Mis†Specification Testing In Retrospect

The primary objective of this paper is threefold. First, to undertake a retrospective view of Mis†Specification (M†S) testing, going back to the early 20th century, with a view to (i) place it in the broader context of modeling and inference and (ii) bring out some of its special features. Second, to call into question several widely used arguments undermining the importance of M†S testing in favor of relying on weak probabilistic assumptions in conjunction with generic robustness claims and asymptotic inference. Third, to bring out the crucial role of M†S testing in securing trustworthy inference results. This is achieved by extending/modifying Fisher's statistical framework with a view to draw a clear line between the modeling and the inference facets of statistical induction. The proposed framework untangles the statistical from the substantive (structural) model and focuses on how to secure the adequacy of the statistical model before probing for substantive adequacy. A case is made for using joint M†S tests based on custom†built auxiliary regressions with a view to enhance the effectiveness and reliability of probing for potential statistical misspecifications.