How do memory limitations affect economic behavior? I develop a model of memory grounded in psychology and biology research to investigate this question. Using this model, I study the case where people apply Bayes rule to the history they recall as if it were the true history. The resulting beliefs exhibit over-reaction on average. They also exhibit under-reaction with the model providing enough structure to allow predictions about which effect dominates when. I then apply this general framework to an otherwise standard model of consumption. It predicts the broad structure of consumption predictability as well as differences in marginal propensity to consume across different income streams. Most important, because it ties the extent of bias to a measurable aspect of the stochastic process being forecasted, the model makes novel, testable empirical predictions. Keywords: psychology, biology, Bayes rule, personal economic history, consumption.