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THE IMPACT OF INTERNATIONAL SCIENCE AND ENGINEERING
GRADUATE STUDENTS ON US INNOVATION
Xiao Yu Wang [email protected]
April 9, 2004
ABSTRACT
The unique impact of international science and engineering graduate students on US innovation has never been systematically studied. Understanding the contributions of these students has become particularly important for proper review of post-9/11 legislation that severely limited student visa issuance, leading to the first decline in international student enrollment in more than a decade. Additionally, understanding such contributions is key to analyzing the rapid growth of India and China, who currently lead in terms of numbers of students sent. Using an idea generation model, I construct an econometric specification consisting of three groups of four equations, where utility patent applications and grants in universities and other institutions are dependent variables. Results indicate that foreign science and engineering graduate students play a significant, positive role in sharpening US innovation, but that this role is not straightforward, and contrasts in important ways with native student contributions.
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1. Introduction
The international presence on US university campuses, both within faculty and the student body,
experienced rapid growth during the 90s. America’s extra-strong economy and expanding educational programs
made her especially attractive to foreign students. The number of international graduate students in particular shot
up as the last of the old origins quotas were repealed and American doors were finally fully opened to Eastern
Europe and Asia. Foreign graduate enrollment in the sciences, engineering, and economics rose across the board as
the economy, and technology-based industries in particular, took off.
After graduation, many of these students chose to stay in the United States, finding employment in
engineering companies, research firms, the technology industry, or academia. Their success encouraged further
inflows of international skill, strengthening doctorate programs across the country in numbers and in research
output.
Today, foreign graduates continue to play major roles in the nation’s academic spheres. For example, 37%
of all MIT graduate students are international, with China, South Korea, and India as the leading countries of origin
(www.mit.edu). Unsurprisingly, in 2005, India, China, and South Korea were the overall leaders in sending students
to the United States. Engineering (23.8%), business (14.9%), and physical/life sciences (13.3%) were the top fields
of graduate study (Open Doors 2005).
Post-9/11 visa restrictions have corresponded with lower applications and enrollment from abroad, an
unsurprising relationship given that 87.4% of all international graduate students travel with F-1 visas, the type
affected by recent legislation (Open Doors 2005). Moreover, other countries are increasingly seen as academically
attractive; Australia in particular has been welcoming larger and larger populations of Asian university students
wishing to study abroad. The loss of international skill has led some to worry that such restrictions will have a
negative effect on US growth, especially since native US students have been less likely to concentrate in science and
engineering fields in the past, where research in such fields is thought to be a major contributing factor to
technological innovation and economic growth.
This paper seeks to analyze the current state of international student enrollment in US science and
engineering (S&E) graduate programs. More specifically, it seeks to evaluate the determinants of US innovation and
growth, to explore whether international students significantly affect these determinants or are determinants
themselves, and to analyze current student visa policy to answer the following questions: does visa policy affect
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international graduate student enrollment (as a whole and by field), and does policy that lowers the population of
international S&E graduate students within US universities affect (positively or negatively) US growth? If so, is
such policy optimal or are there superior alternatives?
I find that a key distinction needs to be made between utility patent applications and grants. That is,
international students in some fields actually had a small negative impact on total patent applications, while native
students largely positively impacted both patents and grants. However, international students had a stronger positive
impact on total patent grants, and especially on total university patent grants, while native students had an especially
strong positive impact on non-university patent grants. This indicates that while international students may
ambiguously affect patent applications, the applications they submit are often considered new and useful by the
patenting office, and are particularly significant for academic research. In general, I find that graduate students in
science and engineering, and university research as a whole are key to US innovation.
The framework of the paper will be as such: part (a) of the following section will discuss historical
international student flows in and out of the United States and the characteristics of these students, and part (b) will
discuss the US patenting process and the history of university research. Part three will review past literature. Part
four will detail and justify methodology, develop a model, and elaborate the specifications. Part five will describe
results. Part six will conclude.
2a. Background: International Students
The 2004-2005 academic year saw a total international graduate student enrollment of 264,410, down from
the previous year’s 274,310, the first decline since 1994 (Open Doors 2005). Many have postulated that this decline
is a result of the harsher and more inhibiting visa and student immigration policies passed in light of the Sept. 11
events. In general, total numbers of international graduate students have increased substantially in the past half-
century (see Appendix 1).
The composition of the international student body in terms of country of origin, however, has been far less
consistent. Today’s mix of Eastern European, Asian, and Latino students is very different from the Western
European-dominated populations of just half a decade ago. This evolution is largely the consequence of a variety of
legislation that has been passed since public sentiment shifted and the US government began to encourage a
representative international student presence.
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The post-9/11 measures are certainly not the only legislation to have affected international student flows.
Previous efforts have been made to limit or at least to monitor the inflows of international students. The past century
in particular was characterized by important legislation varying the restrictiveness and leniency of visa issuance,
employment policies, and applicant screening.
The first major 20th century relaxation of immigration laws was the Hart-Cellar Immigration Act of 1965,
which removed national origins quotas (www.historicaldocuments.com). The Simpson-Mazzoli Immigration
Reform and Control Act of 1982 then criminalized the hiring of an illegal immigrant, while the Immigration and
Nationality Act Amendments of 1986 repealed various documentation requirements and reduced the requisite pre-
naturalization period. In a similar vein, the Immigration Act of 1990 increased the number of legal immigrants
allowed into the US each year, especially from formerly Communist regions, such as Eastern Europe and Asia, two
major contributors of international S&E students. However, the Illegal Immigration Reform and Immigrant
Responsibility Act, passed in 1996, increased penalties for immigration-related offenses, expanded grounds for
deportation, and restricted benefits and sponsorship by relatives (thomas.loc.gov). Finally, the Patriot Act of 2001
required the tracking and fingerprinting of all students and other visa-holding non-immigrant visitors, and the
Enhanced Border Security and Reform Act of 2002 established a foreign student monitoring system and restricted
issuance of student visas (see Appendix 2 for restrictive and lenient periods between 1980 and 2005). (Open Doors
2005)
While lenient legislation may still be in place at the same time a new restrictive bill is passed, the selected
policies are such that their impacts overwhelm the lingering effects of old legislation. For example, while the
Immigration Act of 1990 further increased permitted immigration flows, the PATRIOT Act, passed 11 years later,
was restrictive enough, and the Immigration Act was old enough, such that the restrictive nature of the PATRIOT
Act was enough to transform the nature of its period into one more prohibitive for incoming international students.
