I found the paper where bogle actually describes his methodology used to generate graph posted above:
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To answer my earlier questions in this thread about how he generated his numbers, he uses the initial dividend yield and trailing 10 year average for earnings growth. His also assumes that P/E will revert to the prior 30-year average.
I will note that he used rolling windows on a monthly basis. I think monthly is poor choice as this greatly inflates the number of data points on the graph and
makes his model seem much stronger than can be justified statistically (because of the heavy amount of overlap, the data points on the graph aren't anywhere near independent, etc. etc.).
In his paper, he also redoes his experiment from 1915-2015. Here he obtains an R^2 = 0.44 which is much lower but inline with experimental results for Schiller PE10. I can buy that Bogle's model is roughly as good as Schiller PE but I had hard time accepting an R^2 of 0.65 (
which I think is too good to be true).
If you look at Bogle's graph for a bigger dataset (1915-2014) you can see that this relationship no longer holds and a Bogle prediction of 6% yields an actual return centered around 6%.
The problem is that 1990-2014 is such a short time period that you can get a lot of noise and spurious results.