Abstract Maximum-likelihood estimation is considered for a generalisation of the model of Anderson and Rubin (1949) in which the exogenous variables in the structural equation may not be included in the reduced-form equations. Classical and specification tests are derived for orthogonality hypotheses. A necessary and sufficient condition for their equivalence is presented. The classical tests are compared using Bahadur's asymptotic relative efficiency criterion. It is shown that a generalisation of the Durbin-Wu-Hausman T 2 statistics is asymptotically Bahadur-efficient.