hatton & Williamson (2005), andOrtega & Peri (2014).

7UNESCO estimated that in 2012 over 3 million students at the tertiary education level were studyingoutside their home country. See http://data.uis.unesco.org.

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for the U.S., whose colleges and universities lead the world in hosting over 15% of the stock

of internationally mobile students.8 Furthermore, the determinants of international student

mobility may be quite different than the determinants of international migration. Because

U.S. student visa policy does not permit stay beyond completion of studies, prospective

foreign students may be more myopic than prospective migrants.9 Alternatively, the deter-

minants of foreign student mobility and immigration may be quite similar, and thus, changes

to U.S. immigration policy may result in unintended consequences for the composition of

students at U.S. colleges and universities.

A small number of papers have used empirical methods to identify the determinants of

foreign student flows. These papers implement empirical designs similar to those used to

study the determinants of international migration, often relating international enrollment

to a variety of factors (e.g. home country GDP, population and higher education quality,

exchange rates, trade with the U.S., etc. ).10 Many studies have focused on international

student mobility within the European Union (Brezis & Soueri 2011; Gonzalez et al. 2010;

Van Bouwel & Veugelers 2013) and to the United Kingdom (Naidoo 2007; Jena & Reilly

2013). While the U.S. has been the world leader in hosting international students over the

past half century (Freeman 2010), only a handful of studies have examined international

enrollment in the U.S.

Early work by McMahon (1992) examined the inflow of students to U.S. universities

from 18 developing nations in the decades after World War II, and found trade linkages

established over the 1960’s and 70’s were positively related to international enrollments.

8See the OECD report: http://www.oecd-ilibrary.org/education/

how-is-international-student-mobility-shaping-up_5k43k8r4k821-en.9For example, short-term fluctuations in exchange rates may strongly affect international student flows,

but have no effect on immigration.10Kato & Sparber (2011) is a notable exception in that they use quasi-experimental difference-in-difference

methods to examine how H-1B policy affects the quality of foreign students applying to U.S. universities.

5

Rosenzweig (2006) expanded the analysis to include 125 sending countries, relating student

visas issuances with various economic variables including wages in sending countries. Al-

though the regressions only rely on cross-country variation, the results suggest that higher

wages in home countries are negatively correlated with the number of international students

in the U.S.

Recent studies have begun to improve upon these early papers by using panel data. Using

data from 1993-2006, Liu & Wang (2009) find that Federal support for higher education and

the population of young individuals in sending countries are positively linked with interna-

tional enrollment. Bird & Turner (2014) separately analyze factors affecting undergraduate

and graduate enrollment from abroad. They also find a similarly strong relationship between

exchange rates and undergraduate enrollment that is primarily driven by China. Addition-

ally, they find that real GDP per capita and the college age population in sending countries

have strong positive relationships with both undergraduate and graduate enrollment in the

U.S.

This paper empirically explores the determinants of international student flows to the

United States, building from these prior works. I contribute to the existing literature in

three key ways. First, I compile panel data from a variety of sources to assess a larger

number of economic factors than previously considered. Second, I develop and test two key

measures of the strength and accessibility of U.S. labor markets, which have not previously

been considered in relation to international student flows. Lastly, I leverage a unique natural

experiment to identify the causal impact of decreased U.S. labor market access via a policy

change that reduced the number of H-1B visas available. Before continuing further, the next

section presents some basic descriptive statistics on international students in order to better

understand and frame the results.

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3 Summary Statistics on International Students

International students currently comprise 4% of total higher education enrollment (Open

Doors, 2013). This statistic, however, masks tremendous heterogeneity in foreign student

representation within different areas of higher education. Importantly, the share of inter-

national students varies largely by academic level. Table 1 shows that during the 2012-13

academic year, although international students received only 3.3% of bachelors degrees,

they received nearly 12% of masters degrees, and almost 30% of doctoral degrees. Further-

more, the significant presence of foreign students in U.S. graduate education is not a recent

phenomenon–Bound et al. (2010) document that during the two decades between 1936 and

1956, international students were already receiving more than 10% of all doctoral degrees

awarded in engineering, physical sciences, life sciences, and economics. Understanding the

forces that affect enrollment of international students in the U.S. is crucial for educators,

administrators, and policymakers to properly plan for future demand shocks to higher edu-

cation.11

Even greater heterogeneity in international student representation exists when looking

across fields of study. Table 1 displays the top 5 fields of study by academic level, ranked

by the percent of degrees awarded to international students. In 2012-13 about half of all en-

gineering, computer/information science, and mathematics & statistics PhDs were awarded

to noncitizens. Indeed, the tendency of international students to study such Science, Engi-

neering, Mathematics, and Technology (STEM) based fields12 have made them an important

11There is some evidence that increased students from abroad may crowd natives out of higher education.Borjas (2004) finds that increased graduate students from abroad is associated with lower enrollment ofwhite males in U.S. graduate schools. Similarly, Hoxby (1998) finds that increased foreign students at theundergraduate level is associated with fewer native minorities attending college. In contrast, several studiesfind no evidence of crowding out (e.g. Jackson, 2009; Hunt, 2012).

12Note that engineering, computer/information science, and mathematics & statistics fields receive thehighest share of international students at the bachelors, masters, and doctoral levels.

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contributor to research productivity at U.S. universities and U.S. STEM innovation.13

An additional important fact regarding international students concerns their countries

of origin. While U.S. universities host students from almost every country in the world,

a small number of countries account for the majority of international students. In 2012,

the top 30 sending countries comprise nearly 90% of all international enrollment. The top

10 Asian countries alone account for 66% of total enrollment from abroad. Importantly,

approximately half of all international students come from just two countries: China and

India. Chinese students account for 33% of all international post-secondary students, while

India provides nearly 20% of all enrollment from abroad.14

A final noteworthy feature of international students concerns their sources of funding.

