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The importance of units with pervasive impacts on a large number of other units in a network has become increasingly recognized in the literature. In this paper we propose a new method to detect such pervasive units by basing our analysis on unit-speci c residual error variances in the context of a standard factor model, subject to suitable adjustments due to multiple testing. Our proposed method allows us to estimate and identify pervasive units having neither a priori knowledge of the interconnections amongst cross-section units nor a short list of candidate units. It is applicable even if the cross section dimension exceeds the time dimension, and most importantly it could end up with none of the units selected as pervasive when this is in fact the case. The sequential multiple testing procedure proposed exhibits satisfactory small-sample performance in Monte Carlo simulations and compares well relative to existing approaches. We apply the proposed detection method to sectoral indices of US industrial production, US house price changes by states, and the rates of change of real GDP and real equity prices across the world's largest economies.

A Residual-based Threshold Method for Detection of Units that are Too Big to Fail in Large Factor Models