Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production
AbstractBased on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider 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 are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.
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Bibliographic InfoPaper provided by University of Connecticut, Department of Economics in its series Working papers with number 2005-51.
Length: 42 pages
Date of creation: Aug 2005
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Note: The authors would like to thank Elena Antoniadou, Robert Becker, Manjira Datta, Seppo Heikkil\"a, Len Mirman, Jayaram Sethuraman, Yiannis Vailakis, Itzhak Zilcha, and especially John Stachurski for very helpful discussions on topics related to this paper. All mistakes are our own.
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Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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- Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
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