In this paper it is demonstrated that testing models for misspecification by OLS-based variable addition may lead to the acceptance of reduced form equations or other hybrid relationships derived from the structural form. The awkward result is obtained that in order to acquire consistent estimates of structural parameters some regressors that appear as significant are sometimes better removed from the specification. This illustrates the need for tests on the validity of exogeneity assumptions. From application of the variable addition approach to a single linear simultaneous regression model three basic types of tests for instrument adequacy are developped, viz. tests for exogeneity of the maintained instruments, for exogeneity of excluded regressors, and for exogeneity of included regressors. Finally it is shown Which ordenings of these tests and tests on the adequacy of the specification will lead to asymptotic independence of the test statistics. Such ordenings enable to exercise control over the overall type I error probability in a comprehensive model selection procedure.