Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of minimal state space Markovian equilibrium decision processes (MEDPs) and stationary Markov equilibrium (SME) for a large class of stochastic overlapping generations models. In contrast to previous work, our focus is exclusively on constructive fixed point methods. In addition, we extend results obtained in earlier work to the case of more general reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods provide monotone iterative algorithms the uniformly converge to extremal Markovian equilibrium decision proceesses. Further, those methods can be tied to the computation of extremal equilibrium invariant distributions. Our methods select equilibrium that avoid many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We study cases where MEDPs are unique continuous functions, as well as provide the first results in the literature on the existence and computation of minimal state space MEDPS and SME for the case where capital income is not monotone. We show that our results on minimal state space MEDPs extend to the case of n-period stochastic OLG models. Finally, we conclude with examples common in macroeconomics such as models with social security, we provide a brief discussion of equilibrium comparative statics, and show how some of our results extend to settings with unbounded state spaces.