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Modelling vintage structures with DDEs : principles and applications

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  • Raouf, BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • David de la Croix

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and CORE and FNRS Belgium and UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • Omar Lidandro

    (European University Institute, Firenze, and FEDEA, Madrid)

Abstract

A comprehensive study of the linkages between demographic and economic variables should not only account for vintage specificity but also incorporate the relevant economic and demographic decisions in a complete optimal control set-up. In this paper, a methodological set-up allowing to reach the objectives is described. In this framework, time is continuous but agents take discrete timing decisions. The mixture of continuous and discrete time yields differential-difference equations (DDEs). This paper shows clearly that the approach allows for a relatively complete and rigorous analytical exploration in some special cases (mainly linear or quasi linear models), and for an easy computational appraisal in the general case.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2004004.

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Date of creation: 01 Mar 2004
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Handle: RePEc:ctl:louvir:2004004

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Keywords: Demography; Economic growth; Vintage structures; Optimal control; Differential-difference equations; State-dependence;

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References

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  1. Collard, Fabrice & Licandro, Omar & Puch, Luis, 2005. "The Short-Run Dynamics of Optimal Growth Models with Delays," CEPR Discussion Papers 5414, C.E.P.R. Discussion Papers.
  2. 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.
  3. 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.
  4. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, vol. 65(2), pages 255-263, November.
  5. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos del Instituto Complutense de Análisis Económico 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  6. R. Boucekkine & M. Germain & O. Licandro & A. Magnus, . "Creative destruction, investment volatility, and the average age of capital," Working Papers 97-08, FEDEA.
  7. Raouf BOUCEKKINE & David DE LA CROIX & Omar LICANDRO, 2002. "Early Mortality Declines at the Dawn of Modern Growth," Economics Working Papers ECO2002/11, European University Institute.
  8. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
  9. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996 _036, Society for Computational Economics.
  10. BOUCEKKINE, Raouf & POMMERET, Aude, . "Energy saving technical progress and optimal capital stock: the role of embodiment," CORE Discussion Papers RP -1703, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Journal of Economic Theory, Elsevier, vol. 88(1), pages 161-187, September.
  12. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
  13. David N. Weil & Oded Galor, 1999. "From Malthusian Stagnation to Modern Growth," American Economic Review, American Economic Association, vol. 89(2), pages 150-154, May.
  14. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
  15. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 2001. "Numerical solution by iterative methods of a class of vintage capital models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 655-669, May.
  17. Kelley, Allen C. & Schmidt, Robert M., 1995. "Aggregate Population and Economic Growth Correlations: The Role of the Components of Demographic Change," Working Papers 95-37, Duke University, Department of Economics.
  18. Malcomson, James M., 1975. "Replacement and the rental value of capital equipment subject to obsolescence," Journal of Economic Theory, Elsevier, vol. 10(1), pages 24-41, February.
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