On weak exogeneity of the student's t and elliptical linear regression models

This paper studies weak exogeneity of conditioning variables for the inference of a subset of parameters of the conditional student's t and elliptical linear regression models considered by Spanos (1994). Weak exogeneity of the conditioning variables is shown to hold for the inference of regression parameters of the conditional student's t and elliptical linear regression models. A new definition of weak exogeneity is given which utilizes block-diagonality of the conditional information matrix. A simulation experiment is made to compare the full-likelihood and conditional maximum likelihood estimators in finite samples for the conditional student's t linear regression model. The conditional maximum likelihood estimator of the regression parameters is found to work well in finite samples.