In this paper we derive the necessary and sufficient conditions for
the t-ratio to be Student's t distributed. In
particular, it is demonstrated for a special case that under conditions
of nonnormality characterized by elliptical symmetry, the
t-ratio remains Student's t distributed provided
that the random vector forming the t-ratio has a diagonal
covariance structure. Our results also show that the findings of Magnus
(2002, in A. Ullah, A.T.K. Wan, & A.
Chaturvedi (eds.), Handbook of Applied Econometrics and Statistical
Inference, 277–285) on the sensitivity of the
t-ratio remain invariant in the elliptically symmetric
distribution setting. Extension to the linear model is considered.
Exact results giving finite sample justification for the
t-statistic under nonnormal error terms are derived.
Furthermore, the distribution of the F-ratio assuming
elliptical errors is examined. Our results reject the argument by Zaman
(1996, Statistical Foundations for
Econometric Techniques) that nonnormality of disturbances has in
general no effect on the F-statistic.The authors thank Anurag Banerjee, Judith Clarke, Kazuhiro
Ohtani, and Guohua Zou for their helpful suggestions and advice during
the course of this work. In particular, we are very grateful to Judith
Clarke for bringing to our attention the unpublished work of D.H. Thomas
and to Guohua Zou for his careful reading of an earlier version of this
paper. Thanks also go to the co-editor Benedikt Pötscher and two
anonymous referees for their valuable comments. The second author
gratefully acknowledges financial support from the Hong Kong Research
Grant Council.