Macro Roundup

The @economist notes that “almost all” recent AI breakthroughs have come from large firms, in large part due to their access to the computing power required to develop state-of-the-art AI models, “…Almost all recent breakthroughs in artificial intelligence globally have come from large companies, in large part because they have the computing power. Amazon, whose AI powers its Alexa voice assistant, and Meta, which made waves recently when one of its models beat human players at “Diplomacy,” a strategy board game, respectively produce two-thirds and four-fifths as much AI research as Stanford University, a bastion of computer-science eggheads. Alphabet and Microsoft churn out considerably more, and that is not including DeepMind, Google Research’s sister lab which the parent company acquired in 2014, and the Microsoft-affiliated OpenAI….”

Economist Staff, “The race of the AI labs heats up,” The Economist, January 30, 2023, https://www.economist.com/business/2023/01/30/the-race-of-the-ai-labs-heats-up

Every so often a new technology captures the world’s imagination. The latest example, judging by the chatter in Silicon Valley, as well as on Wall Street and in corporate corner offices, newsrooms and classrooms around the world, is Chatgpt. In just five days after its unveiling in November the artificially intelligent chatbot, created by a startup called Openai, drew 1m users, making it one of the fastest consumer-product launches in history. Microsoft, which has just invested $10bn in Openai, wants Chatgpt-like powers, which include generating text, images, music and video that seem like they could have been created by humans, to infuse much of the software it sells. On January 26th Google published a paper describing a similar model that can create new music from a text description of a song. When Alphabet, its parent company, presents quarterly earnings on February 2nd, investors will be listening out for its answer to Chatgpt. On January 29th Bloomberg reported that Baidu, a Chinese search giant, wants to incorporate a chatbot into its search engine in March.

It is too early to say how much of the early hype is justified. Regardless of the extent to which the generative ai models that underpin Chatgpt and its rivals actually transform business, culture and society, however, it is already transforming how the tech industry thinks about innovation and its engines—the corporate research labs which, like Openai and Google Research, are combining big tech’s processing power with the brain power of some of computer science’s brightest sparks. These rival labs—be they part of big tech firms, affiliated with them or run by independent startups—are engaged in an epic race for ai supremacy (see chart 1). The result of that race will determine how quickly the age of ai will dawn for computer users everywhere—and who will dominate it.

Corporate research-and-development (r&d) organisations have long been a source of scientific advances, especially in America. A century and a half ago Thomas Edison used the proceeds from his inventions, including the telegraph and the lightbulb, to bankroll his workshop in Menlo Park, New Jersey. After the second world war, America Inc invested heavily in basic science in the hope that this would yield practical products. DuPont (a maker of chemicals), ibm and Xerox (which both manufactured hardware) all housed big research laboratories. at&t’s Bell Labs produced, among other inventions, the transistor, laser and the photovoltaic cell, earning its researchers nine Nobel prizes.

In the late 20th century, though, corporate r&d became steadily less about the r than the d. In 2017 Ashish Arora, an economist, and colleagues examined the period from 1980 to 2006 and found that firms had moved away from basic science towards developing existing ideas. The reason, Mr Arora and his co-authors argued, was the rising cost of research and the increasing difficulty of capturing its fruits. Xerox developed the icons and windows now familiar to pc-users but it was Apple and Microsoft that made most of the money from it. Science remained important to innovation, but it became the dominion of not-for-profit universities.

The rise of ai is shaking things up once again. Big corporations are not the only game in town. Startups such as Anthropic and Character ai have built their own Chatgpt challengers. Stability ai, a startup that has assembled an open-source consortium of other small firms, universities and non-profits to pool computing resources, has created a popular model that converts text to images. In China, government-backed outfits such as the Beijing Academy of Artificial Intelligence (baai) are pre-eminent.

But almost all recent breakthroughs in the field globally have come from large companies, in large part because they have the computing power (see chart 2). Amazon, whose ai powers its Alexa voice assistant, and Meta, which made waves recently when one of its models beat human players at “Diplomacy”, a strategy board game, respectively produce two-thirds and four-fifths as much ai research as Stanford University, a bastion of computer-science eggheads. Alphabet and Microsoft churn out considerably more, and that is not including DeepMind, Google Research’s sister lab which the parent company acquired in 2014, and the Microsoft-affiliated Openai (see chart 3).

