1. I think that acceleration is autocorrelated---if things are accelerating rapidly at time T they are also more likely to be accelerating rapidly at time T+1. That's intuitively pretty likely, and it seems to show up pretty strongly in the data. Roodman makes no attempt to model it, in the interest of simplicity and analytical tractability. We are currently in a stagnant period, and so I think you should expect continuing stagnation. I'm not sure exactly how large the effect (and obviously it depends on the model) is but I think it's at least a 20-40 year delay. (There are two related angles to get a sense for the effect: one is to observe that autocorrelations seem to fade away on the timescale of a few doublings, rather than being driven by some amount of calendar time, and the other is to just look at the fact that we've had something like ~40 years of relative stagnation.)
2. I think it's plausible that historical acceleration is driven by population growth, and that just won't really happen going forward. So at a minimum we should be uncertain betwe3en roodman's model and one that separates out population explicitly, which will tend to stagnate around the time population is limited by fertility rather than productivity.

(I agree with Max Daniel below that I don't think that Nordhaus' methodology is inherently more trustworthy. I think it's dealing with a relatively small amount of pretty short-term data, and is generally using a much more opinionated model of what technological change would look like.)

I don't think this would be a good reaction because:

• Nordhaus's paper was only formally published now, but isn't substantially newer than Roodman's work. Nordhaus's paper was available as NBER working paper since at least 2018, and has been widely discussed among longtermists since then (e.g. I remember a conversation in fall 2018, there may have been earlier ones). [ETA: Actually Nordhaus's paper has circulated as a working/discussion paper since at least September 2015, and was e.g. mentioned in this piece of longtermist work from 2017.]
  • There are other similar papers, e.g. by Aghion et al. See e.g. here (there is now also an edited volume of "Econ of AI" conference papers) and the GovAI webinar with Jones & Jones (need to scroll down on that page).
• I've only had the chance to skim Roodman's work, but my quick impression is that it isn't straightforwardly the case that Nordhaus's model is "more detailed and trustworthy". Rather, it seems to me that both models are more detailed along different dimensions: Roodman's model explicitly incorporates noise/stochasticity, and in this sense is significantly more mathematically complex/sophisticated. On the other hand, Nordhaus's model incorporates more theoretical assumptions, e.g. about different types of "factors of production" and their relationship as represented by a "production function", similar to typical economic growth models. (Whereas Roodman is mostly fitting a model to a trend of a single quantity, in a way that's more agnostic about the theoretical mechanisms generating that trend.)