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Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models

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Author Info
Raouf Boucekkine () (Carlos III University, Madrid)
Omar Licandro () (FEDEA and Carlos III University, Madrid)
Christopher Paul () (Mathematics Department, Manchester University)

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Abstract

In this paper, we examine techniques for the analytical and numerical solution of statedependent differential-difference equations. Such equations occur in the continuous time modelling of vintage capital growth models, which form a particularly important class of models in modern economic growth theory. The theoretical treatment of non-statedependent differential-difference equations in economics has already been discussed by Benhabib and Rustichini (1991). In general, though, the state-dependence of a model prevents its analytical solution in all but the simplest of cases. We review a numerical method for solving state-dependent models, using some simple examples to illustrate our discussion. In addition, we analyse the Solow vintage capital growth model. We conclude by mentioning a crucial unresolved issue related to this topic.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1996 with number _036.

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Handle: RePEc:sce:scecf6:_036

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Postal: Department of Econometrics, University of Geneva, 102 Bd Carl-Vogt, 1211 Geneva 4, Switzerland
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Related research
Keywords: Economic growth theory; vintage capital; differential-difference equations; state-dependence; numerical solution.;

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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  1. 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. [Downloadable!] (restricted)
  2. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers 90-22, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
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  3. Thomas F. Cooley & Jeremy Greenwood & Mehmet Yorukoglu, 1994. "The Replacement Problem," Working Papers 9408, Centro de Investigacion Economica, ITAM.
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  4. van Hilten, Onno, 1991. "The optimal lifetime of capital equipment," Journal of Economic Theory, Elsevier, vol. 55(2), pages 449-454, December. [Downloadable!] (restricted)
  5. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Discussion Paper / Institute for Empirical Macroeconomics 24, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  6. Caballero, Ricardo J & Hammour, Mohamad L, 1994. "The Cleansing Effect of Recessions," American Economic Review, American Economic Association, vol. 84(5), pages 1350-68, December. [Downloadable!] (restricted)
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  1. Fabrice Collard & Omar Licandro & Luis A. Puch, 2003. "The short-run dynamics of optimal growth models with delays," Documentos del Instituto Complutense de Análisis Económico 0311, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales. [Downloadable!]
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  2. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer, vol. 31(2), pages 181-206, March. [Downloadable!] (restricted)
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  3. de la Croix, David & Licandro, Omar, 2007. "‘The Child is Father of the Man:’ Implications for the Demographic Transition," CEPR Discussion Papers 6493, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  4. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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  5. Kort, P.M. & Feichtinger, G. & Hartl, R.F. & Veliov, V.M., 2003. "Environmental policy, the porter hypothesis and the composition of capital: effects of learining and techonological progress," Discussion Paper 61, Tilburg University, Center for Economic Research. [Downloadable!]
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  6. Fabbri, Giorgio & Iacopetta, Maurizio, 2007. "Dynamic Programming, Maximum Principle and Vintage Capital," MPRA Paper 5115, University Library of Munich, Germany. [Downloadable!]
  7. Raouf, BOUCEKKINE & David de la Croix, 2004. "Modelling vintage structures with DDEs : principles and applications," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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  8. Cruz Angel Echevarría, 2003. "Life Expectancy, Schooling Time and Endogenous Growth," DFAEII Working Papers 200211, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
  9. David, DE LA CROIX & Bo, MALMBERG, 2006. "Growth and Longevity from the Industrial Revolution to the Future of an Aging Society," Discussion Papers (ECON - Département des Sciences Economiques) 2006037, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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  10. Yuri, YATSENKO & Raouf, BOUCEKKINE & Natali, HRITONENKO, 2008. "Estimating the Dynamics of R&D-based Growth Models," Discussion Papers (ECON - Département des Sciences Economiques) 2008034, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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  11. David de la Croix & Omar Licandro, 2008. "The Child is Father of the Man: by Implications for the Demographic Transition," Working Papers 2008-04, FEDEA. [Downloadable!]
  12. Boucekkine, Raouf & Martinez, Blanca, 1999. "Machine Replacement, Technology Adoption and Convergence," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999025, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
  13. Fabbri, Giorgio, 2007. "Viscosity solutions to delay differential equations in demo-economy," MPRA Paper 2826, University Library of Munich, Germany. [Downloadable!]
  14. Blanca MARTINEZ, 2002. "Adoption Costs, Age of Capital and Technological Substitution," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2002024, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
  15. Dehejia, Vivek & Dwyer, Douglas W, 2000. "Output And Unemployment Dynamics In Transition," CEPR Discussion Papers 2450, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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