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Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models

  • Serguei Maliar

    (Hoover Institution at Stanford University and University of Alicante)

  • Lilia Maliar

    (Hoover Institution at Stanford University and University of Alicante)

  • Kenneth Judd

    (Hoover Institution at Stanford University)

We develop numerically stable stochastic simulation approaches for solving dynamic economic models. We rely on standard simulation procedures to simultaneously compute an ergodic distribution of state variables, its support and the associated decision rules. We differ from existing methods, however, in how we use simulation data to approximate decision rules. Instead of the usual least-squares methods, we examine a variety of alternatives, including the least-squares method using SVD, Tikhonov regularization, least-absolute deviation methods, principal components regression method, all of which are numerically stable and can handle ill-conditioned problems. These new methods enable us to compute high-order polynomial approximations without encountering numerical problems. Our approaches are especially well suitable for high-dimensional applications in which other methods are infeasible.

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Paper provided by Society for Economic Dynamics in its series 2010 Meeting Papers with number 280.

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Date of creation: 2010
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Handle: RePEc:red:sed010:280
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Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA

Web page: http://www.EconomicDynamics.org/
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  1. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
  2. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  3. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  4. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
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  8. Maliar, Lilia & Maliar, Serguei, 2003. "Parameterized Expectations Algorithm and the Moving Bounds," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 88-92, January.
  9. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-85, July.
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  12. 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.
  13. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
  14. 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.
  15. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, May.
  16. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer, vol. 1(3), pages 211-218, September.
  17. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
  18. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  19. Lilia Maliar & Serguei Maliar, 2002. "The Representative Consumer In The Neoclassical Growth Model With Idiosyncratic Shocks," Working Papers. Serie AD 2002-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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