I think that Hanson’s “series of 3 exponentials” is the neatest alternative, although I also think it’s possible that pre-modern growth looked pretty different from clean exponentials (even on average / beneath the noise). There’s also a semi-common narrative in which the two previous periods exhibited (on average) declining growth rates, until there was some ‘breakthrough’ that allowed the growth rate to surge: I suppose this would be a “three s-curve” model. Then there’s the possibility that the growth pattern in each previous era was basically a hard-to-characterize mess, but was constrained by a rough upper bound on the maximum achievable growth rate. This last possibility is the one I personally find most likely, of the non-hyperbolic possibilities.
It seems almost guaranteed that the data is a mess, it just seems like the only difference between the perspectives is “is acceleration fundamentally concentrated into big revolutions or is it just random and we can draw boundaries around periods of high-growth and call those revolutions?”
There may also be some fundamental meta-prior that matters, here, about the relative weight one ought to give to simple unified models vs. complex qualitative/multifactoral stories.
Which growth model corresponds to which perspective? I normally think of “‘industry’ is what changed and is not contiguous with what came before” as the single-factor model, and multifactor growth models tending more towards continuous growth.
A lot of my prior comes down to my impression that the dynamics of growth just *seem * very different to me for forager societies, agricultural/organic, and industrial/fossil-fuel societies.
I’m definitely much more sympathetic to the forager vs agricultural distinction.
Does a discontinuous change from fossil-fuel use even fit the data? It doesn’t seem to add up at all to me (e.g. doesn’t match the timing of acceleration, there are lots of industries that seemed to accelerate without reliance on fossil fuels, etc.), but would only consider a deep dive if someone actually wanted to stake something on that.
I don’t think the post-1500 data is too helpful help for distinguishing between the ‘long run trend’ and ‘few hundred year phase transition’ perspectives.
If there was something like a phase transition, from pre-modern agricultural societies to modern industrial societies, I don’t see any particular reason to expect the growth curve during the transition to look like the sum of two exponentials. (I especially don’t expect this at the global level, since diffusion dynamics are so messy.)
It feels to me like I’m saying: acceleration happens kind of randomly on a timescale roughly determined by the current growth rate. We should use the base rate of acceleration to make forecasts about the future, i.e. have a significant probability of acceleration during each doubling of output. (Though obviously the real model is more complicated and we can start deviating from that baseline, e.g. sure looks like we should have a higher probability of stagnation now given that we’e had decades of it.)
It feels to me like you are saying “No, we can have a richer model of historical acceleration that assigns significantly lower probability to rapid acceleration over the coming decades / singularity.”
So to me it feels like as we add random stuff like “yeah there are revolutions but we don’t have any prediction about what they will look like” makes the richer model less compelling. It moves me more towards the ignorant perspective of “sometimes acceleration happens, maybe it will happen soon?”, which is what you get in the limit of adding infinitely many ex ante unknown bells and whistles to your model.
The papers typically suggest that the thing kicking off the growth surge, within a particular millennium, is the beginning of intensive agriculture in that region — so I don’t think the pivotal triggering event is really different.
Is “intensive agriculture” a well-defined thing? (Not rhetorical.) It didn’t look like “the beginning of intensive agriculture” corresponds to any fixed technological/social/environmental event (e.g. in most cases there was earlier agriculture and no story was given about why this particular moment would be the moment), it just looked like it was drawn based on when output started rising faster.
I wouldn’t necessarily say they were significantly faster. It depends a bit on exactly how you run this test, but, when I run a regression for “(dP/dt)/P = a*P^b” (where P is population) on the dataset up until 1700AD, I find that the b parameter is not significantly greater than 0. (The confidence interval is roughly -.2 to .5, with zero corresponding to exponential growth.)
I mean that if you have 5x growth from 0AD to 1700AD, and growth was at the same rate from 10000BC to 0AD, then you would expect 5^(10,000/1700) = 13,000-fold growth over that period. We have uncertainty about exactly how much growth there was in the prior period, but we don’t have anywhere near that much uncertainty.
