TOP TALENT, ELITE COLLEGES, AND MIGRATION: EVIDENCE FROM THE INDIAN INSTITUTES OF TECHNOLOGY

We study migration in the right tail of the talent distribution using a novel dataset of Indian high school students taking the Joint Entrance Exam (JEE), a college entrance exam used for admission to the prestigious Indian Institutes of Technology (IIT). We find a high incidence of migration after students complete college: among the top 1,000 scorers on the exam, 36% have migrated abroad, rising to 62%for the top 100 scorers. We next document that students who attended the original “Top 5” Indian Institutes of Technology (IIT) were 5 percentage points more likely to migrate for graduate school compared to equally talented students who studied in other institutions. We explore two mechanisms for these patterns: signaling, for which we study migration after one university suddenly gained the IIT designation; and alumni networks, using information on the location of IIT alumni in U.S. computer science departments.


Introduction
Highly skilled immigrants make important contributions to innovation and technology in the United States. Often, they study in elite universities in their home countries before getting advanced degrees abroad. For example, many successful Indian immigrants in the technology industry-including Sundar Pichai, the CEO of Alphabet Inc./Google, and Arvind Krishna, the CEO of IBM-are undergraduate alumni of the selective Indian Institutes of Technology (IITs).
Similarly, Chinese students in U.S. Ph.D. programs overwhelmingly come from a set of highly selective Chinese universities (Gaulé and Piacentini, 2013).
In this paper, we study migration in the very right tail of the talent distribution for high school students in India, focusing on the extent to which elite universities in their home country facilitate migration. We focus on the Indian Institutes of Technology (IITs). The IITs are prestigious and highly selective technical universities with lower acceptance rates than Ivy League colleges, particularly for the original five IIT Campuses. 1 Admission to the IITs is solely through the Joint Entrance Exam (JEE), where nearly one million exam takers compete for less than ten thousand spots. Desai, Kapur, McHale, and Rogers (2009) document anecdotal evidence related to the role of elite institutions in India, such as the IITs and the All India Institute of Medical Sciences, in facilitating skilled migration to the United States. IIT students have even been described as "America's most valuable import from India" (Leung, 2003).
Emigration is often difficult to observe from administrative datasets, and few surveys have been conducted with a focus on top talent that are not selected on future success or mobility. 2 We were able to overcome these challenges by leveraging the unanticipated public release of the names and scores of JEE exam takers in 2010, combined with an intensive manual collection effort on exam takers' outcomes. The result is a novel dataset of high school students who took the JEE exam, linked to college attended and later career, education, and migration outcomes. The data provides individuals' scores received on the exam and their national ranking. An important feature 1 IIT Kharagpur, IIT Bombay, IIT Madras, IIT Kanpur and IIT Delhi. Source regarding selectivity: Leung, Rebecca, "Imported From India," June 19, 2003, https://www.cbsnews.com/news/imported-from-india/, accessed August 22, 2021. 2 Survey evidence of Indian academics suggests that academic performance and educational institutions attended matter for later international mobility, but focusing on academics leads to a sample more likely to be mobile and selected on later success (Czaika and Toma, 2017).
3 of the data is that we can observe the whole set of IITs and majors an individual could have chosen to attend, since admission to an IIT and a major course of study are based solely on the JEE score.
First, we document a salient correlation between an individual's score on the JEE exam and migration up to eight years later among the top exam takers. Among the top 100 scorers, for instance, 62% have migrated abroad, primarily to the U.S. and for graduate school. Among the top 1,000 scorers, 36% have migrated abroad, which is still sizeable but much lower.