Figures from the National Science Foundation (2003) indicate that many of these international graduates
choose to stay in the US—in 1973, 13,600 foreign doctorates were employed in academia alone; by 2003, that
number had risen to 60,400. According to Aslanbeigui and Montecinos (1998), 15% of international students from
developing countries intend permanent residence, with about half indicating a desire to stay at least temporarily.
Thus, it is not unreasonable to expect that US training of these international students will have long-term returns, as
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students contribute to industrial productivity and academic research, and add to the overall innovative capacity of
the nation.
b. The US Patenting Process and University Research
The website of the United States Patent and Trademark Office declares, “The patent laws of the United
States make no discrimination with respect to the citizenship of the inventor. Any inventor, regardless of his/her
citizenship, may apply for a patent on the same basis as a U.S. citizen.” (uspto.gov) In other words, the US patenting
process for citizens and non-citizens is virtually the same, so differences between foreign and native student
patenting behavior should not strictly result from differences in patenting procedure.
Unsurprisingly, there are numerous costs associated with applying for, receiving, and maintaining a patent,
as well as the perpetual possibility of legal battles. These costs include the hiring of a patent attorney or agent, filing
fees, copy fees, postal fees, post-allowance fees, fees associated with reissue, examination and re-examination fees,
publication fees, post-issuance fees, patent search fees, maintenance fees and a host of others (uspto.gov). All these
costs imply that those who complete the patenting process strongly believe in the utility of their inventions, and that
universities will tend to apply for relatively fewer patents compared to the private industrial sector, as a result of
smaller financial endowments (in general). However, the expected importance of these patents is a separate matter,
and can be gauged by examining percentage of successful applications.
Given that the length of stay of foreign graduate students is indeterminate, interrupted by visits home, and
dependent on ease of visa renewal, financial limitations, and numerous other considerations unique to studying
abroad, it is possible that international students may be given second preference by professors involved in patent-
producing research opportunities. On the other hand, such students are almost always legally constrained in the jobs
they are allowed to seek; specifically, these students are normally only permitted to work within the university,
meaning a large percentage of international graduate students end up working in university research institutions.
Furthermore, most international students arrive from math- and science-intensive countries, so they are likely to be
extremely productive in terms of pure research, despite weaker linguistic abilities.
Professors may wish to avoid working with students with limited language skills, but the growing
population of foreign academics may nullify such propensities. A scarcity of fellowships, low salaries, and a lack of
a network base could further limit total population of international graduate students, but the relative prevalence of
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foreign graduate students in the nation’s top universities (Columbia, the University of Wisconsin, the University of
Pennsylvania) indicates that, with the best research facilities and faculty at their disposal, they are especially
equipped to contribute to US innovation (Open Doors 2005). This prevalence is unsurprising—first, because top
S&E and top research universities tend to have bigger and better international student programs, since foreign
students are reputed to be exceptionally able and productive in scientific fields, and second, because such
institutions are relatively more famous abroad and receive more applications from international students.
All this intuition suggests that the effect of international S&E graduate students on patent applications will
be ambiguous, as on one hand, foreign students are disadvantaged practically in terms of language, network, and
visa problems, and on the other, S&E foreign graduates have very strong backgrounds in their fields, are
concentrated in top research universities, and are potentially more involved with academic research. Further
intuition suggests that the former characteristics are more important for quantity of patent applications (language,
network, continuous work time), while the latter characteristics may be more important in the long run, i.e. for
quantity of patent awards (strong math and science backgrounds, top research facilities, longer and more productive
work hours). In other words, we should expect to see more patent applications from native graduate students, and
potentially more patent grants for foreign graduate students. The magnitude of the impact of graduate students on
US innovation, however, depends largely on the significance of university research.
While the importance of university research to general innovation is not known, it is certainly true that
much more of it occurs today than pre-1980, when the Bayh-Dole Act was passed, allowing universities to
commercialize their previously unprofitable research findings. This study takes place entirely in the post-Bayh-Dole
period in an attempt to concentrate solely on the impact of international graduate students on patenting, regardless of
the effects of this Act. In other words, given the passage of Bayh-Dole, what are the effects of S&E graduate
students? This may lead to a slight bias in the estimated R&D effect, despite my framing of R&D university
expenditure in terms of federally-financed R&D expenditures in universities as opposed to spending by universities
themselves, but this bias is negligible and shouldn’t significantly affect the study.
Interestingly, in the last century, all kinds of R&D expenditures have skyrocketed (see Appendix 3)—
notably during the two World Wars, the Cold War, and the 90s with the birth of the technology and software
industries (nsf.gov). Lately, there has been talk of falling behind again in terms of scientific innovation, prompting
Senators John Ensign and Joseph Lieberman to introduce, as recently as December 2005, a bipartisan “National
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Innovation Act” that would nearly double federal research funding (www.technet.org). The introduction of this bill
hints at another wave of national concern about math and science programs, perhaps fueled by the recent growth of
China and India (nations that traditionally emphasize science and engineering), making analysis of the innovative
contribution of international students particularly salient. In other words, even if international students are found to
have a significant positive impact on US research output, should we encourage their presence? Or should we
“protect” native students from this kind of “foreign competition”? Does our policy approach depend on whether or
not these students choose to stay in the United States?
Previous authors have attempted to comment on one or more of these questions in various manners using
various methodologies. While these questions have been by no means resolved, it is important to look to past
literature to understand some of the disagreement and provide a basis for the systematic evaluation I use.
3. Literature review
There is not a very large body of existing literature dealing specifically with the innovative and economic
impacts of international graduate students, but there are several important studies that motivate and lay the
groundwork for this one.
Borjas (2004) argues that foreign students at a specific university crowd out enrollment of native white
males in the graduate programs at that university, even considering the expansion of those programs, and that this
crowding out is most apparent in private, top-tier institutions. (He defines this crowding out “…in the sense that
native enrollment would have risen faster if the university had not increased its supply of foreign students.”) (Borjas
2004) He further claims that while foreign students generate tuition revenue, such revenue is more than offset by the
cost of taxpayer support of public universities and of the limitations on educational opportunities for native white
males (and, marginally, native white females) the international inflow imposes (Borjas 2004).
This paper, then, implies that foreign students are preferred over their equally qualified native counterparts,
since Borjas claims that foreign students are not just fueling expansion of graduate programs, but are actually
replacing native students. However, a study done by Attiyeh and Attiyeh (1996) shows that in most cases, US
students are given preference. Additionally, the inferior performance of native students on international math and
science tests relative to foreign students indicates that the pool of native students wishing to pursue a master’s or
doctoral degree in any science or engineering field may be smaller than the foreign pool. This is particularly possible
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since Borjas (2004) uses figures for all graduate students at some institution, and does not distinguish these students
by field. Strangely, Borjas finds an absolute lack of substitution among native minorities, and a very small potential
replacement of native white women. Given that Borjas dismisses the possibility of better qualification, this implies
that all minorities, women, and international students are given significant unfair preference over native white
males, across the board and particularly in Ivy League institutions. At best, such a situation seems unlikely.
