I have great respect for both. Siegel taught us well about the long-term stock market returns, it is now serving as my first principle in equity investing; Shiller on the other hand is a very sensible economist, who incorporates behavior finance into his economic theories.

But one problem about the CAPE ratio is that it is a rear-view mirror valuation, not forward looking, so it is more like a historical guidance than a prospective evaluation. Nevertheless, the cyclical-adjusted earnings yield (CAEY) is sitting at 3.35%, which is actually still lower than the 10-year average of 1-year treasury rate at 0.7%. CAPE valuation is high versus the history, but not versus its alternatives, e.g. interest rates. In fact, CAEY in 2000 and 2008 were lower than the average interest rates, which explained the overvaluation then.

Hence I'm more inclined to sit in Siegel's camp for this case, but with caution. Shiller has a point though on the secular stagnation phenomena, the trend of low growth and low inflation has been there for too long despite the enormous liquidity. A Black Swan, which by definition we have no idea what it is, is bound to happen some time soon.