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The Stacked-Time Simulator in TROLL: A Robust Algorithm for Solving Forward-Looking Models

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  • Peter Hollinger

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    (Intex Solutions, Inc., Needham, MA)

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    Abstract

    The TROLL econetric modelling system provides two methods to solve forward-looking ``rational expectations models with model-consistent endogenous leads. The traditional Fair-Taylor algorithm solves the model through a specified time horizon by treating the leads as exogenous and then iterating over that process until the leads converge. Fair-Taylor can be considered a sort of ``Gauss-Seidel- over- time. Like Gauss-Seidel, Fair- Taylor may work very well, or it may have trouble converging. Larger shocks, more time periods, or tighter convergence criteria can greatly increase the number of iterations and computer time required to converge or can result in failure to converge. When convergence is successful, the ``solution values may have errors that are large relative to the convergence criterion. One advantage of Fair-Taylor is that it does not require much computer memory. The alternative Stacked-Time algorithm ``stacks all the time periods into one large system of equations and solves them simultaneously using Newton-Raphson. For typical macroeconometric models, Newton-Raphson is usually an efficient and very robust method. With quadratic convergence near the solution, the number of iterations is barely affected by the convergence criteria. The number of iterations also does not seem to change substantially with the number of time periods or the size of the shock, although in some cases large shocks may cause numerical problems such as ``log of a negative number. At convergence, solutions are generally accurate relative to the convergence criterion.

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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1996 with number _026.

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    Handle: RePEc:sce:scecf6:_026

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    Postal: Department of Econometrics, University of Geneva, 102 Bd Carl-Vogt, 1211 Geneva 4, Switzerland
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    1. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-85, July.
    2. Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
    3. Manfred Gilli & Giorgio Pauletto, . "An Application of Nonstationary Iterative Methods for Solving a Multi-Country Model with Rational Expectations," Computing in Economics and Finance 1996 _045, Society for Computational Economics.
    4. Wallart, N. & Burgenmeier, B., 1994. "L'acceptable des taxes incitatives en Suisse," Research Papers by the Department of Economics, University of Geneva 94.06, Département des Sciences Économiques, Université de Genève.
    5. Edison, Hali J. & Marquez, Jaime R. & Tryon, Ralph W., 1987. "The structure and properties of the Federal Reserve Board Multicountry Model," Economic Modelling, Elsevier, vol. 4(2), pages 115-315, April.
    6. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
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