Chellaraj, Maskus, and Mattoo (2005), on the other hand, find that international graduate students and
skilled immigrants have a significant positive impact on US innovation, where innovation is measured in patents
applied for and patents granted (to universities and other institutions). Furthermore, they find that native students
actually have a significant negative effect on innovative output. Additionally, they find that rigorous enforcement of
visa restrictions has a significant negative effect on innovation, and they apply these results to the post-9/11
situation, concluding that Section 214(b) of the Patriot Act threatens US economic growth.
However, these economists were also unable to distinguish science and engineering graduate students from
students of other fields. It’s possible, therefore, that while the post-9/11 restrictions may have negatively impacted
the body of foreign graduate students as a whole, the subpopulation of international engineering graduates may have
remained unaffected. It could be that it is this (large) subpopulation that drives the positive effect that the entire
foreign pool was found to have on US patent applications and awards.
Moreover, the authors never define “international student” so it is unclear which students fall into this
category. For instance, this population could be defined simply as graduate students who are citizens of other
countries, or as students who are in the United States on temporary visas, such as the F-1 (which is how I have
defined it)., where the latter is a subset of the former group.
Further, Chellaraj, Maskus, and Mattoo (2005) examine total amounts of US patent applications and
awards. Utility patents, however, comprise the majority of total patent applications and awards by far, and chiefly
contribute to technological innovation (compare design and plant patents, where the nature of the former is cosmetic
and the nature of the latter is almost completely non-technological). Because technological innovation is widely
acknowledged to be most critical for economic growth (Basu, Fernald, and Shapiro 2001), I examine figures for
utility patent applications and awards alone.
Additionally, the study accounts for visa policy by measuring periods of strict enforcement of visa
regulations with a dummy variable reflecting high and low unemployment. This method is workable because
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Chellaraj et. al. analyze foreign students and skilled immigrants; however, my paper examines only international
graduate students, so this method is not as appropriate (high unemployment is more likely to be correlated with
stricter immigration laws rather than tighter student visa issuance). Therefore, I use a dummy variable based on
restrictiveness or leniency of legislation passed between 1980 and 2005 that affected international students (see
Section 2 for details). The model will not be able to account for post 1999 legislation (namely, the PATRIOT Act
and the Enhanced Border and Security Reform Act), due to the 5- and 7-year lags used to account for time periods
between patent research, application, and grant, but I will be able to comment on expected levels of patent
applications and grants given changes in the size of the foreign student body.
Finally, Chellaraj et. al. incorporate a measure of “non-university real R&D expenditures” into their
regression analysis of non-university patent grants. I modify this to be “industrial real R&D expenditures” for
several reasons: first, because industrial R&D expenditures have comprised about 65-70% of total real R&D
expenditures in the past decade, and second, because the majority of utility patents granted to non-university
institutions are granted to companies (nsf.gov, uspto.gov). This setup is more conducive to examining the
increasingly important link between universities and industries, since it isolates the effect of industries on patenting
and the effects of students on industries, so that we are able to gain some insight into the impact of students on non-
university patents and the impact of university and non-university research on general innovation.
For similar reasons, I measure the R&D expenditures specific to patents granted to universities as federally-
financed R&D at universities and not university R&D expenditure itself. This is largely because industries and
universities increasingly collaborate in research, and university funding of R&D would include federal and private
support, where some of that private support would certainly be double-counted in the “industrial real R&D
expenditures” variable, since industries currently fund a large portion of university research. Also, federally-
financed R&D at universities is more likely to be a consistent presence in and consistently distributed across
universities, unlike university R&D expenditures, which would be influenced by spontaneous alumni donations that
might be effective for a year or for one project in one field but would not necessarily enhance university research as
a whole. Finally, this characterization lends itself more readily to policy prescription as such funding is directly
within government control.
Clearly, there is a lot of disagreement within the limited realm of relevant previous literature. While the
importance of innovation (most notably technological advances) for economic growth is widely acknowledged, the
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overall impact international science and engineering students have on innovation, the contribution of university
research to general innovation, and even the true productivity of R&D expenditures are disputed. Consequently,
relevant policy recommendations are largely contradictory.
I concentrate solely on the impact international S&E graduate students have on US innovation and growth.
A brief examination of the correlations (see Appendix 4) indicates that a large presence of foreign graduate science
and engineering students is strongly correlated with high levels of patent applications and grants. The total numbers
of Ph.D. scientists and engineers in the country, R&D expenditure, and existing knowledge (cumulative total
patents—here, I consider all types of patents, not just cumulative utility patent numbers, to analyze the full “standing
on shoulders” effect) are also strongly positively correlated with high levels of research output. Thus it seems likely
that international graduate S&E students positively impact US innovation.
4. Methodology
Following Chellaraj et. al. I consider the “national ideas production function” used in a variety of
innovation studies (Porter and Stern, 2000):
Ạt=δΗA,t
λAtΦ (1)
where the dependent variable is rate of new ideas production, δ describes changes in US idea productivity over time,
ΗA,t denotes the allocation of resources to the R&D sector, λ is the productivity of those resources, At is the stock of
ideas already in existence, and Φ describes the ability of that stock to support new invention.
The general measure of new ideas production in this study is total utility patent applications and total utility
patent grants, where total utility grants are further broken down to distinguish between those granted to universities
and those granted to other institutions. While patents are not a perfect measure of national innovation, due to the
tremendous variation in the contributions they make (or do not make) to technological advancement, there are
several compelling reasons to use them. First, I consider utility patents only, the most technological of patent types,
second, the patenting process is not easygoing or cheap, so the inventor must truly feel that she has something new
and useful to contribute, third, the patent reviewers grant only the most innovative portion of the applications, and
fourth, extensive patent search databases and rigorous reviewing procedures eliminate most repetition and serve as a
strong foundation for further, new patenting.
