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A Cluster-Grid Projection Method: Solving Problems with High Dimensionality

  • Kenneth L. Judd
  • Lilia Maliar
  • Serguei Maliar

We develop a projection method that can solve dynamic economic models with a large number of state variables. A distinctive feature of our method is that it operates on the ergodic set realized in equilibrium: we simulate a model, distinguish clusters on simulated series and use the clusters' centers as a grid for projections. Making the grid endogenous to the model allows us to avoid costs associated with finding a solution in areas of state space that are never visited in equilibrium. On a standard desktop computer, we calculate linear and quadratic solutions to a multi-country growth model with up to 400 and 80 state variables, respectively. Our solutions are global, and their accuracy does not rapidly decline away from steady state.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15965.

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Date of creation: May 2010
Date of revision:
Handle: RePEc:nbr:nberwo:15965
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  1. Jess Gaspar & Kenneth L. Judd, 1997. "Solving Large Scale Rational Expectations Models," NBER Technical Working Papers 0207, National Bureau of Economic Research, Inc.
  2. John B. Taylor & Harald Uhlig, 1989. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  3. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues WP-97-15, Federal Reserve Bank of Chicago.
  4. Kollmann, Robert & Maliar, Serguei & Malin, Benjamin A. & Pichler, Paul, 2011. "Comparison of solutions to the multi-country Real Business Cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 186-202, February.
  5. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
  6. Maliar, Serguei & Maliar, Lilia & Judd, Kenneth, 2011. "Solving the multi-country real business cycle model using ergodic set methods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 207-228, February.
  7. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
  8. 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.
  9. Serguei Maliar & Lilia Maliar & Kenneth Judd, 2010. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," 2010 Meeting Papers 280, Society for Economic Dynamics.
  10. Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
  11. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-81, September.
  12. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  13. Juillard, Michel & Villemot, Sébastien, 2011. "Multi-country real business cycle models: Accuracy tests and test bench," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 178-185, February.
  14. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  15. Den Haan, Wouter J, 1996. "Heterogeneity, Aggregate Uncertainty, and the Short-Term Interest Rate," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 399-411, October.
  16. 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.
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