TY - JOUR
T1 - A qualitative approach to Markovian equilibrium in infinite horizon economies with capital
AU - Mirman, Leonard J.
AU - Morand, Olivier F.
AU - Reffett, Kevin
N1 - Funding Information:
We thank Roko Aliprantis, Elena Antoniadou, Bob Becker, Hector Chade, John Coleman, Man-jira Datta, Larry Epstein, Andrezej Granas, Jeremy Greenwood, Brigit Grodal, Seppo Heikkilä, Mark Huggett, Mike Jerison, Cuong LeVan, William Lovejoy, Robert Lucas, Jr., Jianjun Miao, Ed Schlee, Chris Shannon, John Stachurski, Yiannis Vailakis, and Tim Van Zandt for helpful conversations and/or comments, as well as participants at the ET meetings in Ischia, Italy, the SWET meetings at Cal Tech, the Summer Econometrics Society Meetings at UCLA, and participants at seminars at Copenhagen, CORE, Erasmus, Indiana, Nova Lisboa, Rochester, SUNY-Albany, Virginia Tech, Virginia, and Warwick for helpful comments. Finally, we would especially like to thank Manuel Santos and an anonymous referee for their extraordinarily helpful conversations and/or comments on all aspects of this paper. Reffett would like to thank the Council of 100 Dean’s Summer Grant program at ASU, as well as the Tinbergen Institute at Erasmus University, Rotterdam and CEntre de Recherche en Mathématiques, Statistique et Economie Mathématiques (CERMSEM) at Université de Paris I for their generous support of this research. All the mistakes remain our own.
PY - 2008/3
Y1 - 2008/3
N2 - Using lattice programming and order theoretic fixpoint theory, we develop a new class of monotone iterative methods that provide a qualitative theory of Markovian equilibrium decision processes for a large class of infinite horizon economies with capital. The class of economies includes models with public policy, valued fiat money, monopolistic competition, production externalities, and various other nonconvexities in the production sets. The results can be adapted to construct symmetric Markov equilibrium in models with many agents and market incompleteness. As the methods are constructive, they provide the foundations for a rigorous analysis of numerical approximation schemes that study extremal Markovian equilibrium. Equilibrium comparative statics results relative to the space of economies are available. Of independent interest, we provide new conditions for preserving complementarity under maximization, and new generalized envelope theorems for nonconcave dynamic programming problems. Our fixed point algorithms are sharp, and are able to distinguish sufficient conditions under which Markovian equilibrium form a complete lattice of Lipschitz continuous, uniformly continuous and semicontinuous monotone functions as well as unique continuously differentiable equilibrium.
AB - Using lattice programming and order theoretic fixpoint theory, we develop a new class of monotone iterative methods that provide a qualitative theory of Markovian equilibrium decision processes for a large class of infinite horizon economies with capital. The class of economies includes models with public policy, valued fiat money, monopolistic competition, production externalities, and various other nonconvexities in the production sets. The results can be adapted to construct symmetric Markov equilibrium in models with many agents and market incompleteness. As the methods are constructive, they provide the foundations for a rigorous analysis of numerical approximation schemes that study extremal Markovian equilibrium. Equilibrium comparative statics results relative to the space of economies are available. Of independent interest, we provide new conditions for preserving complementarity under maximization, and new generalized envelope theorems for nonconcave dynamic programming problems. Our fixed point algorithms are sharp, and are able to distinguish sufficient conditions under which Markovian equilibrium form a complete lattice of Lipschitz continuous, uniformly continuous and semicontinuous monotone functions as well as unique continuously differentiable equilibrium.
KW - Equilibrium comparative statics
KW - Lattice programming
KW - Markovian equilibrium
KW - Order theoretic fixed point theory
KW - Stochastic growth
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U2 - 10.1016/j.jet.2007.05.009
DO - 10.1016/j.jet.2007.05.009
M3 - Article
AN - SCOPUS:38849169723
SN - 0022-0531
VL - 139
SP - 75
EP - 98
JO - Journal of Economic Theory
JF - Journal of Economic Theory
IS - 1
ER -