Immigration and Innovation

Note: This post was crossposted from the Lauren Policy blog by the Forum team, with the author's permission. The author may not see or respond to comments on this post.

Generally, the arguments around migration tend to center on its direct effects.

These arguments tend to focus around two things:

1. Do firms employ fewer of the native-born because they employ migrants instead?
2. Do immigrants contribute more in taxes than they consume in services?

I have written elsewhere about the answers to these two questions. However, I think these debates may ignore the most important part of immigration: its effect on innovation.^[1]

Before we get into the evidence: it’s worth specifying why we care about innovation.

Economists model innovation as the only way to improve living standards (in the long run). Innovation in this sense is not necessarily limited to patents and scientific innovation; it can also include management improvements, process improvements, or any kind of change that improves efficiency. When defined this way, this makes sense; if you do exactly the same things in exactly the same manner, you will get… the same output. For things to improve, something has to change - and those changes are labeled as “innovation”.^[2]

Given this, it is obvious why a society would want to produce more innovation. It is hard to look at life and think that this is the best it could possibly be;^[3] we want to live longer, to work less, to spend more time doing things we want to do and less time doing tedious things we hate. We have to innovate for that to happen. In some sense, producing innovation might be the whole ballgame; perhaps it should be the primary goal for a society.^[4]

Why would innovation be linked with immigration?

Theoretical Reasons

Immigrants Are Weird^[5]

It is not obvious ex ante where people get innovative ideas. Ideas are notoriously hard to pin down; inspiration is a fleeting and fickle beast.^[6] It seems likely, though, that the types of ideas you produce are shaped by your environment. Perhaps an unusual combination of environments - e.g., growing up in one country and migrating to another - will produce unusual ideas. With the low-hanging fruit largely plucked,^[7] we might need more and more unusual thinkers to keep making breakthroughs.

One might argue that immigration isn’t the only way to produce weird people and weird ideas. And that’s true, but it is one way.

Idea Recombination

Furthermore, it is also a way to bring ideas that are old news in one area into another. Matt Clancy has written about how one of the most reliable sources of innovation is combining disparate “old” ideas into a new idea. That is, to produce new ideas, you want to maximize your idea recombination rate.

Since we know that people’s interests and knowledge vary based on their country of origin, combining source-country ideas with the ideas “in the water” in a receiving country could be fertile ground for innovation. You actively want different perspectives, backgrounds, and thought processes bumping up against each other.^[8]

Note that this is different than the above because the first explanation involves the immigrant being more innovative; the second suggests that the combination of immigrants and natives creates more innovation.

The Practical Reasons

OK, that’s a very 30,000 ft view of why innovation and immigration might be linked. But there are more prosaic reasons to think this.

(For the below, I focus on data from the United States because we simply have more data from the US; later on in the post, I’ll discuss how much this applies in other countries.)

Selection

There are many reasons that immigrants might select into R&D careers. In the US, it is undeniably at least partially driven by the world-class university system; some percentage of US immigrants are immigrants because they want to work in the world’s R&D lab.^[9]

The US effectively vacuums up talented people who want to innovate from all over the world and reaps the benefits of their productivity.

Unobservables

Secondly, the unobservable characteristics of immigrants are likely correlated with the characteristics of good innovators. Immigrants are people who have picked up and left their home country in search of better opportunities, which means they tend to be selected for high levels of resilience, tolerance for risk, and general desire to fuck around and find out. Since innovation also involves trying new things, it seems plausible that immigrants are particularly well-suited to this.

Immigrants Are Already The Innovation Workforce

Immigrants are more likely than the native-born to work in STEM, innovation and R&D. Immigrants are considerably more likely to pursue STEM degrees (54%) than the native-born (35%). About a quarter of the US R&D workforce consists of immigrants (compared with 15% of the population).

This means changing the nature and structure of immigration will change the nature and kind of innovation that happens even if you believe absolutely nothing of the story above.

Are immigrants actually more innovative than the native-born?

Yes. Look, I try to convey a reasonable level of uncertainty about most of my conclusions in the academic literature, but this one seems pretty clear.

