Covariates hiding in the tails

Scaling behavior measured in cross-sectional studies through the tail index of a power law is prone to a bias. This hampers inference; in particular, time variation in estimated tail indices may be erroneous. In the case of a linear factor model, the factor biases 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 the factor, how to remedy for the bias and how to apply our methods to financial data and geographic location data.