Self-justified equilibria: existence and computation

This paper introduces the concept of self-justified equilibria as a tractable alternative to rational expectations equilibria in stochastic general equilibrium models with heterogeneous agents. A self-justified equilibrium is a temporary equilibrium where, in each period, agents trade assets and commodities to maximize the sum of their current utility and expected future utilities, which are forecasted based on current endogenous variables and the current exogenous shock. The agents’ forecasting functions are assumed to be mean-squared optimal forecasts within a given compact, finite-dimensional set of functions. We provide sufficient conditions for the existence of self-justified equilibria and develop a simulation-based computational method to approximate them. By leveraging active subspace methods, we reduce the dimensionality of the problem, lower computational complexity, and improve forecasting accuracy, thereby mitigating the curse of dimensionality. We apply our method to high-dimensional overlapping generations models with aggregate shocks, demonstrating that self-justified equilibria can be efficiently computed to analyze complex economic models.