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Is It Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?

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Author Info
Alfonso Novales () (Univ. Complutense de Madrid)
Javier J. PÈrez () (centrA, and Univ. Pablo de Olavide de Sevilla)

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Abstract

We characterize the balanced growth path of the basic neoclassical growth economy using standard numerical solution methods which solve a linear or log-linear approximation to the economic model, as well as methods which preserve the nonlinearity in the original model. We also apply the same methods adding indivisible labor to the basic model, and to a monetary version of that economy, subject to a cash-in-advance constraint. In a unified framework, we show that log-linear approximations should generally be preferred to linear approximations. We also provide evidence that preserving the original nonlinear structure of the model when computing the numerical solution generally yields minor gains in accuracy. Methods that use either a linear or a log-linear approximation to the model can produce solutions as accurate as the parameterized expectations method. However, in extreme parametric cases, the solution may be rather sensible to small numerical errors, and even a log-linear approximation may then be inappropriate. Methods using the nonlinear structure of the original model can then perform significantly better.

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Article provided by Springer in its journal Computational Economics.

Volume (Year): 23 (2004)
Issue (Month): 4 (06)
Pages: 343-377
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Handle: RePEc:kap:compec:v:23:y:2004:i:4:p:343-377

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  1. Christiano, Lawrence J, 1990. "Linear-Quadratic Approximation and Value-Function Iteration: A Comparison," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 99-113, January.
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  3. Gary D. Hansen & Edward C. Prescott, 1992. "Recursive methods for computing equilibria of business cycle models," Discussion Paper / Institute for Empirical Macroeconomics 36, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  4. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June. [Downloadable!] (restricted)
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  5. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June. [Downloadable!] (restricted)
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  6. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
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  7. Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions," Discussion Paper / Institute for Empirical Macroeconomics 91, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  8. Alfonso Novales & Emilio Dominguez & Javier J. Perez & Jesus Ruiz, 1998. "Solving Non-linear Rational Expectations Models By Eigenvalue-Eigenvector Decompositions," QM&RBC Codes 124, Quantitative Macroeconomics & Real Business Cycles. [Downloadable!]
  9. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer, vol. 20(1-2), pages 1-20, October. [Downloadable!]
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  11. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer, vol. 20(1-2), pages 87-116, October. [Downloadable!]
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  12. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November. [Downloadable!] (restricted)
  13. Albert Marcet & Guido Lorenzoni, 1998. "The Parameterized Expectations Approach: Some Practical Issues," QM&RBC Codes 128, Quantitative Macroeconomics & Real Business Cycles. [Downloadable!]
  14. Cooley, Thomas F & Hansen, Gary D, 1989. "The Inflation Tax in a Real Business Cycle Model," American Economic Review, American Economic Association, vol. 79(4), pages 733-48, September. [Downloadable!] (restricted)
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  15. Kydland, Finn E & Prescott, Edward C, 1996. "The Computational Experiment: An Econometric Tool," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 69-85, Winter. [Downloadable!] (restricted)
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  16. Lucas, Robert E, Jr, 1980. "Methods and Problems in Business Cycle Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 12(4), pages 696-715, November. [Downloadable!] (restricted)
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  18. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics. [Downloadable!]
  2. Antonio Morales & Pablo Brañas Garza, 2003. "Computational Errors in Guessing Games1," Economic Working Papers at Centro de Estudios Andaluces E2003/11, Centro de Estudios Andaluces. [Downloadable!]
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