Essays on the Economics of International

Students in US Higher Education

Mingyu Chen

A Dissertation

Presented to the Faculty

of Princeton University

in Candidacy for the Degree

of Doctor of Philosophy

Recommended for Acceptance

by the Department of

Economics

Adviser: Henry Farber

September 2019

© Copyright by Mingyu Chen, 2019.

All rights reserved.

Abstract

This dissertation studies the economics of international students in US higher education from

three distinct perspectives: (1) who studies in the US and how visa policies influence their

decisions; (2) how increases in foreign student enrollment influence US public universities;

and (3) the value of US college education for students who return to home. A common

theme is the use of large datasets and experimental and quasi-experimental designs to answer

policy-relevant questions.

The first chapter, coauthored with Jessica Howell and Jonathan Smith, documents the

academic ability of international students who attend US college and examines how the F-

1 visa restrictiveness influences that decision. Using data on the universe of SAT takers,

we show that foreign students have higher SAT scores than domestic students. Using an

instrumental variable approach, we find that a higher anticipated visa refusal rate decreases

the number of foreign SAT takers and the probability of sending an SAT score to a US

college. The decreases are larger for high-scoring students.

The second chapter studies the impact of education exports on the outcomes of US

public universities. I construct a modified shift-share instrument that exploits variation

in the ability to pay for US education and institutions’ historical networks with different

economies. I find that an increase in international student enrollment leads to a rise in

in-state enrollment and domestic graduates. Per-student spending does not change, and the

top SAT quartile increases for enrolled students. More international students also lead to

lower published in-state tuition and fewer state appropriations.

The third chapter explores how employers in China value US college education. I conduct

a large-scale field experiment by sending over 27,000 fictitious online applications to jobs in

China, randomizing the country of college education. I find that US-educated applicants

are 18 percent less likely to receive a callback than applicants educated in China, with very

selective US institutions underperforming the least selective Chinese institutions. The results

iii

are consistent with employers fearing US-educated applicants have better outside options and

knowing less about American education. A companion survey of 507 hiring managers finds

consistent and supporting evidence for the experimental findings.

iv

Acknowledgements

I am incredibly grateful to my advisers for their incredible mentorship, support, and encour-

agement. I thank Henry Farber for insightful advising that not only pushes me to think more

deeply about economic theories behind empirical facts but shapes me to a better researcher

overall. Hank has taught me the importance of being an independent researcher and given

me the courage to pursue what indeed interests me from my own life experience. I thank

Leah Boustan for inspiring advising that often leads me to more creative thinking. What

I learned from Leah on immigration and her research agenda has helped me connect my

ideas, which ultimately form the structure and foundation of this dissertation. I thank Will

Dobbie for constructive advising that hammers me to ask better questions and convey ideas

more clearly. I have kept valuable notes from meetings with Will since day one of graduate

school, and I have learned numerous lessons on how to do better empirical research. Each

of the three has a unique style for research and mentorship that I feel fortunate to inherit.

I am very grateful to many other members of the Princeton faculty for their thoughtful ad-

vice. Specifically, thank you to Kirill Evdokimov, Bo Honoré, Adam Kapor, Michal Kolesár,

Alan Krueger, Ilyana Kuziemko, David Lee, Alex Mas, Eduardo Morales, Christopher Neil-

son, Richard Rogerson, Cecilia Rouse, and Wei Xiong. I owe a huge debt of gratitude to

Ceci and Dave, who both have given me so much light and support throughout graduate

school despite being busy with high-level administrative work. I have greatly benefited from

Alex’s advice and learning from his research designs. I thank Alan for being so kind to me

and my wife and taking us to various social events. I am also thankful for the generous help

of Laura Hedden and Stephen Redding, especially during the job market.

The Industrial Relations Section is my academic root. In the last seven years, I truly

felt home at the Section. I am thankful for the unyielding help and support of Linda

Belfield, Valerie Ching, Lori Mitrano, Jeannie Moore, Patti Tracey, and many others who

have contributed to the caring and stimulating social life of the Section. I am grateful for

v

the financial support I have received from the Industrial Relations Section, the Graduate

School at Princeton University, and the Fellowship of Woodrow Wilson Scholars.

I cannot imagine my graduate school without meeting many amazing people and am

thankful for the support and friendship of Theresa Andrasfay, David Arnold, Jessica Brown,

David Cho, Liyu Dou, Jonathan Gao, Felipe Goncalves, Daniel Herbst, Paul Ho, Zongbo

Huang, Elisa Jacome, Andrew Langan, Luisa Langan, Pauline Leung, Mark Li, Ernest

Liu, Mathis Maehlum, Graham McKee, Steve Mello, Fernando Mendo, Terry Moon, Simon

Quach, Whitney Rosenbaum, Jakob Schlockermann, Neel Sukhatme, Chang Sun, Julius

Vutz, Yulong Wang, Shanshan Yang, Yifan Yu, Qu Yuan. I am especially indebted to An-

drew Langan and Steve Mello for seven years of accompany and teaching me so much about

what is important in life, to Liyu Dou and Yulong Wang for six years of friendship and

sharing their knowledge on econometrics, and to David Cho for his incredible broad knowl-

edge and spiritual support during the job market. I am also thankful to Jessica Howell and

Jonathan Smith, coauthors of a chapter of my dissertation, for granting me the opportunity

to work with them in DC for a summer and access super cool education data.

Many people guided and supported me before graduate school. I thank Colin Campbell,

Roger Klein, Carolyn Moehling, and Milagros Nores for their mentorship and encouragement

during my undergraduate studies at Rutgers. I thank Carolyn Moehling for recommending

me to work at the Fed and Maria Cannon for her support of me leaving the Fed to work for

the Section. Without looking up the websites of Alan and Ceci when I was an undergraduate,

I would never have the courage to pursue an economics Ph.D. for my interest in education

research. Without working closely with Dave and Alex, I would never be so sure of the path

of applied microeconomics. I also thank Wei Wang for showing me life as an economics

graduate student and Linpeng Zheng and Tal Elmatad for being supportive.

Thank you to my parents Xiao and Haipin for their unconditional love. Their support

of me to first study in the US as an exchange student has led to where I am today. Thank

vi

you to my grandparents Guojing and Danjun, and my aunts and uncles Hui, Yi, Jing, and

Xun for their constant support. Thank you to Ruth and Rich Fluegge for giving me a home

in the thumb of Michigan when I needed it the most.

Finally, I would like to dedicate this dissertation to my wife Chentong, who has given

me so much love and support. Her curious nature, hard-working ethic, and heart-warming

smiles have been an infinite source of inspiration, motivation, and happiness.

vii

To Chentong and the forthcoming joy who currently lives in her body.

viii

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

1 Best and Brightest? The Impact of Student Visa Restrictiveness on Who

Attends College in the US 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Academic Ability of International Students in the US . . . . . . . . . . . . . 11

1.4 Who Comes to the US (and Who Doesn’t) . . . . . . . . . . . . . . . . . . . 15

1.5 Nonimmigrant Visas Institutional Background . . . . . . . . . . . . . . . . . 19

1.6 The Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Appendices 59

.1 Appendix figures and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2 The Impact of Service Exports on the US Higher Education Market 75

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

ix

2.2 Background and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

2.4 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Appendices 101

.1 Appendix figures and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

.2 Appendix on data imputation . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3 The Value of US College Education in Global Labor Markets: Experimen-

tal Evidence from China 111

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.2 Background and prior research . . . . . . . . . . . . . . . . . . . . . . . . . . 118

3.3 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

3.4 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.5 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Appendices 173

.1 Appendix figures and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

.2 Non-Experimental Data Appendix . . . . . . . . . . . . . . . . . . . . . . . . 192

.3 Additional Details on Experiment Implementation . . . . . . . . . . . . . . . 197

.4 Employer Survey in English . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

x

List of Tables

1.1 Summary statistics of SAT enrollees, 2004-2015 cohorts . . . . . . . . . . . . 49

1.2 Nonimmigrant visa statistics, 2004-15 . . . . . . . . . . . . . . . . . . . . . . 50

1.3 Regression of the number and academic ability of new foreign students . . . 51

1.4 Regression of the number and academic ability of new foreign SAT takers . . 52

1.5 Regression of the probability of sending a score . . . . . . . . . . . . . . . . 53

1.6 Regression of the number of score sends . . . . . . . . . . . . . . . . . . . . . 54

1.7 Regression of the selectivity of score sends . . . . . . . . . . . . . . . . . . . 55

1.8 Regression of the probability of enrolling a US college . . . . . . . . . . . . . 56

1.9 Regression of the selectivity of the US college enrolled . . . . . . . . . . . . . 57

1.10 Regression of the probability of enrolling a US college for score senders . . . 58

A.1 Summary statistics of SAT enrollees, 2004-2015 cohorts . . . . . . . . . . . . 64

