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I disagree with (5), that the long-term historical pattern is acceleration (and more specifically, I don't think that the first three charts in your linked piece are sufficient to demonstrate this).

At the frontier, real GDP per person growth has remained remarkably constant for the past ~200 years.

The growth rate for the world might show acceleration, but I understand this as a compositional effect, as more countries leave the zero/low growth regime and experience rapid catch-up growth. But in the long-run each country's growth rate will converge with the roughly constant rate at the frontier. Eventually we'll run out of countries joining the modern growth regime, and I'd then expect world real GDP per capita growth to slow. This paper from Robert Lucas describes the dynamics I'm talking about - see Figure 3 in particular (world growth accelerates and then slows and converges to the rate at the frontier).

And due to the near universal pattern of the Demographic Transition, I'd also expect population growth to trend towards zero in the long-run. So I wouldn't expect acceleration in the growth rate of total GDP either.

(FYI, I'm repeating my reasons for being unconvinced of David Roodman's piece on accelerating growth, which are in also in this Twitter thread).

Hope this is helpful!

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1jasoncrawford1yThat said, I agree that it's possible that the future could hold something different, and the demographic transition is a good reason why. Chad Jones has drawn attention to this. We need more people and more brains to continue growth. I tend to think we will solve this by (1) solving the fertility crisis and getting back to high rates of population growth, and/or (2) using AI to substitute for human researchers.

1SamHughes1yYes, that’s essentially the stylised model I use – i.e. I understand the long-run history of GDP per capita growth at the frontier as a transition from stagnation (/a very low rate) into sustained growth at a roughly constant rate. And it is very stylised (and I allow that the take-off may have been quite gradual), but I still think it works quite well as a basic framework. And I agree that Romer’s backwards projection implies that the rate of GDP per capita growth at the frontier has increased over time; but it doesn’t prove that this took the form of a constant acceleration across all of history, rather than a roughly discrete acceleration (described above). I don’t yet think that the Maddison data supports the idea of accelerating frontier growth across millennia. I think we need better country and year coverage to establish that claim. Better country coverage because the country at the frontier changes over time. Even if we see constant acceleration in country X’s GDP per capita growth rate between (say) 1-1800AD, it is unlikely that it was consistently at the frontier. We need to splice together data from various countries to get a timeseries of frontier growth. And better year coverage to avoid us relying on data points which may just so happen to be at a low or high point in a fluctuating cycle. We might have a higher estimate of GDP per capita in country Y for AD1000 than AD1, but I’d need more convincing to interpret that as long-run growth rather than our data point for AD1000 incidentally being a good year (or at the high point of a cycle which may span generations) and/or our data point for AD1 incidentally being a bad year (/low point in a cycle).

jasoncrawford1y1

FWIW, this Jones & Romer paper names “accelerating growth” as one of the key stylized facts that growth models should explain. See pp. 13–16.

One example of accelerating progress they give is from Nordhaus's famous “price of light” paper:

Between 38,000 B.C. and 1750 B.C., the real price of light fell by a total of about 17%, based on the transition from animal or vegetable fat to sesame oil as a fuel. The use of candles and whale oil reduced the price by a further 87% by the early 1800s, an average annual rate of decline of 0.06% per year. Between

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Where I have landed on “ideas getting harder to find”, in a nutshell

by jasoncrawford1 min read18th Oct 20236 comments

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Some very brief thoughts (for those who are familiar with these issues, sorry I am not including all the background/intro):

Ideas are getting harder to find (in the Jones/Bloom/et al sense of requiring exponentially increasing inputs to sustain exponential growth)
At the same time, we get better at finding them (more efficient and more total inputs)
Rates of growth have to be explained in terms of the balance of these factors, not one alone
Stagnation (i.e., slower growth) the last ~50 yrs is partially but not fully explained by this balance
Deceleration is a historical aberration; the long-term historical pattern is acceleration. This indicates that (2) generally outpaces (1) over the long term, and I see no reason for this to change in the foreseeable future

(If ideas getting harder to find were the only relevant factor, then progress would have been fastest in the hunter-gatherer era—so much low-hanging fruit! But again, the reality is the opposite trend.)

For a longer treatment of some of this, see this draft essay.

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[-]Max Olson1y 2

Agree on these points in general -- and believe this is one of the major reasons for optimism around AI. AI models seem particularly good at navigating high dimensional landscapes if we structure them appropriately. My theory is this will allows us to hugely increase #2, as we now have a better method for searching the solution space.

[-]SamHughes1y 1

I disagree with (5), that the long-term historical pattern is acceleration (and more specifically, I don't think that the first three charts in your linked piece are sufficient to demonstrate this).

