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---

### Key findings and headline statistics
- Among Nobel Prize winners and Fields Medalists, migrants to the U.S. represent 20-33% of frontier knowledge producers.
- Migrants to the U.S. are up to six times more productive than migrants to other countries, even after accounting for teenage talent.
- Migrants to the U.S. are four to six times more productive than stayers; migrants to the U.K. are more than twice as productive as stayers.
- Among developing country IMO participants, 66% dream of studying in the U.S. while only 25% manage to do so.
- Student visas (F1) to the U.S. fell by 70 percent between fiscal years 2019 and 2020.
- Certain ‘push’ incentives that reduce immigration barriers—by addressing financing constraints for top foreign talent—could increase the global scientific output of future cohorts by 42% percent.
- Sample and coverage:
  - Career histories and lifetime scientific output for 2,200 IMO medalists from over one hundred countries.
  - Survey of 610 recent IMO participants (responses from 76 countries).
  - There were 5,666 IMO participants from 2009 to 2018; survey respondents were medalists at a rate of 55% versus 50% among IMO participants.

### Research question, motivation, and data construction
- Objective: quantify how U.S. immigration barriers impact global knowledge production and identify policy actions likely to advance the global knowledge frontier.
- Rationale: restrictive U.S. immigration policies and COVID-19-related disruptions could limit cross-border flows of people and ideas and thereby adversely affect global scientific activity.
- Data sources and construction:
  - IMO medalists database: participants 1981–2000 who received a medal; origin = country represented at the IMO; current occupations and country of residence manually collected; occupation categories include math academia, non-math academia, IT, finance.
  - Migrant definition: country represented at the IMO different from country of work in 2016; migrants to the U.S. if place of work in 2016 was in the U.S. and did not represent the U.S. at the IMO.
  - Productivity measures: mathematics publications weighted by cites via MathSciNet public author pages; invited speaker at the International Congress of Mathematicians (ICM) as a bibliometrics-independent recognition measure.
  - For 55% of IMO medalists in sample, current employment and location as of 2016 were found; for untraced individuals, assumption: remain in origin country (migration estimates are a lower bound).
  - Nobel laureates and Fields Medalists: Nobel laureates in Chemistry, Physics and Physiology and Medicine since 2000; Fields medalists since 1990; migrant = country of birth different from country of main academic affiliation at time of award.

### Survey design and counterfactual choice experiment
- Survey of IMO participants:
  - Retrospective survey conducted June 2019; 610 useable responses from 76 countries; respondents more likely to be medalists (55% vs 50%).
  - Survey content: demographics, career preferences, life satisfaction, reasons for IMO participation, extensive questions on undergraduate study decisions, and counterfactual choice questions between admission offers differing by ranking and funding.
- Counterfactual choice blocks (respondents received either Block A or Block B):
  - Block A examples: University of Cambridge unfunded versus Imperial College funded; Cambridge unfunded versus University of Manchester funded; Cambridge unfunded versus University of Edinburgh funded; Cambridge unfunded versus Swiss Federal Polytechnic School of Lausanne funded.
  - Block B examples: Stanford University unfunded versus New York University funded; Stanford unfunded versus Carnegie Mellon funded; Stanford unfunded versus Boston University funded; Stanford unfunded versus Swiss Federal Polytechnic School of Lausanne funded.
- Choice regression specification:
  - Pr(Preferfunded_i,jk) = β Developi + γ_jk + ε_i,jk, where Developi = indicator if respondent from a developing country and γ_jk = fixed effect for the university pair.

### Empirical strategy and identification
- Core regression (IMO medalists sample):
  - Productivity_ijt = β Migrant_i + η_j + ζ_t + γ_i + ε_i
    - i indexes medalists, t Olympiad years, j origin countries.
    - Productivity measured as number of mathematics publications or cites up to 2017, or indicator for ICM speaker.
    - Controls: η_j (fixed effects for number of points scored by individual i in last IMO participation), ζ_t (fixed effects for year of last participation), γ_i (fixed effects for the country the individual represented at the IMO).
  - Alternative specification: indicators for migrant to the U.S., migrant to the U.K., migrant to other countries.
  - Estimation: Poisson when cites is dependent variable; OLS when becoming an ICM speaker is dependent variable.
- Extensive vs intensive margin analysis:
  - Extensive margin: regressions with occupation (all medalists) to capture choice of academic career.
  - Intensive margin: productivity regressions restricted to those who choose academic careers in math.

### Mechanisms and interpretation
- Productivity premium drivers:
  - Extensive margin: migrants to the U.S. are more likely to choose academic careers when they migrate to the U.S.
  - Intensive margin: among those in math academia, migrants to the U.S. are more productive than stayers.
- Financing as a constraint:
  - Survey conjoint questions show funding availability is salient; financing costs are a key barrier preventing foreign talent—particularly from developing countries—from migrating to pursue education and careers abroad.