A.2 Summary statistics of the sample for student-level analysis . . . . . . . . . . 65

A.3 Regression of SAT score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.4 First-stage regression of the F-1 visa refusal rate . . . . . . . . . . . . . . . . 67

A.5 Regression of the number and academic ability of new foreign students . . . 68

A.6 Regression of the number and academic ability of new foreign students . . . 69

A.7 Regression of enrollment outcomes from student-level analysis . . . . . . . . 70

A.8 Poisson regression of the number of score sends . . . . . . . . . . . . . . . . 71

A.9 Regression of the selectivity of score sends (maximum SAT) . . . . . . . . . 72

xi

A.10 Regression (OLS) results from the economy-year-level analysis for VWP mem-

bers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.11 Regression (OLS) results from the student-level analysis for VWP members . 74

2.1 Summary statistics (mean) by public institutional type in selected years . . . 95

2.2 The effect of new foreign enrollment on new domestic enrollment and graduates 96

2.3 IV regression on student expenditures and new faculty hires . . . . . . . . . 97

2.4 IV regression on SAT quartiles of the freshman class . . . . . . . . . . . . . . 98

2.5 Regression on log state appropriations . . . . . . . . . . . . . . . . . . . . . 99

2.6 IV regression on log listed tuition and log institutional aid . . . . . . . . . . 100

A.1 US trade in services by type in 2018 . . . . . . . . . . . . . . . . . . . . . . . 105

A.2 OLS regression on student expenditures and new faculty hires . . . . . . . . 106

A.3 OLS regression on SAT quartiles of the freshman class . . . . . . . . . . . . 107

A.4 OLS Regression on log state appropriations . . . . . . . . . . . . . . . . . . . 108

A.5 OLS regression on log listed tuition and log institutional aid . . . . . . . . . 109

3.1 Programs and occupations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

3.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

3.3 Callback regressions by occupation . . . . . . . . . . . . . . . . . . . . . . . 163

3.4 Callback regressions by posted salary quartiles . . . . . . . . . . . . . . . . . 164

3.5 Callback regressions by employment status of applicants with US degrees . . 165

3.6 Callback regressions by firm ownership and job English requirement . . . . . 166

3.7 Callback regressions by posted salary quartiles and firm ownership . . . . . . 167

3.8 Callback regressions by signals of pre-college credentials . . . . . . . . . . . . 168

3.9 Callback regressions by US work experience for applicants with US degrees . 169

3.10 Callback regressions by experimental samples (business jobs) . . . . . . . . . 170

3.11 Interview regression from the employer survey’s choice experiment . . . . . . 171

xii

3.12 The most important reason for hiring managers choosing a Chinese university

over a US university in the employer survey . . . . . . . . . . . . . . . . . . 172

A.1 Shares of enrollment and degrees awarded in the US by program . . . . . . . 178

A.2 US institutions used in the experiment . . . . . . . . . . . . . . . . . . . . . 179

A.3 Chinese institutions used in the experiment . . . . . . . . . . . . . . . . . . . 183

A.4 Interview regressions by occupation . . . . . . . . . . . . . . . . . . . . . . . 185

A.5 Callback differences by institution group for all jobs . . . . . . . . . . . . . . 186

A.6 Callback differences by institution group for business jobs . . . . . . . . . . . 187

A.7 Callback differences by institution group for computer science jobs . . . . . . 188

A.8 Callback regressions by posted salary quartiles (alternative measure) . . . . . 189

A.9 Callback regressions by firm ownership and Chinese work experience . . . . . 190

A.10 The most important reason for hiring managers choosing a US university over

a Chinese university in the employer survey . . . . . . . . . . . . . . . . . . 191

xiii

List of Figures

1.1 Aggregate visa refusal rates for student and visitor visas . . . . . . . . . . . 34

1.2 Histogram of F-1 student visa refusal rate across economies in 2017 . . . . . 35

1.3 Foreign undergraduate enrollment in the US . . . . . . . . . . . . . . . . . . 36

1.4 Foreign undergraduate enrollment in the US by economy . . . . . . . . . . . 37

1.5 SAT and IPEDS data comparison for new foreign students in the US . . . . 38

1.6 Cumulative distribution function of SAT score, 2004-15 cohorts . . . . . . . 39

1.7 College graduation rate by residency . . . . . . . . . . . . . . . . . . . . . . 40

1.8 New foreign students in the US by SAT quantiles . . . . . . . . . . . . . . . 41

1.9 New foreign students in top SAT quantiles by economy . . . . . . . . . . . . 42

1.10 Share of foreign students in top SAT quantiles by economy, 2004-15 cohorts . 43

1.11 Aggregate trends of foreign SAT takers, score senders, and enrollees . . . . . 44

1.12 Fraction of SAT takers send a score to at least one US college and enroll by

economy, 2004-15 cohorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.13 SAT median for test takers, score senders, and enrollees by economy . . . . . 46

1.14 Enrollment probability, score sending behavior, and SAT score . . . . . . . . 47

1.15 Visa refusal rate by type and economy . . . . . . . . . . . . . . . . . . . . . 48

A.1 New foreign students in the US by economy . . . . . . . . . . . . . . . . . . 61

A.2 New foreign students in top SAT quantiles by economy by math and verbal . 62

A.3 Visa refusal rate by type and economy . . . . . . . . . . . . . . . . . . . . . 63

xiv

2.1 Listed undergraduate tuition and fees at four-year institutions (2010 USD) . 93

2.2 Foreign undergraduate enrollment in the U.S. by economy . . . . . . . . . . 94

A.1 World tertiary education enrollment by income group (millions) . . . . . . . 103

A.2 Graphic presentation of the first-stage regression . . . . . . . . . . . . . . . . 104

3.1 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

3.2 Distribution of world rankings for sample institutions by country . . . . . . . 156

3.3 Distribution of average test score percentiles for sample institutions by country157

3.4 Callback rates by selectivity groups of institutions . . . . . . . . . . . . . . . 158

3.5 Callback rates by percentiles of the average test score for enrolled students . 159

3.6 Distribution of hiring managers’ self-rated knowledge of undergraduate edu-

cation quality for institutions listed in the employer survey’s choice experiment160

A.1 International undergraduate enrollment in the US by country . . . . . . . . . 174

A.2 Estimated transition probabilities for international/Chinese students who re-

ceived bachelor’s degrees in the US, 2015 and 2016 . . . . . . . . . . . . . . 175

A.3 Distribution of university world ranking by country . . . . . . . . . . . . . . 176

A.4 US-China gap in callback rates by posted salary deciles . . . . . . . . . . . . 177

xv

Chapter 1

Best and Brightest? The Impact of

Student Visa Restrictiveness on Who

Attends College in the US1

1.1 Introduction

An F-1 student visa enables international students to enter the US for their study legally,

and it is the immigration program that brings the US the largest number of highly educated

foreigners. Foreign students typically apply for an F-1 visa at a US Embassy or Consulate

after being admitted to a college. However, despite there being no official cap on F-1 visa

issuance, there is substantial uncertainty in the application process. The F-1 visa refusal

rate ranges from 15 percent to 28 percent between 2003 and 2018 worldwide (see Figure

1.1) with substantial variation across economies (see Figure 1.2). Changes in the expected

probability of obtaining a student visa may influence who decides to pursue an education in

1We thank Leah Boustan, Will Dobbie, Henry Farber, Elisa Jacome, and Kevin Shih for their helpfulcomments and suggestions. Fangyi Xie provided excellent research assistance. The Princeton UniversityIndustrial Relations Section provided generous financial support. This paper does not reflect the views ofthe College Board. All errors are our own.

1

the US. For example, in the wake of trade tensions between the US and China, the Chinese

government warned students about their prospects of receiving a visa, leaving many Chinese

students and US university administrators concerned about the likelihood of studying in the

US (e.g., Redden, 2019).

