We study the consumption based asset pricing model in a discrete-time pure exchange setting with incomplete information. Incomplete information leads to a filtering problem which agents solve using the Kalman filter. We characterize the solution to the asset pricing problem in such a setting. Empirical estimation with US consumption data indicates strong statistical support for the incomplete information model versus the benchmark complete information model. We investigate the ability of the model to replicate some key stylized facts about US equity and risk-free returns.