Comparison of the Anderson-Rubin test for overidentification and the Johansen test for cointegration

In this paper we discuss the similarity between the Anderson-Rubin test for overidentification in a Simultaneous Equations Model and the Johansen test for cointegration in a Vector Autoregressive model. The similar structure of the two models is shown to be important in this respect. An alternative procedure for computing the Anderson-Rubin test is given, which appears to be faster than the conventional method. The derivation of the likelihood ratio test for the hypothesis of reduced rank is given for the general case. Both the Anderson-Rubin test and the Johansen test are shown to be monotonically increasing functions of the singular values of a scaled version of the unrestricted least-squares estimator of the matrix upon which the rank restriction is imposed.