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

  • Raouf Boucekkine

    ()

    (Carlos III University, Madrid)

  • Omar Licandro

    ()

    (FEDEA and Carlos III University, Madrid)

  • Christopher Paul

    ()

    (Mathematics Department, Manchester University)

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
Contact details of provider: Postal: 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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  1. van Hilten, Onno, 1991. "The optimal lifetime of capital equipment," Journal of Economic Theory, Elsevier, vol. 55(2), pages 449-454, December.
  2. Ricardo J. Caballero & Mohamad L. Hammour, 1991. "The Cleansing Effect of Recessions," NBER Working Papers 3922, National Bureau of Economic Research, Inc.
  3. 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.
  4. Cooley, T.F. & Greenwood, J. & Yorukoglu, M., 1995. "The Replacement Problem," UWO Department of Economics Working Papers 9508, University of Western Ontario, Department of Economics.
  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.
  6. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers 90-22, C.V. Starr Center for Applied Economics, New York University.
  7. 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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