The F-1 Visa, the main student visa for foreign nationals to attend accredited post-secondary

institutions, requires applicants to demonstrate the ability to pay full sticker price tuition.

Further, international students are generally not available for federal financial aid. Over

63% of international students report personal and family sources as their primary source

of funding (Open Doors 2013). Thus, because international students generally pay full

sticker tuition price which is funded by personal and family sources, they generate large

revenues for the higher education sector. A recent study (NAFSA, 2013) estimated that

over the 2012-2013 academic year international students contributed over $17 billion to the

U.S. higher education through tuition and fees. Further, NAFSA (2013) estimates that

international students supported 313,000 jobs and contributed a total of $24 billion to the

U.S. economy via spending for tuition, housing, and local services. Thus, the factors that

affect international student enrollment also directly affect the resources available to U.S.

13Chelleraj et al. (2008) show that international students increase innovative activity through increasedpatent applications and grants. Black & Stephan (2007) document that international students and post-doctoral scholars contribute tremendously to scientific research publications.

14See http://www.iie.org/en/Research-and-Publications/Open-Doors/Data/

International-Students/All-Places-of-Origin/2011-13.

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higher education institutions.

4 Theory: Supply and Demand for U.S. Higher Education

U.S. policymakers and educators often speculate about the economic and institutional forces

that affect international student’s decisions to study in the states. For example, Victor

Johnson, a senior adviser for public policy for NAFSA speculates: “If people are coming

here for a couple of days to do nothing but buy a new wardrobe, it would be strange if the

exchange rate didn’t affect their educational decisions.”15 Alternatively, an article describing

a recent surge in Chinese students also presents anecdotal evidence that the ability to explore

different majors is an attractive feature of U.S. higher education, as the rigid Chinese system

forces students to choose majors prior to enrolling in college (Haynie, 2013).

Basic economic theory suggests that the number of foreign students enrolled at U.S.

universities is the resulting equilibrium of supply and demand in the market for higher

education. International student demand for U.S. higher education may be affected by a

multitude of factors that alter the costs and benefits to studying in the states. Factors that

increase the net benefit are likely to increase foreign enrollment. These include, for example,

higher expected returns (wages) to a U.S. degree, greater probability of employment in the

U.S., or better quality universities than at home. In contrast factors that increase the costs

of enrolling in a U.S. university are likely to reduce foreign enrollment. For example, rising

tuition, depreciation of home currency relative to the US dollar, or increasing wages at home

all directly increase the monetary or opportunity costs of studying abroad in the U.S.

Alternatively, the supply of higher education seats available for foreign students is de-

15See Schworm (2008).

9

termined by the costs and benefits to universities of hosting international students.16 For

example, if international students benefit universities through paying higher tuition than

natives, admissions committees may increase the seats available to international students.

Increases in federal higher education funding or declining enrollment of native-born U.S.

students may also increase the capacity of universities to host international students. Alter-

natively, more stringent student visa policy might raise the administrative costs of hosting

international students.17

While theory is a useful starting point, it is unclear which factors should matter the

most. Furthermore, theory cannot shed light on how large of an increase/decrease in en-

rollment from abroad should be expected from fluctuations in factors that affect supply or

demand, unless strict assumptions are imposed on the elasticities of supply and demand

curves. Nevertheless, empirical analysis can provide valuable insight into these issues.

5 Empirical Methods & Data

This paper contributes to existing literature by compiling a wider array of economic deter-

minants than previously considered. The principal source of data on international student

enrollment in the U.S. comes from the Institute of International Education (IIE).18 I collect

yearly undergraduate and graduate enrollment counts by country of origin from the 1998-

2010 Open Doors reports. These data list total enrollment counts by country of origin and

by academic level.

16Importantly, U.S. student visa policy has historically had no caps. Thus, if an international student isaccepted at a U.S. university, and passes various security checks, he/she may receive a student visa.

17There is evidence that heightened restrictions on visa issuances after 9/11 increased the burden foruniversity administrators to process visas (Alberts 2007).

18The IIE was founded in 1919 and has published yearly statistics of international students in U.S. highereducation in volumes called Open Doors since 1954.

10

I supplement this data with a variety of sources that measure economic factors which

might affect the supply or demand for higher education in the U.S. To assess the impact

of opportunity costs in the home country, I use Real GDP per capita as a proxy. Real

GDP by country comes from the Penn World Tables (Feenstra et al., 2013). Specifically, I

use Expenditures-side Real GDP, which better captures real living standards and is more

suitable for analysis across countries and over time.19 I then calculate real GDP per capita

by dividing expenditure-side real GDP by population, also available in the PWT. While

increases in Real GDP may reflect rising wages in the home country and hence increasing

opportunity costs, they may also represent rising income which could enable many more

students to afford study in the U.S.

Exchange rates have often been speculated to be an important factor in the decision to

study in the U.S. To assess their importance, I use exchange rates denominated in home-

currency per USD, also available in the PWT. Holding prices constant, fluctuations in ex-

change rates should raise or lower the cost of attending college in the U.S.20 For example, an

appreciation (increase) in the Euro/USD exchange rate raises the cost of attending a college

in the U.S. for students from Europe. Thus, exchange rates should be negatively correlated

with foreign student enrollment.

As the focus of this analysis is on the quantity of foreign students, it is likely that

demographic shifts in sending countries may affect the number of internationally mobile

students. To assess this channel I gather data on the population of tertiary education/college

age individuals by sending country from UNESCOs Institute for Statistics.21 The college

19Expenditure-side real GDP is calculated at chained Purchasing Power Parities (PPPs), to comparerelative living standards across countries and over time. Using PPPs adjustments are important to capturethe real costs of living which differ across countries. See Feenstra et al. (2013) for detailed description ofthis variable.

