Inconsistency of estimate of the degree of freedom of multivariate student-t disturbances in linear regression models

A moment estimator for the degree of freedom of the jointly multivariate student-t distribution of the disturbances in a linear regression model has been suggested by Singh [Economic letters (1988) 27, 47–53]. In this paper we will show that the distribution of the moment estimate is independent of the true value of the degree of freedom and the estimate converges to infinite in probability as the sample size goes to infinite. Our results show that the moment estimate does not provide any information on the degree of freedom.