Hunt 2011 finds that college-educated immigrants are a bit more than twice as likely to produce patents than the native-born. Bernstein et al. 2022 finds that immigrants who entered the US in their 20s or later ^[10] produced 40% more patents than would be expected based on their percentage of the population.

Neither of these papers studies the full universe of immigrants, but these are large advantages in patenting. Furthermore, almost all patents are filed by the college-educated;^[11] it is not possible for non-college-educated natives to make up this gap in patenting.^[12] Therefore, I feel safe in saying that the average US immigrant is more likely to produce a patent than the average native-born American.

Why are immigrants more innovative?

There is at least some evidence for all of the practical mechanisms outlined above.

1. Immigrants are likely predisposed to want to pursue innovation.

As noted above, immigrants are more likely to pursue STEM degrees and be employed in R&D. They are also more likely to become entrepreneurs. Entrepreneurship and innovation are likely linked; generally, if you create a new firm, it is because you think you can do better than the current state of the art. Azoulay, Jones, Kim, and Miranda 2022 finds that immigrants are about 80% more likely to found a firm than the native-born. About half of venture-backed companies have at least one immigrant founder.

This pattern isn’t unique to the US; 54% of Britain’s fastest-growing companies have an immigrant founder. This is some 3.3x the percentage of immigrants in the British population.

Immigrant-founded firms are also particularly innovative. Brown et al. 2019 looks at 16 different measures of innovation. Immigrant-owned firms were more likely to produce 15 of those kinds of innovation than native-owned firms.

None of this proves that immigrants were definitely more interested in innovation than the native-born even before immigrating, but it is certainly suggestive. It seems very likely to me that immigrants are a population that are particularly likely to want to try new things, and that they choose careers that will let them pursue these innovative ambitions.^[13]

2. Immigrants are selected to be particularly good at innovation.

The universe of people who would like to immigrate to the US is far larger than the number who are actually permitted to move to the US. US immigration policy - and particularly, US universities - can be very selective in who they choose, and they generally try to select the highest potential individuals (who will do particularly good work).

International admission rates to US universities are typically much lower than domestic admission rates. This allows universities to select for only the highest potential individuals.

For instance, Gaulé and Piacentini 2013 finds that Chinese graduate students at US universities are more productive than the average graduate student. They believe this is likely selection - that Chinese graduate students in the US come from “a restricted number of very selective elite institutions in China”.

Combining these two arguments, though, one might worry about brain drain. If the US is simply vacuuming up talent from the rest of the world, this could be a zero-sum game. The US benefits; other countries do not.

I don’t think this is the case, though, because:

Immigration also makes more people more innovative.

Most of this effect is probably “moving to opportunity”. This is often, but not exclusively, in the form of a better job, but it can also include moving to education. A new job market paper by Manfredi Aliberti shows that getting a PhD increases one’s likelihood of patenting. We also know that migrating to a higher-income country makes you more likely to get a PhD. Therefore, moving to a place where you are more likely to get a PhD will also increase your expected number of patents.

Let’s use a stylized example here. Consider a person who is clearly very talented but lives in a not great neighborhood of Kigali, Rwanda. She’s the best science student in her school by a long way, but her parents don’t make a lot of money, and she certainly doesn’t know anyone who is an academic researcher. She manages to get into a US university on a scholarship - not a great one, but a pretty decent one.

Suddenly, her world is changed; being a pharmaceutical researcher is a career that, like, actually exists. After university, she goes on to chemistry graduate school, and then becomes a biochemistry professor. Her research focuses on designing new pharmaceuticals. In this role, she almost certainly produces more innovation than if she had never left Kigali.

It is not that she would have definitely not produced anything in Rwanda. She was a great student; she likely could have attended university at home, perhaps eventually ending up in research after all. But she has more opportunities in the US than she would in Rwanda, and the likelihood of having a high-impact career is higher.

Does this particular person exist? Not that I’m aware of - this particular example is an anonymized amalgam of a number of people - but she serves as an example. It is easier to have a productive research career in a high-income country than it is in a low-income country. Moving to a high-income country both increases your likelihood of pursuing a career focused on research and development and increases your likely productivity in your career.