In this paper, we study whether the US attracts international students with high aca-

demic ability, and how these foreign students’ human capital investments respond to changes

in uncertainties of entry into the US. We compile a student-level dataset that contains infor-

mation on SAT scores, demographics, SAT score sending, and US college enrollment for the

universe of foreign SAT takers in the 2004 to 2015 high school graduating cohorts. Our data

are also matched with economy-year varying visa refusal rates. We observe not only foreign

students who study in the US but also those who have indicated some interest in pursuing

US education. We use this dataset to address two questions: What is the academic ability

of foreign undergraduates in the US? And, how does F-1 visa restrictiveness affect foreign

students’ decisions when investing in US college education?

Understanding who comes to the US to study and why are of particular importance for

education and immigration policy. First, foreign students pay full tuition that subsidizes

American institutions, especially those who face increased tuition and decreased state ap-

propriations (e.g., Bound et al., Forthcoming; Chen, 2019a), yet little is known about the

potential gains for schools beyond tuition revenue such as peer academic ability and diverse

student background. Second, answers to our questions are central to the policy debate on

favoring high-skilled migrants. Foreign students have become the major supply of skilled

foreign workers for US employers. In 2016 and 2017, 78 percent of H-1B visa approved for

new employment were awarded to foreigners on an F-1 visa.2

Our paper begins by documenting the academic ability of foreign students who come

to the US for college, something that is almost entirely unexplored. We show that foreign

2Based on authors’ calculation from data obtained from the USCIS.

2

students have, on average, better academic credentials than their US domestic counterparts.

Focusing on our primary (but not only) measure of academic ability, foreign students score

133.3 SAT points (0.64 standard deviations) more than domestic students and are 20 percent

more likely to be above the 90th percentile of US test takers. The foreign-US gap in SAT

scores is largely driven by the fact that foreign students are more concentrated at selective

institutions which also take domestic students with high SATs. The statistics on pre-college

academic credentials are consistent with long-term college outcomes: the six-year graduation

rate for foreign students is more than 10 percent higher than US students.

We discover that the large increase of foreign students in the US in the last decade is

driven by those with SAT scores in the top quartile of US takers. Chinese students are

the major contributor, who account for one-third of the international undergraduates and

outperform the average foreign student. While the SAT advantage of foreign students mostly

comes from the math section, the amount of foreign students in the top quartile of verbal

section also increases over time.

Next, we show that there are many high-scoring foreign students who appear to seri-

ously consider coming to the US by moving through the college application process but

never enroll. First, foreign students who take SAT have higher scores than domestic SAT

takers. Second, less than half of the foreign SAT takers send official SAT scores to any US

college, which serves as a proxy for college applications (Card and Krueger, 2005; Pallais,

2015; Smith, 2018). Fewer than one-third of foreign SAT takers eventually enroll. Third,

there is a positive selection into score sending and US enrollment—foreign score senders and

enrollees have higher SATs than foreign SAT takers. While the same pattern also holds for

domestic students, the degree of positive selection is much larger for foreign students. Lastly,

conditioning on the same SAT score, foreign students are less likely to send an SAT score or

enroll in the US than domestic students

3

Moving to our second research question, we explore how (expected) F-1 visa restric-

tiveness affect foreign students’ college applications and enrollment outcomes. We measure

anticipated visa restrictiveness with economy-year varying visa refusal rates faced by foreign

students around the time of making SAT taking decisions. Because visa applications can only

happen after college admissions, increased expected restrictiveness may depress SAT taking

and score sending if students perceive a lower expected benefit of the application process

due to a lower probability of visa approval. We refer to this discouragement of action as the

chilling effect. A higher visa refusal rate may also reduce foreign enrollment mechanically

conditional on college applications and acceptances. We do not estimate the mechanical

effect in this paper.

Simply regressing college related outcomes on F-1 visa refusal rate may suffer from si-

multaneity bias because the refusal rate can be driven by changes in the supply of students

and not visa policy restrictiveness. To address this potential issue, we instrument F-1 visa

refusal rate with visitor visa refusal rate, which is not driven by student visa applicants and

isolates the variation in general visa restrictiveness for US entry. Another potential issue is

that visa restrictiveness may be correlated with other economy-level factors that also affect

our outcomes of interest. We include a set of economy-year-level controls or whenever we

can, economy-year fixed effects, to address the potential omitted variable bias. In practice,

the instrument makes an important difference to our estimates while the controls for omitted

variables do not.

Overall, we find that a higher F-1 visa refusal rates decrease both the quantity and

academic ability of the foreign students enrolled at US colleges. A 10 percentage point (pp)

increase in the F-1 visa refusal rate decreases foreign enrollees by 14.84 percent, median SAT

by 10.36 percent, and the share of students above the 75th SAT percentile by 2.90 percent.

We find that these overall effects come from discouragement at all measurable stages of the

college application process. In response to an increase in student visa restrictiveness, fewer

4

foreign students take the SAT and students are less likely to send an SAT score to US college,

conditional on taking SAT. The effects are larger for high-scoring students.

One possibility that high-scoring students are more responsive to visa restrictiveness is

that they have less choice in adjusting their application portfolio. We find that conditional on

sending an SAT score, students send scores to more selective US colleges on average, which

increases the expected benefit of college application. High-scoring students are less responsive

in this dimension than low-scoring students especially for the most selective school where

they send scores to. Presumably, high-scoring students already send scores to selective US

colleges and are limited in changing application portfolio. Other possibilities are discussed

further in Section 1.7.3.

Our paper makes several contributions to both established literatures and policy on edu-

cation and immigration. First, it contributes to the immigration literature on international

students. One million foreign students study in the US every year (Institute of International

Education, 2017), and the number of student visas issued has been larger than the number

of work visas (H-1B) and skill-based green cards combined since as early as 1997. Despite

its importance, research on the international student population has been limited and tradi-

tionally focused on graduate students before the mid-2000 period (e.g., Bound et al., 2009;

Shih, 2017).

There is a renewed research agenda on foreign undergraduate students, likely as a result

of their swelling numbers.3 Bound et al. (Forthcoming) find that reductions in state appro-

priation have led increases in foreign undergraduates who pay full tuition, and Chen (2019a)

finds that exporting undergraduate education subsidizes domestic students and increase de-

grees award spending per student. Chen (2019b) finds that job applicants with US college

education are less likely to receive callbacks from Chinese employers than those educated in

3Between 2006-07 and 2016-17 academic year, foreign student enrollment in the US increased 48 percentfor graduate students and 84 percent for undergraduates. More than half of foreign students in the US areundergraduates.

5

China. Our paper differs from these papers with the richness of the data and the questions

it allows us to answer. Our measures of academic ability demonstrate that there are po-

tential benefits of foreign students on campus beyond finances and the US has historically

attracted relatively high-achieving students. We are the first to quantify and show that the

US does not attract a large fraction of the high-achieving SAT takers, suggesting there is

some low-hanging fruit for US colleges and perhaps the labor market.

Findings from our paper also contribute to our broad understanding of human capital

investment. A large literature has studied educational decisions in response to shocks of labor

market returns (e.g., Jensen, 2010; Abramitzky and Lavy, 2014; Wiswall and Zafar, 2014;

Shah and Steinberg, 2017; Charles et al., 2018; Kuka et al., Forthcoming) and college cost

(e.g., Deming and Dynarski, 2010; Dynarski et al., 2018). In particular, Kato and Sparber

(2013) and Shih (2016) study how foreign students respond to the expected chance of working

in the US after graduation. Kato and Sparber (2013) use data aggregated from a subsample

of SAT takers prior to mid-2000 and find that a reduction in the H-1B visa quota decreases

SAT score sends to US colleges. Shih (2016) finds that the aggregate stock of foreign students

also decreases after the quota reduction. In contrast, we examine how global human capital

investment respond to changes in the expected chance to enter the US. We also uniquely

observe a variety of student-level outcomes throughout the college application process, which

allows us to evaluate the impact of F-1 visa policy on individual-level investment in college

applications, and enrollment. From a policy perspective, if the US wants to attract more

foreign undergraduate students, our results suggest that visa restrictiveness is a path to

consider.