Among students in the top end of the score distribution (top 0.2% of test takers), we find that holding JEE score fixed, those who attended one of the five most prestigious IITs are 4 percentage points more likely to migrate than equally high-scoring students who attended other universities. These similarly talented students attended other institutions in the IIT system, such as IIT Roorkee, IIT Guwahati, or BHU Varanasi, which are organized along similar lines but are relatively less prestigious. The effects are mainly driven by migrating for graduate school and a Ph.D., specifically, while there is no significant effect for migrating for work. 3 We next investigate what mechanisms can explain these patterns. First, we examine whether, among students with identical JEE scores, if those who attend a Top 5 IIT are likely to select different majors, thus providing students with different types of human capital. While students attending a Top 5 do have different majors on average compared to those who do not, we obtain similar results when we control for the major area of study. Second, elite universities could be a signal of quality, effectively solving an information friction about a potential migrant's ability or quality of their human capital to future employers or graduate programs. To explore the role of signaling, we leverage a natural experiment when one institution (Banaras Hindu University, BHU) unexpectedly received IIT status, without any concomitant changes to its staff or curriculum. 4 Comparing students who enrolled at BHU before the change was made, we find that 3 In order to develop a better understanding of the drivers of migration for work in this setting, we conducted several field interviews with placement offices at the IITs. Our interviews revealed that top multinationals had been hiring IIT graduates for their local subsidiaries in India well before the period of study (e.g., McKinsey in 1992, BCG in 1995, Microsoft in 1990, Goldman Sachs in 2006, while the American offices of these firms were explicitly barred from recruiting directly from the IITs. Individuals who migrated to the U.S. for work often do so by transferring within these companies (or after acquiring some work experience in India). By contrast, individuals migrating for graduate school would typically do so right after their IIT degree. We suggest that the signalling value of having a Top 5 IIT degree may be less relevant for people who have work experience, since the work experience itself reveals important information, in particular for transfers within a firm. 4 As we discuss later in Section 6, discussions on granting IIT status to BHU had been ongoing since the 1970s. Thus, while BHU becoming an IIT was a possibility, prospective students could not anticipate whether this change would have occurred by the time they graduated. 4 students who (plausibly exogenously) received an IIT degree were 10 percentage points more likely to migrate than those of preceding cohorts.
The BHU experience allows us to separately identify the signaling value of an IIT degree, as the quality of education/human capital acquired by the students in the cohorts before and after the change remained constant, while only the name of the university on the degree received differed. Importantly, the unanticipated nature of the change implies that we are comparing students who were not expecting to receive an IIT degree and would be similar in terms of unobservable factors such as motivation or ambition.
Another possible mechanism is that students attending elite universities may become part of a network of successful alumni and faculty, many of whom have migrated, and this network can facilitate migration. Prior literature has shown the role of such diaspora networks in lowering migration costs and increasing migration flows, but this literature has not focused on extremely highly skilled migrant networks as we do here (Beine, Docquier, and Özden, 2011). To examine the role of networks, we conduct a case study of which U.S. computer science Ph.D. programs IIT graduates attend. We find that the number of alumni of one's own IIT among a U.S. computer science department's faculty is positively associated with attending that department for a Ph.D. By contrast, we find no such association for the number of alumni of other IITs.
Overall, our results suggest that elite schools play a key role in shaping migration outcomes, both in terms of the overall propensity and the particular migration destination. The BHU evidence suggests that the quality of acquired human capital does not appear to be the mechanism driving this phenomenon. Our evidence, rather, supports the view of elite education as mainly signaling a potential migrant's ability or quality of their human capital, and providing access to valuable networks. U.S. graduate programs-a key pathway for migration-are especially keen to recruit the best and brightest. However, to identify the best and brightest, they must rely on external information and signals, and elite home universities may provide these.
Our paper contributes to the literature on the international migration of highly skilled individuals. International migration, particularly high-skilled migration, is often facilitated by institutional actors. Recent literature has documented the important role firms play in facilitating skilled migration (Kerr and Lincoln, 2010;Clemens, 2013;Kerr, Kerr, and Lincoln, 2015;Choudhury and Kim, 2019). In this paper, we argue that other institutional actors, i.e., elite 5 universities, play an important role in facilitating skilled migration of talent from emerging to developed countries. 5 While prior migration literature has documented the role of universities from the demand side (e.g., Doran, 2012, 2015;Amornsiripanitch, et al., 2021) and the significant enrollment of students from India in U.S. graduate programs (Bound, et al., 2021), arguably an important gap remains relative to studying elite universities from the supply side, i.e., as facilitators of skilled migration. In particular, while Kerr, Kerr, Özden, and Parsons (2016) postulate that host country universities facilitate high-skilled migration through admission decisions, our paper additionally sheds light on the agency of home country elite universities in facilitating high-skilled migration through the twin mechanisms of signaling and networks.