Indeed, Agarwal, Ganguli, Gaulé and Smith 2023 finds the migration-induced productivity increase matters more to the overall level of production than the increase in likelihood of having a research career at all. This would suggest it’s not a zero-sum game: that moving our hypothetical person from Rwanda to the US doesn’t just move her productivity from Rwanda to the US, but increases the total amount of productivity that happens.^[14]

That’s all very nice, but I care about the UK/Europe/Australia/China.

Is all of this unique to the US? One could imagine it would be - the US has the best universities in the world^15[15] and many of the most innovative firms. Perhaps this beneficial effect is specifically about moving to the US, not immigration in general.

In general, I don’t think so. Kahn and MacGarvie 2016 looks at US-trained scientists that return to their home country after their PhD. If a person moves back to a comparatively rich country, their output tends not to decline. If a person moves back to a much poorer country, it does decline. This would suggest that it is not that the US is unique, but rather, the US is one of a set of countries with high innovative output.^[16]

If a country provides more opportunity than a migrant’s source country, it seems plausible to expect migration to increase innovation; if it provides fewer opportunities than the source country, well - why did they move there anyway?

What happens to natives?

Earlier, I posited the idea that the migration of innovative immigrants might increase native innovation as well, through the combination of different ideas and perspectives.

On balance, I think this is likely true - that migration of innovative people likely results in somewhat more innovation among the native-born. But there is at least some evidence for positive effects, no effects, and negative effects.

The Evidence That Immigrants Increase Native Productivity

There are four papers I really like here:

1. Hunt and Marjolaine Gauthier-Loiselle 2008 estimates that the increased likelihood of immigrants to produce patents would lead to a 6% increase in patenting for every 1 percentage point increase in the population of college-graduate immigrants. They actually find that patenting increased 15%. This suggests that patenting rates also increased among the native-born (and indeed, most of the increase in patenting is due to spillovers, not direct production by immigrant inventors).
2. Bernstein et al. 2022 finds more evidence of spillovers from immigrant inventors. When an inventor dies, their collaborators also produce fewer inventions. This effect is stronger for immigrant inventors than for native-born inventors, suggesting that immigrant inventors are more likely to cause others to produce more inventions.
3. Moser, Voena and Waldinger 2014 finds that patenting increased substantially after German-Jewish émigrés came to the US after the Nazis came to power in 1933. The émigrés seem to have drawn in new researchers into their field.
4. There’s even some direct evidence that the mix-and-match theory of innovation is correct. Posch, Schulz and Henrich 2024 finds that places with more surname diversity also produce more patents.

We can also examine total factor productivity.^[17] Peri, Shih and Sparber 2015 finds positive productivity impacts in areas with many H-1B recipients. Ottaviano, Peri and Wright 2018 finds similar results in the UK.

The Evidence That Immigrants Hurt Native Productivity

That’s reasonably strong evidence that immigration increases native productivity. What’s the case against?

Kerr and Lincoln 2010 finds basically no spillovers - Chinese and Indian immigrants produce more patents than the native-born, but there is no change in the number of patents produced by people with Anglo names. But that’s at worst neutral, not harmful.

There is one notable case where it seems like innovative immigrants really did hurt American incumbents. When the Soviet Union fell, about 1,000 mathematicians migrated to other countries, with the plurality going to the US. After their arrival, US mathematicians who studied similar topics experienced large declines in output and often ended up moving to worse academic institutions. There was no expansion in overall mathematics output - it was a zero-sum game where Soviets replaced Americans, and Americans suffered as a result.^[18]

I am not sure I have a good explanation of why this case seems different from the Moser et al 2014 paper cited above. Both concern academic researchers fleeing negative conditions at home to the United States; neither was in response to local demand for researchers. Perhaps there was more slack in the academic market in the 1930s than there was in the 1990s.

Still, most of the papers in this literature seem positive, putting the careers of mathematicians who study integral equations aside. Having a diverse set of collaborators seems to be good for the native-born.

