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

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Listed author(s):
  • Raouf Boucekkine

    ()

    (Carlos III University, Madrid)

  • Omar Licandro

    ()

    (FEDEA and Carlos III University, Madrid)

  • Christopher Paul

    ()

    (Mathematics Department, Manchester University)

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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Department of Econometrics, University of Geneva, 102 Bd Carl-Vogt, 1211 Geneva 4, Switzerland

Web page: http://www.unige.ch/ce/ce96/welcome.html

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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; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
  • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
  • O40 - Economic Development, Innovation, 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.
  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. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 82(3), pages 430-450, June.
  4. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
  5. Cooley, Thomas F. & Greenwood, Jeremy & Yorukoglu, Mehmet, 1997. "The replacement problem," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 457-499, December.
  6. Licandro, Omar & Germain, Marc & Boucekkine, Raouf, 1995. "Creative destruction and business cycles," UC3M Working papers. Economics 3907, Universidad Carlos III de Madrid. Departamento de Economía.
  7. R. M. Solow & J. Tobin & C. C. von Weizsäcker & M. Yaari, 1966. "Neoclassical Growth with Fixed Factor Proportions," Review of Economic Studies, Oxford University Press, vol. 33(2), pages 79-115.
  8. van Hilten, Onno, 1991. "The optimal lifetime of capital equipment," Journal of Economic Theory, Elsevier, vol. 55(2), pages 449-454, December.
  9. Caballero, Ricardo J & Hammour, Mohamad L, 1994. "The Cleansing Effect of Recessions," American Economic Review, American Economic Association, vol. 84(5), pages 1350-1368, December.
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