20These costs may include tuition, living costs, transportation costs, and application fees.21Tertiary age differs depending on the country, but generally cover individuals aged 18-30 who attend

educational levels from undergraduate to graduate education in the U.S. See for more information.

11

age population may be an important determinant of foreign student enrollment in the U.S.

A country that experiences a particularly large birth cohort may mechanically have a larger

number of individuals from that cohort applying and attending college, and naturally some

of this excess demand for higher education may spill over to the U.S.

Trade linkages between countries may foster other types of interaction, including educa-

tional exchange (McMahon 1992). I compile bilateral import and export values from U.S.

census data on import and export values by Harmonized System (HS) codes, U.S. state,

partner country. These data are aggregated across states and HS codes to obtain a total

value of imports and exports between the U.S. and sending countries.22

Finally, I develop measures of U.S. labor market strength and labor market access that

have yet to be included in analysis on the determinants of international student mobility.

In particular studying in the U.S. may be attractive because of the potential to earn U.S.

wages and/or find employment in the U.S. To proxy for expected U.S. wages to students

from sending country c, I calculate average annual wages of immigrants aged 25-40 from

country c with a bachelors degree or higher from the 2000 U.S. Census and the 2001-2010

American Community Surveys.23 Average wages are available for 97 countries of origin, but

unfortunately no surveys are available from 1998 and 1999 that provide enough observations

to accurately estimate averages for each country.24

To proxy for U.S. labor market openness, I gather data on H-1B visas issued by send-

ing country from the State Department (Department of State, 2012). The H-1B visa is a

22These data were kindly made publicly available by Peter Schott. See Schott (2008) for more details.Data were taken from Peter Schott’s website: .

23Immigrants are defined as individuals not born in the U.S. and who are not born abroad to U.S. citizenparents. The sample is limited to immigrants who worked a positive number of weeks in the previous year,reported earning positive wage/salary income, and have a bachelors degree or higher.

24The Current Population Survey is available in 1998 and 1999, but the sample size was too small toaccurately calculate average wages for the 97 countries.

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three year work permit (renewable up to 6 years), generally for highly educated individuals.

Only U.S. employers may apply for H-1B visas on behalf of foreign applicants, and foreign

applicants must have an employment offer–thus the H-1B visa is tied to employment in the

U.S., and changes in the number of H-1B visas issued may reflect changes in employment

opportunities. Additionally, the U.S. government has maintained numerical caps on the

number of H-1B visas allowed in each year. Thus, fluctuations in H-1B visas issued also

reflects policy openness to foreign nations and access to U.S. labor markets. The H-1B is the

visa that international students would most likely transition to in order to work in the U.S.

following completion of their studies.25 In fact, Ruiz (2013) uses data from SEVIS to show

that around 35% of H-1B visas issued in 2010 were to international students transferring

from F-1 visas. Since more than a third of H-1B visas are awarded to foreign students, I

use H-1B visas lagged three years to reduce the possibility of mechanical correlation due to

graduating students transitioning to H-1B in the same year.26

I combine these data to form a panel dataset consisting of 137 sending countries from

1998-2010 and implement the basic empirical specification:

log Ect = α+β1log RGDPct+β2log Popcollegect +β3log Bilateralct+β4log LaborMktUSct +γc+γt+εct

(1)

In specification 1, Ect represents the total number of international students from country

c enrolled in U.S. universities in year t.27 RGDPct represents real GDP per capita of country

c. Popcollegect measures the population of tertiary education/college age (18-30) in sending

countries. Bilateralct include three variables that measure the economic relationships be-

25For more background on the H-1B visa see Kato & Sparber (2013).26Thus H-1B visas issued in 1997 are related to enrollment in 2000, visas issued in 1998 are associated

with enrollment in 2001, etc. Note this strategy is less than perfect because a mechanical correlation maystill occur using lags if H-1B visa holders end up enrolling at U.S. universities at a later point in time.

27Note that enrollment is measured for the academic year from fall of year t to spring of year t + 1. Thusenrollment in year 1998 reflects enrollment for the academic year 1998-1999.

13

tween the sending country and the U.S. These include exchange rates, imports, and exports.

LaborMktUSct represents the two explanatory variables that capture the strength or openness

of the U.S. labor market: average wages of college educated immigrants from country c, and

H-1B visas issued to individuals from country c.28 Lastly I include year effects, γt, to control

for shocks affect all international students, and country fixed effects, gammac to control for

time-invariant, country-specific factors.

6 Results

To begin understanding the determinants of international student enrollment, Table 2 presents

regression results of specification 1 on 137 countries from 1998-2010. Columns (1) and (2)

display results on total international enrollment, while columns (3)-(6) split enrollment by

academic level. Columns (3) and (4) show results for international undergraduate enrollment,

and columns (5) and (6) show results for international graduate enrollment. All variables

are expressed in logs, unless otherwise specified. Regression coefficients are displayed with

standard errors clustered at the country level in parenthesis.

Columns (1), (3), and (5) include log exchange rates, log real GDP per capita, log imports,

log exports, and log tertiary age population as explanatory variables. These specifications

also control for year effects and country fixed effects. The results from column (1) show a

positive and statistically significant relationship between total international enrollment in

the U.S. and both real GDP per capita of sending countries and tertiary age population

in sending countries, and U.S. exports to sending countries. These results suggest that

28Expected wages and employment opportunities in the U.S. conceivably vary by county of origin due toselection of international students. A country that tends to send students from the upper tail of the abilitydistribution can expect its students to have higher wages/employment opportunities in the U.S. than acountry whose students are drawn from the lower tail of the ability distribution, if there is a strong correlationbetween abilities at home and the U.S. These concepts were theoretically and empirically elucidated by Borjas(1987).

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living standards and demographic changes in the home country may influence the number

of students that ultimately study in the U.S. Similar effects are found when splitting by

academic level in columns (3) and (5), although exports lose statistical significance when

examining graduate enrollment from abroad.

