Thanks for these great questions Ben!

To take them point by point:

1. The CES task-based model incorporates Baumol effects, in that after AI automates a task the output on that task increases significantly and so its importance to production decreases. The tasks with low output become the bottlenecks to progress. 
   1. I'm not sure what exactly you mean by technological deflation. But if AI automates therapy and increases the amount of therapists by 100X then my model won't imply that the real $ value of therapy industry increases 100X. The price of therapy falls and so there is a more modest increase in the value of therapy.
   2. Re technological unemployment,  the model unrealistically assumes that when AI automates (e.g.) 20% of tasks, human workers are immediately reallocated to the remaining 80%. I.e. there is no unemployment until AI automates 100% of tasks. I think this makes sense for things like Copilot that automates/accelerates one part of a job; but is wrong for a hypothetical AI that fully automates a particular job.  Modelling delays to reallocating human labour after AI automation would make takeoff slower. My guess is that this will be a bigger deal for the general economy than for AI R&D. Eg maybe AI fully automates the trucking industry, but I don't expect it to fully automate a particular job within AI R&D. Most of the action with capabilities takeoff speed is with AI R&D (the main effect of AI automation is to accelerate hardware and software progress), so I don't think modelling this better would affect takeoff speeds by much. 
   3. Profit incentives. This is a significant weakness of the report - I don't explicitly model the incentives faced by firms to invest in AI R&D and do large training runs at all. (More precisely, I don't endogenise investment decisions as being made to maximise future profits, as happens in some economic models. Epoch is working on a model along these lines.) Instead I assume that once enough significant actors "wake up" to the strategic and economic potential of AI, investments will rise faster than they are today. So one possibility for slower takeoff is that AI firms just really to capture the value they create, and can't raise the money to go much higher than (e.g.) $5b training runs even after many actors have "woken up". 
2. I am using semi-endogenous growth models to predict the rate of  future software and hardware progress, so they're very important. I don't know of a better approach to forecasting how investments in R&D will translate to progress, without investigating the details of where specifically progress might come from (I think that kind of research is very valuable, but it was far beyond the scope of this project). I think semi-endogenous growth models are a better fit to the data than the alternatives (e.g. see this). I do think it's a valid perspective to say "I just don't trust any method that tries to predict the rate of  technological progress from the amount of R&D investment", but if you do want to use such a method then I think this is the ~best you can do. In the Monte Carlo analysis, I put large uncertainty bars on the rate of returns to future R&D to represent the fact that the historical relationship between R&D investment and observed progress may fail to hold in the future. 
   1. I don't expect the papers you link to change my mind about this, from reading the abstracts. It seems like your second link is a critique of endogenous growth theory but not semi-endog theory (it says "According to endogenous growth theory, permanent changes in certain policy variables have permanent effects on the rate of economic growth" but this isn't true of semi-endog theories).  It seems like your first link is either looking at ~irrelevant evidence or drawing a the incorrect conclusion (here's my perspective on the evidence mentioned in its abstract: "the slowing of growth in the OECD countries over the last two decades [Tom: I expect semi-endog theories can explain this better than the neoclassical model. The population growth rate of the scientific workforce as been slowing so we'd expect growth so slow as well; the neoclassical model as (as far as I'm aware) no comparable mechanism for explaining the slowdown.] ; the acceleration of growth in several Asian countries since the early 1960s [this is about catch-up growth so wouldn't expect semi-endog theories to explain it; semi-endog theories are designed to explain growth of the global technological frontier]  ; studies of the determinants of growth in a cross-country context [again, semi-endog growth models aren't designed to explain this kind of thing at all]; and sources of the differences in international productivity levels [again again, semi-endog growth models aren't designed to explain this kind of thing at all]". 
   2. You could see this as an argument for slower takeoff if you think "I'm pretty sure that looking into the details of where future progress might come from would conclude that progress will be slower than is predicted by the semi-endogenous model", although this isn't my current view. 
   3. One way to think about this is to start from a method you may trust more that using semi-endog models: just extrapolating past trends in tech progress. But you might worry about this method if you expect R&D inputs to the relevant fields to rise much faster than in recent history (because you expect people to invest more and you expect AI to automate a lot of the work). Naively, your method is going to underestimate the rate of progress. So then using a semi-endog model addresses this problem. It matches the predictions of your initial method when R&D inputs continue to rise at their recent historical rate, but predicts faster progress in scenarios where R&D inputs rise more quickly than in recent history.
3. > "Does this mean that, if you don't think a discontinuous jump in AI capabilities is likely, you should expect slower take-off than your model suggests? How substantial is this effect?" The results of the Monte Carlo don't include any discontinuous jumps (beyond the possibility that there's a continuous but very-fast transition from "AI that isn't economically useful" to AGI). So adjusting for discontinuities would only make takeoff faster. My own subjective probabilities do increase the probability of very fast takeoff by 5-10% to account for the possibility of other discontinuities. 
   1. "In section 8, the only uncertainty pointing in favour of fast takeoff is "there might be a discontinuous jump in AI capabilities"" There are other ways that I think my conclusions might be biased in favour of slower takeoff, in particular the ones mentioned here.
4. "How did you model the AI production function? Relatedly, how did you model constraints like  energy costs, data costs,  semiconductor costs,  silicon costs etc.?"
   1. In the model the capability of the AI trained just depends on the compute used in training and the quality of AI algorithms used; you combine the two multiplicatively. I didn't model energy/semiconductor/silicon costs except as implicit in FLOP/$ trends); I didn't model or data costs (which feels like a significant limitation). 
   2. The CES task-based model is used as the production function for R&D to improve AI algorithms ("software") and AI chips ("hardware"), and for GDP. It gives slower takeoff than if you used Cobb Douglas bc you get more bottlenecked by the tasks  AI still can't perform (e.g. tasks done by humans, or tasks done with equipment like experiments).
      1. There's a parameter rho that controls how close the behaviour is to Cobb Douglas vs a model with very binding bottlenecks.  I ultimately settled on a values that make GDP much more bottlenecked by physical infrastructure than R&D progress. This was based on it seeming to me that you could speed up R&D a lot by uploading the smartest minds and running  billions of them at 100X speed, but couldn't increase GDP by nearly as much by having those uploads try to provide people with goods and services (holding the level of technology fixed). 
5. "I'm vaguely worried that the report proves too much, in that I'd guess that the basic automation of the industrial revolution also automated maybe 70%+ of tasks by pre-industrial revolution GDP." I agree with this! I don't think it undermines the report - I discuss it here.  Interested to hear pushback if you disagree.

