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Solving the stochastic growth model with a finite element method

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  • Ellen R. McGrattan

Abstract

Since it is the dominant paradigm of the business cycle and growth literatures, the stochastic growth model has been used to test the performance of alternative numerical methods. In this paper I apply the finite element method to this model. I show that the method is easy to apply and that, for examples such as the stochastic growth method, it gives accurate solutions within a second or two on a desktop computer. I also show how inequality constraints can be handled by redefining the optimization problem with penalty functions.

Suggested Citation

  • Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report 164, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:164
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    4. Aiyagari, S. Rao & McGrattan, Ellen R., 1998. "The optimum quantity of debt," Journal of Monetary Economics, Elsevier, vol. 42(3), pages 447-469, October.
    5. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    6. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    7. Christiano, Lawrence J, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 23-26, January.
    8. R. Anton Braun & Ellen R. McGrattan, 1993. "The Macroeconomics of War and Peace," NBER Chapters, in: NBER Macroeconomics Annual 1993, Volume 8, pages 197-258, National Bureau of Economic Research, Inc.
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