Expert opinion varies on who is actually ahead on the merits. The Chinese labs, for example, appear to have a big lead in the subdiscipline of computer vision, which involves analysing images, where they are responsible for the largest share of the most highly cited papers. According to a ranking devised by Microsoft, the top five computer-vision teams in the world are all Chinese. The baai has also built what it says is the world’s biggest natural-language model, Wu Dao 2.0. Meta’s “Diplomacy” player, Cicero, gets kudos for its use of strategic reasoning and deception against human opponents. DeepMind’s models have beat human champions at Go, a notoriously difficult board game, and can predict the shape of proteins, a long-standing challenge in the life sciences.

All these are jaw-dropping feats. Still, when it comes to the “generative” ai that is all the rage thanks to Chatgpt, the biggest battle is between Microsoft and Alphabet. To get a sense of whose tech is superior, The Economist has put both firms’ ais through their paces. With the help of an engineer at Google, we asked Chatgpt, based on an Openai model called gpt-3.5, and Google’s yet-to-be launched chatbot, built upon one called Lamda, a broad array of questions. These included ten problems from an American mathematics competition (“Find the number of ordered pairs of prime numbers that sum to 60”), and ten reading questions from the sat, an American school-leavers’ exam (“Read the passage and determine which choice best describes what happens in it”). To spice things up, we also asked each model for some dating advice (“Given the following conversation from a dating app, what is the best way to ask someone out on a first date?”).

Neither ai was clearly superior. Google’s was slightly better at maths, answering five questions correctly, compared with three for Chatgpt. Their dating advice was uneven: fed some actual exchanges in a dating app each gave specific suggestions on one occasion, and generic platitudes such as “be open minded” and “communicate effectively” on another. Chatgpt, meanwhile, answered nine sat questions correctly compared with seven for its Google rival. It also appeared more responsive to our feedback and got a few questions right on a second try. Another test by Riley Goodside of Scale ai, an AI startup, suggests Anthropic’s chatbot, Claude, might perform better than Chatgpt at realistic-sounding conversation, though it performs worse at generating computer code.

The reason that, at least so far, no model enjoys an unassailable advantage is that ai knowledge diffuses quickly. The researchers from all the competing labs “all hang out with each other”, says David Ha of Stability ai. Many, like Mr Ha, who used to work at Google, move between organisations, bringing their expertise and experience with them. Moreover, since the best ai brains are scientists at heart, they often made their defection to the private sector conditional on a continued ability to publish their research and present results at conferences. That is one reason that Google made public big advances including the “transformer”, a key building block in ai models, giving its rivals a leg-up. (The “t” in Chatgpt stands for transformer.) As a result of all this, reckons Yann LeCun, Meta’s top ai boffin, “Nobody is ahead of anybody else by more than two to six months.”

These are, though, early days. The labs may not remain neck-and-neck for ever. One variable that may help determine the ultimate outcome of the contest is how they are organised. Openai, a small startup with few revenue streams to protect, may find itself with more latitude than its competitors to release its products to the public. That in turn is generating tonnes of user data that could make its models better (“reinforcement learning with human feedback”, if you must know)—and thus attract more users.

This early-mover advantage could be self-reinforcing in another way, too. Insiders note that Openai’s rapid progress in recent years has allowed it to poach a handful of experts from rivals including DeepMind, which despite its various achievements may launch a version of its chatbot, called Sparrow, only later this year. To keep up, Alphabet, Amazon and Meta may need to rediscover their ability to move fast and break things—a delicate task given all the regulatory scrutiny they are receiving from governments around the world.

Another deciding factor may be the path of technological development. So far in generative ai, bigger has been better. That has given rich tech giants a huge advantage. But size may not be everything in the future. For one thing, there are limits to how big the models can conceivably get. Epoch, a non-profit research institute, estimates that at current rates, big language models will run out of high-quality text on the internet by 2026 (though other less-tapped formats, like video, will remain abundant for a while). More important, as Mr Ha of Stability ai points out, there are ways to fine-tune a model to a specific task that “dramatically reduce the need to scale up”. And novel methods to do more with less are being developed all the time.

