| Summary: | Diebold and Yilmaz (2015) recently introduced variance decomposition networks as tools for quantifying and ranking the systemic risk of individual firms. The nature of these networks and their implied rankings depend on the choice decomposition method. The standard choice is the order invariant generalized forecast error variance decomposition of Pesaran and Shin (1998). The shares of the forecast error variation, however, do not add to unity, making difficult to compare risk ratings and risks contributions at two different points in time. As a solution, this paper suggests using the Lanne-Nyberg (2016) decomposition, which shares the order invariance property. To illustrate the differences between both decomposition methods, I analyzed the global financial system during 2001 - 2016. The analysis shows that different decomposition methods yield substantially different systemic risk and vulnerability rankings. This suggests caution is warranted when using rankings and risk contributions for guiding financial regulation and economic policy
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