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Local approximation of DSGE models around the risky steady state

  • Juillard Michel

A DSGE model takes the mathematical form of a system of nonlinear stochastic equations. Except in a very few cases, there is no analytical solution and economists are left using numerical methods in order to obtain approximated solutions. Global approximation methods are available when the state space is not too large, while the most usual approach is local approximation around the deterministic steady state. The perturbation approach introduced in economics by Judd (1996) derives a Taylor expansion of the solution from a Taylor expansion of the original problem, but ?rst order approximation is nothing but linearization that has been used in the RBC literature since its inception. Second order approximations are discussed in several papers: Sims (2000); Collard and Juillard (2001); Kim et al. (2003); Schmitt-Grohe and Uribe (2004). Second order approximations have two merits. In most cases, but not in all, they provide a more accurate approximation of the solution, but, more importantly, they break away from certainty equivalence, that is an inescapable characteristic of linear model. This is crucial to address issues related to attitudes toward risk. There is of course no reason, except size of model, to consider only ?rst or second order approximations. Higher order approximation as also sometimes used: Jin and Judd (2002); Juillard and Kamenik (2004).

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Paper provided by Department of Communication, University of Teramo in its series wp.comunite with number 0087.

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Date of creation: Nov 2011
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Handle: RePEc:ter:wpaper:0087
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  1. Michael B. Devereux & Alan Sutherland, 2008. "Country Portfolios in Open Economy Macro Models," NBER Working Papers 14372, National Bureau of Economic Research, Inc.
  2. Coeurdacier, Nicolas & Kollmann, Robert & Martin, Philippe, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Journal of International Economics, Elsevier, vol. 80(1), pages 100-112, January.
  3. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  4. 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.
  5. Ondrej Kamenik, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Working Papers 2005/10, Czech National Bank, Research Department.
  6. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2004. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Econometric Society 2004 North American Winter Meetings 411, Econometric Society.
  7. Martin D. D. Evans & Viktoria Hnatkovska, 2005. "International Capital Flows, Returns and World Financial Integration," NBER Working Papers 11701, National Bureau of Economic Research, Inc.
  8. Jermann, Urban J., 1998. "Asset pricing in production economies," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 257-275, April.
  9. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer, vol. 18(1), pages 127-157.
  10. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
  11. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
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