At the frontier, real GDP per person growth has remained remarkably constant for the past ~200 years.

(FYI, I'm repeating my reasons for being unconvinced of David Roodman's piece on accelerating growth, which are in also in this Twitter thread).

Hope this is helpful!

[-]jasoncrawford1y 1

No, you're looking at too short a timescale [edit: to be clear, this is referring to your specific point about constant growth rates over the last 200 years]. Zoom out to the last few thousand, or few tens of thousand years.

See this from Paul Romer: https://paulromer.net/speeding-up-and-missed-opportunities-evidence/

Key excerpt:

My conviction that the rate of growth in GDP per capita at the technological frontier had to be increasing over time sprang from a simple calculation. Suppose the modern rate of growth of real GDP per capita (that is the growth rate after taking out the effects of inflation) is equal to 2% per year and that income per capita in year 2000 is $40,000. If this rate had prevailed for the last 1000 years, then in the year 1000, income per capita measured in the purchasing power of dollars today would have been $0.0001, or 0.01 cents. This is way too small to sustain life. If the growth rate had been falling over time instead of remaining constant, then the implied measure of GDP per capita in the year 1000 would have been even lower. …
Reasonable people can differ about what the future holds, but the simple calculation that first got me thinking about this (and which no doubt influenced how Maddison did the backward projections to come up with his estimates) leaves no room for doubt about what happened in the past. The rate of growth of GDP per capita has increased over time. The rate of progress in standards of living has increased even more.

[Further edit for clarity:] I think your contention is: there are basically two growth regimes. There is a low-growth regime, which most countries were in for most of history. Then there is a high-growth regime, which countries enter once they industrialize. This is an acceleration but it's a one-time thing. Any seeming longer-term, more-spread-out acceleration is just a compositional effect.

That is a reasonable hypothesis, but I think it's wrong. It may be true that there are discrete growth regimes, but I think there are more than two of them, historically. Progress was extremely slow in stone age. It sped up somewhat in the early agricultural age. It sped up more in the modern era after Gutenberg, Bacon, etc. It sped up more after industrialization. And I think it will speed up still more in the future—possibly after we cross some next threshold, whatever that is exactly.

[-]jasoncrawford1y 1

That said, I agree that it's possible that the future could hold something different, and the demographic transition is a good reason why. Chad Jones has drawn attention to this. We need more people and more brains to continue growth. I tend to think we will solve this by (1) solving the fertility crisis and getting back to high rates of population growth, and/or (2) using AI to substitute for human researchers.

[-]SamHughes1y 1

Yes, that’s essentially the stylised model I use – i.e. I understand the long-run history of GDP per capita growth at the frontier as a transition from stagnation (/a very low rate) into sustained growth at a roughly constant rate. And it is very stylised (and I allow that the take-off may have been quite gradual), but I still think it works quite well as a basic framework.

And I agree that Romer’s backwards projection implies that the rate of GDP per capita growth at the frontier has increased over time; but it doesn’t prove that this took the form of a constant acceleration across all of history, rather than a roughly discrete acceleration (described above).

I don’t yet think that the Maddison data supports the idea of accelerating frontier growth across millennia. I think we need better country and year coverage to establish that claim. Better country coverage because the country at the frontier changes over time. Even if we see constant acceleration in country X’s GDP per capita growth rate between (say) 1-1800AD, it is unlikely that it was consistently at the frontier. We need to splice together data from various countries to get a timeseries of frontier growth. And better year coverage to avoid us relying on data points which may just so happen to be at a low or high point in a fluctuating cycle. We might have a higher estimate of GDP per capita in country Y for AD1000 than AD1, but I’d need more convincing to interpret that as long-run growth rather than our data point for AD1000 incidentally being a good year (or at the high point of a cycle which may span generations) and/or our data point for AD1 incidentally being a bad year (/low point in a cycle).

[-]jasoncrawford1y 1

FWIW, this Jones & Romer paper names “accelerating growth” as one of the key stylized facts that growth models should explain. See pp. 13–16.

One example of accelerating progress they give is from Nordhaus's famous “price of light” paper:

Between 38,000 B.C. and 1750 B.C., the real price of light fell by a total of about 17%, based on the transition from animal or vegetable fat to sesame oil as a fuel. The use of candles and whale oil reduced the price by a further 87% by the early 1800s, an average annual rate of decline of 0.06% per year. Between 1800 and 1900, the price of light fell at an annual rate that was 38 times faster, 2.3%, with the introduction of the carbon filament lamp. And then in the 20th century, the price of light has fallen at the truly remarkable pace of 6.3% per year with the use of tungsten filaments and fluorescent lighting.