I’ve ended up spending quite a lot of time researching premodern economic growth, as part of a hobby project that got out of hand. I’m sharing an informal but long write-up of my findings here, since I think they may be relevant to other longtermist researchers and I am unlikely to write anything more polished in the near future. Click here for the Google document.[1]
Summary
Over the next several centuries, is the economic growth rate likely to remain steady, radically increase, or decline back toward zero? This question has some bearing on almost every long-run challenge facing the world, from climate change to great power competition to risks from AI.
One way to approach the question is to consider the long-run history of economic growth. I decided to investigate the Hyperbolic Growth Hypothesis: the claim that, from at least the start of the Neolithic Revolution up until the 20th century, the economic growth rate has tended to rise in proportion with the size of the global economy.[2] This claim is made in a classic 1993 paper by Michael Kremer. Beyond influencing other work in economic growth theory, it has also recently attracted significant attention within the longtermist community, where it is typically regarded as evidence in favor of further acceleration.[3] An especially notable property of the hypothesized growth trend is that, if it had continued without pause, it would have produced infinite growth rates in the early twenty-first century.
I spent time exploring several different datasets that can be used to estimate pre-modern growth rates. This included a number of recent archeological datasets that, I believe, have not previously been analyzed by economists. I wanted to evaluate both: (a) how empirically well-grounded these estimates are and (b) how clearly these estimates display the hypothesized pattern of growth.
Ultimately, I found very little empirical support for the Hyperbolic Growth Hypothesis. While we can confidently say that the economic growth rate did increase over the centuries surrounding the Industrial Revolution, there is approximately nothing to suggest that this increase was the continuation of a long-standing hyperbolic trend. The alternative hypothesis that the modern increase in growth rates constituted a one-off transition event is at least as consistent with the evidence.
The premodern growth data we have is mostly extremely unreliable: For example, so far as I can tell, Kremer’s estimates for the period between 10,000BC and 400BC ultimately derive from a single speculative paragraph in a book published decades earlier. Putting aside issues of reliability, the various estimates I considered also, for the most part, do not clearly indicate that pre-modern growth was hyperbolic. The most empirically well-grounded datasets we have are at least weakly in tension with the hypothesis. Overall, though, I think we are in a state of significant ignorance about pre-modern growth rates.
Beyond evaluating these datasets, I also spent some time considering the growth model that Kremer uses to explain and support the Hyperbolic Growth Hypothesis. One finding is that if we use more recent data to estimate a key model parameter, the model may no longer predict hyperbolic growth: the estimation method that we use matters. Another finding, based on some shallow reading on the history of agriculture, is that the model likely overstates the role of innovation in driving pre-modern growth.
Ultimately, I think we have less reason to anticipate a future explosion in the growth rate than might otherwise be supposed.[4][5]
EDIT: See also this addendum comment for an explanation of why I think the alternative "phase transition" interpretation of the Industrial Revolution is plausible.
Thank you to Paul Christiano, David Roodman, Will MacAskill, Scott Alexander, Matt van der Merwe, and, especially, Asya Bergal for helpful comments on an earlier version of the document. ↩︎
By "economic growth rate," here, I mean the growth rate of total output, rather than the growth rate of output-per-person. ↩︎
As one example, which includes a particularly clear summary of the hypothesis, see this Slate Star Codex post. ↩︎
I wrote nearly all of this document before the publication of David Roodman’s recent Open Philanthropy report on long-run economic growth. That report, which I strongly recommend to anyone interested in long-run growth, has some overlap with this document. However, the content is fairly different. First, relative to the report, which makes novel contributions to economic growth modeling, the focus of this doc is more empirical than theoretical. I don’t devote much space to relevant growth models, but I do devote a lot of space to the question: “How well can we actually estimate historical growth rates?” Second, I consider a wider variety of datasets and methods of estimating historical growth rates. Third, for the most part, I am comparing a different pair of hypotheses. The report mostly compares a version of the Hyperbolic Growth Hypothesis with the hypothesis that the economic growth rate has been constant throughout history; I mostly compare the Hyperbolic Growth Hypothesis with the hypothesis that, in the centuries surrounding the Industrial Revolution, there was a kind of step-change in the growth rate. Fourth, my analysis is less mathematically rigorous. ↩︎
There is also ongoing work by Alex Lintz to analyze available archeological datasets far more rigorously than I do in this document. You should keep an eye out for this work, which will likely supersede most of what I write about the archeological datasets here. You can also reach out to him (alex.l.lintz@gmail.com) if you are interested in seeing or discussing preliminary findings. ↩︎
Thanks for the feedback! I probably ought to have said more in the summary.
Essentially:
For the 'old data': I run a non-linear regression on the population growth rate as a function of population, for a dataset starting in 10000BC. The function is (dP/dt)/P = a*P^b, where P represents population. If b = 0, this corresponds to exponential growth. If b = 1, this corresponds to the strict version of the Hyperbolic Growth Hypothesis. If 0 < b < 1, this still corresponds to hyperbolic growth, although the growth rate is less than proportional to the population level. I found that if you start in 10000BC and keep adding datapoints, b is not significantly greater than 0 until roughly 1750 (although it is significantly less than 1). Here's a graph of how the value evolves.
Since the datapoints are unevenly spaced, it can make sense to weigh them in proportion to the length of the interval used to estimate the growth rate for that datapoint. If you do this, then b is actually significantly greater than 0 (although is still less than 1) for most of the interval. However, this is mostly driven by a single datapoint for the period from 10,000BC to 5,000BC. If you remove this single datapoint, which roughly corresponds to the initial transition to agriculture, then b again isn't significantly greater than 0 until roughly the Industrial Revolution. (Here are the equivalent graphs, with and without the initial datapoint.)
A key point is that, if you fit this kind of function to a dataset that includes a large stable increase in the growth rate, you'll typically find that b > 0. (For example: If you run a regression on a dataset where there's no growth before 1700AD, but steady 2% growth after 17000AD, you'll find that b is significantly greater than zero.) Mainly, it's a test of whether there's been a stable increase in the growth rate. So running the test on the full dataset (including the period around the IR) doesn't help us much to distinguish the hyperbolic growth story from the 'phase change'/'inflection point' story. Kremer's paper mainly emphasizes the fact that b approximately equals 1, when you run the regression on the full dataset; I think too much significance has sometimes been attributed to this finding.
If you just do direct curve fitting to the data -- comparing an exponential function and a hyperbolic function for b = 1 -- the exponential function is also a better fit for the period from 5000BC until the couple centuries before the Industrial Revolution. Both functions are roughly similarly bad if you throw in the 10,000BC datapoint. This comparison is just based on the mean squared errors of the two fits.
But I also think this data is really unreliable -- I'd classify a lot of the data points as something close to 'armchair guesses' -- so I don't think we should infer much either way.
There are also more recent datasets for particular regions (e.g. China) that estimate historical population growth curves on the basis of the relative number archeological deposits (such as human remains and charcoal) that have been dated to different time periods. There are various corrections that people do to try to account for things like the tendency of deposits to disappear or be destroyed over time. I found that it was a pain to recreate these population curves, from the available datasets, so I actually didn't do any proper statistical analysis using them. (Alex Lintz is currently doing this.)