This paper derives the exact probability density function of instrumental variable estimators of the coefficient vector of the endogenous variables in a structural equation containing n + 1 endogenous variables and N degrees of overidentification. This generalizes the presently known results for the special cases where n = 1 or 2 and N = 0. The usual classical assumptions [19] are made of nonrandom exogenous variables and normally distributed disturbances. Some numerical computations are reported for the case n = 2.