The capital flowing into generative-ai startups, which last year collectively raised $2.7bn in 110 deals, suggests that venture capitalists are betting that not all the value will be captured by big tech. Alphabet, Microsoft, their fellow technology titans and the Chinese Communist Party will all try to prove these investors wrong. The ai race is only just getting started.

Description automatically generated “…Why have US aggregate profit rates increased while financial market rates decreased since 1980? We propose a mismatch hypothesis: Profit rates in the national accounts track the return on capital for all firms, while financial market rates track the cost of capital for public firms only. We show public-firm profit rates halved since 1980, matching trends in financial markets and suggesting low market power. Mechanically, this residual private capital return series shows private capital returns had to have increased substantially to account for this secular break between aggregate and public firm profitability. The degree of this shift is significant: Private firms’ profit rates are on average 10% higher than public firms’ in the post-2000 period. Nonfinancial domestic private-firm profit rates doubled, suggesting high market power or risk. Size and sector differences cannot explain the divergence, though intangible-intensity might. Our results indicate substantial biases in extrapolating public-firm trends to the aggregate economy….”

The Evidence

Public-Firm Profits Have Fallen

“…Figure 8 shows the return on book capital with separate corrections for R&D and goodwill. This figure shows our adjustments make little difference to the series. Indeed, our results show book capital profit rates are decreasing and other results in this paper are robust are a variety of different treatments of R&D and goodwill. We show the book profit rates Rb for both the IMA data and the Compustat sample in Figure 9. The two series follow each other fairly closely until the mid 1990s, when the publicly listed firm book profit rate drops markedly below the IMA book profit rate. Since then, public firm profits have fallen relative to profits in the national accounts. Figure 9 illustrates the importance of using a representative sample of firms to measure the cost of capital. Since the profit rates of public firms are different from those of private firms, it is not appropriate to apply measures of the cost of capital from public firms to the aggregate economy, which includes private firms….”

“…One alternative to analyzing the return on book in public-firm and aggregate data is to impute the replacement value of capital in Compustat using information from the IMAs. The IMAs provide the replacement and book values of the aggregate capital stock. By assuming the ratio of replacement-to-book values is the same in Compustat, we can infer the return on capital R of publicly listed firms. This approach highlight the quantitative differences in the two profit rates and their secular divergence in recent decades The left panel of Figure 10 shows the ratio of the replacement value of capital to the book value for inventories; property, plant, and equipment (PPE); and intellectual property products (IPP). Since the replacement value is typically above the book value, most of these series are above one most of the time. We can use these three series to transform our book capital profit rates back into our profit rates from above with replacement capital values, assuming Compustat firms have the same replacement-to-book ratios as in the IMA data. The right panel of Figure 10 shows this replacement-to-book ratio from the IMA data, leading to the same conclusion as before: public company profit rates have fallen….”

Increase in Private-Firm Profit Rates

“…If there is no mismeasurement of foreign and domestic activity, this residual return constitutes the return on capital for private firms in the US. We label this the private return on capital, with the important caveat that this measure has issues of measurement of foreign vs domestic activity. Figure 14 shows these results. Mechanically, this residual private capital return series shows private capital returns had to have increased substantially to account for this secular break between aggregate and public firm profitability. The degree of this shift is significant: Private firms’ profit rates are on average 10% higher than public firms’ in the post-2000 period….”

Potential Causes of Divergence

“…The first hypothesis we consider is that Compustat overrepresents large firms, so perhaps the secular shift is just driven by changes in the profit rates of large firms relative to those of smaller firms. The second hypothesis we consider is that public and private firms generally operate in different sectors Our third hypothesis posits that the disparity in profit rates between public and private firms can be attributed to the relative concentration of intangible assets capital as intangible instead of physical. To investigate this theory, we will examine whether the difference in profit rates between firms that are heavily invested in intangible assets and those that have a lower concentration of such assets explains the gap in return on the capital between public and private companies….”

