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Reverse Shooting Made Easy: Solving for the Global Nonlinear Saddle Path

Author

Listed:
  • Manoj Atolia

    (Department of Economics, Florida State University)

  • Edward F. Buffie

    (Department of Economics, Indiana University)

Abstract

We present the blueprints for a set of innovative reverse shooting algorithms that trap the global saddle path in systems with 2-4 state variables. The solution procedure is built around a new distance mapping and refined simplex algorithms. Since the algorithms are completely reliable and always work in the same way, we have been able to develop canned programs that solve for the global nonlinear saddle path in any model with 2-4 state variables. The programs are written in the spirit of plug and play: the user types in the equations of the model and then waits for the solution.

Suggested Citation

  • Manoj Atolia & Edward F. Buffie, 2004. "Reverse Shooting Made Easy: Solving for the Global Nonlinear Saddle Path," Working Papers wp2009_01_01, Department of Economics, Florida State University, revised Jan 2009.
    • Handle: RePEc:fsu:wpaper:wp2009_01_01
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    References listed on IDEAS

    as
    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 635-656, May.
    2. Ric Herbert & Peter Stemp, 2003. "Exploiting Model Structure to Solve the Dynamics of a Macro Model," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 203-207, June.
    3. Herbert, Ric D. & Stemp, Peter J. & Griffiths, William E., 2005. "Assessing two common approaches for solving models with saddle-path instabilities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(1), pages 78-89.
    4. Lipton, David, et al, 1982. "Multiple Shooting in Rational Expectations Models [The Solution of Linear Difference Models under Rational Expectations]," Econometrica, Econometric Society, vol. 50(5), pages 1329-1333, September.
    5. Judd, Kenneth L., 2002. "The parametric path method: an alternative to Fair-Taylor and L-B-J for solving perfect foresight models," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1557-1583, August.
    6. 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.
    7. Manoj Atolia & Edward Buffie, 2009. "Smart Forward Shooting," Computational Economics, Springer;Society for Computational Economics, vol. 33(1), pages 1-30, February.
    8. Atolia, Manoj & Buffie, Edward F., 2011. "Solving The Unit Root Problem In Models With An Exogenous World Market Interest Rate," Macroeconomic Dynamics, Cambridge University Press, vol. 15(5), pages 681-712, November.
    9. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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, vol. 34(9), pages 1550-1571, September.
    2. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    3. Atolia, Manoj & Chatterjee, Santanu & Turnovsky, Stephen J., 2012. "Growth and inequality: Dependence on the time path of productivity increases (and other structural changes)," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 331-348.
    4. Millner, Antony & Dietz, Simon, 2015. "Adaptation to climate change and economic growth in developing countries," LSE Research Online Documents on Economics 57863, London School of Economics and Political Science, LSE Library.
    5. Manuel A. Gómez, 2010. "The welfare cost of external habits: a quantitative assessment," Estudios de Economia, University of Chile, Department of Economics, vol. 37(1 Year 20), pages 5-26, June.
    6. Atolia, Manoj & Papageorgiou, Chris & Turnovsky, Stephen J., 2021. "Re-opening after the lockdown: Long-run aggregate and distributional consequences of COVID-19," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    7. Antony Millner & Simon Dietz, 2011. "Adaptation to climate change and economic growth in developing countries," GRI Working Papers 60, Grantham Research Institute on Climate Change and the Environment.
    8. Manoj Atolia & Edward Buffie, 2009. "Smart Forward Shooting," Computational Economics, Springer;Society for Computational Economics, vol. 33(1), pages 1-30, February.
    9. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    10. Johannus Janmaat, 2012. "Fishing in a Shallow Lake: Exploring a Classic Fishery Model in a Habitat with Shallow Lake Dynamics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 51(2), pages 215-239, February.
    11. Paul Luk & David Vines, 2014. "Debt Deleveraging and the Zero Bound: Potentially Perverse Effects of Real Exchange Rate Movements," Working Papers 202014, Hong Kong Institute for Monetary Research.
    12. Hillebrand, Elmar & Hillebrand, Marten, 2023. "Who pays the bill? Climate change, taxes, and transfers in a multi-region growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    13. Millner, Antony & Dietz, Simon, 2015. "Adaptation to climate change and economic growth in developing countries," Environment and Development Economics, Cambridge University Press, vol. 20(3), pages 380-406, June.
    14. Roumasset, James A. & Wada, Christopher A., 2012. "Ordering the extraction of renewable resources: The case of multiple aquifers," Resource and Energy Economics, Elsevier, vol. 34(1), pages 112-128.
    15. Gómez Manuel A. & Sequeira Tiago Neves, 2012. "The Transitional Dynamics of an Endogenous Growth Model: Generalizing Production Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(5), pages 1-27, December.

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    More about this item

    Keywords

    Reverse shooting; global saddle path; distance mapping;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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