Doing a regression on yearly growth rates seems like a bad way to approach this. It seems like the key question is: did growth speed up a lot in between the agricultural and industrial revolutions? It seems like the way to pick that is to try to use points that are as spaced out as possible to compare growth rates in the beginning and late part of the interval from 10000BC to 1500AD. (The industrial revolution is usually marked much later, but for the purpose of the “2 revolutions” view I think you definitely need it to start by then.)
So almost all of the important measurement error is going to be in the bit of growth in the 0AD to 1500AD phase. If in fact there was only 2x growth in that period (say because the 0AD number was off by 50%) then that would only predict 100-fold growth from 10,000BC to 0AD, which is way more plausible.
The industrial era is, in comparison, less obviously different from the farming era, but it also seems pretty different. My list of pretty distinct features of pre-modern agricultural economies is: (a) the agricultural sector constituted the majority of the economy; (b) production and (to a large extent) transportation were limited by the availability of agricultural or otherwise ‘organic’ sources of energy (plants to power muscles and produce fertiliser); (c) transportation and information transmission speeds were largely limited by windspeed and the speed of animals; (d) nearly everyone was uneducated, poor, and largely unfree; (e) many modern financial, legal, and political institutions did not exist; (f) certain cultural attitudes (such as hatred of commerce and lack of belief in the possibility of progress) were much more common; and (g) scientifically-minded research and development projects played virtually no role in the growth process.
If you just keep listing things, it stops being a plausible source of a discontinuity—you then need to give some story for why your 7 factors all change at the same time. If they don’t, e.g. if they just vary randomly, then you are going to get back to continuous change.
So to me it feels like as we add random stuff like “yeah there are revolutions but we don’t have any prediction about what they will look like” makes the richer model less compelling. It moves me more towards the ignorant perspective of “sometimes acceleration happens, maybe it will happen soon?”, which is what you get in the limit of adding infinitely many ex ante unknown bells and whistles to your model.
I agree the richer stories, if true, imply a more ignorant perspective. I just think it’s plausible that the more ignorant perspective is the correct perspective.
My general feeling towards the evolution of the economy over the past ten thousand years, reading historical analysis, is something like: “Oh wow, this seems really complex and heterogeneous. It’d be very surprising if we could model these processes well with a single-variable model, a noise term, and a few parameters with stable values.” It seems to me like we may in fact just be very ignorant.
Does a discontinuous change from fossil-fuel use even fit the data? It doesn’t seem to add up at all to me (e.g. doesn’t match the timing of acceleration, there are lots of industries that seemed to accelerate without reliance on fossil fuels, etc.), but would only consider a deep dive if someone actually wanted to stake something on that.
Fossil fuels wouldn’t be the cause of the higher global growth rates, in the 1500-1800 period; coal doesn’t really matter much until the 19th century. The story with fossil fuels is typically that there was a pre-existing economic efflorescence that supported England’s transition out of an ‘organic economy.’ So it’s typically a sort of tipping point story, where other factors play an important role in getting the economy to the tipping point.
Is “intensive agriculture” a well-defined thing? (Not rhetorical.) It didn’t look like “the beginning of intensive agriculture” corresponds to any fixed technological/social/environmental event (e.g. in most cases there was earlier agriculture and no story was given about why this particular moment would be the moment), it just looked like it was drawn based on when output started rising faster.
I’m actually unsure of this. Something that’s not clear to me is to what extent the distinction is being drawn in a post-hoc way (i.e. whether intensive agriculture is being implicitly defined as agriculture that kicks off substantial population growth). I don’t know enough about this.
Doing a regression on yearly growth rates seems like a bad way to approach this.
I don’t think I agree, although I’m not sure I understand your objection. Supposing we had accurate data, it seems like the best approach is running a regression that can accommodate either hyperbolic or exponential growth — plus noise — and then seeing whether we can reject the exponential hypothesis. Just noting that the growth rate must have been substantially higher than average within one particular millennium doesn’t necessarily tell us enough; there’s still the question of whether this is plausibly noise.
Of course, though, we have very bad data here—so I suppose this point doesn’t matter too much either way.
If you just keep listing things, it stops being a plausible source of a discontinuity—you then need to give some story for why your 7 factors all change at the same time. If they don’t, e.g. if they just vary randomly, then you are going to get back to continuous change.
