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Solving DSGE models with a nonlinear moving average

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  • Lan, Hong
  • Meyer-Gohde, Alexander

Abstract

We propose a nonlinear infinite moving average as an alternative to the standard state space policy function for solving nonlinear DSGE models. Perturbation of the nonlinear moving average policy function provides a direct mapping from a history of innovations to endogenous variables, decomposes the contributions from individual orders of uncertainty and nonlinearity, and enables familiar impulse response analysis in nonlinear settings. When the linear approximation is saddle stable and free of unit roots, higher order terms are likewise saddle stable and first order corrections for uncertainty are zero. We derive the third order approximation explicitly, examine the accuracy of the method using Euler equation tests, and compare with state space approximations.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:12:p:2643-2667
    DOI: 10.1016/j.jedc.2013.06.014
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    Cited by:

    1. Aruoba, S. Borağan & Bocola, Luigi & Schorfheide, Frank, 2017. "Assessing DSGE model nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 34-54.
    2. Michael K. Johnston & Robert G. King & Denny Lie, 2014. "Straightforward approximate stochastic equilibria for nonlinear rational expectations models," CAMA Working Papers 2014-59, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    3. Holden, Tom D., 2016. "Computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 144569, ZBW - German National Library of Economics.
    4. Grzegorz R. Dlugoszek, 2016. "Solving DSGE Portfolio Choice Models with Asymmetric Countries," SFB 649 Discussion Papers SFB649DP2016-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Simon Voigts, 2014. "Why the split of payroll taxation between firms and workers matters for macroeconomic stability," SFB 649 Discussion Papers SFB649DP2014-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Bonciani, Dario & Roye, Björn van, 2016. "Uncertainty shocks, banking frictions and economic activity," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 200-219.
    7. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - German National Library of Economics.
    8. repec:eee:dyncon:v:80:y:2017:i:c:p:1-16 is not listed on IDEAS
    9. repec:oup:restud:v:85:y:2018:i:1:p:1-49. is not listed on IDEAS
    10. repec:kap:compec:v:51:y:2018:i:1:d:10.1007_s10614-017-9670-z is not listed on IDEAS
    11. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 1-49.
    12. 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.
    13. Hong Lan & Alexander Meyer-Gohde, 2012. "Existence and Uniqueness of Perturbation Solutions to DSGE Models," SFB 649 Discussion Papers SFB649DP2012-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Hong Lan, 2018. "Comparing Solution Methods for DSGE Models with Labor Market Search," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 1-34, January.
    15. Hong Lan & Alexander Meyer-Gohde, 2013. "Decomposing Risk in Dynamic Stochastic General Equilibrium," SFB 649 Discussion Papers SFB649DP2013-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Andrew Binning, 2013. "Third-order approximation of dynamic models without the use of tensors," Working Paper 2013/13, Norges Bank.

    More about this item

    Keywords

    Perturbation; Nonlinear impulse response; DSGE; Solution methods; Volterra series;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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