One should be very careful in using the "non-informative" priors suggested in the Bayesian econometric literature for the covariance matrix of residuals in simultaneous equations models. To highlight the inadequacies of the prior, this paper shows that the prior leads to sharp posterior distributions even in under identified models. Similar problems also arise with the 2SLS method, but one can apply tests for underidentification. Something similar has to be done in the Bayesian context.