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Solving optimal growth models with vintage capital: The dynamic programming approach

  • Fabbri, Giorgio
  • Gozzi, Fausto

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39-72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 143 (2008)
Issue (Month): 1 (November)
Pages: 331-373

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Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:331-373
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
  2. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos de Trabajo del ICAE 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  3. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
  4. BOUCEKKINE, RAOUF & de la CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs : principles and applications," CORE Discussion Papers 2004047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Giuseppe Freni & Fausto Gozzi & Neri Salvadori, 2006. "Existence of optimal strategies in linear multisector models," Economic Theory, Springer, vol. 29(1), pages 25-48, September.
  6. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V.M., 2006. "Anticipation effects of technological progress on capital accumulation : A vintage capital approach," Other publications TiSEM 9a8debb0-5030-46fa-b89e-b, Tilburg University, School of Economics and Management.
  7. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
  8. Kocherlakota, Narayana R & Yi, Kei-Mu, 1996. "A Simple Time Series Test of Endogenous vs. Exogenous Growth Models: An Application to the United States," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 126-34, February.
  9. Askenazy, Philippe & Le Van, 1997. "A model of optimal growth strategy," CEPREMAP Working Papers (Couverture Orange) 9707, CEPREMAP.
  10. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers 767, UCLA Department of Economics.
  11. Giorgio Fabbri, 2008. "Viscosity Solutions to Delay Differential Equations in Demo-Economy," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(1), pages 27-54.
  12. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  13. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
  14. Aghion, Philippe & Howitt, Peter, 1994. "Growth and Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 61(3), pages 477-94, July.
  15. repec:fda:fdaddt:2004-07 is not listed on IDEAS
  16. Michael Gort & Jeremy Greenwood & Peter Rupert, 1998. "Measuring the rate of technological progress in structures," Working Paper 9806, Federal Reserve Bank of Cleveland.
  17. Freni, Giuseppe & Gozzi, Fausto & Pignotti, Cristina, 2008. "Optimal strategies in linear multisector models: Value function and optimality conditions," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 55-86, January.
  18. Kocherlakota, Narayana R. & Yi, Kei-Mu, 1995. "Can convergence regressions distinguish between exogenous and endogenous growth models?," Economics Letters, Elsevier, vol. 49(2), pages 211-215, August.
  19. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
  20. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
  21. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
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