The rest of the paper proceeds as follows. In Section 1.2, we discuss data sources and

compare our data with the few external data sources on international students. In Section

1.3, we first provide summary statistics on various measures of academic ability for interna-

tional students in the US and make comparisons with their US peers. We then study the

6

trends in foreign students and their economy of origin by SAT quartiles. Section 1.4 contains

an exploration of three foreign student groups in our data: SAT takers, score senders, and

enrollees. We provide descriptive information on their SAT scores, score sending behaviors,

and enrollment probability. In Section 1.5, we describe the necessary institutional back-

grounds of nonimmigrant visa programs in the US. We lay out our empirical strategy and

discuss our analysis sample in Section 1.6. We present the estimation results and discuss

their interpretations and robustness in Section 1.7. Section 1.8 concludes.

1.2 Data

1.2.1 Data sources

Our primary data source is student-level data from the College Board on the universe of SAT

takers in the 2004-2015 high school graduating cohorts. The SAT is one of the two primary

standardized tests for US college entrance. Throughout the paper, we consider SAT scores

from the math and verbal section, each of which has a minimum of 200 and maximum of

800, making the combined score between 400 and 1,600.4

We define an international test taker as someone who had a foreign mailing address and

attended a foreign high school.5 A student’s economy of origin is defined as the economy

listed on the mailing address. We observe close to one million foreign test takers. Along

with SAT scores, the data also contains information on where students sent their official

score reports (“score sends” hereafter), basic demographics such as gender, age, parental

education, and family income, along with addition information on academic ability such as

4The writing section was introduced after 2006. For consistency across years, we do not include thewriting section. Our results do not change qualitatively if including the writing section.

5The College Board does not directly asks the question of nationality at test registration. We do notconsider US territories as foreign and we exclude addresses for foreign US military bases and foreign schoolsfor US armed forces.

7

SAT subject tests, Advanced Placement (AP) exams and self-reported high school GPA and

class rank.

We complement our analysis with several other datasets. First, we track US enrollment

by merging the SAT taking data with the National Student Clearinghouse (NSC), which

tracks 97 percent of college enrollments at Title-IV, degree-granting institutions. We do not

include enrollment at online institutions, and we use the first college that a student enrolls

in as the enrollment outcome. Second, we obtain information on institutional characteristics

such as graduation rates from the US Department of Education’s Integrated Postsecondary

Education Data System (IPEDS).

Third, for our analysis on the impact of F-1 visa restrictiveness on students’ score sending

behaviors and US enrollment outcomes, we obtain annual economy-specific refusal rates for

student and travel visas via Freedom of Information Act requests to the US Department of

State. We measure visa restrictiveness with refusal rates around the time students making

college application decisions, and we describe in more detail in Section 1.5.

Fourth, we use an additional set of variables that vary at the economy-year-level coming

from a variety of sources. Information on economic conditions including real GDP per capi-

tal in USD, exports, and imports are from the Penn World Table 9.1. For each economy, the

college-aged population and postsecondary enrollment in other popular destinations (Aus-

tralia, Canada, and U.K.) are obtained from a combination of the UNESCO Institute for

Statistics, manual collections from official local government websites, and requests to release

information.

When studying the selectivity of score sends and the schools enrolled, we construct mea-

sures of school selectivity based on the SAT scores of each school’s entering freshman class

reported in IPEDS. It is common in the literature to measure college selectivity with test

scores of the matriculated students (e.g., Loury and Garman, 1995; Dale and Krueger, 2002;

Hoxby and Turner, 2013; Pallais, 2015; Mountjoy and Hickman, 2019). In practice, we take

8

the average of the 25th and 75th percentile, and following Pallais (2015), we use test scores

from a base year, 2003, prior to our sample period, so that the analysis is not confounded

by changes in selectivity over time.

1.2.2 Aggregate enrollment trends and comparison to external

data sources

Despite our data having detailed information on international students, it is not a census

of foreign students in the US. We take pause to look at two external sources to better

understand the advantages and deficiencies of our data, along with aggregate trends from a

global perspective.

One of the primary data sources on international students comes from the Fall Enroll-

ment Survey in IPEDS. The data provides two relevant data points at the school-year level:

total foreign student enrollment and new foreign student enrollment at the undergraduate

level. Figure 1.3 plots the trends for these two variables. Between 2002/03 and 2007/08

academic years, there was relatively little change in the total number of foreign undergradu-

ates enrolled at US institutions. Between 2008/09 and 2017/18, the aggregate count jumped

from approximately 250,000 foreign students to 450,000 students. Although the number of

new foreign undergraduate students is much smaller than the total stock of international

students, we see a similar pattern that equates to a nearly doubling of new foreign students

with sharp increases after 2007/08.

The other most commonly used data on international students comes from an annual

college survey conducted by the Institute of International Education (IIE), covering about

3,000 US institutions. The survey collects information on total foreign student enrollment

by academic level and economy of origin. Figure 1.3 shows that the levels and trends of IIE

data on total foreign enrollment closely mirrors that of IPEDS.

9

IIE data diverges from IPEDS, as does our SAT data, by having enrollment information

by economy of origin. Figure 2.2 shows the trends of total foreign students enrolled in the

US by economy. China is a clear outlier. Between 2007/08 and 2017/18, the total number

of Chinese undergraduates grew from about 10,000 to almost 150,000, contributing to 70

percent of the total foreign student increase over this period and accounting for one-third

of international students today. While all other countries are dwarfed by China, there are

sizable increases in the number of students from India, Saudi Arabia, South Korea, and

Vietnam.

Our SAT data allow us to create aggregate counts of newly enrolled undergraduates,

but not the stock of total students. We first compare the trends of new foreign students in

SAT data with IPEDS in Panel (a) of Figure 1.5. The SAT data accounts for 59 percent of

new international student enrollees at all undergraduate institutions in IPEDS, suggesting

that there are alternative paths to the US, such as taking the ACT or enrolling in colleges

that do not require college entrance exams.6 In Panel (b) of Figure 1.5, we show the same

trends for four-year colleges and 231 selective institutions defined by Barron’s rankings that

are more likely to require a college entrance exam. We have slightly better coverage at

four-year colleges (63 percent of IPEDS), where most of foreign students enroll. At selective

institutions, our coverage is much better (82 percent of IPEDS).7 Lastly, we reproduce

Figure 2.2 that uses IIE data at economy-year-level but with our SAT data for newly enrolled

students. Appendix Figure A.1 shows similar aggregate patterns whereby there are increases

in international students since around 2008 that are primarily driven by China.

6To our best knowledge, foreign ACT takers is only about 10 percent of all foreign students who takeeither an SAT or ACT in 2014.

7Note that the increase in the gap between our data and IPEDS since 2012 is partially due to an increasein the blocking of institutional information at NSC.

10

1.3 Academic Ability of International Students in the US

1.3.1 Summary statistics on academic ability and demographics

We start by documenting the average academic ability of international students enrolled in

the US for the 2004-15 cohorts and make comparisons with domestic US students. Table

1.1 shows summary statistics of various academic measures as well as demographics for US

and foreign students. Because in Section 1.2.2 we show that China has become the economy

with the most number of students in the US and contributing to the most of international

student growth, we also separately report the same summary statistics for Chinese students.

The first section of Table 1.1 shows statistics related to standardized tests administrated

by the College Board, where we have data points for all 15 million US students and 267

thousands foreign students (including about 50 thousands Chinese students). On average,

compared to US students, foreign students score 133.3 points (or 13 percent) higher on SAT

with similar standard deviation and Chinese students score 207 points (or 20 percent) higher

with a smaller standard deviation. The foreign- and China-US gaps in SAT score mostly

come from the math section, where foreign students score 104.9 points higher on math and

Chinese students score 195.7 points higher on math.

Foreign students on average sent SAT scores to 2.3 more US colleges than domestic

students (conditional on sending to at least one school). They are more than twice as likely

to take an SAT subject test and an AP exam. They also score higher on SAT subject tests

and AP exams. As it was the case for SAT, Chinese students do better than the average

foreign student on these measures.

The second section of Table 1.1 shows self-reported high school rankings and GPA. Among

foreign students, about 60 percent reported that they are among top 10 percent in their high

school class, a quarter of reported that they are among top 11-20 percent, and close to 10

percent reported that they are among top 21-40 percent. Chinese students reported very

11

similar ranking distribution, while rankings for US students are not as concentrated at top.

The reported GPA for US students is 0.11 lower than foreign students and 0.38 lower than

Chinese students. One concern for these reported measures is that the non-reporting rates

for foreign students are much higher than US students. We find that foreign students who

did not report class ranking have SAT score similar to those ranked top 11-20 percent, and

foreign students who did not report GPA score 40 points lower on SAT than those who

reported. The foreign non-reporters for both class ranking and GPA have much higher SAT

scores than US non-reporters.

