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

We characterize the balanced growth path of the basic neoclassical growth economy using standard, almost linear numerical solution methods, as well as the parameterized expectations approach, which preserves the nonlinearity in the model. We also apply the same methods after 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 tackle the question of how much of the nonlinear structure of the original problem is useful to maintain when using an “almost” linear method. We show that it is possible to find an almost linear method to solve these models as accurately as by parameterizing expectations. Our results show the importance of performing log-linear approximations, as well as the convenience of refining a linear solution method by mixing some structure of the original non-linear problem with structure of the approximated system.

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Paper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2002/15.

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Length: 45 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:cea:doctra:e2002_15
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  2. 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.
  3. Gary Hansen, 2010. "Indivisible Labor and the Business Cycle," Levine's Working Paper Archive 233, David K. Levine.
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  6. Alfonso Novales & Javier J. PÈrez, 2004. "Is It Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?," Computational Economics, Society for Computational Economics, vol. 23(4), pages 343-377, 06.
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  10. 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.
  11. 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.
  12. 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.
  13. John Y. Campbell, 1992. "Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model," NBER Working Papers 4188, National Bureau of Economic Research, Inc.
  14. 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.
  15. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  16. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, March.
  17. Ilaski Barañano & Amaia Iza & Jesús Vázquez, 2002. "A comparison between the log-linear and the parameterized expectations methods," Spanish Economic Review, Springer, vol. 4(1), pages 41-60.
  18. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  19. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  20. Sims, Christopher A, 1990. "Solving the Stochastic Growth Model by Backsolving with a Particular Nonlinear Form for the Decision Rule," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 45-47, January.
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  23. Albert Marcet & Guido Lorenzoni, 1998. "The Parameterized Expectations Approach: Some Practical Issues," QM&RBC Codes 128, Quantitative Macroeconomics & Real Business Cycles.
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