We show that inflation expectations are heterogeneous and depend on past individual experiences. We propose a diagnostic expectations-augmented Kalman filter to represent consumers’ heterogeneous inflation expectations-formation process, where heterogeneity comes from an anchoring-to-the-past mechanism. We estimate the diagnosticity parameter that governs the inflation expectations-formation process and show that the model can replicate systematic differences in inflation expectations across cohorts in the US. We introduce this mechanism into a New Keynesian model and find that heterogeneous expectations anchor aggregate responses to the agents’ memory, making shocks more persistent. Central banks should be more active to prevent agents from remembering current shocks far into the future.