“…To understand exactly how representative public firms are of the aggregate economy, we plot the number of employees, as a fraction of aggregate employment, of various types of firms. We use both BDS and Compustat employment data to make the comparison. The left panel of Figure 16 shows the employment share of primarily goods-producing (instead of primarily service-providing) Compustat and BDS firms. The BDS series shows goods production has declined in aggregate in terms of employment shares. The Compustat series shows this decline has been less pronounced for public firms. The right panel of this figure shows the fraction of employment of mega-firms in the economy overall (see the BDS series) and the fraction of public mega-firm employment from Compustat. Note that a fairly stable 30% of aggregate employment is at mega-firms, while 80% or more of total public-firm employment is at mega-firms. Unsurprisingly, Compustat is not representative in terms of sector or firm size…”

“…Figure 17 combines the weights from 16 and shows neither the firm size nor sectoral composition hypotheses alone can explain the public and private firm mismatch. The left panel shows the rewighted Compustat book returns for both the goods and services sectors. The service sector has lower returns than the goods sector, so the over-representation of goods-producing firms in Compustat means the public and private firm mismatch is all the more puzzling. The right panel shows the reweighted book returns for Compustat mega-firms and other Compustat firms, revealing that mega-firm trend returns are higher than small-firm returns. Since public firms are disproportionately mega-firms, this also fails to explain the mismatch. Note the figure only shows public firm returns by sector and size because private firm returns are not freely available. Neverthless, reweighting suggests that neither size nor sectoral composition alone can explain the divergence in profit rates of public and private firms–otherwise we would expect to see the same divergence in trends between those groups within public firms….”

“…To determine if the trend of the public-private mismatch is influenced by firms that are heavily invested in intangible assets, we compared the return on capital of firms with R&D to book capital ratios above the median to those with lower ratios. The results, depicted in Figure 18, reveal there is no significant difference in returns on capital between the two groups of firms. This suggests the discrepancy in the concentration of intangible assets between public and private firms is not a driving factor behind the public-private return on capital mismatch….”

The Brass Tacks

“…In the US, aggregate profit rates have increased while financial market rates have decreased since 1980. We call their gap the “puzzle rate” and its rise the “profit puzzle.” The profit puzzle has led to suggestions that rising markups, risk, or intangible capital are contributing factors. In this paper, we propose an alternative hypothesis: Profit rates in the national accounts track the return on capital for all firms, while financial market rates track the cost of capital for public firms only. The capital profiles of public and private firms differ and vary over time, which can lead to financial market rates misrepresenting the cost of capital faced by a representative firm. Supporting this view, there is a large literature in asset pricing documenting higher returns for private firms compared to public firms. We call thisexplanation the “mismatch hypothesis.” To test our hypothesis, we analyze data on public-firm profit rates and find they have halved since 1980, matching trends in financial markets. Our results are robust to assumptions about the capitalization of R&D and goodwill, as well as the measurement of capital stocks at book or replacement value. When adjusted for differences in depreciation and tax rates, we find a tight link between the return on and cost of public-firm capital. The puzzle rate for public firms is small and well within statistical discrepancy. Hence, we view the mismatch hypothesis as a promising solution to the profit puzzle. Subsetting to nonfinancial domestic firms so we can compare Compustat and the IMAs, we estimate public firms represent 60% of the capital stock. Inferring from the residual, we find private-firm profit rates moved in lockstep until 1980, when they diverge. Private-firm profit rates are now over twice as high as public-firm profit rates. We show this secular shift is not driven by differences in the representation of size or sector of public-firms, though intangible-intensity offers a promising direction for future research….” Carter Davis, Alexandre Sollaci and James Traina, “Profit Puzzles,” Kelley School of Business Research Paper, February 1, 2023, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4015573