Columns (2), (4), and (6) adds in very demanding country specific linear time trends

to control for linear growth of home-specific factors, such as constant growth in educational

quality. While the coefficients on real GDP per capita and exports lose statistical significance,

note that the coefficients on tertiary age population remains robust to these demanding

controls. The size of the coefficients suggest that a 1% increase in a country’s college age

population is associated with a 1% increase in undergraduate enrollment from that country,

and a 0.7% increase in graduate enrollment from that country.

Demographic shifts that increase the number of individuals in a birth cohort can increase

the numbers of students studying in the U.S. when that cohort reaches college age through

a variety of mechanisms. Increases in the size of birth cohorts may mechanically lead to

increased numbers of students studying abroad if preferences for U.S. education are relatively

fixed within countries and over time. For example, assuming U.S. higher education supply is

not operating at capacity, if one out of every two college age individuals prefer studying in the

U.S. instead of at home, increases in the college age population will mechanically increase the

number of students from that country studying in the U.S. Alternatively, larger cohort size

may lead to increased competition within that cohort for college admission. If universities in

the home country cannot absorb this higher demand, students will forgo college education

unless they can seek opportunities abroad.29

29Bound & Turner (2007) find that increased cohort size is associated with lower undergraduate degreeattainment in the U.S. Bird & Turner (2014) find that the impact of college age population growth is lowerin countries with many universities per population.

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The strength of the relationship between college age population can be visualized in

Figure 2, which displays a scatterplot of changes in tertiary age population against changes

in graduate or undergraduate enrollment from 1998-2004, and from 2004-2010. While the

positive relationship identified in regressions is salient in the scatterplots as well, figure 2

reveals two possible outliers may drive the results. India dominated both population growth

and growth in international student enrollment in the first half of the sample, while China

has emerged as the leader in the most recent decade. It is quite plausible that India and

China are the main drivers of the strong relationship between cohort size and international

student enrollment in earlier regressions.

Table 3 examines whether the relationship between enrollment and college age population

remains after removing India and China from the regressions. Column (1) runs nearly the

same regression as in column (2) of table 2, but also removes China and India. Columns

(2) and (3) also remove China and India and replicate the regressions of columns (4) and

(6) in table 2, respectively. Interestingly, the results show that the positive and significant

relationship between population growth and enrollment is robust to the exclusion of India

and China. Coefficients do not change much and remain highly statistically significant.

6.1 The impact of expected U.S. wages and labor market openness

The regression analysis presented thus far has focused more on the impact of home country

characteristics (Real GDP per capita, college age population), while excluding many impor-

tant U.S. characteristics that may attract international students. An important factor in

the decision to study abroad in the U.S. may be the possibility of future employment in the

U.S., and/or the wages associated with working in the U.S. To test the importance of access

to U.S. employment I add log of H-1B visas issued (lagged three years) to each country.

16

To evaluate the effect of potential earnings in the U.S. I use the log of average U.S. yearly

earning of college educated immigrants from each country. Because the availability of wages

by country are limited, the analyses which include log average yearly earnings of immigrants

is limited to 91 countries from 2000-2010.

Table 4 shows regression results that add log H-1B visas issued four years prior, in columns

(1), (3), and (5), and log average annual earnings, in columns (2), (4), and (6). Columns

(1) and (2) present results for total enrollment, columns (3) and (4) show results for under-

graduate enrollment, and column (5) and (6) presents results for graduate enrollment. The

results show that college age population continues to have a strong positive relationship with

enrollment from abroad. Interestingly, while average wages seem to have little relation to

international enrollment, the number of H-1B visas issued is positive and statistically sig-

nificant in all but one specification. These correlations suggest that when students evaluate

whether or not to apply and enroll in a U.S. university, their decisions may be heavily influ-

enced by the probability of securing employment in the U.S. after completing their studies.

Therefore, changes in immigration policy and the availability of employment opportunities

in the U.S. may be an important factor that determines the flow of students from abroad.

Although the positive and statistically significant relationship between international stu-

dent enrollment and both college age population and H-1B visas issued is compelling, the

empirical design is not without flaws. Many factors may bias the results, thus preventing a

causal interpretation. For example, increasing rates of educational attainment in countries

may cause increases in both the number of H-1B visa recipients and the number of students

enrolled at U.S. universities, leading the coefficient on H-1B visas issued to be biased upward.

I thus present a basic robustness check that exploits the fact that H-1B visas limits do not

apply to all countries, and later turn to a policy-driven analysis.

17

As stated earlier, changes in H-1B visas issuances generally reflect changes in access

to U.S. labor markets.30 However, a few countries, since 2004, have established preferential

agreements with the U.S. that allow its college educated workforce to circumvent H-1B limits.

Nationals of Australia, Canada, Chile, Mexico, and Singapore can acquire alternative work

permits that are not bound by H-1B restrictions.31 Thus, if a truly positive relationship

between H-1B visas and foreign student enrollment exists because potential foreign students

are attracted by access to U.S. labor markets, then it should also be true that countries

whose access to U.S. labor markets are less bound by H-1B policy should show little to no

relationship between enrollment of foreign students and visas issued. Put differently, for

countries whose college educated nationals have several other alternatives to obtaining work

permits in the U.S., changes in H-1B issuance should not be a very good signal of access to

U.S. labor markets, and thus foreign students should respond very little.

I formalize this robustness check by interacting log H-1B visas issued with a dummy

variable that equals one if the country currently has substitutes to the H-1B visa via prefer-

ential trade agreements.32 If the aforementioned theory is true, then it is necessary (but not

sufficient) that the coefficient on the interaction term be negative. This is because the total

effect of H-1B visas for countries not bound by H-1B policy–the coefficient on log H-1B visas

issued plus the coefficient on the interaction term–should be less than the effect of H-1B

visas for countries bound by H-1B policy, which is simply the coefficient on log H-1B visas.

