  In the post-crisis era, financial regulators and policymakers are
increasingly interested in data-driven tools to measure systemic risk and to
identify systemically important firms. Granger Causality (GC) based techniques
to build networks among financial firms using time series of their stock
returns have received significant attention in recent years. Existing GC
network methods model conditional means, and do not distinguish between
connectivity in lower and upper tails of the return distribution - an aspect
crucial for systemic risk analysis. We propose statistical methods that measure
connectivity in the financial sector using system-wide tail-based analysis and
is able to distinguish between connectivity in lower and upper tails of the
return distribution. This is achieved using bivariate and multivariate GC
analysis based on regular and Lasso penalized quantile regressions, an approach
we call quantile Granger causality (QGC). By considering centrality measures of
these financial networks, we can assess the build-up of systemic risk and
identify risk propagation channels. We provide an asymptotic theory of QGC
estimators under a quantile vector autoregressive model, and show its benefit
over regular GC analysis on simulated data. We apply our method to the monthly
stock returns of large U.S. firms and demonstrate that lower tail based
networks can detect systemically risky periods in historical data with higher
accuracy than mean-based networks. In a similar analysis of large Indian banks,
we find that upper and lower tail networks convey different information and
have the potential to distinguish between periods of high connectivity that are
governed by positive vs negative news in the market.