### Quantitative counterfactual scenario and aggregation
- Main quantitative scenario: if all IMO participants who dream of studying in the U.S. were able to do so, total scientific output of each future cohort would increase by 42%.
- Survey composition and counterfactual shares:
  - Sample of survey respondents: 610.
  - Current shares among respondents: 67% are stayers, 15% are migrants to the U.S., 19% are migrants to other countries.
  - Counterfactual if all respondents who have their dream undergraduate institution in the U.S. could indeed study in the U.S.: share of migrants to the U.S. would jump to 41%, share of stayers down to 48%, share of migrants to other countries down to 11%.
- Productivity multipliers used (preserved exactly as presented):
  - Migrants to the U.S. are 4.2 times more productive than stayers (exp(1.65)-1).
  - Migrants to other countries are 2.2 times more productive than stayers.
- Aggregate output calculation (preserved exactly):
  - Total output would be 42% higher [(0.48*1+0.41*4.2+0.11*2.2) / (0.67*1+0.15*4.2+0.19*2.2)].
- Calculation assumptions: interprets productivity differences causally and assumes independence from the number of stayers and migrants.

### Key empirical estimates and table highlights (preserved exactly)
- Table 1 coefficients (selected, sample: IMO medalists 1981–2000):
  - Migrant: 1.445*** (standard error 0.218) for cites-weighted math publications.
  - Migrant to the U.S.: 1.653*** (standard error 0.216) for cites-weighted math publications.
  - Migrant to the U.K.: 1.020*** (standard error 0.368) for cites-weighted math publications.
  - Migrant to other countries: 1.158*** (standard error 0.294) for cites-weighted math publications.
  - Mean of dependent variable for stayers (cites-weighted math publications): 38.1.
  - Observations: 2,195 (columns using publications), 2,272 (columns using propensity to become an ICM speaker).
- Occupation regressions (Table 2, selected):
  - Panel A migrant coefficients:
    - Migrant: 0.238*** for Academia (math) (standard error 0.022).
    - Migrant: 0.158*** for Academia (not math) (standard error 0.019).
    - Migrant: 0.060*** for Finance (standard error 0.012).
    - Migrant: 0.146*** for IT (standard error 0.018).
  - Mean for stayers (Academia (math)): 0.179.
  - Observations: 2,272.
  - Panel B by destination (selected):
    - Migrant to the U.S.: 0.208*** for Academia (math) (standard error 0.028).
    - Migrant to the U.K.: 0.264*** for Academia (math) (standard error 0.066).
    - Migrant to other countries: 0.281*** for Academia (math) (standard error 0.036).
- Migrant productivity conditional on math academia (Table 3, selected):
  - Migrant: 1.053*** (standard error 0.231) for cites-weighted math publications.
  - Migrant to the U.S.: 1.329*** (standard error 0.250) for cites-weighted math publications.
  - Mean of dependent variable for stayers (cites-weighted math publications): 161.3.
  - Observations: 527 (publications), 548 (ICM speaker propensity).
- Counterfactual choice regression (Table 4, dependent variable: choose funded offer):
  - Specification (1): From a developing country (0/1): 0.270 *** (0.036); Observations: 1539; Mean dep. var.: 0.54.
  - Specification (2): From a developing country (0/1): 0.196 *** (0.056); Medalist (0/1): -0.113 ** (0.048); From a developing country x medalist: 0.136 * (0.072); Observations: 1539; Mean dep. var.: 0.54.
  - Significance notation: * p < 0.1; ** p < 0.05; *** p < 0.01.

### Survey findings on dreams vs reality and financing
- Among developing participants:
  - 66% dream to study in the U.S.
  - 11% dream to study in their origin country.
  - Actual allocation for developing participants: 25% actually study in the U.S.; 51% study in their origin country.
- Financing importance:
  - 40% of respondents report availability of financial assistance was a “very important” or “extremely important” factor in their decision to attend their undergraduate institution (rising to 56% for developing country participants).
  - Hypothetical funded vs unfunded choices:
    - Respondents overall chose the funded offer 54% of the time.
    - Share choosing funded offer was 81% for students from developing countries.
    - With pair fixed effects, developing country respondents are 27% more likely to choose the funded offer compared to advanced country respondents (p=0.36).
- Counterfactual U.S. border closure scenario:
  - Under the U.S. border closure scenario, the share of IMO participants studying in their origin country would rise to 71% (that is 40% higher than current levels).