Like Chellaraj et. al. I redefine ΗA,tλ , but in more detail, such that:
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ΗA,tλ = [(Hλr) RD, t][(Hλe)ENG, t][(Hλpl)PL, t][(Hλk)SK, t] (2)
where HRD represents total R&D expenditure and λr represents its productivity, [(Hλe)ENG, t]=[(Hλef)F, t][(Hλen)N,t]
and represents flows of foreign and native engineering graduate students, with λef, λen representing respective
productivities, [(Hλpl)PL, t]=[(Hλpf)F, t][(Hλpn)N,t] represents flows of foreign and native physical and life science
graduate students and their productivities, and HSK represents total Ph.D. scientists and engineers, with λk
representing that population’s productivity. (Physical and life sciences are defined to include all mathematical
sciences, health sciences, biological sciences, physical sciences, earth/atmospheric and oceanic sciences, and
agricultural sciences.)
To account for the AtΦ term, that is, to measure the “standing on shoulders” effect of existing knowledge
stock, I take cumulative numbers of total patent stock, total university patent stock, and total non-university patent
stock, where the 2000 level is the sum of the 1996-2000 inclusive annual levels. The δ parameter in equation (1)
measures changes in US idea productivity over time and is taken to be both a function of time and, more
importantly, of policy changes, such as legislation affecting international student inflow.
Several other factors must be considered before constructing an econometric specification. First, following
Chellaraj et. al. I have taken into consideration time lags between commencing research and patent application, and
between patent application and grant. After reevaluating lags of previous studies, I have determined that 5 years is
still the most appropriate average lag for the time between science and engineering research and patent application,
and 2 years is still most appropriate for the time between patent application and grant (Johnson, et. al. 2003). In
other words, resources employed in 1980, such as numbers of foreign graduate students and R&D expenditures,
affect the 1985 number of patent applications, and the 1987 number of patent grants. It is important to note that lag
time, especially between application and grant, has not remained constant over the years, and has in fact increased
post-1995 due to increases in patent application and to decisions reached in the GATT Uruguay Round (Johnson et.
al. 2003), so these figures should be treated as rough estimates. Additionally, lag time varies severely across
industry—pharmaceutical breakthroughs generally require much longer periods of research (NIST Status Report
2003)—and depends on length and number of legal battles as well, since patent legitimacy is solely upheld by the
courts.
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Preserving stationarity of the variables is key, given the time series analysis. Therefore, I have scaled all
variables with respect to annual US labor force. However, this alone may not be sufficient—it might be necessary to
examine the percent differences annually for each variable to truly preserve stationarity, since the percentage of US
labor force that is international science graduate students may have experienced a significant upward trend.
Nevertheless, the growth in US labor force should be sufficient to ensure minimal trend effects, so the following
econometric specification remains legitimate; the results may be negligibly affected but will provide an accurate
general idea. Finally, estimation technique is ordinary least squares (OLS).
A.
lnTPA(t+5)= K1A + (λ11
A)lnFORENG + (λ12A)lnNENG + (Φ1
A)lnTOTPSTOCK + (λ13A)lnSK + (λ14
A)lnRD + (δ1A)ED + η1t
A
lnTPG(t+7) = K2A + (λ21
A)lnFORENG + (λ22A)lnNENG + (Φ2
A)lnTOTPSTOCK + (λ23A)lnSK + (λ24
A)lnRD + (δ2A)ED + η2t
A
lnUIPG(t+7) = K3A + (λ31
A)lnFORENG + (λ32A)lnNENG + (Φ3
A)lnUPSTOCK + (λ33A)lnSK + (λ34
A)lnFRD + (δ3A)ED + η3t
A
lnOIPG(t+7) = K4A + (λ41
A)lnFORENG + (λ42A)lnNENG+ (Φ4
A)lnOPSTOCK + (λ43A)lnSK + (λ44
A)lnIRD + (δ4A)ED + η4t
A
B.
lnTPA(t+5)= K1B + (λ11
B)lnFORPL + (λ12B)lnNPL + (Φ1
B)lnTOTPSTOCK + (λ13B)lnSK + (λ14
B)lnRD + (δ1B)ED + η1t
B
lnTPG(t+7) = K2B + (λ21
B)lnFORPL + (λ22B)lnNPL + (Φ2
B)lnTOTPSTOCK + (λ23B)lnSK + (λ24
B)lnRD + (δ2B)ED + η2t
B
lnUIPG(t+7) = K3B + (λ31
B)lnFORPL + (λ32B)lnNPL + (Φ3
B)lnUPSTOCK + (λ33B)lnSK + (λ34
B)lnFRD + (δ3B)ED + η3t
B
lnOIPG(t+7) = K4B + (λ41
B)lnFORPL + (λ42B)lnNPL+ (Φ4
B)lnOPSTOCK + (λ43B)lnSK + (λ44
B)lnIRD + (δ4B)ED + η4t
B
C.
lnTPA(t+5) = K1C + ( λ11
C)lnFORSE + (λ12C)lnNSE + (Φ1
C)lnTOTPSTOCK + η1tC
lnTPG(t+7) = K2C + (λ21
C)lnFORSE + (λ22C)lnNSE + (Φ2
C)lnTOTPSTOCK + η2tC
lnUIPG(t+7) = K3C + (λ31
C)lnFORSE + (λ32C)lnNSE + (Φ3
C)lnUPSTOCK + (Φ3C’)lnOPSTOCK + η3t
C
lnOIPG(t+7) = K4C + (λ41
C)lnFORSE + (λ42C)lnNSE + (Φ4
C)lnUPSTOCK + (Φ4C’)lnOPSTOCK + η4t
C
Individual fields were regressed separately against each dependent variable. A logarithmic approach seemed most
appropriate in determining the effect of growth in research inputs on innovative growth. TPA(t+5) represents total
utility patent applications with a 5-year lag, TPG(t+7) represents total utility patent grants with a 7-year lag, UIPG(t+7)
represents total utility patents granted to universities with a 7-year lag, and OIPG(t+7) represents total utility patents
granted to other institutions with a 7-year lag. K is the constant term. The prefixes “FOR” and “N” denote “foreign”
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and “native,” respectively, SK refers to total Ph.D. scientists and engineers, TOTPSTOCK, UPSTOCK, OPSTOCK
refer to cumulative utility patent stock, cumulative university patent stock, and cumulative other institutional patent
stock, RD, FRD, IRD refer to total real R&D expenditure, total real federally-financed R&D expenditure at
universities, and total real industrial R&D expenditure, and ED is the enforcement dummy variable distinguishing
between restrictive and lenient periods of visa enforcement and issuance.
Foreign graduate students are defined as students in US university graduate programs holding temporary
visas, such as F-1 student visas. The enforcement dummy ED measures periods of restrictive visa issuance and
enforcement based on legislation passed since 1980. Thus, a negative coefficient on this variable would indicate that
today’s restrictive legislation, specifically Section 214(b) of the PATRIOT Act and the Enhanced Border Security
and Visa Entry Reform Act of 2002, has a significant negative impact on total utility patent applications and grants.
