Modeling the Human Trajectory(David Roodman) (summarized by Nicholas): This post analyzes the human trajectory from 10,000 BCE to the present and considers its implications for the future. The metric used for this is Gross World Product (GWP), the sum total of goods and services produced in the world over the course of a year.
Looking at GWP over this long stretch leads to a few interesting conclusions. First, until 1800, most people lived near subsistence levels. This means that growth in GWP was primarily driven by growth in population. Since then population growth has slowed and GWP per capita has increased, leading to our vastly improved quality of life today. Second, an exponential function does not fit the data well at all. In an exponential function, the time for GWP to double would be constant. Instead, GWP seems to be doubling faster, which is better fit by a power law. However, the conclusion of extrapolating this relationship forward is extremely rapid economic growth, approaching infinite GWP as we near the year 2047.
Next, Roodman creates a stochastic model in order to analyze not just the modal prediction, but also get the full distribution over how likely particular outcomes are. By fitting this to only past data, he analyzes how surprising each period of GWP was. This finds that the industrial revolution and the period after it was above the 90th percentile of the model’s distribution, corresponding to surprisingly fast economic growth. Analogously, the past 30 years have seen anomalously lower growth, around the 25th percentile. This suggests that the model’s stochasticity does not appropriately capture the real world—while a good model can certainly be “surprised” by high or low growth during one period, it should probably not be consistently surprised in the same direction, as happens here.
In addition to looking at the data empirically, he provides a theoretical model for how this accelerating growth can occur by generalizing a standard economic model. Typically, the economic model assumes technology is a fixed input or has a fixed rate of growth and does not allow for production to be reinvested in technological improvements. Once reinvestment is incorporated into the model, then the economic growth rate accelerates similarly to the historical data.
Nicholas’s opinion: I found this paper very interesting and was quite surprised by its results. That said, I remain confused about what conclusions I should draw from it. The power law trend does seem to fit historical data very well, but the past 70 years are fit quite well by an exponential trend. Which one is relevant for predicting the future, if either, is quite unclear to me.
The theoretical model proposed makes more sense to me. If technology is responsible for the growth rate, then reinvesting production in technology will cause the growth rate to be faster. I’d be curious to see data on what fraction of GWP gets reinvested in improved technology and how that lines up with the other trends.
Rohin’s opinion: I enjoyed this post; it gave me a visceral sense for what hyperbolic models with noise look like (see the blog post for this, the summary doesn’t capture it). Overall, I think my takeaway is that the picture used in AI risk of explosive growth is in fact plausible, despite how crazy it initially sounds. Of course, it won’t literally diverge to infinity—we will eventually hit some sort of limit on growth, even with “just” exponential growth—but this limit could be quite far beyond what we have achieved so far. See also this related post.
The latest edition of the Alignment Newsletter includes a good summary of Roodman’s post, as well as brief comments by Nicholas Joseph and Rohin Shah: