An Indirect Least Squares Estimator for Overidentified Equations - Khazzoom, J. Daniel (Econometrica, 1976)
[In this paper, we propose a procedure based on the use of the Moore-Penrose inverse of matrices for deriving unique indirect least squares (ILS) estimates of the structural parameters in the overidentified case. The procedure makes use of all reduced form estimates in deriving the unique structural estimates. The estimator is shown to be consistent. We derive the relationship between this estimator, the two stage least squares (2SLS) estimator, and instrumental variables (IV) estimators. We also derive the asymptotic distribution of the proposed estimator, and extend the procedure to a full information ILS estimator (FILS). The results of sampling experiments are summarized.]