  A criterion is proposed for testing hypothesis about the nature of the error
variance in the dependent variable in linear model, which separates correctly
and incorrectly specified models. In the former only measurement errors
determine the variance (i.e., dependent variable is correctly explained by
independent ones, up to measurement errors), while in the latter the model
lacks some independent covariates (or has nonlinear structure). The proposed
MEM-V (Measurement Error Model Validity) test checks the validity of the model
when both dependent and independent covariates are measured with errors. The
criterion has asymptotic character, but numerical simulations outlined
approximate boundaries where estimates make sense. A practical example of the
implementation of the test is discussed in detail; it shows ability of the test
to detect wrong specification even in seemingly perfect models. This type of
relation between measurement errors and model specification has not been
studied before, and the proposed criterion may stimulate future research in
this important area.
