Abstract
We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitz Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitz (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact nonlinear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 505-544 |
| Number of pages | 40 |
| Journal | Journal of Mathematical Economics |
| Volume | 41 |
| Issue number | 4-5 SPEC. ISS. |
| DOIs | |
| State | Published - Aug 2005 |
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Keywords
- Lattice Programming
- Markovian equilibrium
- Monotone methods
ASJC Scopus subject areas
- Economics and Econometrics
- Applied Mathematics
Cite this
Markovian equilibrium in infinite horizon economies with incomplete markets and public policy. / Datta, Manjira; Mirman, Leonard J.; Morand, Olivier F.; Reffett, Kevin.
In: Journal of Mathematical Economics, Vol. 41, No. 4-5 SPEC. ISS., 08.2005, p. 505-544.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Markovian equilibrium in infinite horizon economies with incomplete markets and public policy
AU - Datta, Manjira
AU - Mirman, Leonard J.
AU - Morand, Olivier F.
AU - Reffett, Kevin
PY - 2005/8
Y1 - 2005/8
N2 - We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitz Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitz (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact nonlinear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.
AB - We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitz Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitz (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact nonlinear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.
KW - Lattice Programming
KW - Markovian equilibrium
KW - Monotone methods
UR - http://www.scopus.com/inward/record.url?scp=20344402531&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=20344402531&partnerID=8YFLogxK
U2 - 10.1016/j.jmateco.2005.01.001
DO - 10.1016/j.jmateco.2005.01.001
M3 - Article
AN - SCOPUS:20344402531
VL - 41
SP - 505
EP - 544
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
IS - 4-5 SPEC. ISS.
ER -