You don’t need a story about why they changed at roughly the same time to believe that they did change at roughly the same time (i.e. over the same few century period). And my impression is that that, empirically, they did change at roughly the same time. At least, this seems to be commonly believed.
I don’t think we can reasonably assume they’re independent. Economic histories do tend to draw casual arrows between several of these differences, sometimes suggesting a sort of chain reaction, although these narrative causal diagrams are admittedly never all that satisfying; there’s still something mysterious here. On the other hand, higher population levels strike me as a fairly unsatisfying underlying cause.
[[EDIT: Just to be clear, I don’t think the phase-transition/inflection-point story is necessarily much more plausible than the noisy hyperbolic story. I don’t have very resilient credences here. But I think that, in the absence of good long-run growth data, they’re at least comparably plausible. I think that economic history narratives, the fairly qualitative differences between modern and pre-modern economies, and evidence from between-country variation in modern times count for at least as much as the simplicity prior.]]
Economic histories do tend to draw casual arrows between several of these differences, sometimes suggesting a sort of chain reaction, although these narrative causal diagrams are admittedly never all that satisfying; there’s still something mysterious here.
Just to make this more concrete:
One example of an IR narrative that links a few of these changes together is Robert Allen’s. To the extent that I understand/remember it, the narrative is roughly: The early modern expansion of trade networks caused an economic boom in England, especially in textile manufacturing. As a result, wages in England became unusually high. These high wages created unusually strong incentives to produce labor-saving technology. (One important effect of the Malthusian conditions is that they make labor dirt cheap.) England, compared to a few other countries that had similarly high wages at other points in history, also had access to really unusually cheap energy; they had huge and accessible coal reserves, which they were already burning as a replacement for wood. The unusually high levels of employment in manufacturing and trade also supported higher levels of literacy and numeracy. These conditions came together to support the development of technologies for harnessing fossil fuels, in the 19th century, and the rise of intensive R&D; these may never have been economically rational before. At this point, there was now a virtuous cycle that allowed England’s growth—which was initially an unsustainable form of growth based on trade, rather than technological innovation—to become both sustained and innovation-driven. The spark then spread to other countries.
This particular tipping point story is mostly a story about why growth rates increased from the 19th century onward, although the growth surge in the previous few centuries, largely caused by the Colombian exchange and expansion of trade networks, still plays an important causal role; the rapid expansion of trade networks drives British wages up and makes it possible for them to profitably employ a large portion of their population in manufacturing.
It feels like you are drawing some distinction between “contingent and complicated” and “noise.” Here are some possible distinctions that seem relevant to me but don’t actually seem like disagreements between us:
If something is contingent and complicated, you can expect to learn about it with more reasoning/evidence, whereas if it’s noise maybe you should just throw up your hands. Evidently I’m in the “learn about it by reasoning” category since I spend a bunch of time thinking about AI forecasting.
If something is contingent and complicated, you shouldn’t count on e.g. the long-run statistics matching the noise distribution—there are unmodeled correlations (both real and subjective). I agree with this and think that e.g. the singularity date distributions (and singularity probability) you get out of Roodman’s model are not trustworthy in light of that (as does Roodman).
So it’s not super clear there’s a non-aesthetic difference here.
If I was saying “Growth models imply a very high probability of takeoff soon” then I can see why your doc would affect my forecasts. But where I’m at from historical extrapolations is more like “maybe, maybe not”; it doesn’t feel like any of this should change that bottom line (and it’s not clear how it would change that bottom line) even if I changed my mind everywhere that we disagree.
“Maybe, maybe not” is still a super important update from the strong “the future will be like the recent past” prior that many people implicitly have and I might otherwise take very seriously. It also leads me to mostly dismiss arguments like “this is obviously not the most important century since most aren’t.” But it mostly means that I’m actually looking at what is happening technologically.
You may be responding to writing like this short post where I say “We have been in a period of slowing growth for the last forty years. That’s a long time, but looking over the broad sweep of history I still think the smart money is on acceleration eventually continuing, and seeing something like [hyperbolic growth]...”. I stand by the claim that this is something like the modal guess—we’ve had enough acceleration that the smart money is on it continuing, and this seems equally true on the revolutions model. I totally agree that any specific thing is not very likely to happen, though I think it’s my subjective mode. I feel fine with that post but totally agree it’s imprecise and this is what you get for being short.