Finally, our paper contributes to the literature on the labor market returns to attending selective colleges. In general, the findings on the impact of attending an elite college have been mixed (e.g., Dale and Krueger, 2002;Pop-Eleches and Urquiola, 2013;Abdulkadiroğlu, Angrist, and Pathak, 2014;Zimmerman, 2019). Interestingly, this literature tends not to find effects of college selectivity on earnings in the U.S., but some effects on earnings and career outcomes in Italy (Anelli, 2020) and in several developing country contexts, including Chile (Zimmerman, 2019), India (Sekhri, 2020;Bertrand, Hanna, and Mullainathan, 2010) and Colombia (Barrera-Osorio and Bayona-Rodriguez, 2019). These effects tend to appear to be driven by signaling or networks, complementary to our findings regarding the attending an elite home country institution and migration.
The rest of the paper proceeds as follows. Section 2 provides historical background on the development of the IITs and details about the admissions process. Section 3 describes the data, 6 followed by the empirical strategy in Section 4. Our main results are discussed in Section 5, followed by the potential mechanisms in Section 6. Section 7 concludes.

IITs: Historical Background and Context
As India transitioned to independence after World War II, national leaders sought to establish higher education institutions focused on developing India's technological capacity. The institutions would conduct research in addition to teaching undergraduate and postgraduate students. Prominent IIT alumni include current CEO of Google and Alphabet Sundar Pichai, Sun Microsystems co-founder Vinod Khosla, and former IMF Chief Economist Raghuram Rajan.
The first of these higher technical institutions-called the Indian Institute of Technologywas founded in 1951 in Kharagpur. Over the following decade, another four IIT campuses opened: in Bombay (1958), Kanpur (1959), Madras (1959), and Delhi (1961. The five original IITs were spread across the country, each located in a different region. The Institutes expanded in the late 1990s and early 2000s to include 23 branches (see Appendix Table A1). A few of the new branches-including IIT (BHU) Varanasi-were converted from existing institutions, which we will leverage in our analysis. We will refer to the five initial campuses as the "Top 5" IITs, as they have stronger reputations and rank higher than the newer institutes (for the locations of the Top 5 IITs, see Appendix Figure A1). 6 At the undergraduate level, admissions to the IIT system are determined solely based on student performance on the annual Joint Entrance Examination (JEE), a centrally administered exam covering mathematics, chemistry, and physics. The competition is fierce; in 2010, for instance, around 450,000 individuals took the JEE, competing for less than 10,000 IIT places. Some IIT spots are reserved for special categories, including individuals from disadvantaged castes. We focus here on the general category where the majority of participants compete.
After the JEE results are released, test takers rank their top institution and major pairs (e.g., IIT Delhi/Electrical Engineering). Seats are then allocated by rank, with each student in turn "allotted" to their top still available institution-major seat. 7 The most popular combinations fill up 7 quickly: IIT Bombay/Computer Science, for instance, only has around 40 seats available, and a rank of 100 in India would not be sufficient for admittance to that particular program (for opening and closing ranks for key institution/major combinations, see Appendix Table A2).
