Detection of units with pervasive effects in large panel data models

The importance of units that influence 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-specific residual error variances subject to suitable adjustments due to the multiple testing issues involved. Accordingly, a sequential multiple testing (SMT) procedure is proposed, which allows identification of pervasive units (if any) without a priori knowledge of the interconnections amongst cross-section units or availability of a short list of candidate units to search over. The proposed method is applicable even if the cross-section dimension exceeds the time series dimension, and most importantly it could end up with none of the units selected as pervasive when this is in fact the case. The SMT procedure exhibits satisfactory small-sample performance in Monte Carlo simulations and compares well relative to existing approaches. We apply the SMT detection method to sectoral indices of U.S. industrial production, U.S. house price changes by states, and the rates of change of real GDP and real equity prices across the world's largest economies.