Local Sensitivity and Diagnostic Tests

In this paper we confront sensitivity analysis with diagnostic testing. Every model is misspecified, 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 e ect 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 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, propose a sensitivity test, give conditions under which the diagnostic and sensitivity tests 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