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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 first 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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  • Juillard Michel, 2011. "Local approximation of DSGE models around the risky steady state," wp.comunite 0087, Department of Communication, University of Teramo.
  • Handle: RePEc:ter:wpaper:0087
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    File URL: http://www.mjui.fr/juillard/papers/mj_riksy_ss.pdf
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    References listed on IDEAS

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    1. Evans, Martin D.D. & Hnatkovska, Viktoria V., 2014. "International capital flows, returns and world financial integration," Journal of International Economics, Elsevier, vol. 92(1), pages 14-33.
    2. OndŘej KamenÍk, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 167-187, February.
    3. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
    4. 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.
    5. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
    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. Jermann, Urban J., 1998. "Asset pricing in production economies," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 257-275, April.
    8. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    9. 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.
    10. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 127-157.
    11. Michael B. Devereux & Alan Sutherland, 2011. "Country Portfolios In Open Economy Macro‐Models," Journal of the European Economic Association, European Economic Association, vol. 9(2), pages 337-369, April.
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    Cited by:

    1. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    2. Tom Holden & Michael Paetz, 2012. "Efficient Simulation of DSGE Models with Inequality Constraints," Quantitative Macroeconomics Working Papers 21207b, Hamburg University, Department of Economics.
    3. M. Marx & B. Mojon & F. Velde, 2017. "Why Have Interest Rates Fallen far Below the Return on Capital," Working papers 630, Banque de France.
    4. Michel Guillard & Hubert Kempf, 2017. "Public Debt Sustainability and Defaults," CESifo Working Paper Series 6554, CESifo Group Munich.
    5. Grzegorz R. Dlugoszek, 2016. "Solving DSGE Portfolio Choice Models with Asymmetric Countries," SFB 649 Discussion Papers SFB649DP2016-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Sandra Eickmeier & Norbert Metiu & Esteban Prieto, 2016. "Time-varying volatility, financial intermediation and monetary policy," CAMA Working Papers 2016-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. Francois Velde & Benoït Mojon & Magali Marx, 2016. "Why are real interest rates so low?," 2016 Meeting Papers 1581, Society for Economic Dynamics.
    8. Julio A. Carrillo & Gert Peersman & Joris Wauters, 2013. "Endogenous Wage Indexation and Aggregate Shocks," Working Papers 2013-19, Banco de México.
    9. Vivek Prasad, 2015. "Balanced Budget Tax Cuts in a Liquidity-Constrained Economy," Manchester School, University of Manchester, vol. 83, pages 87-119, September.
    10. Meyer-Gohde, Alexander, 2015. "Risk-Sensitive Linear Approximations," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113057, Verein für Socialpolitik / German Economic Association.
    11. repec:kap:compec:v:51:y:2018:i:1:d:10.1007_s10614-017-9670-z is not listed on IDEAS
    12. 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.
    13. 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.
    14. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    15. 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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