Some small-sample properties of instrumental-variables estimators of block triangular models

Economists sometimes produce linear, simultaneous-equations models which would be recursive were it not for the non-diagonal character of their contemporaneous error covariance matrices. When the instrumental-variables estimator is applied to such triangular models there is some latitude in choosing the instruments to be employed. This paper shows that the exact distribution of the estimator depends on only the number of extra instruments used, not on which instruments are chosen. Nagar's (Econometrica 27 (1959) 575-595) approximation to the determinant of the MSE matrix is used to provide useful rules for selecting the number of extra instruments to employ.