Models with errors-in-variables (EIV) often employ instrumental variable approaches to remove the EIV bias. This paper points out that in such models the issue of nonstandard inference can arise even when the instruments are strong. Moreover, this occurs at very important points of parameter space; for instance, when the coefficient on the mismeasured regressor in a nonlinear regression is close to zero. The root of the problem is weak identification of the nuisance parameters, such as the distribution of the measurement error or control variable. These parameters are weakly identified when the mismeasured variable has small effect on the outcomes. As a result, the estimators of the parameters of interest generally are not asymptotically normal and the standard tests and confidence sets can be invalid. We illustrate how this issue arises in several estimation approaches. This complication can be particularly problematic when the nuisance parameters are infinite-dimensional.

Making use of the specific structure of the EIV problem, the paper proposes simple approaches to conducting uniformly valid inference about the parameter of interest. The highlevel conditions are illustrated by a detailed analysis of a semiparametric approach to EIV in the general moment condition settings.