This is a linkpost for a paper I wrote recently, “Endogenous Growth and Excess Variety”, along with a summary.

Two schools in growth theory

Roughly speaking:

In Romer’s (1990) growth model, output per person is interpreted as an economy’s level of “technology”, and the economic growth rate—the growth rate of “real GDP” per person—is proportional to the amount of R&D being done. As Jones (1995) pointed out, populations have grown greatly over the last century, and the proportion of people doing research (and the proportion of GDP spent on research) has grown even more quickly, yet the economic growth rate has not risen. Growth theorists have mainly taken two approaches to reconciling [research] population growth with constant economic growth.

“Semi-endogenous” growth models (introduced by Jones (1995)) posit that, as the technological frontier advances, further advances get more difficult. Growth in the number of researchers, and ultimately (if research is not automated) population growth, is therefore necessary to sustain economic growth.

“Second-wave endogenous” (I’ll write “SWE”) growth models posit instead that technology grows exponentially with a constant or with a growing population. The idea is that process efficiency—the quantity of a given good producible with given labor and/or capital inputs—grows exponentially with constant research effort, as in a first-wave endogenous model; but when population grows, we develop more goods, leaving research effort per good fixed. (We do this, in the model, because each innovator needs a monopoly on his or her invention in order to compensate for the costs of developing it.) Improvements in process efficiency are called “vertical innovations” and increases in good variety are called “horizontal innovations”. Variety is desirable, so the one-off increase in variety produced by an increase to the population size increases real GDP, but it does not increase the growth rate. Likewise exponential population growth raises the technology growth rate from the positive rate that obtains when the population is fixed, by adding a horizontal dimension to the constant vertical dimension, but the result is still a constant rather than an ever-rising growth rate.

There are other approaches. For instance:

• Dinopoulos and Syropoulos (2007) explore the possibility that a growing population does not yield a faster growth rate because the increase in research capacity is offset by an increase in rent-seeking behavior.
• Patrick Collison suggested in 2019 that researchers have gotten dramatically less productive over time due to rises in red tape and, relatedly, perhaps changes in culture. Naturally, the “progress studies” movement he helped to launch largely studies how to restore the institutions and culture that, on this view, once allowed a small number of researchers to get a lot done.

But the semi-endogenous and SWE approaches are easily the main two in the current growth theory literature.

The EA community’s use of growth theory

As far as I’m aware, when people in the EA community have used a growth model to predict the impact of advanced AI—or indeed for any other purpose—it’s almost always been semi-endogenous. Leopold Aschenbrenner used the semi-endogenous approach in the original draft of his (originally 2019) paper on existential risk and growth; Anton Korinek and I use it almost exclusively when discussing the automation of R&D in our (originally 2020) literature review on AI and growth; Davidson (2021) predominantly endorses the semi-endogenous approach when evaluating the growth impact of advanced AI; Davidson (2022) uses it when evaluating whether Open Phil should fund basic science; Erdil et al. (2023) use it in their survey paper on estimating the technology production function; and Davidson et al. (2025) and the Epoch team (2025) use it in their respective models of the feedback loops underlying an intelligence explosion.

On (a standard implementation of) the semi-endogenous approach, the developed world is already growing about as fast as it can. Since both schools agree that the main bottleneck to output at a given time is lack of labor, and since on a semi-endogenous growth account the main bottleneck to growth in output per unit of labor is a lack of R&D talent broadly construed, relieving these bottlenecks through automation will accelerate growth dramatically. Even sufficiently partially automating production and R&D is enough to make growth hyperbolic.^[1]

My own best guess is that the idea behind the semi-endogenous approach—that it’s harder to make technological progress when technology is further advanced—is responsible for most of the long slowdown in technological progress per unit of research effort. But not all, even on my inside view; and my outside view can’t ignore the fact that a lot of growth theorists believe the SWE story.^[2] Bloom et al. (2020) tried to settle the debate by showing that a growth in research effort has been necessary to sustain exponential growth even in our efficiency at producing various individual goods, but they didn’t. As Aghion et al. (2025) point out, this observation is compatible with the possibility that the number of product lines remains proportional to the population, but that when vertical innovation on a given product gets too difficult, entrepreneurs replace it with a new product with room for vertical innovation.

All told, I've been a bit worried for a while that the EA community has anchored too much on the semi-endogenous view, due to flukes like the fact that its main proponent (Chad Jones) has also long been interested in AI, x-risk, and the long term, and the fact that various EA researchers (including Tom Davidson and me) happen to find it compelling.

