Asset Pricing with Incomplete Information under Stable Shocks

We study a consumption based asset pricing model with incomplete information and alpha-stable shocks. Incomplete information leads to a non-Gaussian filtering problem. Bayesian updating generates fluctuating confidence in the agents' estimate of the persistent component of the dividends' growth rate. Similar results are obtained with alternate distributions exhibiting fat tails (Extreme Value distribution, Pearson Type IV distribution) while they are not with a thin-tail distribution (Binomial distribution). This has the potential to generate time variation in the volatility of model-implied returns, without relying on discrete shifts in the drift rate of dividend growth rates. A test of the model using US consumption data indicates strong support in the sense that the implied returns display significant volatility persistence of a magnitude comparable to that in the data.