Infinite-variance, Alpha-stable Shocks in Monetary SVAR

Greg Hannsgen

Economics Working Paper Archive from Levy Economics Institute

Abstract: The process of constructing impulse-response functions (IRFs) and forecast-error variance decompositions (FEVDs) for a structural vector autoregression (SVAR) usually involves a factorization of an estimate of the error-term variance-covariance matrix V. Examining residuals from a monetary VAR, this paper finds evidence suggesting that all of the variances in V are infinite. Specifically, this study estimates alpha-stable distributions for the reduced-form error terms. The ML estimates of the residuals' characteristic exponents "alpha" range from 1.5504 to 1.7734, with the Gaussian case lying outside 95 percent asymptotic confidence intervals for all six equations of the VAR. Variance-stabilized P-P plots show that the estimated distributions fit the residuals well. Results for subsamples are varied, while GARCH(1,1) filtering yields standardized shocks that are also all likely to be non-Gaussian alpha stable. When one or more error terms have infinite variance, V cannot be factored. Moreover, by Proposition 1, the reduced-form DGP cannot be transformed, using the required nonsingular matrix, into an appropriate system of structural equations with orthogonal, or even finite-variance, shocks. This result holds with arbitrary sets of identifying restrictions, including even the null set. Hence, with one or more infinite-variance error terms, structural interpretation of the reduced-form VAR within the standard SVAR model is impossible.

Keywords: Structural Vector Autoregression; VAR; Levy-stable Distribution; Infinite Variance; Monetary Policy Shocks; Heavy-tailed Error Terms; Factorization; Impulse Response Function; Transformability Problem (search for similar items in EconPapers)
JEL-codes: C32 C46 E30 E52 (search for similar items in EconPapers)
Date: 2010-05
New Economics Papers: this item is included in nep-cba and nep-ecm
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Citations: View citations in EconPapers (1)

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Journal Article: Infinite-variance, alpha-stable shocks in monetary SVAR (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:lev:wrkpap:wp_596

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