Should We Restrict Immigration To Encourage Innovation?

The High-Wage Hypothesis Considered in the Present Day

One of the theories of the causes of the Industrial Revolution is that high wages led capitalists to substitute away from labor to capital intensive technologies. Inventions like the steam engine might only have been profitable to use if labor costs are sufficiently high, and since the steam engine is progressively improved as people use it, switching to steam engines leads in the long-run to far better outcomes than if wages were low. A similar story is told about American industrialization, where the relative labor scarcity led to greater investment into technology. (This is the Habbakuk thesis).

A clear implication of this is that we might not want there to be as much immigration. Immigration need not tend to reduce total wages, as they also demand products, but it is extremely plausible for immigrants to reduce wages in certain sectors, to the extent that their skills differ from others. (Intuitively: if we were to create an exact double of everyone in America, we need not expect wages to decline because the double would also demand the same mix of products. Whether it would increase wages would depend on if there are, generally, increasing or decreasing returns to scale. It’s only if the skills of the immigrants differ that we could shift who wins and loses, such that it is possible for some people to lose out. This is really just Krugman (1981), except that instead of another country it’s another group of people!)

We can identify a few plausible channels by which immigration affects the direction and pace of technological development, and they point in opposite directions. First, replacing labor with capital goods may have spillovers, which seems highly plausible. We are much more able to make innovations in the design of machines than we are in the organization of people, and even when we do find better ways of managing people those innovations seem far less portable from organization to organization than machines. On the other hand, cheaper labor frees up people to work in more innovative sectors. For example, a woman might choose between being a stay at home mom, or hiring a nanny. In addition, a larger supply of labor increases the number of potential users. Suppose a technology requires a fixed cost to find. Then a larger number of laborers, even cheap ones, will tend to make the technology worthwhile. And of course, if inventors benefit from being closer to other people in their field, then allowing immigration would directly increase innovation. What prevails?

We can break the story where immigration frees up additional people to work as innovators away from the other two channels, and deal with the two first. The key theoretical paper here is Daron Acemoglu’s 2010 paper “When Does Labor Scarcity Improve Innovation?”. Whether it does can be answered by the effect of the technology on the marginal product of labor. If it decreases the marginal product, it saves labor. If it increases it, it is labor complementing. If it is the latter, labor scarcity will not help innovation one bit. Of course, the future direction of technological progress is not known, but less us grant that things such as automated crop pickers might be labor replacing.

In this context, labor shocks led to increased innovation. Shmuel San studies the ending of the bracero program in the United States, which allowed many people to immigrate to the United States to work as agricultural laborers. Clemens, Lewis, and Postel (2018) had already shown that the ending of the bracero program had increased the adoption of new technology, but San is able to look at the patents themselves and show that it increases patenting activity in the affected sectors. Hornbeck and Naidu (2014) do something similar with agricultural technology in the American South, when the Great Mississippi Flood of 1927 led to the outmigration of thousands of Black workers. Places which got flooded adopted more capital intensive technology and modernized their farms, which creates the conditions for more innovation.

We can also have some (weaker) inferences from the literature on direct research subsidies. We should expect subsidies to increase innovation whether or not technological change is labor complementing or not, but in the cases where it is labor replacing these will be very similar to each other. Azoulay, Graff Zivin, Li, and Sampat (2018) used variation in grant funding to find that $10 million gets you 2.7 patents. Any plausible calculation of the social benefits would put that as a net positive – at the very least, $1 in NIH spending leads to $2.34 in eventual drug sales. A deregulation is also similar to a subsidy, which Parker Rogers (2023) uses to measure the impacts of medical device deregulation on innovation. In general, the FDA increasing costs for drug manufacturers will decrease the number of drugs discovered. (Many citations here: try Mulligan (2021) for starters.

