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

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  • Kenneth L. Judd
  • Lilia Maliar
  • Serguei Maliar

Abstract

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.

Suggested Citation

  • Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2010. "A Cluster-Grid Projection Method: Solving Problems with High Dimensionality," NBER Working Papers 15965, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:15965
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    References listed on IDEAS

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    Cited by:

    1. Marco Del Negro & Marc P. Giannoni & Frank Schorfheide, 2015. "Inflation in the Great Recession and New Keynesian Models," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 168-196, January.
    2. S Borağan Aruoba & Pablo Cuba-Borda & Frank Schorfheide, 2018. "Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 87-118.
    3. S. Bogan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2021. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 96-120, July.
    4. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    5. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    6. Grey Gordon, 2020. "Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution," Economic Quarterly, Federal Reserve Bank of Richmond, issue 2Q, pages 61-95.
    7. Richter Alexander W. & Throckmorton Nathaniel A., 2015. "The zero lower bound: frequency, duration, and numerical convergence," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 1-26, January.
    8. S. Bogan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2021. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 96-120, July.
    9. Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Inna Tsener, 2017. "How to solve dynamic stochastic models computing expectations just once," Quantitative Economics, Econometric Society, vol. 8(3), pages 851-893, November.
    10. Mertens, Thomas M. & Judd, Kenneth L., 2018. "Solving an incomplete markets model with a large cross-section of agents," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 349-368.
    11. 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.
    12. Senbeta, Sisay, 2011. "How applicable are the new keynesian DSGE models to a typical low-income economy?," MPRA Paper 30931, University Library of Munich, Germany.
    13. S. Boragan Aruoba & Frank Schorfheide, 2013. "Macroeconomic dynamics near the ZLB: a tale of two equilibria," Working Papers 13-29, Federal Reserve Bank of Philadelphia.
    14. Hong Lan, 2018. "Comparing Solution Methods for DSGE Models with Labor Market Search," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 1-34, January.

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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