Publication: Useful results for the simulation of non-optimal economies with heterogeneous agents
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2021-09-07
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Abstract
This paper deals with infinite horizon non-optimal economies with aggregate uncertainty and a finite number of heterogeneous agents. It derives sufficient conditions for the existence of a recursive structure,an ergodic, a stationary, and a non-stationary equilibria. It also gives an answer to the following question: is it possible to derive a general framework which guarantees that numerical simulations truly reflect the behavior of endogenous variables in the model? We provide sufficient conditions to give an affirmative answer to this question for endowment economies with incomplete markets and uncountable exogenous shocks. These conditions guarantee the ergodicity of the process and hold for a particular selection mechanism. For economies with finitely many shocks or for an arbitrary selection in economies with uncountable shocks, it is only possible to show that a computable, time independent and recursive representation generates a stationary Markov process. The results in this paper suggest that often a well defined stochastic steady state in heterogenous agent models is sensitive to the initial conditions of the economy; a fact which imply that heterogeneity may have irreversible long-lasting effects.
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Non-Optimal Economies, Markov Equilibrium, Heterogeneous Agents, Simulations