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Dynamic Programming, Maximum Principle and Vintage Capital

  • Fabbri, Giorgio
  • Iacopetta, Maurizio

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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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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  1. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class of vintage capital models," Working Papers 98-20, FEDEA.
  2. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
  3. Paul, Christopher & Licandro, Omar & Boucekkine, Raouf, 1995. "Differential-difference equations in economics: on the numerical solution of vintage capital growth models," UC3M Working papers. Economics 3951, Universidad Carlos III de Madrid. Departamento de Economía.
  4. Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 7334, University Library of Munich, Germany.
  5. 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.
  6. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
  7. Charles I. Jones, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, Oxford University Press, vol. 110(2), pages 495-525.
  8. R. Boucekkine & F. del Rio & O. Licandro & Luis A. Puch, 2000. "Vintage Capital and the Dynamics of the AK Model," Econometric Society World Congress 2000 Contributed Papers 0436, Econometric Society.
  9. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
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