Since 1900, the global economy has grown by about 3% each year, meaning that it doubles in size every 20–30 years. I’ve written a report assessing whether significantly faster growth might occur this century. Specifically, I ask whether growth could be ten times faster, with the global economy growing by 30% each year. This would mean it doubled in size every 2–3 years; I call this possibility ‘explosive growth’.
The report builds on the work of my colleague, David Roodman. Although recently growth has been fairly steady, in the distant past it was much slower. David developed a mathematical model for extrapolating this pattern into the future; after calibration to data for the last 12,000 years, the model predicts that the global economy will grow ever faster over time and that explosive growth is a couple of decades away! My report assesses David’s model, and compares it to other methods for extrapolating growth into the future.
At first glance, it might seem that explosive growth is implausible — that it is somehow absurd or economically naive. Contrary to this view, I offer three considerations from economic history and growth theory that suggest advanced AI could drive explosive growth. In brief:
- The pace of growth has increased significantly over the course of history. Absent a deeper understanding of the mechanics driving growth, it would be strange to rule out future increases in growth.
- One important mechanism that increased growth over long-run history is the ideas feedback loop: more ideas → more people → more ideas. Sufficiently advanced AI systems could increase growth further via an analogous feedback loop: more ideas → more AI systems → more ideas.
- When you plug the assumption that AI systems can replace human workers into standard growth models (designed to explain growth since 1900), they often predict explosive growth.
These arguments don’t prove that advanced AI would drive explosive growth, but I think they show that it is a plausible scenario.
For AI to drive explosive growth, AI systems would have to be capable enough to replace human workers in most jobs, including cutting-edge scientific research, starting new businesses, and running and upgrading factories.
We think it’s plausible that sufficiently capable AI systems will be developed this century. My colleague Joe Carlsmith’s report estimates the computational power needed to match the human brain. Based on this and other evidence, my colleague Ajeya Cotra’s draft report estimates when we’ll develop human-level AI; she finds we’re 80% likely to do so by 2100. In a previous report I took a different approach to the question, drawing on analogies between developing human-level AI and various historical technological developments. My central estimate was that there’s a ~20% probability of developing human-level AI by 2100. These probabilities are consistent with the predictions of AI practitioners. Grace et al. (2017). Note, the precise definition of ‘human-level AI’ in these different forecasting methodologies discussed in this paragraph is slightly different.
Overall, I place at least 10% probability on advanced AI driving explosive growth this century. Roughly speaking, this corresponds to > 30% probability that human-level AI is developed in time for growth to ramp up to 30% by 2100, and > 1/3 that explosive growth actually happens conditional upon human-level AI being developed.
The report also discusses reasons to think growth could slow; I place at least 25% probability on the global economy only doubling every ~50 years by 2100.
This research informs Open Phil’s thinking about what kinds of impact advanced AI systems might have on society, and when such systems might be developed. This is relevant to how much to prioritize risks from advanced AI relative to other focus areas, and also to prioritizing within this focus area.
We elicited a number of reviews of drafts of the report.
The structure of this blog post is as follows:
- I clarify the question the report is answering: what would explosive growth actually look like? More.
- I say more about why Open Phil is interested in the question of explosive growth. More.
- I discuss the three reasons to think that explosive growth could occur this century. More.
- I briefly discuss objections to explosive growth occurring this century. More.
Note, many issues discussed in the report are not included in this blog. For example, the reasons for thinking the pace of growth might slow this century, the apparent difficulty of finding a convincing theory implying 21st century growth will be exponential, discussion of many of the objections to explosive growth occurring this century, and a model I developed for extrapolating GWP into the future.
I’d recommend that readers with a background in these issues read the report instead.
