Hidden in Plain Sight: Influential Sets in Linear Models

Assessing the robustness of the results of econometric analysis is a long standing subject of lively research. The majority of the literature focuses on sensitivity to model specification, while the quantification of sensitivity to sets of influential observations has received relatively little attention. A major obstacle in this context is masking, a phenomenon where influential observations obscure each other, which makes their identification particularly challenging. We show how inferential measures are affected by influential sets of observations and present two adaptive algorithms aimed at identifying such sets. We demonstrate the merits of these algorithms via simulation studies and empirical applications. These exercises show that masking problems and a pronounced sensitivity to influential sets are present in a wide range of scenarios. Overall, our findings suggest that increased attention to influential sets is warranted and comprehensive robustness measures for regression analysis are required.