Instead of attending an IIT, test takers may attend a variety of other institutions, with the most popular options being the Birla Institute of Technology (BITS Pilani, ranked among the top 10 engineering colleges in India in 2020 8 ) and one of the National Institutes of Technology or NITs (see Appendix Table A3). Admission into the NITs is also based on the JEE examination. 9

Data
Studying who migrates, empirically, is challenging since it requires information both about stayers and migrants. Few surveys have been conducted with a specific focus (or good coverage of) top talent. 10 To overcome the lack of relevant survey data, we use observational data generated by the unanticipated public posting of the results of the 2010 JEE online. 11,12 The data released included full name and scores (math, chemistry, and physics). After receiving their JEE results, students enter the "allotment process" by which they are matched to institutions and major according to their preferences, rank, and available seats. We observe the result of this allotment process in the released JEE data, which in turn gives a good indication of where individuals studied behaviour in choosing particular IIT/course combinations is not a major issue, unlike in the case of similarly selective exams where preferences are indicated in advance of taking the exam. 8 India Today. "List of Top Engineering Colleges 2020 in India." https://www.indiatoday.in/bestcolleges/2020/ranks/1824927, accessed August 22, 2021. 9 Careers360. "How to Get a Seat in NIT?" April 30, 2020. https://engineering.careers360.com/articles/how-getseat-in-nit, accessed August 22, 2021. 10 One exception is Agarwal, et al. (2023), who survey around 500 former participants in the International Mathematical Olympiads, with a focus on the decision to migrate for undergraduate studies. 11 Abhay Rana, a programmer also known as Nemo, found a way to scrape the JEE 2010 results and released them at https://captnemo.in/projects/iitjee/. Previously, the results of the JEE 2009 had been released in bulk format on the IIT-JEE website. Both the JEE 2010 and JEE 2009 data include names and scores, but the JEE 2010 data also includes the allotted institution and course course. 12 The use in research of potentially confidential data made publicly available through third parties is potentially controversial. A recent example of such use is Alstadsaeter, Johannesen, and Zucman (2019), who combine the "Panama papers" with administrative wealth records in Scandinavia to study tax evasion. Relatedly, Braguinsky, Mityakov, and Liscovich (2010) and Braguinsky and Mityakov (2015) use leaked administrative income data on Moscow citizens to shed light on issues of transparency and hidden earnings. In contrast to these studies, the data we use is rather less sensitive and confidential. Indeed, every year the names and scores of the top JEE scorers tend to be publicized by both coaching and testing centers. Moreover, following a freedom of information request, the Indian government released the full results of the 2009 JEE exams through the IIT-JEE website. The data released included information on names, names of the parents, scores, and locality for more than 400,000 individuals. The data we use is considerably smaller and generally has less information, but has the advantage of including the IIT and major individuals have chosen. 8 for their undergraduate degree. 13 To complement the released JEE data, we systemically collected data on migration outcomes through an intensive manual data collection effort. Given the costs involved in the data collection, we focused on test takers from the very top (scoring 243 and above, corresponding to roughly the top 2,500 scorers in the general category). Summary statistics of individuals are shown in Table 1. Appendix Figure A2 shows the distribution of total scorers for whom we manually collected outcomes. Individuals in this range would have the option to attend a Top 5 IIT in their choice set. Our final sample includes 2,470 test takers. The data collection team used various sources to locate outcomes for individuals, including LinkedIn profiles, College alumni yearbooks, Github, AngelList, ResearchGate, and other sources. In searching for individuals, we leveraged the fact that we know not only their names but also the undergraduate institution they attended, and when they finished high school. We were able to find career and education histories (and thus directly infer migration information) for close to 90% of the sample.
For the remainder, we assume that they have not migrated. We believe that this is a reasonable assumption given the widespread prevalence of LinkedIn in the U.S. (the main migration destination among identified migrants) and the sectors in which IIT graduates tend to work. For instance, in 2022, LinkedIn was reported to have 175 million U.S. users, compared to a U.S.
working-age population of 205 million. In the results section, we conduct sensitivity checks to alternative assumptions on the migration status of individuals with missing career histories.
(Insert Table 1 About Here) We additionally collected outcomes for scorers lower in the score distribution, in ranks 5,000 to 8,291, corresponding to scores of 197-220. However, we were only able to find migration outcomes for 68% of individuals in this sample. Individuals in this range (ranks 5,000 to 8,291) would have the option to attend a less prestigious IIT, but not one of the Top 5 IITs. Given the lower quality of this data, we only use it descriptively, to assess the share of migrants by score and rank (as in Figure 1), but not in the main analysis.

9
Our empirical analysis compares migration outcomes of individuals who had the same score in the Joint Entrance Exam governing entry to the Indian Institutes of Technology. By comparing individuals with the same score, we control not just for ability (or prior stock of human capital) but also for the choice set faced by individuals. Indeed, a key advantage of our setting is that admissions are offered purely on the score in the Joint Entrance Exam and do not factor in unobservables such as essay quality, as would be the case in the U.S. context (Dale andKrueger, 2002, Arcidiacono, Kinsler, andRansom, 2020).