Summary

So: the evidence suggests:

1. Immigrants are more innovative than the native-born.
2. Moving to opportunity makes immigrants more innovative than they otherwise would be.
3. Immigration probably improves the productivity and innovation of the native-born.

All of this seems very good - and likely quite important. Indeed, if we only consider immigration’s fiscal effects, we may significantly underestimate the benefits of immigration.

1. ^{^}

   Matt Clancy’s living literature review has already looked at innovators who immigrate; this post is an attempt to expand on Matt’s excellent work.

2. ^{^}

   Highly recommend Brian Potter’s new book The Origins of Efficiency on how production innovation works.

3. ^{^}

   OK, maybe some British Boomers think this.

^{^}

This is perhaps a bit stronger of a statement than I actually believe. There are many other things that one might spend societal time on; politics, in particular, might be not that well-suited to incentivizing innovation. You also probably get some innovation “for free”; humans just like solving problems.

^{^}

Not WEIRD - Western, Educated, Industrialized, Rich, and Democratic - though they are sometimes that too.

^{^}

If inspiration was easy to produce on demand, this series would be published on a more regular schedule.

^{^}

See “Are Ideas Getting Harder to Find?” and the idea of the burden of knowledge.

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Historically, centers of innovation have often been at the intersection of trade routes. While this is partially explicable by the fact that these places were rich and only rich places could afford full-time thinkers, it seems likely that it was helpful that these places were centers of idea recombination.

^{^}

This is something the US should not take lightly; it is a tremendous advantage that smart people want to move to the US. It is also an advantage the US could lose; Ganguli and MacGarvie 2025 notes the popularity of doing a degree in the United States has declined in recent years.

^{^}

This may seem a weird distinction about immigrants, but it’s an artifact of how they identify non-US citizens. They use Social Security numbers to identify immigrants; someone whose Social Security number was assigned in their 20s or later is very likely to be an immigrant. Someone whose Social Security number was assigned at 16 could be an immigrant, or could be someone who was born in the US whose parents didn’t apply at birth and then got one so they could get their first job.

^{^}

The Hamilton Project estimates 93% of patents are filed by people with a college degree.

^{^}

For natives: ~33% have a college degree, 67% don’t have a college degree. Thus, the native patenting rate = (0.33 * 1) + (0.67 * R_n), where R_n is the non-college native patenting rate relative to college-educated natives. We know that 93% of patents are produced by the 33% of people with a college degree, so R_n = 0.037. For immigrants, ~35% have a college degree, 65% don’t have a college degree, so that the immigrant patent rate = (0.35 * 2.22) + (0.65 * R_i), where R_i is the non-college immigrant patenting rate. For the native patent rate to be greater than the immigrant patent rate, then, we have (0.33 * 1) + (0.67 * 0.037) = 0.35479 = (0.35 * 2.22) + (0.65 * R_i) = 0.777 + 0.65 R_i. R_i must be negative for that to be true - and non-college-educated immigrants do not create a negative number of patents.

^{^}

Hunt and Gauthier-Loiselle 2008 argues the opposite, that immigrants do not have an innovation advantage over natives because immigrants and natives have the same inherent likelihood of creating patents conditional on majoring in STEM. I think this is a weird argument, as college majors are not chosen at random, and selecting a STEM major is an observable trait that makes one more likely to engage in some types of innovative activity.

^{^}

Note that it is possible that this is still net negative to Rwanda - one might imagine that Rwanda would benefit more from this person producing fewer things in Rwanda than producing more things in the US. The world, though, presumably benefits most from the maximum amount of innovation.

^{^}

Sorry Oxbridge grads.

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I would be remiss if I didn’t include a counterexample paper: Gibson and McKenzie 2014. Returnees to high-GDP/capita New Zealand did have much lower productivity than those who stayed abroad. New Zealand is very small and very remote, though. Seems plausible that it’s not amazing for your research career to live somewhere with the world’s most annoying time zone for international collaboration.

^{^}

TFP isn’t my favorite measure, as it’s a black box, so I put more weight on the previous papers.

^{^}

I leave it as an exercise to the reader to determine if “forced to get a job outside academic mathematics” constitutes suffering, or in fact a blessing in disguise.

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