Evidence that major productivity gains in research result from allowing scientists and researchers to cluster with other highly skilled inventors. Allowing more high-skilled immigration could boost per capita GDP growth rates by 9%. “…Moving to the USA raises citations to math publications four-fold, or 2.5-fold if you restrict attention to people who become a math academic at home or abroad. Comparing New Zealander migrants who return or stay abroad – the ones who stay abroad get up to four times as many citations as those who return. PhD students who stay in the USA get 4-6 times as many citations to their work as their peers in the same program who end up moving back to a country with GDP per capita outside the top 25%. That’s a pretty consistently large effect. And we get similar kinds of results when we look at other proxies for scientific achievement, whether it’s counting publications, patents, or becoming an invited speaker to the International Congress of Mathematicians. A model of the innovation/immigration/trade economy between the US and EU…implies if the USA doubled the H-1B visa cap from 65,000 to 130,000, it would raise the real GDP per capita growth rate in each region by 9% in the long run….”

Matt Clancy, “Innovators Who Immigrate,” What’s New Under The Sun,” February 1, 2023, https://mattsclancy.substack.com/p/innovators-who-immigrate

Innovators Who Immigrate

Talent is spread equally over the planet, but opportunity is not. Today I want to look at some papers that try to quantify the costs to science and innovation from barriers to immigration. Specifically, let’s look at a set of papers on what happens to individuals with the potential to innovate when they immigrate versus when they do not. (See my post Importing Knowledge for some discussion on the impact of immigration on native scientists and inventors)

All of these papers confront the same fundamental challenge: successfully immigrating is (usually) a matter of choice, selection, and luck. For the purposes of investigating the impact of immigration on innovation, that means we can’t simply compare immigrants to non-immigrants. For example, immigrants (usually) choose to migrate, and if they do so because they believe they will be more successful abroad, that signals something about their underlying level of ambition and risk tolerance. That, in turn, might mean they are more likely to be innovative scientists or inventors, even if they had not migrated. Compounding this problem, countries impose all sorts of rules about who is allowed to migrate and many of these rules make it easier to migrate if you can demonstrate some kind of aptitude and talent. That means successful immigrants are often going to be drawn from a pool of people more likely to have the talent to succeed in science and invention, even if they had not immigrated.

These are challenges; but there is also a degree of capricious luck in immigration (and life in general). There are people – perhaps many people – who want to immigrate and have extraordinary talent, but who do not for all sorts of random reasons. Compared to otherwise identical people who do migrate, they might lack information, financial resources, or face higher barriers to legal immigration. Indeed, in many cases, immigration is literally handed out by lottery! The papers we’ll look at employ various strategies to try and find comparable groups of people who immigrate and people who do not, to infer the impact of immigration and place on innovation.

Talented High Schoolers

One way to deal with the selection effect is to try and measure the talent of a sample of both immigrants and non-immigrants and then compare immigrants and non-immigrants who appear to have similar underlying talent. Agrawal and Gaule (2020) and Agrawal et al. (2023) does this with the International Mathematical Olympiads.

The International Mathematical Olympiads is a prominent math competition for high school students from around the world that’s been held annually for decades. Up to six representatives from each country are selected via regional and national competitions, and then travel to a common city and try to solve six different (presumably very hard) math problems. Because it’s an Olympiad, winners take home gold, silver and bronze medals. Agrawal and coauthors know the scores of all the competitors from 1981 to 2000 and then look to see what happens to the competitors later in life. In Agrawal and Gaule (2020) they show that scores on these math competitions strongly predicts later success as a mathematician. That in itself is surprising, given that the talents for doing creative mathematical research may, in principle, differ substantially from performance in a competition.

Their dataset also establishes something else: students from low income countries are less likely to obtain PhDs in math than students with the same score from high-income countries. In Agrawal et al. (2023) they use this dataset to look at the different fates of those who immigrate from their home country and those who do not. On average, a migrant is about twice as likely to be employed in academia as a mathematician as someone from the same county who got the same math score but did not migrate.

Of course, while math scores help address the problem of selection, this doesn’t really get at the problem of choice. Perhaps people who really want to be mathematicians are disproportionately likely to migrate, since the highest ranked mathematics departments tend to be in the USA, and it’s this difference in career intention that explains the difference in career outcomes between migrants and non-migrants.

