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Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method

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  • Benjamin Malin
  • Dirk Krueger
  • Felix Kubler

Abstract

We describe a sparse grid collocation algorithm to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method may be in applications by computing the nonlinear 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 2, 4, and 6 countries (i.e., up to 12 continuous state variables).

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  • Benjamin Malin & Dirk Krueger & Felix Kubler, 2007. "Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method," NBER Technical Working Papers 0345, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0345
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    1. 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.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    3. Finn E. Kydland (ed.), 1995. "Business Cycle Theory," Books, Edward Elgar Publishing, number 565.
    4. 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.
    5. David Backus & Patrick J. Kehoe & Finn E. Kydland, 1993. "International Business Cycles: Theory and Evidence," NBER Working Papers 4493, National Bureau of Economic Research, Inc.
    6. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
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    2. Grey Gordon, 2020. "Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution," Economic Quarterly, Federal Reserve Bank of Richmond, issue 2Q, pages 61-95.
    3. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 240-251, February.
    4. Zhou, Wei, 2015. "Three essays on modeling biofuel feedstock supply," ISU General Staff Papers 201501010800005728, Iowa State University, Department of Economics.
    5. K. Rebecca Scott, 2012. "Rational Habits and Uncertain Prices: Simulating Gasoline Consumption Behavior," Economics Series Working Papers 596, University of Oxford, Department of Economics.
    6. Michael Reiter, 2015. "Solving OLG Models with Asset Choice," 2015 Meeting Papers 1509, Society for Economic Dynamics.
    7. Rong Hai & Andrew Postlewaite & Dirk Krueger, 2013. "On the Welfare Cost of Consumption Fluctuations in the Presence of Memorable Goods, Second Version," PIER Working Paper Archive 14-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 15 Apr 2014.
    8. Ángel Gavilán & Juan A. Rojas, 2009. "Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm," Working Papers 0838, Banco de España.
    9. Zhou, Wei & Babcock, Bruce A., 2014. "Endogenous Price in a Dynamic Model for Agricultural Supply Analysis," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170584, Agricultural and Applied Economics Association.
    10. Reiter, Michael, 2015. "Solving OLG Models with Many Cohorts, Asset Choice and Large Shocks," Economics Series 320, Institute for Advanced Studies.
    11. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.

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    More about this item

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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