### Policy implications and recommended interventions
- Main policy levers considered:
  - Push: easing financial constraints through scholarships and financial assistance to enable top talent to realize migration/study plans.
  - Pull: increasing visas for permanent work-based immigration (e.g., offering green cards).
- Survey-based implications:
  - Only a small minority (around 11-15%) cite the immigration climate as very important in their decision not to apply to U.S. schools.
  - A much larger share cite tuition or living costs as very important:
    - 57% among developing country participants.
    - 37% among advanced country participants.
- Policy recommendations:
  - Prioritize scholarships for talented students if political capital is limited; targeted push programs could be significantly more effective than improving the immigration climate alone.
  - Combine stable open borders, full scholarships for top talent (especially from lower income countries), and a top-ranked university to replicate the U.S. success.
  - Alternative models: geographic relocation of learning centers, strengthening public hubs, and improving centers of learning in developing countries.
  - Complementary use of pull incentives (green cards) and push programs (financial assistance) to advance the global knowledge frontier.

### Limitations and caveats
- Selection concerns: immigrants to the U.S. could be positively selected above and beyond IMO score; IMO score controls mitigate but do not eliminate this concern.
- Survey limitations: potential selective response bias; sample of 610 from a range of countries and years helps but does not fully remove concerns.
- External validity: hypothetical conjoint choices may not fully capture actual behavior.
- Back-of-the-envelope aggregation caveats:
  - More migrants could crowd out natives or previous immigrants in faculty positions or graduate program spots, or generate positive knowledge spillovers; prior literature documents ambiguous directions.
  - Aggregation assumes causal interpretation of productivity differences and independence from the number of stayers and migrants.

*Source: wpiea2021042-print-pdf*

### Section 1

### Why U.S. Immigration Matters for the Global Advancement of Science (Section 1)

### Key findings and headline statistics
- Among Nobel Prize winners and Fields Medalists, migrants to the U.S. represent 20-33% of frontier knowledge producers.
- Migrants to the U.S. are up to six times more productive than migrants to other countries, even after accounting for teenage talent.
- Migrants to the U.S. are four to six times more productive than stayers; migrants to the U.K. are more than twice as productive as stayers.
- Among developing country IMO participants, 66% dream of studying in the U.S. while only 25% manage to do so.
- Student visas (F1) to the U.S. fell by 70 percent between fiscal years 2019 and 2020.
- Certain ‘push’ incentives that reduce immigration barriers—by addressing financing constraints for top foreign talent—could increase the global scientific output of future cohorts by 42% percent.
- Sample and data coverage statistics:
  - Career histories of migration and lifetime scientific output for 2,200 IMO medalists from over one hundred countries.
  - Survey of 610 recent IMO participants (responses from 76 countries).
  - There were 5,666 IMO participants from 2009 to 2018; survey respondents were medalists at a rate of 55% versus 50% among IMO participants.

### Research question and motivation
- Objective: quantify how U.S. immigration barriers impact global knowledge production and identify policy actions likely to advance the global knowledge frontier.
- Rationale: the U.S. has been a global hub for foreign talent; restrictive U.S. immigration policies and COVID-19-related disruptions could adversely affect global scientific activity by limiting cross-border flows of people and ideas.

### Data sources and construction
- IMO medalists database:
  - Extracted from the official IMO website for participants between 1981 and 2000 who received a medal.
  - Origin country is the country represented at the IMO. Current occupations and country of residence manually collected (Google, LinkedIn, similar sources).
  - Occupation categories: math academia, non-math academia, information technology (IT), finance.
  - Migrant definition: country represented at the IMO different from country of work in 2016; migrants to the U.S. defined if place of work in 2016 was in the U.S. and did not represent the U.S. at the IMO.
  - Productivity measures: mathematics publications weighted by cites via MathSciNet public author pages; invited speaker at the International Congress of Mathematicians (ICM) as a bibliometrics-independent recognition measure.
  - For 55% of IMO medalists in sample, current employment and location as of 2016 were found; for those untraced, assumption is they remain in origin country (migration estimates are a lower bound).
  - Note: a substantial (45%) share of the sample cannot be matched to any occupation.

- Nobel laureates and Fields Medalists database:
  - Nobel laureates selected for awards in Chemistry, Physics and Physiology and Medicine since 2000.
  - Fields medalists selected since 1990.
  - Migrant classification: country of birth different from country of main academic affiliation at time of the award; migrants to the U.S. if main affiliation at award time was in the U.S. and country of birth was not the U.S.

- Survey of IMO participants:
  - Retrospective survey conducted June 2019; approved by the Social Science Research Ethics Committee at the University of Bath; consent form and information sheet included.
  - Distribution facilitated via IMO country representatives; incentives included five Amazon vouchers worth 80 British pounds (or equivalent charity donation) and access to two new mathematical problems.
  - Received 610 useable responses from 76 countries; respondents more likely to be medalists (55% vs 50%).
  - Survey content: demographics, career preferences, life satisfaction, reasons for IMO participation; extensive questions on undergraduate study decisions (institutions considered, applied to, admitted to, attended; top-of-world preference); importance of factors for enrollment choices; counterfactual choice questions between admission offers differing by ranking and funding (funded vs unfunded).

### Empirical strategy and identification
- Core regression for migrant productivity (IMO medalists sample):
  - Productivity_ijt = β Migrant_i + η_j + ζ_t + γ_i + ε_i
    - i indexes medalists, t Olympiad years, j origin countries.
    - Productivity_ijt is number of mathematics publications or cites up to 2017, or indicator for being an ICM speaker.
    - Migrant_i is indicator for whether individual is observed as a migrant.
    - Controls: η_j (fixed effects for number of points scored by individual i in last IMO participation), ζ_t (fixed effects for year of last participation), γ_i (fixed effects for the country the individual represented at the IMO).
  - By controlling for IMO score fixed effects, comparisons are made among individuals with the same level of problem-solving ability in their late teens to mitigate endogeneity from early indicators of talent.
  - Alternative specification replaces the migrant indicator with indicators for migrant to the U.S., migrant to the U.K., and migrant to other countries.
  - Estimation methods: Poisson when cites is dependent variable; Ordinary Least Squares when becoming an ICM speaker is dependent variable.

- Extensive vs intensive margin analysis:
  - Separate regressions where dependent variable is (a) occupation (sample: all medalists) to capture extensive margin (choice of academic career), and (b) productivity restricted to those who choose academic careers in math to capture intensive margin (productivity conditional on academic career).

### Mechanisms and interpretation
- Productivity premium drivers:
  - Extensive margin: migrants to the U.S. are more likely to choose academic careers when they migrate to the U.S.
  - Intensive margin: among those choosing math academic careers, migrants to the U.S. are more productive than stayers.
- Financing as a constraint:
  - Survey conjoint questions reveal funding availability is a salient factor; financing costs are a key factor preventing foreign talent from migrating to pursue education and careers abroad, particularly for those from developing countries.

### Policy implications and scenarios analyzed
- Reducing immigration barriers via ‘push’ incentives that address financing constraints for top foreign talent could substantially increase global scientific output: estimated increase of 42% percent for future cohorts.
- Discussion in the paper includes policy options for the U.S. and the global scientific community with particular focus on the effectiveness of scholarships versus other science policy actions such as offering green cards to foreign talent.

*Source: wpiea2021042-print-pdf - Section 1*

### Section 2

### Section 2

### III. b Counterfactual choices questions and regressions
- Designed hypothetical choice questions where respondents choose between two undergraduate offers: an unfunded offer from a higher ranked institution (according to the Shanghai rankings) and a funded offer from a somewhat lower ranked institution, usually in the same country.
- Choice blocks:
  - Block A: (1) University of Cambridge unfunded versus Imperial College funded, (2) University of Cambridge unfunded versus University of Manchester funded, (3) University of Cambridge unfunded versus University of Edinburgh funded, (4) University of Cambridge unfunded versus Swiss Federal Polytechnic School of Lausanne funded.
  - Block B: (1) Stanford University unfunded versus New York University funded, (2) Stanford University unfunded versus Carnegie Mellon funded, (3) Stanford University unfunded versus Boston University funded, (4) Stanford University unfunded versus Swiss Federal Polytechnic School of Lausanne funded.
  - To reduce respondent burden, respondents received either Block A or Block B but not both.
- Econometric specification for choice regressions:
  - Pr(Preferfunded_i,jk) = β Developi + γ_jk + ε_i,jk
  - i indexes students; j and k index undergraduate institutions in the offer set.
  - Preferfunded_i,jk is an indicator for choosing the funded option.
  - Developi is an indicator if the respondent is from a developing country.
  - γ_jk is a fixed effect for the choice (university pair).
  - With pair fixed effects, comparison is between developing and advanced country respondents confronted with the exact same choice.