if they had explained why their views were not moved by the expert reviews OpenPhil has already solicited.

I included responses to each review, explaining  my reactions to it. What kind of additional explanation were you hoping for?

Davidson 2021 on semi-informative priors received three reviews.

By my judgment, all three made strong negative assessments, in the sense (among others) that if one agreed with the review, one would not use the report's reasoning to inform decision-making in the manner advocated by Karnofsky (and by Beckstead).

For Hajek&Strasser's and Halpern’s  reviews, I don't think "strong negative assessment" is supported by your quotes. The quotes focus on things like 'the reported numbers are too precise' and 'we should use more than a single probability measure' rather than whether the estimate is too high or too low overall or whether we should be worrying more vs less about TAI. I also think the reviews are more positive overall than you imply, e.g. Halpern's review says "This seems to be the most serious attempt to estimate when AGI will be developed that I’ve seen" 

 Davidson 2021 on explosive growth received many reviews... Two of them made strong negative assessments.

I agree that these two reviewers assign much lower probabilities to explosive growth than I do (I explain why I continue to disagree with them in my responses to their reviews). Again though, I think these reviews are more positive overall than you imply, e.g. Jones states that the report "is balanced, engaging a wide set of viewpoints and acknowledging debates and uncertainties...  is also admirably clear in its arguments and in digesting the literature... engages key ideas in a transparent way, integrating perspectives and developing its analysis clearly and coherently." This is important as it helps us move from "maybe we're completely missing a big consideration" to "some experts continue to disagree for certain reasons, but we have a solid understanding of the relevant considerations and can hold our own in a disagreement". 

