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Dynamic Programming, Maximum Principle and Vintage Capital

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  • Fabbri, Giorgio
  • Iacopetta, Maurizio

Abstract

We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of macroeconomic models, capital is homogeneous and depreciates at a constant exogenous rate. In the other view each piece of capital has its own finite productive life cycle (vintage capital). The interpretation of the time patterns of macroaggregates is quite different between the two cases. A technological shock generates an oscillatory movement in the time pattern of per capita output when capital has a vintage structure; conversely an instantaneous adjustment with no transitional dynamics occurs when capital is homogeneous. From a methodological point of view it emerges that the DP approach delivers sharper results than the MP approach (for instance it delivers a closed form solution for the optimal investment strategy) under slacker parameter restrictions. Cross-time and cross-country data on investments, income, and consumption drawn from the Penn World Table version 6.2 are used to evaluate the vintage and standard Ak model.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5115.

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Date of creation: 25 Sep 2007
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Handle: RePEc:pra:mprapa:5115

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Keywords: Vintage Capital; Penn World Table; Maximum Principle; Hilbert Space;

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  1. 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.
  2. Raouf, BOUCEKKINE & David, DE LA CROIX & Omar, LICANDRO, 2006. "Vintage Capital," Discussion Papers (ECON - Département des Sciences Economiques) 2006014, Université catholique de Louvain, Département des Sciences Economiques.
  3. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class on vintage capital models," Working Papers 97-26, FEDEA.
  4. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V.M., 2005. "Anticipation effects of technological progress on capital accumulation : a vintage capital approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-148454, Tilburg University.
  5. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 1999. "Vintage Capital and the Dynamics of the AK Model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  6. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
  7. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
  8. Jones, Charles I, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 495-525, May.
  9. repec:pra:mprapa:2863 is not listed on IDEAS
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Cited by:
  1. Bondarev, Anton A., 2010. "The long run Dynamics of heterogeneous Product and Process Innovations for a Multi Product Monopolist," MPRA Paper 35195, University Library of Munich, Germany, revised 26 Nov 2011.

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