There is always a risk in overemphasising the predictive nature of measures, such as the CAPE.

For example, even without looking at the results of CAPE to date most analysts (or people with a grounded understanding of business valuation more generally) would probably agree that over the long term market values should, more or less, reflect the real value of the constituent's earnings over a business cycle. Personally I think Shiller's CAPE is a very logical measure, but I'm not sure it's too helpful in making investment predictions.

This leads us to the question as to why the CAPE is such a poor predictor of future performance as surely most astute investors should (if even half rational) pursue investment horizons much longer than even two or three business cycles.

In this case the CAPE model fitting too well over the medium term (30 yrs+) may be more a reflection of a paradigm shift than a flaw in the model. For example, as countries develop it's normal to expect to see advances in production methods, technology and infrastructure, as well as changes in consumption patterns; this is followed by increased foreign capital and reduced costs of lending and lower (at least perceived lower) market/geopolitical risk. These accelerated periods of growth aren't (as far as I know) incorporated in the CAPE, which means that comparing historical CAPE to current isn't really a like-for-like comparison. Of course in the case of mature, developed economies we see the opposite happen as lower inflation and interest rate expectations lead to higher prices being paid for future earnings.