In our main analysis, we run the following regression at the individual level: Where i indexes individual exam takers and j exam scores (sum of mathematics, chemistry, and physics scores), with j being the score obtained by individual i. is an indicator variable for whether the individual migrated out of India after graduation (in some specifications, we distinguish whether the individual migrated for graduate school-Ph.D. or Masters-or migrated for work). 5 is an indicator variable for attending one of the five original IITs (IIT Bombay, IIT Kanpur, IIT Kharagpur, IIT Madras, and IIT Delhi). Technically, we observe which IIT individuals are "allotted" to attend, but this matches very closely with the institution individuals actually attend in our sample.
∑ ( ) is a set of score fixed effects and is a vector of individual characteristics, including gender and major. By including score fixed effects, we compare equally talented students who scored high enough to study in a Top 5 IIT but chose not to attend.
As discussed earlier, selection by colleges is based on a student's entrance exam score, and we can control for scores directly in our regressions. However, there could be endogenous enrollment decisions in this setting or self-selection into IIT attendance, for instance, if individuals who are more motivated to migrate are also more likely to attend a Top 5 IIT. If so, our analysis would overstate the causal effect of attending a Top 5 IIT on migration.
A regression discontinuity research design based on scores in the Joint Entrance Exam would alleviate such concerns most effectively. However, there are no clear thresholds in JEE score that would lead to a large jump in IIT attendance, which prevents us from estimating the impact on the marginal attendee. For instance, as shown in Appendix Figure A3, the minimum 10 rank that allows entry into a Top 5 IIT is 6,653, yet the share of scorers just above this rank going to a Top 5 IIT is quite low. The reason is that a score in this range would only suffice for an unpopular major at a Top 5 IIT (e.g., architecture rather than computer science) and that other IITs or engineering colleges are effectively more appealing. Similar issues apply to other plausible thresholds. 14

5a. Migration
We first document that a large share of JEE test-takers eventually migrate abroad and, more generally, that the incidence is very high at the extreme right tail of the distribution. Figure 1 shows the share of migrants across the score distribution and the share migrating for graduate school.
Among the top 10 scorers, nine have migrated. Among the top 100 scorers, 62% have migrated, and 36% among the top 1,000. While the incidence of migration is sizeable throughout our sample, it is striking that it increases dramatically towards the extreme right tail of the score distribution.
To put things in perspective, more than 20 million people were born in India in 1992 and reached age 18 in 2010. Thus, the top 1,000 scorers corresponds to 0.2% of the test takers and to 0.00005% of the birth cohort.
(Insert Figure 1 About Here) The U.S. is the main destination country, with 65% of the migrants heading to the US, 3% to Canada, 5% to the UK, and 16% to other countries (see Appendix Figure A4). Regarding the type of migration, as evident from Figure 1, most individuals are migrating for graduate school. In our sample, 83% of individuals migrated to pursue a Master's or Ph.D. degree, with only 17% migrating for work. Among the top 10 scorers, only four migrated for graduate school and the others to work. The dominant type of migration in our sample is thus migrants going to graduate school in the United States. Naturally, these migrants may subsequently work in the U.S., but they first come to the U.S. as students.

5b. Determinants of Top 5 IIT Attendance
A key concern in estimating the relationship between attending a Top 5 IIT and migration is the role of selection or endogenous enrollment decisions. As discussed earlier, attendance is determined solely by performance on the JEE exam, which also gives us a measure of ability that shows that having to travel further to school or college is associated with higher costs, and distance to a school or college is used as an instrument for educational attainment (e.g., Card, 1995).
Research has also suggested that women may differentially respond to the increased costs of traveling to a college further away from home. Borker (2021), for example, shows that in Delhi, women are willing to attend a lower quality college if the travel route is perceived to be unsafe.
