This paper shows how valid inferences can be made when an instrumental variable does not perfectly satisfy the orthogonality condition. When there is a mild violation of the orthogonality condition, the Anderson and Rubin (1949) test is oversized. In order to correct this problem, the...

We show that when instruments are nearly exogenous, the two stage least squares t-statistic unpredictably over-rejects or under-rejects the null hypothesis that the endogenous regressor is insignificant and Anderson-Rubin test over-rejects the null. We prove that in the limit these tests are no...

Valid instrumental variables must be relevant and exogenous. However, in practice it is difficult to find instruments that are exogenous in that they satisfy the knife-edged orthogonality condition and at the same time are strongly correlated with the endogenous regressors. In this paper we show...

We show that when instruments are nearly exogenous, the two stage least squares t-statistic unpredictably over-rejects or under-rejects the null hypothesis that the endogenous regressor is insignificant and Anderson-Rubin test over-rejects the null. We prove that in the limit these tests are no...

Instrumental variable methods are widely used to make inferences about the impact of some variable on economic outcomes; for example, whether or not institutions influence long term growth. However, the test-statistics used for making these inferences are based on the generally unrealistic...