The story with fossil fuels is typically that there was a pre-existing economic efflorescence that supported England’s transition out of an ‘organic economy.’ So it’s typically a sort of tipping point story, where other factors play an important role in getting the economy to the tipping point.
OK, but if those prior conditions led to a great acceleration before the purported tipping point, then I feel like that’s mostly what I want to know about and forecast.
Supposing we had accurate data, it seems like the best approach is running a regression that can accommodate either hyperbolic or exponential growth — plus noise — and then seeing whether we can object the exponential hypothesis. Just noting that the growth rate must have been substantially higher than average within one particular millennium doesn’t necessarily tell us enough; there’s still the question of whether this is plausibly noise.
I don’t think that’s what I want to do. My question is, given a moment in history, what’s the best way to guess whether and in how long there will be significant acceleration? If I’m testing the hypothesis “The amount of time before significant acceleration tends to be a small multiple of the current doubling time” then I want to look a few doublings ahead and see if things have accelerated, averaging over a doubling (etc. etc.), rather than do a regression that would indirectly test that hypothesis by making additional structural assumptions + would add a ton of sensitivity to noise.
You don’t need a story about why they changed at roughly the same time to believe that they did change at roughly the same time (i.e. over the same few century period). And my impression is that that, empirically, they did change at roughly the same time. At least, this seems to be commonly believed.
I don’t think we can reasonably assume they’re independent. Economic histories do tend to draw casual arrows between several of these differences, sometimes suggesting a sort of chain reaction, although these narrative causal diagrams are admittedly never all that satisfying; there’s still something mysterious here. On the other hand, higher population levels strike me as a fairly unsatisfying underlying cause.
It looked like you were listing those things to help explain why you have a high prior in favor of discontinuities between industrial and agricultural societies. “We don’t know why those things change together discontinuously, they just do” seems super reasonable (though whether that’s true is precisely what’s at issue). But it does mean that listing out those factors adds nothing to the a priori argument for discontinuity.
Indeed, if you think that all of those are relevant drivers of growth rates then all else equal I’d think you’d expect more continuous progress, since all you’ve done is rule out one obvious way that you could have had discontinuous progress (namely by having the difference be driven by something that had a good prima facie reason to change discontinuously, as in the case of the agricultural revolution) and now you’ll have to posit something mysterious to get to your discontinuous change.
It seems almost guaranteed that the data is a mess, it just seems like the only difference between the perspectives is “is acceleration fundamentally concentrated into big revolutions or is it just random and we can draw boundaries around periods of high-growth and call those revolutions?”
Which growth model corresponds to which perspective? I normally think of “‘industry’ is what changed and is not contiguous with what came before” as the single-factor model, and multifactor growth models tending more towards continuous growth.
I’m definitely much more sympathetic to the forager vs agricultural distinction.
Does a discontinuous change from fossil-fuel use even fit the data? It doesn’t seem to add up at all to me (e.g. doesn’t match the timing of acceleration, there are lots of industries that seemed to accelerate without reliance on fossil fuels, etc.), but would only consider a deep dive if someone actually wanted to stake something on that.
It feels to me like I’m saying: acceleration happens kind of randomly on a timescale roughly determined by the current growth rate. We should use the base rate of acceleration to make forecasts about the future, i.e. have a significant probability of acceleration during each doubling of output. (Though obviously the real model is more complicated and we can start deviating from that baseline, e.g. sure looks like we should have a higher probability of stagnation now given that we’e had decades of it.)
It feels to me like you are saying “No, we can have a richer model of historical acceleration that assigns significantly lower probability to rapid acceleration over the coming decades / singularity.”
So to me it feels like as we add random stuff like “yeah there are revolutions but we don’t have any prediction about what they will look like” makes the richer model less compelling. It moves me more towards the ignorant perspective of “sometimes acceleration happens, maybe it will happen soon?”, which is what you get in the limit of adding infinitely many ex ante unknown bells and whistles to your model.
