Dynamic Programming, Maximum Principle and Vintage Capital

Giorgio Fabbri and Maurizio Iacopetta ()

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Vintage Capital; Penn World Table; Maximum Principle; Hilbert Space (search for similar items in EconPapers)
JEL-codes: C61 E22 E37 O41 O47 (search for similar items in EconPapers)
Date: 2007-09-25
New Economics Papers: this item is included in nep-dge and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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