The results of this robustness check are shown in table 5. Columns (1), (2), and (3)

present results for total, undergraduate, and graduate enrollment, respectively. In all cases

30Additionally, changes in H-1B visas issued may reflect changing supply of college educated workers inhome countries. Controlling for college age population partially accounts for this, but does not completelyrule out a home country supply side story.

31See Kato & Sparber (2013) for a complete description of the policies surrounding these nations.32I.e. the dummy variable equals one if the country is Australia, Canada, Chile, or Mexico. Singapore is

excluded from all analysis in the paper because of a lack of data.

18

the coefficients on the interaction term are negative and statistically significant.33 Further, a

wald test of the equality of the log H-1B coefficient and the coefficient on the interaction term

fails to reject the null hypothesis that they are equal. Thus the results are consistent with

the hypothesis stated earlier–availability of H-1B visas seems to be positively correlated with

international student enrollment, except for countries who have alternative visa programs to

the H-1B visa.

7 Unintended Consequences - an H-1B Policy Experiment

The results presented thus far have revealed that U.S. labor market openness might be an

attractive factor that prospective international students weigh when deciding whether to

enroll in the U.S. undergraduate or graduate programs. The regression analysis uncovered a

strong positive relationship between H-1B visas and foreign enrollment in U.S. universities.

Importantly, however, these results still fall short from establishing a causal relationship.

There may be various unobserved confounding factors that vary within countries and over

time, that are correlated with both enrollment in the U.S. and H-1B visa issuances. For

example, the strong presence of U.S. firms in a sending country may simultaneously foster

knowledge diffusion that increases opportunities to secure H-1B visas and study at U.S.

universities.

Policy changes to the H-1B program offer unique natural experiments to estimate the

causal impact of H-1B visas, and hence labor market access, on the decision to study in the

U.S. The H-1B program began in 1990 with a congressionally mandated cap of 65,000 visas

per year. The cap was increased in 1998 to 115,000, and again to 195,000 in 2000.34

33To be precise, the combined effect of a 1% increase in H-1B visas issued on graduate enrollment fromCanada would be -0.68–the main effect of H-1B visas (0.143) plus the effect of the interaction (-0.211).

34The expansion of the cap to 195,000 was a part of the American Competitiveness in the Twenty-First

19

A series of policy changes in 2004, in particular, provide a very good natural experiment

to explore impacts on foreign enrollment. In 2004, the H-1B cap fell, from 195,000, to its

original level of 65,000 per year, marking a dramatic decrease in foreign access to the U.S.

labor market. Interestingly, however, this fall in the cap did not necessarily signal lower

access to the U.S. labor market for all countries. Importantly by 2004, four countries–

Canada, Chile, Mexico, and Singapore–had signed agreements with the U.S. that provided

their highly educated workers alternatives to the H-1B visa. In 2005, Australia also signed a

preferential agreement that provided an alternative for highly educated Australian nationals

to work in the U.S.35 Thus, while students from most countries experienced a dramatic

restriction in access to the U.S. labor market (treated countries), students from 5 “control”

countries did not. Comparing changes in foreign enrollment from treated countries against

enrollment changes from the five control countries could provide causal estimates of the

impact of H-1B policy on foreign enrollment.

This difference-in-differences design is used by Kato & Sparber (2011) to examine the

impact of H-1B policy on the quality of foreign students. They assess how SAT score reports

to from international students to universities evolved after the 2004 fall in the cap. While

they do not provide formal difference-in-differences analysis on international student quality,

they do note that from 2001 to 2006, undergraduate enrollment from the 5 control countries

remained relatively constant, while undergraduate enrollment at other countries declined by

14%.

Century Act (AC21).35Specifically, Canada, Mexico, Chile, and Singapore signed free trade agreements with the U.S. These

agreements created alternative visas which were very similar to the H-1B visa. In particular, TN visaswere created in 1994 under the North American Free Trade agreement for citizens of Canada and Mexico.While there is no cap on TN visas, there is an approved list of occupations that is more restrictive thanthe H-1B. H-1B1 visa program was enacted in September 2003, which essentially set aside 1,400 of theavailable H-1B visas for citizens of Chile, and 5,400 for citizens of Singapore. Lastly, in May 2005 a billwas enacted establishing E-3 visas for Australian citizens. Capped at 10,500 visas per year, the E-3 visaprovided Australian professionals a close substitute to the H-1B visa. For further details regarding thesepolicy changes see Kato & Sparber (2011).

20

The difference-in-difference design is difficult to implement empirically as only having 5

countries in the control group may afford too small of a sample size to detect any mean-

ingful effects. Interestingly, however, another reform in 2004 provides an additional control

group–the government mandated that 20,000 additional H-1B visas, not included in the cap

of 65,000, were to be reserved only for individuals with graduate degrees. Additionally, after

2000 foreign highly educated workers hired by non-profit organizations and universities were

exempt from the cap. These two reforms meant that the H-1B cap reduction in 2004 repre-

sented much smaller declines in U.S. labor market access to students from abroad deciding

whether to enroll in U.S. graduate programs. Thus, comparing the enrollment behavior of

foreign undergraduates (treated students) relative to foreign graduate students (control stu-

dents) adds another dimension of plausibly exogenous variation to identify the causal impact

of H-1B policy on foreign enrollment.

Thus I build on the insights of Kato & Sparber (2011) and formalize these various reforms

in a classic triple difference regression framework to estimate the causal impact of the H-1B

visa policy on international student enrollment. I gather data from 2000 to 2007 on 149

countries that send undergraduate and graduate students to the U.S. I consider the five

countries–Canada, Mexico, Australia, Chile, and Singapore–to be control countries, whereas

all other countries are treated. I define the pre-treatment period from 2000-2003, and the

post-treatment period from 2005-2007. I remove 2004 from the analysis as Australia was

still considered to be “treated” in 2004. Enrollments are separated by undergraduate and

graduate levels, and I consider undergraduates as treated students, and graduate students

as control students.

