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Hidden in plain sight: Influential sets in linear regression

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Influential sets are sets of observations that have considerable impact on econometric results. In this paper, we present a disciplined and insightful method for assessing the sensitivity of regression-based inference to influential sets. We explore algorithmic approaches to identify influential sets, discuss interpretation, and assess the sensitivity of earlier studies to these sets. We apply our method to established results in development economics, and show that results are driven by small influential sets. Identifying and analyzing these sets can reveal potential omitted variable bias, unobserved heterogeneity, a lack of external validity, and technical limitations of the methodological approach used.

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