Acknowledgements: My thanks to Holden Karnofsky for prompting this investigation; to Ajeya Cotra for extensive guidance and support throughout; to Ben Jones, Dietrich Vollrath, Paul Gaggl, and Chad Jones for helpful comments on the report; to Anton Korinek, Jakub Growiec, Phil Trammel, Ben Garfinkel, David Roodman, and Carl Shulman for reviewing drafts of the report in depth; to Harry Mallinson for reviewing code I wrote for this report and helpful discussion; to Joseph Carlsmith, Nick Beckstead, Alexander Berger, Peter Favaloro, Jacob Trefethen, Zachary Robinson, Luke Muehlhauser, and Luisa Rodriguez for valuable comments and suggestions; and to Eli Nathan for extensive help with citations and the website.
What exactly do you mean by ‘explosive growth’?
One popular measure of the size of the global economy is Gross World Product (GWP). It generalizes the country-specific notion of Gross Domestic Product (GDP) to apply to the whole world. GWP is equal to the global population multiplied by the average annual global income:
$$ GWP=(number of people in the world)×(average income per person) $$
To double GWP you could, for example, double the number of people while keeping the average income the same. Or you could double the average income while keeping the number of people the same. In practice, GWP growth has historically involved increases in both the number of people and their incomes.
There’s another way to think about GWP. It also measures the total amount of stuff that the global economy produces each year, with each thing weighted by its value. This ‘stuff’ includes goods (food, clothes, books, gadgets) and services (Spotify, haircuts, doctors appointments, counseling, teaching). So to calculate GWP, just add up the value of all those goods and services bought during the year. Why are these two ways of defining GWP equivalent? GWP is complicated, but the rough idea is that all the money spent on goods and services ends up contributing to someone’s income.
With this way of thinking about it, there are again a few ways to double GWP. You could, for example, make twice as many things, holding the value of those things fixed (e.g. produce more food and more clothes each year). Or you could make the same number of things, but make them twice as valuable (e.g. make higher quality phones and laptops). Again, in practice GWP growth has involved both increases in the number of goods and services and increases in their quality.
So what would explosive growth look like? I define explosive growth as 30% GWP growth each year. As mentioned above, GWP currently doubles every 20–30 years; with explosive growth it would double every 2–3 years. Growth would be ten times faster. All the economic growth that currently happens in ten years worth of improvements to housing, medical care, computers, and software would all be crammed into just one year. Similarly, ten years’ worth of progress in physical sciences, engineering, life sciences and social sciences, agriculture, and manufacturing techniques, would on average happen every year. Certain sectors might see bigger increases in growth than others, as long as total growth is ten times faster. For example, fundamental physics might not grow any faster than today, but other sectors grow faster enough that overall economic growth is ten times faster than it is today.
Within ten years, we’d make as much technological and economic progress as has happened in the last 100 years.
This includes both developing new technologies and products and integrating them into the economy. For example, the process of electrification happened between 1880 and 1950 in the UK and the US. This involved moving from steam and water power to electricity in factories, and bringing electricity to individual households. If growth were ten times as fast, this process would have taken only 7 years.
Another example: the first commercial mobile phone was released in 1983; it cost about $10,000, a full charge took 10 hours, and it offered 30 minutes talk time. Today (2021) around 3.5 billion people use smartphones. See here. If growth were 10X faster, this change would have taken only 4 years.
Essentially, with explosive growth it would look as if technological change was happening much faster.
I should be clear that explosive growth would not necessarily be a good outcome; this depends on its effects on human welfare and the planet more generally.
Why are we interested in explosive growth?
Our interest in explosive growth mostly relates to one of our focus areas: potential risks from advanced AI. As part of this area, we want to know about the size and the timing of the impact of AI on society. The larger the impact, and the sooner the impact will be felt, the stronger the case for working on this focus area.
This report has relevance for both the size and the timing of the impact from advanced AI.
The relevance to size is clear. I conclude that an AI-driven growth explosion is a plausible scenario; so the size of AI’s impact could be very large indeed.
The relevance to timing is slightly more complex.
In her draft report, my colleague Ajeya Cotra uses the phrase ‘transformative AI’ (TAI) to mean ‘AI which drives Gross World Product (GWP) to grow at ~20–30% per year’. She estimates a high probability of TAI by 2100 (~80%), and a substantial probability of TAI by 2050 (~50%).
