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Infinite-variance, Alpha-stable Shocks in Monetary SVAR

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  • Greg Hannsgen

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.

Suggested Citation

  • Greg Hannsgen, 2010. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR," Economics Working Paper Archive wp_596, Levy Economics Institute.
  • Handle: RePEc:lev:wrkpap:wp_596
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    References listed on IDEAS

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    1. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier.
    2. Markku Lanne & Helmut Luetkepohl, 2008. "A Statistical Comparison of Alternative Identification Schemes for Monetary Policy Shocks," Economics Working Papers ECO2008/23, European University Institute.
    3. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    4. John C. Frain, 2007. "Small sample power of tests of normality when the alternative is an alpha-stable distribution," Trinity Economics Papers tep0207, Trinity College Dublin, Department of Economics.
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    More about this item

    Keywords

    Structural Vector Autoregression; VAR; Levy-stable Distribution; Infinite Variance; Monetary Policy Shocks; Heavy-tailed Error Terms; Factorization; Impulse Response Function; Transformability Problem;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • 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

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