Mis-Specification Testing in Retrospect and Prospect

The primary objective of this paper is threefold. First, to take a retrospective view of Mis-Specification (M-S) testing, going back to Karl Pearson (1900). Second, to critically discuss several arguments questioning the value and role of M-S testing. Instead, they favor relying on weak, but non-testable probabilistic assumptions, combined with invoking asymptotic results and vague robustness claims. Third, to make a case for extending/modifying Fisher’s statistical framework by clearly separating the modeling from the inference facet. The proposed framework separates, specification, estimation, M-S and respecification with a view to secure a statistically adequate model, from inference proper. The proposed framework helps to elucidate various foundational issues associated with M-S testing. A case is made for employing joint M-S tests based on auxiliary regressions to enhance the effectiveness and reliability of probing for potential statistical misspecifications.