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Are foreign-born researchers more innovative? Self-selection and the production of knowledge among PhD recipients in the USA


When analyzing knowledge production, the evidence suggests that within the USA, foreign-born researchers exhibit more productivity than their domestic counterparts. Previous literature indicates that productivity differences can be explained by higher academic ability and the selection of more research-oriented fields among foreign-born. In this study, we use individual data from the restricted-access version of the Survey of Doctoral Recipients between 1995 and 2003 to extend this notion and compare knowledge production, in terms of papers presented, articles published, patent applications, and patents granted, of foreign-born and domestic PhD recipients. Our results strongly support the notion that foreign-born researchers, and especially naturalized US citizens, outperform their domestic counterparts in all four of our measures of knowledge production. We show that while aspects associated with academic training, quality of the school, occupation mismatch, and fields of study, among others, play a role in productivity differentials, they only account for a small proportion of the variability. We develop a theoretical a model to show that non-directly observable aspects associated with non-academic ability of foreign-born and a better match between the student and the PhD program, associated with differing opportunity costs of attending the program, may explain the results. Different specifications and robustness checks are conducted to provide support to our theory.

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  1. Notice that as foreign-born PhD recipients often come to the US from less-developed, and on-average less-educated countries, controlling for parents’ education can bias the results upward as it suggests that foreign-born are less able than domestics. To account for this potential bias, we also include region of origin fixed effects. These fixed effects capture all elements that are common to the region from which the student is coming, such as education, income, average ability, etc. Therefore, parents’ ability is only capturing the within-region variation. To more explicitly control for within-region variation, we interact region of origin with education of the mother. We thank one of our referees for pointing out this aspect.

  2. The reference period are April 1990–April 1995 for the 1995 survey and October 1998–October 2003 for the 2003 survey.

  3. This section was improved by the comments of three anonymous referees. Note also that our approach resembles Hunter et al. (2009) in terms of the existence of different abilities and costs of migration.

  4. Notice that in our sample most of the immigrants come from developing countries, such as China (34% of the sample) and India (25%). The first developed country in the list is Canada (7.5%).

  5. We thank an anonymous referee for suggesting that we draw out more fully the implications of the likely significant differences between opportunity costs of domestic and foreign students.

  6. The interpretation would be that, because of cultural differences, the “more foreign,” first, would face higher costs associated with living in the US and flourishing in an academic environment that is grounded in Western—and particularly in Anglo-Saxon—culture (a higher k); and, second, would, in terms of employment in their home cultures, face opportunity costs that are less correlated (a lower b) with the aptitudes that would be useful in a professional world structured around Western/US standards of academic performance.

  7. A large negative idiosyncratic component could also be interpreted to include the psychic benefits that someone might derive from the academic life, independent of monetary remunerations.

  8. In our sample, 30% of the journal articles, 29% of the papers, 27% of the patent applications, and 24% of granted patents are produced by researchers whose fathers had graduate studies. Conversely, only 17% of the journal articles, 17% of the papers, 19% of the patent applications, and 20% of the patents granted are produced by those whose father had less than a high school education.

  9. We thank one of our referees for suggesting this potential bias.

  10. Given the large amount of countries of origin and, in most cases, the relative small number of students from each country, the use of country-of-origin fixed effects is impracticable. To retain all observations and account for specific characteristics at the smallest possible level, we use region of origin fixed effects. The regions are Europe, Asia, North America (non-US), Central America + Mexico, Caribbean, South America, Africa, and Oceania. Other authors (e.g., Grogger and Hanson 2013) use only a small sample of countries, reducing significantly the sample size.

  11. Results do not change significantly whether we use mother or father’s education in the interaction, but previous literature has suggested mother’s education as the main driven factor of children’s achievement (e.g., see Chevalier et al. (2013) for a review of the literature).

  12. The actual answers in the survey are closely related, somewhat related, and not related at all.

  13. However, note that PhD institutional quality is part of the effect of self-selectivity difference between the foreign and domestic student, and thus controlling for this quality may reduce the effect we are trying to measure.

  14. For this, we exclude a small sample (81 observations) of workers working out of the US, but keep those working in US territories and in regions within the US with non-specified states. The reader should note that running the regressions without state fixed effects do not alter the results.

  15. In an additional specification (available upon request,) we exclude foreign-born researchers that arrived in the US as dependents. The exclusion of the foreign-born who arrived as dependents from the analysis is only available for the 2003 survey, and so the restriction can only be applied to that year. Results from this specification are very similar to the ones obtained in our third specification.

  16. We thank one of anonymous referee for suggesting this as a potential mechanism.

  17. This measure is conservative because it also excludes those who came to the country at later stages (around the age of entering to College). Alternative specifications, (e.g., excluding only those who entered the country before 15 years old) were also considered. These specifications do not change the results.

  18. Whereas only 31% of journal articles are produced in the private sector (non-educational), 84% of patent applications and patents granted are from non-educational institutions. Note in Table 9 that working in academia reduces the likelihood of applying to patent an invention in every educational institution.

