Bounded Foresight Equilibrium in Large Dynamic Economies with Heterogeneous Agents and Aggregate Shocks

Abstract: Large dynamic economies with heterogeneous agents and aggregate shocks are central to many important applications, yet their equilibrium analysis remains computationally challenging. This is because the standard solution approach, rational expectations equilibria require agents to predict the evolution of the full cross-sectional distribution of state variables, leading to an extreme curse of dimensionality. In this paper, we introduce a novel equilibrium concept, N-Bounded Foresight Equilibrium (N-BFE), and establish its existence under mild conditions. In N-BFE, agents optimize over an infinite horizon but form expectations about key economic variables only for the next N periods. Beyond this horizon, they assume that economic variables remain constant and use a predetermined continuation value. This equilibrium notion reduces computational complexity and draws a direct parallel to lookahead policies in reinforcement learning, where agents make near-term calculations while relying on approximate valuations beyond a computationally feasible horizon. At the same time, it lowers cognitive demands on agents while better aligning with the behavioral literature by incorporating time inconsistency and limited attention, all while preserving desired forward-looking behavior and ensuring that agents still respond to policy changes. Importantly, in N-BFE equilibria, forecast errors arise endogenously. We measure the foresight errors for different foresight horizons and show that foresight significantly influences the variation in endogenous equilibrium variables, distinguishing our findings from traditional risk aversion or precautionary savings channels. This variation arises from a feedback mechanism between individual decision-making and equilibrium variables, where increased foresight induces greater non-stationarity in agents' decisions and, consequently, in economic variables.