Advertisement

Journal of Evolutionary Economics

, Volume 27, Issue 5, pp 1205–1220 | Cite as

Global convergence in an overlapping generations model with two-sided altruism

  • Takaaki Aoki
  • Kazuo Nishimura
Regular Article

Abstract

We study the evolutionary dynamics of an overlapping generations economy with two-sided altruism, where each generation cares about the utilities of its parental generation, its offspring, and its own. We assume that the young and old generations in each period act jointly, as a central planner. We then introduce the concepts of a two-sided altruistic path and a two-sided altruistic stationary path. Then, we go on to prove that the former always converges to the latter, in the two-sided altruistic model. This stationary capital level is higher than the steady-state level in the model with a constant discount factor.

Keywords

Two-sided altruism Global convergence Euler equation Principle of optimality 

JEL classification

C61 D91 O41 

Notes

Acknowledgements

We thank the editor and two anonymous referees for helpful comments and suggestions. We also thank Sadao Kanaya for the useful conversations during the initial stage of this research. This work was supported by the Japan Society for the Promotion of Science, Grants-in-Aid for Research #15H05729 and #16H0233598.

Compliance with ethical standards

Funding

This study is funded by Japan Society for the Promotion of Science (Grants-in-Aid for Research #15H05729 and #16H0233598).

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Abel AB (1987) Operative gift and bequest motives. Am Econ Rev 77:1037–1047Google Scholar
  2. Altig D, Davis SJ (1993) Borrowing constraints and two-sided altruism with an application to social security. J Econ Dyn Control 17:467–494CrossRefGoogle Scholar
  3. Aoki T, Nishimura K (2014) On the convergence of optimal solutions in infinite horizon discrete time models. J Differ Equ Appl 20:875–882CrossRefGoogle Scholar
  4. Barro RJ (1974) Are government bonds net wealth? J Polit Econ 81:1095–1117CrossRefGoogle Scholar
  5. Blackburn K, Cipriani GP (2005) Intergenerational transfers and demographic transition. J Dev Econ 78:191–214CrossRefGoogle Scholar
  6. Cass D (1965) Optimum growth in an aggregative model of capital accumulation. Rev Econ Stud 32:233–240CrossRefGoogle Scholar
  7. Dechert DW, Nishimura K (1983) A complete characterization of optimal growth paths in an aggregated model with a non-concave production function. J Econ Theory 31:332–354CrossRefGoogle Scholar
  8. Hommes C (2009) Bounded rationality and learning in complex markets. Handbook of research on complexity, Chapter 5, Edward Elgar PublishingGoogle Scholar
  9. Hori H (1997) Dynamic allocation in an altruistic overlapping generations economy. J Econ Theory 73:292–315CrossRefGoogle Scholar
  10. Hori H, Kanaya S (1989) Utility functionals with nonpaternalistic intergenerational altruism. J Econ Theory 49:241–265CrossRefGoogle Scholar
  11. Kimball MS (1987) Making sense of two-sided altruism. J Monetary Econ 20:301–326CrossRefGoogle Scholar
  12. Koopmans TC (1965) On the concept of optimal economic growth. Pontificae Academiae Scientiarum Scripta Varia 28:225–300Google Scholar
  13. Lambrecht S, Michel P, Thibault E (2006) Capital accumulation and fiscal policy in an OLG model with family altruism. Journal of Public Econ Theory 8:465–486CrossRefGoogle Scholar
  14. Lane D, Malerba F, Maxfield R, Orsenigo L (1996) Choice and action. J Evol Econ 6:43–76CrossRefGoogle Scholar
  15. Lucas RE (1972) Econometric testing of the natural rate hypothesis. In: O. Eckstein (ed.) The econometrics of price determination Conference, Board of Governors of the Federal Reserve System and Social Science Research CouncilGoogle Scholar
  16. Michel P, Thibault E (2007) The failure of ricardian equivalence under dynastic altruism. J Math Econ 43:606–614CrossRefGoogle Scholar
  17. Muth JF (1961) Rational expectations and the theory of price movements. Econometrica 29:315–335CrossRefGoogle Scholar
  18. Ramsey F (1928) A mathematical theory of saving. Econ J 38:543–559CrossRefGoogle Scholar
  19. Raut LK (2006) Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models. Economic Theory 27:729–736CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Economic ResearchKyoto UniversityKyotoJapan
  2. 2.Research Institute for Economics & Business AdministrationKobe UniversityKobeJapan
  3. 3.Research Institute of EconomyTrade and IndustryTokyoJapan
  4. 4.Santa Fe InstituteSanta FeUSA

Personalised recommendations