Is “intensive agriculture” a well-defined thing? (Not rhetorical.) It didn’t look like “the beginning of intensive agriculture” corresponds to any fixed technological/social/environmental event (e.g. in most cases there was earlier agriculture and no story was given about why this particular moment would be the moment), it just looked like it was drawn based on when output started rising faster.
I mean that if you have 5x growth from 0AD to 1700AD, and growth was at the same rate from 10000BC to 0AD, then you would expect 5^(10,000/1700) = 13,000-fold growth over that period. We have uncertainty about exactly how much growth there was in the prior period, but we don’t have anywhere near that much uncertainty.
Doing a regression on yearly growth rates seems like a bad way to approach this. It seems like the key question is: did growth speed up a lot in between the agricultural and industrial revolutions? It seems like the way to pick that is to try to use points that are as spaced out as possible to compare growth rates in the beginning and late part of the interval from 10000BC to 1500AD. (The industrial revolution is usually marked much later, but for the purpose of the “2 revolutions” view I think you definitely need it to start by then.)
So almost all of the important measurement error is going to be in the bit of growth in the 0AD to 1500AD phase. If in fact there was only 2x growth in that period (say because the 0AD number was off by 50%) then that would only predict 100-fold growth from 10,000BC to 0AD, which is way more plausible.
If you just keep listing things, it stops being a plausible source of a discontinuity—you then need to give some story for why your 7 factors all change at the same time. If they don’t, e.g. if they just vary randomly, then you are going to get back to continuous change.
I agree the richer stories, if true, imply a more ignorant perspective. I just think it’s plausible that the more ignorant perspective is the correct perspective.
My general feeling towards the evolution of the economy over the past ten thousand years, reading historical analysis, is something like: “Oh wow, this seems really complex and heterogeneous. It’d be very surprising if we could model these processes well with a single-variable model, a noise term, and a few parameters with stable values.” It seems to me like we may in fact just be very ignorant.
Fossil fuels wouldn’t be the cause of the higher global growth rates, in the 1500-1800 period; coal doesn’t really matter much until the 19th century. The story with fossil fuels is typically that there was a pre-existing economic efflorescence that supported England’s transition out of an ‘organic economy.’ So it’s typically a sort of tipping point story, where other factors play an important role in getting the economy to the tipping point.
I’m actually unsure of this. Something that’s not clear to me is to what extent the distinction is being drawn in a post-hoc way (i.e. whether intensive agriculture is being implicitly defined as agriculture that kicks off substantial population growth). I don’t know enough about this.
I don’t think I agree, although I’m not sure I understand your objection. Supposing we had accurate data, it seems like the best approach is running a regression that can accommodate either hyperbolic or exponential growth — plus noise — and then seeing whether we can reject the exponential hypothesis. Just noting that the growth rate must have been substantially higher than average within one particular millennium doesn’t necessarily tell us enough; there’s still the question of whether this is plausibly noise.
Of course, though, we have very bad data here—so I suppose this point doesn’t matter too much either way.
You don’t need a story about why they changed at roughly the same time to believe that they did change at roughly the same time (i.e. over the same few century period). And my impression is that that, empirically, they did change at roughly the same time. At least, this seems to be commonly believed.
I don’t think we can reasonably assume they’re independent. Economic histories do tend to draw casual arrows between several of these differences, sometimes suggesting a sort of chain reaction, although these narrative causal diagrams are admittedly never all that satisfying; there’s still something mysterious here. On the other hand, higher population levels strike me as a fairly unsatisfying underlying cause.
[[EDIT: Just to be clear, I don’t think the phase-transition/inflection-point story is necessarily much more plausible than the noisy hyperbolic story. I don’t have very resilient credences here. But I think that, in the absence of good long-run growth data, they’re at least comparably plausible. I think that economic history narratives, the fairly qualitative differences between modern and pre-modern economies, and evidence from between-country variation in modern times count for at least as much as the simplicity prior.]]
