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Title:Infinite-variance, alpha-stable shocks in monetary SVAR PDF Logo
Authors:Hannsgen, Greg
Issue Date:2010
Series/Report no.:Working paper, Levy Economics Institute 596
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 reducedform error terms. The ML estimates of the residuals' characteristic exponents » 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.
Subjects:structural vector autoregression
VAR
Lévy-stable distribution
infinite variance
monetary policy shocks
heavy-tailed error terms
factorization
impulse response function
transformability problem
JEL:C32
C46
E30
E52
Document Type:Working Paper
Appears in Collections:Working Papers, Levy Economics Institute of Bard College

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