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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.

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  • Ellen R. McGrattan, . "Solving the stochastic growth model with a finite element method," Staff Report, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:164
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    1. Aiyagari, S. Rao & McGrattan, Ellen R., 1998. "The optimum quantity of debt," Journal of Monetary Economics, Elsevier, vol. 42(3), pages 447-469, October.
    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. 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.
    4. 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.
    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. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report, Federal Reserve Bank of Minneapolis.
    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. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    Cited by:

    1. 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.
    2. Miguel Viegas & Ana Paula Ribeiro, 2011. "Welfare-improving Government Behaviour and Inequality - Inspection Using a Heterogeneous-agent Model," CEF.UP Working Papers 1103, Universidade do Porto, Faculdade de Economia do Porto.
    3. Jeffrey C. Fuhrer & C. Hoyt Bleakley, "undated". "Computationally Efficient Solution and Maximum Likelihood Estimation of Nonlinear Rational Expectations Models," Computing in Economics and Finance 1997 35, Society for Computational Economics.
    4. Brown, Ward & Haegler, Urs, 2004. "Financing constraints and inventories," European Economic Review, Elsevier, vol. 48(5), pages 1091-1123, October.
    5. Michel Juillard & Fabrice Collard, 1999. "Stochastic Simulations of a Non-Linear Phillips Curve Model," Computing in Economics and Finance 1999 144, Society for Computational Economics.
    6. Tessa Bold, 2008. "Implications of Endogenous Group Formation for Efficient Risk-Sharing," Economics Series Working Papers 387, University of Oxford, Department of Economics.
    7. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report, Federal Reserve Bank of Minneapolis.
    8. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report, Federal Reserve Bank of Minneapolis.

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