Because the restrictive legislation has a negative impact on the foreign student presence due to imposed limitations
on visa issuance, the implication is that foreign students have a significant positive impact on US innovation and
economic growth, implying that a lesser foreign student population is detrimental to US expansion.
The econometric specifications are divided by field to isolate the effect each subpopulation has on the
dependent variables. The subpopulations could not be combined into one regression due to insufficient number of
observations. The final grouping, (C), determines the general effect of foreign science graduate students, native S&E
graduate students, and cumulative patent stock on each of the dependent variables (new ideas production in terms of
patents).
This model was implemented using annual data between 1980 and 2003. The dataset was compiled using a
variety of sources. The Institute for International Education’s annual publication, Open Doors, and the National
Science Foundation’s Science and Engineering Indicators, and Historical Statistics provided R&D figures and data
on graduate student enrollment by citizenship and field. US Labor Force figures were taken from the Bureau of
Labor Statistics website. Data on Ph.D.-holding scientists and engineers were taken from Chellaraj et. al. (2005),
and all patent data were taken from the United States Trademark and Patenting Office website’s Patent Statistics.
5. Results and Discussion
Regression results are presented in Appendices 5-7. Each Appendix corresponds with specifications (A)-
(C) introduced in the previous section, where (A) and (B) focus on field and (C) focuses on citizenship.
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Examining the effects of citizenship on innovation, it may be seen that foreign students ambiguously
impact total utility patent applications but positively impact total patent grants, and have the most positive impact on
university patent grants. Native students, on the other hand, positively affect total patent applications and grants in
most cases, but the effect is smaller. Further, native students most positively affect other institution patent grants.
Examining foreign and native S&E graduate students in (C) shows that as a whole, foreign science students’
elasticities were 0.24, 0.65, 1.25, and 0.15 for total applications, grants, university grants, and other institution grants
(Appendix 7, row (ii)), whereas native science students’ elasticities were -1.51, 1.21, 0.85, and 1.53 for applications,
grants, university grants, and other institution grants, respectively (Appendix 7, row (iii)). All results were
significant at the 10% level or better. Note that Chellaraj et. al. (2005) similarly found foreign elasticities to be about
0.3 for total applications and grants, and 0.6 and 0.4 for university and other institution grants. However, that study
contradictorily found native students’ elasticities to be around -0.39, -0.42, -0.49, and -0.53 for total applications,
total grants, university grants, and other institution grants (Chellaraj et. al. 2005). (Recall that Chellaraj et. al. used
populations of all foreign and native graduate students without being able to differentiate by field, and considered
levels of total patents instead of the subpopulation of utility patents.)
To put these numbers into perspective, observe that a 10% increase in foreign S&E (social science
inclusive) graduate students, from its sample mean level of 83,615, would lead to 2,000 more utility patent
applications (0.9% of the sample mean level of utility patent applications) and 5,452 more utility patent grants (5%
of the sample mean level of utility patent grants). This effect is quite substantial.
In general, I find that foreign and native students have significant positive impacts on innovation, but that
they affect research output in different ways. While results indicate varying effects on total utility patent
applications, it is more important and more interesting to note the positive effect on patent grants, and, specifically,
the innovative differences between foreign and native S&E students in universities versus in other institutions. In
accordance with our intuition, the relatively stronger presence of foreign students in the nation’s (top) universities
(as a result of professional constraints and foreign student reputation in S&E fields), and the relatively stronger
background international students have in math and science, strengthen their effectiveness in academic innovation.
In contrast, native students, who are able to find employment outside of the university, have a very strong positive
effect on innovation in other institutions, which are, more often than not, industries. This relationship holds by field
as well—foreign engineering and physical life sciences students had elasticities of 1.244 and 1.822 on university
14
patent grants (significantly different from 0 at the 1% level) (Appendix 5 and 6, row (ii), column 3), and native
engineering and physical life sciences students had elasticities of 0.87and 1.503 on other institution patent grants
(significantly different from 0 at the 1% and 5% levels) (Appendix 5 and 6, row (iii), column 4). But how important
are university and other institution innovations for general innovation?
Results are encouraging—examining Appendix 7, row (vi), we see that a 1% increase in cumulative patent
stock leads to a 0.813% increase in total utility patent grants, where cumulative patent stock is largely composed of
cumulative university and other institution patent stock. Further, when populations of engineering students are
accounted for, cumulative patent stock grows in importance, where a 1% increase in total patent stock now leads to a
1.189% increase in total patent grants. With physical and life sciences students, this elasticity becomes 0.583. In
particular, the spillover effect of university innovation on other institution innovation is 0.47 (Appendix 7, row (iv),
column (5)), while the spillover effect of other institution innovation on university innovation is a startling -1.1
(Appendix 7, row (v), column (4)).
In other words, cumulative university patent stock was important for university and other institution patent
grants, while cumulative other institution patent stock actually had a negative impact on both. This emphasizes the
importance of university research in particular for national innovation as a whole, magnifying the strong positive
impact international S&E graduate students have overall. In general, previous knowledge is exceptionally important
in motivating future research—this dramatic “standing on shoulders” effect is not unexpected, as the accessibility of
all previous patents makes it easy for an aspiring inventor to see “what’s been done,” to be inspired by gaps in
previous inventions, and to decide what could be done, knowing what has been tried, what has failed, and what has
succeeded.
This conclusion is supported by the Chellaraj et. al. (2005) paper, which also found cumulative patent stock
to be a key determinant of innovation, with an average elasticity of 0.14 at 5% significance. The paper also found
university patent stock to be important for non-university innovation, where the university patent stock spillover
elasticity fell between 0.19 and 0.26 (Chellaraj et. al. 2005).
Research and development expenditures also had consistent, significant, and positive effects on patent
applications. A 1% increase in total R&D expenditure increases total patent applications by 1.82% and total patent
grants by 0.18% in Appendix 5 (row (vii)). The physical and life sciences regression yields total R&D elasticities of
1.399 and -0.192 for applications and grants, respectively. This tells us that, while R&D significantly increases the
15
number of research opportunities in the nation, so that we see many more patent applications as a result,
expenditures do not necessarily improve the quality of the research—few of these additional applications are
actually granted. Given that this is usually the tool government innovation policy uses (recall the proposed National
Innovation Act, the main feature of which would be to double federal R&D expenditure), we may want to reconsider
our policies in light of these results.
