In a political economy framework, we study how false narratives emerge in response to limitations in recipients' memory, proposing an approach based on partial identification. Coarse memory allows voters to recall policy and outcome frequencies but not their correlations. Politicians exploit this by crafting plausible narratives to inflate their policies’ effectiveness. We find that the less a policy is implemented, the more optimistic the narrative can be. In a competition model, opposing narratives become polarized, fostering political cycles where office tenure is independent of policy quality. Our mechanisms are consistent with an analysis of U.S. Congress members' rhetorical strategies.