21

7.1 Comparison of Means

The top panel of Table 6 shows a simple comparison of average log undergraduate enrollment

for treatment and control countries, before and after the 2004 reforms. The table is divided

into four cells by time (pre-2004 reform vs. post-2004 reform) and country (treated vs.

control). Each cell shows standard errors, clustered at the country level, in parenthesis,

while the number of observations appear in brackets.

Average undergraduate enrollment fell by around 5% for control countries, while falling

12.2% for treated countries. Thus, enrollment fell in treatment countries relative to control

countries by -6.8%. This difference-in-difference estimate (DDTS ) suggests that the 2004

reduction in the H-1B visa cap lowered undergraduate enrollment by nearly 7%. However,

the DDTS estimate is statistically insignificant, likely due to the small number of observations

in the control group. Further, the validity of this difference-in-difference estimate requires

that enrollment in treatment and control countries would have trended similarly in the fall

in the H-1B cap.

We can partially examine this assumption by observing the behavior of graduate enroll-

ment over this period. As stated earlier, by 2004 several reforms had created alternative

pathways for graduate students to gain access to the U.S. labor market. The bottom panel

of Table 6 shows similar mean comparisons of log graduate enrollment. The simple differ-

ences in means show that graduate enrollment declined by a statistically insignificant 1.4%

for control countries, while increasing by 0.9% in treated countries. Thus, the difference-in-

difference estimate for graduate students (DDCS ) suggests that the 2004 drop in the H-1B

visa cap increased graduate enrollment by 2.3%. However, the DDCS estimate is statistically

indistinguishable from zero.

To better assess the fall in the H-1B visa cap of 2004, I turn to a triple difference (DDD)

22

framework. The validity of DDD estimates requires that there were no other shocks that co-

incided with the fall in the H-1B cap and also differentially affected undergraduates in treated

countries. Further, DDD estimate removes trends within-country and within-academic level.

The final row in Table 6 provides the triple difference comparisons in means. The DDD esti-

mate shows that the H-1B reform of 2004 led to nearly a 10% fall in international enrollment

in the U.S.

7.2 Robustness

I examine the robustness of DDD results by using a regression framework. Importantly,

treatment and control countries may differ in a variety of factors that may lead to bias. To

this end I use data from the Penn World Tables on various country-level attributes, and

control for these in the regressions. Formally, I use the following design:

log Elct = α + γc + γl + γt + β1(P × TC) + β2(P × TS) + β3(TC × TS)

+ β4(P × TC × TS) + δXct + εlct (2)

The dependent variable in specification 2 represents log enrollment, which varies by

academic level (l = undergraduates or graduates), country (c) and year (t). I control for

academic level, country, and year effects (γl, γc, and γt, respectively) and all two-way inter-

actions of P (a dummy equal to 1 for all years after the 2004 drop in the H-1B visa cap), TC

(a dummy equal to one for treated countries), and TS (a dummy equal to one for treated

students (undergraduates). The coefficient on the triple interaction, β4, gives the DDD esti-

mate. To explore the robustness of β4, I include various controls (Xct) that vary by country

23

and year. These include population, employment, real GDP per capita, bilateral exchange

rates with the U.S., the value of imports and exports with the U.S., and an Index of Human

Capital per person (from the Barro and Lee Education Indicators Dataset, see Feenstra et

al. (2013) for more details. All control variables are specified in logs except for the Human

Capital Index. The data for control variables all come from the Penn World Tables.

Table 7 reports coefficient estimates of β4 from specification 2. Each column subsequently

adds more controls. Column 1 replicates the DDD result from Table 6. Column 2 adds the

log of population and log of employment.36 Column 3 further adds log of real GDP per

capita. Column 4 includes log bilateral exchange rates. Column 5 adds log of imports (from

the U.S.) and log of exports (to the U.S.). Finally, column 6 includes the Human Capital

Index.37

The results from Table 7 are robust and stable to the inclusion of additional controls. The

estimates suggest that the fall in the H-1B visa cap in 2004 reduced international student

enrollment by between 9.2 and 9.4%. Further, all results are statistically significant at the

10% level. Overall, the findings point to the fact that the changes to H-1B policy have an

unintended impact on foreign students. In this case, decreases in the H-1B cap signal lower

access to the U.S. labor market, which discourages prospective international students from

enrolling in U.S. colleges and universities.

8 Conclusion

International students are an important part of U.S. higher education. Yet very little is

known about the economic forces that encourage or discourage students from abroad to

36Note two countries do not provide employment for all sample years and thus are dropped.37Note that no Human Capital Index is available for 24 countries, and thus they are dropped from the

analysis.

24

apply and attend U.S. colleges and universities. This paper provides an empirical analysis

of the determinants of international student enrollment in the U.S. I find that changes in

college age population to be a strong determinant of international student flows. I find little

role for factors such as exchange rates, living standards in home countries, or trade.

I introduce and test the importance of two novel variables that provide measures of the

strength and access to U.S. labor markets: average wages earned by immigrants in the U.S.,

and H-1B visas issued to sending countries. The results suggest that the availability of H-1B

visas, which are tied to employment in the U.S., are also potentially important for attracting

both undergraduate and graduate students from abroad. Students from around the world

may see potential access to U.S. labor markets as an additional benefit to studying at U.S.

universities.

Finally, I examine a unique natural experiment that restricted labor market access to

some countries, but not others, and also restricted access to some students (undergraduates),

but not others (graduate students). I use a triple difference framework to evaluate the 2004

fall in the H-1B visas cap from 195,000 to 65,000. Comparing enrollment from treated

countries to control countries, and also to treated students and control students, I find

that the 2004 reforms to the H-1B visa program had severe unintended consequences on

international student enrollment in the U.S. The fall in the cap led to a fall in international

enrollment by 9%.

