For instance, my understanding is that European nations experienced substantial per-capita growth in the centuries leading up to the industrial revolution. And unlike farming, the industrial revolution had no single cause that we can point to that makes it a distinct technological “revolution”, or phase shift. An alternative explanation is that what we call the industrial revolution is simply the latest part of the hyperbolic growth trend that humanity has experienced since roughly 10,000 BC.
Your first point is not correct according to the data I have. It’s only the UK and the Netherlands that experienced substantial per capita growth before the end of the Napoleonic Wars, and their growth pattern is consistent with a smoother phase transition.
I don’t think it’s necessary for a new phase to be associated clearly with a new technology. I agree that such an association makes the break from the previous phase much clearer, but I already think the break between the last phase and the current phase is clear, so...
I really don’t think hyperbolic growth fits the data well at all. I’m honestly mystified by how so many people seem to take it so seriously—how does hyperbolic growth explain two centuries of approximately constant GDP per capita growth trend in the US or in the UK? A stochastic model can just explain it as a coincidence, but then the likelihood ratio should lead you to update away from a hyperbolic model.
One interesting fact about our era is that growth has recently slowed since 1960.
I think this is very unclear because of difficulties in measuring inflation accurately due to changes in the nature of goods produced that have taken place since 1960. I think it’s possible (20%) that in fact growth didn’t slow down at all.
In particular, I am inclined towards Michael Kremer’s explanation that the rate of technological progress is proportional to the total population.
The fact that the Industrial Revolution began in Europe and not China or India, and the fact that it was so difficult of a process for it to spread to those places once it was already here, is evidence against this view. I agree more people is good for growth for this reason and others (specialization & division of labor, for example) but it only explains a small fraction of the variance in outcomes here. Even in Europe the Industrial Revolution began in Britain and the Netherlands, not France or Spain as this population model would have led us to expect.
Compared to the exponential growth sequence model, Kremer’s model provides a much stronger theoretical foundation for AI-accelerated growth. This is because if we assume that AI can substitute for labor, then the effect of declining population growth from the demographic transition can be negated by growth in AI, allowing us to proceed on our previous hyperbolic trajectory.
Even if this happened, my model of what would happen is not hyperbolic. I think it would more or less be another phase shift which would last for some number of doublings before we hit diminishing returns or something else happened. A hyperbolic trajectory just seems like wishful thinking to me.
Relatedly, I agree that the outside view of historical economic growth provides a relatively weak reason to expect transformative growth in the relative near-term (say, the next 100 years), but I think we shouldn’t rely too much on simple extrapolation in this case. The main reason why the long-run historical growth data is important is because it validates the model that population growth and technological progress work together, in a way that predicts a singularity. Since this model is the primary justification given for transformative growth under AI in economic models, the long-run data provides a relatively strong update towards the plausibility of transformative growth this century.
I don’t agree that long-run historical growth data actually validates this. My belief that population size matters for technological growth comes mostly from my own priors rather than any updates I’ve made on the basis of looking at what happened in the past.
Overall, I really want someone who is a proponent of the hyperbolic model to explain to me why this model is so popular, because to me it seems obviously wrong. I’d be happy to schedule a call with someone just for this purpose.
Overall, I really want someone who is a proponent of the hyperbolic model to explain to me why this model is so popular, because to me it seems obviously wrong. I’d be happy to schedule a call with someone just for this purpose.
Could you describe an alternative model that you think has a less bad fit to the historical data?
(If you are just saying this on the basis of qualitative data, I disagree but don’t think it’s going to be helpful to try to resolve here.)
I think mixture of exponentials is a significantly worse fit and have tried to do this exercise myself. If you disagree then I’d be quite happy for you to describe a probability distribution over time series which you think is better than the natural stochastic hyperbolic model (and I will bring the stochastic hyperbolic model). By default I won’t include an explicit model of autocorrelations unless you do, and if I did it would be a very simple representation with a reasonable prior over any hyperparameters involved rather than hard-coding them.
You can pick the times and places where you think the data is good enough that it’s worth modeling, and even provide your own time series if you think the hyperbolic growth proponents are making a mistake about which data to trust. E.g. I’d be fine if you want to do it in just the UK or europe, or using best guess global time series, or using best guess global time series since 1000 AD if you don’t trust them before that (since they are quite wild guesses). Or if you want to fit to a variety of different local time series. Whichever.
I think if this exercise favored a mixture of exponentials that would be a significant update for me. So far every time I’ve looked into it a mixture of exponentials has seemed significantly worse, which is a large part of how I ended up with this view (e.g. it basically ends up with totally different hyperparameters for each population studied, fitting it up through year X gives you bad predictions about year X+100, when I do the calculation formally it looks bad...). But I think those exercises have been hamstrung by not having any proponent of the mixtures of exponential view write down a formal model that could be evaluated without hindsight bias.
how does hyperbolic growth explain two centuries of approximately constant GDP per capita growth trend in the US or in the UK?
It seems to me like this fact is often overstated or cherry-picked. E.g. Our world in data has UK GDP per capita at 2.3k pounds in 1800, 4.9k in 1900, and 24.4k in 2000. That’s more than twice as fast in the second century as the first. Moreover, from 1800-1900 the UK seems much more plausible to me than the US as a proposal for a frontier economy (rather than one benefiting from catchup growth and expansion into new territory).
Hyperbolic models are definitely surprised that acceleration here was more like 2x instead of 4x. There are obvious factors they ignore like low fertility that seem crucial to explaining that gap. But most of all they are surprised by the apparent slowdown in growth since 1960 instead of continued acceleration.
I don’t find the accusation particularly compelling unless you want to suggest an alternative model.
