IDEAS home Printed from https://ideas.repec.org/p/han/dpaper/dp-363.html
   My bibliography  Save this paper

Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution

Author

Listed:
  • Trimborn, Timo

Abstract

We derive the well-known continuity principle for adjoint variables for preannounced or anticipated changes in parameters for continuous-time, infinite-horizon, perfect foresight optimization models. For easy and intuitive numerical computation of the resulting multi point boundary value problem we suggested to simulate the resulting differential algebraic system representing the first order conditions. By ensuring that the state variables and the adjoint variables are continuous, potential jumps in the control variables are calculated automatically. This can be easily conducted with the relaxation algorithm as proposed by Trimborn et al. (2007). We solve a Ramsey model extended by an elementary Government sector numerically. Simulations of a preannounced increase in the consumption tax show a qualitative different pattern depending on the intertemporal elasticity of substitution.

Suggested Citation

  • 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.
  • Handle: RePEc:han:dpaper:dp-363
    as

    Download full text from publisher

    File URL: http://diskussionspapiere.wiwi.uni-hannover.de/pdf_bib/dp-363.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    2. Judd, Kenneth L, 1985. "Short-run Analysis of Fiscal Policy in a Simple Perfect Foresight Model," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 298-319, April.
    3. 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.
    4. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    5. 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.
    6. Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1.
      • Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1, June.
    7. Howitt, Peter & Sinn, Hans-Werner, 1989. "Gradual Reforms of Capital Income Taxation," American Economic Review, American Economic Association, vol. 79(1), pages 106-124, March.
    8. 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.
    9. Auernheimer, Leonardo & Lozada, Gabriel A, 1990. "On the Treatment of Anticipated Shocks in Models of Optimal Control with Rational Expectations: An Economic Interpretation," American Economic Review, American Economic Association, vol. 80(1), pages 157-169, March.
    10. 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.
    11. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, vol. 52(3), pages 665-680, May.
    12. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mário Amorim Lopes & Fernando A. C. C. Fontes & Dalila A. C. C. Fontes, 2013. "Optimal Control of Infinite-Horizon Growth Models — A direct approach," FEP Working Papers 506, Universidade do Porto, Faculdade de Economia do Porto.

    More about this item

    Keywords

    anticipated shocks; continuous-time optimization; numerical solution;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:han:dpaper:dp-363. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Heidrich, Christian). General contact details of provider: http://edirc.repec.org/data/fwhande.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.