IDEAS home Printed from
   My bibliography  Save this paper

Visualizing Multi-Dimensional Functions In Economics


  • William L. Goffe

    (University of Southern Mississippi)


This paper shows how a forward-shooting algorithm can be easily implemented using the Matlab programming language. In the paper we develop and implement a forward-shooting numerical algorithm for computing the dynamics of a small representative agent macroeconomic model when subjected to an exogenous shock. The model has a number of important characteristics that effect its dynamic solution. These characteristics are common to a wide range of economic models. One characteristic is that the model is highly non-linear so that numeric solutions to the dynamics are necessary. Another characteristic is that the solution must lie on a stable manifold. This requires the model to contain jumping variables and makes the numeric solution of the dynamics difficult as the solution will easily 'fall off' the stable manifold. The model terminal solution is particularly sensitive to initial conditions and to computational errors introduced in the solution.A forward-shooting algorithm can be used to find the necessary jumps to ensure the model lies on the stable manifold. In the paper we use computer visualisation techniques to show the algorithm searching for the necessary jumps to determine the dynamic solution. The algorithm searches for the initial conditions of the jumping variables that result in the terminal solution of the model being close to the known values.The paper shows how the algorithm, and its visualisation, can be implemented in the Matlab programming language using standard Matlab routines. The program implements a Nelder-Mead simplex search to find the particular initial conditions of the jumping variables that minimises the 2-norm between known terminal solution and that generated by the candidate initial conditions. For each candidate initial conditions a Runge-Kutta solver is used to generate the dynamics of the model, and plotting routines are used to visualise these dynamics.

Suggested Citation

  • William L. Goffe, 2000. "Visualizing Multi-Dimensional Functions In Economics," Computing in Economics and Finance 2000 127, Society for Computational Economics.
  • Handle: RePEc:sce:scecf0:127

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    1. Svensson, Lars-E-O, 2001. "The Zero Bound in an Open Economy: A Foolproof Way of Escaping from a Liquidity Trap," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 277-312, February.
    2. Tetlow, Robert J. & von zur Muehlen, Peter, 2001. "Simplicity versus optimality: The choice of monetary policy rules when agents must learn," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 245-279, January.
    3. Lars E. O. Svensson, 1996. "Price Level Targeting vs. Inflation Targeting: A Free Lunch?," NBER Working Papers 5719, National Bureau of Economic Research, Inc.
    4. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence," NBER Chapters,in: NBER Macroeconomics Annual 1989, Volume 4, pages 185-246 National Bureau of Economic Research, Inc.
    5. repec:fth:harver:1435 is not listed on IDEAS
    6. McCallum, Bennett T & Nelson, Edward, 1999. "An Optimizing IS-LM Specification for Monetary Policy and Business Cycle Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 296-316, August.
    7. Svensson, Lars E O, 1999. " Inflation Targeting: Some Extensions," Scandinavian Journal of Economics, Wiley Blackwell, vol. 101(3), pages 337-361, September.
    8. Arturo Estrella & Jeffrey C. Fuhrer, 2002. "Dynamic Inconsistencies: Counterfactual Implications of a Class of Rational-Expectations Models," American Economic Review, American Economic Association, vol. 92(4), pages 1013-1028, September.
    9. Martin S. Feldstein, 1997. "The Costs and Benefits of Going from Low Inflation to Price Stability," NBER Chapters,in: Reducing Inflation: Motivation and Strategy, pages 123-166 National Bureau of Economic Research, Inc.
    10. Glenn Rudebusch & Lars E.O. Svensson, 1999. "Policy Rules for Inflation Targeting," NBER Chapters,in: Monetary Policy Rules, pages 203-262 National Bureau of Economic Research, Inc.
    11. Wolman, Alexander L, 2005. "Real Implications of the Zero Bound on Nominal Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(2), pages 273-296, April.
    12. Christina D. Romer & David H. Romer, 1997. "Reducing Inflation: Motivation and Strategy," NBER Books, National Bureau of Economic Research, Inc, number rome97-1, January.
    13. Fuhrer, Jeffrey C & Moore, George R, 1995. "Monetary Policy Trade-offs and the Correlation between Nominal Interest Rates and Real Output," American Economic Review, American Economic Association, vol. 85(1), pages 219-239, March.
    14. John C. Williams, 2003. "Simple rules for monetary policy," Economic Review, Federal Reserve Bank of San Francisco, pages 1-12.
    15. Frederic S. Mishkin & Adam S. Posen, 1997. "Inflation targeting: lessons from four countries," Economic Policy Review, Federal Reserve Bank of New York, issue Aug, pages 9-110.
    16. Batini, Nicoletta & Yates, Anthony, 2003. " Hybrid Inflation and Price-Level Targeting," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(3), pages 283-300, June.
    17. Jeffrey C. Fuhrer, 2000. "Habit Formation in Consumption and Its Implications for Monetary-Policy Models," American Economic Review, American Economic Association, vol. 90(3), pages 367-390, June.
    18. Jeff Fuhrer & George Moore, 1995. "Inflation Persistence," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 127-159.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:sce:scecf0:127. 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: (Christopher F. Baum). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.