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This is: Some thoughts on David Roodman’s model of economic growth and its relation to AI timelines, published by Tom_Davidson on the LessWrong.
[Also posted on LW.]
I’ve been working on a report (see blog) assessing possible trajectories for Gross World Product (GWP) out to 2100. A lot of my early work focussed on analysing a paper of my colleague David Roodman. Roodman fits a growth model to long-run GWP; the model predicts a 50% probability that annual GWP growth is >= 30% by 2043.
I was thinking about whether to trust this model’s GWP forecasts, compared with the standard extrapolations that predict GWP growth of ~3% per year or less.[1] I was also thinking about how the model might relate to AI timelines.
This post briefly describes some of my key takeaways, as they don’t figure prominently in the report. I explain them briefly and directly, rather than focussing on nuance or caveats.[2] I expect it to be useful mostly for people who already have a rough sense for how Roodman’s model works. Many points here have already been made elsewhere.
Although for brevity I sometimes refer to “Roodman’s extrapolations”, what I really mean is the extrapolations of his univariate model once it’s been fitted to long-run GWP data. Of course, David does not literally believe these extrapolations. More generally, this post is not about David’s beliefs at all but rather about possible uses and interpretations of his model.
[Views are my own, not my employers]
Economic theory doesn’t straightforwardly support Roodman’s extrapolation over standard extrapolations
Early on in the project, I had the following rough picture in my mind (oversimplifying for readability):
Standard extrapolations use what are called ‘exogenous growth models’. These fit the post-1900 data well. However, the exponential growth is put in by hand and isn’t justified by economic theory. (Exogenous growth models assume technology grows exponentially but don’t attempt to justify this assumption; the exponential growth of technology then drives exponential growth of GDP/capita.)
On the other hand, endogenous growth models can explain growth without putting in the answer by hand. They explain technological progress as resulting from economic activity (e.g. targeted R&D), and they find that exponential growth is implausible - a knife-edge case. Ignoring this knife-edge case, growth is either sub- or super- exponential. Roodman fits an endogenous growth model to the data and finds super-exponential growth (because growth has increased over the long-run on average).
So Roodman’s model uses a better growth model (endogenous rather than exogenous). Roodman’s model also has the advantage of taking more data in account (standard economists typically don‘t use pre-1900 data to inform their extrapolations).
Overall, we should put more weight on Roodman than standard extrapolation, at least over the long-run.
I no longer see things this way. My attitude is more like (again oversimplifying for readability):
Although exogenous growth models don’t justify the assumption of exponential growth of technology, semi-endogenous growth models justify this claim pretty nicely._[3] _These semi-endogenous models can explain the post-1900 exponential growth and the pre-1900 super-exponential growth in a pretty neat way - for example see Jones (2001).
Roodman’s model departs from these semi-endogenous models primarily in that it assumes population is ‘output-bottlenecked’._[4] _This assumption means that if we produced more output (e.g. food, homes), population would become larger as a result: more output → more people. This assumption hasn’t been true over the last 140 years, and doesn’t seem to be true currently: since the demographic transition in ~1880 fertility has decreased even while output per person increased. (That said, significant behav...
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