Self-Justified Equilibria: Existence and Computation

Abstract

In this paper, we introduce 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 in assets and commodities to maximize the sum of current utility and expected future utilities that are forecasted on the basis of current endogenous variables and the current exogenous shock. Agents' characteristics include a loss function that prescribes how the agent trades off the accuracy and the computational complexity of possible forecasts. We provide sufficient conditions for the existence of self-justified equilibria, and we develop a computational method to approximate them numerically. For this, we focus on a convenient special case where we use Gaussian process regression coupled to active subspaces to model agents' forecasts. We demonstrate that this framework allows us to solve stochastic overlapping generations models with hundreds of heterogeneous agents and very accurate forecasts.