The elasticities of the population of Ph.D. scientists and engineers were generally positive, although
statistically insignificant. Surprisingly, they seemed to have the smallest effect on other institution patent grants,
while having a strong positive effect on total utility patent applications and university patent grants. Appendices 5
and 6, row (iv) show us that a 1% increase in Ph.D. scientists and engineers, holding all else constant, leads to an
average of a 0.5% increase in total utility patent applications, a negligible effect on total patent grants, a 0.27%
increase in university patent grants, and a slightly negative effect on other institution patent grants. However, given
the increasing collaboration between industries and universities, and given that this is the population of scientists
and engineers with Ph.D.s, it does not seem so implausible that they would have stronger impacts on university
patents rather than other institutions.
Restrictive enforcement seems to have very slight positive effects on the dependent variables, but the
coefficients were never statistically significant, and the observed effects were very small, so it is impossible to make
any conclusive statements based on the regressions. However, Chellaraj et. al. (2005), using an indicator variable for
employment, did find restrictive visa issuance policies to have a significant negative effect (around -0.22 elasticity)
on US innovation.
Knowing that international students face legal employment constraints, interrupted research time, risk of
visa loss, financial, linguistic, and cultural barriers, and the disadvantage of smaller networks, but benefit from
stronger elementary backgrounds in math and science, from being among the strongest students in their home
countries, and from being relatively concentrated in the top research universities, implies ambiguous effects on
patent applications but probable positive effects on patent grants (because the latter characteristics are more
important for research quality). Results confirm this intuition. Similarly, results confirm the intuition that native
students should have a stronger positive impact on other institution patent grants, because they tend to be employed
in these other institutions, since they are not legally obligated to stay within university research. In sum,
contradicting Borjas (2004), foreign S&E graduate students were found to have significant positive effects on US
16
innovation, especially within academia; contradicting Chellaraj et. al. (2005), native S&E graduate students were
also found to have significant positive effects on US innovation, especially within industry.
Existing knowledge, in turn, is shown to be a significant contributor to general innovation, with university
patent stock proving to be a particularly significant factor. Research and development expenditures were seen to
definitively boost patent applications, but not patent grants, implying that other provisions need to be attached to
such funding for the dollars spent to truly augment national innovative capacity.
6. Conclusion
While the results show that, in answer to questions posed in the beginning of this paper, international
students significantly and positively affect US innovation, and strict visa enforcement and issuance have
indeterminate effects on university patenting (which is in turn important for general new idea production), the policy
questions remain difficult to answer. For instance, optimal policy would depend on national goals. If we were only
concerned with generating as much innovative output as possible, then current policies (Section 214(b), the
Enhanced Border Reform and Security Act) are detrimental to our goals because, by discouraging international
student inflows, they lower our potential for technological advancement and growth. However, if we are more
concerned with sheer numbers of native students in science and engineering fields, then the policies are not
necessarily bad.
The official goal of the recent policies is to maintain homeland security. However, to determine whether
the PATRIOT Act and other legislation are optimal for the country, we need to decide whether the value of potential
increased security is greater than or at least balanced by the loss in potential innovation, especially at our
universities. The policy leads to an overall decrease in numbers of international students, but also shifts the
composition of this international student body in terms of countries of origin. As per the study, international
engineering students negatively affected patent applications and less positively impacted patent grants, in
comparison with physical and life sciences students. Moreover, most S&E students are Asian or Middle Eastern. If
this is in fact true, should we shape future policy to target only those students who seem more likely to make
innovative contributions? Or is this, again, not our goal when we welcome international students into our schools?
Whatever our objectives may be, it is important that we rectify the inconsistencies in our international
student policies. US officials issue visas based on the probability that the student returns home—in other words, a
17
student who indicates a desire to stay in the United States is much more likely to be rejected than a student who
swears to go home. Similarly, foreign countries are much more reluctant to issue visas to students who express
intentions of staying in the United States. Such policies mean that the students who do end up studying in the United
States are those most likely to return home. Yet conventional wisdom dictates that we should only educate those
students who stay in the country and make long term contributions to the US economy. Consequently, international
students who want to stay are punished and international students who wish to return home are disliked. Optimal
international student inflows cannot be achieved until these contradictions are resolved.
It is important to recognize the limitations of this study. Statistical significance of the estimates of the
coefficients was a consistent problem. Stationarity of data, too, is something that needs to be re-examined, where
perhaps differences from year to year are taken for each variable, instead of mere scaling with respect to labor force.
Additional observations would have improved the study, although no reliable data on international and native
graduate students by field exists pre-1980. Patent lags were exceptionally difficult to measure, given their variability
and inconstancy over time. This has implications for the results—for example, it could be that foreign students, for
whatever reason, work slower than native students (perhaps due to discontinuous residence in the US). Then the
negative effects we see on patent applications are perhaps not a “bad” thing—the negative elasticities would simply
indicate slower rate of research completion, which might partially explain international students’ higher percentages
of patent grants. However, this is just conjecture.
This study did not take into account software copyright as a further measure of new ideas production,
because no such data is available (also, software is a much more recent development). Furthermore, no good
measure of fellowships/grants/publications was able to be found. The study also does not consider foreign
academics or visiting scholars.
The enforcement variable requires much further experimentation—the measurement I employ is slightly
arbitrary in some sense, because it is difficult to determine when any piece of legislation truly takes effect—does the
period of restrictive enforcement begin when the bill is introduced, when it is passed, or a couple years after that,
when it has had time to really gain potency? If the last is true, how do we determine that particular lag? Other
methods of accounting for such enforcement are possible; determining the optimal measurement will be difficult.
The increasing number of international students in economics bears observation and is certainly interesting
when applied to students who return to their home countries. It could be asked how these international students, in
18
perhaps applying their knowledge of the US economy, affect the economic policy of their countries. Alternatively,
one could examine the effects these students have on the US economy if they stay and combine their knowledge of
their home country with what they learn in this country. The idea is that international students can definitively shape
the economies of the US and their home countries without patenting and making technological contributions.
However, this was not addressed due to lack of data.
Finally, quality of patents was not captured by this study. For example, foreign students may significantly
affect total utility patents granted, but it is difficult to say anything about the usefulness of these awarded patents. A
possible method would be to count the citations these patents have received. Either way, it is entirely possible that,
while native and international students positively impact patent levels, these new patents are not very useful in terms
of economic growth or motivating other research.
