Infinite-variance, Alpha-stable Shocks in Monetary SVAR
AbstractThe 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.
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Bibliographic InfoPaper provided by Levy Economics Institute in its series Economics Working Paper Archive with number wp_596.
Date of creation: May 2010
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Structural Vector Autoregression; VAR; Levy-stable Distribution; Infinite Variance; Monetary Policy Shocks; Heavy-tailed Error Terms; Factorization; Impulse Response Function; Transformability Problem;
Other versions of this item:
- Greg Hannsgen, 2012. "Infinite-variance, alpha-stable shocks in monetary SVAR," International Review of Applied Economics, Taylor & Francis Journals, vol. 26(6), pages 755-786, April.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
- E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-18 (All new papers)
- NEP-CBA-2010-06-18 (Central Banking)
- NEP-ECM-2010-06-18 (Econometrics)
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