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Dynamic Programming, Maximum Principle and Vintage Capital

Author

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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.

Suggested Citation

  • Fabbri, Giorgio & Iacopetta, Maurizio, 2007. "Dynamic Programming, Maximum Principle and Vintage Capital," MPRA Paper 5115, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:5115
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    File URL: https://mpra.ub.uni-muenchen.de/5115/1/MPRA_paper_5115.pdf
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    References listed on IDEAS

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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. 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).
    3. 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.
    4. 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.
    5. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    6. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. Anton Bondarev, 2012. "The long-run dynamics of product and process innovations for a multi-product monopolist," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 21(8), pages 775-799, November.

    More about this item

    Keywords

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

    JEL classification:

    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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