  19. In particular, we exclude Guam, Puerto Rico, Virgin Islands, and observations classified under “US territory”. We also excluded a small portion of observations for PhD recipients employed outside of the US We keep Alaska and Hawaii, but excluding them from the sample to consider only the contiguous 48 states plus the District of Columbia do not affect the estimates.

  20. Only 5.5% and 10.3% of the domestic and foreign-born samples come from the year 2003, respectively.

  21. Notice however that 1.3% of the domestic sample (US citizens, native) declare that they were born outside of the US. Similarly, 0.4% of the foreign-born sample (Non-US citizens) declare that they were born in the US. We use the definition of citizenship to distinguish between domestic and foreign-born, because it allows us to compare across specifications.

  22. Notice that the IRR is computed as: \( IRR = e^{\beta } \). The difference in productivity with respect to the base category (native US citizens) is calculated as \( e^{\beta } - 1 \).

  23. Note that the survey asks questions about visa status “at the moment of the survey”. On the other hand, questions regarding the production of journal articles, papers, and patents, consider the production of the preceding five years. Some of the researchers could have been publishing journal articles and patenting inventions before gaining citizenship, and have gained citizenship just before the survey. If this is a generalized trend, affecting most of the sample, then the potential mechanism of search of citizenship cannot be ruled out. Despite this being unlikely, we acknowledge that we cannot entirely rule out this possibility. Nonetheless, we have no reason to believe that a large portion of the sample was granted citizenship in any given year, so that the process can be treated as random. In fact, the Department of Homeland Security reports that in the year 2003, only 463,204 citizenships were granted. This figure is 13.8% less than in 2004 and 19.3% less than 2002. Similarly, in 1995 only 488,088 foreign-born were naturalized in the US, a number that is 53% below those of 1996. These statistics can be found in

  24. Results for patent applications and patents granted did not converge when using state fixed effects, because of the small sample that we are able to use for these measures.

  25. Results are similar if we also exclude young US domestic researchers to compare the same cohorts between researchers. We do this in addition, because by only excluding young foreign-born researchers and keeping the full sample of US domestics, we are comparing the outcomes of more experienced researchers (foreign-born) to those of younger and inexperienced domestic PhD recipients. Results from these regressions yield similar results with differentials of 19%, 20%, and 86% for journal articles, papers, and patents granted among those with at least five years of experience, and 108% more patent application among those with ten or more years of experience.

  26. These controls are only available when restricting the sample to academics. A full description of the Carnegie Classification can be found at


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Correspondence to Rodrigo Perez-Silva.

Appendix: Demonstration of Eq. (8)

Appendix: Demonstration of Eq. (8)

The person attends the PhD program if the idiosyncratic component of opportunity cost is less than the average net remuneration given aptitude and probability of program fit: \( \varepsilon \le L\left( {\alpha ,\beta } \right) = I\left( \beta \right) + \alpha \gamma - C\left( \beta \right) \), where we approximate the average opportunity cost as \( C\left( \beta \right) = k + b\beta \). The number of potential students of aptitude \( \beta \) who opt into a PhD program is given by

$$ N\left( \beta \right) = h\left( \beta \right)\mathop \int \limits_{ - \infty }^{L\left( \beta \right)} g\left( \varepsilon \right){\text{d}}\varepsilon , $$

where the first function, \( h\left( \beta \right), \) on the right-hand side of Eq. (A.1) represents the number of potential students of aptitude \( \beta \), and the integral represents the proportion of potential students of aptitude \( \beta \) whose idiosyncratic component to their opportunity cost are sufficiently low such that they enter PhD programs. The marginal impact on this number of students of changes in k and b are given by

$$ \frac{\partial N\left( \beta \right)}{\partial k} = - h\left( \beta \right)g\left[ {L\left( \beta \right)} \right] , $$
$$ \frac{\partial N\left( \beta \right)}{\partial b} = - \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right] . $$

The total number of PhDs across all aptitude levels is given by

$$ N_{T} = \mathop \int \limits_{0}^{1} N\left( \beta \right){\text{d}}\beta , $$

and so the marginal impact on the total number of students due to changes in k and b are given by

$$ \frac{{\partial N_{T} }}{\partial k} = \mathop \int \limits_{0}^{1} - h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta , $$
$$ \frac{{\partial N_{T} }}{\partial b} = \mathop \int \limits_{0}^{1} - \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta . $$

The average aptitude of PhDs is given by

$$ \overline{\beta } = \frac{1}{{N_{T} }}\mathop \int \limits_{0}^{1} \beta N\left( \beta \right){\text{d}}\beta , $$

and so the marginal impact on the average aptitude PhDs due to a change in k is given by

$$ \frac{{\partial \overline{\beta } }}{\partial k} = - \frac{{\mathop \int \nolimits_{0}^{1} \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{N_{T} }} + \frac{{\overline{\beta } }}{{N_{T} }}\mathop \int \limits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta , $$

which, after collecting terms, can be written in terms of the average aptitude of all PhDs (\( \overline{\beta } \)), the average aptitude of the marginal (or indifferent) PhDs (\( \overline{\beta }_{M} \)), and the proportion of all PhDs who are marginal (A):

$$ \frac{{\partial \overline{\beta } }}{\partial k} = \left( {\frac{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{N_{T} }}} \right)\left( {\overline{\beta } - \frac{{\mathop \int \nolimits_{0}^{1} \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}} \right) = A\left( {\overline{\beta } - \overline{\beta }_{M} } \right) , $$


$$ A = \left( {\frac{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{N_{T} }}} \right) . $$