Understanding the determinants of international enrollment in the U.S. is an important

agenda. It is important to note that the focus of this paper has been on the quantity of

foreign students that come to the U.S. and the various economic forces that might lead to

changes in these quantities. However, economic factors may also lead to changes in quality of

foreign students (e.g. Kato & Sparber 2011). Understanding adjustments that take place on

25

both the quality and quantity margins are necessary to understand how various international

economic forces may influence U.S. higher education.

26

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29

Table 1: Top 5 Fields of International students by level, 2012-2013 academic year

Field Total Int'l % Int'l

Mathematics & Statistics 18,903 1,641 8.7%Engineering 82,598 6,353 7.7%Architecture & Related Services 9,847 571 5.8%Business, Management, Marketing, etc. 371,625 21,032 5.7%Computer/Information Sciences 48,072 2,372 4.9%

All fields (Total Bachelor Level) 3,627,046 119,416 3.3%

Legal Professions/Studies 6,616 3,456 52.2%Computer/Information Sciences 21,409 9,378 43.8%Engineering 41,480 17,183 41.4%Mathematics & Statistics 6,280 2,504 39.9%Physical Sciences 6,930 1,976 28.5%

All fields (Total Masters Level) 1,530,404 179,380 11.7%

Engineering 8,766 4,891 55.80%Computer/Information Sciences 1,695 872 51.45%Mathematics & Statistics 1,672 818 48.92%Physical Sciences 5,399 2,155 39.91%Social Sciences 3,623 1,164 32.13%

All fields (Total Doctoral Level) 124,812 33,796 27.1%Note: Data from IPEDS 20122013 Completions Survey on degrees awarded by race/ethnicity, gender, academic level, and field of study. International students are defined within IPEDS as nonresident aliensa person who is not a citizen or national of the U.S. and who is on a visa or temporary basis and does not have the right to remain indefinitely.

Bachelors

Ph.D.

Masters

30

Table 2: Determinants of International Undergraduate Enrollment

(1) (2) (3) (4) (5) (6)Total Total Undergrad. Undergrad. Grad. Grad.

Exchange Rate -0.018 0.036 -0.010 0.066 0.035 0.058(0.044) (0.040) (0.048) (0.044) (0.061) (0.109)

Real GDP per capita 0.279∗∗ 0.170 0.319∗∗ 0.176 0.185∗∗ 0.227(0.121) (0.202) (0.147) (0.223) (0.085) (0.201)

Imports -0.022 -0.019 -0.026 -0.026∗ -0.015 -0.006(0.026) (0.013) (0.031) (0.015) (0.025) (0.018)

Exports 0.068∗∗ 0.028 0.088∗∗ 0.032 0.040 0.012(0.032) (0.023) (0.039) (0.027) (0.031) (0.026)

Tertiary Age Population 0.871∗∗∗ 0.836∗∗∗ 1.029∗∗∗ 0.973∗∗∗ 0.722∗∗∗ 0.628∗∗

(0.202) (0.259) (0.240) (0.311) (0.181) (0.246)

Year effects x x x x x xCountry effects x x x x x xCountry trends x x xObservations 1,781 1,781 1,781 1,781 1,781 1,781Countries 137 137 137 137 137 137

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Note: Regressions use panel data on 137 countries from 1998-2010. The dependent variable in all specificationsis the natural log of undergraduate enrollment. All explanatory variables are expressed in natural logarithms.Models estimated using panel fixed effects (within) estimator. Standard errors are clustered at the country levelto account for serial correlation in residuals within countries.

31

Table 3: Determinants of International Enrollment, excl. China and India

(1) (2) (3)Total Undergrad. Grad.

Exchange Rate 0.036 0.066 0.058(0.040) (0.044) (0.109)

Real GDP per capita 0.170 0.176 0.227(0.202) (0.223) (0.201)

Imports -0.019 -0.026∗ -0.006(0.013) (0.015) (0.018)

Exports 0.028 0.032 0.012(0.023) (0.027) (0.026)

Tertiary Age Population 0.836∗∗∗ 0.973∗∗∗ 0.628∗∗

(0.259) (0.311) (0.246)

Year effects x x xCountry effects x x xCountry trends x x xObservations 1,781 1,781 1,781Countries 137 137 137

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Note: Regressions exclude China and India from the analysis, and thus use panel dataon 135 countries from 1998-2010. The dependent variable in specifications is eitherthe natural log of undergraduate or graduate enrollment. All explanatory variables areexpressed in natural logarithms. Models estimated using panel fixed effects (within)estimator. Standard errors are clustered at the country level to account for serialcorrelation in residuals within countries.

32

Table 4: Determinants of International Enrollment, Wages & H-1B visas

(1) (2) (3) (4) (5) (6)Total Total Undergrad. Undergrad. Grad. Grad.

Exchange Rate -0.117 0.016 -0.113 0.050 -0.016 0.058(0.072) (0.075) (0.092) (0.097) (0.062) (0.085)

Real GDP per capita 0.231∗ 0.242∗ 0.270∗ 0.343∗∗ 0.177 0.149(0.122) (0.123) (0.158) (0.156) (0.107) (0.128)

Imports -0.034 -0.005 -0.036 0.004 -0.015 -0.022(0.028) (0.041) (0.034) (0.049) (0.026) (0.038)

Exports 0.041 -0.048 0.057 -0.081 0.030 0.001(0.039) (0.046) (0.049) (0.053) (0.033) (0.042)

Tertiary Age Population 0.818∗∗∗ 0.687∗∗∗ 0.962∗∗∗ 0.816∗∗ 0.693∗∗∗ 0.780∗∗∗

(0.236) (0.252) (0.292) (0.356) (0.208) (0.203)

H1B Visas Issued 0.068∗ 0.101 0.085∗ 0.138∗ 0.075∗∗ 0.134∗∗

(0.039) (0.067) (0.046) (0.076) (0.033) (0.054)

Average Annual Wage -0.001 -0.007 -0.029(0.025) (0.032) (0.025)

Year effects x x x x x xCountry effects x x x x x xObservations 1,465 998 1,465 998 1,465 998Countries 137 91 137 91 137 91

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Note: Due to the availability of wage data, regressions use panel data on 91 countries from 2000-2010. The depen-dent variable in specifications is either the natural log of undergraduate or graduate enrollment. All explanatoryvariables are expressed in natural logarithms. 3 year lags of H-1B visas are used to reduce mechanical correlationwith the outcome variables. Models estimated using panel fixed effects (within) estimator. Standard errors areclustered at the country level to account for serial correlation in residuals within countries.

