In this paper we analyze implications of a singular contemporaneous disturbance covariance matrix for the estimation and hypothesis testing of systems of equations with autoregressive disturbances. We find that this singularity imposes restrictions on the parameters of the autoregressive process. When these restrictions are not imposed, the specification, maximum likelihood estimates, and likelihood ratio test statistics are conditional on the equation deleted. Furthermore, singularity of the contemporaneous disturbance covariance matrix raises issues concerning identification of parameters of the autoregressive process. This identification problem complicates the interpretation of likelihood ratio statistics. The above results are illustrated with an empirical example.