I will have to think about this further to debate the rationality behind this approach. However, I do have some initial thoughts.
1. The results do not surprise me all that much. We know that stock valuation includes a portion of inflation and a portion of risk, in the valuation of returns. As such, stocks should return rates higher than inflation to compensate for the short-term volatility of equities.
2. In periods of high inflation the value of companies can be eroded due to "real" decreases in prices if prices do not match the rate of inflation. Considering the periods of higher inflation, or stagnation of the market without appreciation at inflation, would result in an erosion of value.
3. The overall annual return of 1.64% seems low to me, mainly because most studies show annual rates of return around 10%. One likely cause would be the exclusion of dividends in the equation of returns, which remove value from the index while providing return outside the auspices of the index itself. Another factor could be the mechanics of the index itself.
The study wasn't tying the index value to the dollar, it was removing the rate of inflation from the equation. However, periods of reduced appreciation could be prolonged lulls in the appreciation, or the returning of rationality. The recent "boom" outside of inflation could either be a removal of rationality, resulting in a big asset bubble, or the real long-term rate of appreciation for this economy.
Given that P/E ratios are not exactly irrational, I would hazard to guess that the appreciation seen in the recent years isn't too far outside of the "norm" and that the long-term rate of appreciation is above the 1.64% presented.
Of course, additional noise can be included with the adjustments made to CPI, such as technology improvement divisors and such. Additional noise can be seen in the different make-ups of the economy, which is why it would be interesting to repeat this for the S&P500 or other indexes, as well as international indexes.
I will ponder more and also await the feedback of other members who might have some great thoughts of this. although I do expect from RPBs to pop in here and add some tripe.