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Plausibility of big shocks within a linear state space setting with skewness

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  • Koloch, Grzegorz

Abstract

In this paper we provide formulae for likelihood function, filtration densities and prediction densities of a linear state space model in which shocks are allowed to be skewed. In particular we work with the closed skew normal distribution, see González-Farías et al. (2004), which nests a normal distribution as a special case. Closure of the csn distribution with respect to all necessary transformations in the state space setting is guaranteed by a simple state dimension reduction procedure which does not influence the value of the likelihood function. Presented formulae allow for estimation, filtration and prediction of vector autoregressions and first order perturbations of DSGE models with skewed shocks. This allows to assess asymmetries in shocks, observed data, impulse responses and forecasts confidence intervals. Some of the advantages of using the outlined approach may involve capturing asymmetric inflation risks in central banks forecasts or producing more plausible probabilities of deep but rare recessionary episodes with DSGE/VAR filtration. Exemplary estimation results are provided which show that within a linear setting with skewness frequency of big shocks can be rather plausibly identifed.

Suggested Citation

  • Koloch, Grzegorz, 2016. "Plausibility of big shocks within a linear state space setting with skewness," MPRA Paper 69001, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:69001
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    File URL: https://mpra.ub.uni-muenchen.de/69001/1/MPRA_paper_69001.pdf
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    References listed on IDEAS

    as
    1. Vasco Cúrdia & Marco Negro & Daniel L. Greenwald, 2014. "Rare Shocks, Great Recessions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1031-1052, November.
    2. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
    3. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    4. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Maximum likelihood estimation; state space models; closed skew-normal distribution; DSGE; VAR;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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