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Optimal Control of Infinite-Horizon Growth Models — A direct approach

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  • Mário Amorim Lopes

    ()
    (FEP)

  • Fernando A. C. C. Fontes

    ()
    (FEUP)

  • Dalila A. C. C. Fontes

    ()
    (FEP)

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    Abstract

    We propose a framework to solve dynamic nonlinear infinite-horizon models like those found in the standard economic growth literature. We employ a direct method to solve the underlying optimal control problem, something novel in the economic literature. Instead of deriving the necessary optimality conditions and solving the originated ordinary differential equations, this method first discretizes and then optimizes, in effect transforming the prob- lem into a nonlinear programming problem to be optimized at each sampling instant. We incorporate the work of Fontes (2001) in order to transform the infinite-horizon problem into an equivalent finite-horizon representation of the model. This framework presents several advantages in comparison to the available alternatives that use indirect methods. First, no linearization is required, which sometimes can be erroneous. The problem can be studied in its nonlinear form. Secondly, it enables the simulation of a shock when the economy is not at its steady state, a broad assumption required by all available numerical methods. Thirdly, it allows for the easy study of anticipated shocks. It also allows for the analysis of multiple, sequential shocks. Finally, it is extremely robust and easy to use. We illustrate the application of the framework by solving the standard Ramsey-Cass-Koopsman exogenous growth model and the Uzawa-Lucas endogenous two-sector growth model.

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    Bibliographic Info

    Paper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 506.

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    Length: 24 pages
    Date of creation: Oct 2013
    Date of revision:
    Handle: RePEc:por:fepwps:506

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    Related research

    Keywords: optimal control; direct methods; transitional dynamics; economic growth; non-steady state shocks; sequential shocks.;

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    References

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    1. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-56, May.
    2. Ambler, Steve & Pelgrin, Florian, 2010. "Time-consistent control in nonlinear models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2215-2228, October.
    3. Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(03), pages 301-319, June.
    4. Trimborn, Timo, 2007. "Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution," Hannover Economic Papers (HEP) dp-363, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
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    7. Charles I. Jones & John C. Williams, 1999. "Too Much of a Good Thing? The Economics of Investment in R&D"," Working Papers 99015, Stanford University, Department of Economics.
    8. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
    9. Manoj Atolia & Santanu Chatterjee & Stephen J. Turnovsky, 2008. "How Misleading is Linearization? Evaluating the Dynamics of the Neoclassical Growth Model," Working Papers wp2008_11_01, Department of Economics, Florida State University, revised Sep 2008.
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    11. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    12. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262025531, December.
    13. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
    14. Minea, Alexandru & Villieu, Patrick, 2013. "Debt Policy Rule, Productive Government Spending, And Multiple Growth Paths: A Note," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 947-954, June.
    15. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    16. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
    17. Futagami, Koichi & Iwaisako, Tatsuro & Ohdoi, Ryoji, 2008. "Debt Policy Rule, Productive Government Spending, And Multiple Growth Paths," Macroeconomic Dynamics, Cambridge University Press, vol. 12(04), pages 445-462, September.
    18. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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