Thus, gender and geography are important determinants of college attendance in some settings, but it is unclear whether they will play a similar role in this sample of top talent aiming to attend elite institutions. Next, we investigate whether gender and geography are significant determinants of attending a Top 5 IIT. Figure 2 shows the share of test takers attending a Top 5 IIT by rank and gender (in 200-person bins). We can see that for the top 800-ranked test takers, while all women choose to attend a Top 5, and a small share of men do not attend a Top 5 in this part of the distribution, there do not seem to be large gender differences in the expected direction of women being less likely to attend a Top 5. After 1,000, the share attending a Top 5 falls, and there are no clear patterns in differences by gender. We note that Figure 2 also shows clearly that at the top of the distribution, almost all test takers go to an IIT, which means that in this sample, almost no one is going to study in the U.S. instead of attending an IIT. 15 In Table 2, we estimate the determinants of attending a Top 5 IIT. In column 1, we see that scoring higher on the JEE is significantly associated with attending a Top 5, which is expected as the sole criterion for admission to an IIT is score on the JEE. In column 2, we see that there is a 12 negative relationship between being from a state with a Top 5 IIT located in it and attending a Top 5 IIT. 16 As evident in Figure A1 showing the location of the IITs, the Top 5 are indeed in 'all corners' of India, so geography may not play the driving force it might in other settings. In Column 3, we interact gender and state with a Top 5 IIT and find no significant gender differences in the role of geography. While we cannot account for the role of unobserved factors playing a role in attending a Top 5 IIT, this analysis suggests that scores are indeed the biggest determinant of attending a Top 5. We will explore the robustness of our main results to concerns about geography further in the next section.
(Insert Table 2 About Here)

Association of IIT Attendance with Migration, Conditional on Test Scores
Now we turn to our analysis of the relationship between attending a Top 5 IIT and subsequent migration. In Table 3 As discussed earlier, a key concern with the regressions in Table 3 is endogenous enrollment decisions. One way that endogenous enrollment can impact the estimates is if among two equally scoring individuals, one who has more family responsibilities or who has a strong attachment to the home region chooses to stay close to home and not attend a Top 5IIT. This would be a problem for our main estimates as these individuals would also be less likely to move abroad, biasing our estimates for attending a Top 5 on migration upwards.
To probe the extent to which our results from the main specification may be driven by individuals who are geographically bound to their home location, we run the regressions from above, excluding individuals who study close to home. 17 First, we note that the share of students studying close to home is small: 86% of students study outside their home states and 82% study more than 200 km away. In Table 4, Panel A, where we exclude those who study in the same state, the results are quite similar across all outcomes to the main specification. In Table 4, Panel B, where we exclude those who study more than 200 km away, only the main effect of migrating for a Ph.D. holds, but the point estimates for the other outcomes are similar. Overall, this evidence provides some reassurance that the results are not driven by pre-existing (and persistent) geographical mobility constraints.
A separate concern relates to the fact that we impute migration status to non-migrant for individuals in our sample who have missing career histories (11 percent of the sample). In Appendix Table A4, we report the result of a sensitivity exercise where we assume instead that all individuals with missing career histories are migrants. The results are similar to those of the main specification despite the very conservative assumption, possibly due to the fact that having a missing career history is not correlated with attending a Top 5 IIT (controlling for score).

14
One potential explanation for the estimates in Table 3 is differences in the human capital obtained by those attending Top 5 IITs. One way human capital can differ is if the quality of education differs across Top 5 IITs and other institutions attended by individuals in our sample.
While we cannot directly test for differences in the quality of education, the Top 5 IITs and other IITs and non-IIT engineering colleges are known to provide high-quality instruction. Another way human capital could differ is if those who attend a Top 5 IIT pursue different courses of study or majors. As discussed in section 2, admission to a particular IIT is course-specific, so individuals are choosing an institution and a course of study simultaneously. Individuals in our sample commonly face a choice between pursuing a more popular major (such as computer science) outside a Top 5 engineering college or a less popular major in a Top 5 IIT.