Agrawal et al. (2023) provides some additional evidence that this is not purely an outcome of career choice. For one, looking only at migrant and non-migrant students who both become math academics (in their own country or abroad), they find the migrants go on to garner about 85% more citations to their publications than their domestic peers (remember, with the same score in math competitions). We might think citations aren’t a great measure of math skill (see my post Do Academic Citations Measures the Value of Ideas?), but they also show migrant academics are about 70% more likely to become speakers at the International Congress of Mathematicians (a non-citation-based measure of community recognition). So among people who ended up becoming academic mathematicians (either at home or abroad), the ones who migrated went on to have more distinguished careers, as compared to their peers who did equally well in high school on math.

But this is still pretty indirect evidence. Fortunately, Agrawal and coauthors also just asked Olympiad medalists directly about their preferences in a survey. From respondents in low- and middle-income countries, 66% said they would have liked to do their undergraduate degree in the USA if they could have studied anywhere. Only 25% actually did. Just 11% said their first choice was to study in their home country. In fact, 51% did.

Why didn’t they study abroad if that’s what they wanted to do? A bunch of the survey evidence suggests the problem was money. For 56% of the low- and middle-income respondents, they said the availability of financial assistance was very or extremely important. Students from low- and middle-income countries were also much more likely to choose a hypothetical funded offer of admission at a lower ranked school than their peers in high-income countries.

Gibson and McKenzie (2014) provides some complementary evidence outside of mathematics. As part of a larger project on migration and brain drain, they identify 851 promising young New Zealanders who graduated high school between 1976 and 2004. These students either represented New Zealand on the International Mathematical Olympiad teams, the International Chemistry Olympiad team, were top in exams, or earned the New Zealand equivalent of the valedictorian rank. Like Agrawal and coauthors, they can then see what happens to New Zealanders who migrate, versus those who remain. They find researchers who moved abroad publish more than those who do not.

As noted, this poses some potential problems; even though we know all these students were talented, those who migrate may have different unobserved levels of skill, ambition, risk tolerance, or something. One way they attempt to deal with this is to focus their attention on the subset of researchers who actually do migrate away from New Zealand, and then looking to see what happens to their research output when they move back. The idea here is those who left were, at least initially, displaying similar levels of skill, ambition, risk tolerance, and so forth (if so, why did they return? We’ll get to that).

For each New Zealand migrant researcher who returns to New Zealand, Gibson and McKenzie try to find another migrant who stayed abroad, but is similar in age, gender, what they studied in high school, highest degree, and so on. They then look to see what happens to the number of citations to their academic work. While both groups had essentially the same citations prior to return migration, after one group returned to New Zealand, the citations to their work declined substantially relative to the citations of migrants who remained abroad.

Again, we see that being abroad was good for research productivity. But again, perhaps we are concerned that there is an important but unstated difference between New Zealanders who stayed abroad and those who returned home. Perhaps the ones who came back simply couldn’t cut it?

But we actually don’t see much evidence of that. The figure above matches each returnee to someone who stayed abroad based on a number of characteristics. But one characteristic they were not matched on is citations to their academic work. And yet, prior to returning, their citations were on a very similar trajectory. And like Agrawal and coauthors, Gibson and McKenzie also surveyed their subjects to see why they moved back. Most of the answers were not related to individual research productivity, but had to do with, for example, concerns about aging parents, child-raising, and the location of extended family.

Scholarship Restrictions

Another line of evidence comes from Kahn and MacGarvie (2016), which focuses on PhD students who come to America from abroad. The paper’s big idea is to compare students who come on the prestigious Fulbright program to similar peers who were not Fulbright fellows. The students and their matches are really similar in this case: they graduated from the same PhD program, either studying under the exact same advisor and graduating within 3 years of each other, or merely studying in the same program but graduating in the same year. The only difference was the Fulbright students have a requirement to leave the USA for two years after finishing their studies, whereas the matched students faced no such restrictions on their ability to stay.