Changes in demand will also direct innovation toward different things, perhaps even making it such that, in the long run, increases in demand decrease cost. Acemoglu and Linn (2004) use shifts in demographics as a plausibly exogenous shifter for the demand from different diseases, and find that (for example) having more old people will increase drug discoveries which treat diseases which affect the old. Xavier Jaravel (2019) uses incredibly disaggregated data on consumer purchases to show that, with rising income inequality, people at the top of the income spectrum saw more innovation and variety in the products which they tend to purchase.

The fundamental weakness of this literature is that it gives us partial equilibrium results, but cannot answer general equilibrium questions. Perhaps the loss of cheap labor resulted in more patents in that sector, but we cannot answer if it increased the total amount of innovation. That is invisible to us. We can’t see the people drawn out of research in other fields which may have been more fruitful, or drawn out of research altogether. In the case of direct subsidies, the total effects on patenting will probably be smaller than the partial equilibrium results, but it is at least pretty certain that it will draw more people into research as a whole. (It is also possible for the partial equilibrium results to be an underestimate, to the extent that we do not pick up on ideas in other fields which might be inspired by the research done there. However, I do not think this is that likely).

What about the effects of pushing natives into other, more innovative professions? We cannot directly measure it, but we can use an indirect argument. Suppose that it is now cheaper to hire a gardener or nanny. We can say that this is similar to a tax cut, and there is a substantial literature on the effect of tax rates on innovation. Akcigit, Grigsby, Nicholas, and Stantcheva (2022) use variation in state level corporate tax rates to draw out plausibly general equilibrium effects on innovation. “Do Tax Cuts Produce More Einsteins?” throws some cold water on this, though, with tax cuts having only a limited impact on the extensive margin. Since people vary in their talents, and the returns to innovating are incredibly skewed, changes in relatively low tax rates might have only an extremely limited impact on the total value of innovation, as Hall and Woodward (2010) argue. For a general overview, I highly recommend reading Chad Jones’ 2022 paper “Taxing Top Incomes in a World of Ideas”.

And of course, allowing high-skilled immigration increases the finding of new ideas. Marta Prato’s astonishing paper “The Global Race for Talent” documents that migrants who move between the EU and the US increase their patenting rate by 42% on average, relative to otherwise identical people who stayed behind, and that it actually increases the patenting rate of the people they worked with before they moved. These immigrant inventors are especially productive, with Bernstein, Diamond, Jiranaphawiboon, McQuade, and Pousada (2022) estimating that, despite being only 16% of total inventors, they are directly responsible for 23% of all inventive output, and plausible responsible 36% of all innovation through their spillovers. It is wildly implausible that keeping incredibly smart people from working in American universities is making our country better, and any sensible immigration policy would not do this. (cough).

My view is that I do not expect high prices which come from barriers to trade to lead to better outcomes in the long run. While there is a mechanism for it to do so, I expect it to be outweighed by other channels, and for new technologies to not be systematically labor replacing. I do not think we would make ourselves more prosperous in the long run by imposing minimum wages, or restricting immigration, or similar things to this.

(But Nicholas, what about Uzawa’s theorem? Shouldn’t all innovation be labor augmenting in the long run? Thank you, little demon of esotericism, for that objection. I think (to the extent I understand it) that Uzawa’s theorem is based around capital accumulating, but labor not. If there is an optimal ratio of capital to labor, and technology (“A” in the production function) improves, then capital will accumulate until it balances out. However, L in the production function includes human capital as well. Since we do not have a good way to disaggregate things, L is not actually labor, and it’s perfectly plausible for wages to go down due to automation.)

What does seem true to me is that we are substantially underinvesting in research and development. The optimal use of money on the margin isn’t obvious – it would not surprise me if the best course is to improve the pipeline of researchers, rather than rewarding the presently successful (especially if people are risk-averse and government policy is uncertain) – but we are so far from optimal that anything will do. We need to trade tens of billions of dollars in consumption subsidies for seniors for investment and research.