Thanks for this!

I won't address all of your points right now, but I will say that I hadn't considered that "R&D is compensating for natural resources becoming harder to extract over time", which would increase the returns somewhat. However, my sense is that raw resource extraction is a small % of GDP, so I don't think this effect would be large.

Sorry for the slow reply!

I agree you can probably beat this average by aiming specifically at R&D for boosting economic growth.

I'd be surprised if you could spend $100s millions per year and consistently beat the average by a large amount (>5X) though:

• The $2 trillion number also excludes plenty of TFP-increasing research work done by firms that don't report R&D like Walmart and many services firms.
• The broad areas where this feels most plausible to me (R&D in computing or fundamental bio-tech) are also the areas that have the biggest potential downsides risks.
• To have impact you need to fund projects that wouldn't otherwise receive funding
• Governments and other funders want to fund things that increase growth. I'm sceptical you can be (e.g.) 10X as good as these funders at identifying bets ex ante.

Another relevant point is that some interventions increase R&D inputs in a non-targeted, or weakly targeted, way. E.g. high-skill immigration to the US or increasing government funding for broad R&D pots. The 'average R&D' number seems particularly useful for these interventions.

Great question!

I would read Appendix G as conditional on "~no civilizational collapse (from any cause)", but not conditional on "~no AI-triggered fundamental reshaping of society that unexpectedly prevents growth". I think the latter would be incorporated in "an unanticipated bottleneck prevents explosive growth".

I think the question of GDP measurement is a big deal here. GDP deflators determine what counts as "economic growth" compared to nominal price changes, but deflators don't really know what to do with new products that didn't exist. What was the "price" of an iPhone in 2000? Infinity? Could this help recover Roodman's model? If ideas being produced end up as new products that never existed before, could that mean that GDP deflators should be "pricing" these replacements as massively cheaper, thus increasing the resulting "real" growth rate?

This is an interesting idea. It wasn't a focus of my work, but my loose impression is that when economists have attempted to correct for these kinds of problems the resulting adjustment isn't nearly large enough to make Roodman's model consistent with the recent data. Firstly, measurements of growth in the 1700s and 1800s face the same problem, so it's far from clear that the adjustment would raise recent growth relative to old growth (which is what Roodman's model would need). Secondly, I think that when economists have tried to measure willingness to pay for 'free' goods like email and social media, the willingness is not high enough to make a huge difference to GDP growth.

Thank you for this comment! I'll make reply to different points in different comments.

But then the next point seems very clear: there's been tons of population growth since 1880 and yet growth rates are not 4x 1880 growth rates despite having 4x the population. The more people -> more ideas thing may or may not be true, but it hasn't translated to more growth.

So if AI is exciting because AIs could start expanding the number of "people" or agents coming up with ideas, why aren't we seeing huge growth spurts now?

The most plausible models have diminishing returns to efforts to generate new ideas. In these models, you need an exponentially growing population to sustain exponential growth. So these models aren't surprised that growth hasn't increased since 1880.

At the same time, these same models imply that if increasing output causes the population to increase (more output -> more people), then there can be super-exponential growth. This is because the population can grow super-exponentially with this feedback loop.

So my overall opinion is that it's 100% consistent to think:

1. The increased population of the last 100 years didn't lead to faster growth
2. If AGI means that more output -> more people, growth will accelerate.

Great suggestion - thanks! Have edited.

Hey - interesting question! 

This isn't something I looked into in depth, but I think that if AI drives explosive economic growth then you'd probably see large rises in both absolute energy use and in energy efficiency.