Intuitively speaking, these are very high probabilities to assign to an ‘extraordinary claim’. Are there strong reasons to dismiss these estimates as too high? One possibility is economic forecasting. If economic extrapolations gave us strong reasons to think GWP will grow at ~3% a year until 2100, this would rule out explosive growth and so rule out TAI being developed this century.
My report suggests economic considerations of this kind don’t provide a good reason to dismiss the possibility of TAI being developed in this century. In fact, there is a plausible economic perspective from which sufficiently advanced AI systems are expected to cause explosive growth. Explaining this perspective is the focus of the next section.
Why think explosive growth could occur this century?
I discuss three reasons to take the prospect of explosive growth seriously.
Growth has become much faster
The global economy, measured as GWP, currently doubles in size roughly every 30 years. But it used to grow much more slowly. Estimates suggest that, ten thousand years ago, GWP took around 3000 years to double. See, for example, data series from De Long (1998), McEvedy and Jones (1978), and Roodman (2020). The data on global population and living standards this early is highly uncertain. What is clear, however, is that growth was significantly slower at this time.
At earlier times, growth was even slower. This means that growth has perhaps accelerated 100X over the course of human history.
If growth has already become 100X faster, perhaps it will become another 10X faster in the future.
It is tempting to dismiss this possibility, and say that we cannot imagine anything that could drive such fast growth. But we should be wary of making arguments that would have led us astray in the past. Could hypothetical economists a thousand years ago, who saw the economy grow at a snail’s pace, have imagined how the processes of industrialization and technological innovation would allow the modern economy to double every 30 years? Probably not. We may be in a similar situation, unaware of mechanisms that could lead to growth becoming significantly faster.
One counter-argument is that growth of the richest countries’ economies hasn’t become faster since 1900, and in fact seems to have been slowing down over the last 20 years. This suggests that growth has reached its peak, and is now declining.
This argument has some appeal. However, 120 years of constant or slowing growth isn’t enough to confidently rule out growth increasing again in the future. For example, growth seems to have increased in the period 10,000 BCE to 1 CE, but then slowed over the next 1000 years (perhaps relating to the decline of the Roman Empire). But after this period growth picked up again, and eventually became much faster.
This first argument appeals to our humility. If we don’t understand why growth has become so much faster over long-run history, we should be open to it becoming faster still in the future. The next two arguments refer to specific theories of growth, arguing that they suggest that advanced AI could drive explosive growth.
A good explanation of long-run growth patterns implies advanced AI could drive explosive growth
The very long-run history of growth is roughly as follows. Until around 1700, GWP growth was very slow; it took hundreds of years for the economy to double in size. By 1900, growth was much faster, with the economy doubling every 20–30 years. Since then, growth has stayed pretty constant. See the following graph: Notice the y-axis is on a log-scale, and I have spaced the x-axis unevenly to show data going back to 10,000 BCE. The data is taken from the GWP series in Roodman (2020). The growth rates are calculated by assuming constant exponential growth between each pair of data points.
(Note: the graph seems to show growth increasing fairly smoothly over the last 10,000 years. However, the data is very uncertain, and it is possible that growth was roughly constant in the period 5,000 BCE to 1500 CE.)
Ten thousand years ago there was a relatively small human population that was very poor. Some of those people came up with ideas that allowed the population to grow in size. For example, one idea might be a new farming technique that allows you to feed a larger population; another might be a custom that reduces the chance of becoming unwell. To be concrete, let’s imagine that every 100 new ideas allows you to double the size of the population. Initially, the small population takes a long time — 3000 years — to come up with the 100 ideas needed to double the size of the population. But as the population increases, there are more people coming up with ideas, so it takes less time for the whole group to accumulate 100 new ideas. After a while there are enough people that it only takes 1000 years to come up with another 100 ideas, and so the population doubles in size more quickly. Later there’s even more people, and so it only takes 300 years to come up with the ideas needed to double the size of the population again. And so on.
So there is a feedback loop: more ideas → better farming techniques (or other innovations) → more food → more people → more ideas → … that leads growth to speed up over time. And if the population grows more and more quickly over time, so does GWP.
