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).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
- Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-93, September.
- Aoki Takaaki, 2011. "On the Implications of Two-Sided Altruism in Human Capital Based OLG Model," Asian Journal of Law and Economics, De Gruyter, vol. 2(2), pages 1-40, July.
- Andrew B. Abel, 1988.
"Operative Gift and Bequest Motives,"
NBER Working Papers
2331, National Bureau of Economic Research, Inc.
- Andrew B. Abel, . "Operative Gift and Bequest Motives," Rodney L. White Center for Financial Research Working Papers 9-87, Wharton School Rodney L. White Center for Financial Research.
- Andrew B. Abel, . "Operative Gift and Bequest Motives," Rodney L. White Center for Financial Research Working Papers 09-87, Wharton School Rodney L. White Center for Financial Research.
- Hori, Hajime & Kanaya, Sadao, 1989. "Utility functionals with nonpaternalistic intergenerational altruism," Journal of Economic Theory, Elsevier, vol. 49(2), pages 241-265, December.
- Kimball, Miles S., 1987. "Making sense of two-sided altruism," Journal of Monetary Economics, Elsevier, vol. 20(2), pages 301-326, September.
- Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
- Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
- Hori, Hajime, 1997. "Dynamic Allocation in an Altruistic Overlapping Generations Economy," Journal of Economic Theory, Elsevier, vol. 73(2), pages 292-315, April.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.