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Local approximation of DSGE models around the risky steady state

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  • Juillard Michel

Abstract

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. 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.
  2. Nicolas Coeurdacier & Robert Kollmann & Philippe Martin, 2009. "International portfolios, capital accumulation and foreign assets dynamics," Globalization and Monetary Policy Institute Working Paper 27, Federal Reserve Bank of Dallas.
  3. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
  4. Jermann, Urban J., 1998. "Asset pricing in production economies," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 257-275, April.
  5. 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.
  6. 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.
  7. Martin D D Evans & Viktoria Hnatkovska, 2006. "International Capital Flows Returns and World Financial Integration," 2006 Meeting Papers 60, Society for Economic Dynamics.
  8. Ondrej Kamenik, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Working Papers 2005/10, Czech National Bank, Research Department.
  9. Michael B. Devereux & Alan Sutherland, 2008. "Country portfolios in open economy macro models," Globalization and Monetary Policy Institute Working Paper 09, Federal Reserve Bank of Dallas.
  10. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer, vol. 18(1), pages 127-157.
  11. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
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Cited by:
  1. Tom Holden & Michael Paetz, 2012. "Efficient Simulation of DSGE Models with Inequality Constraints," Quantitative Macroeconomics Working Papers 21207b, Hamburg University, Department of Economics.
  2. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
  3. Hong Lan & Alexander Meyer-Gohde, 2013. "Pruning in Perturbation DSGE Models - Guidance from Nonlinear Moving Average Approximations," SFB 649 Discussion Papers SFB649DP2013-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. de Groot, Oliver, 2013. "Computing the risky steady state of DSGE models," Economics Letters, Elsevier, vol. 120(3), pages 566-569.

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