Let’s call this dynamic the ideas feedback loop. Its essence is more ideas → more people → more ideas. Idea-based theories of long-run growth claim that the ideas feedback loop caused growth to speed up over the last 10,000 years.
These theories are confirmed by the pattern of growth over the last 150 years.
Since around 1880, people in the richer countries have chosen to have fewer children even as they become wealthier. Since that point, “more ideas” have not led to “more people”, but instead to richer people: more ideas → richer people → more ideas. So the ideas feedback loop was broken.
Idea-based theories claim that the ideas feedback loop caused growth to speed up throughout history. The feedback loop was broken in ~1880, so these theories expect growth to stop increasing shortly after this time. Indeed, this is what happened. Since 1900, growth has been roughly constant, More precisely, growth of GDP/capita in countries on the economic frontier has been pretty constant since 1900. Growth of GWP actually increased from 1900 to 1960 due to increasing amounts of catch-up growth.
as idea-based theories would expect. Even though population has been increasing since 1900, idea-based theories do not imply that growth should have increased over this period. These theories can incorporate diminishing returns to efforts to generate more ideas, so that an exponentially growing population generates constant growth.
New ideas have caused GWP to increase in this period by increasing people’s wealth, but GWP growth itself has not increased as the ideas feedback loop is broken.
So idea-based theories provide a plausible explanation for why growth increased historically, and why it is now roughly constant.
Idea-based theories imply that advanced AI could cause growth to increase again.
Imagine if AIs could generate new ideas just as well as humans. They could come up with better computer designs (better hardware), and more efficient ways of running AIs on those computers (better software). As a result, more AIs could run on each computer. In addition, the AIs’ ideas could create wealth that is invested into creating more computers on which to run AIs.
The feedback loop would become: more ideas → better software, better hardware, and more wealth → more AI systems → more ideas →… The essence of this is another ideas feedback loop: more ideas → more AI systems → more ideas. This is closely analogous to the ideas feedback discussed above: more ideas → more people → more ideas. Before, the ideas feedback loop led to growth speeding up over time. It is natural to expect the same thing to happen in the case of AI.
To recap, the ideas feedback loop caused growth to speed up until ~1880, when it was broken. Since then, growth has been roughly constant. But advanced AI could cause the ideas feedback loop to apply once more. If this happens, growth should start speeding up again.
|Period||Ideas feedback loop?||Pattern of growth|
|Pre-1880||Yes: more ideas → more people → more ideas||GWP growth becomes faster over time|
|1880 – present||No: more ideas → richer people → more ideas||GWP grows at a constant rate|
|If human-level AI is developed||Yes: more ideas → more AI systems → more ideas||GWP growth becomes faster over time|
For this new ideas feedback loop to occur, AI would have to be capable enough to replace humans in a very wide-range of tasks relating to the discovery and implementation of new ideas. Examples include running start-ups, doing cutting edge scientific research, and making factories more efficient. If there are tasks essential to the discovery and implementation of new ideas that require humans, then humans may end up bottlenecking the growth process. With plausible parameter values (including the diminishing returns to idea discovery), these models predict explosive growth if you add in the assumption that AI can replace humans in all jobs. For interim cases, where AI can automate some but not all jobs, the growth outcome depends on the degree of diminishing returns to idea discovery and the importance of automated jobs to idea discovery and to economic output.
It implies that growth increased continuously over hundreds and thousands of years as the feedback loop gradually gathered momentum. However, most papers on long-run growth emphasize a different story, in which a structural change around the time of the industrial revolution causes a one-off increase in growth. For example, Hansen and Prescott (2002) discuss a model in which a phase transition in the methods of production increases growth. Initially the economy faces diminishing returns to labor due to the fixed factor land. But once the level of technology is high enough, it becomes profitable for firms to use less land-intensive production processes; this phase transition increases growth. Other examples of theories featuring one-off structural changes around the industrial revolution include Goodfriend and McDermott (1995), Lucas (1998), Stokey (2001), Tamura (2002) and Hanson (2000).