A new challenge for the SWE approach

So I figured that, instead of yet another refinement of the semi-endogenous take on automation and growth, it might be worth doing a first-pass look at what the impact of automation on growth will be if the SWE approach is right after all. In the process I noticed something strange about SWE models that hadn’t been noted in the literature before.

Davidson (2021) made me suspect the issue by helpfully noting that one SWE paper, Peretto (2018), under most parameter values implies that if only we fixed the range of products and kept our total R&D efforts fixed, growth would be hyperbolic. It turns out that the issue is much more pervasive, and much worse. Almost all SWE papers, including Peretto (2018) under all parameter values, imply that if we quickly shrank the range of products, we could produce infinite real GDP in arbitrarily little time!^[3] What happens is:

1. The reason why growth is exponential with a fixed population is that a fixed population doesn’t spread its research effort across an ever wider array of products. To conclude that this isn’t wildly inefficient, we say that it’s possible to make up for a lack of new products with sufficiently large quantities of the old products.
2. But by stipulation, with a constant number of researchers per product, growth is exponential. So if we shrank the range of products to zero, then even with a fixed population, growth in the remaining products would be superexponential. By (1), this would make up for the lack of variety. The faster we shrink the range, the better.

Taken literally, this conclusion relies on the assumption that the range of products is a continuum (so it can shrink toward zero) and that it’s feasible to instantaneously reallocate research effort from one product to another. But even if we acknowledge some frictions of this sort, the conclusion that it would be extremely, extremely desirable to shrink the range of products (and subsidize R&D on the existing range, so people do it despite not getting a monopoly afterward) seems hard to avoid within a standard SWE model. This seems implausible on its face, and especially implausible when we remember that any country, or even firm or philanthropic organization, could have implemented it this whole time.

Two responses, and their implications for the growth impact of automation

Only one SWE model avoids a conclusion along these lines: the first one, Young (1998). It avoids the conclusion by positing that vertical innovation faces severely diminishing returns to research labor, so that in effect, a larger population can only be employed productively in research if the range of goods widens.

So it seems that, if we accept the SWE approach, there are basically two possibilities. As it happens, they respectively widen the range of possibilities around the baseline of “hyperbolic growth past some automation threshold” we would get from a semi-endogenous model.

First, maybe there are severely diminishing returns to investments in vertical innovation. In the extreme case, maybe the exponential growth rate in how efficiently we can produce any given product is bounded above by some g, no matter how many people (or automated researchers) are working simultaneously on improving this efficiency. This doesn’t seem so crazy to me: maybe no research team, however large or brilliant, could double the process efficiency of a given assembly line (let alone supply chain) in five minutes. On this view, even in the event of full automation, output will grow at best double-exponentially, like $e^{e^{gt}}$: fixing process efficiency, output would grow exponentially, as the robots build more robots, but the rate at which the robots self-replicate is itself growing exponentially. In this case, the growth rate rises without bound after full automation, but it may rise relatively slowly.

Second, and I think much less plausibly, maybe economic growth has proceeded insanely inefficiently this whole time. We could have had hyperbolic growth all along by focusing our research efforts on a narrow range of products, but because each entrepreneur needs a new patent or trade secret, we keep pouring immense resources into reinventing the wheel, and all we get for it is a mildly desirable increase in the variety of wheels to buy. In this case, we will be able to get extremely fast growth simply by creating automated researchers that can coordinate well enough to avoid this issue, even if they can’t self-replicate or build anything at all, and even if they’re no smarter or more numerous than the population of human researchers generations ago.

1. ^{^}

   See Aghion et al. (2019), Section 4.1, example 3. For a corrected proof see Trammell and Korinek (2023), Section 6.

2. ^{^}

   See the paper for an up-to-date literature review. I do think a disproportionate number of growth theorists wind up writing about the SWE approach because it’s trickier to get it to work: the same reason I and many utilitarians give for why relatively few moral philosophers are utilitarians. If you think Bentham solved ethics in 1861, or Jones solved growth in 1995, you’re more likely to work on problems you see as unsolved. Still, while some position remains a common view in its academic field I'm reluctant to completely dismiss it.

3. ^{^}

   It's pretty obvious once you see it, but no one in the Stanford growth group, including Jones—and, as far as I can tell, none of the SWE authors I’ve emailed—had noticed this!