Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics
AbstractThis article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. We analyzed the special case where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions with distinct steady states (indeterminacy of self-consistent policy functions).
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 44994.
Date of creation: 10 Mar 2013
Date of revision:
Bellman equation; Two-sided altruism; Dynamic inconsistency; Self-consistent policy functions; Indeterminacy; Overlapping generations model.;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-05 (All new papers)
- NEP-DGE-2013-08-05 (Dynamic General Equilibrium)
- NEP-UPT-2013-08-05 (Utility Models & Prospect Theory)
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