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Dynamic Programming, Maximum Principle and Vintage Capital

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Author Info
Fabbri, Giorgio
Iacopetta, Maurizio

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

Find related papers by JEL classification:
E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
E22 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
O47 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Measurement of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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  1. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. 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. [Downloadable!]
    Other versions:
    • Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute. [Downloadable!]
    • BOUCEKKINE, Raouf & DE LA CROIX, David & LICANDRO, Omar, 2006. "Vintage capital," CORE Discussion Papers 2006024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  6. 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. [Downloadable!] (restricted)
  7. Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 2863, University Library of Munich, Germany. [Downloadable!]
  8. Raouf BOUCEKKINE & Omar LICANDRO & Luis A. PUCH & Fernando DEL RIO, 2002. "Vintage Capital And the Dynamics of the AK Model," Economics Working Papers ECO2002/07, European University Institute. [Downloadable!]
    Other versions:
  9. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 2001. "Numerical solution by iterative methods of a class of vintage capital models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 655-669, May. [Downloadable!] (restricted)
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