Revisiting the omitted variables argument: Substantive vs. statistical adequacy

The problem of omitted variables is commonly viewed as a statistical misspecification issue which renders the inference concerning the influence of X t on yt unreliable, due to the exclusion of certain relevant factors W t . That is, omitting certain potentially important factors W t may confound the influence of X t on yt . The textbook omitted variables argument attempts to assess the seriousness of this unreliability using the sensitivity of the estimator [image omitted]   to the inclusion/exclusion of W t , by tracing that effect to the potential bias/inconsistency of [image omitted]   . It is argued that the confounding problem is one of substantive inadequacy in so far as the potential error concerns subject-matter, not statistical, information. Moreover, the textbook argument in terms of the sensitivity of point estimates provides a poor basis for addressing the confounding problem. The paper reframes the omitted variables question into a hypothesis testing problem, supplemented with a post-data evaluation of inference based on severe testing. It is shown that this testing perspective can deal effectively with assessing the problem of confounding raised by the omitted variables argument. The assessment of the confouding effect using hypothesis testing is related to the conditional independence and faithfulness assumptions of graphical causal modeling.