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Intergenerational interactions in human capital accumulation

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Author Info
Woźny, Łukasz
Growiec, Jakub

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Abstract

We analyze an economy populated by a sequence of generations who decide over their consumption levels and the levels of investment in human capital of their immediate descendants. The objective of the paper is to identify the impact of strategic interactions between consecutive generations on the time path of human capital accumulation. To this end, we characterize the Markov perfect equilibrium (MPE) in such an economy and derive the sufficient conditions for its existence and uniqueness. The equilibrium path is computed using a novel constructive approach: extending Reffett and Woźny (2008), we put forward an iterative procedure which converges to the MPE as its limit. To benchmark our results, we also calculate the optimal human capital accumulation paths for (i) a Ramsey-type model with dynastic optimization, and (ii) a model with joy-of-giving altruism. We prove analytically that human capital accumulation is unambiguously lower in the "strategic" model than in the Ramsey-type dynastic model. We complement our results with a series of numerical exercises.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10308.

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Date of creation: 20 Jul 2008
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Handle: RePEc:pra:mprapa:10308

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Related research
Keywords: human capital intergenerational interactions Markov perfect equilibrium stochastic transition constructive approach

Find related papers by JEL classification:
I20 - Health, Education, and Welfare - - Education - - - General
J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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  1. Jacob Mincer, 1958. "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, University of Chicago Press, vol. 66, pages 281. [Downloadable!] (restricted)
  2. Galor, Oded & Tsiddon, Daniel, 1997. " The Distribution of Human Capital and Economic Growth," Journal of Economic Growth, Springer, vol. 2(1), pages 93-124, March. [Downloadable!] (restricted)
    Other versions:
  3. Amir, Rabah, 1996. "Strategic Intergenerational Bequests with Stochastic Convex Production," Economic Theory, Springer, vol. 8(2), pages 367-76, August.
    Other versions:
  4. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August. [Downloadable!] (restricted)
  5. Leininger, Wolfgang, 1986. "The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations," Review of Economic Studies, Blackwell Publishing, vol. 53(3), pages 349-67, July. [Downloadable!] (restricted)
  6. Becker, Gary S & Tomes, Nigel, 1986. "Human Capital and the Rise and Fall of Families," Journal of Labor Economics, University of Chicago Press, vol. 4(3), pages S1-39, July. [Downloadable!] (restricted)
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  7. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July. [Downloadable!] (restricted)
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  8. Andrzej Nowak, 2006. "On perfect equilibria in stochastic models of growth with intergenerational altruism," Economic Theory, Springer, vol. 28(1), pages 73-83, 05. [Downloadable!] (restricted)
  9. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer, vol. 32(1), pages 121-132, December. [Downloadable!] (restricted)
  10. Rangazas, Peter, 2000. "Schooling and economic growth: A King-Rebelo experiment with human capital," Journal of Monetary Economics, Elsevier, vol. 46(2), pages 397-416, October. [Downloadable!] (restricted)
  11. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June. [Downloadable!] (restricted)
  12. Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, vol. 95(1), pages 71-78, November. [Downloadable!] (restricted)
  13. Bernheim, B Douglas & Ray, Debraj, 1987. "Economic Growth with Intergenerational Altruism," Review of Economic Studies, Blackwell Publishing, vol. 54(2), pages 227-41, April. [Downloadable!] (restricted)
  14. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July. [Downloadable!] (restricted)
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  15. Yoram Ben-Porath, 1967. "The Production of Human Capital and the Life Cycle of Earnings," Journal of Political Economy, University of Chicago Press, vol. 75, pages 352. [Downloadable!] (restricted)
  16. Lionel Artige & Carmen Camacho & David De La Croix, 2004. "Wealth Breeds Decline: Reversals of Leadership and Consumption Habits," Journal of Economic Growth, Springer, vol. 9(4), pages 423-449, December. [Downloadable!]
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  17. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141. [Downloadable!] (restricted)
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