There was a time where macroeconomics was ruled by adaptive (or backward-looking) expectations, like the much-ridiculed chartists. Then there was a revolution and rational (typically forward-looking) expectations were widely adopted, realizing that people are not stupid and will try to use the available information, including what other agents may do, to figure out what the future holds. Rationality, and in particular rational expectations, has recently come under attack because models failed to predict recent bubbles and crashes. I think this is mistaken, as detailed on several occasions on this blog.
Gregory Chow, however, longs for a return to adaptive expectations for three other reasons. The first is that it is empirically more plausible. Exhibit A is a regression of the stock prices of 50 blue chips in Taiwan on current dividends and past dividend growth. Despite a lowly R2 of 0.111, the fact that the coefficient on dividend growth is positive and significant is taken as evidence of adaptive expectations. I do not find this convincing, as a similar result could emerge with rational expectations if the dividend growth process is persistent.
The second reason is that "there is no reason to believe that the expected values [computed from an econometric model of the rational expectations] will have a sum, after discounting, which equals the actual current price." I think the underlying reasoning is that a statistician can only use a linear combination of past observations, thus economic agents will, too, and this all looks like adaptive expectations. But economic agents, and nowadays statisticians, are more sophisticated than that, and a gigantic literature in finance has shown that, for example, non-linearities and endogenous volatility, too name a few, are important. Even though statisticians have become much more sophisticated, they are still running behind economic agents and are far removed from being linearly backward-looking.
The third reason is that macroeconomists started using rational expectations simply because it was required to deal with the Lucas Critique, empirical evidence be damned. While I can be sympathetic to the argument that rational expectations was adopted without much direct empirical evidence, I also believe that economic agents do try and avoid systematic mistakes and that their expectations contain at least some rationality. And as much literature has shown, a modicum of rationality can bring markets darn close to prices that look like perfectly rational ones.