The Exact Distribution of Exogenous Variable Coefficient Estimators
This paper derives the exact probability density function of the instrumental variable (IV) estimator of the exogenous variable coeﬀicient vector in a structural equation containing n + 1 endogenous variables and N degrees of overidentiﬁcation. A leading case of the general distribution that is more amenable to analysis and computation is also presented. Conventional classical assumptions or normally distributed errors and nonrandom exogenous variables are employed.
Phillips, Peter C.B., "The Exact Distribution of Exogenous Variable Coefficient Estimators" (1983). Cowles Foundation Discussion Papers. 914.