The third section of Table 1.1 shows self-reported demographics. While age and gender

are required fields, family income and parental education are not. On average, there is little

age difference between foreign students and US students, but foreign students are less likely

to be female. While foreign students in the US may be on average richer than their peers

at home, the reported family income shows that twice more of them are from the bottom

income category relative to US students. This suggests that some of the foreign families may

finance their children’s American education via loans, high savings, or other types of assets

such as housing. Lastly, one striking difference is that parents of foreign (Chinese) students

26.0 (16.1 percent more likely to be college educated than US students.

Thus far, we are comparing all foreign students with all domestic students in the SAT

data without constraining to particular sets of schools. While a quarter of US students who

took SAT are enrolled at two-year colleges, most foreign students are enrolled at four-year

colleges. Appendix Table A.1 reproduces Table 1.1 for US students in the same set of schools

as the foreign students. The numbers are similar and the patterns discussed above are the

same. This implies that the set of colleges attended by US students in our SAT data are

very similar to the set attended by foreign students.

Figure 1.6 compares the cumulative distribution of SAT score across foreign students,

Chinese students, US students, and US students in the same schools as foreign students. We

12

plot the SAT distributions at all schools in Panel (a) and at selective (four-year) colleges in

Panel (b). The foreign-US gap in SAT score persists even among the selective colleges, even

though the gap is much smaller. For example, Panel (a) shows that about 30 percent of

foreign students have SAT scores above the 90th percentile of the US test takers in the same

cohort, compared to about 10 percent of domestic students. Panel (b) shows among selective

institutions, 45 percent of foreign students have SAT scores above the 90th percentile of the

US takers, compared to about 35 percent of domestic students. These patterns suggest

while on average foreign students in the US have higher SAT scores than US students, the

difference in the type of college where students are concentrated can explain much of the

foreign-US gap in SAT.8

We provide one additional piece of evidence on international student academic ability—

college graduate rate from IPEDS. Panel (a) of Figure 1.7 reports trends of graduate rates

by college sector. For both four-year institutions and two-year institutions, foreign students

are about 10 pp more likely to graduate than domestic students in recent cohorts. Panel (b)

of Figure 1.7 focuses on the four-year colleges and reports graduate rates by whether schools

are covered by SAT data. Consistent with other academic measures discussed earlier, foreign

students have higher 6-year graduation rates than domestic students at schools covered by

SAT data. This difference in graduate rate is even larger at schools not covered by SAT data

for recent cohorts.9 Hence, international students at schools not covered by our SAT data

are unlikely underperforming than their US peers. In the rest of the paper, we will focus on

SAT score as the academic measure measure of students.

8In Appendix Table A.3, I regress SAT score on whether a student is foreign. It shows that after controllingfor school fixed effects, the foreign-US difference in SAT largely diminishes, suggesting foreign students aremore concentrated at selective institutions. The Table also shows that foreign students at public and lessselective institutions have higher scores than their domestic peers, but not otherwise.

9The graduate rates for foreign students at schools not covered by SAT data are volatile for cohorts priorto 2006. This is due to small number of enrolled students from those cohorts.

13

1.3.2 Students with high SAT scores

In this subsection, we focus on high ability international students, as measured by SAT

scores, and explore their trends and economy of origin. In Panel (a) of Figure 1.8, we split

the students into four groups based on their SAT quartile. We also create a group for

students with score above the 90th percentile. All SAT quantiles mentioned in this paper are

relative to domestic US test takers in the same high school cohort. It is clear in Panel (a)

that relative to students from quantiles with high SAT scores, the number of foreign students

in the two bottom quartiles experienced only minor growth. Low-scoring foreign students is

the smallest share of foreign students.

In contrast, the numbers of international students in the top SAT quartile (above the 75th

percentile) have been growing dramatically over time. In 2004, there were approximately

6,000 of these international students, five times the number of students in the bottom quar-

tile. By 2017, the number of high-scoring foreign students jumped to over 18,000 students,

nearly nine times the students in the bottom quartile. The trends for students with score

above the 90th percentile are qualitatively similar. Overall, these patterns suggest that the

US are more likely to attract foreign students with high SAT scores and increasingly so.

Panel (b) of Figure 1.8 shows that these trends are coming primarily, but not exclusively,

from international students with extremely high scores on the math section of the SAT.

We examine where the high-scoring international students are coming from and how

it has changed over time in Figure 1.9. The trends of five economies that send the most

students to the US with SAT scores above the 75th percentile are shown in Panel (a) and

with SAT scores above the 90th percentile are shown in Panel (b). South Korea, Canada,

and Singapore follow similar patterns, each slightly increasing in numbers of high achievers

from 2004 to 2011 and a slight decline after. India, on the other hand, continues its upward

trajectory and has pulled away from those three economies since 2012. In a league of their

own, high-scoring Chinese students start to come to the US in 2007 and the numbers grow

14

exponentially in all subsequent years. In fact, the number of Chinese students with high

SAT scores nearly matches the number of high achieving students from all economies other

than the top five combined in the recent years. Appendix Figure A.2 reproduces Figure 1.9

but separately for math and verbal subsections.

Figure 1.9 masks the relative proportions of high achievers from each economy, which

Figure 1.10 remedies with pie charts. The left side shows the fraction of foreign students

scoring above the 75th SAT percentile from each economy and by test section: 34 percent

of all such students come from China, 9 percent from India, and 44 percent from all other

economies combined. The right side shows this pattern is similar for students above the 90th

percentile. However, while China sends 45 percent of all the foreign students with math

scores above the 90th percentile, largely drawing from the “other” countries, it only sends

24 percent of foreign students with verbal scores above the 90th percentile, largely drawn by

the “other” countries. This is substantially lower than the proportion of Chinese math high

achievers but still quite substantial given the language differences.

1.4 Who Comes to the US (and Who Doesn’t)

1.4.1 SAT takers, score senders, and enrollees

An advantage of the College Board data relative to other datasets on international students

is that we observe students who have shown some interest in studying in the US (by taking

the SAT and/or sending SAT scores to US colleges) but do not necessarily end up enrolling

in the US. Less than half of the foreign SAT takers send SAT scores to a US college and less

than one third enroll.

We focus our discussion on three groups of international students—SAT takers, score

senders, and enrollees. A score sender is an SAT taker who sends score to at least a US

college. Score sends are often costly. Students can choose up to four schools before taking

15

the test to send their score for free, and this decision cannot be altered after the test. Each

score send ordered after taking the SAT or beyond the four free sends before the test costs

around $10 during our sample period. An enrollee is an SAT taker who is enrolled at a US

college. Not all enrollees are score senders, since one can enroll at a college that doesn’t

require standardized tests or send an ACT score. About 5 percent of foreign SAT takers

enroll a US college without sending an SAT score.

Figure 1.11 shows trends in the number of SAT takers, score senders, and enrollees.

Around 60,000 foreign students took SAT from the 2004 high school graduating cohort, and

the number stayed relatively flat until the 2007 cohort. The number of SAT takers per cohort

increased consistently after 2007 with a notable spike in 2011. By 2015, the number reached

over 120,000—doubling in eight years. Score senders and enrollees follow similar trends as

SAT takers, although they become a smaller fraction of the takers over time. Still, there

is a near tripling of score senders over the sample period. We have shown previously that

the number of foreign enrollees are climbing, especially in recent years in large part due to

Chinese students

Figure 1.12 shows the fractions of SAT takers who are score senders and who are enrollees,

both in aggregate and by 30 economy with the most SAT takers between 2004 and 2015.

Only 46.7 percent of international SAT takers send a score to at least one US institution and

27.1 percent enroll. In contrast, 72.7 percent of US SAT takers are score senders and 87.9

percent are enrollees. These fractions vary dramatically by economy. To name a few, 74.4

(55.6) percent of Chinese are score senders (enrollees), 52.8 (25.5) percent of Canadians are

score senders (enrollees), 45.9 (36.3) for Japan, and below 25 (15) percent for Thailand and

Saudi Arabia.10

10Lebanon and Egypt have extraordinarily low shares of score senders and enrollees relative to othereconomies, due to that the SAT is used as the college entrance exam for prestigious universities in these twocountries. In our regression analysis, we include economy fixed effects to account for this phenomenal.

