Some problems with the power law extrapolation for GDP:

The graph is for the whole world, not just the technological leading edge, which obscures the thing which is conceivably relevant (the endogenous trend in tech advancement at the leading edge)

The power law model is a bad fit for the GDP per capita of the first world in the last 50-100 years

Having built a toy endogenous model of economic growth, I see no gears-level reason to expect power law growth in our current regime. (Disclaimer: I’m not an economist, and haven’t tested my model on anything.) The toy model presented in the OpenPhil report is much simpler and IMO less realistic.

Agreed on points 1+2. On 3, depends on what you mean by current regime—seems like AI tech could totally lead to much faster growth than today, and in particular faster than exponential growth. Are you modelling history as a series of different regimes, each one of which is exponential but taken together comprise power-law growth?

seems like AI tech could totally lead to much faster growth than today, and in particular faster than exponential growth

Strongly agree.

Are you modelling history as a series of different regimes, each one of which is exponential but taken together comprise power-law growth?

I am not. The model is fully continuous, and involves the variables {science, technology, population, capital}. When you run the model, it naturally gives rise to a series of “phase changes”. The phase changes are smooth^{[1]} but still quite distinct. Some of them are caused by changes in which inputs are bottlenecking a certain variable.

The phases predicted are:^{[2]}

Super-exponential growth (Sci&Tech bottlenecked by labor surplus; ∞ BC to ~1700 AD (??))

Steady exponential growth

Fast exponential growth for a short period (population growth slows, causing less consumption)

Slow exponential growth for some time (less population growth --> less science --> less economic growth after a delay)

Super-exponential growth as AI replaces human researchers (population stops bottlenecking Sci&Tech as capital can be converted into intelligence)

My claim is that:

We are in phase 4, and that we don’t have enough automation of research to see the beginnings of phase 5 in GDP data.

Extrapolating GDP data tells us basically zero about when phase 5 will start. The timing can only be predicted with object-level reasoning about AI.

Phase 4 doesn’t fit the model of “growth always increases from one phase to the next”. Indeed, if you look at real economic data, the first world has had lower growth in recent decades than it did previously. Hence, power law extrapolation across phases is inappropriate.

As I think about this more and compare to what actually happened in history, I’m starting to doubt my model a lot more, since I’m not sure if the timing and details of the postulated phases line up properly with real world data.

Some problems with the power law extrapolation for GDP:

The graph is for the whole world, not just the technological leading edge, which obscures the thing which is conceivably relevant (the endogenous trend in tech advancement at the leading edge)

The power law model is a bad fit for the GDP per capita of the first world in the last 50-100 years

Having built a toy endogenous model of economic growth, I see no gears-level reason to expect power law growth in our current regime. (Disclaimer: I’m not an economist, and haven’t tested my model on anything.) The toy model presented in the OpenPhil report is much simpler and IMO less realistic.

Agreed on points 1+2. On 3, depends on what you mean by current regime—seems like AI tech could totally lead to much faster growth than today, and in particular faster than exponential growth. Are you modelling history as a series of different regimes, each one of which is exponential but taken together comprise power-law growth?

Strongly agree.

I am not. The model is fully continuous, and involves the variables {science, technology, population, capital}. When you run the model, it naturally gives rise to a series of “phase changes”. The phase changes are smooth

^{[1]}but still quite distinct. Some of them are caused by changes in which inputs are bottlenecking a certain variable.The phases predicted are:

^{[2]}Super-exponential growth (Sci&Tech bottlenecked by labor surplus; ∞ BC to ~1700 AD (??))

Steady exponential growth

Fast exponential growth for a short period (population growth slows, causing less consumption)

Slow exponential growth for some time (less population growth --> less science --> less economic growth after a delay)

Super-exponential growth as AI replaces human researchers (population stops bottlenecking Sci&Tech as capital can be converted into intelligence)

My claim is that:

We are in phase 4, and that we don’t have enough automation of research to see the beginnings of phase 5 in GDP data.

Extrapolating GDP data tells us basically zero about when phase 5 will start. The timing can only be predicted with object-level reasoning about AI.

Phase 4 doesn’t fit the model of “growth always increases from one phase to the next”. Indeed, if you look at real economic data, the first world has had lower growth in recent decades than it did previously. Hence, power law extrapolation across phases is inappropriate.

I don’t mean this in a mathematically rigorous way

As I think about this more and compare to what actually happened in history, I’m starting to doubt my model a lot more, since I’m not sure if the timing and details of the postulated phases line up properly with real world data.

I’d be very interested to read more about the assumptions of your model, if there’s a write-up somewhere.