### IV. a Importance of Migrants to the U.S. in the Global Knowledge Network of Science
- Migration patterns of Nobel laureates (Chemistry, Physics, Physiology and Medicine since 2000):
  - Nodes: countries of birth and countries of residence at time of prize; ties: migration flows (thicker lines = larger flows).
  - A few high-income countries—the U.S., the U.K., France and Germany—act as hubs attracting talent from multiple origin countries (which tend to be middle-income).
  - In-degree centrality measure for the U.S. is 14.
  - Migrants to the U.S. account for one in five worldwide Nobel Prize Winners in science.
- International Mathematical Olympiad (IMO) gold medalists (1981-2000):
  - Network shows the U.S. as a major magnet; in-degree centrality measure for the U.S. is 19.
  - Origin countries include many low and lower middle-income countries.
  - The number of medalists living in the U.S. is five times larger than the number of medalists produced by the U.S. (ratio far higher than for any other country).
- Quantification of immigrant contributions to frontier knowledge:
  - For Nobel prizes (physics, chemistry, physiology/medicine 2001-2019) and Fields Medal (1990-2018):
    - 21% of Nobel prize winners are migrants to the U.S.
    - 33% of Fields medalists are migrants to the U.S.
    - A further 11% of Nobel prize winners are migrants to countries other than the U.S.
    - A further 30% of Fields medalists are migrants to countries other than the U.S.
  - These results underscore the role of immigrants in global knowledge production and the importance of the U.S. as a migration destination.

### IV. b Are Migrants to the U.S. More Productive than Stayers and Migrants to Other Countries?
- Motivation: If migration changes individual productivity, migration barriers affect global knowledge production.
- Empirical strategy:
  - Focus on IMO medalists to reduce survivorship bias and control for observable teenage talent (IMO score).
  - Estimate Poisson regressions with mathematics publications (or citation-weighted publications) as outcomes.
  - Regress publications on indicators for being a migrant, being a migrant to the U.S., or a migrant to another country, controlling for country-of-origin fixed effects, year of IMO participation fixed effects, and IMO score fixed effects.
- Key productivity findings:
  - Migrants are approximately three times more productive than stayers in terms of citation-weighted publications (see Table 1 column 1).
  - Distinguishing destinations:
    - Migrants to the U.S. are four times more productive than stayers (citation-weighted publications).
    - Migrants to the U.K. or to other countries are only around twice as productive as stayers (Table 1 Column 2).
  - International Congress of Mathematicians (ICM) speaker outcomes:
    - Migrants are four times more likely than stayers to become ICM speakers (Table 1 Column 3).
    - Migrants to the U.S. are six times more likely than stayers to become ICM speakers.
    - Point estimates for migrants to the U.K. and to other countries are small and not significantly different from zero.
  - Interpretation: Migration to the U.S. is associated with a considerably greater productivity premium than migration to other advanced countries.
  - Note on Poisson coefficient interpretation: Given that a Poisson coefficient of 1.445 implies a relative effect of exp(1.445)-1 ≈3.2.

### IV. c What Explains the Migration Productivity Premium?
- Distinguish between two margins:
  - Extensive margin: migrants are more likely to choose academic careers in math (or academia generally).
  - Intensive margin: among those in academic math careers, migrants are more productive than stayers.
- Extensive margin results (Table 2):
  - Compared to stayers, migrants are at least twice as likely to be employed in math academia and in academic careers more broadly.
  - Migrants were also more likely to be employed in finance or IT.
  - By destination:
    - Excess propensity of migrants to enter academic careers (math or non-math) holds for migrants to the U.S., U.K., and other destinations (Table 2 Panel B columns 1 and 2).
    - For non-academic occupations: IMO medalists who move to the U.S. are most likely to enter IT occupations compared to stayers; those who move to the U.K. are most likely to enter finance occupations (Table 2 Panel B columns 3 and 4).
- Intensive margin results (Table 3):
  - Restricting the sample to those who enter academic careers in math, migrants are considerably more productive and more likely to become ICM speakers than stayers.
  - Migrants to the U.S. are 2.5 more productive than stayers.
  - There is no productivity difference between migrants to the U.K. and stayers.
- Synthesis:
  - Both extensive and intensive margins contribute to the productivity premium of migrants to the U.S.
  - For migrants to the U.K. and other non-U.S. destinations, the productivity premium is largely explained by the extensive margin alone.
  - The absence of a substantial intensive margin for non-U.S. destinations helps explain why migrating to the U.S. yields a relatively larger productivity premium.

