Thanks for this Phil,

A couple of questions regarding SWE:

“Second-wave endogenous” (I’ll write “SWE”) growth models posit instead that technology grows exponentially with a constant or with a growing population. The idea is that process efficiency—the quantity of a given good producible with given labor and/or capital inputs—grows exponentially with constant research effort, as in a first-wave endogenous model; but when population grows, we develop more goods, leaving research effort per good fixed.

Only one SWE model avoids a conclusion along these lines: the first one, Young (1998). It avoids the conclusion by positing that vertical innovation faces severely diminishing returns to research labor, so that in effect, a larger population can only be employed productively in research if the range of goods widens.

So does this mean that in the research production function, the exponent on the stock of 'ideas' is one, and the exponent on the number of researchers is significantly less than one? It might be nice to see the equation.

Relatedly, isn't endogenous growth a knife-edge case? Intuitively, it seems unlikely to be true, and SWE doesn't seem to address this issue.

I'm imagining something that is Cobb-Douglas between capital and land. Growth should be exponential (not super exponential) when A_auto is growing at a constant rate, same as a regular Cobb-Douglas production function between capital and labor. Specifically, I was thinking something like this:

X_old^beta(A_old K_old^alpha L^{1-alpha})^(1-beta) + X_auto^beta(A_auto K_auto)^(1-beta)

st X_old + X_auto = X_total (allocating land between the two production technologies)

As to your second point, yes, you are correct, as long as A_old is constant wages would not increase.

Thanks! Looks like I have access through my university.

Diverging utilities can be an issue. You can also get infinite output in finite time. The larger issue is that the economy has no steady state. In economic growth models, a steady state (or balanced growth path (BGP)) represents a long-run equilibrium where key economic variables per capita (like capital per worker, output per worker, consumption per worker) grow at constant rates. This greatly simplifies the analysis.

For example, I have a paper in which I analyze how households would behave if they expected TAI to transform the economy. To do this, I calculated the steady state the economy was in prior to households learning about the potential of TAI as well as the post-TAI steady state. I could then calculate the transition path between these two steady states. I thought of using the same production function you used here, but then there wouldn't have been a post-TAI steady state, which is necessary to be able to find the transition path.

A production function that I have mused about is one like yours, but with land. This should solve the issue, as the post-TAI economy will no longer be AK. It also addresses another issue I have with growth models: it's really tricky to get wages to decrease in the long run. For the production function you use, if A_{old} was also growing at a constant rate, then wages would eventually rise. This is because the new production technology doesn't harm the old technology other than by taking capital away. Each production technology could work next to the other without interfering. In reality, there is a limited amount of space on earth and once the new technology is more efficient, it isn't profit maximizing to 'waste space' on the old style of production. I don't know if it is worth modeling for what you are doing, might be too many bells and whistles, but it is something I've been thinking about.

Thanks for this. If I understand correctly, the result is primarily driven by the elastic labor supply, which is a function of W and not of R, and the constant supply of capital. This seems most relevant for very fast takeoff scenarios.

My intuition is that as people realize that their jobs are being automated away, they will want to work more to bolster their savings before we move into the new regime where their labor is worthless and capital is all that matters. This would require fully modeling the household's intertemporal utility and endogenizing the capital supply. This might be tricky, however, with your production function, because if A_{auto} is increasing at a constant rate and households are allowed to save, you will get superexponential growth.

Thanks for this excellent primer and case study! I learned a lot about causal analysis from your explanation. The section on using three waves to control for confounders while avoiding controlling for potential mediators was particularly helpful. I would be interested in hearing more about how the sensitivity analysis for unmeasured confounders works.

The positive effect of activism on meat consumption that you found is especially concerning and important. I hope that we can gain more insight into this soon. If this finding replicates, then a lot of organizations might have to reevaluate their methods.

Hi Matthew,

Thank you for your comment. I think this is a reasonable criticism! There is definitely an endogenous link between investment and AI timelines that this model misses. I think that this might be hard to model in a realistic way, but I encourage people to try!

On the other hand, I think the strategic motivation is important as well. For example, here is Satya Nadella on the Dwarkesh Podcast:

And by the way, one of the things is that there will be overbuild. To your point about what happened in the dotcom era, the memo has gone out that, hey, you know, you need more energy, and you need more compute. Thank God for it. So, everybody's going to race.

In reality, both mechanisms are probably in play. My paper is intended to focus on the race mechanism.

Two more notes: higher savings imply lower consumption in the short term. However, even if TAI isn't invented, consumption will rise higher than in the stationary equilibrium purely from capital accumulation.

Lastly, the main thrust of the paper is on the implications for interest rates, I do not intend to make strong claims about social welfare.

Why would Knightian uncertainty be an argument against AI as an existential risk? If anything, our deep uncertainty about the possible outcomes of AI should lead us to be even more careful.

Similar campaigns have worked really well for animal advocacy, so I’m excited to see what you can accomplish.

I’m wondering, what kinds of tasks can volunteers help with? If I have no social media accounts or experience trying to promote causes on social media is there anything I can do?