We indeed find that those who attend a Top 5 IIT pursue different majors than individuals not attending an IIT. In Appendix Table A5, we show that controlling for the total score, those who attend a Top 5 IIT are less likely to complete a computer science, electrical engineering, or mechanical engineering major. However, once we control for major area of study in our main regression estimating the impact of Top 5 IIT on migration (shown in Table 5), we find similar results as in Table 2. This suggests that human capital differences in terms of major area of study are likely not playing a large role in the differences in migration probabilities. Appendix Table A6 also shows interactions of Top 5 and different majors on our main outcomes. There do not seem to be clear differences in the role of a Top 5 by major. Further, course selectivity does not appear to be correlated with migration when controlling for Top 5 IIT attendance (shown in Appendix Table A7)

6b. Signaling: The BHU Name Change
Next, we examine whether the IIT 'brand' may play a signaling role that facilitates migration. Distinguishing the signaling value of the IIT brand from other features of an IIT education is challenging. However, we are able to leverage an interesting situation whereby one university received IIT designation without any concomitant changes to its staff, curriculum, or admission system, similar to the approach used by studies of the signaling value of university names (Acton, 2022) or degrees (Tyler, Murnane, and Willett, 2000) net of human capital effects.
We note that similar to Acton (2022), the signaling value of the IIT brand here does not imply 15 signaling on students' innate ability, but rather that the IIT diploma may provide a signal of the quality of the human capital gained in an IIT to graduate schools or employers after graduation.   Table 6 shows the regression estimates comparing the migration probability of students graduating in 2013-2015 vs. earlier years before the change to an IIT. This shows that controlling for a linear time trend, the designation of BHU as an IIT led to a 5.4 percentage point increase in the probability of migration for graduate school. Compared to a baseline propensity of 10.5 percent prior to IIT designation, our estimates correspond to a roughly 50 percent increase in the propensity to migrate for graduate school. While sizeable, this effect size is noticeably smaller than in the main specification of section 5. The difference could be due to Top 5 IITs providing a stronger signal, to the main specification estimates, or both.
One limitation of the preceding results is that they are based on time effects within BHU graduates. To provide some reassurance on the validity of the analysis, we also compare BHU graduates to graduates from two other engineering colleges that did not gain IIT designation in a simple difference-in-differences setting (shown in Appendix Table A8). The point estimate for the diff-in-diff coefficient is positive and significant, and larger in magnitude than in the main exercise. However, the diff-in-diff results are also noisy due to shorter time coverage and the relatively small number of students in the control institutes.
Taken as a whole, the results from this subsection suggest that the IIT brand by itself facilitates migration and that signaling may play a role in the greater incidence of migration among IIT graduates.

6c. Role of Alumni Networks
Lastly, we examine whether alumni networks can facilitate migration. Alumni networks can lower the costs of migration for IIT students by providing information about educational and employment opportunities. Alumni may also facilitate access to particular programs where they have influence over admissions or hiring decisions.
To examine the role of networks, we consider the case of computer science graduate programs in the U.S., where we are able to precisely observe the composition and, importantly, the undergraduate education of faculty members, thanks to a community data collection effort (Papoutsaki, et al., 2015). The computer science faculty data cover around 2,400 faculty members in 55 top U.S. graduate programs. Remarkably, 134 (5.6%) of these faculty members are alumni of one of the IITs. The distribution of these IIT alumni is uneven, with 12 programs having no IIT alumni at all and MIT and the University of Illinois each having as many as eight.
We next combine the faculty data with information on which universities IIT graduates in our sample attended for their U.S. graduate studies. We focus here on the 39 individuals in our sample who enrolled in a U.S. graduate program in computer science and the top 25 graduate programs in the U.S. News of the World ranking. 23 For each individual, we consider the 25 potential destinations and estimate a multinomial logit model of the type:  Table 7 reports the results of the multinomial logistic model as relative risk ratios. An additional alumnus from one's own IIT in a particular destination is associated with a 30% increase in the likelihood of enrolling in that destination. By contrast, the number of IIT alumni from other IITs does not appear to correlate with the decision to enroll in a program: the point estimate of the relative risk ratio is not just insignificant, but is also very close to one. Overall, the results suggest that alumni networks may facilitate access to particular U.S. graduate programs.

