Local sensitivity and diagnostic tests

Summary  In this paper, we confront sensitivity analysis with diagnostic testing. Every model is misspecified (in the sense that no model coincides with the data‐generating process), but a model is useful if the parameters of interest (the focus) are not sensitive to small perturbations in the underlying assumptions. The study of the effect of these violations on the focus is called sensitivity analysis. Diagnostic testing, on the other hand, attempts to find out whether a nuisance parameter is (statistically) ‘large’ or ‘small’. Both aspects are important, but traditional applied econometrics tends to use only diagnostics and forget about sensitivity analysis. We develop a theory of sensitivity in a maximum likelihood framework, give conditions under which the diagnostic and the sensitivity are asymptotically independent, and demonstrate with three core examples that this independence is the rule rather than the exception, thus underlying the importance of sensitivity analysis.