Just to make this more concrete:
One example of an IR narrative that links a few of these changes together is Robert Allen’s. To the extent that I understand/remember it, the narrative is roughly: The early modern expansion of trade networks caused an economic boom in England, especially in textile manufacturing. As a result, wages in England became unusually high. These high wages created unusually strong incentives to produce labor-saving technology. (One important effect of the Malthusian conditions is that they make labor dirt cheap.) England, compared to a few other countries that had similarly high wages at other points in history, also had access to really unusually cheap energy; they had huge and accessible coal reserves, which they were already burning as a replacement for wood. The unusually high levels of employment in manufacturing and trade also supported higher levels of literacy and numeracy. These conditions came together to support the development of technologies for harnessing fossil fuels, in the 19th century, and the rise of intensive R&D; these may never have been economically rational before. At this point, there was now a virtuous cycle that allowed England’s growth—which was initially an unsustainable form of growth based on trade, rather than technological innovation—to become both sustained and innovation-driven. The spark then spread to other countries.
This particular tipping point story is mostly a story about why growth rates increased from the 19th century onward, although the growth surge in the previous few centuries, largely caused by the Colombian exchange and expansion of trade networks, still plays an important causal role; the rapid expansion of trade networks drives British wages up and makes it possible for them to profitably employ a large portion of their population in manufacturing.
It feels like you are drawing some distinction between “contingent and complicated” and “noise.” Here are some possible distinctions that seem relevant to me but don’t actually seem like disagreements between us:
If something is contingent and complicated, you can expect to learn about it with more reasoning/evidence, whereas if it’s noise maybe you should just throw up your hands. Evidently I’m in the “learn about it by reasoning” category since I spend a bunch of time thinking about AI forecasting.
If something is contingent and complicated, you shouldn’t count on e.g. the long-run statistics matching the noise distribution—there are unmodeled correlations (both real and subjective). I agree with this and think that e.g. the singularity date distributions (and singularity probability) you get out of Roodman’s model are not trustworthy in light of that (as does Roodman).
So it’s not super clear there’s a non-aesthetic difference here.
If I was saying “Growth models imply a very high probability of takeoff soon” then I can see why your doc would affect my forecasts. But where I’m at from historical extrapolations is more like “maybe, maybe not”; it doesn’t feel like any of this should change that bottom line (and it’s not clear how it would change that bottom line) even if I changed my mind everywhere that we disagree.
“Maybe, maybe not” is still a super important update from the strong “the future will be like the recent past” prior that many people implicitly have and I might otherwise take very seriously. It also leads me to mostly dismiss arguments like “this is obviously not the most important century since most aren’t.” But it mostly means that I’m actually looking at what is happening technologically.
You may be responding to writing like this short post where I say “We have been in a period of slowing growth for the last forty years. That’s a long time, but looking over the broad sweep of history I still think the smart money is on acceleration eventually continuing, and seeing something like [hyperbolic growth]...”. I stand by the claim that this is something like the modal guess—we’ve had enough acceleration that the smart money is on it continuing, and this seems equally true on the revolutions model. I totally agree that any specific thing is not very likely to happen, though I think it’s my subjective mode. I feel fine with that post but totally agree it’s imprecise and this is what you get for being short.
OK, but if those prior conditions led to a great acceleration before the purported tipping point, then I feel like that’s mostly what I want to know about and forecast.
I don’t think that’s what I want to do. My question is, given a moment in history, what’s the best way to guess whether and in how long there will be significant acceleration? If I’m testing the hypothesis “The amount of time before significant acceleration tends to be a small multiple of the current doubling time” then I want to look a few doublings ahead and see if things have accelerated, averaging over a doubling (etc. etc.), rather than do a regression that would indirectly test that hypothesis by making additional structural assumptions + would add a ton of sensitivity to noise.
It looked like you were listing those things to help explain why you have a high prior in favor of discontinuities between industrial and agricultural societies. “We don’t know why those things change together discontinuously, they just do” seems super reasonable (though whether that’s true is precisely what’s at issue). But it does mean that listing out those factors adds nothing to the a priori argument for discontinuity.
Indeed, if you think that all of those are relevant drivers of growth rates then all else equal I’d think you’d expect more continuous progress, since all you’ve done is rule out one obvious way that you could have had discontinuous progress (namely by having the difference be driven by something that had a good prima facie reason to change discontinuously, as in the case of the agricultural revolution) and now you’ll have to posit something mysterious to get to your discontinuous change.