Covariates Hiding in the Tails

Abstract: Summary: Scaling behaviour measured in cross-sectional studies through the tail index of a power law is prone to a bias. This hampers inference; in particular, observed time variation in estimated tail indices may not originate from the data-generating process. In the case of a linear factor model, the factors bias the tail indices in the left and right tail in opposite directions. This fact can be exploited to reduce the bias. We show how this bias arises from factors, how to remedy for the bias, and how to apply our methods to financial data and geographic location data.