Further research should improve the data in general by including more observations, by ensuring
stationarity of variables, by using time series analysis to make predictions about current policies that were unable to
be included in the study due to the lagged periods, and by accounting somehow for patent quality. It should also
improve the enforcement variable, and could improve measurement of new ideas production, if possible. However,
this area is underdeveloped and could benefit from more study in general. Detailed policy recommendations cannot
be made, despite solid indication that international graduate students do positively impact US innovation and
economic growth, until more is understood about the relationship between enrollment of foreign and native graduate
students, between student enrollment and patenting activity, and between patenting activity and innovation. We
may know that increased inflows of international students are beneficial for US innovation, but we still do not know
the best way to orchestrate such increased inflows. Nevertheless, it is clear that policies restricting international
intellect are detrimental to efforts to expand our knowledge stock, and will not lead to economic growth.
19
References
1. Aslanbeigui, N. and V. Montecinos. 1998. “Foreign Students in U.S. Doctoral Programs.” Journal of Economic Perspectives 12: 171-182. 2. Attiyeh, G. and R. Attiyeh, 1996. “Testing for Bias in Graduate School Admissions.” The Journal of Human Resources 32: 524-548. 3. Basu, S., J.G. Fernald, and M.D. Shapiro. 2001. “Productivity Growth in the 1990s: Technology, Utilization, or Adjustment?” Working Paper, No. w8359, NBER. 4. Borjas, G.J. 2004. “Do Foreign Students Crowd out Native Students from Graduate Programs?” Working Paper No. 10349, NBER. 5. Chellaraj, G., K. Maskus, and A. Mattoo. 2005. “The Contribution of Skilled Immigration and International Graduate Students to US Innovation.” Working Paper No. 3588, World Bank. 6. Henderson, R. and A. Jaffe. 1998. “Universities as a Source of Commercial Technology: Detailed Analysis of University Patenting, 1965-1988.” Review of Economics and Statistics 80: 119-127.
7. Hock, Jim. 2005. “TechNet Hails Introduction of National Innovation Act of 2005.” http://www.technet.org/press/Press_Releases/?newsReleaseId=3996
8. “The Immigration and Naturalization Act of 1965.” Historical Documents. http://www.historicaldocuments.com/ImmigrationActof1965.htm
9. Institute for International Education, 1948-2004. Open Doors. 10. Johnson, D.K.N., T. Juhl, and B. Popp. 2003. “Time in Purgatory: Determinants of the Grant Lag for US Patent Applications.” Working Paper No. W9518, NBER. 11. Laursen, K. and A. Salter. 2004. “Searching High and Low: What Types of Firms use Universities as a Source of Innovation?” Research Policy 33: 1201-1215. 12. The Library of Congress: THOMAS. Bills, Resolutions. http://thomas.loc.gov/home/bills_res.html 13. MIT. MIT Facts 2006: “International Students and Scholars.” http://web.mit.edu/facts/international.shtml 14. National Science Foundation. 1993-2005. Science and Engineering Statistics. 15. Porter, M.E. and S. Stern. 2000. “Measuring the 'Ideas' Production Function: Evidence from International Patent Output.” Working Paper No. 7891, NBER. 16. US Census Bureau. 1958-2003. Statistical Abstract of the United States. 17. US Patent and Trademark Office. 1963-2004. Patent Statistics.
20
Appendix 1: Science and Engineering (S&E) Graduate Student Enrollment in US Universities,
1980-2003
Science and Engineering (S&E) Graduate Students in US Unviersities, 1980-2003
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
450,000
500,000
1980 1983 1986 1989 1992 1995 1998 2001
Year
Num
ber
of S
tude
nts
Total S&E Graduate Students
Native S&E Graduate Students
S&E Graduate Students with TemporaryVisas
Data from National Science Foundation, Science and Engineering Statistics, 2003
21
Appendix 2: Major Legislation Affecting International Student Inflows, 1965-2005
Time Period Legislation Effect
1. 1965-1982 Hart-Cellar Immigration Act of 1965 Lenient
2. 1982-1986 Simpson-Mazzoli Immigration Reform and Control Act of 1982 Restrictive
3. 1986-1995 Immigration and Nationality Act Amendments of 1986,
Immigration Act of 1990
Lenient
4. 1996-2000 Illegal Immigration Reform and Immigrant Responsibility Act Restrictive
5. 2001 PATRIOT Act of 2001 Restrictive
6. 2002 Enhanced Border Security and Reform Act of 2002 Restrictive
22
Appendix 3: Real-Valued R&D Expenditure in the United States, 1953-2004
Data from National Science Foundation, Science and Engineering Statistics, 2005
Real-valued R&D Expenditure in the United States, 1953-2004
0
50000
100000
150000
200000
250000
300000
350000
1/1/00
Year
R&
D e
xpen
ditu
re, i
n m
illio
ns o
f rea
l dol
lars
Federally-financed R&DExpenditures at universit iesIndustrial R&D Expenditures
Total R&D Expenditures
1953
23
Appendix 4: Basic Correlations
Notes: TPA is total utility patent applications, FORENG is population of international engineering graduate students, NENG is population of native engineering graduate students, FORPL is population of international physical and life science students, NPL is population of native physical and life science students, and SK is population of Ph.D. holding scientists and engineers employed in the United States. RD is total R&D expenditure in the US, FRD is total federally-funded R&D expenditure at US universities, and IRD is total industrial R&D expenditure. All these numbers are annual. UPSTOCK is cumulative university patent stock (where the 2000 figure is the sum of 1996-2000 levels of utility patents awarded to universities), OPSTOCK is cumulative other institution patent stock, and TOTPSTOCK is total cumulative patent stock.