16

Overall, many foreign students who take the SAT do not send a score to any US colleges

and many do not enroll. The next subsection provides SAT score information for all three

groups of international students and explores the extent of high-scoring SAT takers not

sending score and enrolling in the US.

1.4.2 SAT scores for takers, score senders, and enrollees

Figure 1.13 shows the SAT median for SAT takers, score senders, and enrollees, both in

aggregate and by 30 economy with the most SAT takers between 2004 and 2015. All scores

are rescaled by the median of US takers in the sample period (1,010). To understand the

figure, consider the top row for US students. The hollow diamond is the median SAT score

of domestic test takers, which perfectly coincides with the US median, denoted by the black

vertical line. The rightmost hollow square is the SAT median for score senders. Being to

the right of the diamond suggests that score senders are a positively selected subset of SAT

takers. The filled circle in between the diamond and square is the SAT median for enrollees.

The US circle is relatively close to its diamond because, as we mentioned, nearly 88 percent

of US SAT takers enroll in a US institution in our data.

In comparison, the second row aggregates all international students. The first thing to

note is that all “Foreign Total” shapes are to the right of US shapes. That is, the median

foreign students score higher on the SAT than US students in all three groups of interest.

In fact, even the SAT median of foreign test takers is higher than the median for US score

senders. The median for foreign score senders and enrollees hover around the 75th percentile

of US takers (and enrollees). We also see foreign score senders and enrollees are positively

selected from foreign SAT takers by a larger stretch compared to the US case. Also, while

domestic enrollees are closer to domestic SAT takers, foreign enrollees are almost as positively

selected as score senders. It is important to note that relative to domestic students, we cannot

17

distinguish whether international students are more positively selected into taking the SAT

or simply have higher SAT scores on average.

There is a lot of variation in all three shapes by economy in Figure 1.13. We summarize

three notable patterns. First, among the 30 economies with the most number of test takers,

10 have lower SAT median for their test takers than US takers and 20 have higher. When

looking at the median for enrollees, all 30 economies but for the Bahamas are higher than

the US enrollees. The magnitudes also varies substantially. For example, while the median

for SAT takers from Singapore and South Korea is about 300 points higher than the US

takers, test takers from the Bahamas and Egypt are about 100 points lower.

Second, SAT takers are always to the left of score senders and enrollees, in varying

degrees. This implies that the positive selection into senders and enrollees is a worldwide

phenomenon, not just true on average. Third, score senders are typically not far to the right

of enrollees, which suggests that not all high-scoring senders end up enrolling or some takers

with lower SAT enroll without sending a score. But there are exceptions. For example, in

India, the SAT median of score senders is lower than the median of enrollees, which suggests

more positive selection into enrollees than score senders.

While Figure 1.13 shows positive selection into score senders and enrollees, Figure 1.14

explores the extent foreign SAT takers not sending a score and enrolling given an SAT score.

Panel (a) of Figure 1.14 plots the number of score sends against the full spectrum of SAT

score, by foreign status and separately for SAT takers and score senders. Panel (b) replaces

the number of score sends by the enrollment probability.

Several important patterns can be seen. First, both the number of score sends and

probability of US college enrollment increase in SAT score with some degrees of nonlinearity.

Second, for a given SAT score, the number of score sends and enrollment probability are

higher for score senders (triangles) than all SAT takers (circles). The gap between triangles

and circles for score sends is driven by the probability of sending score to at least one school—

18

the larger the gap, the smaller probability of being a score sender. Hence the score sending

probability also increases in SAT score.

Third, on average, foreign takers send fewer SAT score sends than US takers for a given

SAT score. The difference decreases in SAT score and nearly vanishes beyond 1,300. How-

ever, foreign score senders send scores to more schools than US senders when SAT is above

1,000 and send to slightly less schools when below. Finally, foreign test takers and score

senders are much less likely to enroll than their US counterparts throughout the SAT distri-

bution. Even among the highest scoring students, foreign students are more than 30 pp less

likely to enroll at a US college than domestic students.

1.5 Nonimmigrant Visas Institutional Background

In order to enter the US, foreign citizens are generally required to obtain a visa. The Im-

migration and Nationality Act (INA) establishes the visa types for different travel purposes.

A nonimmigrant visa such as F-1 (student) visa or B (business/tourism visitor) visa is for

temporary stay, and an immigrant visa such as Green Card is for permanent residence. This

section focuses the discussion on the application procedure for nonimmigrant visas, especially

the student visa and visitor visa.

Table 1.2 shows selected information for nonimmigrant visas based on data from the State

Department between the 2004 and 2015 fiscal year. Columns 1-4 of Panel A list descriptive

statistics on visa issuance for five nonimmigrant visa types with the highest annual issuance

and a combination of the remaining 72 types. Based on columns 1 and 2, the B visa has the

highest issuance among all nonimmigrant visa types, with an annual average over 5.4 million.

The F-1 visa is the second largest, with an annual average close to 400,000. Compared to

other visa types, the annual issuance for F-1 and B visas has much larger standard deviation,

indicating a lot of variation over time. In fact, over 8.8 million B visas and 700,000 F-1 visas

19

were issued in 2015. Columns 3 and 4 show that annual issuance to B and F-1 visas account

for 78.4 percent of all nonimmigrant visas issued.

Applying for a visa is costly. Besides filling out lengthy application forms, preparing for

various supporting documents, and paying an application fee of $160 (as of 2019), applicants

are generally required by law to be interviewed by a consular officer at a US Embassy or

Consulate. In addition, before the interview, student visa applicants need to be registered

on the Student and Exchange Visitor Information System (SEVIS) and issued a Form I-20

by a Student and Exchange Visitor Program–certified school that she is admitted to and

has decided to enroll. Applicants have to pay a fee of $200 for SEVIS registration, which

increased to $350 in June of 2019.

Despite the cost, visa applications can be denied. Under US immigration law section

104(a) of the INA, consular officers have the exclusive authority to approve or deny visa

applications. Column 5 of Panel A in Table 1.2 shows that on average, both B and F-1 visa

applications have about 20 percent chance of being denied—much higher than other major

visa types. The refusal rates are adjusted for denials that are later overcome or waived.

Column 6 of Panel A shows the refusal rates for B and F-1 visa have larger annual variations

than other visa types.

Furthermore, Figure 1.15 and Appendix Figure A.3 shows that the refusal rate for both

visa types varies significantly across economies and over time. In our analysis sample, the F-

1 visa refusal rate at the economy-year-level has an average of 24.15 percent with a standard

deviation of 20.33 percent, a maximum of 86.7 percent, and a minimum of 0.1 percent. The

B visa refusal rate has an average of 25.82 percent with a standard deviation of 17.09 percent,

a maximum of 73.5 percent and a minimum of 0.4 percent.

When a visa application is denied, US consular officers will provide the applicant a reason

based on ineligibilities listed in INA and other immigration laws. While there are more than

60 reasons, Panel B of Table 1.2 shows that “INA 214(b): immigrant intent” is assigned as 93

20

percent of all reasons. This means that the consular officer did not think the visa applicant

overcame the presumption of being an intending immigrant. While some visa categories such

as H-1B temporary worker visa allows applicants to have immigrant intent, B and F-1 visas

do not. Applicants refused under INA 214(b) can re-apply with additional evidence of their

qualifications.

Visa refusal rates for B and F-1 visas at least partially reflect the restrictiveness of

immigration policies on US entry for three reasons. First, despite being the two largest

nonimmigrant visa programs, B and F-1 visas do not have official annual caps. Second,

while consular officers have the entire discretion to approve and deny visa applications,

the judgement on whether applicants are eligible such as overcoming the immigrant intent

presumption is subjective. In fact, according to the State Department’s visa application

guidelines, evidence to support applicants’ intent to depart the US after the trip or upon

completion of the course of study is only optional.11 Third, even though B and F-1 visas are

for different group of foreigners, their visa refusal refusal rates exhibit strong co-movement

(with a correlation of 0.78 in 2003-14) at economy-year-level. Hence, a more restrictive policy

on granting B and F-1 visas can translate to higher visa refusal rates.

Citizens of 38 economies that are members of the Visa Waiver Program (VWP) may enter

the US for business and tourism without obtaining a B visa. The program is a comprehensive

security partnership between America and its allies—about 20 million travelers under this

program entered the US in 2014.12 The existence of VWP affects our choice of economies

for empirical analysis and we describe the details in the next section.

