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Improving tatonnement methods for solving heterogenous agent models

  • Alexander Ludwig

This paper develops a globally convergent algorithm which modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogenous agent models. It is shown that the restrictions on the structure of the Jacobi matrix implicit in any such first-order iterative method can easily be relaxed for these models. Instead of relying on {\it ad hoc} and fixed dampening factors, standard Quasi-Newton methods can be used to determine the exact Jacobi matrix for steady state calculations and to update its elements by Broyden's method as the iteration proceeds. By transforming variables such that they are constant in the steady states, very few elements of the Jacobian have to be determined. For transition calculations the resulting steady state Jacobi matrix can be used as an approximation of the true transition Jacobi matrix. This extension of standard Gauss-Seidel iterations is shown to considerably improve convergence both in terms of speed as well as robustness relative to an ad hoc choice of fixed dampening factors. In addition, the relative advantage of the modified algorithm increases in the number of state variables of the model. The algorithm is particularly attractive since it is easy to implement - it only augments conventional and intuitive tatonnement iterations by standard numerical methods

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Paper provided by Society for Economic Dynamics in its series 2004 Meeting Papers with number 498.

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Date of creation: 2004
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Handle: RePEc:red:sed004:498
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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. Juillard, Michel & Laxton, Douglas & McAdam, Peter & Pioro, Hope, 1998. "An algorithm competition: First-order iterations versus Newton-based techniques," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1291-1318, August.
  2. Martin Floden & David Domeij, 2004. "Population Aging and International Capital Flows," 2004 Meeting Papers 490, Society for Economic Dynamics.
  3. David Altig, 2001. "Simulating Fundamental Tax Reform in the United States," American Economic Review, American Economic Association, vol. 91(3), pages 574-595, June.
  4. Judd, Kenneth L., 2002. "The parametric path method: an alternative to Fair-Taylor and L-B-J for solving perfect foresight models," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1557-1583, August.
  5. Axel Börsch-Supan & Alexander Ludwig & Joachim Winter, 2005. "Aging, Pension Reform, and Capital Flows: A Multi-Country Simulation Model," DNB Working Papers 065, Netherlands Central Bank, Research Department.
  6. Ray C. Fair & John B. Taylor, 1980. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Cowles Foundation Discussion Papers 564, Cowles Foundation for Research in Economics, Yale University.
  7. repec:adr:anecst:y:1990:i:17:p:04 is not listed on IDEAS
  8. repec:adr:anecst:y:1990:i:17 is not listed on IDEAS
  9. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
  10. Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
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