The high welfare cost of small information failures

Are stock markets efficient in the sense that stock prices reflect all available information? This question has preoccupied finance lately as many have started to doubt the efficient market hypothesis during the latest crisis. One critical aspect of this is whether current tests of the hypothesis actually give an accurate picture, and if not whether this matters in a significant way.

Tarek Hassan and Thomas Mertens
claim that it is possible for stock markets to aggregate information properly, that small errors at the household level can accumulate and amplify if these errors are correlated, and that the welfare consequences can be substantial even if the initial errors were small. This cost emerges for a portfolio misallocation due to the higher volatility of stock prices. To get to such a result, they take a standard real business cycle model, add to it that households get a noisy private signal about future total factor productivity. They then look at the stock market for additional information to form expectations. If you allow households to be on average more optimistic than rationality in some state, and more pessimistic in others, you get the above results. Interestingly, Hassan and Mertens show that households face little incentives to correct individually for these small common errors (0.01% of average consumption), but collectively the consequences are large (2.4%). Talk about an amplification.