@techreport{Hannsgen2010Infinite,
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 \guillemotright{} 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.},
address = {Annandale-on-Hudson, NY},
author = {Greg Hannsgen},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C32; C46; E30; E52; 330; structural vector autoregression; VAR; L\'{e}vy-stable distribution; infinite variance; monetary policy shocks; heavy-tailed error terms; factorization; impulse response function; transformability problem},
language = {eng},
number = {596},
publisher = {Levy Economics Institute of Bard College},
title = {Infinite-variance, alpha-stable shocks in monetary SVAR},
type = {Working paper, Levy Economics Institute},
url = {http://hdl.handle.net/10419/57001},
year = {2010}
}