The mechanisms in these papers have a lesser tendency to suggest that advanced AI would increase growth.
The pre-modern data points are highly uncertain, so it’s hard to use them to assess the importance of the ideas feedback loop relative to other mechanisms. Kremer (1993) provides some additional evidence for the ideas feedback loop. Kremer looks at the development of five isolated regions and finds that the technology levels of the regions in 1500 are perfectly rank-correlated with their initial populations in 10,000 BCE. This is just what the ideas feedback loop mechanism would predict.
The report discusses the evidence that we do have in more detail. Overall, I think that while significant structural changes did happen around the industrial revolution, the ideas feedback loop played an important role in causing growth to accelerate over the last 10,000 years. For this reason, I take idea-based theories seriously, including their implication that sufficiently advanced AI would drive explosive growth.
When you plug the assumption that AI systems can replace human workers into standard growth models, they often predict explosive growth
Imagine if I built 1 billion laptops of the highest quality, and gave them to the human workers whose work productivity would most benefit from a new laptop. The laptops would make the workers more productive, raising GWP. Then suppose I made another 1 billion laptops, again distributing them to people whose productivity would benefit the most. This would still raise productivity somewhat, as some people could still be made more productive with new laptops. But by the time I’ve already made 10 billion laptops, the next billion will make little difference to global productivity. This is because the laptops need human workers in order to be useful, and there’s a limited supply of human workers. This puts a limit to how much I can boost GWP just by making laptops. The same is true of many other physical machines and gadgets I might make to boost productivity.
But now suppose that, as well as making laptops, I can also make AI systems that can use a laptop to do any work that a human could do with it. In this scenario, there would not be a limited supply of workers. So there may be a much higher limit on how much I can boost GWP by making more laptops and making more AI systems together. In this scenario, the returns to creating more physical machines (in this case AI systems and laptops) are much higher because human workers have been removed as a bottleneck.
Economic growth models used to explain growth since 1900 reinforce this point. They typically show diminishing returns to physical equipment and machines (‘capital‘), holding the number of human workers fixed. This means that each new machine adds less and less value to the economy. These diminishing returns limit the amount of growth you can have solely by producing more physical machines.
But when you plug into these models the assumption that AI can replace human workers in a very wide range of tasks, In many models, the specific assumption required is that the elasticity of substitution between capital and labor rises above 1.
The diminishing returns to physical machines can disappear, as machines can now play the role previously played by human workers. Many models predict that explosive growth occurs in this scenario. If AIs allow us to automate all jobs, both in goods and services production and in idea discovery, these models predict explosive growth for realistic parameter values. If we can only automate goods and services production (but not idea discovery), or only idea discovery (but not goods and services), then these models predict explosive growth for some realistic parameter values but not for others. In interim cases, where we can automate only a subset of the tasks in goods and services production and idea discovery, then the pace of growth depends on the parameter values and on how quickly new tasks become automatable.
To put things another way, consider the following feedback loop: machines produce goods and services, increasing our wealth; we invest some of this wealth into making more machines; we now have even more machines with which to create even more wealth; and so on. In short: more machines → more wealth → more machines →…. At the moment, this feedback loop is fairly weak because there are diminishing returns to additional machines. But if the machines included AI systems that can replace human workers (a key assumption), then this feedback loop becomes more powerful and can drive explosive growth.
Recap of reasons to expect explosive growth
So we’ve seen three arguments to think explosive growth is plausible:
- The pace of growth has increased significantly over the course of history. Absent a deeper understanding of the mechanics driving growth, it would be strange to rule out future increases in growth.
- Idea-based theories claim that growth increased in the past due to an ideas feedback loop: more ideas → more people → more ideas. Sufficiently advanced AI systems could drive explosive growth via an analogous feedback loop: more ideas → more AI systems → more ideas.
- When you plug the assumption that AI systems can replace human workers into standard growth models (designed to explain the last 100 years of growth), they often predict explosive growth.
