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Comparing Solution Methods for Dynamic Equilibrium Economies

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  • S. B. Aruoba
  • Jesús Fernández-Villaverde
  • Juan F. Rubio-Ramirez

Abstract

This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity and accuracy and we present some conclusions about our preferred approaches based on the reported evidence.
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  • S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:122247000000000855
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    File URL: http://www.econ.upenn.edu/~jesusfv/comparison.pdf
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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.
    2. Martin S. Feldstein & Jeffrey B. Liebman, 2002. "The Distributional Effects of an Investment-Based Social Security System," NBER Chapters, in: The Distributional Aspects of Social Security and Social Security Reform, pages 263-326, National Bureau of Economic Research, Inc.
    3. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    4. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    5. Hugo Benitez-Silva & John Rust & Gunter Hitsch & Giorgio Pauletto & George Hall, 2000. "A Comparison Of Discrete And Parametric Methods For Continuous-State Dynamic Programming Problems," Computing in Economics and Finance 2000 24, Society for Computational Economics.
    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.
    7. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    8. Ellen R. McGrattan & Edward C. Prescott, 2000. "Is the stock market overvalued?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Fall), pages 20-40.
    9. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2001. "Comparing dynamic equilibrium economies to data," FRB Atlanta Working Paper 2001-23, Federal Reserve Bank of Atlanta.
    10. 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.
    11. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    12. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    13. R. E. Hall, 1971. "The Dynamic Effects of Fiscal Policy in an Economy with Foresight," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 229-244.
    14. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
    15. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    16. 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.
    17. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 127-157.
    18. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    19. Santos, Manuel S., 1999. "Numerical solution of dynamic economic models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 5, pages 311-386, Elsevier.
    20. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
    21. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    22. Albert Marcet & Guido Lorenzoni, 1998. "Parameterized expectations approach; Some practical issues," Economics Working Papers 296, Department of Economics and Business, Universitat Pompeu Fabra.
    23. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    24. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    25. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    26. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    27. repec:cup:macdyn:v:1:y:1997:i:1:p:45-75 is not listed on IDEAS
    28. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    29. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    30. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 45-75, January.
    31. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    32. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
    33. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    34. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
    35. 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.
    36. Miranda, Mario J & Helmberger, Peter G, 1988. "The Effects of Commodity Price Stabilization Programs," American Economic Review, American Economic Association, vol. 78(1), pages 46-58, March.
    37. 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.
    38. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Some Results on the Solution of the Neoclassical Growth Model," PIER Working Paper Archive 04-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    39. S. Boragan Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," FRB Atlanta Working Paper 2003-27, Federal Reserve Bank of Atlanta.
      • S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Finite Elements Method," QM&RBC Codes 118, Quantitative Macroeconomics & Real Business Cycles.
    40. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
    41. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    42. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    43. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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