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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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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0345.

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Date of creation: Oct 2007
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Handle: RePEc:nbr:nberte:0345

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  1. David K. Backus & Patrick J. Kehoe & Finn E. Kydland, 1987. "International real business cycles," Working Papers, Federal Reserve Bank of Minneapolis 426, Federal Reserve Bank of Minneapolis.
  2. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  3. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(7), pages 1411-1436, April.
  4. David K. Backus & Patrick J. Kehoe & Finn E. Kydland, 1993. "International Business Cycles: Theory and Evidence," Working Papers, New York University, Leonard N. Stern School of Business, Department of Economics 93-21, New York University, Leonard N. Stern School of Business, Department of Economics.
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Cited by:
  1. Ángel Gavilán & Juan A. Rojas, 2009. "Solving Portfolio Problems with the Smolyak-Parameterized Expectations Algorithm," Banco de Espa�a Working Papers 0838, Banco de Espa�a.
  2. K. Rebecca Scott, 2012. "Rational Habits and Uncertain Prices: Simulating Gasoline Consumption Behavior," Economics Series Working Papers, University of Oxford, Department of Economics 596, University of Oxford, Department of Economics.
  3. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series, Institute for Advanced Studies 258, Institute for Advanced Studies.
  4. Rong Hai & Dirk Krueger & Andrew Postlewaite, 2013. "On the Welfare Cost of Consumption Fluctuations in the Presence of Memorable Goods," NBER Working Papers 19386, National Bureau of Economic Research, Inc.
  5. Grey Gordon, 2011. "Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution," PIER Working Paper Archive 11-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(2), pages 240-251, February.
  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.

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