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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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  • Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    • Handle: RePEc:eee:dyncon:v:21:y:1997:i:2-3:p:347-362
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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. Cooley, Thomas F. & Greenwood, Jeremy & Yorukoglu, Mehmet, 1997. "The replacement problem," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 457-499, December.
    5. R. M. Solow & J. Tobin & C. C. Weizsäcker & M. Yaari, 1971. "Neoclassical Growth with Fixed Factor Proportions," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 9, pages 68-102, Palgrave Macmillan.
    6. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1995. "Creative destruction and business cycles," UC3M Working papers. Economics 3907, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    8. 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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    More about this item

    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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