### IV. d American Dream vs. Reality: Immigration Barriers for Foreign Talent
- Survey of 610 recent IMO participants (2019) focuses on undergraduate study decisions, admissions, attendance, and hypothetical funded vs. unfunded offers.
- Preferred vs. actual undergraduate study allocations (Figure 3):
  - Among developing participants:
    - 66% dream to study in the U.S.
    - 11% dream to study in their origin country (Figure 3b).
  - Actual allocation for developing participants:
    - 25% actually study in the U.S.
    - 51% study in their origin country (Figure 3d).
  - The gap between dream and reality is large and has been widening over time (Figure A2).
    - In the 2018 cohort, about half of all non-U.S. IMO participants dreamt of studying in the U.S., while only 15% actually enrolled in a U.S. undergraduate institution.
- Financing as a key constraint:
  - 40% of respondents report availability of financial assistance was a “very important” or “extremely important” factor in their decision to attend their undergraduate institution (rising to 56% for developing country participants).
  - Hypothetical choice questions (funded lower-ranked vs. unfunded higher-ranked):
    - Respondents overall chose the funded offer 54% of the time.
    - Share choosing funded offer was 81% for students from developing countries.
    - Regression with pair fixed effects: developing country respondents are 27% more likely to choose the funded offer compared to advanced country respondents (p=0.36) (see Table 4).
- Counterfactual U.S. border closure scenario (hypothetical choice analysis):
  - Under the U.S. border closure scenario, the share of IMO participants studying in their origin country would rise to 71% (that is 40% higher than current levels), as most of the immigrants currently going to the U.S. do not have non-U.S. admission offers.
- Conclusion: Limited financing availability is the main factor driving the gap between dreams and actual destinations among talented youth.

### IV. e Policies to Reduce Immigration Barriers: Green Cards vs. Scholarships?
- Two policy levers considered:
  - Easing financial constraints through scholarships (push program: reduces constraints to realize migration/study).
  - Increasing visas for permanent work-based immigration (e.g., offering green cards) (pull incentive: makes rewards of migrating more attractive).
- Survey evidence on reasons for not applying to U.S. undergraduate institutions:
  - Only a small minority (around 11-15%) in either the developing or advanced country group cite the immigration climate as very important in their decision not to apply to U.S. schools (see Figure A3).
  - A much larger share cite tuition or living costs as a very important reason:
    - 57% among developing country participants.
    - 37% among advanced country participants.
- Implication:
  - Relaxing financing constraints could be much more effective than improving the immigration climate in attracting talented students.
  - Both pull incentives (green cards) and push programs (financial assistance) can complement each other; targeted push programs could be an effective complementary tool for advancing the knowledge frontier.

*Italic: Source: wpiea2021042-print-pdf - Section 2*

### Section 3

### wpiea2021042-print-pdf - Section 3

### Main quantitative scenario: lowering immigration barriers
- Back-of-the-envelope estimate: under the scenario in which all IMO participants who dream of studying in the U.S. are able to do so, the total scientific output of each future cohort would increase by 42%.
- This result is mainly driven by the productivity premium enjoyed by foreign talent in the U.S.
- Survey composition and counterfactual shares:
  - Sample of survey respondents: 610.
  - Current shares among respondents: 67% are stayers, 15% are migrants to the U.S., 19% are migrants to other countries.
  - Counterfactual if all respondents who have their dream undergraduate institution in the U.S. could indeed study in the U.S.: share of migrants to the U.S. would jump to 41%, share of stayers down to 48%, share of migrants to other countries down to 11%.
- Productivity multipliers used in the calculation:
  - Migrants to the U.S. are 4.2 times more productive than stayers (exp(1.65)-1).
  - Migrants to other countries are 2.2 times more productive than stayers.
- Aggregate output calculation (preserved exactly as presented):
  - Total output would be 42% higher [(0.48*1+0.41*4.2+0.11*2.2) / (0.67*1+0.15*4.2+0.19*2.2)].
- The calculation assumes that the productivity difference between stayers, migrants to the U.S. and migrants to other countries can be interpreted causally and does not depend on the number of stayers and migrants.

### Key empirical findings from regressions and occupation analysis
- Migrant productivity regressions (sample: IMO medalists participating at the IMO between 1981 and 2000):
  - Table 1 coefficients (selected):
    - Migrant: 1.445*** (standard error 0.218) for cites-weighted math publications.
    - Migrant to the U.S.: 1.653*** (standard error 0.216) for cites-weighted math publications.
    - Migrant to the U.K.: 1.020*** (standard error 0.368) for cites-weighted math publications.
    - Migrant to other countries: 1.158*** (standard error 0.294) for cites-weighted math publications.
  - Mean of dependent variable for stayers (cites-weighted math publications): 38.1.
  - Observations: 2,195 (columns using publications), 2,272 (columns using propensity to become a speaker at the International Congress of Mathematicians).
- Migration and occupations (Table 2, sample: IMO medalists 1981–2000):
  - Panel A migrant coefficients (selected):
    - Migrant: 0.238*** for Academia (math) (standard error 0.022).
    - Migrant: 0.158*** for Academia (not math) (standard error 0.019).
    - Migrant: 0.060*** for Finance (standard error 0.012).
    - Migrant: 0.146*** for IT (standard error 0.018).
  - Mean of dependent variable for stayers (Academia (math)): 0.179.
  - Observations: 2,272.
  - Panel B disaggregates by destination (selected):
    - Migrant to the U.S.: 0.208*** for Academia (math) (standard error 0.028).
    - Migrant to the U.K.: 0.264*** for Academia (math) (standard error 0.066).
    - Migrant to other countries: 0.281*** for Academia (math) (standard error 0.036).
- Migrant productivity conditional on being in math academia (Table 3, sample: IMO medalists employed in math academia as of 2017):
  - Migrant: 1.053*** (standard error 0.231) for cites-weighted math publications.
  - Migrant to the U.S.: 1.329*** (standard error 0.250) for cites-weighted math publications.
  - Mean of dependent variable for stayers (cites-weighted math publications): 161.3.
  - Observations: 527 (columns using publications), 548 (columns using propensity to become a speaker).

