From the abstract
the lowest sustainable withdrawal rates (which give us our idea of the safe
withdrawal rate) tend to follow prolonged bull markets, while the highest sustainable withdrawal
rates tend to follow prolonged bear markets.
We've discussed this idea here. If you retire when P/E ratios are high, you should plan on a lower withdrawal rate. If you retire when P/E ratios are low, you can plan for a higher withdrawal rate.
So, people who were planning to retire around 2000 would notice their nest eggs are growing fast in the 1990s. They should not slow their savings rate because the fast growth was the result of higher P/E's which implied lower withdrawal rates at retirement. That makes sense to me.
OTOH, people who were planning to retire around 1980 would notice their nest eggs are growing slowly in the 1970s. They should not increase their savings rate because the slow growth was the result of low P/E's which implied higher withdrawal rates at retirement. Although that seems plausible, and did work with 20/20 hindsight, I wonder how many of us would have the belief to actually do that.
Here's a different way of looking at it.
The typical American planning to retire at 62 (not people on this board) can save money at age 28 and assume that particular bucket of money will grow exactly 35 years until it is withdrawn at 62.
The money saved at 29 goes into a different bucket and grows 35 years until it's withdrawn at 63.
...
The money saved at 61 will grow 35 years until it's withdrawn at 96.
In this view, the nest egg at 62 and the SWR is irrelevant. As long as you believe that over any 35 year period you'll get a pretty "average" return, you simply ignore all the ups and downs along the way and plan to spend anything that happens to be in the designated bucket each year in retirement.