I've thought a lot about the CAPE (some long readers of this thread may remember my own invention of the "I-E-S-CAPE" or "idiot-something-something-CAPE" which sounded cute at the time) and its dogmatic reliance on P/E ratios as a governing metric for market behavior.
It's a well-accepted principal that the intrinsic value of a stock is related to expected future earnings, which might be loosely to strongly associated with past earnings, inferred from P/E. However, anybody I've ever discussed investments with is much more interested in future growth of the stock than future earnings and associated dividends, so value is, in my mind, much more strongly linked (in the psychology of the crowd, not that of selected investors, say value investors) to expectations of growth, which are often disconnected from past earnings (and maybe strongly anti-correlated; solid dividend stocks are rarely also high growth stocks).
Also, the intrinsic value of something is often only loosely linked to its market value. Looking at home values, one might expect a strong connection with the cost of building the home, and this is very frequently the case, perhaps in most markets, where the cost of land is a small fraction of that of the value of the house plus land. However, in expensive housing markets, the value of the land (which has no intrinsic meaning, only an emotional / psychological one) governs the cost / value of the house plus land.
When stock markets fluctuate upward above the historic trend, whether in true bubbles or large (but less steeply rising) random fluctuations, total valuation becomes less connected to intrinsic value (of the underlying value of the company) and more controlled by emotions, and what people (the crowd) are willing to pay for the possibility of further growth.
My own view is that the cycles we observe in all financial markets are the result of "noise traders" (all of us) ratcheting prices up and down based on chaotic collective action, independent of true information about the future value of the market (my belief is that no such information exists), and largely independent of the intrinsic value of companies being bought and sold. Very rapid rises are likely to be followed by significant negative corrections, and vice versa. The rest, I think, is noise.
So I think. Of course, Shiller's CAPE may very well turn out to prove me a bigger idiot than I already think I am. :-)