### Mechanisms and interpretation
- Primary binding constraint: financing constraints prevent over half of top talent who dream of studying in the U.S. from doing so.
- Immigration-attractiveness policies (e.g., automatic green cards) expand the pool of dreamers but do not relax the more binding financing constraint for those already desiring to come to the U.S.
- A large majority of top talent already dream of studying in the U.S.; financing is the chief barrier to realizing those dreams.
- The estimated productivity differences between U.S. and other destinations are large and described as being in the order of four to six times, which underlies the sizable aggregate effects in the counterfactual.

### Policy implications and recommendations
- If policymakers have limited political capital, prioritizing scholarships for talented students may be significantly more effective than improving the immigration climate alone (for example, promising a green card after graduation).
- To replicate the U.S. success in attracting top talent, policy-makers in other countries would need to combine:
  - Stable open borders,
  - Full scholarships for top talent (especially from lower income countries),
  - A top-ranked university serving as a home for global talent.
- Alternative models to overcome immigration barriers:
  - Geographic re-location of learning centers (examples in the survey: New York University in Abu Dhabi; Yale-National University of Singapore campus in Singapore).
  - Strengthening public hubs (example cited: Instituto de Matemática Pura e Aplicada (IMPA) in Brazil).
  - Improving centers of learning in developing countries to nurture domestic talent.
- Timely action by global policymakers and the scientific community is needed to ensure equal opportunities for talented individuals and to accelerate the global advancement of science and knowledge.

### Limitations and caveats
- Selection bias: immigrants to the U.S. could be positively selected above and beyond IMO score; the authors partially mitigate this by controlling for IMO score but note residual concerns about unobserved differences in talent or motivation.
- Survey limitations: potential selective response bias, though a large sample of 610 respondents from a range of countries and participation years is said to alleviate concerns.
- External validity of hypothetical survey questions: conjoint pair survey designs may come close to behavioral benchmarks (Hainmueller, Hangartner, Yamamoto 2015), but concerns remain.
- Back-of-the-envelope calculation caveats:
  - Arrival of more migrants could crowd out natives or previous immigrants in faculty positions or graduate program spots, or generate positive knowledge spillovers; prior literature documents ambiguous direction and magnitude.
  - The calculation assumes causal interpretation of productivity differences and independence from the number of stayers and migrants.
  - Even with smaller migration production premiums than estimated (due to selection or crowding out), enabling financially constrained top talent to study in the U.S. would likely still translate into a sizable effect on global scientific output because estimated magnitudes of productivity differences are large.

*Source: wpiea2021042-print-pdf - Section 3*

### Section 4

### wpiea2021042-print-pdf - Section 4

### Regression specifications and estimation details
- Specifications in column 1 and 2 use mathematics publications weighted by the number of forward cites received until 2017 as dependent variable and are estimated with Poisson regressions.
- Specifications in columns 3 and 4 use the propensity to become a speaker at the International Congress of Mathematicians as dependent variable and are estimated with OLS.
- Robust Standard errors are reported in parentheses.
- Significance notation:
  - * p < 0.1
  - ** p < 0.05
  - *** p < 0.01

### Table 4. Counterfactual choice regressions — key estimates and sample information
- Dependent variable: choose funded offer (0/1)
- Specification (1):
  - From a developing country (0/1): 0.270 *** (0.036)
  - Choice Fixed Effects: Yes
  - Observations: 1539
  - Mean of dependent variable: 0.54
- Specification (2):
  - From a developing country (0/1): 0.196 *** (0.056)
  - Medalist (0/1): -0.113 ** (0.048)
  - From a developing country x medalist: 0.136 * (0.072)
  - Choice Fixed Effects: Yes
  - Observations: 1539
  - Mean of dependent variable: 0.54
- Survey setup:
  - Respondents chose between two undergraduate admission offers: an unfunded offer from a higher ranked institution (according to the Shanghai rankings) and a funded offer from a somewhat lower ranked institution.
  - Regressions analyze the propensity to accept the funded offer in these counterfactual choices.
- Standard errors in parentheses.
- Significance notation repeated:
  - * p < 0.1
  - ** p < 0.05
  - *** p < 0.01

