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Solving the stochastic growth model with a finite element method

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Ellen R. McGrattan

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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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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 164.

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Date of creation: 1993
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Publication status: Published in Journal of Economic Dynamics and Control (Vol 20, Num 1-3, March 1996, pp. 19-42)
Handle: RePEc:fip:fedmsr:164

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Keywords: Econometric models;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March. [Downloadable!] (restricted)
  2. S. Rao Aiyagari & Ellen R. McGrattan, 1994. "The optimal quantity of debt," Working Papers 538, Federal Reserve Bank of Minneapolis.
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  3. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December. [Downloadable!] (restricted)
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  4. 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.
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  5. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  6. 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.
  7. 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. [Downloadable!]
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