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Solving the multi-country real business cycle model using a Smolyak-collocation method

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  • Malin, Benjamin A.
  • Krueger, Dirk
  • Kubler, Felix

Abstract

We describe a sparse-grid collocation method to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method can be in applications by computing the non-linear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy, the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with up to 10 countries (i.e., up to 20 continuous-valued state variables).

Suggested Citation

  • Malin, Benjamin A. & Krueger, Dirk & Kubler, Felix, 2011. "Solving the multi-country real business cycle model using a Smolyak-collocation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 229-239, February.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:2:p:229-239
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Backus, David K & Kehoe, Patrick J & Kydland, Finn E, 1992. "International Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 745-775, August.
    4. 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.
    5. Kollmann, Robert & Kim, Jinill & Kim, Sunghyun H., 2011. "Solving the multi-country Real Business Cycle model using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 203-206, February.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    7. Finn E. Kydland (ed.), 1995. "Business Cycle Theory," Books, Edward Elgar Publishing, number 565.
    8. 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.
    9. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2011. "Computational suite of models with heterogeneous agents II: Multi-country real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 175-177, February.
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