INSTRUMENTAL VARIABLES ESTIMATION IN ERRORS-IN-VARIABLES MODELS WHEN INSTRUMENTS ARE CORRELATED WITH ERRORS

Consistency of an instrumental variable (IV) estimator is based on the orthogonality assumption of the IV's and the regression equation errors. If this assumption is in doubt, there is not much hope left for the IV estimator. The assumption can be tested, but such a test usually requires another set of IV's for which the assumption holds. In this paper it is shown that in an errors-in-variables model tighter bounds can be found in the presence of IV's even if they are correlated with the regression equation errors, and that these bounds can be made tighter still if one has prior information restricting the extent of this correlation. Moreover, the result is used to establish a sufficient condition for the OLS estimator to be inconsistent when orthogonality is suspect so that the Wu-Hausman test is not applicable. This condition is useful even when the above type of prior information is not directly available.