Kahn and MacGarvie first show that these migration restrictions matter; whereas 66% of foreign students doing PhDs in the USA end up remaining, only 12% of the Fulbright fellows do. They then estimate the impact of being abroad on future academic outcomes, but using a statistical model (instrumental variables) that tries to identify the impact of being abroad deriving solely from the restrictions imposed on the Fulbright program. With this approach, they find leaving the USA due to Fulbright requirements is associated with about 65% fewer publications and fewer citations received, and nearly 80% fewer publications in high-impact journals.

Moving Back to China

Shi, Liu, and Wang (2023) takes a similar approach as the above to evaluate the impact of China’s Young Thousand Talents program. This is an ongoing effort to increase China’s domestic scientific capacity by attracting talented scientists to move to China with salary subsidies and research funding. The program isn’t restricted to Chinese citizens, but in practice that’s mostly the population who chooses to take up the offer.

Shi, Liu, and Wang focus on 339 Chinese scientists who obtained PhDs abroad and then moved back to China as part of the program. Similar to Kahn and MacGarvie, they compare this population to a set of Chinese scientists who went to the same overseas university, in the same field, and graduated within three years, but chose to stay abroad. They also try to identify scientists with similar publication and citation trajectories, prior to the date of the return to China.

The figure above plots the publication trajectory of returnees, relative to those who stayed abroad. After a few years of adjustment, those who returned start publishing more than their peers who stayed abroad, with this increase concentrated in last-authored publications (which signals that the scientist is running a lab).

Why are migrants more productive?

In the above, moving abroad is associated with more productivity for mathematicians. Returning home is associated with lower productivity among New Zealand migrant researchers and Fulbright scholars. But returning home is associated with higher productivity among Chinese scientists. What’s going on?

There’s a pretty simple story that runs through all these studies. It’s not migrating that’s good for scientists, it’s about migrating to a place that’s good for science. That might mean a place with the resources to conduct science, or it might mean being in a place with lots of good scientists to collaborate with. Most of the time, it means both, since good scientists tend to go where they have the resources to conduct science. Most people intuitively know this and hence they don’t move (moving is a pain!) unless they think it’ll be good for their career. Hence, the reason we see such a big impact on moving is because people are disproportionately likely to move to places good for science.

For example, in Agrawal et al. (2023), which looked at the effect of moving on the careers of mathematicians, the authors also tried to break down the impact of moving by destination. The USA houses more top math universities (by various ranking) than any other country, and tends to compensate academics well by international standards, so if the moving effect is mostly about moving to places with more support for science, we might expect to see a bigger impact among mathematicians who move to the USA. Indeed, Agrawal and coauthors find that moving specifically to the USA is associated with receiving four times as many citations as not moving, whereas moving to other countries is associated with “only” twice as many. Migrants to the USA also end up six times as likely to become invited speakers at the International Congress of Mathematicians; again compared to twice as likely for migrants to other countries. (Recall, this is when we compare two people from the same country, who received the same score in high school on International Mathematical Competitions!)

Kahn and MacGarvie’s work on Fulbright scholars also tells a similar story. In their case, they focus on the level of GDP per capita in the country that Fulbright fellows return to. They find the penalty associated with return migration becomes increasingly severe as students return to countries with progressively lower GDP per capita. A student returning to a country whose GDP per capita is at the 90th percentile (i.e., only 10% of students in their sample are from richer countries) receive 6% more citations than those who remain in the USA (though the effect is not statistically distinguishable from zero), those whose GDP per capita is at the 50th percentile receive 45% fewer citations than remaining scholars, and those returning to countries at the 25th percentile receive 55% fewer citations than remaining scholars.

GDP per capita in China is not in the top 10%, and so we might expect a penalty for scientists moving back to China. But the Chinese Young Thousands Talent program is explicitly about providing resources to scientists to do science. Indeed, in another analysis, Shi, Liu, and Wang try to take into account the extra funding Chinese returnees in their sample get, by gathering data on grants and the size of the teams they coauthor with. Once you take into account teams and grants, the impact of returning is more muted; much of the advantage of returning is about getting access to funding and a peer network that Chinese PhD students abroad struggled to get.

