Recursive equilibria in dynamic economies with bounded rationality

Abstract

I provide a new way to model bounded rationality and show the existence of recursive equilibria with bounded rational agents. The existence proof applies to dynamic stochastic general equilibrium models with infinitely lived heterogeneous agents and incomplete markets. In this type of models, recursive methods are widely used to compute equilibria, yet recursive equilibria do not exist generically with rational agents. I change the rational expectation assumption and model bounded rationality as follows. Different from a rational agent, a bounded rational agent does not know the true Markov transition of the state space of the economy. In order to make decisions, the bounded rational agent would try to compute a stationary distribution of the state space using a numerical method and then use the Markov transition associated with it to maximize utility. For a certain distribution of the current period, given other agents' strategies, the agent would get its next-period transition: the distribution of the state space in the next period that results from the competitive equilibrium in the next period. However, if a distribution stays ``closer'' to its next-period transition than the minimum error the numerical method can observe, the agent would consider it as computational stationary. In equilibrium, each agent maximizes utility with a computational stationary distribution and markets clear. I use the Kantorovich-Rubinshtein norm to characterize the distance between distributions of the state space. With this set up, usual convergence criteria used in the literature can be incorporated and thus many computed equilibria in the literature using recursive methods can be categorized as bounded rational recursive equilibria in the sense of this paper.