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Solving a non-linear model: The importance of model specification for deriving a suitable solution

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  • Herbert, Ric D.
  • Stemp, Peter J.

Abstract

In this paper, we consider a macroeconomic model with alternative linear and non-linear specifications. One version of the model, expressed in levels, is highly non-linear and has at least two steady-state equilibria. One of these equilibria has an economically meaningful interpretation, while the other does not have a sensible economic interpretation. A second version of the model, expressed in logarithms, is linear and has a unique steady-state equilibrium, which corresponds to the economically meaningful equilibrium of the non-linear version of the model. The dynamic solution of each model version has a combination of stable and unstable eigenvalues so that any dynamic solution requires the calculation of appropriate “jumps” in endogenous variables. Attempts to solve these models, using forward-shooting and reverse-shooting algorithms, show that the forward-shooting algorithm chooses the “wrong” solution for the non-linear model, but the “right” solution for the linear model. The reverse-shooting algorithm chooses the “right” solution in both cases. We demonstrate how this result is driven by particular properties of the two versions of the model.

Suggested Citation

  • Herbert, Ric D. & Stemp, Peter J., 2009. "Solving a non-linear model: The importance of model specification for deriving a suitable solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2847-2855.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:9:p:2847-2855
    DOI: 10.1016/j.matcom.2008.04.010
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    References listed on IDEAS

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    1. Stemp, Peter J. & Herbert, Ric D., 2008. "Comparing different approaches for solving optimizing models with significant nonlinearities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 357-366.
    2. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, April.
    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. Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, vol. 41(6), pages 1043-1048, November.
    5. Peter Stemp & Ric Herbert, 2006. "Solving Non-Linear Models with Saddle-Path Instabilities," Computational Economics, Springer;Society for Computational Economics, vol. 28(2), pages 211-231, September.
    6. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
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