The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables

IN THE LATE 1960's, Richardson [18] and Sawa [20] derived the exact distribution of the two-stage least squares (2SLS) estimator in a structural equation (of a simultaneous system) that contained two endogenous variables and an arbitrary number of degrees of overidentification. Their results refer to the 2SLS estimator of the coefficient of the endogenous variable included on the right hand side of the equation and were obtained under the classical assumptions (to use the term employed by Sargan [19]) of normally distributed disturbances and nonrandom exogenous variables. Very little exact finite sample theory has been published so far for estimators in structural equations containing more than two endogenous variables. Basmann et al. [4] extract the joint probability density function (p.d.f.) of the 2SLS estimator in a just identified equation containing three endogenous variables. Basmann [3] quotes a result due to Richardson for the same set up but with an 2 arbitrary number of degrees of overidentification . In Basmann's notation, this last result characterizes the subclass

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