Conclusion
Using a novel dataset of students taking the JEE exam and their education and career outcomes, we have documented that the incidence of migration among top talent is sizeable, and particularly so at the very right tail of the talent distribution. Among the top 1,000 scorers at the JEE (corresponding to 0.2% of the test takers and 0.00005% of the birth cohort), the share of migrants is around 36%, rising to 62% among the top 100 scorers, and to 9 out of the top 10 scorers.
While prior literature has documented that the incidence of migration rises with educational attainment (Saint-Paul, 2004;Docquier and Marfouk, 2006;Docquier and Rapoport, 2012;Grogger and Hanson, 2011;Kerr, et al., 2016), our work reveals that this masks considerable heterogeneity among the tertiary-educated in the ability dimension. Indeed, the incidence of migration rises dramatically among the most extraordinarily able, as conjectured by Saint-Paul (2004).
We have also documented that graduates of the most elite IITs are more likely to migrate abroad after graduating compared to equally talented individuals who chose other IITs. Prior research has documented the large enrollment of Indian students in U.S. graduate programs (Bound, et al., 2021). We show that Indian educational institutions are playing an important role in facilitating this enrollment, as Top 5 IIT graduates are more likely to migrate for graduate school than others, and to migrate to the U.S. to attend Ph.D. programs, in particular. We find that this is likely due to the signaling value of the IIT brand, as well as to the networks that are formed among alumni of specific IIT campuses. In fact, these networks likely play an even larger role than our analysis of computer science faculty alumni networks suggests.
While prior work has emphasized the gatekeeping role of elite universities in host countries (Kerr, et al., 2016, Amornsiripanitch, et al., 2021, our paper surfaces the similar role played by elite universities in source countries. While we cannot observe the full extent of the mechanisms contributing to these effects, our analysis suggests that through a combination of signaling and network effects, elite universities in source countries play a key role in shaping migration outcomes, both in terms of the overall propensity and the particular migration destination. We note 19 that the fact that elite home universities act as gatekeepers for migration further raises the stakes of their own admission policies.
We conclude by mentioning two lines of inquiry that could be explored in future research.
The first is why the incidence of migration rises dramatically at the very right tail of the talent distribution (above and beyond the gatekeeping role of universities). One potential explanation is that the private return to extraordinary ability is higher in destination countries (perhaps due to agglomeration effects) than in source countries. This raises the question of whether home countries should make special efforts to retain their top talent. It will be interesting to study whether patterns

. Share of Test Takers Attending a Top 5 IIT by Rank and Gender
Notes: Admission to the Indian Institutes of Technology is exclusively through the Joint Entrance Exam (JEE). The horizontal axis is the rank at the JEE (All India Rank).     Notes: Individuals who forego studying at a Top 5 IIT may do so to stay closer to family (say to take care of an ailing parent or younger sibling) or because they have a strong attachment to their home region. This, in turn, could lead to lower migration propensities. This table investigates the robustness of our results to excluding individuals who study close to home and may thus be "geographically bound." Panel A replicates Table 3, panel B is run on the subsample of individuals who study outside their home state, and panel C is run on the subsample of individuals who study outside a 200 km radius from the location where they took the JEE test. All specifications include JEE score fixed effects and gender. Robust standard errors in parentheses. + p < 0.10, * p < 0.05, ** p < 0.01   Table 3 assuming these individuals did migrate (in terms of type of migration-migrating for work/graduate school/Ph.D./Master's-we assume each type occurs in the same proportion as in the observed migration episodes). Note that share of observation with missing career histories is similar across those who attended a Top 5 or not. Robust standard errors in parentheses. + p < 0.10, * p < 0.05, ** p < 0.01 Appendix Notes: Course selectivity is the minimum score required to enter a particular IIT/major combination. Robust standard errors in parentheses. + p < 0.10, * p < 0.05, ** p < 0.01  Table 6 due to limited data availability for the two control institutes). Our variable of interest is a dummy taking value one for BHU graduates graduating after 2013, and we control for cohort fixed effects and the main effect attending BHU. Robust standard errors in parentheses. + p < 0.10, * p < 0.05, ** p < 0.01