MIS-SPECIFICATION TESTING IN RETROSPECT
Department of Economics
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
Error probabilities; Misspeciﬁcation testing; Neyman–Pearson testing; Nontestable
nssumptions; Reliability of inference; Respeciﬁcation; Robustness; Speciﬁcation; Statistical model;
Statistical vs. substantive adequacy; Weak probabilistic assumptions
The problem of misspeciﬁcation arises when certain assumptions invoked by a statistical inference
procedure are invalid. Departures from the invoked assumptions distort the sampling distribution of a
statistic (estimator, test, and predictor), and as a result, the reliability of an inference procedure is often
undermined. For instance, invalid assumptions could give rise to inconsistent estimators or/and sizeable
discrepancies between the actual types I and II error probabilities and the nominal ones – the ones derived
by invoking these assumptions. Applying a 0.05 signiﬁcance level test, when the actual type I error is
closer to 0.9, will lead an inference astray.
Mis-Speciﬁcation (M-S) testing aims to assess the validity of the assumptions comprising a statistical
(i) it can alert a modeler to potential problems with unreliable inferences,
(ii) it can shed light on the nature of departures from the model assumptions.
Corresponding author contact email: firstname.lastname@example.org; Tel: +540 231 7707.
Journal of Economic Surveys (2018) Vol. 32, No. 2, pp. 541–577
2017 John Wiley & Sons Ltd.