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

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    1. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(2), pages 410-452, December.
    2. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(1), pages 3-42, July.
    3. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
    4. Karl-Josef Koch & Timo Trimborn & Thomas M. Steger, 2005. "Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure," Volkswirtschaftliche Diskussionsbeiträge, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht 121-05, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
    5. Charles I. Jones & John C. Williams, . "Too Much of a Good Thing? The Economics of Investment in R&D," Working Papers, Stanford University, Department of Economics 95006, Stanford University, Department of Economics.
    6. Atolia, Manoj & Chatterjee, Santanu & Turnovsky, Stephen J., 2010. "How misleading is linearization? Evaluating the dynamics of the neoclassical growth model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 34(9), pages 1550-1571, September.
    7. Futagami, Koichi & Iwaisako, Tatsuro & Ohdoi, Ryoji, 2008. "Debt Policy Rule, Productive Government Spending, And Multiple Growth Paths," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 445-462, September.
    8. Tjalling C. Koopmans, 1963. "Appendix to 'On the Concept of Optimal Economic Growth'," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 163A, Cowles Foundation for Research in Economics, Yale University.
    9. Minea, Alexandru & Villieu, Patrick, 2013. "Debt Policy Rule, Productive Government Spending, And Multiple Growth Paths: A Note," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 17(04), pages 947-954, June.
    10. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 163, Cowles Foundation for Research in Economics, Yale University.
    11. Ambler, Steve & Pelgrin, Florian, 2010. "Time-consistent control in nonlinear models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 34(10), pages 2215-2228, October.
    12. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 98(5), pages S103-26, October.
    13. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, The MIT Press, edition 2, volume 1, number 0262025531, December.
    14. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 26(5), pages 737-753, May.
    15. 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.
    16. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, Econometric Society, vol. 62(3), pages 635-56, May.
    17. Paul M. Romer, 1994. "The Origins of Endogenous Growth," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 8(1), pages 3-22, Winter.
    18. Trimborn, Timo, 2007. "Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-363, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
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