Tpa Foreng Neng Forpl Npl Sk Rd Frd Ird Ed Upstock Opstock Totpstock
Tpa 1
Foreng .40 1
Neng .17 .77 1
Forpl .57 0.96 0.78 1
Npl .65 -.25 .24 -.13 1
Sk .90 .57 .60 .67 .45 1
Rd .82 0.82 .70 .92 -.01 .65 1
Frd .96 .67 .71 .80 .43 .90 .82 1
Ird .95 .73 .70 .85 .31 85 .92 .96 1
Ed -.05 -.40 -.14 -.45 -.10 -.52 -.33 -.59 -.44 1
Upstock .98 .42 .63 .65 .62 .90 .71 .97 .91 -.65 1
Opstock .92 .57 .51 .54 .65 .90 .54 .91 .80 -.55 .96 1
Totpstock .91 .43 .52 .65 .65 .90 .54 .91 .80 -.39 .96 1 1
24
Appendix 5: Foreign and Native Engineering Graduate Students, Total Utility Patent Applications, Total Utility Patent Grants, University Patent Grants, and Non-University Patent Grants, 1980-1996 (1) (2) (3) (4) lnTPA lnTPG lnUIPG lnOIPG
(i) CONSTANT -15.810
(4.229)*
4.760
(3.924)
7.885
(6.704)
2.739
(4.402)
(ii) lnFORENG -.922
(.298)*
-.025
(.318)
1.244
(.358)*
-.109
(.298)
(iii) lnNENG .573
(.176)*
.862
(.280)**
.315
(.342)
.870
(.261)*
(iv) lnSK .583
(.392)
-.088
(.431)
.181
(.426)
-.180
(.418)
(v) lnFRD .091
(.426)
(vi) lnIRD .239
(.240)
(vii) lnRD 1.820
(.270)*
.180
(.431)
(viii) lnUPSTOCK .511
(.254)***
(ix) lnOPSTOCK 1.087
(.259)*
(x) lnTOTPSTOCK .739
(.186)*
1.189
(.198)*
(xi) ED -.006
(.024)
.067
(.037)***
.082
(.047)
.054
(.045)
R-squared 0.980 0.961 0.982 0.961
Notes: All variables (except ED, enforcement) are proportions of labor force. lnTPA is natural log of total utility patent applications, lnTPG is natural log of total utility patents granted, lnUIPG is natural log of utility patents granted to universities, and lnOIPG is natural log of those granted to other institutions. lnFORENG is natural log of foreign engineering graduate students, lnNSOC is natural log of native engineering graduate students, lnSK is natural log of total PhD scientists and engineers, lnRD is natural log of total real US R&D expenditure, lnFRD is natural log of real federally-financed R&D expenditure, and lnIRD is natural log of real industrial R&D expenditure. lnTOTPSTOCK is natural log of cumulative utility patents awarded, lnUPSTOCK is natural log of cumulative university utility patents awarded, and lnOPSTOCK is natural log of cumulative utility patents awarded to other institutions. ED is a dummy variable for restrictive and lenient student visa issuance and enforcement. Variables in the lnTPA equations are lagged five years; variables in the lnTPG, lnUIPG, and lnOIPG equations are lagged seven years. Figures in parentheses are the standard errors and are marked as significantly different from zero at the one-percent (*), five-percent (**), and ten-percent (***) levels. Estimation technique is ordinary least squares (OLS).
25
Appendix 6: Foreign and Native Physical and Life Sciences Graduate Students, Total Utility Patent Applications, Total Utility Patent Grants, University Patent Grants, and Non-University Patent Grants, 1980-1996 (1) (2) (3) (4)
Notes: All variables (except ED, enforcement) are proportions of labor force. lnTPA is natural log of total utility patent applications, lnTPG is natural log of total utility patents granted, lnUIPG is natural log of utility patents granted to universities, and lnOIPG is natural log of those granted to other institutions. lnFORPL is natural log of foreign physical and life sciences graduate students, lnNSOC is natural log of native physical and life sciences graduate students, lnSK is natural log of total PhD scientists and engineers, lnRD is natural log of total real US R&D expenditure, lnFRD is natural log of real federally-financed R&D expenditure, and lnIRD is natural log of real industrial R&D expenditure. lnTOTPSTOCK is natural log of cumulative utility patents awarded, lnUPSTOCK is natural log of cumulative university utility patents awarded, and lnOPSTOCK is natural log of cumulative utility patents awarded to other institutions. ED is a dummy variable for restrictive and lenient student visa issuance and enforcement. Variables in the lnTPA equations are lagged five years; variables in the lnTPG, lnUIPG, and lnOIPG equations are lagged seven years. Figures in parentheses are the standard errors and are marked as significantly different from zero at the one-percent (*), five-percent (**), and ten-percent (***) levels. Estimation technique is ordinary least squares (OLS).
lnTPA lnTPG lnUIPG lnOIPG
(i) CONSTANT -3.221
(5.681)
16.239
(4.945)*
22.194
(11.326)***
12.461
(6.186)***
(ii) lnFORPL -.051
)243(.
.745
(.255)**
1.822
(.524)*
557.
(.277)***
(iii) lnNPL 1.183
(.588)***
1.535
(.611)**
.407
(1.019)
1.503
(.597)**
(iv) lnSK .426
(.469)
.176
(.503)
.362
(.478)
.208
(.429)
(v) lnFRD -.898
(.808)
(vi) lnIRD .070
(.384)
(vii) lnRD 1.399
(.351)*
-.192
(.423)
(viii) lnUPSTOCK .884
(.527)
(ix) lnOPSTOCK .531
(.442)
(x) lnTOTPSTOCK .473
(.303)
.583
(.360)
(xi) ED .003
(.037)
.047
(.053)
.052
(.056)
.0318
(.0645)
R-squared 0.96 0.946 0.9767 0.945
26
Appendix 7: Foreign and Native Science and Engineering Students, Total Utility Patent Applications, Total Utility Patent Grants, University Patent Grants, and Non-University Patent Grants, 1980-1996 (1) (3) (4) (5) lnTPA lnTPG lnUIPG lnOIPG
(i) CONSTANT -5.497
(3.372)
10.833
(4.356)**
5.913
(3.980)
6.025
(2.693)**
(ii) lnFORSE .236
(.273)
.652
(.232)**
1.253
(.221)*
.154
(.187)**
(iii) lnNSE -1.509
(.422)*
1.290
(.706)***
.852
(.488)***
1.527
(.370)*
(iv) lnUPSTOCK .803
(.145)*
.469
(.115)*
(v) lnOPSTOCK -1.085
(.454)**
-.510
(.355)
(vi)lnTOTPSTOCK 1.598
(.188)*
.813
(.294)**
R-squared 0.866 0.892 0.973 0.948
Notes: All variables are proportions of labor force. lnTPA is natural log of total utility patent applications, lnTPG is natural log of total utility patents granted, lnUIPG is natural log of utility patents granted to universities, and lnOIPG is natural log of those granted to other institutions. lnFORSE is natural log of foreign science and engineering graduate students, lnNSE is natural log of native science and engineering graduate students. lnTOTPSTOCK is natural log of cumulative utility patents awarded, lnUPSTOCK is natural log of cumulative university utility patents awarded, and lnOPSTOCK is natural log of cumulative utility patents awarded to other institutions. Variables in the lnTPA equations are lagged five years; variables in the lnTPG, lnUIPG, and lnOIPG equations are lagged seven years. Figures in parentheses are the standard errors and are marked as significantly different from zero at the one-percent (*), five-percent (**), and ten-percent (***) levels. Estimation technique is ordinary least squares (OLS).