The first argument will be more convincing if you’re skeptical of the specific models of growth underlying the second and third arguments.
The second and third arguments unite in pointing to advanced AI as a possible cause of faster growth. In fact, they are closely linked. Both stem from the fact that when you change standard growth models by introducing the strong assumption that AIs can replace human workers in wide-ranging tasks, these models typically predict that growth will accelerate. Though the mathematical models underlying the second and third arguments are partially overlapping, the arguments differ in their emphasis. The second argument emphasizes very long-run data in which growth has in fact increased over time; we then draw an analogy between the mechanisms driving the growth increase and the mechanisms of advanced AI. To doubt this second argument, you can either doubt its explanation of why growth increased in the past, or the analogy with AI. The third argument emphasizes models based on recent data in which growth is constant. It augments these models with an extreme assumption (machines can replace human workers) and notes that the models then predict explosive growth. To doubt this third argument, you can either question the models’ explanation of the recent data, or whether the models’ predictions can be trusted when such an extreme assumption has been made.
How likely is explosive growth to actually happen?
Predicting the pattern of long-run growth is inevitably speculative. Though I think the above arguments are suggestive, they do not prove that advanced AI would cause explosive growth. There are many possible reasons for skepticism:
- Perhaps some unanticipated bottleneck will slow down growth.
- For example, economic growth might require extracting and transporting raw materials (e.g. to make new computers). If this process can’t be sped up beyond a certain point, this could bottleneck growth.
- Alternatively, growth might require conducting experiments to make scientific and technological progress. If these experiments take a long time, this could bottleneck growth.
- I view this as one of the strongest objections to explosive growth occurring.
- Perhaps we will choose to grow slowly and sustainably, even if AI gives us the ability to grow much faster.
- There is evidence that ideas are becoming harder to find. If this trend continues, perhaps it will prevent AIs finding ideas quickly enough to drive explosive growth? The models I have seen predict that, if AI systems can replace human workers, there will be explosive growth despite ideas becoming harder to find. However, if this effect becomes significantly more pronounced, it could prevent explosive growth.
- Perhaps there will be some essential tasks that advanced AI never automates, and these will bottleneck the growth process.
- Perhaps there are fundamental limits to how good our technology can become, and we will approach these limits before explosive growth occurs.
- Perhaps the accumulation of physical or human capital has been the most important driver of historical growth, and advanced AI will not significantly accelerate this process. I argue in favor of idea-based theories over these accumulation theories in the full report, but still assign some weight to accumulation theories (10–20%). Though some accumulation theories imply that advanced AI could drive explosive growth (if they can replace human workers), some do not straightforwardly imply this (e.g. it would depend on how advanced AI affects the rate of human capital accumulation, or how quickly AIs accumulate their own equivalent to human capital).
- Perhaps our understanding of the determinants of growth is very poor, and the true determinants simply will not lead to explosive growth regardless of the AI systems we develop.
I discuss these reasons for skepticism, and many others, in the full report. I find some of them partially convincing, and they reduce the probability I assign to explosive growth. However, I don’t think they justify ruling out explosive growth. I personally assign at least 10% probability to explosive growth occurring by 2100.Roughly speaking, this corresponds to > 30% probability that human-level AI is developed in time for growth to ramp up to 30% by 2100, and > 1/3 that explosive growth actually happens conditional upon human-level AI being developed. My central estimate of the probability of explosive growth is not stable, but it is currently around 25% — see Appendix G of the report.
The full report also discusses a contrasting possibility, that growth stagnates. I find this scenario to be highly plausible, and assign it at least 25% probability. Again, my central estimate is not stable, but it is currently around 40%.
There’s evidence that technological progress is becoming increasingly difficult. According to one plausible theory, we’ve only maintained steady growth since 1900 by increasing the number of researchers exponentially over time. But population projections suggest this exponential increase cannot be sustained (assuming we don’t develop AI systems to do the research for us). In this case, growth in living standards will slow.
Thus my view is that the possibilities for long-run growth are wide open. Both explosive growth and stagnation are plausible.