Something under-appreciated: If you pretend a company is paying out 100% of profits as dividends (which it theoretically potentially could, and is useful as a financial modelling tool), then the inverse of P/E, E/P, is an interest rate on the price of the stock.

Ideal P/Es thus shouldn't be flat, they should be tracking long-term bond rates. This isn't an empirical observation, just a theoretical one of what "ideal" should be. But one should rationally expect P/Es to go up when interest rates drop.

It is disappointing to me that even Shiller doesn't really consider this much.