Shi, Liu, and Wang also find the biggest impact of the program among returnees for whom the funds from the Young Thousands Talent program probably really mattered: those in fields that most require access to funding, such as chemistry and the life sciences, and those who were probably struggling more to get funds abroad, because they had not secured faculty positions, and were not among the top 10% most productive. Indeed, among scientists less likely to need funding – those in mathematics or physics, those with faculty positions prior to their return, and the top 10% most productive prior to return – the impact of returning to China was negative for their productivity, though the effects were too small to be statistically distinguishable from zero.

Even Gibson and McKenzie’s study on migrant researchers who return to New Zealand suggests lower productivity upon return is at least partially driven by funding. In their survey of these scientists, Gibson and McKenzie asked them what policies they would personally recommend to government officials and universities trying to entice researchers to return. The survey responses mentioned things like “low salaries and high teaching loads, poorly funded scientific laboratories and the low success rate of grant funding requests.”

When Inventors Migrate

What about inventors, rather than scientists? Prato (2022) looks at patent-holders in the USA and European Union. Among the 1.2mn who file more than one patent with the European Patent Office between 1978-2016, she identifies about 1500 who do so from the USA in some cases and the EU in others, which forms her set of migrating inventors. For each of these migrating inventors, she finds another inventor from the same country with a similar patenting career up to the year the migrant starts patenting in the other region. This is meant to be her set of comparable inventors, if we think patenting history accurately captures things like talent, ambition, and all the other potential differences between immigrants and non-immigrants that we’re worried may be confounding our results. She then looks to see if the patenting trajectory of these groups diverges in the years after half of them immigrate. As we can see below, it does.

In general, inventors who move take out about 40% more patents per year after they move, as compared to inventors from the same country with a similar patent career up until the year the immigrant moved.

Note, these effects stem entirely from migration between comparatively rich countries (the EU and the USA). About 65% of these migrants moved from the EU to the US and 35% went in the other direction. This is not so much a story about people migrating from a place where probably do not have the resources to invent to a place where they do. Instead, Prato argues this is a story about how migration expands your inventor network and allows you to work in the place best suited for your particular technology field.

How much is at stake?

In one way, the results of these papers are not surprising: moving to places with more resources (and peers?) to do science raises your output of science (and invention). But what is perhaps more surprising is how large the implied size of moving is.

As one point of comparison, several of these papers report an estimate of citations received by academic work.

1 Agrawal and coauthors find moving to the USA raises citations to math publications four-fold, or 2.5-fold if you restrict attention to people who become a math academic at home or abroad. Gibson and McKenzie find similar results by comparing New Zealander migrants who return or stay abroad – the ones who stay abroad get up to four times as many citations as those who return. Kahn and MacGarvie find PhD students who stay in the USA get 4-6 times as many citations to their work as their peers in the same program who end up moving back to a country with GDP per capita outside the top 25%.

That’s a pretty consistently large effect. And we get similar kinds of results when we look at other proxies for scientific achievement, whether it’s counting publications, patents, or becoming an invited speaker to the International Congress of Mathematicians. Moreover, Agrawal’s survey results suggests, in math (and it’s hard to believe only in math), there is a large population of talented students who want to study abroad but can’t.

Still, it’s a bit hard to see how this cashes out in terms of it’s ultimate impact: while faster progress in science would probably lead to faster progress in technology, it’s tough to say much about how much faster things could be with this data.

One estimate of the potential impact comes from Prato (2022), which builds a model of the innovation/immigration/trade economy between the US and EU. The model takes into account many subtleties, such as the fact that people with more talent for inventing are more likely to move to places where the rewards for invention are higher, and in turn benefit from working with other high skilled inventors. Her model implies if the USA doubled the H-1B visa cap from 65,000 to 130,000, it would raise the real GDP per capita growth rate in each region by 9% in the long run.

But there’s reason to think that’s an under-estimate of the ultimate impact. Prato’s model is calibrated on migration between the US and EU, two regions with the resources to fund invention and science. As we’ve seen, the impacts of immigration are likely to be much stronger for other regions.

1 These papers have multiple analyses each, and so some of the estimates listed here differ a bit from the estimates noted earlier because sometimes I pulled from different analyses.