This paper derives the exact distribution of the Wald statistic for testing general linear restrictions on the coeﬀicients in the multivariate linear model. This generalizes all previously known results including those for the standard F statistic in linear regression, for Hotelling’s T 2 test and for Hotelling’s generalized T 0 2 test. Conventional classical assumptions of normally distributed errors and nonrandom exogenous variables are employed.
Phillips, Peter C.B., "The Exact Distribution of the Wald Statistic" (1984). Cowles Foundation Discussion Papers. 961.