1.6 The Empirical Strategy

We are interested in estimating the effect of the expected F-1 visa restrictiveness affect

foreign student enrollment and composition in the US through influencing students’ college-

11https://travel.state.gov/content/travel/en/us-visas/study/student-visa.html12https://www.dhs.gov/visa-waiver-program

21

https://travel.state.gov/content/travel/en/us-visas/study/student-visa.htmlhttps://www.dhs.gov/visa-waiver-program

going behaviors. We measure anticipated restrictiveness for US entry with economy-year

varying F-1 visa refusal rates faced by foreign students around the time of making SAT

taking and score sending decisions. Students typically take SAT or send test scores in the

fall (or earlier) prior to their graduation year. For example, the visa refusal rate used for

students graduating in May 2015 is the average rate between October 2013 and September

2014 (or 2014 fiscal year).

A lower expected chance of obtaining a student visa may decrease the expected benefit

of applying for US colleges, and hence an increase in visa refusal rate may depress SAT

taking and score sending as they are costly. We refer to this discouragement of action and

associated enrollment impact as the chilling effect. While our timing of the visa refusal rate

captures the chilling effect, a higher refusal rate in general may reduce foreign enrollment

mechanically conditional on college applications and acceptances. We discuss in Section

1.7.3 how our results on enrollment may be influenced by the mechanical effect.

We first study how student visa restrictiveness affects the aggregate quantity and aca-

demic ability of international student inflow to the US. Specifically, we employ the following

regression model:

Yjt = αFRRjt +Xjtθ + ωj + γt + �jt (1.1)

where the dependent variable is the aggregate number of new foreign students enrolled at a

US undergraduate institution from economy j in cohort year t. It can also be measures of

academic ability for the newly enrolled students such as the median SAT score and the share

of students above the 75th percentile (of the US takers in the same cohort). The independent

variable of interest, FRRjt, is the F-1 visa refusal rate faced by students in cohort year t

from economy j in the time period prior to students’ potential visa appointment. Xjt is a

vector of control variables (e.g. real GDP per capita) that vary at economy-year level. The

timing of Xjt is set to be the calendar year prior to cohort year t. Visa refusal rate and

22

Xjt are both measured in natural logs. ωj and γt represent economy and year fixed effects,

respectively.

After examining the impact of student visa restrictiveness on the aggregate quantity and

academic ability of international students in the US, we leverage our student-level data to

study how F-1 visa restrictiveness affect individual behaviors in score sending and enrollment

outcomes, and whether the effect varies by student test score. We employ the following

empirical framework:

Pijt = β1FRRjt + β2FRRjt × 1SAT ≥ 75th pctl +Wijtδ +Xjtρ+ µj + τt + ηijt (1.2)

where the dependent variable is an indicator for student i from economy j in cohort year

t sending SAT score to at least one US undergraduate institution, or an indicator for i

enrolling at a US undergraduate institution. The dependent variable can also be the number

of score sends to US colleges, the selectivity of schools received scores, and the selectivity

of the school attended by i. Coefficient β2 is the impact of F-1 visa refusal rate on the

outcome for students with SAT score above the 75th percentile relative to those below. Wijt

is a vector of student-level controls including SAT score and demographics (gender, age,

parental education and family income). µj and τt represent economy and year fixed effects,

respectively. In some specifications, economy-year fixed effects are included. Standard errors

are clustered at the economy-year level at all times.

Both endogeneity and simultaneity bias can prevent a causal interpretation on the co-

efficient of F-1 visa refusal rate. First, F-1 visa refusal rate for a given economy may be

correlated with economy-specific identities (e.g. political similarity with the US), general

time trends (e.g. globalization of education), and economy-time-variant characteristics (e.g.

economic growth) that can also influence aggregate foreign student inflow and academic

ability to the US and student decision to attend US colleges. We address endogeneity by

including economy and year fixed effects in all specifications and a number of economy-

23

time-variant controls in preferred specifications. In our student-level analysis, we also test

the sensitivity of the coefficient for the interaction term between F-1 visa refusal rate and

SAT score by including economy-year fixed effects, which removes the issue of there being

economy-year unobservables correlated with visa refusal rates.

Second, F-1 visa refusal rate can also be driven by the quantity and academic ability of

international students (i.e., simultaneity bias). For example, if there is a capacity constraint

on the number of visas that can be processed or more disqualified applicants try to get an

F-1 visa, the refusal rate will be higher. To address this issue, we instrument F-1 visa refusal

rate with B visa refusal rate for the same economy in the same time period. B visas are not

for international students but their refusal rates also reflect the restrictiveness of immigration

policies on US entry. Hence, B visa refusal rate likely satisfy the exclusion restriction, and

it isolates the part of the variation in visa restrictiveness. As described in Section 1.5, the

refusal rates for B and F-1 visas have similar magnitude in variation and strong co-movement

within economy. Other major nonimmigrant visa types have much lower refusal rates with

little variation over time. We formally test for the relevance assumption whenever reporting

IV estimates.

B visa issuance is also the largest among all visa categories, making its refusal rates

insensitive to small numbers of applications and less sensitive to potential capacity constraint

of processing. In addition, by isolating the variation in visa policy restrictiveness and not

driven by student visa applicants, instrumenting with B visa refusal rate helps us estimating

the chilling effect of F-1 visa restrictiveness instead of the mechanical effect.

Note that we are interested in the impact of the economy-level anticipated uncertainty

in obtaining a visa and our IV strategy isolates the variation in visa restrictiveness not

driven by the composition of students. Theoretically, F-1 visa refusal rates may be specific

to certain types of students. One particular concern is that whether school selectivity is

correlated with the chance of obtaining a visa. While we cannot obtain access to refusal

24

data at individual-level, it is unclear whether school selectivity will be correlated with the

refusal rates. For example, while visa officers may suspect the intention of a student for going

to a non-selective school, they may also suspect that students who are going to a selective

school may be more likely to stay after graduation.

Throughout the empirical analysis in the rest of this paper, our estimation sample includes

data from 102 economies with the most number of SAT takers in 2004-15. We start with

a sample of 125 economies with complete data on visa refusal rates covering more than 99

percent of all foreign SAT takers in the sample period. We exclude 22 economies that are

members of the VWP since we do not have valid B visa refusal rates for them. During

our sample period, 10 economies joined the VWP at different time but all of them have at

least 5 years not in the VWP. We exclude the time periods when these 10 economies are in

the VWP.13 We also exclude Canada as Canadians do not need neither B visa nor F visa.

Economies in our analysis cover 75 percent of all foreign SAT takers in the sample period.

1.7 Results

1.7.1 Impact on the aggregate quantity and academic ability

Table 1.3 reports estimates for equation (1.1). We start by estimating the impact of student

visa restrictiveness on the aggregate quantity of international student inflow to the US in

columns 1-3. Column 1 shows the OLS estimate with year and economy fixed effects and it

suggests that higher F-1 visa refusal rate is associated with lower number of foreign students

enrolled. Column 2 adds a set of economy-year variant controls to mitigate the potential

endogeneity. The change on the coefficient for the visa refusal rate is minimal. In column

3, we report the estimates after instrumenting F-1 visa refusal rate with B visa refusal rate.

The F-statistic for the excluded instrument in the first stage is 156.45, passing the test of

13Our main results are robust when excluding the 10 economies entirely. We also report our main resultsfor VWP member economies in the Appendix.

25

weak instrument. The complete estimates from the first-stage are reported in column 1 of

Appendix Table A.4. The IV estimate shows that the OLS estimate for the coefficient of

interest is upward-biased, suggesting simultaneity bias is important. On average, a 10 pp

increase in the F-1 visa refusal rate leads to a 13.84 log points (or 14.84 percent) decrease

of new international students enrolled in the US.

Columns 4-6 of Table 1.3 provide OLS and IV estimates for the impact of F-1 visa refusal

rate on the academic ability of enrollees with economy-year variant controls. We measure

academic ability with two outcome variables: median SAT and share of students with a

score above the 75th percentile (“high-scoring students” hereafter).14 OLS estimates are

again upward-biased. IV estimates show that a 10 pp increase in F-1 visa refusal rate leads

to a 11.43 points decrease in median SAT among enrolled students and about 2.9 pp decrease

in the share of high-scoring students.

