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Evaluating Approximate Equilibria of Dynamic Economic Models

This paper evaluates the performances of Perturbation Methods, the Parameterized Expectations Algorithm and Projection Methods in finding approximate decision rules of the basic neoclassical stochastic growth model. In contrast to the existing literature, we focus on comparing numerical methods for a given functional form of the approximate decision rules, and we repeat the evaluation for many di®erent parameter sets. We ¯nd that signi¯cant gains in accuracy can be achieved by moving from linear to higher-order approximations. Our results show further that among linear and quadratic approximations, Perturbation Methods yield particularly good results, whereas Projection Methods are well suited to derive higher-order approximations. Finally we show that although the structural parameters of the model economy have a large e®ect on the accuracy of numerical approximations, the ranking of competing methods is largely independent from the calibration.

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File URL: http://homepage.univie.ac.at/Papers.Econ/RePEc/vie/viennp/vie0510.pdf
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Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0510.

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Date of creation: Dec 2005
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Handle: RePEc:vie:viennp:0510
Contact details of provider: Web page: http://www.univie.ac.at/vwl

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  1. Uhlig, H.F.H.V.S., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  2. Maliar, Lilia & Maliar, Serguei, 2003. "Parameterized Expectations Algorithm and the Moving Bounds," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 88-92, January.
  3. Eric Swanson & Gary Anderson & Andrew Levin, 2004. "Higher-Order Solutions to Dynamic, Discrete-Time Rational Expectations Models: Methods and an Application to Optimal Monetary Policy," Econometric Society 2004 North American Winter Meetings 576, Econometric Society.
  4. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  5. Heer, Burkhard & Maußner, Alfred, 2008. "Computation Of Business Cycle Models: A Comparison Of Numerical Methods," Macroeconomic Dynamics, Cambridge University Press, vol. 12(05), pages 641-663, November.
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  7. Javier J. Pérez, 2001. "A Log-linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Economic Working Papers at Centro de Estudios Andaluces E2001/02, Centro de Estudios Andaluces.
  8. Gary S. Anderson, 2000. "A Systematic Comparison Of Alternative Linear Rational Expectation Model Solution Techniques," Computing in Economics and Finance 2000 142, Society for Computational Economics.
  9. 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.
  10. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  11. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  12. John B. Taylor & Harald Uhlig, 1989. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  13. Lawrence J. Christiano & Jonas D.M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues 94-6, Federal Reserve Bank of Chicago.
  14. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," FRB Atlanta Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  15. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  16. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  18. Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
  19. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  20. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, May.
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