Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics
This 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).
|Date of creation:||10 Mar 2013|
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- Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-1393, 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 727-732, May.
- Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, 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.
- Kimball, Miles S., 1987. "Making sense of two-sided altruism," Journal of Monetary Economics, Elsevier, vol. 20(2), pages 301-326, September.
- Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
- Abel, Andrew B, 1987.
"Operative Gift and Bequest Motives,"
American Economic Review,
American Economic Association, vol. 77(5), pages 1037-1047, December.
- Andrew B. Abel, "undated". "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, 1987. "Operative Gift and Bequest Motives," NBER Working Papers 2331, National Bureau of Economic Research, Inc.
- Andrew B. Abel, "undated". "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, 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.
- Hori, Hajime & Kanaya, Sadao, 1989. "Utility functionals with nonpaternalistic intergenerational altruism," Journal of Economic Theory, Elsevier, vol. 49(2), pages 241-265, December. Full references (including those not matched with items on IDEAS)
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