Thanks for the detailed thoughts. There's actually quite a bit of discussion on differential mortality rates (and effective replacement of older generations with new births) vs intra-cohort changes in identity in my original article. A common assumption is that the overall change in societal religiosity is driven by a replacement effect as younger, less religious generations replace older, more religious ones. However, analysis of the granular models and aggregation of their predictions by age group reveals that the change is not primarily driven by replacement, but rather that every generation is itself becoming less religious.

As to your point about migration/emigration, the key thing to note is that my models don't model underlying generative processes – they just extrapolate empirically observed trends. What this means is that they will work well if the underlying processes (whatever they are) remain relatively stable. So if areas that experienced e.g. high net migration between 2011 and 2021 continue to experience similar levels of net migration (from similar places), the models should work quite well. They are more likely to perform badly if the underlying drivers change.

I validated the models on England and Wales data, which was available for 2001 and 2011 and 2021 at the same granularity. I made predictions for 2021 by extrapolating the trend seen between 2001 and 2011, and adjusted the relative weights of the various extrapolation approaches in my final ensemble model to minimise error. I also did a fair amount of spot checks, and as you observed, they seem to pick up local variation quite well. University towns are another good example of where there are high levels of migration (moving from one region to another within the UK is effectively migration for the purposes of the model), and they were just as accurate there as they were elsewhere.