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Forecasting with Second-Order Approximations and Markov-Switching DSGE Models


This paper considers the out-of-sample forecasting performance of first- and second-order perturbation approximations for DSGE models that incorporate Markov-switching behaviour in the policy reaction function and the volatility of shocks. The results suggest that second-order approximations provide an improved forecasting performance in models that do not allow for regime-switching, while for the MS-DSGE models, a first-order approximation would appear to provide better out-of-sample properties. In addition, we find that over short-horizons, the MS-DSGE models provide superior forecasting results when compared to those models that do not allow for regime-switching (at both perturbation orders).

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  1. Lindé (2018) provides a recent summary of the use of DSGE models within academic and policy-making institutions, while da Silva (2018) and Tovar (2009) make note of their use within central banks. Several other authors, including Blanchard (2016) and Reis (2018), suggest that while we need to improve upon the existing framework, it would be wrong to suggest that this framework should be discarded.

  2. In addition, higher-order model solutions could also be used to capture important features that relate to asset pricing or welfare effects.

  3. As an alternative to high-order perturbation techniques, Fernández-Villaverde and Levintal (2017) describe the use of three projection methods that may be used to solve calibrated versions of a nonlinear DSGE model.

  4. See Sect. 4 for specific details relating to the potential sources of these forecasting errors.

  5. The RISE toolbox can be downloaded at: It does not currently include the MSQKF that was used for the models that employ second-order approximations for the model solution.

  6. In a similar study, Aruoba et al. (2006) compare the use of both perturbation and projection methods for the solution of a calibrated stochastic neoclassical growth model using various methods of accuracy and robustness.

  7. The “Online Appendix” also includes tables for all these results.


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The authors would like to thank the anonymous referees for valuable comments. All remaining errors are ours.

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Correspondence to Kevin Kotzé.

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Table 4 Significance test of equal forecasting quality of models and VAR
Table 5 Significance test of equal forecasting quality of models and AR

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Ivashchenko, S., Çekin, S.E., Kotzé, K. et al. Forecasting with Second-Order Approximations and Markov-Switching DSGE Models. Comput Econ 56, 747–771 (2020).

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  • Regime-switching
  • Second-order approximation
  • Non-linear MS-DSGE estimation
  • Forecasting

JEL Classifications

  • C13
  • C32
  • E37