Broadly speaking I think that on hyperbolic models the “great stagnation” is definitely a real thing and it’s a lot of noise, and it generates a lot of ongoing surprise if you don’t include autocorrelations.
(Whereas on growth mode models this is the typical state of affairs punctuated by periodic transitions—unless you want to use something like Robin’s model, which is also surprised by the great stagnation rather than ongoing acceleration to 12%/year growth.)
Even if this happened, my model of what would happen is not hyperbolic. I think it would more or less be another phase shift which would last for some number of doublings before we hit diminishing returns or something else happened. A hyperbolic trajectory just seems like wishful thinking to me.
To be clear, I don’t think anyone relevant in this debate has suggested that growth will literally go to infinity. The claim is typically that we will proceed on a hyperbolic trajectory until we run into physical constraints, coupled with the claim that physical constraints aren’t very limiting. For example, many people think it’s plausible that with AI, we could get to >1000% world GDP growth before running out of steam.
Your first point is not correct according to the data I have. It’s only the UK and the Netherlands that experienced substantial per capita growth before the end of the Napoleonic Wars, and their growth pattern is consistent with a smoother phase transition.
I don’t think it’s necessary for a new phase to be associated clearly with a new technology. I agree that such an association makes the break from the previous phase much clearer, but I already think the break between the last phase and the current phase is clear, so...
I really don’t think hyperbolic growth fits the data well at all. I’m honestly mystified by how so many people seem to take it so seriously—how does hyperbolic growth explain two centuries of approximately constant GDP per capita growth trend in the US or in the UK? A stochastic model can just explain it as a coincidence, but then the likelihood ratio should lead you to update away from a hyperbolic model.
I think this is very unclear because of difficulties in measuring inflation accurately due to changes in the nature of goods produced that have taken place since 1960. I think it’s possible (20%) that in fact growth didn’t slow down at all.
The fact that the Industrial Revolution began in Europe and not China or India, and the fact that it was so difficult of a process for it to spread to those places once it was already here, is evidence against this view. I agree more people is good for growth for this reason and others (specialization & division of labor, for example) but it only explains a small fraction of the variance in outcomes here. Even in Europe the Industrial Revolution began in Britain and the Netherlands, not France or Spain as this population model would have led us to expect.
Even if this happened, my model of what would happen is not hyperbolic. I think it would more or less be another phase shift which would last for some number of doublings before we hit diminishing returns or something else happened. A hyperbolic trajectory just seems like wishful thinking to me.
I don’t agree that long-run historical growth data actually validates this. My belief that population size matters for technological growth comes mostly from my own priors rather than any updates I’ve made on the basis of looking at what happened in the past.
Overall, I really want someone who is a proponent of the hyperbolic model to explain to me why this model is so popular, because to me it seems obviously wrong. I’d be happy to schedule a call with someone just for this purpose.
Could you describe an alternative model that you think has a less bad fit to the historical data?
(If you are just saying this on the basis of qualitative data, I disagree but don’t think it’s going to be helpful to try to resolve here.)
I think mixture of exponentials is a significantly worse fit and have tried to do this exercise myself. If you disagree then I’d be quite happy for you to describe a probability distribution over time series which you think is better than the natural stochastic hyperbolic model (and I will bring the stochastic hyperbolic model). By default I won’t include an explicit model of autocorrelations unless you do, and if I did it would be a very simple representation with a reasonable prior over any hyperparameters involved rather than hard-coding them.
You can pick the times and places where you think the data is good enough that it’s worth modeling, and even provide your own time series if you think the hyperbolic growth proponents are making a mistake about which data to trust. E.g. I’d be fine if you want to do it in just the UK or europe, or using best guess global time series, or using best guess global time series since 1000 AD if you don’t trust them before that (since they are quite wild guesses). Or if you want to fit to a variety of different local time series. Whichever.
I think if this exercise favored a mixture of exponentials that would be a significant update for me. So far every time I’ve looked into it a mixture of exponentials has seemed significantly worse, which is a large part of how I ended up with this view (e.g. it basically ends up with totally different hyperparameters for each population studied, fitting it up through year X gives you bad predictions about year X+100, when I do the calculation formally it looks bad...). But I think those exercises have been hamstrung by not having any proponent of the mixtures of exponential view write down a formal model that could be evaluated without hindsight bias.
It seems to me like this fact is often overstated or cherry-picked. E.g. Our world in data has UK GDP per capita at 2.3k pounds in 1800, 4.9k in 1900, and 24.4k in 2000. That’s more than twice as fast in the second century as the first. Moreover, from 1800-1900 the UK seems much more plausible to me than the US as a proposal for a frontier economy (rather than one benefiting from catchup growth and expansion into new territory).
Hyperbolic models are definitely surprised that acceleration here was more like 2x instead of 4x. There are obvious factors they ignore like low fertility that seem crucial to explaining that gap. But most of all they are surprised by the apparent slowdown in growth since 1960 instead of continued acceleration.
I don’t find the accusation particularly compelling unless you want to suggest an alternative model.
Broadly speaking I think that on hyperbolic models the “great stagnation” is definitely a real thing and it’s a lot of noise, and it generates a lot of ongoing surprise if you don’t include autocorrelations.
(Whereas on growth mode models this is the typical state of affairs punctuated by periodic transitions—unless you want to use something like Robin’s model, which is also surprised by the great stagnation rather than ongoing acceleration to 12%/year growth.)
To be clear, I don’t think anyone relevant in this debate has suggested that growth will literally go to infinity. The claim is typically that we will proceed on a hyperbolic trajectory until we run into physical constraints, coupled with the claim that physical constraints aren’t very limiting. For example, many people think it’s plausible that with AI, we could get to >1000% world GDP growth before running out of steam.