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Some results on the solution of the neoclassical growth model

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  • Jesus Fernandez-Villaverde
  • Juan Francisco Rubio-Ramírez

Abstract

This paper presents some new results on the solution of the stochastic neoclassical growth model with leisure. We use the method of Judd (2003) to explore how to change variables in the computed policy functions that characterize the behavior of the economy. We find a simple closed-form relation between the parameters of the linear and the loglinear solution of the model. We extend this approach to a general class of changes of variables and show how to find the optimal transformation. We thus reduce the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first-order policy functions and how we can keep a linear representation of the model’s laws of motion if we use a nearly optimal transformation. We conclude by discussing how to apply our results to estimate dynamic equilibrium economies.

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Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2003-34.

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Date of creation: 2003
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Handle: RePEc:fip:fedawp:2003-34

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  1. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2004. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Econometric Society 2004 North American Winter Meetings 411, Econometric Society.
  2. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  3. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 1999. "The Perils of Taylor Rules," CEPR Discussion Papers 2314, C.E.P.R. Discussion Papers.
  5. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  6. Ellen R. McGrattan & Edward C. Prescott, 2001. "Is the Stock Market Overvalued?," NBER Working Papers 8077, National Bureau of Economic Research, Inc.
  7. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  8. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
  9. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  10. 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.
  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. Campbell, John, 1994. "Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model," Scholarly Articles 3196342, Harvard University Department of Economics.
  13. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
  14. 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.
  15. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
  16. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
  17. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  18. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
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Cited by:
  1. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez & Manuel Santos, 2004. "Convergence Properties of the Likelihood of Computed Dynamic Models," PIER Working Paper Archive 04-034, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.

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