The marginal impact on the average aptitude PhDs due to a change in b is given by

$$ \frac{{\partial \overline{\beta } }}{\partial b} = - \frac{{\mathop \int \nolimits_{0}^{1} \beta^{2} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{N_{T} }} + \frac{{\overline{\beta } }}{{N_{T} }}\mathop \int \limits_{0}^{1} \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta . $$

Note that

$$ \frac{{\partial \overline{\beta } }}{\partial b} = \left( {\frac{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{N_{T} }}} \right)\left( {\overline{\beta } \frac{{\mathop \int \nolimits_{0}^{1} \beta h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }} - \frac{{\mathop \int \nolimits_{0}^{1} \beta^{2} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}} \right) , $$

and so

$$ \frac{{\partial \overline{\beta } }}{\partial b} = A\left( {\overline{\beta } \overline{\beta }_{M} - \frac{{\mathop \int \nolimits_{0}^{1} \beta^{2} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}} \right) , $$

Making use of

$$ \left( {\beta - \overline{\beta }_{M} } \right)^{2} = \beta^{2} + \overline{\beta }_{M}^{2} - 2\beta \overline{\beta }_{M} \Rightarrow \beta^{2} = \left( {\beta - \overline{\beta }_{M} } \right)^{2} - \overline{\beta }_{M}^{2} + 2\beta \overline{\beta }_{M} , $$

one replaces \( \beta^{2} \) in A.12 to find

$$ \frac{{\partial \overline{\beta } }}{\partial b} = A\left( {\overline{\beta } \overline{\beta }_{M} - \frac{{\mathop \int \nolimits_{0}^{1} \left[ {\left( {\beta - \overline{\beta }_{M} } \right)^{2} - \overline{\beta }_{M}^{2} + 2\beta \overline{\beta }_{M} } \right]h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}{{\mathop \int \nolimits_{0}^{1} h\left( \beta \right)g\left[ {L\left( \beta \right)} \right]{\text{d}}\beta }}} \right) . $$

Various terms in Eq. (A.14) cancel to give, after collecting terms, the marginal effect of a change in b written in terms of the average aptitude of all PhDs (\( \overline{\beta } \)), the average aptitude of the marginal (or indifferent) PhDs (\( \overline{\beta }_{M} \)), the proportion of all PhDs who are marginal (A), and the variance of aptitude of the marginal (or indifferent) PhDs (\( \sigma_{M}^{2} \)):

$$ \frac{{\partial \overline{\beta } }}{\partial b} = A\left( {\overline{\beta } \overline{\beta }_{M} - \sigma_{M}^{2} - \overline{\beta }_{M}^{2} } \right) = A\left( {\overline{\beta } - \overline{\beta }_{M} } \right)\overline{\beta }_{M} - A\sigma_{M}^{2} . $$

Finally note that

$$ \left. {\frac{{{\text{d}}b}}{{{\text{d}}k}}} \right|_{{\Delta N_{T} = 0}} = - \frac{{\partial N_{T} }}{\partial k}/\frac{{\partial N_{T} }}{\partial b} = - \frac{1}{{\overline{\beta }_{M} }} . $$

And so the impact on average aptitude of the rotation of the average opportunity cost as a function of aptitude, \( \beta \), is given by

$$ \left. {\frac{{{\text{d}}\overline{\beta } }}{{{\text{d}}k}}} \right|_{{\Delta N_{T} = 0}} = \frac{{\partial \overline{\beta } }}{\partial k} + \frac{{\partial \overline{\beta } }}{\partial b}\left. {\frac{{{\text{d}}b}}{{{\text{d}}k}}} \right|_{{\Delta N_{T} = 0}} = A\frac{{\sigma_{M}^{2} }}{{\overline{\beta }_{M} }} \ge 0 , $$

which is Eq. (8) in the text (Tables 6, 7, 8, 9).

Table 6 Estimated coefficients for productivity differentials among PhD recipients: papers presented at conferences
Table 7 Estimated coefficients for productivity differentials among PhD recipients: patents granted
Table 8 Estimated coefficients for productivity differentials among PhD recipients: journal articles. Full set of estimates
Table 9 Estimated coefficients for productivity differentials among PhD recipients: patent applications. Full set of estimates

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Perez-Silva, R., Partridge, M.D. & Foster, W.E. Are foreign-born researchers more innovative? Self-selection and the production of knowledge among PhD recipients in the USA. J Geogr Syst 21, 557–594 (2019).

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  • Innovation
  • Knowledge production
  • Self-selection
  • Occupation mismatch
  • PhD recipients

JEL Classification

  • D83
  • J24
  • J61