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Differential-difference equations in economics: On the numerical solution of vintage capital growth models

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  • Boucekkine, Raouf
  • Licandro, Omar
  • Paul, Christopher

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 21 (1997)
Issue (Month): 2-3 ()
Pages: 347-362

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Handle: RePEc:eee:dyncon:v:21:y:1997:i:2-3:p:347-362

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  1. Cooley, T.F. & Greenwood, J. & Yorukoglu, M., 1997. "The Replacement Problem," RCER Working Papers 444, University of Rochester - Center for Economic Research (RCER).
  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. van Hilten, Onno, 1991. "The optimal lifetime of capital equipment," Journal of Economic Theory, Elsevier, vol. 55(2), pages 449-454, December.
  4. 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.
  5. Caballero, R.J. & Hammour, M.L., 1991. "The Cleansing Effect of Recessions," Discussion Papers 1991_59, Columbia University, Department of Economics.
  6. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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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