Energy use might grow via (e.g.) massively expanding solar power to the world's deserts (see this blog from Carl Shulman). Energy efficiency might grow via replacing human  workers with AIs (allowing services to be delivered with less energy input), rapid tech progress further increasing the energy efficiency of existing goods and services, the creation of new valuable products that use very little energy (e.g. amazing virtual realities), or in other ways. 

Thanks for these thoughts! You raise many interesting points.

 On footnote 16, you "For example, the application of Laplace’s law described below implies that there was a 50% chance of AGI being developed in the first year of effort". But historically, participants in the Dartmouth conference were gloriously optimistic

I'm not sure whether the participants at Dartmouth would have assigned 50% to creating AGI within a year and >90% within a decade, as implied by the Laplace prior. But either way I do think these probabilities would have been too high. It's very rare, perhaps unprecedented, for such transformative tech progress to be made with so little effort. Even listing some of the best examples of quick and dramatic tech progress, I found the average time for a milestone to be achieved was >50 years, and the list omits the many failed projects.

That said, I agree that the optimism before Dartmouth is some reason to use a high first-trial probability (though I don't think as high as 50%).

 

The point that Laplace's prior depends on the unit of time chosen is really interesting, but it ends up not mattering once a bit of time has passed.

Agreed! (Interestingly, it only doesn't matter once enough time has passed that Laplace strongly expects AGI to have already happened.) Still, Laplace's predictions about the initial years of effort do depend on the trial definition: defining a 'trial' as 1 day, 1 year, or 30 years gives very different results. I think this shows something is wrong with the rule more generally. The root of the problem is that that Laplace assigns 50% probability of the first trial succeeding no matter how we define a trial. I think my alternative rule, where you choose the trial definition and the first-trial probability in tandem, addresses this issue.

 

 If you rule out AGI until 2028 (as you do in your report), the Laplace prior gives you 1 - (1-[1/(2028-1956)+1])^(2036-2028) ≈ 10.4% ≈ 10%, which is well withing your range of 1% to 18%, and really near to your estimate of 8%

My estimate of 8% only rules out AGI by the end of 2020. If I rule out AGI by the end of 2028, it becomes ~4%. This is quite a lot smaller than the 10% from Laplace.

The top of my range would be 9%, which is close to Laplace. However, this high-end is driven by forecasting that the inputs to AI R&D will grow faster than their historical average, so more trials occur per year. I don't think such high values would be reasonable without taking these forecasts into account.

 

When you write "I also find that pr(AGI by 2036) from Laplace’s law is too high," what outside-view consideration are you basing that on? Also, is it really too high?

I find it too low mostly because it follows from aggressive assumptions about the chance of success in the first few years of effort, but also because of the reference classes discussed in the report.

Another way to justify ruling out Laplace is that if you had a hyper-prior, putting some weight on Laplace and some on more conservative rules, you would put extremely little weight on Laplace by now. (Although I personally wouldn't put much weight on Laplace even in an initial hyper-prior.)

There's a counter-intuitive example that illustrates this hyper-prior behaviour nicely. Suppose you assigned 20% to "AGI impossible" and 80% to another prior. If the other prior is Laplace, then your weight on "AGI impossible" rises to 92% by 2020, and you only assign 8% to Laplace. Your pr(AGI by 2036) is 1.6%. By contrast, if you reduce the first-trial probability in Laplace down to 1/100 then your weight on "AGI impossible" only rises to 29% by 2020 and your pr(AGI by 2036) is 6.3%. So having a lower first-trial probability ends up increasingpr(AGI by 2036).

It is not clear to me that by adjusting the Laplace prior down when you categorize AGI as a "highly ambitious but feasible technology" you are not updating twice

This is an interesting idea, thanks. I think  the description "highly ambitious" would have been appropriate in 1956: AGI would allow automation of ~all labour. In addition, it did seem hard to me to find reference classes supporting first-trial probability values above 1/50, and some reference classes I looked into suggest lower values.

That said, it's possible that my favoured range for the first-trial probability [1/100, 1/1000] was influenced by my knowledge that we failed to develop AGI. If so, this would have made the range too conservative.