Abstract This paper analyzes how information-processing limitations affect consumption in a dynamic full-fledged non-linear quadratic Gaussian (LQG) setting. In the model, risk-averse consumers rationally choose the quantity and quality of information to process about their wealth, while constrained by a Shannon channel. The main contribution of the paper is methodological. It proposes a solution to rational inattention problems in rich theoretical environments. The main prediction of the model is that consumption responses to wealth shocks are asymmetric, with negative shocks producing faster and stronger reaction than positive shocks. The model also predicts that information-processing constraints increase persistence and volatility of consumption behavior.