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Solvability of perturbation solutions in DSGE models

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  • Lan, Hong
  • Meyer-Gohde, Alexander

Abstract

We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.

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  • 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.
    • Handle: RePEc:eee:dyncon:v:45:y:2014:i:c:p:366-388
    DOI: 10.1016/j.jedc.2014.06.005
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    Cited by:

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    2. Alexander Meyer-Gohde & Daniel Neuhoff, 2015. "Generalized Exogenous Processes in DSGE: A Bayesian Approach," SFB 649 Discussion Papers SFB649DP2015-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Martin Kliem & Alexander Meyer‐Gohde, 2022. "(Un)expected monetary policy shocks and term premia," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 477-499, April.
    4. Frank Hespeler & Marco M. Sorge, 2018. "Does Near†Rationality Matter In First†Order Approximate Solutions? A Perturbation Approach," Bulletin of Economic Research, Wiley Blackwell, vol. 70(1), pages 97-113, January.
    5. Sergei Seleznev, 2016. "Solving DSGE models with stochastic trends," Bank of Russia Working Paper Series wps15, Bank of Russia.
    6. Parra-Alvarez, Juan Carlos & Polattimur, Hamza & Posch, Olaf, 2021. "Risk matters: Breaking certainty equivalence in linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    7. Grzegorz R. Dlugoszek, 2016. "Solving DSGE Portfolio Choice Models with Asymmetric Countries," SFB 649 Discussion Papers SFB649DP2016-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Meyer-Gohde, Alexander & Neuhoff, Daniel, 2015. "Solving and estimating linearized DSGE models with VARMA shock processes and filtered data," Economics Letters, Elsevier, vol. 133(C), pages 89-91.
    9. Lott, Sherwin, 2019. "Perturbations in DSGE models: An odd derivatives theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    10. Dmitry Kreptsev & Sergei Seleznev, 2018. "Forecasting for the Russian Economy Using Small-Scale DSGE Models," Russian Journal of Money and Finance, Bank of Russia, vol. 77(2), pages 51-67, June.

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    More about this item

    Keywords

    Perturbation; DSGE; Nonlinear; Sylvester equations; Solvability; Bézout׳s theorem;
    All these keywords.

    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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