Abstract A large psychology literature argues that, due to selective memory recall, decision-makers’ forecasts of the future are overly influenced by the perceived news. We adopt the diagnostic expectations (DE) paradigm [Bordalo et al. (2018), Journal of Finance, 73, 199–227] to capture this feature of belief formation, develop a method to incorporate DE in business cycle models, and study the implications for aggregate dynamics. First, we address (1) the theoretical challenges associated with modelling the feedback between optimal actions and agents’ DE beliefs and (2) the time-inconsistencies that arise under distant memory (i.e. when news is perceived with respect to a more distant past than just the immediate one). Second, we show that under distant memory the interaction between actions and DE beliefs naturally generates repeated boom–bust cycles in response to a single initial shock. We also propose a portable solution method to study DE in dynamic stochastic general equilibrium models and use it to estimate a quantitative DE New Keynesian model. Both endogenous states and distant memory play a critical role in successfully replicating the boom–bust cycle observed in response to a monetary policy shock.