While a higher F-1 visa refusal rate decreases both the quantity and academic ability of

new foreign students enrolled, a part of this impact can come from change in the number and

composition of SAT takers. We examine the impact of F-1 visa refusal rate on SAT takers

using the same framework as equation (1.1). Table 1.4 has the same structure as Table 1.3

and shows the results for SAT takers. The pattern for the visa refusal rate coefficient is the

same as in the case of enrollment but with different magnitudes. The IV estimates indicate

that on average, a 10 pp increase in F-1 visa refusal rate leads to a decrease of 7.7 log points

(or 8 percent) in the number of new foreign SAT takers, 9.85 points in median SAT, and

2.12 pp in the share of high-scoring takers.

Results from Table 1.4 suggest that the influence of F-1 visa restrictiveness on the number

of SAT takers only partially contributes to its impact on new students enrolled in US colleges.

A 10 pp increase in F-1 visa refusal rate leads to 14.84 percent decrease in enrollees but only

8 percent decrease in SAT takers. Since all of our enrollees are SAT takers, an 8 percent

14For these two measures to make sense, we require a data point to have minimum enrollment of three.

26

decrease in SAT takers translates to an 8 percent decrease in enrollees. Nevertheless, the

influence of F-1 visa restrictiveness on the academic ability of SAT takers closely matches

its impact on the academic ability of enrollees.

Note that although coefficients for the economy-year variant controls are not the focus

of our paper, they are of interest in the literature on macro determinants of migration.

Our estimates show that higher ability to pay for US education (measured by real GDP per

capital in USD), higher demand for college education (measured by college-aged population),

greater trends of studying abroad (measured by enrollment in other popular destinations),

and better chance of obtaining a work visa (measured by H-1B visa issuance) are associated

with higher foreign student enrollment and SAT takers. There is no consistent evidence that

these factors influence enrollee and test taker academic ability by a large extent. Some of

these measures can be quite noisy. For example, H-1B visa issuance may also reflect the

number of H-1B applicants and the taste of staying in the US for employment.

1.7.2 Impact on students’ score sending behaviors and enrollment

We start by examining the impact of F-1 visa restrictiveness on foreign students’ score

sending behaviors and the heterogeneity by academic ability. Table 1.5 shows the coefficient

estimates from equation (1.2) when the outcome is an indicator for sending SAT score to

at least one US college. Panel A reports OLS estimates and Panel B reports IV estimates.

For both panels, column 1 includes only F-1 visa refusal rate variable and economy and

year fixed effects. Column 2 adds a set of student-level controls including SAT quadratic

and demographics. Column 3 adds further a set of economy-year-level controls, the same

as those included in Table 1.3 and 1.4. Column 4 includes the interaction term between

the visa refusal rate and an indicator for being a high-scoring student. Column 5 focuses

on the interaction term and includes economy-year fixed effects to effectively control for

unobservables at the level of the visa refusal rate. Finally, column 6 interacts visa refusal

27

rate with a more flexible measure of academic ability, an SAT quadratic. Appendix Table

A.2 provides summary statistics for outcome variables, visa refusal rates, and student-level

controls.

Estimates from Table 1.5 show that a more restrictive F-1 visa policy has a negative

impact on foreign students’ probability of sending a score and the impact is twice as large

for high-scoring students than for low-scoring students. Consistent with earlier analysis

on aggregate quantity and academic ability, our estimates have little change after adding

economy-year-level controls in column 3 or after adding economy-year fixed effects in column

5. Also, OLS estimates for the visa refusal rate are again upward biased. The F-statistics

for the excluded instruments in the first-stage pass the weak instrument test. IV estimates

in columns 3-4 indicate that on average, a 10 pp increase in visa refusal rate decreases the

probability of score sending by 1.53 pp, where it is about 1.2 pp for low-scoring students

and 2.2 pp for high-scoring students. Lastly, note that column 6 shows qualitatively the

same results as column 5 when using SAT quadratic instead of an indicator for high-scoring

students.

In Table 1.6 and 1.7, we further examine the composition of score sends conditional on

sending at least one score. Both tables follow the same structure as Table 1.5. Interestingly,

while Table 1.6 shows that more restrictive F-1 visa policy has no effect on the number of

score sends to US colleges, Table 1.7 shows that scores are sent to more selective schools.

The effect of score sending selectivity is larger for low-scoring students than high-scoring

students, which is more evident in Table A.9 when using the maximum SAT among schools

received scores instead of the average. This is presumably because high-scoring students

were already applying for very selective schools. The IV estimate from Column 3 of Table

1.7 indicate that on average, a 10 pp increase in F-1 visa refusal rate decreases the average

SAT for score sends by 3.62 points.15

15Because the number of score sends is count data in nature, we report estimates from Poisson regressionsin Table A.8.

28

Thus far, we find that F-1 visa restrictiveness has an impact on students’ score sending

behaviors. We now examine whether students’ enrollment outcomes are ultimately influ-

enced. Column 3 and 4 of Table 1.8 show that on average, a 10 pp increase in the visa

refusal rate decreases enrollment probability at a US college by 1.13 pp (or 4.3 percent of

the average enrollment probability). High-scoring students are slightly less influenced but

the difference from low-scoring students is not statistically significant. Table 1.9 shows that

the same change in visa refusal rate increases SAT score of the school enrolled by about 3.6

points for high-scoring students. The impact for low-scoring students is negative but not sta-

tistically significant. Hence, despite sending to a more selective pool of schools, high-scoring

students are enrolled at more selective places while low-scoring students are not.

Although the negative impact of a higher visa refusal rate on enrollment probability is

similar in magnitude by student SAT score, there are important differences. For low-scoring

students, a higher refusal rate discourages them from sending a score and encourages them

to send scores to more selective places that did not work out. For high-scoring students,

they are discouraged even more from sending a score and also encouraged to send scores to

more selective places. However, high-scorers ended up enrolling at colleges that are more

selective. In fact, Table 1.10 shows that conditional on sending a score, the impact of visa

refusal rate on enrollment probability mostly comes from the low-scoring students.

Hence, for low-scoring students, the impact of visa refusal rate on enrollment probability

comes from both the effect on score sending probability and the effect on sending score

to more selective schools that are harder to get in. For high-scoring students, the impact

of visa refusal rate comes more from the effect on score sending probability. Note that the

enrollment probability conditional on sending a score is higher for high-scoring students than

for low-scoring students (see Figure 1.14).

29

1.7.3 Interpretation of results

We find that an increase in the expected F-1 visa restrictiveness decreases both the quan-

tity and academic ability of the new foreign students enrolled. These impacts come from

changes in SAT takings and student score sending behaviors conditional on taking SAT.

Since SAT taking and score sending are decisions made before potential visa appointments,

the estimated impact of F-1 visa refusal rate on related outcomes represents the chilling

effect. That is, foreign students change their behaviors in response changes in the expected

chance of obtaining a student visa.

Because going through the college application process is costly, an increase in the F-1

visa refusal rate decreases the expected value of pursuing US education. We find that when

the uncertainty increases for entering the US (a higher refusal rate), foreign students respond

by giving up on coming to the US (not taking SAT or not sending any score) and increasing

the expected value of studying in the US via sending scores to more selective institutions.

Notably, high-scoring students are more responsive to changes in visa restrictiveness than

low-scoring students in terms of taking SAT and sending a score to any US college. There are

at least three possible reasons. First, while sending scores to more selective US institutions

increases the expected benefit of college applications, we show in Section 1.7.2 that high-

scoring students are less responsive in this dimension especially for the most selective school

where they send scores to. This is likely because high-scoring students already send scores to

selective US colleges and are limited in changing application portfolio. In fact, the maximum

SAT of score sends for high-scoring students is 1,392, and Appendix Table A.9 shows that

a 10 pp increase in the F-1 visa refusal rate increases this maximum by 30 points—beating

the 99th percentile of the school selectivity (1,420). In contrast, the maximum SAT of score

sends for high-scoring students is only 1,272.

Second, high-scoring students may use visas restrictiveness more effectively than low-

scoring students. For example, high-scoring may either have better access to the information

30

on visa refusal rates, or more accurately calculate the expected benefit of completing the

college application and visa process. It could also be that high-scoring students more risk

averse, so that they dislike more a higher level of uncertainty. In practice, the influence of visa

restrictiveness may operate through parents, friends, high schools, and college application