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Table 5: Determinants of International Enrollment, H-1B Robustness

(1) (2) (3)Total Undergrad. Grad.

Real GDP per capita 0.246∗∗ 0.348∗∗ 0.153(0.123) (0.155) (0.127)

Imports -0.004 0.004 -0.022(0.041) (0.049) (0.038)

Exports -0.047 -0.080 0.002(0.046) (0.053) (0.042)

Tertiary Age Population 0.682∗∗∗ 0.810∗∗ 0.777∗∗∗

(0.253) (0.357) (0.204)

Average Annual Wage -0.003 -0.009 -0.030(0.025) (0.032) (0.025)

H1B Visas Issued 0.105 0.143∗ 0.137∗∗

(0.068) (0.077) (0.055)

H1B Visas Issued x non-H1B country -0.151 -0.211∗∗ -0.133∗

(0.116) (0.085) (0.075)

Year effects x x xCountry effects x x xObservations 998 998 998Countries 91 91 91

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Note: Due to the availability of wage data, regressions use panel data on 91 countriesfrom 2000-2010. The dependent variable in specifications is either the natural log of un-dergraduate or graduate enrollment. All explanatory variables are expressed in naturallogarithms. 3 year lags of H-1B visas are used to reduce mechanical correlation withthe outcome variables. Models estimated using panel fixed effects (within) estimator.Standard errors are clustered at the country level to account for serial correlation inresiduals within countries.

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Table 6: Triple Difference Estimate of H-1B Policy

Pre (20002003) Post (20052007) Post Pre7.967 7.914 0.054

(0.568) (0.612) (0.056)[20] [15]

6.170 6.048 0.122(0.128) (0.124) (0.032)[576] [432]

DD TS -0.068(0.059)

7.751 7.737 0.014(0.482) (0.513) (0.038)

[20] [15]5.520 5.530 0.009

(0.151) (0.146) (0.025)[576] [432]

DD CS 0.023(0.042)

DDD -0.092(0.05)

Note: Table displays crosstabulated mean log enrollment by country (treatment vs. control countries) and time (Pre2004 vs. Post2004). The year 2004 is dropped from the analysis as Australia did not have an alternative to the H1B visa until 2005. These means are separately calculated for undergraduate and graduate enrollment. Standard errors are reported in parenthesis and are clustered at the country level. The number of observations is reported in brackets.

Control Countries

Treated Countries

Control Countries

Treated Countries

Undergraduates

Graduates

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Table 7: Triple Difference Robustness

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

P X TC X TS -0.092∗ -0.094∗ -0.094∗ -0.094∗ -0.094∗ -0.093∗

(0.052) (0.052) (0.052) (0.052) (0.052) (0.052)

Population x x x x xEmployment x x x x xReal GDP per cap x x x xExchange Rate x x xImports/Exports x xHuman-capital Index xNo. of Countries 149 147 147 147 147 123Obs. 2,086 2,046 2,046 2,046 2,046 1,722

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗ p < 0.01

Note: The pre-treatment years are 2000-2003, and post-treatment years are 2005-2007. Coefficients and standarderrors are reported for triple interaction terms. All specifications control for year effects, country fixed effects,and academic level effects. Additionally, all specifications control for all two way interactions. All other controlvariables are specified in logs except for the Human Capital Index. Standard errors are clustered at the countrylevel to allow for serial correlation of error terms within countries.

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Figure 1: International Student Enrollment Trends in the U.S.

12,118

311,204

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

1954 1975 1982 1986 1990 1994 1998 2002 2006 2010

19,101

339,993

1954 1975 1982 1986 1990 1994 1998 2002 2006 2010

Graduate Undergraduate

Note: Figure uses IIE data, available at http://www.iie.org/Research-and-Publications/Open-Doors/Data

37

Figure 2: International Student Enrollment and Cohort Size

India

China

−5

05

10

∆Enr

ollm

ent

(in 1

000s

)

−2,000 0 2,000 4,000 6,000 8,000 10,000∆College Age

Population (in 1000s)

Undergrad. 1998−2004

India

China

−20

020

4060

∆Enr

ollm

ent

(in 1

000s

)0 5,000 10,000 15,000 20,000 25,000

∆College AgePopulation (in 1000s)

Undergrad. 2004−2010

India

China

−10

010

2030

∆Enr

ollm

ent

(in 1

000s

)

−2,000 0 2,000 4,000 6,000 8,000 10,000∆College Age

Population (in 1000s)

Grad. 1998−2004

India

China

010

2030

∆Enr

ollm

ent

(in 1

000s

)

0 5,000 10,000 15,000 20,000 25,000∆College Age

Population (in 1000s)

Grad. 2004−2010

Note: Figure shows scatterplots between changes in enrollment and changes in college age population for 137countries. Changes are taken over two time periods: 1998-2004 (1st half of sample) and 2004-2010 (2nd halfof sample). Each circle represents an individual country, and circles are weighted by country population atthe start of the period. Lines show best fit line, where the slope of the line (not reported) is the correlationbetween the plotted variables.

38