The 2025 Brookings Papers conference had a sesssion on this.
The slides from Lukasz Rachel and the discussants are available.
The discussant Adrien Auclert makes some very nice points. I picked up on some.
First, the framework. R* is the price that balances demand for capital for use in production by firms with the supply of savings by consumers. But terminology is hard here: the savings by consumers causes them to build up wealth, which is in part demand for durable assets (e.g. a house). So wealth accumulation is asset demand which is capital supply. And the demand for the use of capital is by firms and governments to produce goods/svcs, and they issue claims on the owernship of such assets e.g. shares (and for government, government debt). So the value of assets issued by firms and government is asset supply or capital demand. This is nicely illustrated by his graph which highlights the demand/supply nomenclature
Thus he talks nicely about forces that raise asset supply which raise r*
And forces that raise asset demand, which lower r*
He summarises the main finding of the paper as being that asset demand has won
with the main drivers falling productivity, rising aging and rising risk
Here is the prediction for the future
Thus we have
1. business as usual, small and gentle fall in r*
2. more productivity growth, r* rises.