### Figures — descriptions and notes
- Figure 1A. Global Knowledge Network for Nobel Prize winners in Chemistry, Physics and Physiology or Medicine from 2000 to 2019
  - Weighted, directed network graph: nodes = countries; edges with arrows represent flows from prize winners' countries of birth to countries at the time of award.
  - Thicker edges indicate larger flows.
  - Nodes weighted by number of prize winners in the country at the time of award.
  - Countries classified into high income, upper middle, lower middle and low income based on the 2000 World Bank classification.
- Figure 1B. Global Knowledge Network for IMO gold medalists 1981-2000
  - Weighted, directed network graph: nodes = countries; edges with arrows represent flows from gold medalists’ origin countries (at the time of the IMO competition) to current country.
  - Thicker edges indicate larger flows.
  - Nodes weighted by number of gold medalists currently in the country.
  - Countries classified into high income, upper middle, lower middle and low income based on the 2000 World Bank classification.
- Figure 2. Share of migrants to the U.S. in frontier knowledge production
  - (Figure title provided; no numeric values in source text.)
- Figure 3. Studying abroad: dream and reality
  - Based on a survey of recent participants of the International Medal Olympiads.
  - Respondents were asked where they enrolled for their undergraduate studies (panels a and b) and where they would have wanted to study if they could have studied anywhere in the world (panels c and d).
  - Panel labels and category shares (from figure graphic):
    - a: Advanced countries: actual
    - b: Developing countries: actual
    - c: Advanced countries: dream
    - d: Developing countries: dream
    - Country categories shown in graphic: USA, UK, Other countries, Origin country
    - Percent figures appearing in the figure graphic: 6%, 12%, 3%, 79%, 25%, 6%, 18%, 51%, 21%, 25%, 3%, 51%, 66%, 15%, 8%, 11% (presented in the figure as shown)

### Appendix Table A1. Summary statistics: Survey respondents vs. All IMO participants (sample means)
- Sample periods and groups: IMO participants (2009-2018), Survey respondents, Difference
- Received a medal:
  - IMO participants: 0.498 (0.500)
  - Survey respondents: 0.549 (0.498)
  - Difference: 0.052 ** (0.021)
- Region of origin (World Bank region) — selected rows (means and standard deviations in parentheses; difference with significance where shown):
  - Europe and Central Asia:
    - IMO participants: 0.505 (0.500)
    - Survey respondents: 0.579 (0.494)
    - Difference: 0.073 *** (0.021)
  - North America:
    - IMO participants: 0.028 (0.165)
    - Survey respondents: 0.020 (0.139)
    - Difference: -0.008 (0.007)
  - East Asia and Pacific:
    - IMO participants: 0.172 (0.378)
    - Survey respondents: 0.148 (0.355)
    - Difference: -0.025 (0.016)
  - Latin America and the Caribbean:
    - IMO participants: 0.130 (0.337)
    - Survey respondents: 0.179 (0.383)
    - Difference: 0.048 *** (0.015)
  - South Asia:
    - IMO participants: 0.043 (0.202)
    - Survey respondents: 0.010 (0.099)
    - Difference: -0.033 *** (0.008)
  - Middle East and North Africa:
    - IMO participants: 0.073 (0.260)
    - Survey respondents: 0.030 (0.169)
    - Difference: -0.043 *** (0.011)
  - Sub-Saharan Africa:
    - IMO participants: 0.049 (0.216)
    - Survey respondents: 0.036 (0.187)
    - Difference: -0.013 (0.009)
- Observations:
  - IMO participants: 5,666
  - Survey respondents: 610
  - Total: 6,276

### Appendix figures — captions and data notes
- Figure A1. Talent ratios: talent living in country/talent produced by country based upon IMO medalists
  - (Caption provided; no numeric table values in source text.)
- Fig. A2: Studying Abroad: Dream vs. Reality over time
  - Time series axis: IMO participation year (2010, 2012, 2014, 2016, 2018)
  - Series in figure:
    - enrolled in a U.S. undergraduate institution
    - would have liked to study in the U.S.
  - Vertical axis labeled: Share of IMO participants who:
  - Data points shown from 0 to 0.5 on vertical axis (figure graphic)
- Fig. A3: Role of Financial Costs vs. Immigration Climate: Share of Respondents Citing Financial Costs or Immigration Climate as ‘Very Important’ Reason for Not Applying to US Institutions
  - Separate series for Developing Country Respondents and Developed Country Respondents
  - (Caption provided; no numeric values in source text.)

*Source: wpiea2021042-print-pdf - Section 4*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021042-print-pdf.pdf_