In the interest of fairness, here is a view saying that comparing interest rates and PE ratios is a useless exercise: http://www.marketwatch.com/story/are-stocks-really-undervalued-2010-09-03?dist=beforebell
I have several issues with the way the study was conducted as it seems a painfully simply regression analysis for a firm that specializes in it. What I found in my own research was that periods of a big positive spread between earnings yield and interest rates correlated very highly with periods before a major bull market and the inverse was also true. There was one period where this relationship broke down badly which was the 1990s, but that was the only one I could find.
I will do my own regression along the lines of the way they designed it and try to figure out how they came up with what they did because my knowledge of the data does not seem to support the notion here. Now, they used real rates of return against nominal comparisons of PE ratios and interest rates, whereas I kept everything in nominal terms.