As a summer research fellow at FHI, I’ve been working on using economic theory to better understand the relationship between economic growth and existential risk. I’ve finished a preliminary draft; see below. I would be very interesting in hearing your thoughts and feedback!
Draft: leopoldaschenbrenner.com/xriskandgrowth
Abstract:
Technological innovation can create or mitigate risks of catastrophes—such as nuclear war, extreme climate change, or powerful artificial intelligence run amok—that could imperil human civilization. What is the relationship between economic growth and these existential risks? In a model of endogenous and directed technical change, with moderate parameters, existential risk follows a Kuznets-style inverted U-shape. This suggests we could be living in a unique “time of perils,” having developed technologies advanced enough to threaten our permanent destruction, but not having grown wealthy enough yet to be willing to spend much on safety. Accelerating growth during this “time of perils” initially increases risk, but improves the chances of humanity's survival in the long run. Conversely, even short-term stagnation could substantially curtail the future of humanity. Nevertheless, if the scale effect of existential risk is large and the returns to research diminish rapidly, it may be impossible to avert an eventual existential catastrophe.
That's an interesting and the little i skimmed was somewhat straight forward if you can get through the dialect or notation, which is standard in econ papers ---which i'd call neoclassical. ( I got up to about page 20 -- discussions of effects of scientists/workers switching to safety production rather than consumption production).
This raises to me a few issues. you have probably seen https://arxiv.org/abs/1410.5787 Given debates about risks of other envirojmental risks like GMOs and nuclear energy, its even unclear what is 'safety' or 'precautionary' versus consumption production. Its also unclear how much 'science can come to the rescue' (discussed many places like AAAS).
There are also the behavioral issues---even if your model (like the Kuznets curve) is basically correct and one can calculate 'effectively altruistic' policies, whether they will be supported by the public/government and entice scientists and other workers to switch to 'green jobs' (whether technical or, say organic farming ) is a sociopolitical issue.
(Its possible other sorts of models, or variants of yours using some behavioral data, might be able to assess both effects of policies as you do, and include factors describing the plausibility they will be adopted. (I googled you at Columbia and see you also studied public opinion spread via Twitter, etc. and that gives ideas about dynamics of behavioral variables. Presumably these are already implicit in your various parameters beta, epsilon, etc. I guess these are also implicit in the discount factors discussed by Nordhaus and others--but they may have their own dynamics, rather than being constants. )
Alot of current climate activists promote 'degrowth' and lifestyle change (diet, transport, etc.) (eg extinction rebellion) , partly because because they think that maybe more important than growth, and don't trust growth will be applied to 'safety' rather than activities that contribute to AGW risks. Also many of them don't trust economic models, and many if not most people do understand them much (I can can only get a rough understanding partly because going through the math details is both often beyond my competency, and I have other things to do (i'm trying to sketch more simple models that attempt to catch the main ideas which might be comprehensible to and useful for a wider audience. ) As noted, a variant of your model could probably include some of these sociopolitical issues.)
Anyway, thought provoking paper.